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
[ 21, 73, 42, 82 ]
98
[ "21*42=882", "82-73=9", "882/9=98" ]
Current State: 98:[21, 73, 42, 82], Operations: [] Exploring Operation: 21*42=882, Resulting Numbers: [73, 82, 882] Generated Node #2: [73, 82, 882] from Operation: 21*42=882 Current State: 98:[73, 82, 882], Operations: ['21*42=882'] Exploring Operation: 82-73=9, Resulting Numbers: [882, 9] Generated Node #3: [882, 9] from Operation: 82-73=9 Current State: 98:[882, 9], Operations: ['21*42=882', '82-73=9'] Exploring Operation: 882/9=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[21, 73, 42, 82], Operations: [] Exploring Operation: 82-73=9, Resulting Numbers: [21, 42, 9] Generated Node #0,0: 98:[21, 42, 9] Operation: 82-73=9 Exploring Operation: 21+73=94, Resulting Numbers: [42, 82, 94] Generated Node #0,1: 98:[42, 82, 94] Operation: 21+73=94 Exploring Operation: 73-21=52, Resulting Numbers: [42, 82, 52] Generated Node #0,2: 98:[42, 82, 52] Operation: 73-21=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[21, 42, 9], Operations: ['82-73=9'] Exploring Operation: 21-9=12, Resulting Numbers: [42, 12] Generated Node #0,0,0: 98:[42, 12] Operation: 21-9=12 Exploring Operation: 42/21=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 98:[9, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [9, 21] Generated Node #0,0,2: 98:[9, 21] Operation: 42-21=21 Moving to Node #0,0,1 Current State: 98:[9, 2], Operations: ['82-73=9', '42/21=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,98 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[42, 12], Operations: ['82-73=9', '21-9=12'] Exploring Operation: 42*12=504, Resulting Numbers: [504] 504,98 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[9, 21], Operations: ['82-73=9', '42-21=21'] Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,98 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[42, 82, 52], Operations: ['73-21=52'] Exploring Operation: 82-42=40, Resulting Numbers: [52, 40] Generated Node #0,2,0: 98:[52, 40] Operation: 82-42=40 Exploring Operation: 42+52=94, Resulting Numbers: [82, 94] Generated Node #0,2,1: 98:[82, 94] Operation: 42+52=94 Exploring Operation: 52-42=10, Resulting Numbers: [82, 10] Generated Node #0,2,2: 98:[82, 10] Operation: 52-42=10 Moving to Node #0,2,0 Current State: 98:[52, 40], Operations: ['73-21=52', '82-42=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,98 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,98 unequal: No Solution Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[82, 10], Operations: ['73-21=52', '52-42=10'] Exploring Operation: 82+10=92, Resulting Numbers: [92] 92,98 unequal: No Solution Exploring Operation: 82*10=820, Resulting Numbers: [820] 820,98 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[82, 94], Operations: ['73-21=52', '42+52=94'] Exploring Operation: 82*94=7708, Resulting Numbers: [7708] 7708,98 unequal: No Solution Exploring Operation: 82+94=176, Resulting Numbers: [176] 176,98 unequal: No Solution Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,98 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 #0,1 Current State: 98:[42, 82, 94], Operations: ['21+73=94'] Exploring Operation: 82-42=40, Resulting Numbers: [94, 40] Generated Node #0,1,0: 98:[94, 40] Operation: 82-42=40 Exploring Operation: 94-42=52, Resulting Numbers: [82, 52] Generated Node #0,1,1: 98:[82, 52] Operation: 94-42=52 Exploring Operation: 94-82=12, Resulting Numbers: [42, 12] Generated Node #0,1,2: 98:[42, 12] Operation: 94-82=12 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[42, 12], Operations: ['21+73=94', '94-82=12'] Exploring Operation: 42*12=504, Resulting Numbers: [504] 504,98 unequal: No Solution Exploring Operation: 42+12=54, Resulting Numbers: [54] 54,98 unequal: No Solution Exploring Operation: 42-12=30, Resulting Numbers: [30] 30,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[94, 40], Operations: ['21+73=94', '82-42=40'] Exploring Operation: 94+40=134, Resulting Numbers: [134] 134,98 unequal: No Solution Exploring Operation: 94*40=3760, Resulting Numbers: [3760] 3760,98 unequal: No Solution Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[82, 52], Operations: ['21+73=94', '94-42=52'] Exploring Operation: 82+52=134, Resulting Numbers: [134] 134,98 unequal: No Solution Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,98 unequal: No Solution Exploring Operation: 82*52=4264, Resulting Numbers: [4264] 4264,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 35, 56, 84, 30 ]
37
[ "35+56=91", "84-30=54", "91-54=37" ]
Current State: 37:[35, 56, 84, 30], Operations: [] Exploring Operation: 35+56=91, Resulting Numbers: [84, 30, 91] Generated Node #2: [84, 30, 91] from Operation: 35+56=91 Current State: 37:[84, 30, 91], Operations: ['35+56=91'] Exploring Operation: 84-30=54, Resulting Numbers: [91, 54] Generated Node #3: [91, 54] from Operation: 84-30=54 Current State: 37:[91, 54], Operations: ['35+56=91', '84-30=54'] Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[35, 56, 84, 30], Operations: [] Exploring Operation: 84-35=49, Resulting Numbers: [56, 30, 49] Generated Node #0,0: 37:[56, 30, 49] Operation: 84-35=49 Exploring Operation: 84-56=28, Resulting Numbers: [35, 30, 28] Generated Node #0,1: 37:[35, 30, 28] Operation: 84-56=28 Exploring Operation: 84-30=54, Resulting Numbers: [35, 56, 54] Generated Node #0,2: 37:[35, 56, 54] Operation: 84-30=54 Moving to Node #0,1 Current State: 37:[35, 30, 28], Operations: ['84-56=28'] Exploring Operation: 35+30=65, Resulting Numbers: [28, 65] Generated Node #0,1,0: 37:[28, 65] Operation: 35+30=65 Exploring Operation: 30+28=58, Resulting Numbers: [35, 58] Generated Node #0,1,1: 37:[35, 58] Operation: 30+28=58 Exploring Operation: 35+28=63, Resulting Numbers: [30, 63] Generated Node #0,1,2: 37:[30, 63] Operation: 35+28=63 Moving to Node #0,0 Current State: 37:[56, 30, 49], Operations: ['84-35=49'] Exploring Operation: 56-49=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 37:[30, 7] Operation: 56-49=7 Exploring Operation: 49-30=19, Resulting Numbers: [56, 19] Generated Node #0,0,1: 37:[56, 19] Operation: 49-30=19 Exploring Operation: 56-30=26, Resulting Numbers: [49, 26] Generated Node #0,0,2: 37:[49, 26] Operation: 56-30=26 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[49, 26], Operations: ['84-35=49', '56-30=26'] Exploring Operation: 49*26=1274, Resulting Numbers: [1274] 1274,37 unequal: No Solution Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 49+26=75, Resulting Numbers: [75] 75,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[30, 7], Operations: ['84-35=49', '56-49=7'] Exploring Operation: 30*7=210, Resulting Numbers: [210] 210,37 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[35, 56, 84, 30], Operations: [] Exploring Operation: 84-35=49, Resulting Numbers: [56, 30, 49] Generated Node #0,0: 37:[56, 30, 49] Operation: 84-35=49 Moving to Node #0,0 Current State: 37:[56, 30, 49], Operations: ['84-35=49'] Exploring Operation: 56-49=7, Resulting Numbers: [30, 7] Generated Node #0,0,0: 37:[30, 7] Operation: 56-49=7 Moving to Node #0,0,0 Current State: 37:[30, 7], Operations: ['84-35=49', '56-49=7'] Exploring Operation: 30+7=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 12, 2, 48, 32 ]
38
[ "48/12=4", "2+32=34", "4+34=38" ]
Current State: 38:[12, 2, 48, 32], Operations: [] Exploring Operation: 48/12=4, Resulting Numbers: [2, 32, 4] Generated Node #2: [2, 32, 4] from Operation: 48/12=4 Current State: 38:[2, 32, 4], Operations: ['48/12=4'] Exploring Operation: 2+32=34, Resulting Numbers: [4, 34] Generated Node #3: [4, 34] from Operation: 2+32=34 Current State: 38:[4, 34], Operations: ['48/12=4', '2+32=34'] Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[12, 2, 48, 32], Operations: [] Exploring Operation: 48-12=36, Resulting Numbers: [2, 32, 36] Generated Node #0,0: 38:[2, 32, 36] Operation: 48-12=36 Moving to Node #0,0 Current State: 38:[2, 32, 36], Operations: ['48-12=36'] Exploring Operation: 36-32=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 38:[2, 4] Operation: 36-32=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[2, 4], Operations: ['48-12=36', '36-32=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,38 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
[ 26, 8, 2, 45 ]
76
[ "45-26=19", "8/2=4", "19*4=76" ]
Current State: 76:[26, 8, 2, 45], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [8, 2, 19] Generated Node #2: [8, 2, 19] from Operation: 45-26=19 Current State: 76:[8, 2, 19], Operations: ['45-26=19'] Exploring Operation: 8/2=4, Resulting Numbers: [19, 4] Generated Node #3: [19, 4] from Operation: 8/2=4 Current State: 76:[19, 4], Operations: ['45-26=19', '8/2=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[26, 8, 2, 45], Operations: [] Exploring Operation: 26+45=71, Resulting Numbers: [8, 2, 71] Generated Node #0,0: 76:[8, 2, 71] Operation: 26+45=71 Exploring Operation: 45-8=37, Resulting Numbers: [26, 2, 37] Generated Node #0,1: 76:[26, 2, 37] Operation: 45-8=37 Exploring Operation: 26-8=18, Resulting Numbers: [2, 45, 18] Generated Node #0,2: 76:[2, 45, 18] Operation: 26-8=18 Exploring Operation: 26+8=34, Resulting Numbers: [2, 45, 34] Generated Node #0,3: 76:[2, 45, 34] Operation: 26+8=34 Exploring Operation: 45-26=19, Resulting Numbers: [8, 2, 19] Generated Node #0,4: 76:[8, 2, 19] Operation: 45-26=19 Start Sub Search at level 1: Moving to Node #0,4 Current State: 76:[8, 2, 19], Operations: ['45-26=19'] Exploring Operation: 8-2=6, Resulting Numbers: [19, 6] Generated Node #0,4,0: 76:[19, 6] Operation: 8-2=6 Exploring Operation: 8*2=16, Resulting Numbers: [19, 16] Generated Node #0,4,1: 76:[19, 16] Operation: 8*2=16 Exploring Operation: 2*19=38, Resulting Numbers: [8, 38] Generated Node #0,4,2: 76:[8, 38] Operation: 2*19=38 Exploring Operation: 8/2=4, Resulting Numbers: [19, 4] Generated Node #0,4,3: 76:[19, 4] Operation: 8/2=4 Exploring Operation: 8+2=10, Resulting Numbers: [19, 10] Generated Node #0,4,4: 76:[19, 10] Operation: 8+2=10 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 76:[19, 4], Operations: ['45-26=19', '8/2=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[26, 8, 2, 45], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [8, 2, 19] Generated Node #0,4: 76:[8, 2, 19] Operation: 45-26=19 Moving to Node #0,4 Current State: 76:[8, 2, 19], Operations: ['45-26=19'] Exploring Operation: 8/2=4, Resulting Numbers: [19, 4] Generated Node #0,4,3: 76:[19, 4] Operation: 8/2=4 Moving to Node #0,4,3 Current State: 76:[19, 4], Operations: ['45-26=19', '8/2=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 9, 63, 24, 49 ]
97
[ "9+63=72", "49-24=25", "72+25=97" ]
Current State: 97:[9, 63, 24, 49], Operations: [] Exploring Operation: 9+63=72, Resulting Numbers: [24, 49, 72] Generated Node #2: [24, 49, 72] from Operation: 9+63=72 Current State: 97:[24, 49, 72], Operations: ['9+63=72'] Exploring Operation: 49-24=25, Resulting Numbers: [72, 25] Generated Node #3: [72, 25] from Operation: 49-24=25 Current State: 97:[72, 25], Operations: ['9+63=72', '49-24=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[9, 63, 24, 49], Operations: [] Exploring Operation: 9+24=33, Resulting Numbers: [63, 49, 33] Generated Node #0,0: 97:[63, 49, 33] Operation: 9+24=33 Exploring Operation: 9+49=58, Resulting Numbers: [63, 24, 58] Generated Node #0,1: 97:[63, 24, 58] Operation: 9+49=58 Exploring Operation: 9+63=72, Resulting Numbers: [24, 49, 72] Generated Node #0,2: 97:[24, 49, 72] Operation: 9+63=72 Moving to Node #0,0 Current State: 97:[63, 49, 33], Operations: ['9+24=33'] Exploring Operation: 63+33=96, Resulting Numbers: [49, 96] Generated Node #0,0,0: 97:[49, 96] Operation: 63+33=96 Exploring Operation: 49+33=82, Resulting Numbers: [63, 82] Generated Node #0,0,1: 97:[63, 82] Operation: 49+33=82 Exploring Operation: 63+49=112, Resulting Numbers: [33, 112] Generated Node #0,0,2: 97:[33, 112] Operation: 63+49=112 Moving to Node #0,1 Current State: 97:[63, 24, 58], Operations: ['9+49=58'] Exploring Operation: 63+24=87, Resulting Numbers: [58, 87] Generated Node #0,1,0: 97:[58, 87] Operation: 63+24=87 Exploring Operation: 24+58=82, Resulting Numbers: [63, 82] Generated Node #0,1,1: 97:[63, 82] Operation: 24+58=82 Exploring Operation: 63-24=39, Resulting Numbers: [58, 39] Generated Node #0,1,2: 97:[58, 39] Operation: 63-24=39 Moving to Node #0,2 Current State: 97:[24, 49, 72], Operations: ['9+63=72'] Exploring Operation: 24+72=96, Resulting Numbers: [49, 96] Generated Node #0,2,0: 97:[49, 96] Operation: 24+72=96 Exploring Operation: 24+49=73, Resulting Numbers: [72, 73] Generated Node #0,2,1: 97:[72, 73] Operation: 24+49=73 Exploring Operation: 49-24=25, Resulting Numbers: [72, 25] Generated Node #0,2,2: 97:[72, 25] Operation: 49-24=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[49, 96], Operations: ['9+63=72', '24+72=96'] Exploring Operation: 49*96=4704, Resulting Numbers: [4704] 4704,97 unequal: No Solution Exploring Operation: 49+96=145, Resulting Numbers: [145] 145,97 unequal: No Solution Exploring Operation: 96-49=47, Resulting Numbers: [47] 47,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[72, 73], Operations: ['9+63=72', '24+49=73'] Exploring Operation: 72*73=5256, Resulting Numbers: [5256] 5256,97 unequal: No Solution Exploring Operation: 72+73=145, Resulting Numbers: [145] 145,97 unequal: No Solution Exploring Operation: 73-72=1, Resulting Numbers: [1] 1,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[72, 25], Operations: ['9+63=72', '49-24=25'] Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,97 unequal: No Solution Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,97 unequal: No Solution Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[9, 63, 24, 49], Operations: [] Exploring Operation: 9+63=72, Resulting Numbers: [24, 49, 72] Generated Node #0,2: 97:[24, 49, 72] Operation: 9+63=72 Moving to Node #0,2 Current State: 97:[24, 49, 72], Operations: ['9+63=72'] Exploring Operation: 49-24=25, Resulting Numbers: [72, 25] Generated Node #0,2,2: 97:[72, 25] Operation: 49-24=25 Moving to Node #0,2,2 Current State: 97:[72, 25], Operations: ['9+63=72', '49-24=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 95, 54, 21, 8 ]
70
[ "95-54=41", "21+8=29", "41+29=70" ]
Current State: 70:[95, 54, 21, 8], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [21, 8, 41] Generated Node #2: [21, 8, 41] from Operation: 95-54=41 Current State: 70:[21, 8, 41], Operations: ['95-54=41'] Exploring Operation: 21+8=29, Resulting Numbers: [41, 29] Generated Node #3: [41, 29] from Operation: 21+8=29 Current State: 70:[41, 29], Operations: ['95-54=41', '21+8=29'] Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[95, 54, 21, 8], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [21, 8, 41] Generated Node #0,0: 70:[21, 8, 41] Operation: 95-54=41 Exploring Operation: 95-21=74, Resulting Numbers: [54, 8, 74] Generated Node #0,1: 70:[54, 8, 74] Operation: 95-21=74 Exploring Operation: 54-21=33, Resulting Numbers: [95, 8, 33] Generated Node #0,2: 70:[95, 8, 33] Operation: 54-21=33 Exploring Operation: 54+21=75, Resulting Numbers: [95, 8, 75] Generated Node #0,3: 70:[95, 8, 75] Operation: 54+21=75 Moving to Node #0,0 Current State: 70:[21, 8, 41], Operations: ['95-54=41'] Exploring Operation: 21+41=62, Resulting Numbers: [8, 62] Generated Node #0,0,0: 70:[8, 62] Operation: 21+41=62 Exploring Operation: 41-21=20, Resulting Numbers: [8, 20] Generated Node #0,0,1: 70:[8, 20] Operation: 41-21=20 Exploring Operation: 41-8=33, Resulting Numbers: [21, 33] Generated Node #0,0,2: 70:[21, 33] Operation: 41-8=33 Exploring Operation: 21-8=13, Resulting Numbers: [41, 13] Generated Node #0,0,3: 70:[41, 13] Operation: 21-8=13 Moving to Node #0,1 Current State: 70:[54, 8, 74], Operations: ['95-21=74'] Exploring Operation: 54+8=62, Resulting Numbers: [74, 62] Generated Node #0,1,0: 70:[74, 62] Operation: 54+8=62 Exploring Operation: 74-54=20, Resulting Numbers: [8, 20] Generated Node #0,1,1: 70:[8, 20] Operation: 74-54=20 Exploring Operation: 54-8=46, Resulting Numbers: [74, 46] Generated Node #0,1,2: 70:[74, 46] Operation: 54-8=46 Exploring Operation: 74-8=66, Resulting Numbers: [54, 66] Generated Node #0,1,3: 70:[54, 66] Operation: 74-8=66 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 70:[8, 20], Operations: ['95-21=74', '74-54=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[74, 62], Operations: ['95-21=74', '54+8=62'] Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,70 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,70 unequal: No Solution Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 70:[74, 46], Operations: ['95-21=74', '54-8=46'] Exploring Operation: 74*46=3404, Resulting Numbers: [3404] 3404,70 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 74+46=120, Resulting Numbers: [120] 120,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 70:[54, 66], Operations: ['95-21=74', '74-8=66'] Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,70 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 54*66=3564, Resulting Numbers: [3564] 3564,70 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: 70:[95, 8, 33], Operations: ['54-21=33'] Exploring Operation: 8+33=41, Resulting Numbers: [95, 41] Generated Node #0,2,0: 70:[95, 41] Operation: 8+33=41 Exploring Operation: 95+8=103, Resulting Numbers: [33, 103] Generated Node #0,2,1: 70:[33, 103] Operation: 95+8=103 Exploring Operation: 95-33=62, Resulting Numbers: [8, 62] Generated Node #0,2,2: 70:[8, 62] Operation: 95-33=62 Exploring Operation: 95-8=87, Resulting Numbers: [33, 87] Generated Node #0,2,3: 70:[33, 87] Operation: 95-8=87 Moving to Node #0,3 Current State: 70:[95, 8, 75], Operations: ['54+21=75'] Exploring Operation: 95-75=20, Resulting Numbers: [8, 20] Generated Node #0,3,0: 70:[8, 20] Operation: 95-75=20 Exploring Operation: 95+8=103, Resulting Numbers: [75, 103] Generated Node #0,3,1: 70:[75, 103] Operation: 95+8=103 Exploring Operation: 95-8=87, Resulting Numbers: [75, 87] Generated Node #0,3,2: 70:[75, 87] Operation: 95-8=87 Exploring Operation: 75-8=67, Resulting Numbers: [95, 67] Generated Node #0,3,3: 70:[95, 67] Operation: 75-8=67 Moving to Node #0,0,1 Current State: 70:[8, 20], Operations: ['95-54=41', '41-21=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,70 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[41, 13], Operations: ['95-54=41', '21-8=13'] Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,70 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,70 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,70 unequal: No Solution Moving to Node #0,3,0 Current State: 70:[8, 20], Operations: ['54+21=75', '95-75=20'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,70 unequal: No Solution Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,70 unequal: No Solution Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[8, 62], Operations: ['95-54=41', '21+41=62'] Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,70 unequal: No Solution Exploring Operation: 8+62=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[95, 54, 21, 8], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [21, 8, 41] Generated Node #0,0: 70:[21, 8, 41] Operation: 95-54=41 Moving to Node #0,0 Current State: 70:[21, 8, 41], Operations: ['95-54=41'] Exploring Operation: 21+41=62, Resulting Numbers: [8, 62] Generated Node #0,0,0: 70:[8, 62] Operation: 21+41=62 Moving to Node #0,0,0 Current State: 70:[8, 62], Operations: ['95-54=41', '21+41=62'] Exploring Operation: 8+62=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.959201
hs_4
mult_heuristic
[ 40, 6, 78, 38 ]
74
[ "40-6=34", "78-38=40", "34+40=74" ]
Current State: 74:[40, 6, 78, 38], Operations: [] Exploring Operation: 40-6=34, Resulting Numbers: [78, 38, 34] Generated Node #2: [78, 38, 34] from Operation: 40-6=34 Current State: 74:[78, 38, 34], Operations: ['40-6=34'] Exploring Operation: 78-38=40, Resulting Numbers: [34, 40] Generated Node #3: [34, 40] from Operation: 78-38=40 Current State: 74:[34, 40], Operations: ['40-6=34', '78-38=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[40, 6, 78, 38], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [6, 78, 2] Generated Node #0,0: 74:[6, 78, 2] Operation: 40-38=2 Exploring Operation: 78-40=38, Resulting Numbers: [6, 38, 38] Generated Node #0,1: 74:[6, 38, 38] Operation: 78-40=38 Exploring Operation: 78-6=72, Resulting Numbers: [40, 38, 72] Generated Node #0,2: 74:[40, 38, 72] Operation: 78-6=72 Exploring Operation: 40-6=34, Resulting Numbers: [78, 38, 34] Generated Node #0,3: 74:[78, 38, 34] Operation: 40-6=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[6, 38, 38], Operations: ['78-40=38'] Exploring Operation: 38-6=32, Resulting Numbers: [38, 32] Generated Node #0,1,0: 74:[38, 32] Operation: 38-6=32 Exploring Operation: 38/38=1, Resulting Numbers: [6, 1] Generated Node #0,1,1: 74:[6, 1] Operation: 38/38=1 Exploring Operation: 38-6=32, Resulting Numbers: [38, 32] Generated Node #0,1,2: 74:[38, 32] Operation: 38-6=32 Exploring Operation: 38+38=76, Resulting Numbers: [6, 76] Generated Node #0,1,3: 74:[6, 76] Operation: 38+38=76 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[6, 1], Operations: ['78-40=38', '38/38=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,74 unequal: No Solution No 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: 74:[38, 32], Operations: ['78-40=38', '38-6=32'] Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,74 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,74 unequal: No Solution No 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: 74:[38, 32], Operations: ['78-40=38', '38-6=32'] Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,74 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,74 unequal: No Solution No 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: 74:[6, 76], Operations: ['78-40=38', '38+38=76'] Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,74 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,74 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: 74:[40, 38, 72], Operations: ['78-6=72'] Exploring Operation: 72-40=32, Resulting Numbers: [38, 32] Generated Node #0,2,0: 74:[38, 32] Operation: 72-40=32 Exploring Operation: 72-38=34, Resulting Numbers: [40, 34] Generated Node #0,2,1: 74:[40, 34] Operation: 72-38=34 Exploring Operation: 40+38=78, Resulting Numbers: [72, 78] Generated Node #0,2,2: 74:[72, 78] Operation: 40+38=78 Exploring Operation: 40-38=2, Resulting Numbers: [72, 2] Generated Node #0,2,3: 74:[72, 2] Operation: 40-38=2 Moving to Node #0,2,3 Current State: 74:[72, 2], Operations: ['78-6=72', '40-38=2'] Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,74 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[40, 6, 78, 38], Operations: [] Exploring Operation: 78-6=72, Resulting Numbers: [40, 38, 72] Generated Node #0,2: 74:[40, 38, 72] Operation: 78-6=72 Moving to Node #0,2 Current State: 74:[40, 38, 72], Operations: ['78-6=72'] Exploring Operation: 40-38=2, Resulting Numbers: [72, 2] Generated Node #0,2,3: 74:[72, 2] Operation: 40-38=2 Moving to Node #0,2,3 Current State: 74:[72, 2], Operations: ['78-6=72', '40-38=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 96, 21, 94, 87 ]
54
[ "96-94=2", "21+87=108", "108/2=54" ]
Current State: 54:[96, 21, 94, 87], Operations: [] Exploring Operation: 96-94=2, Resulting Numbers: [21, 87, 2] Generated Node #2: [21, 87, 2] from Operation: 96-94=2 Current State: 54:[21, 87, 2], Operations: ['96-94=2'] Exploring Operation: 21+87=108, Resulting Numbers: [2, 108] Generated Node #3: [2, 108] from Operation: 21+87=108 Current State: 54:[2, 108], Operations: ['96-94=2', '21+87=108'] Exploring Operation: 108/2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[96, 21, 94, 87], Operations: [] Exploring Operation: 96-94=2, Resulting Numbers: [21, 87, 2] Generated Node #0,0: 54:[21, 87, 2] Operation: 96-94=2 Exploring Operation: 96-87=9, Resulting Numbers: [21, 94, 9] Generated Node #0,1: 54:[21, 94, 9] Operation: 96-87=9 Exploring Operation: 94-87=7, Resulting Numbers: [96, 21, 7] Generated Node #0,2: 54:[96, 21, 7] Operation: 94-87=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[21, 87, 2], Operations: ['96-94=2'] Exploring Operation: 87-21=66, Resulting Numbers: [2, 66] Generated Node #0,0,0: 54:[2, 66] Operation: 87-21=66 Exploring Operation: 87-2=85, Resulting Numbers: [21, 85] Generated Node #0,0,1: 54:[21, 85] Operation: 87-2=85 Exploring Operation: 21-2=19, Resulting Numbers: [87, 19] Generated Node #0,0,2: 54:[87, 19] Operation: 21-2=19 Moving to Node #0,0,0 Current State: 54:[2, 66], Operations: ['96-94=2', '87-21=66'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,54 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,54 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[21, 85], Operations: ['96-94=2', '87-2=85'] Exploring Operation: 21*85=1785, Resulting Numbers: [1785] 1785,54 unequal: No Solution Exploring Operation: 85-21=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 21+85=106, Resulting Numbers: [106] 106,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[87, 19], Operations: ['96-94=2', '21-2=19'] Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,54 unequal: No Solution Exploring Operation: 87+19=106, Resulting Numbers: [106] 106,54 unequal: No Solution Exploring Operation: 87*19=1653, Resulting Numbers: [1653] 1653,54 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:[21, 94, 9], Operations: ['96-87=9'] Exploring Operation: 21+9=30, Resulting Numbers: [94, 30] Generated Node #0,1,0: 54:[94, 30] Operation: 21+9=30 Exploring Operation: 94-9=85, Resulting Numbers: [21, 85] Generated Node #0,1,1: 54:[21, 85] Operation: 94-9=85 Exploring Operation: 94-21=73, Resulting Numbers: [9, 73] Generated Node #0,1,2: 54:[9, 73] Operation: 94-21=73 Moving to Node #0,1,2 Current State: 54:[9, 73], Operations: ['96-87=9', '94-21=73'] Exploring Operation: 9*73=657, Resulting Numbers: [657] 657,54 unequal: No Solution Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 9+73=82, Resulting Numbers: [82] 82,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[21, 85], Operations: ['96-87=9', '94-9=85'] Exploring Operation: 21+85=106, Resulting Numbers: [106] 106,54 unequal: No Solution Exploring Operation: 85-21=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 21*85=1785, Resulting Numbers: [1785] 1785,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[94, 30], Operations: ['96-87=9', '21+9=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,54 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[96, 21, 7], Operations: ['94-87=7'] Exploring Operation: 96-7=89, Resulting Numbers: [21, 89] Generated Node #0,2,0: 54:[21, 89] Operation: 96-7=89 Exploring Operation: 21/7=3, Resulting Numbers: [96, 3] Generated Node #0,2,1: 54:[96, 3] Operation: 21/7=3 Exploring Operation: 96-21=75, Resulting Numbers: [7, 75] Generated Node #0,2,2: 54:[7, 75] Operation: 96-21=75 Moving to Node #0,2,2 Current State: 54:[7, 75], Operations: ['94-87=7', '96-21=75'] Exploring Operation: 7+75=82, Resulting Numbers: [82] 82,54 unequal: No Solution Exploring Operation: 7*75=525, Resulting Numbers: [525] 525,54 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[21, 89], Operations: ['94-87=7', '96-7=89'] Exploring Operation: 21+89=110, Resulting Numbers: [110] 110,54 unequal: No Solution Exploring Operation: 21*89=1869, Resulting Numbers: [1869] 1869,54 unequal: No Solution Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[96, 3], Operations: ['94-87=7', '21/7=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,54 unequal: No Solution Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,54 unequal: No Solution Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,54 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
[ 74, 40, 5, 75 ]
76
[ "5+75=80", "80/40=2", "74+2=76" ]
Current State: 76:[74, 40, 5, 75], Operations: [] Exploring Operation: 5+75=80, Resulting Numbers: [74, 40, 80] Generated Node #2: [74, 40, 80] from Operation: 5+75=80 Current State: 76:[74, 40, 80], Operations: ['5+75=80'] Exploring Operation: 80/40=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 80/40=2 Current State: 76:[74, 2], Operations: ['5+75=80', '80/40=2'] Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[74, 40, 5, 75], Operations: [] Exploring Operation: 74+5=79, Resulting Numbers: [40, 75, 79] Generated Node #0,0: 76:[40, 75, 79] Operation: 74+5=79 Exploring Operation: 40-5=35, Resulting Numbers: [74, 75, 35] Generated Node #0,1: 76:[74, 75, 35] Operation: 40-5=35 Exploring Operation: 75-74=1, Resulting Numbers: [40, 5, 1] Generated Node #0,2: 76:[40, 5, 1] Operation: 75-74=1 Exploring Operation: 74-40=34, Resulting Numbers: [5, 75, 34] Generated Node #0,3: 76:[5, 75, 34] Operation: 74-40=34 Moving to Node #0,2 Current State: 76:[40, 5, 1], Operations: ['75-74=1'] Exploring Operation: 40/1=40, Resulting Numbers: [5, 40] Generated Node #0,2,0: 76:[5, 40] Operation: 40/1=40 Exploring Operation: 40*1=40, Resulting Numbers: [5, 40] Generated Node #0,2,1: 76:[5, 40] Operation: 40*1=40 Exploring Operation: 5-1=4, Resulting Numbers: [40, 4] Generated Node #0,2,2: 76:[40, 4] Operation: 5-1=4 Exploring Operation: 40-1=39, Resulting Numbers: [5, 39] Generated Node #0,2,3: 76:[5, 39] Operation: 40-1=39 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[40, 4], Operations: ['75-74=1', '5-1=4'] Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[5, 39], Operations: ['75-74=1', '40-1=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[5, 40], Operations: ['75-74=1', '40/1=40'] Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,76 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[5, 40], Operations: ['75-74=1', '40*1=40'] Exploring Operation: 5*40=200, Resulting Numbers: [200] 200,76 unequal: No Solution Exploring Operation: 40/5=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 40-5=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 5+40=45, Resulting Numbers: [45] 45,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 76:[74, 75, 35], Operations: ['40-5=35'] Exploring Operation: 74-35=39, Resulting Numbers: [75, 39] Generated Node #0,1,0: 76:[75, 39] Operation: 74-35=39 Exploring Operation: 75-35=40, Resulting Numbers: [74, 40] Generated Node #0,1,1: 76:[74, 40] Operation: 75-35=40 Exploring Operation: 74+35=109, Resulting Numbers: [75, 109] Generated Node #0,1,2: 76:[75, 109] Operation: 74+35=109 Exploring Operation: 75-74=1, Resulting Numbers: [35, 1] Generated Node #0,1,3: 76:[35, 1] Operation: 75-74=1 Moving to Node #0,0 Current State: 76:[40, 75, 79], Operations: ['74+5=79'] Exploring Operation: 79-40=39, Resulting Numbers: [75, 39] Generated Node #0,0,0: 76:[75, 39] Operation: 79-40=39 Exploring Operation: 75-40=35, Resulting Numbers: [79, 35] Generated Node #0,0,1: 76:[79, 35] Operation: 75-40=35 Exploring Operation: 79-75=4, Resulting Numbers: [40, 4] Generated Node #0,0,2: 76:[40, 4] Operation: 79-75=4 Exploring Operation: 40+75=115, Resulting Numbers: [79, 115] Generated Node #0,0,3: 76:[79, 115] Operation: 40+75=115 Moving to Node #0,3 Current State: 76:[5, 75, 34], Operations: ['74-40=34'] Exploring Operation: 5+34=39, Resulting Numbers: [75, 39] Generated Node #0,3,0: 76:[75, 39] Operation: 5+34=39 Exploring Operation: 75-34=41, Resulting Numbers: [5, 41] Generated Node #0,3,1: 76:[5, 41] Operation: 75-34=41 Exploring Operation: 75/5=15, Resulting Numbers: [34, 15] Generated Node #0,3,2: 76:[34, 15] Operation: 75/5=15 Exploring Operation: 5+75=80, Resulting Numbers: [34, 80] Generated Node #0,3,3: 76:[34, 80] Operation: 5+75=80 Moving to Node #0,1,0 Current State: 76:[75, 39], Operations: ['40-5=35', '74-35=39'] Exploring Operation: 75*39=2925, Resulting Numbers: [2925] 2925,76 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 75+39=114, Resulting Numbers: [114] 114,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[40, 4], Operations: ['74+5=79', '79-75=4'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 40*4=160, Resulting Numbers: [160] 160,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[75, 39], Operations: ['74+5=79', '79-40=39'] Exploring Operation: 75+39=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 75*39=2925, Resulting Numbers: [2925] 2925,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[75, 39], Operations: ['74-40=34', '5+34=39'] Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 75+39=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 75*39=2925, Resulting Numbers: [2925] 2925,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[35, 1], Operations: ['40-5=35', '75-74=1'] Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[74, 40], Operations: ['40-5=35', '75-35=40'] Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,76 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[5, 41], Operations: ['74-40=34', '75-34=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 5*41=205, Resulting Numbers: [205] 205,76 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[79, 35], Operations: ['74+5=79', '75-40=35'] Exploring Operation: 79*35=2765, Resulting Numbers: [2765] 2765,76 unequal: No Solution Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,76 unequal: No Solution Exploring Operation: 79+35=114, Resulting Numbers: [114] 114,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[34, 80], Operations: ['74-40=34', '5+75=80'] Exploring Operation: 34*80=2720, Resulting Numbers: [2720] 2720,76 unequal: No Solution Exploring Operation: 80-34=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 34+80=114, Resulting Numbers: [114] 114,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[34, 15], Operations: ['74-40=34', '75/5=15'] Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,76 unequal: No Solution Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,76 unequal: No Solution Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[75, 109], Operations: ['40-5=35', '74+35=109'] Exploring Operation: 75+109=184, Resulting Numbers: [184] 184,76 unequal: No Solution Exploring Operation: 109-75=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 75*109=8175, Resulting Numbers: [8175] 8175,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[79, 115], Operations: ['74+5=79', '40+75=115'] Exploring Operation: 115-79=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 79*115=9085, Resulting Numbers: [9085] 9085,76 unequal: No Solution Exploring Operation: 79+115=194, Resulting Numbers: [194] 194,76 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 68, 78, 89, 23 ]
76
[ "78-68=10", "89-23=66", "10+66=76" ]
Current State: 76:[68, 78, 89, 23], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [89, 23, 10] Generated Node #2: [89, 23, 10] from Operation: 78-68=10 Current State: 76:[89, 23, 10], Operations: ['78-68=10'] Exploring Operation: 89-23=66, Resulting Numbers: [10, 66] Generated Node #3: [10, 66] from Operation: 89-23=66 Current State: 76:[10, 66], Operations: ['78-68=10', '89-23=66'] Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[68, 78, 89, 23], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [78, 23, 21] Generated Node #0,0: 76:[78, 23, 21] Operation: 89-68=21 Exploring Operation: 89-78=11, Resulting Numbers: [68, 23, 11] Generated Node #0,1: 76:[68, 23, 11] Operation: 89-78=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[78, 23, 21], Operations: ['89-68=21'] Exploring Operation: 23+21=44, Resulting Numbers: [78, 44] Generated Node #0,0,0: 76:[78, 44] Operation: 23+21=44 Exploring Operation: 23-21=2, Resulting Numbers: [78, 2] Generated Node #0,0,1: 76:[78, 2] Operation: 23-21=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[78, 2], Operations: ['89-68=21', '23-21=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[68, 78, 89, 23], Operations: [] Exploring Operation: 89-68=21, Resulting Numbers: [78, 23, 21] Generated Node #0,0: 76:[78, 23, 21] Operation: 89-68=21 Moving to Node #0,0 Current State: 76:[78, 23, 21], Operations: ['89-68=21'] Exploring Operation: 23-21=2, Resulting Numbers: [78, 2] Generated Node #0,0,1: 76:[78, 2] Operation: 23-21=2 Moving to Node #0,0,1 Current State: 76:[78, 2], Operations: ['89-68=21', '23-21=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 65, 95, 49, 62 ]
52
[ "65-62=3", "49*3=147", "147-95=52" ]
Current State: 52:[65, 95, 49, 62], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [95, 49, 3] Generated Node #2: [95, 49, 3] from Operation: 65-62=3 Current State: 52:[95, 49, 3], Operations: ['65-62=3'] Exploring Operation: 49*3=147, Resulting Numbers: [95, 147] Generated Node #3: [95, 147] from Operation: 49*3=147 Current State: 52:[95, 147], Operations: ['65-62=3', '49*3=147'] Exploring Operation: 147-95=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[65, 95, 49, 62], Operations: [] Exploring Operation: 95-62=33, Resulting Numbers: [65, 49, 33] Generated Node #0,0: 52:[65, 49, 33] Operation: 95-62=33 Exploring Operation: 95-49=46, Resulting Numbers: [65, 62, 46] Generated Node #0,1: 52:[65, 62, 46] Operation: 95-49=46 Exploring Operation: 95-65=30, Resulting Numbers: [49, 62, 30] Generated Node #0,2: 52:[49, 62, 30] Operation: 95-65=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[49, 62, 30], Operations: ['95-65=30'] Exploring Operation: 49-30=19, Resulting Numbers: [62, 19] Generated Node #0,2,0: 52:[62, 19] Operation: 49-30=19 Exploring Operation: 62-49=13, Resulting Numbers: [30, 13] Generated Node #0,2,1: 52:[30, 13] Operation: 62-49=13 Exploring Operation: 62-30=32, Resulting Numbers: [49, 32] Generated Node #0,2,2: 52:[49, 32] Operation: 62-30=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[30, 13], Operations: ['95-65=30', '62-49=13'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 30*13=390, Resulting Numbers: [390] 390,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[49, 32], Operations: ['95-65=30', '62-30=32'] Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,52 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[62, 19], Operations: ['95-65=30', '49-30=19'] Exploring Operation: 62*19=1178, Resulting Numbers: [1178] 1178,52 unequal: No Solution Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 62+19=81, Resulting Numbers: [81] 81,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[65, 49, 33], Operations: ['95-62=33'] Exploring Operation: 49-33=16, Resulting Numbers: [65, 16] Generated Node #0,0,0: 52:[65, 16] Operation: 49-33=16 Exploring Operation: 65-33=32, Resulting Numbers: [49, 32] Generated Node #0,0,1: 52:[49, 32] Operation: 65-33=32 Exploring Operation: 65-49=16, Resulting Numbers: [33, 16] Generated Node #0,0,2: 52:[33, 16] Operation: 65-49=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[49, 32], Operations: ['95-62=33', '65-33=32'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[33, 16], Operations: ['95-62=33', '65-49=16'] Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,52 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[65, 16], Operations: ['95-62=33', '49-33=16'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,52 unequal: No Solution Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[65, 62, 46], Operations: ['95-49=46'] Exploring Operation: 65-46=19, Resulting Numbers: [62, 19] Generated Node #0,1,0: 52:[62, 19] Operation: 65-46=19 Exploring Operation: 65-62=3, Resulting Numbers: [46, 3] Generated Node #0,1,1: 52:[46, 3] Operation: 65-62=3 Exploring Operation: 62-46=16, Resulting Numbers: [65, 16] Generated Node #0,1,2: 52:[65, 16] Operation: 62-46=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[46, 3], Operations: ['95-49=46', '65-62=3'] Exploring Operation: 46+3=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 46*3=138, Resulting Numbers: [138] 138,52 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[62, 19], Operations: ['95-49=46', '65-46=19'] Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 62*19=1178, Resulting Numbers: [1178] 1178,52 unequal: No Solution Exploring Operation: 62+19=81, Resulting Numbers: [81] 81,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[65, 16], Operations: ['95-49=46', '62-46=16'] Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,52 unequal: No Solution Exploring Operation: 65+16=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 65*16=1040, Resulting Numbers: [1040] 1040,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 5, 39, 32, 21 ]
15
[ "5*21=105", "39-32=7", "105/7=15" ]
Current State: 15:[5, 39, 32, 21], Operations: [] Exploring Operation: 5*21=105, Resulting Numbers: [39, 32, 105] Generated Node #2: [39, 32, 105] from Operation: 5*21=105 Current State: 15:[39, 32, 105], Operations: ['5*21=105'] Exploring Operation: 39-32=7, Resulting Numbers: [105, 7] Generated Node #3: [105, 7] from Operation: 39-32=7 Current State: 15:[105, 7], Operations: ['5*21=105', '39-32=7'] Exploring Operation: 105/7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[5, 39, 32, 21], Operations: [] Exploring Operation: 39-32=7, Resulting Numbers: [5, 21, 7] Generated Node #0,0: 15:[5, 21, 7] Operation: 39-32=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[5, 21, 7], Operations: ['39-32=7'] Exploring Operation: 21/7=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 15:[5, 3] Operation: 21/7=3 Moving to Node #0,0,0 Current State: 15:[5, 3], Operations: ['39-32=7', '21/7=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[5, 39, 32, 21], Operations: [] Exploring Operation: 39-32=7, Resulting Numbers: [5, 21, 7] Generated Node #0,0: 15:[5, 21, 7] Operation: 39-32=7 Moving to Node #0,0 Current State: 15:[5, 21, 7], Operations: ['39-32=7'] Exploring Operation: 21/7=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 15:[5, 3] Operation: 21/7=3 Moving to Node #0,0,0 Current State: 15:[5, 3], Operations: ['39-32=7', '21/7=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 25, 4, 35, 40 ]
96
[ "25-4=21", "35+40=75", "21+75=96" ]
Current State: 96:[25, 4, 35, 40], Operations: [] Exploring Operation: 25-4=21, Resulting Numbers: [35, 40, 21] Generated Node #2: [35, 40, 21] from Operation: 25-4=21 Current State: 96:[35, 40, 21], Operations: ['25-4=21'] Exploring Operation: 35+40=75, Resulting Numbers: [21, 75] Generated Node #3: [21, 75] from Operation: 35+40=75 Current State: 96:[21, 75], Operations: ['25-4=21', '35+40=75'] Exploring Operation: 21+75=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[25, 4, 35, 40], Operations: [] Exploring Operation: 40/4=10, Resulting Numbers: [25, 35, 10] Generated Node #0,0: 96:[25, 35, 10] Operation: 40/4=10 Exploring Operation: 40-25=15, Resulting Numbers: [4, 35, 15] Generated Node #0,1: 96:[4, 35, 15] Operation: 40-25=15 Exploring Operation: 40-4=36, Resulting Numbers: [25, 35, 36] Generated Node #0,2: 96:[25, 35, 36] Operation: 40-4=36 Exploring Operation: 40-35=5, Resulting Numbers: [25, 4, 5] Generated Node #0,3: 96:[25, 4, 5] Operation: 40-35=5 Exploring Operation: 4+40=44, Resulting Numbers: [25, 35, 44] Generated Node #0,4: 96:[25, 35, 44] Operation: 4+40=44 Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[25, 4, 5], Operations: ['40-35=5'] Exploring Operation: 25/5=5, Resulting Numbers: [4, 5] Generated Node #0,3,0: 96:[4, 5] Operation: 25/5=5 Exploring Operation: 25+4=29, Resulting Numbers: [5, 29] Generated Node #0,3,1: 96:[5, 29] Operation: 25+4=29 Exploring Operation: 5-4=1, Resulting Numbers: [25, 1] Generated Node #0,3,2: 96:[25, 1] Operation: 5-4=1 Exploring Operation: 4+5=9, Resulting Numbers: [25, 9] Generated Node #0,3,3: 96:[25, 9] Operation: 4+5=9 Exploring Operation: 25+5=30, Resulting Numbers: [4, 30] Generated Node #0,3,4: 96:[4, 30] Operation: 25+5=30 Moving to Node #0,3,0 Current State: 96:[4, 5], Operations: ['40-35=5', '25/5=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,96 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[25, 9], Operations: ['40-35=5', '4+5=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,96 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,96 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[25, 1], Operations: ['40-35=5', '5-4=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[4, 30], Operations: ['40-35=5', '25+5=30'] Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,96 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[5, 29], Operations: ['40-35=5', '25+4=29'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,96 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,96 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:[4, 35, 15], Operations: ['40-25=15'] Exploring Operation: 35+15=50, Resulting Numbers: [4, 50] Generated Node #0,1,0: 96:[4, 50] Operation: 35+15=50 Exploring Operation: 35-4=31, Resulting Numbers: [15, 31] Generated Node #0,1,1: 96:[15, 31] Operation: 35-4=31 Exploring Operation: 35-15=20, Resulting Numbers: [4, 20] Generated Node #0,1,2: 96:[4, 20] Operation: 35-15=20 Exploring Operation: 15-4=11, Resulting Numbers: [35, 11] Generated Node #0,1,3: 96:[35, 11] Operation: 15-4=11 Exploring Operation: 4+15=19, Resulting Numbers: [35, 19] Generated Node #0,1,4: 96:[35, 19] Operation: 4+15=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[4, 50], Operations: ['40-25=15', '35+15=50'] Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,96 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[15, 31], Operations: ['40-25=15', '35-4=31'] Exploring Operation: 15+31=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 31-15=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 15*31=465, Resulting Numbers: [465] 465,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[4, 20], Operations: ['40-25=15', '35-15=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,96 unequal: No Solution Exploring Operation: 4+20=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 #0,1,3 Current State: 96:[35, 11], Operations: ['40-25=15', '15-4=11'] Exploring Operation: 35*11=385, Resulting Numbers: [385] 385,96 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 35+11=46, Resulting Numbers: [46] 46,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 96:[35, 19], Operations: ['40-25=15', '4+15=19'] Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,96 unequal: No Solution Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,96 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[25, 35, 10], Operations: ['40/4=10'] Exploring Operation: 35-10=25, Resulting Numbers: [25, 25] Generated Node #0,0,0: 96:[25, 25] Operation: 35-10=25 Exploring Operation: 35-25=10, Resulting Numbers: [10, 10] Generated Node #0,0,1: 96:[10, 10] Operation: 35-25=10 Exploring Operation: 25+10=35, Resulting Numbers: [35, 35] Generated Node #0,0,2: 96:[35, 35] Operation: 25+10=35 Exploring Operation: 35+10=45, Resulting Numbers: [25, 45] Generated Node #0,0,3: 96:[25, 45] Operation: 35+10=45 Exploring Operation: 25-10=15, Resulting Numbers: [35, 15] Generated Node #0,0,4: 96:[35, 15] Operation: 25-10=15 Moving to Node #0,0,0 Current State: 96:[25, 25], Operations: ['40/4=10', '35-10=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 25/25=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[25, 45], Operations: ['40/4=10', '35+10=45'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 25+45=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 25*45=1125, Resulting Numbers: [1125] 1125,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[10, 10], Operations: ['40/4=10', '35-25=10'] Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,96 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 10+10=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[35, 15], Operations: ['40/4=10', '25-10=15'] Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,96 unequal: No Solution Exploring Operation: 35+15=50, Resulting Numbers: [50] 50,96 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[35, 35], Operations: ['40/4=10', '25+10=35'] Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,96 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,96 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:[25, 35, 36], Operations: ['40-4=36'] Exploring Operation: 36-25=11, Resulting Numbers: [35, 11] Generated Node #0,2,0: 96:[35, 11] Operation: 36-25=11 Exploring Operation: 35-25=10, Resulting Numbers: [36, 10] Generated Node #0,2,1: 96:[36, 10] Operation: 35-25=10 Exploring Operation: 25+35=60, Resulting Numbers: [36, 60] Generated Node #0,2,2: 96:[36, 60] Operation: 25+35=60 Exploring Operation: 25+36=61, Resulting Numbers: [35, 61] Generated Node #0,2,3: 96:[35, 61] Operation: 25+36=61 Exploring Operation: 36-35=1, Resulting Numbers: [25, 1] Generated Node #0,2,4: 96:[25, 1] Operation: 36-35=1 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 96:[25, 1], Operations: ['40-4=36', '36-35=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,96 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 #0,2,0 Current State: 96:[35, 11], Operations: ['40-4=36', '36-25=11'] Exploring Operation: 35+11=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 35*11=385, Resulting Numbers: [385] 385,96 unequal: No Solution Exploring Operation: 35-11=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 #0,2,1 Current State: 96:[36, 10], Operations: ['40-4=36', '35-25=10'] Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 36*10=360, Resulting Numbers: [360] 360,96 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 #0,2,2 Current State: 96:[36, 60], Operations: ['40-4=36', '25+35=60'] Exploring Operation: 60-36=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 36+60=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[25, 4, 35, 40], Operations: [] Exploring Operation: 40-4=36, Resulting Numbers: [25, 35, 36] Generated Node #0,2: 96:[25, 35, 36] Operation: 40-4=36 Moving to Node #0,2 Current State: 96:[25, 35, 36], Operations: ['40-4=36'] Exploring Operation: 25+35=60, Resulting Numbers: [36, 60] Generated Node #0,2,2: 96:[36, 60] Operation: 25+35=60 Moving to Node #0,2,2 Current State: 96:[36, 60], Operations: ['40-4=36', '25+35=60'] Exploring Operation: 36+60=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.921007
hs_5
mult_heuristic
[ 13, 38, 46, 2 ]
88
[ "13-2=11", "46-38=8", "11*8=88" ]
Current State: 88:[13, 38, 46, 2], Operations: [] Exploring Operation: 13-2=11, Resulting Numbers: [38, 46, 11] Generated Node #2: [38, 46, 11] from Operation: 13-2=11 Current State: 88:[38, 46, 11], Operations: ['13-2=11'] Exploring Operation: 46-38=8, Resulting Numbers: [11, 8] Generated Node #3: [11, 8] from Operation: 46-38=8 Current State: 88:[11, 8], Operations: ['13-2=11', '46-38=8'] Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[13, 38, 46, 2], Operations: [] Exploring Operation: 38+46=84, Resulting Numbers: [13, 2, 84] Generated Node #0,0: 88:[13, 2, 84] Operation: 38+46=84 Exploring Operation: 13-2=11, Resulting Numbers: [38, 46, 11] Generated Node #0,1: 88:[38, 46, 11] Operation: 13-2=11 Exploring Operation: 38/2=19, Resulting Numbers: [13, 46, 19] Generated Node #0,2: 88:[13, 46, 19] Operation: 38/2=19 Exploring Operation: 46-38=8, Resulting Numbers: [13, 2, 8] Generated Node #0,3: 88:[13, 2, 8] Operation: 46-38=8 Exploring Operation: 38-13=25, Resulting Numbers: [46, 2, 25] Generated Node #0,4: 88:[46, 2, 25] Operation: 38-13=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[13, 2, 8], Operations: ['46-38=8'] Exploring Operation: 2+8=10, Resulting Numbers: [13, 10] Generated Node #0,3,0: 88:[13, 10] Operation: 2+8=10 Exploring Operation: 13-8=5, Resulting Numbers: [2, 5] Generated Node #0,3,1: 88:[2, 5] Operation: 13-8=5 Exploring Operation: 13+8=21, Resulting Numbers: [2, 21] Generated Node #0,3,2: 88:[2, 21] Operation: 13+8=21 Exploring Operation: 13-2=11, Resulting Numbers: [8, 11] Generated Node #0,3,3: 88:[8, 11] Operation: 13-2=11 Exploring Operation: 8/2=4, Resulting Numbers: [13, 4] Generated Node #0,3,4: 88:[13, 4] Operation: 8/2=4 Moving to Node #0,3,3 Current State: 88:[8, 11], Operations: ['46-38=8', '13-2=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[13, 38, 46, 2], Operations: [] Exploring Operation: 46-38=8, Resulting Numbers: [13, 2, 8] Generated Node #0,3: 88:[13, 2, 8] Operation: 46-38=8 Moving to Node #0,3 Current State: 88:[13, 2, 8], Operations: ['46-38=8'] Exploring Operation: 13-2=11, Resulting Numbers: [8, 11] Generated Node #0,3,3: 88:[8, 11] Operation: 13-2=11 Moving to Node #0,3,3 Current State: 88:[8, 11], Operations: ['46-38=8', '13-2=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 23, 11, 10, 16 ]
73
[ "16-11=5", "10*5=50", "23+50=73" ]
Current State: 73:[23, 11, 10, 16], Operations: [] Exploring Operation: 16-11=5, Resulting Numbers: [23, 10, 5] Generated Node #2: [23, 10, 5] from Operation: 16-11=5 Current State: 73:[23, 10, 5], Operations: ['16-11=5'] Exploring Operation: 10*5=50, Resulting Numbers: [23, 50] Generated Node #3: [23, 50] from Operation: 10*5=50 Current State: 73:[23, 50], Operations: ['16-11=5', '10*5=50'] Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[23, 11, 10, 16], Operations: [] Exploring Operation: 23+16=39, Resulting Numbers: [11, 10, 39] Generated Node #0,0: 73:[11, 10, 39] Operation: 23+16=39 Exploring Operation: 23+10=33, Resulting Numbers: [11, 16, 33] Generated Node #0,1: 73:[11, 16, 33] Operation: 23+10=33 Exploring Operation: 23+11=34, Resulting Numbers: [10, 16, 34] Generated Node #0,2: 73:[10, 16, 34] Operation: 23+11=34 Exploring Operation: 11*10=110, Resulting Numbers: [23, 16, 110] Generated Node #0,3: 73:[23, 16, 110] Operation: 11*10=110 Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[23, 16, 110], Operations: ['11*10=110'] Exploring Operation: 110-16=94, Resulting Numbers: [23, 94] Generated Node #0,3,0: 73:[23, 94] Operation: 110-16=94 Exploring Operation: 23-16=7, Resulting Numbers: [110, 7] Generated Node #0,3,1: 73:[110, 7] Operation: 23-16=7 Exploring Operation: 23+16=39, Resulting Numbers: [110, 39] Generated Node #0,3,2: 73:[110, 39] Operation: 23+16=39 Exploring Operation: 110-23=87, Resulting Numbers: [16, 87] Generated Node #0,3,3: 73:[16, 87] Operation: 110-23=87 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 73:[23, 94], Operations: ['11*10=110', '110-16=94'] Exploring Operation: 94-23=71, Resulting Numbers: [71] 71,73 unequal: No Solution Exploring Operation: 23+94=117, Resulting Numbers: [117] 117,73 unequal: No Solution Exploring Operation: 23*94=2162, Resulting Numbers: [2162] 2162,73 unequal: No Solution No 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: 73:[110, 39], Operations: ['11*10=110', '23+16=39'] Exploring Operation: 110*39=4290, Resulting Numbers: [4290] 4290,73 unequal: No Solution Exploring Operation: 110-39=71, Resulting Numbers: [71] 71,73 unequal: No Solution Exploring Operation: 110+39=149, Resulting Numbers: [149] 149,73 unequal: No Solution No 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: 73:[16, 87], Operations: ['11*10=110', '110-23=87'] Exploring Operation: 16+87=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 16*87=1392, Resulting Numbers: [1392] 1392,73 unequal: No Solution Exploring Operation: 87-16=71, Resulting Numbers: [71] 71,73 unequal: No Solution No 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: 73:[110, 7], Operations: ['11*10=110', '23-16=7'] Exploring Operation: 110+7=117, Resulting Numbers: [117] 117,73 unequal: No Solution Exploring Operation: 110*7=770, Resulting Numbers: [770] 770,73 unequal: No Solution Exploring Operation: 110-7=103, Resulting Numbers: [103] 103,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[11, 10, 39], Operations: ['23+16=39'] Exploring Operation: 11+10=21, Resulting Numbers: [39, 21] Generated Node #0,0,0: 73:[39, 21] Operation: 11+10=21 Exploring Operation: 11*10=110, Resulting Numbers: [39, 110] Generated Node #0,0,1: 73:[39, 110] Operation: 11*10=110 Exploring Operation: 10+39=49, Resulting Numbers: [11, 49] Generated Node #0,0,2: 73:[11, 49] Operation: 10+39=49 Exploring Operation: 11+39=50, Resulting Numbers: [10, 50] Generated Node #0,0,3: 73:[10, 50] Operation: 11+39=50 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[39, 110], Operations: ['23+16=39', '11*10=110'] Exploring Operation: 39+110=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 110-39=71, Resulting Numbers: [71] 71,73 unequal: No Solution Exploring Operation: 39*110=4290, Resulting Numbers: [4290] 4290,73 unequal: No Solution No 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: 73:[39, 21], Operations: ['23+16=39', '11+10=21'] Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,73 unequal: No Solution Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,73 unequal: No Solution Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,73 unequal: No Solution No 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: 73:[11, 49], Operations: ['23+16=39', '10+39=49'] Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 11*49=539, Resulting Numbers: [539] 539,73 unequal: No Solution Exploring Operation: 11+49=60, Resulting Numbers: [60] 60,73 unequal: No Solution No 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: 73:[10, 50], Operations: ['23+16=39', '11+39=50'] Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,73 unequal: No Solution Exploring Operation: 10*50=500, Resulting Numbers: [500] 500,73 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[11, 16, 33], Operations: ['23+10=33'] Exploring Operation: 16-11=5, Resulting Numbers: [33, 5] Generated Node #0,1,0: 73:[33, 5] Operation: 16-11=5 Exploring Operation: 11+16=27, Resulting Numbers: [33, 27] Generated Node #0,1,1: 73:[33, 27] Operation: 11+16=27 Exploring Operation: 11+33=44, Resulting Numbers: [16, 44] Generated Node #0,1,2: 73:[16, 44] Operation: 11+33=44 Exploring Operation: 16+33=49, Resulting Numbers: [11, 49] Generated Node #0,1,3: 73:[11, 49] Operation: 16+33=49 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[33, 27], Operations: ['23+10=33', '11+16=27'] Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,73 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,73 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,73 unequal: No Solution No 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: 73:[16, 44], Operations: ['23+10=33', '11+33=44'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,73 unequal: No Solution Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,73 unequal: No Solution Exploring Operation: 16*44=704, Resulting Numbers: [704] 704,73 unequal: No Solution No 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: 73:[11, 49], Operations: ['23+10=33', '16+33=49'] Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 11*49=539, Resulting Numbers: [539] 539,73 unequal: No Solution Exploring Operation: 11+49=60, Resulting Numbers: [60] 60,73 unequal: No Solution No 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: 73:[33, 5], Operations: ['23+10=33', '16-11=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,73 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[10, 16, 34], Operations: ['23+11=34'] Exploring Operation: 16+34=50, Resulting Numbers: [10, 50] Generated Node #0,2,0: 73:[10, 50] Operation: 16+34=50 Exploring Operation: 16-10=6, Resulting Numbers: [34, 6] Generated Node #0,2,1: 73:[34, 6] Operation: 16-10=6 Exploring Operation: 10+34=44, Resulting Numbers: [16, 44] Generated Node #0,2,2: 73:[16, 44] Operation: 10+34=44 Exploring Operation: 10+16=26, Resulting Numbers: [34, 26] Generated Node #0,2,3: 73:[34, 26] Operation: 10+16=26 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[10, 50], Operations: ['23+11=34', '16+34=50'] Exploring Operation: 10*50=500, Resulting Numbers: [500] 500,73 unequal: No Solution Exploring Operation: 10+50=60, Resulting Numbers: [60] 60,73 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,73 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,73 unequal: No Solution No 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: 73:[16, 44], Operations: ['23+11=34', '10+34=44'] Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,73 unequal: No Solution Exploring Operation: 16*44=704, Resulting Numbers: [704] 704,73 unequal: No Solution Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,73 unequal: No Solution No 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: 73:[34, 26], Operations: ['23+11=34', '10+16=26'] Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 34*26=884, Resulting Numbers: [884] 884,73 unequal: No Solution Exploring Operation: 34+26=60, Resulting Numbers: [60] 60,73 unequal: No Solution No 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: 73:[34, 6], Operations: ['23+11=34', '16-10=6'] Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,73 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 63, 54, 57, 38 ]
12
[ "63*38=2394", "2394/57=42", "54-42=12" ]
Current State: 12:[63, 54, 57, 38], Operations: [] Exploring Operation: 63*38=2394, Resulting Numbers: [54, 57, 2394] Generated Node #2: [54, 57, 2394] from Operation: 63*38=2394 Current State: 12:[54, 57, 2394], Operations: ['63*38=2394'] Exploring Operation: 2394/57=42, Resulting Numbers: [54, 42] Generated Node #3: [54, 42] from Operation: 2394/57=42 Current State: 12:[54, 42], Operations: ['63*38=2394', '2394/57=42'] Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[63, 54, 57, 38], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [57, 38, 9] Generated Node #0,0: 12:[57, 38, 9] Operation: 63-54=9 Exploring Operation: 63-57=6, Resulting Numbers: [54, 38, 6] Generated Node #0,1: 12:[54, 38, 6] Operation: 63-57=6 Moving to Node #0,1 Current State: 12:[54, 38, 6], Operations: ['63-57=6'] Exploring Operation: 54-38=16, Resulting Numbers: [6, 16] Generated Node #0,1,0: 12:[6, 16] Operation: 54-38=16 Exploring Operation: 54/6=9, Resulting Numbers: [38, 9] Generated Node #0,1,1: 12:[38, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[6, 16], Operations: ['63-57=6', '54-38=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[38, 9], Operations: ['63-57=6', '54/6=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,12 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: 12:[57, 38, 9], Operations: ['63-54=9'] Exploring Operation: 57-38=19, Resulting Numbers: [9, 19] Generated Node #0,0,0: 12:[9, 19] Operation: 57-38=19 Exploring Operation: 57-9=48, Resulting Numbers: [38, 48] Generated Node #0,0,1: 12:[38, 48] Operation: 57-9=48 Moving to Node #0,0,0 Current State: 12:[9, 19], Operations: ['63-54=9', '57-38=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[38, 48], Operations: ['63-54=9', '57-9=48'] Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 38+48=86, Resulting Numbers: [86] 86,12 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 35, 60, 21, 43 ]
73
[ "35+60=95", "43-21=22", "95-22=73" ]
Current State: 73:[35, 60, 21, 43], Operations: [] Exploring Operation: 35+60=95, Resulting Numbers: [21, 43, 95] Generated Node #2: [21, 43, 95] from Operation: 35+60=95 Current State: 73:[21, 43, 95], Operations: ['35+60=95'] Exploring Operation: 43-21=22, Resulting Numbers: [95, 22] Generated Node #3: [95, 22] from Operation: 43-21=22 Current State: 73:[95, 22], Operations: ['35+60=95', '43-21=22'] Exploring Operation: 95-22=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[35, 60, 21, 43], Operations: [] Exploring Operation: 35+21=56, Resulting Numbers: [60, 43, 56] Generated Node #0,0: 73:[60, 43, 56] Operation: 35+21=56 Moving to Node #0,0 Current State: 73:[60, 43, 56], Operations: ['35+21=56'] Exploring Operation: 43+56=99, Resulting Numbers: [60, 99] Generated Node #0,0,0: 73:[60, 99] Operation: 43+56=99 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[60, 99], Operations: ['35+21=56', '43+56=99'] Exploring Operation: 99-60=39, Resulting Numbers: [39] 39,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 47, 28, 47, 72 ]
43
[ "47/47=1", "72-28=44", "44-1=43" ]
Current State: 43:[47, 28, 47, 72], Operations: [] Exploring Operation: 47/47=1, Resulting Numbers: [28, 72, 1] Generated Node #2: [28, 72, 1] from Operation: 47/47=1 Current State: 43:[28, 72, 1], Operations: ['47/47=1'] Exploring Operation: 72-28=44, Resulting Numbers: [1, 44] Generated Node #3: [1, 44] from Operation: 72-28=44 Current State: 43:[1, 44], Operations: ['47/47=1', '72-28=44'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[47, 28, 47, 72], Operations: [] Exploring Operation: 72-28=44, Resulting Numbers: [47, 47, 44] Generated Node #0,0: 43:[47, 47, 44] Operation: 72-28=44 Exploring Operation: 72-47=25, Resulting Numbers: [47, 28, 25] Generated Node #0,1: 43:[47, 28, 25] Operation: 72-47=25 Exploring Operation: 72-47=25, Resulting Numbers: [28, 47, 25] Generated Node #0,2: 43:[28, 47, 25] Operation: 72-47=25 Exploring Operation: 47-28=19, Resulting Numbers: [47, 72, 19] Generated Node #0,3: 43:[47, 72, 19] Operation: 47-28=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[47, 47, 44], Operations: ['72-28=44'] Exploring Operation: 47-44=3, Resulting Numbers: [47, 3] Generated Node #0,0,0: 43:[47, 3] Operation: 47-44=3 Exploring Operation: 47-47=0, Resulting Numbers: [44, 0] Generated Node #0,0,1: 43:[44, 0] Operation: 47-47=0 Exploring Operation: 47-44=3, Resulting Numbers: [47, 3] Generated Node #0,0,2: 43:[47, 3] Operation: 47-44=3 Exploring Operation: 47/47=1, Resulting Numbers: [44, 1] Generated Node #0,0,3: 43:[44, 1] Operation: 47/47=1 Moving to Node #0,0,3 Current State: 43:[44, 1], Operations: ['72-28=44', '47/47=1'] Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[47, 28, 47, 72], Operations: [] Exploring Operation: 72-28=44, Resulting Numbers: [47, 47, 44] Generated Node #0,0: 43:[47, 47, 44] Operation: 72-28=44 Moving to Node #0,0 Current State: 43:[47, 47, 44], Operations: ['72-28=44'] Exploring Operation: 47/47=1, Resulting Numbers: [44, 1] Generated Node #0,0,3: 43:[44, 1] Operation: 47/47=1 Moving to Node #0,0,3 Current State: 43:[44, 1], Operations: ['72-28=44', '47/47=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 63, 80, 69, 71 ]
97
[ "71-69=2", "80*2=160", "160-63=97" ]
Current State: 97:[63, 80, 69, 71], Operations: [] Exploring Operation: 71-69=2, Resulting Numbers: [63, 80, 2] Generated Node #2: [63, 80, 2] from Operation: 71-69=2 Current State: 97:[63, 80, 2], Operations: ['71-69=2'] Exploring Operation: 80*2=160, Resulting Numbers: [63, 160] Generated Node #3: [63, 160] from Operation: 80*2=160 Current State: 97:[63, 160], Operations: ['71-69=2', '80*2=160'] Exploring Operation: 160-63=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[63, 80, 69, 71], Operations: [] Exploring Operation: 63+71=134, Resulting Numbers: [80, 69, 134] Generated Node #0,0: 97:[80, 69, 134] Operation: 63+71=134 Exploring Operation: 63+69=132, Resulting Numbers: [80, 71, 132] Generated Node #0,1: 97:[80, 71, 132] Operation: 63+69=132 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[80, 71, 132], Operations: ['63+69=132'] Exploring Operation: 132-80=52, Resulting Numbers: [71, 52] Generated Node #0,1,0: 97:[71, 52] Operation: 132-80=52 Exploring Operation: 132-71=61, Resulting Numbers: [80, 61] Generated Node #0,1,1: 97:[80, 61] Operation: 132-71=61 Moving to Node #0,1,1 Current State: 97:[80, 61], Operations: ['63+69=132', '132-71=61'] Exploring Operation: 80-61=19, Resulting Numbers: [19] 19,97 unequal: No Solution Exploring Operation: 80+61=141, Resulting Numbers: [141] 141,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[71, 52], Operations: ['63+69=132', '132-80=52'] Exploring Operation: 71+52=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 71-52=19, Resulting Numbers: [19] 19,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[80, 69, 134], Operations: ['63+71=134'] Exploring Operation: 134-69=65, Resulting Numbers: [80, 65] Generated Node #0,0,0: 97:[80, 65] Operation: 134-69=65 Exploring Operation: 134-80=54, Resulting Numbers: [69, 54] Generated Node #0,0,1: 97:[69, 54] Operation: 134-80=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[80, 65], Operations: ['63+71=134', '134-69=65'] Exploring Operation: 80+65=145, Resulting Numbers: [145] 145,97 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[69, 54], Operations: ['63+71=134', '134-80=54'] Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,97 unequal: No Solution Exploring Operation: 69+54=123, Resulting Numbers: [123] 123,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 75, 21, 88, 23 ]
62
[ "23-21=2", "75*2=150", "150-88=62" ]
Current State: 62:[75, 21, 88, 23], Operations: [] Exploring Operation: 23-21=2, Resulting Numbers: [75, 88, 2] Generated Node #2: [75, 88, 2] from Operation: 23-21=2 Current State: 62:[75, 88, 2], Operations: ['23-21=2'] Exploring Operation: 75*2=150, Resulting Numbers: [88, 150] Generated Node #3: [88, 150] from Operation: 75*2=150 Current State: 62:[88, 150], Operations: ['23-21=2', '75*2=150'] Exploring Operation: 150-88=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[75, 21, 88, 23], Operations: [] Exploring Operation: 88-23=65, Resulting Numbers: [75, 21, 65] Generated Node #0,0: 62:[75, 21, 65] Operation: 88-23=65 Exploring Operation: 88-21=67, Resulting Numbers: [75, 23, 67] Generated Node #0,1: 62:[75, 23, 67] Operation: 88-21=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[75, 21, 65], Operations: ['88-23=65'] Exploring Operation: 75-21=54, Resulting Numbers: [65, 54] Generated Node #0,0,0: 62:[65, 54] Operation: 75-21=54 Exploring Operation: 75-65=10, Resulting Numbers: [21, 10] Generated Node #0,0,1: 62:[21, 10] Operation: 75-65=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[65, 54], Operations: ['88-23=65', '75-21=54'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 65+54=119, Resulting Numbers: [119] 119,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[21, 10], Operations: ['88-23=65', '75-65=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,62 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[75, 23, 67], Operations: ['88-21=67'] Exploring Operation: 75-23=52, Resulting Numbers: [67, 52] Generated Node #0,1,0: 62:[67, 52] Operation: 75-23=52 Exploring Operation: 75-67=8, Resulting Numbers: [23, 8] Generated Node #0,1,1: 62:[23, 8] Operation: 75-67=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[23, 8], Operations: ['88-21=67', '75-67=8'] Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[67, 52], Operations: ['88-21=67', '75-23=52'] Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 67+52=119, Resulting Numbers: [119] 119,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 4, 63, 54, 80 ]
75
[ "63-4=59", "54+80=134", "134-59=75" ]
Current State: 75:[4, 63, 54, 80], Operations: [] Exploring Operation: 63-4=59, Resulting Numbers: [54, 80, 59] Generated Node #2: [54, 80, 59] from Operation: 63-4=59 Current State: 75:[54, 80, 59], Operations: ['63-4=59'] Exploring Operation: 54+80=134, Resulting Numbers: [59, 134] Generated Node #3: [59, 134] from Operation: 54+80=134 Current State: 75:[59, 134], Operations: ['63-4=59', '54+80=134'] Exploring Operation: 134-59=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[4, 63, 54, 80], Operations: [] Exploring Operation: 4+63=67, Resulting Numbers: [54, 80, 67] Generated Node #0,0: 75:[54, 80, 67] Operation: 4+63=67 Exploring Operation: 80-63=17, Resulting Numbers: [4, 54, 17] Generated Node #0,1: 75:[4, 54, 17] Operation: 80-63=17 Exploring Operation: 80-54=26, Resulting Numbers: [4, 63, 26] Generated Node #0,2: 75:[4, 63, 26] Operation: 80-54=26 Exploring Operation: 63-54=9, Resulting Numbers: [4, 80, 9] Generated Node #0,3: 75:[4, 80, 9] Operation: 63-54=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[4, 80, 9], Operations: ['63-54=9'] Exploring Operation: 9-4=5, Resulting Numbers: [80, 5] Generated Node #0,3,0: 75:[80, 5] Operation: 9-4=5 Exploring Operation: 4+9=13, Resulting Numbers: [80, 13] Generated Node #0,3,1: 75:[80, 13] Operation: 4+9=13 Exploring Operation: 80-4=76, Resulting Numbers: [9, 76] Generated Node #0,3,2: 75:[9, 76] Operation: 80-4=76 Exploring Operation: 80-9=71, Resulting Numbers: [4, 71] Generated Node #0,3,3: 75:[4, 71] Operation: 80-9=71 Moving to Node #0,3,0 Current State: 75:[80, 5], Operations: ['63-54=9', '9-4=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[4, 63, 54, 80], Operations: [] Exploring Operation: 63-54=9, Resulting Numbers: [4, 80, 9] Generated Node #0,3: 75:[4, 80, 9] Operation: 63-54=9 Moving to Node #0,3 Current State: 75:[4, 80, 9], Operations: ['63-54=9'] Exploring Operation: 9-4=5, Resulting Numbers: [80, 5] Generated Node #0,3,0: 75:[80, 5] Operation: 9-4=5 Moving to Node #0,3,0 Current State: 75:[80, 5], Operations: ['63-54=9', '9-4=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 8, 56, 46, 14 ]
67
[ "56/8=7", "46+14=60", "7+60=67" ]
Current State: 67:[8, 56, 46, 14], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [46, 14, 7] Generated Node #2: [46, 14, 7] from Operation: 56/8=7 Current State: 67:[46, 14, 7], Operations: ['56/8=7'] Exploring Operation: 46+14=60, Resulting Numbers: [7, 60] Generated Node #3: [7, 60] from Operation: 46+14=60 Current State: 67:[7, 60], Operations: ['56/8=7', '46+14=60'] Exploring Operation: 7+60=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[8, 56, 46, 14], Operations: [] Exploring Operation: 8+56=64, Resulting Numbers: [46, 14, 64] Generated Node #0,0: 67:[46, 14, 64] Operation: 8+56=64 Exploring Operation: 8+46=54, Resulting Numbers: [56, 14, 54] Generated Node #0,1: 67:[56, 14, 54] Operation: 8+46=54 Exploring Operation: 8+14=22, Resulting Numbers: [56, 46, 22] Generated Node #0,2: 67:[56, 46, 22] Operation: 8+14=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[46, 14, 64], Operations: ['8+56=64'] Exploring Operation: 46+14=60, Resulting Numbers: [64, 60] Generated Node #0,0,0: 67:[64, 60] Operation: 46+14=60 Exploring Operation: 46-14=32, Resulting Numbers: [64, 32] Generated Node #0,0,1: 67:[64, 32] Operation: 46-14=32 Exploring Operation: 14+64=78, Resulting Numbers: [46, 78] Generated Node #0,0,2: 67:[46, 78] Operation: 14+64=78 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[64, 60], Operations: ['8+56=64', '46+14=60'] Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,67 unequal: No Solution Exploring Operation: 64*60=3840, Resulting Numbers: [3840] 3840,67 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:[46, 78], Operations: ['8+56=64', '14+64=78'] Exploring Operation: 78-46=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 46*78=3588, Resulting Numbers: [3588] 3588,67 unequal: No Solution Exploring Operation: 46+78=124, Resulting Numbers: [124] 124,67 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 #0,0,1 Current State: 67:[64, 32], Operations: ['8+56=64', '46-14=32'] Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,67 unequal: No Solution Exploring Operation: 64+32=96, Resulting Numbers: [96] 96,67 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,67 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:[56, 14, 54], Operations: ['8+46=54'] Exploring Operation: 56+14=70, Resulting Numbers: [54, 70] Generated Node #0,1,0: 67:[54, 70] Operation: 56+14=70 Exploring Operation: 14+54=68, Resulting Numbers: [56, 68] Generated Node #0,1,1: 67:[56, 68] Operation: 14+54=68 Exploring Operation: 56-14=42, Resulting Numbers: [54, 42] Generated Node #0,1,2: 67:[54, 42] Operation: 56-14=42 Moving to Node #0,1,1 Current State: 67:[56, 68], Operations: ['8+46=54', '14+54=68'] Exploring Operation: 56+68=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,67 unequal: No Solution Exploring Operation: 56*68=3808, Resulting Numbers: [3808] 3808,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[54, 70], Operations: ['8+46=54', '56+14=70'] Exploring Operation: 54+70=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 54*70=3780, Resulting Numbers: [3780] 3780,67 unequal: No Solution Exploring Operation: 70-54=16, Resulting Numbers: [16] 16,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[54, 42], Operations: ['8+46=54', '56-14=42'] Exploring Operation: 54*42=2268, Resulting Numbers: [2268] 2268,67 unequal: No Solution Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,67 unequal: No Solution Exploring Operation: 54+42=96, Resulting Numbers: [96] 96,67 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 Current State: 67:[56, 46, 22], Operations: ['8+14=22'] Exploring Operation: 56-22=34, Resulting Numbers: [46, 34] Generated Node #0,2,0: 67:[46, 34] Operation: 56-22=34 Exploring Operation: 56+22=78, Resulting Numbers: [46, 78] Generated Node #0,2,1: 67:[46, 78] Operation: 56+22=78 Exploring Operation: 46+22=68, Resulting Numbers: [56, 68] Generated Node #0,2,2: 67:[56, 68] Operation: 46+22=68 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 67:[56, 68], Operations: ['8+14=22', '46+22=68'] Exploring Operation: 56*68=3808, Resulting Numbers: [3808] 3808,67 unequal: No Solution Exploring Operation: 56+68=124, Resulting Numbers: [124] 124,67 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,67 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 #0,2,1 Current State: 67:[46, 78], Operations: ['8+14=22', '56+22=78'] Exploring Operation: 78-46=32, Resulting Numbers: [32] 32,67 unequal: No Solution Exploring Operation: 46*78=3588, Resulting Numbers: [3588] 3588,67 unequal: No Solution Exploring Operation: 46+78=124, Resulting Numbers: [124] 124,67 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 #0,2,0 Current State: 67:[46, 34], Operations: ['8+14=22', '56-22=34'] Exploring Operation: 46+34=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 46*34=1564, Resulting Numbers: [1564] 1564,67 unequal: No Solution Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,67 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_3
mult_heuristic
[ 47, 45, 95, 11 ]
76
[ "47-11=36", "95*36=3420", "3420/45=76" ]
Current State: 76:[47, 45, 95, 11], Operations: [] Exploring Operation: 47-11=36, Resulting Numbers: [45, 95, 36] Generated Node #2: [45, 95, 36] from Operation: 47-11=36 Current State: 76:[45, 95, 36], Operations: ['47-11=36'] Exploring Operation: 95*36=3420, Resulting Numbers: [45, 3420] Generated Node #3: [45, 3420] from Operation: 95*36=3420 Current State: 76:[45, 3420], Operations: ['47-11=36', '95*36=3420'] Exploring Operation: 3420/45=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[47, 45, 95, 11], Operations: [] Exploring Operation: 47-45=2, Resulting Numbers: [95, 11, 2] Generated Node #0,0: 76:[95, 11, 2] Operation: 47-45=2 Exploring Operation: 47-11=36, Resulting Numbers: [45, 95, 36] Generated Node #0,1: 76:[45, 95, 36] Operation: 47-11=36 Exploring Operation: 95-47=48, Resulting Numbers: [45, 11, 48] Generated Node #0,2: 76:[45, 11, 48] Operation: 95-47=48 Exploring Operation: 95-11=84, Resulting Numbers: [47, 45, 84] Generated Node #0,3: 76:[47, 45, 84] Operation: 95-11=84 Exploring Operation: 95-45=50, Resulting Numbers: [47, 11, 50] Generated Node #0,4: 76:[47, 11, 50] Operation: 95-45=50 Moving to Node #0,2 Current State: 76:[45, 11, 48], Operations: ['95-47=48'] Exploring Operation: 45-11=34, Resulting Numbers: [48, 34] Generated Node #0,2,0: 76:[48, 34] Operation: 45-11=34 Exploring Operation: 48-45=3, Resulting Numbers: [11, 3] Generated Node #0,2,1: 76:[11, 3] Operation: 48-45=3 Exploring Operation: 11+48=59, Resulting Numbers: [45, 59] Generated Node #0,2,2: 76:[45, 59] Operation: 11+48=59 Exploring Operation: 48-11=37, Resulting Numbers: [45, 37] Generated Node #0,2,3: 76:[45, 37] Operation: 48-11=37 Exploring Operation: 45+48=93, Resulting Numbers: [11, 93] Generated Node #0,2,4: 76:[11, 93] Operation: 45+48=93 Moving to Node #0,3 Current State: 76:[47, 45, 84], Operations: ['95-11=84'] Exploring Operation: 47+45=92, Resulting Numbers: [84, 92] Generated Node #0,3,0: 76:[84, 92] Operation: 47+45=92 Exploring Operation: 47+84=131, Resulting Numbers: [45, 131] Generated Node #0,3,1: 76:[45, 131] Operation: 47+84=131 Exploring Operation: 84-47=37, Resulting Numbers: [45, 37] Generated Node #0,3,2: 76:[45, 37] Operation: 84-47=37 Exploring Operation: 84-45=39, Resulting Numbers: [47, 39] Generated Node #0,3,3: 76:[47, 39] Operation: 84-45=39 Exploring Operation: 47-45=2, Resulting Numbers: [84, 2] Generated Node #0,3,4: 76:[84, 2] Operation: 47-45=2 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 76:[45, 37], Operations: ['95-11=84', '84-47=37'] Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 45+37=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 45*37=1665, Resulting Numbers: [1665] 1665,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 76:[84, 2], Operations: ['95-11=84', '47-45=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 76:[47, 39], Operations: ['95-11=84', '84-45=39'] Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 76:[84, 92], Operations: ['95-11=84', '47+45=92'] Exploring Operation: 84*92=7728, Resulting Numbers: [7728] 7728,76 unequal: No Solution Exploring Operation: 84+92=176, Resulting Numbers: [176] 176,76 unequal: No Solution Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 76:[45, 131], Operations: ['95-11=84', '47+84=131'] Exploring Operation: 45*131=5895, Resulting Numbers: [5895] 5895,76 unequal: No Solution Exploring Operation: 131-45=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 45+131=176, Resulting Numbers: [176] 176,76 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: 76:[95, 11, 2], Operations: ['47-45=2'] Exploring Operation: 95-11=84, Resulting Numbers: [2, 84] Generated Node #0,0,0: 76:[2, 84] Operation: 95-11=84 Exploring Operation: 95-2=93, Resulting Numbers: [11, 93] Generated Node #0,0,1: 76:[11, 93] Operation: 95-2=93 Exploring Operation: 11*2=22, Resulting Numbers: [95, 22] Generated Node #0,0,2: 76:[95, 22] Operation: 11*2=22 Exploring Operation: 11+2=13, Resulting Numbers: [95, 13] Generated Node #0,0,3: 76:[95, 13] Operation: 11+2=13 Exploring Operation: 11-2=9, Resulting Numbers: [95, 9] Generated Node #0,0,4: 76:[95, 9] Operation: 11-2=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[2, 84], Operations: ['47-45=2', '95-11=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,76 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[95, 22], Operations: ['47-45=2', '11*2=22'] Exploring Operation: 95+22=117, Resulting Numbers: [117] 117,76 unequal: No Solution Exploring Operation: 95-22=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 95*22=2090, Resulting Numbers: [2090] 2090,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[11, 93], Operations: ['47-45=2', '95-2=93'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 11*93=1023, Resulting Numbers: [1023] 1023,76 unequal: No Solution Exploring Operation: 11+93=104, Resulting Numbers: [104] 104,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 76:[95, 9], Operations: ['47-45=2', '11-2=9'] Exploring Operation: 95+9=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 95-9=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 95*9=855, Resulting Numbers: [855] 855,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 76:[95, 13], Operations: ['47-45=2', '11+2=13'] Exploring Operation: 95*13=1235, Resulting Numbers: [1235] 1235,76 unequal: No Solution Exploring Operation: 95+13=108, Resulting Numbers: [108] 108,76 unequal: No Solution Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 76:[45, 95, 36], Operations: ['47-11=36'] Exploring Operation: 95+36=131, Resulting Numbers: [45, 131] Generated Node #0,1,0: 76:[45, 131] Operation: 95+36=131 Exploring Operation: 45+36=81, Resulting Numbers: [95, 81] Generated Node #0,1,1: 76:[95, 81] Operation: 45+36=81 Exploring Operation: 95-36=59, Resulting Numbers: [45, 59] Generated Node #0,1,2: 76:[45, 59] Operation: 95-36=59 Exploring Operation: 95-45=50, Resulting Numbers: [36, 50] Generated Node #0,1,3: 76:[36, 50] Operation: 95-45=50 Exploring Operation: 45-36=9, Resulting Numbers: [95, 9] Generated Node #0,1,4: 76:[95, 9] Operation: 45-36=9 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 76:[36, 50], Operations: ['47-11=36', '95-45=50'] Exploring Operation: 36+50=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 36*50=1800, Resulting Numbers: [1800] 1800,76 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[95, 81], Operations: ['47-11=36', '45+36=81'] Exploring Operation: 95-81=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 95*81=7695, Resulting Numbers: [7695] 7695,76 unequal: No Solution Exploring Operation: 95+81=176, Resulting Numbers: [176] 176,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[45, 59], Operations: ['47-11=36', '95-36=59'] Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,76 unequal: No Solution Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 76:[95, 9], Operations: ['47-11=36', '45-36=9'] Exploring Operation: 95+9=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 95*9=855, Resulting Numbers: [855] 855,76 unequal: No Solution Exploring Operation: 95-9=86, Resulting Numbers: [86] 86,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[45, 131], Operations: ['47-11=36', '95+36=131'] Exploring Operation: 131-45=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 45*131=5895, Resulting Numbers: [5895] 5895,76 unequal: No Solution Exploring Operation: 45+131=176, Resulting Numbers: [176] 176,76 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: 76:[47, 11, 50], Operations: ['95-45=50'] Exploring Operation: 47+50=97, Resulting Numbers: [11, 97] Generated Node #0,4,0: 76:[11, 97] Operation: 47+50=97 Exploring Operation: 50-11=39, Resulting Numbers: [47, 39] Generated Node #0,4,1: 76:[47, 39] Operation: 50-11=39 Exploring Operation: 47-11=36, Resulting Numbers: [50, 36] Generated Node #0,4,2: 76:[50, 36] Operation: 47-11=36 Exploring Operation: 11+50=61, Resulting Numbers: [47, 61] Generated Node #0,4,3: 76:[47, 61] Operation: 11+50=61 Exploring Operation: 50-47=3, Resulting Numbers: [11, 3] Generated Node #0,4,4: 76:[11, 3] Operation: 50-47=3 Moving to Node #0,2,1 Current State: 76:[11, 3], Operations: ['95-47=48', '48-45=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,76 unequal: No Solution Moving to Node #0,4,4 Current State: 76:[11, 3], Operations: ['95-45=50', '50-47=3'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,76 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[45, 37], Operations: ['95-47=48', '48-11=37'] Exploring Operation: 45+37=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 45*37=1665, Resulting Numbers: [1665] 1665,76 unequal: No Solution Exploring Operation: 45-37=8, Resulting Numbers: [8] 8,76 unequal: No Solution Moving to Node #0,4,1 Current State: 76:[47, 39], Operations: ['95-45=50', '50-11=39'] Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,76 unequal: No Solution Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[48, 34], Operations: ['95-47=48', '45-11=34'] Exploring Operation: 48*34=1632, Resulting Numbers: [1632] 1632,76 unequal: No Solution Exploring Operation: 48+34=82, Resulting Numbers: [82] 82,76 unequal: No Solution Exploring Operation: 48-34=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,4,2 Current State: 76:[50, 36], Operations: ['95-45=50', '47-11=36'] Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 50*36=1800, Resulting Numbers: [1800] 1800,76 unequal: No Solution Exploring Operation: 50-36=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,4,3 Current State: 76:[47, 61], Operations: ['95-45=50', '11+50=61'] Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 47*61=2867, Resulting Numbers: [2867] 2867,76 unequal: No Solution Exploring Operation: 47+61=108, Resulting Numbers: [108] 108,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[11, 93], Operations: ['95-47=48', '45+48=93'] Exploring Operation: 11+93=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 11*93=1023, Resulting Numbers: [1023] 1023,76 unequal: No Solution Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[45, 59], Operations: ['95-47=48', '11+48=59'] Exploring Operation: 45+59=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 45*59=2655, Resulting Numbers: [2655] 2655,76 unequal: No Solution Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[11, 97], Operations: ['95-45=50', '47+50=97'] Exploring Operation: 11*97=1067, Resulting Numbers: [1067] 1067,76 unequal: No Solution Exploring Operation: 97-11=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 11+97=108, Resulting Numbers: [108] 108,76 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 70, 75, 36, 2 ]
33
[ "75-70=5", "36+2=38", "38-5=33" ]
Current State: 33:[70, 75, 36, 2], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [36, 2, 5] Generated Node #2: [36, 2, 5] from Operation: 75-70=5 Current State: 33:[36, 2, 5], Operations: ['75-70=5'] Exploring Operation: 36+2=38, Resulting Numbers: [5, 38] Generated Node #3: [5, 38] from Operation: 36+2=38 Current State: 33:[5, 38], Operations: ['75-70=5', '36+2=38'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[70, 75, 36, 2], Operations: [] Exploring Operation: 70-36=34, Resulting Numbers: [75, 2, 34] Generated Node #0,0: 33:[75, 2, 34] Operation: 70-36=34 Exploring Operation: 75-36=39, Resulting Numbers: [70, 2, 39] Generated Node #0,1: 33:[70, 2, 39] Operation: 75-36=39 Exploring Operation: 70/2=35, Resulting Numbers: [75, 36, 35] Generated Node #0,2: 33:[75, 36, 35] Operation: 70/2=35 Exploring Operation: 75-70=5, Resulting Numbers: [36, 2, 5] Generated Node #0,3: 33:[36, 2, 5] Operation: 75-70=5 Moving to Node #0,3 Current State: 33:[36, 2, 5], Operations: ['75-70=5'] Exploring Operation: 36-5=31, Resulting Numbers: [2, 31] Generated Node #0,3,0: 33:[2, 31] Operation: 36-5=31 Exploring Operation: 36-2=34, Resulting Numbers: [5, 34] Generated Node #0,3,1: 33:[5, 34] Operation: 36-2=34 Exploring Operation: 2*5=10, Resulting Numbers: [36, 10] Generated Node #0,3,2: 33:[36, 10] Operation: 2*5=10 Exploring Operation: 5-2=3, Resulting Numbers: [36, 3] Generated Node #0,3,3: 33:[36, 3] Operation: 5-2=3 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 33:[2, 31], Operations: ['75-70=5', '36-5=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,33 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,33 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[70, 75, 36, 2], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [36, 2, 5] Generated Node #0,3: 33:[36, 2, 5] Operation: 75-70=5 Moving to Node #0,3 Current State: 33:[36, 2, 5], Operations: ['75-70=5'] Exploring Operation: 36-5=31, Resulting Numbers: [2, 31] Generated Node #0,3,0: 33:[2, 31] Operation: 36-5=31 Moving to Node #0,3,0 Current State: 33:[2, 31], Operations: ['75-70=5', '36-5=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 18, 54, 1, 49 ]
85
[ "54-18=36", "1*49=49", "36+49=85" ]
Current State: 85:[18, 54, 1, 49], Operations: [] Exploring Operation: 54-18=36, Resulting Numbers: [1, 49, 36] Generated Node #2: [1, 49, 36] from Operation: 54-18=36 Current State: 85:[1, 49, 36], Operations: ['54-18=36'] Exploring Operation: 1*49=49, Resulting Numbers: [36, 49] Generated Node #3: [36, 49] from Operation: 1*49=49 Current State: 85:[36, 49], Operations: ['54-18=36', '1*49=49'] Exploring Operation: 36+49=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[18, 54, 1, 49], Operations: [] Exploring Operation: 54-49=5, Resulting Numbers: [18, 1, 5] Generated Node #0,0: 85:[18, 1, 5] Operation: 54-49=5 Exploring Operation: 54+49=103, Resulting Numbers: [18, 1, 103] Generated Node #0,1: 85:[18, 1, 103] Operation: 54+49=103 Exploring Operation: 18+54=72, Resulting Numbers: [1, 49, 72] Generated Node #0,2: 85:[1, 49, 72] Operation: 18+54=72 Exploring Operation: 54/18=3, Resulting Numbers: [1, 49, 3] Generated Node #0,3: 85:[1, 49, 3] Operation: 54/18=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[18, 1, 5], Operations: ['54-49=5'] Exploring Operation: 18*1=18, Resulting Numbers: [5, 18] Generated Node #0,0,0: 85:[5, 18] Operation: 18*1=18 Exploring Operation: 18/1=18, Resulting Numbers: [5, 18] Generated Node #0,0,1: 85:[5, 18] Operation: 18/1=18 Exploring Operation: 18-1=17, Resulting Numbers: [5, 17] Generated Node #0,0,2: 85:[5, 17] Operation: 18-1=17 Exploring Operation: 1*5=5, Resulting Numbers: [18, 5] Generated Node #0,0,3: 85:[18, 5] Operation: 1*5=5 Moving to Node #0,0,2 Current State: 85:[5, 17], Operations: ['54-49=5', '18-1=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[18, 54, 1, 49], Operations: [] Exploring Operation: 54-49=5, Resulting Numbers: [18, 1, 5] Generated Node #0,0: 85:[18, 1, 5] Operation: 54-49=5 Moving to Node #0,0 Current State: 85:[18, 1, 5], Operations: ['54-49=5'] Exploring Operation: 18-1=17, Resulting Numbers: [5, 17] Generated Node #0,0,2: 85:[5, 17] Operation: 18-1=17 Moving to Node #0,0,2 Current State: 85:[5, 17], Operations: ['54-49=5', '18-1=17'] Exploring Operation: 5*17=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 27, 20, 4, 48 ]
85
[ "48-20=28", "4*28=112", "112-27=85" ]
Current State: 85:[27, 20, 4, 48], Operations: [] Exploring Operation: 48-20=28, Resulting Numbers: [27, 4, 28] Generated Node #2: [27, 4, 28] from Operation: 48-20=28 Current State: 85:[27, 4, 28], Operations: ['48-20=28'] Exploring Operation: 4*28=112, Resulting Numbers: [27, 112] Generated Node #3: [27, 112] from Operation: 4*28=112 Current State: 85:[27, 112], Operations: ['48-20=28', '4*28=112'] Exploring Operation: 112-27=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[27, 20, 4, 48], Operations: [] Exploring Operation: 48/4=12, Resulting Numbers: [27, 20, 12] Generated Node #0,0: 85:[27, 20, 12] Operation: 48/4=12 Exploring Operation: 48-27=21, Resulting Numbers: [20, 4, 21] Generated Node #0,1: 85:[20, 4, 21] Operation: 48-27=21 Exploring Operation: 27+48=75, Resulting Numbers: [20, 4, 75] Generated Node #0,2: 85:[20, 4, 75] Operation: 27+48=75 Moving to Node #0,1 Current State: 85:[20, 4, 21], Operations: ['48-27=21'] Exploring Operation: 20/4=5, Resulting Numbers: [21, 5] Generated Node #0,1,0: 85:[21, 5] Operation: 20/4=5 Exploring Operation: 21-4=17, Resulting Numbers: [20, 17] Generated Node #0,1,1: 85:[20, 17] Operation: 21-4=17 Exploring Operation: 4*21=84, Resulting Numbers: [20, 84] Generated Node #0,1,2: 85:[20, 84] Operation: 4*21=84 Moving to Node #0,2 Current State: 85:[20, 4, 75], Operations: ['27+48=75'] Exploring Operation: 20/4=5, Resulting Numbers: [75, 5] Generated Node #0,2,0: 85:[75, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [75, 16] Generated Node #0,2,1: 85:[75, 16] Operation: 20-4=16 Exploring Operation: 4+75=79, Resulting Numbers: [20, 79] Generated Node #0,2,2: 85:[20, 79] Operation: 4+75=79 Moving to Node #0,0 Current State: 85:[27, 20, 12], Operations: ['48/4=12'] Exploring Operation: 27-20=7, Resulting Numbers: [12, 7] Generated Node #0,0,0: 85:[12, 7] Operation: 27-20=7 Exploring Operation: 20-12=8, Resulting Numbers: [27, 8] Generated Node #0,0,1: 85:[27, 8] Operation: 20-12=8 Exploring Operation: 27-12=15, Resulting Numbers: [20, 15] Generated Node #0,0,2: 85:[20, 15] Operation: 27-12=15 Moving to Node #0,1,1 Current State: 85:[20, 17], Operations: ['48-27=21', '21-4=17'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,85 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[20, 84], Operations: ['48-27=21', '4*21=84'] Exploring Operation: 84-20=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 20*84=1680, Resulting Numbers: [1680] 1680,85 unequal: No Solution Exploring Operation: 20+84=104, Resulting Numbers: [104] 104,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[21, 5], Operations: ['48-27=21', '20/4=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,85 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[20, 15], Operations: ['48/4=12', '27-12=15'] Exploring Operation: 20*15=300, Resulting Numbers: [300] 300,85 unequal: No Solution Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 20+15=35, Resulting Numbers: [35] 35,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[12, 7], Operations: ['48/4=12', '27-20=7'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,85 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[20, 79], Operations: ['27+48=75', '4+75=79'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,85 unequal: No Solution Exploring Operation: 20*79=1580, Resulting Numbers: [1580] 1580,85 unequal: No Solution Exploring Operation: 20+79=99, Resulting Numbers: [99] 99,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[75, 5], Operations: ['27+48=75', '20/4=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,85 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[75, 16], Operations: ['27+48=75', '20-4=16'] Exploring Operation: 75+16=91, Resulting Numbers: [91] 91,85 unequal: No Solution Exploring Operation: 75*16=1200, Resulting Numbers: [1200] 1200,85 unequal: No Solution Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[27, 8], Operations: ['48/4=12', '20-12=8'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,85 unequal: No Solution Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,85 unequal: No Solution Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,85 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 22, 47, 1, 94 ]
22
[ "94/47=2", "2-1=1", "22*1=22" ]
Current State: 22:[22, 47, 1, 94], Operations: [] Exploring Operation: 94/47=2, Resulting Numbers: [22, 1, 2] Generated Node #2: [22, 1, 2] from Operation: 94/47=2 Current State: 22:[22, 1, 2], Operations: ['94/47=2'] Exploring Operation: 2-1=1, Resulting Numbers: [22, 1] Generated Node #3: [22, 1] from Operation: 2-1=1 Current State: 22:[22, 1], Operations: ['94/47=2', '2-1=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[22, 47, 1, 94], Operations: [] Exploring Operation: 94-47=47, Resulting Numbers: [22, 1, 47] Generated Node #0,0: 22:[22, 1, 47] Operation: 94-47=47 Exploring Operation: 94/47=2, Resulting Numbers: [22, 1, 2] Generated Node #0,1: 22:[22, 1, 2] Operation: 94/47=2 Exploring Operation: 47-22=25, Resulting Numbers: [1, 94, 25] Generated Node #0,2: 22:[1, 94, 25] Operation: 47-22=25 Moving to Node #0,1 Current State: 22:[22, 1, 2], Operations: ['94/47=2'] Exploring Operation: 22/1=22, Resulting Numbers: [2, 22] Generated Node #0,1,0: 22:[2, 22] Operation: 22/1=22 Exploring Operation: 1*2=2, Resulting Numbers: [22, 2] Generated Node #0,1,1: 22:[22, 2] Operation: 1*2=2 Exploring Operation: 22*1=22, Resulting Numbers: [2, 22] Generated Node #0,1,2: 22:[2, 22] Operation: 22*1=22 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[2, 22], Operations: ['94/47=2', '22/1=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,22 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 #0,1,1 Current State: 22:[22, 2], Operations: ['94/47=2', '1*2=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,22 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 #0,1,2 Current State: 22:[2, 22], Operations: ['94/47=2', '22*1=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,22 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: 22:[22, 1, 47], Operations: ['94-47=47'] Exploring Operation: 47-22=25, Resulting Numbers: [1, 25] Generated Node #0,0,0: 22:[1, 25] Operation: 47-22=25 Exploring Operation: 22*1=22, Resulting Numbers: [47, 22] Generated Node #0,0,1: 22:[47, 22] Operation: 22*1=22 Exploring Operation: 47-1=46, Resulting Numbers: [22, 46] Generated Node #0,0,2: 22:[22, 46] Operation: 47-1=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[1, 25], Operations: ['94-47=47', '47-22=25'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,22 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 #0,0,2 Current State: 22:[22, 46], Operations: ['94-47=47', '47-1=46'] Exploring Operation: 22*46=1012, Resulting Numbers: [1012] 1012,22 unequal: No Solution Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,22 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:[47, 22], Operations: ['94-47=47', '22*1=22'] Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 47*22=1034, Resulting Numbers: [1034] 1034,22 unequal: No Solution Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,22 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: 22:[1, 94, 25], Operations: ['47-22=25'] Exploring Operation: 94-25=69, Resulting Numbers: [1, 69] Generated Node #0,2,0: 22:[1, 69] Operation: 94-25=69 Exploring Operation: 25-1=24, Resulting Numbers: [94, 24] Generated Node #0,2,1: 22:[94, 24] Operation: 25-1=24 Exploring Operation: 94-1=93, Resulting Numbers: [25, 93] Generated Node #0,2,2: 22:[25, 93] Operation: 94-1=93 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[1, 69], Operations: ['47-22=25', '94-25=69'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,22 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 #0,2,1 Current State: 22:[94, 24], Operations: ['47-22=25', '25-1=24'] Exploring Operation: 94*24=2256, Resulting Numbers: [2256] 2256,22 unequal: No Solution Exploring Operation: 94+24=118, Resulting Numbers: [118] 118,22 unequal: No Solution Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,22 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 #0,2,2 Current State: 22:[25, 93], Operations: ['47-22=25', '94-1=93'] Exploring Operation: 25+93=118, Resulting Numbers: [118] 118,22 unequal: No Solution Exploring Operation: 93-25=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 25*93=2325, Resulting Numbers: [2325] 2325,22 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
[ 45, 40, 96, 23 ]
85
[ "45*96=4320", "4320/40=108", "108-23=85" ]
Current State: 85:[45, 40, 96, 23], Operations: [] Exploring Operation: 45*96=4320, Resulting Numbers: [40, 23, 4320] Generated Node #2: [40, 23, 4320] from Operation: 45*96=4320 Current State: 85:[40, 23, 4320], Operations: ['45*96=4320'] Exploring Operation: 4320/40=108, Resulting Numbers: [23, 108] Generated Node #3: [23, 108] from Operation: 4320/40=108 Current State: 85:[23, 108], Operations: ['45*96=4320', '4320/40=108'] Exploring Operation: 108-23=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[45, 40, 96, 23], Operations: [] Exploring Operation: 45+40=85, Resulting Numbers: [96, 23, 85] Generated Node #0,0: 85:[96, 23, 85] Operation: 45+40=85 Exploring Operation: 45-40=5, Resulting Numbers: [96, 23, 5] Generated Node #0,1: 85:[96, 23, 5] Operation: 45-40=5 Moving to Node #0,0 Current State: 85:[96, 23, 85], Operations: ['45+40=85'] Exploring Operation: 96-85=11, Resulting Numbers: [23, 11] Generated Node #0,0,0: 85:[23, 11] Operation: 96-85=11 Exploring Operation: 96-23=73, Resulting Numbers: [85, 73] Generated Node #0,0,1: 85:[85, 73] Operation: 96-23=73 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[23, 11], Operations: ['45+40=85', '96-85=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,85 unequal: No Solution No 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: 85:[85, 73], Operations: ['45+40=85', '96-23=73'] Exploring Operation: 85+73=158, Resulting Numbers: [158] 158,85 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,85 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: 85:[96, 23, 5], Operations: ['45-40=5'] Exploring Operation: 96-5=91, Resulting Numbers: [23, 91] Generated Node #0,1,0: 85:[23, 91] Operation: 96-5=91 Exploring Operation: 96-23=73, Resulting Numbers: [5, 73] Generated Node #0,1,1: 85:[5, 73] Operation: 96-23=73 Moving to Node #0,1,0 Current State: 85:[23, 91], Operations: ['45-40=5', '96-5=91'] Exploring Operation: 23+91=114, Resulting Numbers: [114] 114,85 unequal: No Solution Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[5, 73], Operations: ['45-40=5', '96-23=73'] Exploring Operation: 5+73=78, Resulting Numbers: [78] 78,85 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,85 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 78, 77, 62, 32 ]
61
[ "78+77=155", "62+32=94", "155-94=61" ]
Current State: 61:[78, 77, 62, 32], Operations: [] Exploring Operation: 78+77=155, Resulting Numbers: [62, 32, 155] Generated Node #2: [62, 32, 155] from Operation: 78+77=155 Current State: 61:[62, 32, 155], Operations: ['78+77=155'] Exploring Operation: 62+32=94, Resulting Numbers: [155, 94] Generated Node #3: [155, 94] from Operation: 62+32=94 Current State: 61:[155, 94], Operations: ['78+77=155', '62+32=94'] Exploring Operation: 155-94=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[78, 77, 62, 32], Operations: [] Exploring Operation: 78-32=46, Resulting Numbers: [77, 62, 46] Generated Node #0,0: 61:[77, 62, 46] Operation: 78-32=46 Exploring Operation: 62-32=30, Resulting Numbers: [78, 77, 30] Generated Node #0,1: 61:[78, 77, 30] Operation: 62-32=30 Exploring Operation: 77-32=45, Resulting Numbers: [78, 62, 45] Generated Node #0,2: 61:[78, 62, 45] Operation: 77-32=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[77, 62, 46], Operations: ['78-32=46'] Exploring Operation: 62-46=16, Resulting Numbers: [77, 16] Generated Node #0,0,0: 61:[77, 16] Operation: 62-46=16 Exploring Operation: 77-62=15, Resulting Numbers: [46, 15] Generated Node #0,0,1: 61:[46, 15] Operation: 77-62=15 Exploring Operation: 77-46=31, Resulting Numbers: [62, 31] Generated Node #0,0,2: 61:[62, 31] Operation: 77-46=31 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[62, 31], Operations: ['78-32=46', '77-46=31'] Exploring Operation: 62/31=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 62-31=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 62+31=93, Resulting Numbers: [93] 93,61 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:[77, 16], Operations: ['78-32=46', '62-46=16'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[78, 77, 62, 32], Operations: [] Exploring Operation: 78-32=46, Resulting Numbers: [77, 62, 46] Generated Node #0,0: 61:[77, 62, 46] Operation: 78-32=46 Moving to Node #0,0 Current State: 61:[77, 62, 46], Operations: ['78-32=46'] Exploring Operation: 62-46=16, Resulting Numbers: [77, 16] Generated Node #0,0,0: 61:[77, 16] Operation: 62-46=16 Moving to Node #0,0,0 Current State: 61:[77, 16], Operations: ['78-32=46', '62-46=16'] Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 92, 78, 14, 60 ]
60
[ "92-78=14", "14+60=74", "74-14=60" ]
Current State: 60:[92, 78, 14, 60], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [14, 60, 14] Generated Node #2: [14, 60, 14] from Operation: 92-78=14 Current State: 60:[14, 60, 14], Operations: ['92-78=14'] Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,60 equal: Goal Reached Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[92, 78, 14, 60], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [14, 60, 14] Generated Node #0,0: 60:[14, 60, 14] Operation: 92-78=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[14, 60, 14], Operations: ['92-78=14'] Exploring Operation: 14/14=1, Resulting Numbers: [60, 1] Generated Node #0,0,0: 60:[60, 1] Operation: 14/14=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[60, 1], Operations: ['92-78=14', '14/14=1'] Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[92, 78, 14, 60], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [14, 60, 14] Generated Node #0,0: 60:[14, 60, 14] Operation: 92-78=14 Moving to Node #0,0 Current State: 60:[14, 60, 14], Operations: ['92-78=14'] Exploring Operation: 14/14=1, Resulting Numbers: [60, 1] Generated Node #0,0,0: 60:[60, 1] Operation: 14/14=1 Moving to Node #0,0,0 Current State: 60:[60, 1], Operations: ['92-78=14', '14/14=1'] Exploring Operation: 60*1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 62, 94, 92, 96 ]
65
[ "94-92=2", "62/2=31", "96-31=65" ]
Current State: 65:[62, 94, 92, 96], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [62, 96, 2] Generated Node #2: [62, 96, 2] from Operation: 94-92=2 Current State: 65:[62, 96, 2], Operations: ['94-92=2'] Exploring Operation: 62/2=31, Resulting Numbers: [96, 31] Generated Node #3: [96, 31] from Operation: 62/2=31 Current State: 65:[96, 31], Operations: ['94-92=2', '62/2=31'] Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[62, 94, 92, 96], Operations: [] Exploring Operation: 96-92=4, Resulting Numbers: [62, 94, 4] Generated Node #0,0: 65:[62, 94, 4] Operation: 96-92=4 Exploring Operation: 96-94=2, Resulting Numbers: [62, 92, 2] Generated Node #0,1: 65:[62, 92, 2] Operation: 96-94=2 Exploring Operation: 94-92=2, Resulting Numbers: [62, 96, 2] Generated Node #0,2: 65:[62, 96, 2] Operation: 94-92=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[62, 94, 4], Operations: ['96-92=4'] Exploring Operation: 62+4=66, Resulting Numbers: [94, 66] Generated Node #0,0,0: 65:[94, 66] Operation: 62+4=66 Exploring Operation: 94-4=90, Resulting Numbers: [62, 90] Generated Node #0,0,1: 65:[62, 90] Operation: 94-4=90 Exploring Operation: 94-62=32, Resulting Numbers: [4, 32] Generated Node #0,0,2: 65:[4, 32] Operation: 94-62=32 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 65:[4, 32], Operations: ['96-92=4', '94-62=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,65 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,65 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,65 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:[62, 90], Operations: ['96-92=4', '94-4=90'] Exploring Operation: 62+90=152, Resulting Numbers: [152] 152,65 unequal: No Solution Exploring Operation: 62*90=5580, Resulting Numbers: [5580] 5580,65 unequal: No Solution Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,65 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 #0,0,0 Current State: 65:[94, 66], Operations: ['96-92=4', '62+4=66'] Exploring Operation: 94+66=160, Resulting Numbers: [160] 160,65 unequal: No Solution Exploring Operation: 94-66=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 94*66=6204, Resulting Numbers: [6204] 6204,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[62, 92, 2], Operations: ['96-94=2'] Exploring Operation: 92-62=30, Resulting Numbers: [2, 30] Generated Node #0,1,0: 65:[2, 30] Operation: 92-62=30 Exploring Operation: 92/2=46, Resulting Numbers: [62, 46] Generated Node #0,1,1: 65:[62, 46] Operation: 92/2=46 Exploring Operation: 62+2=64, Resulting Numbers: [92, 64] Generated Node #0,1,2: 65:[92, 64] Operation: 62+2=64 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[2, 30], Operations: ['96-94=2', '92-62=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,65 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 #0,1,1 Current State: 65:[62, 46], Operations: ['96-94=2', '92/2=46'] Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,65 unequal: No Solution Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,65 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,65 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 #0,1,2 Current State: 65:[92, 64], Operations: ['96-94=2', '62+2=64'] Exploring Operation: 92*64=5888, Resulting Numbers: [5888] 5888,65 unequal: No Solution Exploring Operation: 92+64=156, Resulting Numbers: [156] 156,65 unequal: No Solution Exploring Operation: 92-64=28, Resulting Numbers: [28] 28,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[62, 96, 2], Operations: ['94-92=2'] Exploring Operation: 96-62=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 65:[2, 34] Operation: 96-62=34 Exploring Operation: 96/2=48, Resulting Numbers: [62, 48] Generated Node #0,2,1: 65:[62, 48] Operation: 96/2=48 Exploring Operation: 62+2=64, Resulting Numbers: [96, 64] Generated Node #0,2,2: 65:[96, 64] Operation: 62+2=64 Moving to Node #0,2,1 Current State: 65:[62, 48], Operations: ['94-92=2', '96/2=48'] Exploring Operation: 62+48=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 62*48=2976, Resulting Numbers: [2976] 2976,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[2, 34], Operations: ['94-92=2', '96-62=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,65 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[96, 64], Operations: ['94-92=2', '62+2=64'] Exploring Operation: 96+64=160, Resulting Numbers: [160] 160,65 unequal: No Solution Exploring Operation: 96*64=6144, Resulting Numbers: [6144] 6144,65 unequal: No Solution Exploring Operation: 96-64=32, Resulting Numbers: [32] 32,65 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
[ 23, 6, 92, 54 ]
15
[ "92/23=4", "6+54=60", "60/4=15" ]
Current State: 15:[23, 6, 92, 54], Operations: [] Exploring Operation: 92/23=4, Resulting Numbers: [6, 54, 4] Generated Node #2: [6, 54, 4] from Operation: 92/23=4 Current State: 15:[6, 54, 4], Operations: ['92/23=4'] Exploring Operation: 6+54=60, Resulting Numbers: [4, 60] Generated Node #3: [4, 60] from Operation: 6+54=60 Current State: 15:[4, 60], Operations: ['92/23=4', '6+54=60'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[23, 6, 92, 54], Operations: [] Exploring Operation: 92-54=38, Resulting Numbers: [23, 6, 38] Generated Node #0,0: 15:[23, 6, 38] Operation: 92-54=38 Moving to Node #0,0 Current State: 15:[23, 6, 38], Operations: ['92-54=38'] Exploring Operation: 38-23=15, Resulting Numbers: [6, 15] Generated Node #0,0,0: 15:[6, 15] Operation: 38-23=15 Moving to Node #0,0,0 Current State: 15:[6, 15], Operations: ['92-54=38', '38-23=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,15 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 22, 15, 41, 39 ]
26
[ "41-39=2", "22/2=11", "15+11=26" ]
Current State: 26:[22, 15, 41, 39], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [22, 15, 2] Generated Node #2: [22, 15, 2] from Operation: 41-39=2 Current State: 26:[22, 15, 2], Operations: ['41-39=2'] Exploring Operation: 22/2=11, Resulting Numbers: [15, 11] Generated Node #3: [15, 11] from Operation: 22/2=11 Current State: 26:[15, 11], Operations: ['41-39=2', '22/2=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[22, 15, 41, 39], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [22, 15, 2] Generated Node #0,0: 26:[22, 15, 2] Operation: 41-39=2 Exploring Operation: 41-15=26, Resulting Numbers: [22, 39, 26] Generated Node #0,1: 26:[22, 39, 26] Operation: 41-15=26 Exploring Operation: 41-22=19, Resulting Numbers: [15, 39, 19] Generated Node #0,2: 26:[15, 39, 19] Operation: 41-22=19 Moving to Node #0,0 Current State: 26:[22, 15, 2], Operations: ['41-39=2'] Exploring Operation: 22/2=11, Resulting Numbers: [15, 11] Generated Node #0,0,0: 26:[15, 11] Operation: 22/2=11 Exploring Operation: 15-2=13, Resulting Numbers: [22, 13] Generated Node #0,0,1: 26:[22, 13] Operation: 15-2=13 Exploring Operation: 22+2=24, Resulting Numbers: [15, 24] Generated Node #0,0,2: 26:[15, 24] Operation: 22+2=24 Moving to Node #0,1 Current State: 26:[22, 39, 26], Operations: ['41-15=26'] Exploring Operation: 39-26=13, Resulting Numbers: [22, 13] Generated Node #0,1,0: 26:[22, 13] Operation: 39-26=13 Exploring Operation: 39-22=17, Resulting Numbers: [26, 17] Generated Node #0,1,1: 26:[26, 17] Operation: 39-22=17 Exploring Operation: 26-22=4, Resulting Numbers: [39, 4] Generated Node #0,1,2: 26:[39, 4] Operation: 26-22=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[22, 13], Operations: ['41-15=26', '39-26=13'] Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,26 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[26, 17], Operations: ['41-15=26', '39-22=17'] Exploring Operation: 26+17=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,26 unequal: No Solution Exploring Operation: 26*17=442, Resulting Numbers: [442] 442,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[39, 4], Operations: ['41-15=26', '26-22=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,26 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,26 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: 26:[15, 39, 19], Operations: ['41-22=19'] Exploring Operation: 39-15=24, Resulting Numbers: [19, 24] Generated Node #0,2,0: 26:[19, 24] Operation: 39-15=24 Exploring Operation: 19-15=4, Resulting Numbers: [39, 4] Generated Node #0,2,1: 26:[39, 4] Operation: 19-15=4 Exploring Operation: 39-19=20, Resulting Numbers: [15, 20] Generated Node #0,2,2: 26:[15, 20] Operation: 39-19=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 26:[19, 24], Operations: ['41-22=19', '39-15=24'] Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,26 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 26:[15, 20], Operations: ['41-22=19', '39-19=20'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,26 unequal: No Solution Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,26 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 26:[39, 4], Operations: ['41-22=19', '19-15=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,26 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,26 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,26 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: 26:[15, 11], Operations: ['41-39=2', '22/2=11'] Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,26 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[22, 15, 41, 39], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [22, 15, 2] Generated Node #0,0: 26:[22, 15, 2] Operation: 41-39=2 Moving to Node #0,0 Current State: 26:[22, 15, 2], Operations: ['41-39=2'] Exploring Operation: 22/2=11, Resulting Numbers: [15, 11] Generated Node #0,0,0: 26:[15, 11] Operation: 22/2=11 Moving to Node #0,0,0 Current State: 26:[15, 11], Operations: ['41-39=2', '22/2=11'] Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 89, 5, 66, 15 ]
100
[ "89-66=23", "5*23=115", "115-15=100" ]
Current State: 100:[89, 5, 66, 15], Operations: [] Exploring Operation: 89-66=23, Resulting Numbers: [5, 15, 23] Generated Node #2: [5, 15, 23] from Operation: 89-66=23 Current State: 100:[5, 15, 23], Operations: ['89-66=23'] Exploring Operation: 5*23=115, Resulting Numbers: [15, 115] Generated Node #3: [15, 115] from Operation: 5*23=115 Current State: 100:[15, 115], Operations: ['89-66=23', '5*23=115'] Exploring Operation: 115-15=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[89, 5, 66, 15], Operations: [] Exploring Operation: 66-15=51, Resulting Numbers: [89, 5, 51] Generated Node #0,0: 100:[89, 5, 51] Operation: 66-15=51 Exploring Operation: 89-66=23, Resulting Numbers: [5, 15, 23] Generated Node #0,1: 100:[5, 15, 23] Operation: 89-66=23 Moving to Node #0,1 Current State: 100:[5, 15, 23], Operations: ['89-66=23'] Exploring Operation: 5+15=20, Resulting Numbers: [23, 20] Generated Node #0,1,0: 100:[23, 20] Operation: 5+15=20 Exploring Operation: 15-5=10, Resulting Numbers: [23, 10] Generated Node #0,1,1: 100:[23, 10] Operation: 15-5=10 Moving to Node #0,0 Current State: 100:[89, 5, 51], Operations: ['66-15=51'] Exploring Operation: 89+5=94, Resulting Numbers: [51, 94] Generated Node #0,0,0: 100:[51, 94] Operation: 89+5=94 Exploring Operation: 89-51=38, Resulting Numbers: [5, 38] Generated Node #0,0,1: 100:[5, 38] Operation: 89-51=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[51, 94], Operations: ['66-15=51', '89+5=94'] Exploring Operation: 51+94=145, Resulting Numbers: [145] 145,100 unequal: No Solution Exploring Operation: 94-51=43, Resulting Numbers: [43] 43,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[5, 38], Operations: ['66-15=51', '89-51=38'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,100 unequal: No Solution Exploring Operation: 5+38=43, Resulting Numbers: [43] 43,100 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: 100:[23, 20], Operations: ['89-66=23', '5+15=20'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[23, 10], Operations: ['89-66=23', '15-5=10'] Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,100 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,100 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 92, 8, 80, 44 ]
97
[ "92+44=136", "136/8=17", "80+17=97" ]
Current State: 97:[92, 8, 80, 44], Operations: [] Exploring Operation: 92+44=136, Resulting Numbers: [8, 80, 136] Generated Node #2: [8, 80, 136] from Operation: 92+44=136 Current State: 97:[8, 80, 136], Operations: ['92+44=136'] Exploring Operation: 136/8=17, Resulting Numbers: [80, 17] Generated Node #3: [80, 17] from Operation: 136/8=17 Current State: 97:[80, 17], Operations: ['92+44=136', '136/8=17'] Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[92, 8, 80, 44], Operations: [] Exploring Operation: 8+80=88, Resulting Numbers: [92, 44, 88] Generated Node #0,0: 97:[92, 44, 88] Operation: 8+80=88 Moving to Node #0,0 Current State: 97:[92, 44, 88], Operations: ['8+80=88'] Exploring Operation: 44+88=132, Resulting Numbers: [92, 132] Generated Node #0,0,0: 97:[92, 132] Operation: 44+88=132 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[92, 132], Operations: ['8+80=88', '44+88=132'] Exploring Operation: 132-92=40, Resulting Numbers: [40] 40,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 57, 5, 83, 3 ]
93
[ "57-5=52", "83-52=31", "3*31=93" ]
Current State: 93:[57, 5, 83, 3], Operations: [] Exploring Operation: 57-5=52, Resulting Numbers: [83, 3, 52] Generated Node #2: [83, 3, 52] from Operation: 57-5=52 Current State: 93:[83, 3, 52], Operations: ['57-5=52'] Exploring Operation: 83-52=31, Resulting Numbers: [3, 31] Generated Node #3: [3, 31] from Operation: 83-52=31 Current State: 93:[3, 31], Operations: ['57-5=52', '83-52=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[57, 5, 83, 3], Operations: [] Exploring Operation: 57/3=19, Resulting Numbers: [5, 83, 19] Generated Node #0,0: 93:[5, 83, 19] Operation: 57/3=19 Exploring Operation: 57-5=52, Resulting Numbers: [83, 3, 52] Generated Node #0,1: 93:[83, 3, 52] Operation: 57-5=52 Exploring Operation: 83-57=26, Resulting Numbers: [5, 3, 26] Generated Node #0,2: 93:[5, 3, 26] Operation: 83-57=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[5, 3, 26], Operations: ['83-57=26'] Exploring Operation: 5-3=2, Resulting Numbers: [26, 2] Generated Node #0,2,0: 93:[26, 2] Operation: 5-3=2 Exploring Operation: 5+26=31, Resulting Numbers: [3, 31] Generated Node #0,2,1: 93:[3, 31] Operation: 5+26=31 Exploring Operation: 3+26=29, Resulting Numbers: [5, 29] Generated Node #0,2,2: 93:[5, 29] Operation: 3+26=29 Moving to Node #0,2,1 Current State: 93:[3, 31], Operations: ['83-57=26', '5+26=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,93 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[57, 5, 83, 3], Operations: [] Exploring Operation: 83-57=26, Resulting Numbers: [5, 3, 26] Generated Node #0,2: 93:[5, 3, 26] Operation: 83-57=26 Moving to Node #0,2 Current State: 93:[5, 3, 26], Operations: ['83-57=26'] Exploring Operation: 5+26=31, Resulting Numbers: [3, 31] Generated Node #0,2,1: 93:[3, 31] Operation: 5+26=31 Moving to Node #0,2,1 Current State: 93:[3, 31], Operations: ['83-57=26', '5+26=31'] Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 87, 5, 3, 95 ]
19
[ "95-87=8", "3*8=24", "24-5=19" ]
Current State: 19:[87, 5, 3, 95], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [5, 3, 8] Generated Node #2: [5, 3, 8] from Operation: 95-87=8 Current State: 19:[5, 3, 8], Operations: ['95-87=8'] Exploring Operation: 3*8=24, Resulting Numbers: [5, 24] Generated Node #3: [5, 24] from Operation: 3*8=24 Current State: 19:[5, 24], Operations: ['95-87=8', '3*8=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[87, 5, 3, 95], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [5, 3, 8] Generated Node #0,0: 19:[5, 3, 8] Operation: 95-87=8 Exploring Operation: 95/5=19, Resulting Numbers: [87, 3, 19] Generated Node #0,1: 19:[87, 3, 19] Operation: 95/5=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[5, 3, 8], Operations: ['95-87=8'] Exploring Operation: 3*8=24, Resulting Numbers: [5, 24] Generated Node #0,0,0: 19:[5, 24] Operation: 3*8=24 Exploring Operation: 5*3=15, Resulting Numbers: [8, 15] Generated Node #0,0,1: 19:[8, 15] Operation: 5*3=15 Moving to Node #0,0,1 Current State: 19:[8, 15], Operations: ['95-87=8', '5*3=15'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[5, 24], Operations: ['95-87=8', '3*8=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[87, 5, 3, 95], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [5, 3, 8] Generated Node #0,0: 19:[5, 3, 8] Operation: 95-87=8 Moving to Node #0,0 Current State: 19:[5, 3, 8], Operations: ['95-87=8'] Exploring Operation: 3*8=24, Resulting Numbers: [5, 24] Generated Node #0,0,0: 19:[5, 24] Operation: 3*8=24 Moving to Node #0,0,0 Current State: 19:[5, 24], Operations: ['95-87=8', '3*8=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 12, 50, 28, 68 ]
34
[ "12+50=62", "28+68=96", "96-62=34" ]
Current State: 34:[12, 50, 28, 68], Operations: [] Exploring Operation: 12+50=62, Resulting Numbers: [28, 68, 62] Generated Node #2: [28, 68, 62] from Operation: 12+50=62 Current State: 34:[28, 68, 62], Operations: ['12+50=62'] Exploring Operation: 28+68=96, Resulting Numbers: [62, 96] Generated Node #3: [62, 96] from Operation: 28+68=96 Current State: 34:[62, 96], Operations: ['12+50=62', '28+68=96'] Exploring Operation: 96-62=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[12, 50, 28, 68], Operations: [] Exploring Operation: 50-12=38, Resulting Numbers: [28, 68, 38] Generated Node #0,0: 34:[28, 68, 38] Operation: 50-12=38 Exploring Operation: 68-28=40, Resulting Numbers: [12, 50, 40] Generated Node #0,1: 34:[12, 50, 40] Operation: 68-28=40 Exploring Operation: 68-50=18, Resulting Numbers: [12, 28, 18] Generated Node #0,2: 34:[12, 28, 18] Operation: 68-50=18 Exploring Operation: 50-28=22, Resulting Numbers: [12, 68, 22] Generated Node #0,3: 34:[12, 68, 22] Operation: 50-28=22 Exploring Operation: 68-12=56, Resulting Numbers: [50, 28, 56] Generated Node #0,4: 34:[50, 28, 56] Operation: 68-12=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[12, 28, 18], Operations: ['68-50=18'] Exploring Operation: 12+28=40, Resulting Numbers: [18, 40] Generated Node #0,2,0: 34:[18, 40] Operation: 12+28=40 Exploring Operation: 12+18=30, Resulting Numbers: [28, 30] Generated Node #0,2,1: 34:[28, 30] Operation: 12+18=30 Exploring Operation: 18-12=6, Resulting Numbers: [28, 6] Generated Node #0,2,2: 34:[28, 6] Operation: 18-12=6 Exploring Operation: 28-12=16, Resulting Numbers: [18, 16] Generated Node #0,2,3: 34:[18, 16] Operation: 28-12=16 Exploring Operation: 28-18=10, Resulting Numbers: [12, 10] Generated Node #0,2,4: 34:[12, 10] Operation: 28-18=10 Moving to Node #0,2,3 Current State: 34:[18, 16], Operations: ['68-50=18', '28-12=16'] Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,34 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[12, 50, 28, 68], Operations: [] Exploring Operation: 68-50=18, Resulting Numbers: [12, 28, 18] Generated Node #0,2: 34:[12, 28, 18] Operation: 68-50=18 Moving to Node #0,2 Current State: 34:[12, 28, 18], Operations: ['68-50=18'] Exploring Operation: 28-12=16, Resulting Numbers: [18, 16] Generated Node #0,2,3: 34:[18, 16] Operation: 28-12=16 Moving to Node #0,2,3 Current State: 34:[18, 16], Operations: ['68-50=18', '28-12=16'] Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 15, 84, 38, 4 ]
57
[ "15+84=99", "38+4=42", "99-42=57" ]
Current State: 57:[15, 84, 38, 4], Operations: [] Exploring Operation: 15+84=99, Resulting Numbers: [38, 4, 99] Generated Node #2: [38, 4, 99] from Operation: 15+84=99 Current State: 57:[38, 4, 99], Operations: ['15+84=99'] Exploring Operation: 38+4=42, Resulting Numbers: [99, 42] Generated Node #3: [99, 42] from Operation: 38+4=42 Current State: 57:[99, 42], Operations: ['15+84=99', '38+4=42'] Exploring Operation: 99-42=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[15, 84, 38, 4], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [15, 38, 21] Generated Node #0,0: 57:[15, 38, 21] Operation: 84/4=21 Exploring Operation: 84-38=46, Resulting Numbers: [15, 4, 46] Generated Node #0,1: 57:[15, 4, 46] Operation: 84-38=46 Moving to Node #0,1 Current State: 57:[15, 4, 46], Operations: ['84-38=46'] Exploring Operation: 15+4=19, Resulting Numbers: [46, 19] Generated Node #0,1,0: 57:[46, 19] Operation: 15+4=19 Exploring Operation: 15+46=61, Resulting Numbers: [4, 61] Generated Node #0,1,1: 57:[4, 61] Operation: 15+46=61 Moving to Node #0,0 Current State: 57:[15, 38, 21], Operations: ['84/4=21'] Exploring Operation: 38-15=23, Resulting Numbers: [21, 23] Generated Node #0,0,0: 57:[21, 23] Operation: 38-15=23 Exploring Operation: 15+38=53, Resulting Numbers: [21, 53] Generated Node #0,0,1: 57:[21, 53] Operation: 15+38=53 Moving to Node #0,1,1 Current State: 57:[4, 61], Operations: ['84-38=46', '15+46=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[15, 84, 38, 4], Operations: [] Exploring Operation: 84-38=46, Resulting Numbers: [15, 4, 46] Generated Node #0,1: 57:[15, 4, 46] Operation: 84-38=46 Moving to Node #0,1 Current State: 57:[15, 4, 46], Operations: ['84-38=46'] Exploring Operation: 15+46=61, Resulting Numbers: [4, 61] Generated Node #0,1,1: 57:[4, 61] Operation: 15+46=61 Moving to Node #0,1,1 Current State: 57:[4, 61], Operations: ['84-38=46', '15+46=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 89, 80, 49, 48 ]
88
[ "89-80=9", "49+48=97", "97-9=88" ]
Current State: 88:[89, 80, 49, 48], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [49, 48, 9] Generated Node #2: [49, 48, 9] from Operation: 89-80=9 Current State: 88:[49, 48, 9], Operations: ['89-80=9'] Exploring Operation: 49+48=97, Resulting Numbers: [9, 97] Generated Node #3: [9, 97] from Operation: 49+48=97 Current State: 88:[9, 97], Operations: ['89-80=9', '49+48=97'] Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[89, 80, 49, 48], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [49, 48, 9] Generated Node #0,0: 88:[49, 48, 9] Operation: 89-80=9 Exploring Operation: 49-48=1, Resulting Numbers: [89, 80, 1] Generated Node #0,1: 88:[89, 80, 1] Operation: 49-48=1 Moving to Node #0,0 Current State: 88:[49, 48, 9], Operations: ['89-80=9'] Exploring Operation: 49-9=40, Resulting Numbers: [48, 40] Generated Node #0,0,0: 88:[48, 40] Operation: 49-9=40 Exploring Operation: 49-48=1, Resulting Numbers: [9, 1] Generated Node #0,0,1: 88:[9, 1] Operation: 49-48=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[9, 1], Operations: ['89-80=9', '49-48=1'] Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[48, 40], Operations: ['89-80=9', '49-9=40'] Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[89, 80, 49, 48], Operations: [] Exploring Operation: 89-80=9, Resulting Numbers: [49, 48, 9] Generated Node #0,0: 88:[49, 48, 9] Operation: 89-80=9 Moving to Node #0,0 Current State: 88:[49, 48, 9], Operations: ['89-80=9'] Exploring Operation: 49-9=40, Resulting Numbers: [48, 40] Generated Node #0,0,0: 88:[48, 40] Operation: 49-9=40 Moving to Node #0,0,0 Current State: 88:[48, 40], Operations: ['89-80=9', '49-9=40'] Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 37, 52, 74, 9 ]
86
[ "74/37=2", "52-9=43", "2*43=86" ]
Current State: 86:[37, 52, 74, 9], Operations: [] Exploring Operation: 74/37=2, Resulting Numbers: [52, 9, 2] Generated Node #2: [52, 9, 2] from Operation: 74/37=2 Current State: 86:[52, 9, 2], Operations: ['74/37=2'] Exploring Operation: 52-9=43, Resulting Numbers: [2, 43] Generated Node #3: [2, 43] from Operation: 52-9=43 Current State: 86:[2, 43], Operations: ['74/37=2', '52-9=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[37, 52, 74, 9], Operations: [] Exploring Operation: 74+9=83, Resulting Numbers: [37, 52, 83] Generated Node #0,0: 86:[37, 52, 83] Operation: 74+9=83 Exploring Operation: 52-9=43, Resulting Numbers: [37, 74, 43] Generated Node #0,1: 86:[37, 74, 43] Operation: 52-9=43 Exploring Operation: 37+52=89, Resulting Numbers: [74, 9, 89] Generated Node #0,2: 86:[74, 9, 89] Operation: 37+52=89 Exploring Operation: 74/37=2, Resulting Numbers: [52, 9, 2] Generated Node #0,3: 86:[52, 9, 2] Operation: 74/37=2 Exploring Operation: 74-37=37, Resulting Numbers: [52, 9, 37] Generated Node #0,4: 86:[52, 9, 37] Operation: 74-37=37 Moving to Node #0,3 Current State: 86:[52, 9, 2], Operations: ['74/37=2'] Exploring Operation: 9-2=7, Resulting Numbers: [52, 7] Generated Node #0,3,0: 86:[52, 7] Operation: 9-2=7 Exploring Operation: 52+9=61, Resulting Numbers: [2, 61] Generated Node #0,3,1: 86:[2, 61] Operation: 52+9=61 Exploring Operation: 52-9=43, Resulting Numbers: [2, 43] Generated Node #0,3,2: 86:[2, 43] Operation: 52-9=43 Exploring Operation: 52-2=50, Resulting Numbers: [9, 50] Generated Node #0,3,3: 86:[9, 50] Operation: 52-2=50 Exploring Operation: 52+2=54, Resulting Numbers: [9, 54] Generated Node #0,3,4: 86:[9, 54] Operation: 52+2=54 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 86:[2, 43], Operations: ['74/37=2', '52-9=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[37, 52, 74, 9], Operations: [] Exploring Operation: 74/37=2, Resulting Numbers: [52, 9, 2] Generated Node #0,3: 86:[52, 9, 2] Operation: 74/37=2 Moving to Node #0,3 Current State: 86:[52, 9, 2], Operations: ['74/37=2'] Exploring Operation: 52-9=43, Resulting Numbers: [2, 43] Generated Node #0,3,2: 86:[2, 43] Operation: 52-9=43 Moving to Node #0,3,2 Current State: 86:[2, 43], Operations: ['74/37=2', '52-9=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 25, 87, 57, 78 ]
83
[ "87-25=62", "78-57=21", "62+21=83" ]
Current State: 83:[25, 87, 57, 78], Operations: [] Exploring Operation: 87-25=62, Resulting Numbers: [57, 78, 62] Generated Node #2: [57, 78, 62] from Operation: 87-25=62 Current State: 83:[57, 78, 62], Operations: ['87-25=62'] Exploring Operation: 78-57=21, Resulting Numbers: [62, 21] Generated Node #3: [62, 21] from Operation: 78-57=21 Current State: 83:[62, 21], Operations: ['87-25=62', '78-57=21'] Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[25, 87, 57, 78], Operations: [] Exploring Operation: 25+57=82, Resulting Numbers: [87, 78, 82] Generated Node #0,0: 83:[87, 78, 82] Operation: 25+57=82 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[87, 78, 82], Operations: ['25+57=82'] Exploring Operation: 87-78=9, Resulting Numbers: [82, 9] Generated Node #0,0,0: 83:[82, 9] Operation: 87-78=9 Moving to Node #0,0,0 Current State: 83:[82, 9], Operations: ['25+57=82', '87-78=9'] Exploring Operation: 82+9=91, Resulting Numbers: [91] 91,83 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
[ 3, 81, 41, 44 ]
30
[ "81/3=27", "44-41=3", "27+3=30" ]
Current State: 30:[3, 81, 41, 44], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [41, 44, 27] Generated Node #2: [41, 44, 27] from Operation: 81/3=27 Current State: 30:[41, 44, 27], Operations: ['81/3=27'] Exploring Operation: 44-41=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 44-41=3 Current State: 30:[27, 3], Operations: ['81/3=27', '44-41=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[3, 81, 41, 44], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [3, 44, 40] Generated Node #0,0: 30:[3, 44, 40] Operation: 81-41=40 Exploring Operation: 44-41=3, Resulting Numbers: [3, 81, 3] Generated Node #0,1: 30:[3, 81, 3] Operation: 44-41=3 Exploring Operation: 81-3=78, Resulting Numbers: [41, 44, 78] Generated Node #0,2: 30:[41, 44, 78] Operation: 81-3=78 Exploring Operation: 81-44=37, Resulting Numbers: [3, 41, 37] Generated Node #0,3: 30:[3, 41, 37] Operation: 81-44=37 Exploring Operation: 81/3=27, Resulting Numbers: [41, 44, 27] Generated Node #0,4: 30:[41, 44, 27] Operation: 81/3=27 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[3, 41, 37], Operations: ['81-44=37'] Exploring Operation: 37-3=34, Resulting Numbers: [41, 34] Generated Node #0,3,0: 30:[41, 34] Operation: 37-3=34 Exploring Operation: 3+37=40, Resulting Numbers: [41, 40] Generated Node #0,3,1: 30:[41, 40] Operation: 3+37=40 Exploring Operation: 41-37=4, Resulting Numbers: [3, 4] Generated Node #0,3,2: 30:[3, 4] Operation: 41-37=4 Exploring Operation: 3+41=44, Resulting Numbers: [37, 44] Generated Node #0,3,3: 30:[37, 44] Operation: 3+41=44 Exploring Operation: 41-3=38, Resulting Numbers: [37, 38] Generated Node #0,3,4: 30:[37, 38] Operation: 41-3=38 Moving to Node #0,3,2 Current State: 30:[3, 4], Operations: ['81-44=37', '41-37=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[37, 38], Operations: ['81-44=37', '41-3=38'] Exploring Operation: 37*38=1406, Resulting Numbers: [1406] 1406,30 unequal: No Solution Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[41, 34], Operations: ['81-44=37', '37-3=34'] Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,30 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[41, 40], Operations: ['81-44=37', '3+37=40'] Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,30 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[37, 44], Operations: ['81-44=37', '3+41=44'] Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 37*44=1628, Resulting Numbers: [1628] 1628,30 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:[3, 44, 40], Operations: ['81-41=40'] Exploring Operation: 44-3=41, Resulting Numbers: [40, 41] Generated Node #0,0,0: 30:[40, 41] Operation: 44-3=41 Exploring Operation: 44-40=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 30:[3, 4] Operation: 44-40=4 Exploring Operation: 40-3=37, Resulting Numbers: [44, 37] Generated Node #0,0,2: 30:[44, 37] Operation: 40-3=37 Exploring Operation: 3+44=47, Resulting Numbers: [40, 47] Generated Node #0,0,3: 30:[40, 47] Operation: 3+44=47 Exploring Operation: 3+40=43, Resulting Numbers: [44, 43] Generated Node #0,0,4: 30:[44, 43] Operation: 3+40=43 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[3, 4], Operations: ['81-41=40', '44-40=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[40, 41], Operations: ['81-41=40', '44-3=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[44, 37], Operations: ['81-41=40', '40-3=37'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,30 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 30:[40, 47], Operations: ['81-41=40', '3+44=47'] Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,30 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 30:[44, 43], Operations: ['81-41=40', '3+40=43'] Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,30 unequal: No Solution Exploring Operation: 44+43=87, Resulting Numbers: [87] 87,30 unequal: No Solution Exploring Operation: 44*43=1892, Resulting Numbers: [1892] 1892,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 30:[41, 44, 27], Operations: ['81/3=27'] Exploring Operation: 44+27=71, Resulting Numbers: [41, 71] Generated Node #0,4,0: 30:[41, 71] Operation: 44+27=71 Exploring Operation: 44-41=3, Resulting Numbers: [27, 3] Generated Node #0,4,1: 30:[27, 3] Operation: 44-41=3 Exploring Operation: 41-27=14, Resulting Numbers: [44, 14] Generated Node #0,4,2: 30:[44, 14] Operation: 41-27=14 Exploring Operation: 41+27=68, Resulting Numbers: [44, 68] Generated Node #0,4,3: 30:[44, 68] Operation: 41+27=68 Exploring Operation: 44-27=17, Resulting Numbers: [41, 17] Generated Node #0,4,4: 30:[41, 17] Operation: 44-27=17 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 30:[27, 3], Operations: ['81/3=27', '44-41=3'] Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,30 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[3, 81, 41, 44], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [41, 44, 27] Generated Node #0,4: 30:[41, 44, 27] Operation: 81/3=27 Moving to Node #0,4 Current State: 30:[41, 44, 27], Operations: ['81/3=27'] Exploring Operation: 44-41=3, Resulting Numbers: [27, 3] Generated Node #0,4,1: 30:[27, 3] Operation: 44-41=3 Moving to Node #0,4,1 Current State: 30:[27, 3], Operations: ['81/3=27', '44-41=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 78, 53, 27, 9 ]
18
[ "78-53=25", "27-25=2", "9*2=18" ]
Current State: 18:[78, 53, 27, 9], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [27, 9, 25] Generated Node #2: [27, 9, 25] from Operation: 78-53=25 Current State: 18:[27, 9, 25], Operations: ['78-53=25'] Exploring Operation: 27-25=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 27-25=2 Current State: 18:[9, 2], Operations: ['78-53=25', '27-25=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[78, 53, 27, 9], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [27, 9, 25] Generated Node #0,0: 18:[27, 9, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 18:[27, 9, 25], Operations: ['78-53=25'] Exploring Operation: 27-25=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 18:[9, 2] Operation: 27-25=2 Moving to Node #0,0,0 Current State: 18:[9, 2], Operations: ['78-53=25', '27-25=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[78, 53, 27, 9], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [27, 9, 25] Generated Node #0,0: 18:[27, 9, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 18:[27, 9, 25], Operations: ['78-53=25'] Exploring Operation: 27-25=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 18:[9, 2] Operation: 27-25=2 Moving to Node #0,0,0 Current State: 18:[9, 2], Operations: ['78-53=25', '27-25=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 45, 29, 17, 43 ]
43
[ "45-29=16", "17-16=1", "43*1=43" ]
Current State: 43:[45, 29, 17, 43], Operations: [] Exploring Operation: 45-29=16, Resulting Numbers: [17, 43, 16] Generated Node #2: [17, 43, 16] from Operation: 45-29=16 Current State: 43:[17, 43, 16], Operations: ['45-29=16'] Exploring Operation: 17-16=1, Resulting Numbers: [43, 1] Generated Node #3: [43, 1] from Operation: 17-16=1 Current State: 43:[43, 1], Operations: ['45-29=16', '17-16=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[45, 29, 17, 43], Operations: [] Exploring Operation: 45+17=62, Resulting Numbers: [29, 43, 62] Generated Node #0,0: 43:[29, 43, 62] Operation: 45+17=62 Exploring Operation: 29+17=46, Resulting Numbers: [45, 43, 46] Generated Node #0,1: 43:[45, 43, 46] Operation: 29+17=46 Exploring Operation: 45-17=28, Resulting Numbers: [29, 43, 28] Generated Node #0,2: 43:[29, 43, 28] Operation: 45-17=28 Exploring Operation: 29-17=12, Resulting Numbers: [45, 43, 12] Generated Node #0,3: 43:[45, 43, 12] Operation: 29-17=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[45, 43, 46], Operations: ['29+17=46'] Exploring Operation: 45-43=2, Resulting Numbers: [46, 2] Generated Node #0,1,0: 43:[46, 2] Operation: 45-43=2 Exploring Operation: 45+43=88, Resulting Numbers: [46, 88] Generated Node #0,1,1: 43:[46, 88] Operation: 45+43=88 Exploring Operation: 46-43=3, Resulting Numbers: [45, 3] Generated Node #0,1,2: 43:[45, 3] Operation: 46-43=3 Exploring Operation: 46-45=1, Resulting Numbers: [43, 1] Generated Node #0,1,3: 43:[43, 1] Operation: 46-45=1 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[45, 3], Operations: ['29+17=46', '46-43=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,43 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 43:[43, 1], Operations: ['29+17=46', '46-45=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[45, 29, 17, 43], Operations: [] Exploring Operation: 29+17=46, Resulting Numbers: [45, 43, 46] Generated Node #0,1: 43:[45, 43, 46] Operation: 29+17=46 Moving to Node #0,1 Current State: 43:[45, 43, 46], Operations: ['29+17=46'] Exploring Operation: 46-45=1, Resulting Numbers: [43, 1] Generated Node #0,1,3: 43:[43, 1] Operation: 46-45=1 Moving to Node #0,1,3 Current State: 43:[43, 1], Operations: ['29+17=46', '46-45=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 84, 1, 42, 44 ]
21
[ "84/42=2", "44/2=22", "22-1=21" ]
Current State: 21:[84, 1, 42, 44], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [1, 44, 2] Generated Node #2: [1, 44, 2] from Operation: 84/42=2 Current State: 21:[1, 44, 2], Operations: ['84/42=2'] Exploring Operation: 44/2=22, Resulting Numbers: [1, 22] Generated Node #3: [1, 22] from Operation: 44/2=22 Current State: 21:[1, 22], Operations: ['84/42=2', '44/2=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[84, 1, 42, 44], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [1, 44, 2] Generated Node #0,0: 21:[1, 44, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [1, 44, 42] Generated Node #0,1: 21:[1, 44, 42] Operation: 84-42=42 Exploring Operation: 84-44=40, Resulting Numbers: [1, 42, 40] Generated Node #0,2: 21:[1, 42, 40] Operation: 84-44=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[1, 44, 2], Operations: ['84/42=2'] Exploring Operation: 44/2=22, Resulting Numbers: [1, 22] Generated Node #0,0,0: 21:[1, 22] Operation: 44/2=22 Exploring Operation: 44-1=43, Resulting Numbers: [2, 43] Generated Node #0,0,1: 21:[2, 43] Operation: 44-1=43 Exploring Operation: 1+2=3, Resulting Numbers: [44, 3] Generated Node #0,0,2: 21:[44, 3] Operation: 1+2=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[1, 22], Operations: ['84/42=2', '44/2=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[84, 1, 42, 44], Operations: [] Exploring Operation: 84/42=2, Resulting Numbers: [1, 44, 2] Generated Node #0,0: 21:[1, 44, 2] Operation: 84/42=2 Moving to Node #0,0 Current State: 21:[1, 44, 2], Operations: ['84/42=2'] Exploring Operation: 44/2=22, Resulting Numbers: [1, 22] Generated Node #0,0,0: 21:[1, 22] Operation: 44/2=22 Moving to Node #0,0,0 Current State: 21:[1, 22], Operations: ['84/42=2', '44/2=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 37, 45, 31, 39 ]
12
[ "37+45=82", "31+39=70", "82-70=12" ]
Current State: 12:[37, 45, 31, 39], Operations: [] Exploring Operation: 37+45=82, Resulting Numbers: [31, 39, 82] Generated Node #2: [31, 39, 82] from Operation: 37+45=82 Current State: 12:[31, 39, 82], Operations: ['37+45=82'] Exploring Operation: 31+39=70, Resulting Numbers: [82, 70] Generated Node #3: [82, 70] from Operation: 31+39=70 Current State: 12:[82, 70], Operations: ['37+45=82', '31+39=70'] Exploring Operation: 82-70=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[37, 45, 31, 39], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [37, 31, 6] Generated Node #0,0: 12:[37, 31, 6] Operation: 45-39=6 Moving to Node #0,0 Current State: 12:[37, 31, 6], Operations: ['45-39=6'] Exploring Operation: 37-31=6, Resulting Numbers: [6, 6] Generated Node #0,0,0: 12:[6, 6] Operation: 37-31=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[6, 6], Operations: ['45-39=6', '37-31=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[37, 45, 31, 39], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [37, 31, 6] Generated Node #0,0: 12:[37, 31, 6] Operation: 45-39=6 Moving to Node #0,0 Current State: 12:[37, 31, 6], Operations: ['45-39=6'] Exploring Operation: 37-31=6, Resulting Numbers: [6, 6] Generated Node #0,0,0: 12:[6, 6] Operation: 37-31=6 Moving to Node #0,0,0 Current State: 12:[6, 6], Operations: ['45-39=6', '37-31=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 11, 41, 55, 95 ]
22
[ "55/11=5", "95/5=19", "41-19=22" ]
Current State: 22:[11, 41, 55, 95], Operations: [] Exploring Operation: 55/11=5, Resulting Numbers: [41, 95, 5] Generated Node #2: [41, 95, 5] from Operation: 55/11=5 Current State: 22:[41, 95, 5], Operations: ['55/11=5'] Exploring Operation: 95/5=19, Resulting Numbers: [41, 19] Generated Node #3: [41, 19] from Operation: 95/5=19 Current State: 22:[41, 19], Operations: ['55/11=5', '95/5=19'] Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[11, 41, 55, 95], Operations: [] Exploring Operation: 95-55=40, Resulting Numbers: [11, 41, 40] Generated Node #0,0: 22:[11, 41, 40] Operation: 95-55=40 Exploring Operation: 95-41=54, Resulting Numbers: [11, 55, 54] Generated Node #0,1: 22:[11, 55, 54] Operation: 95-41=54 Exploring Operation: 55-41=14, Resulting Numbers: [11, 95, 14] Generated Node #0,2: 22:[11, 95, 14] Operation: 55-41=14 Moving to Node #0,0 Current State: 22:[11, 41, 40], Operations: ['95-55=40'] Exploring Operation: 41-40=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 22:[11, 1] Operation: 41-40=1 Exploring Operation: 41-11=30, Resulting Numbers: [40, 30] Generated Node #0,0,1: 22:[40, 30] Operation: 41-11=30 Exploring Operation: 40-11=29, Resulting Numbers: [41, 29] Generated Node #0,0,2: 22:[41, 29] Operation: 40-11=29 Moving to Node #0,1 Current State: 22:[11, 55, 54], Operations: ['95-41=54'] Exploring Operation: 55-54=1, Resulting Numbers: [11, 1] Generated Node #0,1,0: 22:[11, 1] Operation: 55-54=1 Exploring Operation: 55/11=5, Resulting Numbers: [54, 5] Generated Node #0,1,1: 22:[54, 5] Operation: 55/11=5 Exploring Operation: 55-11=44, Resulting Numbers: [54, 44] Generated Node #0,1,2: 22:[54, 44] Operation: 55-11=44 Moving to Node #0,2 Current State: 22:[11, 95, 14], Operations: ['55-41=14'] Exploring Operation: 14-11=3, Resulting Numbers: [95, 3] Generated Node #0,2,0: 22:[95, 3] Operation: 14-11=3 Exploring Operation: 95-14=81, Resulting Numbers: [11, 81] Generated Node #0,2,1: 22:[11, 81] Operation: 95-14=81 Exploring Operation: 95-11=84, Resulting Numbers: [14, 84] Generated Node #0,2,2: 22:[14, 84] Operation: 95-11=84 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[11, 81], Operations: ['55-41=14', '95-14=81'] Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,22 unequal: No Solution Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,22 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,22 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 #0,2,2 Current State: 22:[14, 84], Operations: ['55-41=14', '95-11=84'] Exploring Operation: 14+84=98, Resulting Numbers: [98] 98,22 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,22 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 #0,2,0 Current State: 22:[95, 3], Operations: ['55-41=14', '14-11=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,22 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,22 unequal: No Solution Exploring Operation: 95*3=285, Resulting Numbers: [285] 285,22 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: 22:[11, 1], Operations: ['95-55=40', '41-40=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[11, 1], Operations: ['95-41=54', '55-54=1'] Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[41, 29], Operations: ['95-55=40', '40-11=29'] Exploring Operation: 41*29=1189, Resulting Numbers: [1189] 1189,22 unequal: No Solution Exploring Operation: 41+29=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[40, 30], Operations: ['95-55=40', '41-11=30'] Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,22 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[54, 5], Operations: ['95-41=54', '55/11=5'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,22 unequal: No Solution Exploring Operation: 54+5=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 54*5=270, Resulting Numbers: [270] 270,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[54, 44], Operations: ['95-41=54', '55-11=44'] Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,22 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,22 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 65, 7, 15, 5 ]
30
[ "65*7=455", "455-5=450", "450/15=30" ]
Current State: 30:[65, 7, 15, 5], Operations: [] Exploring Operation: 65*7=455, Resulting Numbers: [15, 5, 455] Generated Node #2: [15, 5, 455] from Operation: 65*7=455 Current State: 30:[15, 5, 455], Operations: ['65*7=455'] Exploring Operation: 455-5=450, Resulting Numbers: [15, 450] Generated Node #3: [15, 450] from Operation: 455-5=450 Current State: 30:[15, 450], Operations: ['65*7=455', '455-5=450'] Exploring Operation: 450/15=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[65, 7, 15, 5], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [7, 15, 13] Generated Node #0,0: 30:[7, 15, 13] Operation: 65/5=13 Moving to Node #0,0 Current State: 30:[7, 15, 13], Operations: ['65/5=13'] Exploring Operation: 13-7=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 30:[15, 6] Operation: 13-7=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[15, 6], Operations: ['65/5=13', '13-7=6'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 47, 65, 80, 44 ]
18
[ "65-47=18", "80-44=36", "36-18=18" ]
Current State: 18:[47, 65, 80, 44], Operations: [] Exploring Operation: 65-47=18, Resulting Numbers: [80, 44, 18] Generated Node #2: [80, 44, 18] from Operation: 65-47=18 Current State: 18:[80, 44, 18], Operations: ['65-47=18'] Exploring Operation: 80-44=36, Resulting Numbers: [18, 36] Generated Node #3: [18, 36] from Operation: 80-44=36 Current State: 18:[18, 36], Operations: ['65-47=18', '80-44=36'] Exploring Operation: 36-18=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[47, 65, 80, 44], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [47, 44, 15] Generated Node #0,0: 18:[47, 44, 15] Operation: 80-65=15 Exploring Operation: 80-47=33, Resulting Numbers: [65, 44, 33] Generated Node #0,1: 18:[65, 44, 33] Operation: 80-47=33 Exploring Operation: 65-44=21, Resulting Numbers: [47, 80, 21] Generated Node #0,2: 18:[47, 80, 21] Operation: 65-44=21 Exploring Operation: 65-47=18, Resulting Numbers: [80, 44, 18] Generated Node #0,3: 18:[80, 44, 18] Operation: 65-47=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[47, 44, 15], Operations: ['80-65=15'] Exploring Operation: 47-15=32, Resulting Numbers: [44, 32] Generated Node #0,0,0: 18:[44, 32] Operation: 47-15=32 Exploring Operation: 44-15=29, Resulting Numbers: [47, 29] Generated Node #0,0,1: 18:[47, 29] Operation: 44-15=29 Exploring Operation: 47+15=62, Resulting Numbers: [44, 62] Generated Node #0,0,2: 18:[44, 62] Operation: 47+15=62 Exploring Operation: 47-44=3, Resulting Numbers: [15, 3] Generated Node #0,0,3: 18:[15, 3] Operation: 47-44=3 Moving to Node #0,0,3 Current State: 18:[15, 3], Operations: ['80-65=15', '47-44=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[47, 65, 80, 44], Operations: [] Exploring Operation: 80-65=15, Resulting Numbers: [47, 44, 15] Generated Node #0,0: 18:[47, 44, 15] Operation: 80-65=15 Moving to Node #0,0 Current State: 18:[47, 44, 15], Operations: ['80-65=15'] Exploring Operation: 47-44=3, Resulting Numbers: [15, 3] Generated Node #0,0,3: 18:[15, 3] Operation: 47-44=3 Moving to Node #0,0,3 Current State: 18:[15, 3], Operations: ['80-65=15', '47-44=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 31, 65, 46, 43 ]
93
[ "31+65=96", "46-43=3", "96-3=93" ]
Current State: 93:[31, 65, 46, 43], Operations: [] Exploring Operation: 31+65=96, Resulting Numbers: [46, 43, 96] Generated Node #2: [46, 43, 96] from Operation: 31+65=96 Current State: 93:[46, 43, 96], Operations: ['31+65=96'] Exploring Operation: 46-43=3, Resulting Numbers: [96, 3] Generated Node #3: [96, 3] from Operation: 46-43=3 Current State: 93:[96, 3], Operations: ['31+65=96', '46-43=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[31, 65, 46, 43], Operations: [] Exploring Operation: 65-46=19, Resulting Numbers: [31, 43, 19] Generated Node #0,0: 93:[31, 43, 19] Operation: 65-46=19 Exploring Operation: 46-43=3, Resulting Numbers: [31, 65, 3] Generated Node #0,1: 93:[31, 65, 3] Operation: 46-43=3 Exploring Operation: 65-43=22, Resulting Numbers: [31, 46, 22] Generated Node #0,2: 93:[31, 46, 22] Operation: 65-43=22 Exploring Operation: 31+65=96, Resulting Numbers: [46, 43, 96] Generated Node #0,3: 93:[46, 43, 96] Operation: 31+65=96 Moving to Node #0,0 Current State: 93:[31, 43, 19], Operations: ['65-46=19'] Exploring Operation: 43-31=12, Resulting Numbers: [19, 12] Generated Node #0,0,0: 93:[19, 12] Operation: 43-31=12 Exploring Operation: 31-19=12, Resulting Numbers: [43, 12] Generated Node #0,0,1: 93:[43, 12] Operation: 31-19=12 Exploring Operation: 31+43=74, Resulting Numbers: [19, 74] Generated Node #0,0,2: 93:[19, 74] Operation: 31+43=74 Exploring Operation: 43-19=24, Resulting Numbers: [31, 24] Generated Node #0,0,3: 93:[31, 24] Operation: 43-19=24 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[31, 24], Operations: ['65-46=19', '43-19=24'] Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,93 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,93 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 #0,0,0 Current State: 93:[19, 12], Operations: ['65-46=19', '43-31=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,93 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,93 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,93 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:[43, 12], Operations: ['65-46=19', '31-19=12'] Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,93 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,93 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 #0,0,2 Current State: 93:[19, 74], Operations: ['65-46=19', '31+43=74'] Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,93 unequal: No Solution Exploring Operation: 19*74=1406, Resulting Numbers: [1406] 1406,93 unequal: No Solution Exploring Operation: 19+74=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[31, 65, 46, 43], Operations: [] Exploring Operation: 65-46=19, Resulting Numbers: [31, 43, 19] Generated Node #0,0: 93:[31, 43, 19] Operation: 65-46=19 Moving to Node #0,0 Current State: 93:[31, 43, 19], Operations: ['65-46=19'] Exploring Operation: 31+43=74, Resulting Numbers: [19, 74] Generated Node #0,0,2: 93:[19, 74] Operation: 31+43=74 Moving to Node #0,0,2 Current State: 93:[19, 74], Operations: ['65-46=19', '31+43=74'] Exploring Operation: 19+74=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 21, 53, 9, 34 ]
57
[ "53-21=32", "34-9=25", "32+25=57" ]
Current State: 57:[21, 53, 9, 34], Operations: [] Exploring Operation: 53-21=32, Resulting Numbers: [9, 34, 32] Generated Node #2: [9, 34, 32] from Operation: 53-21=32 Current State: 57:[9, 34, 32], Operations: ['53-21=32'] Exploring Operation: 34-9=25, Resulting Numbers: [32, 25] Generated Node #3: [32, 25] from Operation: 34-9=25 Current State: 57:[32, 25], Operations: ['53-21=32', '34-9=25'] Exploring Operation: 32+25=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[21, 53, 9, 34], Operations: [] Exploring Operation: 53-34=19, Resulting Numbers: [21, 9, 19] Generated Node #0,0: 57:[21, 9, 19] Operation: 53-34=19 Moving to Node #0,0 Current State: 57:[21, 9, 19], Operations: ['53-34=19'] Exploring Operation: 21-9=12, Resulting Numbers: [19, 12] Generated Node #0,0,0: 57:[19, 12] Operation: 21-9=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[19, 12], Operations: ['53-34=19', '21-9=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,57 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
[ 77, 99, 5, 3 ]
20
[ "99-77=22", "5-3=2", "22-2=20" ]
Current State: 20:[77, 99, 5, 3], Operations: [] Exploring Operation: 99-77=22, Resulting Numbers: [5, 3, 22] Generated Node #2: [5, 3, 22] from Operation: 99-77=22 Current State: 20:[5, 3, 22], Operations: ['99-77=22'] Exploring Operation: 5-3=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 5-3=2 Current State: 20:[22, 2], Operations: ['99-77=22', '5-3=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[77, 99, 5, 3], Operations: [] Exploring Operation: 99-77=22, Resulting Numbers: [5, 3, 22] Generated Node #0,0: 20:[5, 3, 22] Operation: 99-77=22 Exploring Operation: 99/3=33, Resulting Numbers: [77, 5, 33] Generated Node #0,1: 20:[77, 5, 33] Operation: 99/3=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[5, 3, 22], Operations: ['99-77=22'] Exploring Operation: 5-3=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 20:[22, 2] Operation: 5-3=2 Exploring Operation: 22-3=19, Resulting Numbers: [5, 19] Generated Node #0,0,1: 20:[5, 19] Operation: 22-3=19 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[5, 19], Operations: ['99-77=22', '22-3=19'] Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,20 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[22, 2], Operations: ['99-77=22', '5-3=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[77, 99, 5, 3], Operations: [] Exploring Operation: 99-77=22, Resulting Numbers: [5, 3, 22] Generated Node #0,0: 20:[5, 3, 22] Operation: 99-77=22 Moving to Node #0,0 Current State: 20:[5, 3, 22], Operations: ['99-77=22'] Exploring Operation: 5-3=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 20:[22, 2] Operation: 5-3=2 Moving to Node #0,0,0 Current State: 20:[22, 2], Operations: ['99-77=22', '5-3=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 13, 83, 41, 11 ]
21
[ "13-11=2", "83-41=42", "42/2=21" ]
Current State: 21:[13, 83, 41, 11], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [83, 41, 2] Generated Node #2: [83, 41, 2] from Operation: 13-11=2 Current State: 21:[83, 41, 2], Operations: ['13-11=2'] Exploring Operation: 83-41=42, Resulting Numbers: [2, 42] Generated Node #3: [2, 42] from Operation: 83-41=42 Current State: 21:[2, 42], Operations: ['13-11=2', '83-41=42'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[13, 83, 41, 11], Operations: [] Exploring Operation: 83-41=42, Resulting Numbers: [13, 11, 42] Generated Node #0,0: 21:[13, 11, 42] Operation: 83-41=42 Moving to Node #0,0 Current State: 21:[13, 11, 42], Operations: ['83-41=42'] Exploring Operation: 42-13=29, Resulting Numbers: [11, 29] Generated Node #0,0,0: 21:[11, 29] Operation: 42-13=29 Moving to Node #0,0,0 Current State: 21:[11, 29], Operations: ['83-41=42', '42-13=29'] Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,21 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 56, 13, 4, 95 ]
48
[ "56-13=43", "95-4=91", "91-43=48" ]
Current State: 48:[56, 13, 4, 95], Operations: [] Exploring Operation: 56-13=43, Resulting Numbers: [4, 95, 43] Generated Node #2: [4, 95, 43] from Operation: 56-13=43 Current State: 48:[4, 95, 43], Operations: ['56-13=43'] Exploring Operation: 95-4=91, Resulting Numbers: [43, 91] Generated Node #3: [43, 91] from Operation: 95-4=91 Current State: 48:[43, 91], Operations: ['56-13=43', '95-4=91'] Exploring Operation: 91-43=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[56, 13, 4, 95], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [13, 4, 39] Generated Node #0,0: 48:[13, 4, 39] Operation: 95-56=39 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[13, 4, 39], Operations: ['95-56=39'] Exploring Operation: 39/13=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 48:[4, 3] Operation: 39/13=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[4, 3], Operations: ['95-56=39', '39/13=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,48 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 No solution found.
0
hs_1
sum_heuristic
[ 3, 45, 38, 66 ]
62
[ "45-3=42", "38+66=104", "104-42=62" ]
Current State: 62:[3, 45, 38, 66], Operations: [] Exploring Operation: 45-3=42, Resulting Numbers: [38, 66, 42] Generated Node #2: [38, 66, 42] from Operation: 45-3=42 Current State: 62:[38, 66, 42], Operations: ['45-3=42'] Exploring Operation: 38+66=104, Resulting Numbers: [42, 104] Generated Node #3: [42, 104] from Operation: 38+66=104 Current State: 62:[42, 104], Operations: ['45-3=42', '38+66=104'] Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[3, 45, 38, 66], Operations: [] Exploring Operation: 38-3=35, Resulting Numbers: [45, 66, 35] Generated Node #0,0: 62:[45, 66, 35] Operation: 38-3=35 Exploring Operation: 66-38=28, Resulting Numbers: [3, 45, 28] Generated Node #0,1: 62:[3, 45, 28] Operation: 66-38=28 Exploring Operation: 45-38=7, Resulting Numbers: [3, 66, 7] Generated Node #0,2: 62:[3, 66, 7] Operation: 45-38=7 Exploring Operation: 45-3=42, Resulting Numbers: [38, 66, 42] Generated Node #0,3: 62:[38, 66, 42] Operation: 45-3=42 Exploring Operation: 66-45=21, Resulting Numbers: [3, 38, 21] Generated Node #0,4: 62:[3, 38, 21] Operation: 66-45=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[3, 66, 7], Operations: ['45-38=7'] Exploring Operation: 3+7=10, Resulting Numbers: [66, 10] Generated Node #0,2,0: 62:[66, 10] Operation: 3+7=10 Exploring Operation: 66-3=63, Resulting Numbers: [7, 63] Generated Node #0,2,1: 62:[7, 63] Operation: 66-3=63 Exploring Operation: 66-7=59, Resulting Numbers: [3, 59] Generated Node #0,2,2: 62:[3, 59] Operation: 66-7=59 Exploring Operation: 7-3=4, Resulting Numbers: [66, 4] Generated Node #0,2,3: 62:[66, 4] Operation: 7-3=4 Exploring Operation: 3+66=69, Resulting Numbers: [7, 69] Generated Node #0,2,4: 62:[7, 69] Operation: 3+66=69 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[3, 59], Operations: ['45-38=7', '66-7=59'] Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,62 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[3, 45, 38, 66], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [3, 66, 7] Generated Node #0,2: 62:[3, 66, 7] Operation: 45-38=7 Moving to Node #0,2 Current State: 62:[3, 66, 7], Operations: ['45-38=7'] Exploring Operation: 66-7=59, Resulting Numbers: [3, 59] Generated Node #0,2,2: 62:[3, 59] Operation: 66-7=59 Moving to Node #0,2,2 Current State: 62:[3, 59], Operations: ['45-38=7', '66-7=59'] Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 29, 22, 90, 5 ]
55
[ "29-22=7", "5*7=35", "90-35=55" ]
Current State: 55:[29, 22, 90, 5], Operations: [] Exploring Operation: 29-22=7, Resulting Numbers: [90, 5, 7] Generated Node #2: [90, 5, 7] from Operation: 29-22=7 Current State: 55:[90, 5, 7], Operations: ['29-22=7'] Exploring Operation: 5*7=35, Resulting Numbers: [90, 35] Generated Node #3: [90, 35] from Operation: 5*7=35 Current State: 55:[90, 35], Operations: ['29-22=7', '5*7=35'] Exploring Operation: 90-35=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[29, 22, 90, 5], Operations: [] Exploring Operation: 90-22=68, Resulting Numbers: [29, 5, 68] Generated Node #0,0: 55:[29, 5, 68] Operation: 90-22=68 Exploring Operation: 90-29=61, Resulting Numbers: [22, 5, 61] Generated Node #0,1: 55:[22, 5, 61] Operation: 90-29=61 Moving to Node #0,1 Current State: 55:[22, 5, 61], Operations: ['90-29=61'] Exploring Operation: 61-5=56, Resulting Numbers: [22, 56] Generated Node #0,1,0: 55:[22, 56] Operation: 61-5=56 Exploring Operation: 22-5=17, Resulting Numbers: [61, 17] Generated Node #0,1,1: 55:[61, 17] Operation: 22-5=17 Moving to Node #0,0 Current State: 55:[29, 5, 68], Operations: ['90-22=68'] Exploring Operation: 29-5=24, Resulting Numbers: [68, 24] Generated Node #0,0,0: 55:[68, 24] Operation: 29-5=24 Exploring Operation: 68-29=39, Resulting Numbers: [5, 39] Generated Node #0,0,1: 55:[5, 39] Operation: 68-29=39 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[5, 39], Operations: ['90-22=68', '68-29=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,55 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:[68, 24], Operations: ['90-22=68', '29-5=24'] Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,55 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: 55:[22, 56], Operations: ['90-29=61', '61-5=56'] Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,55 unequal: No Solution Exploring Operation: 22+56=78, Resulting Numbers: [78] 78,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[61, 17], Operations: ['90-29=61', '22-5=17'] Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 61+17=78, Resulting Numbers: [78] 78,55 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 54, 74, 47, 95 ]
80
[ "54+74=128", "95-47=48", "128-48=80" ]
Current State: 80:[54, 74, 47, 95], Operations: [] Exploring Operation: 54+74=128, Resulting Numbers: [47, 95, 128] Generated Node #2: [47, 95, 128] from Operation: 54+74=128 Current State: 80:[47, 95, 128], Operations: ['54+74=128'] Exploring Operation: 95-47=48, Resulting Numbers: [128, 48] Generated Node #3: [128, 48] from Operation: 95-47=48 Current State: 80:[128, 48], Operations: ['54+74=128', '95-47=48'] Exploring Operation: 128-48=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[54, 74, 47, 95], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [74, 95, 7] Generated Node #0,0: 80:[74, 95, 7] Operation: 54-47=7 Exploring Operation: 95-54=41, Resulting Numbers: [74, 47, 41] Generated Node #0,1: 80:[74, 47, 41] Operation: 95-54=41 Exploring Operation: 74-54=20, Resulting Numbers: [47, 95, 20] Generated Node #0,2: 80:[47, 95, 20] Operation: 74-54=20 Exploring Operation: 95-74=21, Resulting Numbers: [54, 47, 21] Generated Node #0,3: 80:[54, 47, 21] Operation: 95-74=21 Moving to Node #0,1 Current State: 80:[74, 47, 41], Operations: ['95-54=41'] Exploring Operation: 47+41=88, Resulting Numbers: [74, 88] Generated Node #0,1,0: 80:[74, 88] Operation: 47+41=88 Exploring Operation: 74-41=33, Resulting Numbers: [47, 33] Generated Node #0,1,1: 80:[47, 33] Operation: 74-41=33 Exploring Operation: 47-41=6, Resulting Numbers: [74, 6] Generated Node #0,1,2: 80:[74, 6] Operation: 47-41=6 Exploring Operation: 74-47=27, Resulting Numbers: [41, 27] Generated Node #0,1,3: 80:[41, 27] Operation: 74-47=27 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[74, 6], Operations: ['95-54=41', '47-41=6'] Exploring Operation: 74*6=444, Resulting Numbers: [444] 444,80 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,80 unequal: No Solution Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[54, 74, 47, 95], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [74, 47, 41] Generated Node #0,1: 80:[74, 47, 41] Operation: 95-54=41 Moving to Node #0,1 Current State: 80:[74, 47, 41], Operations: ['95-54=41'] Exploring Operation: 47-41=6, Resulting Numbers: [74, 6] Generated Node #0,1,2: 80:[74, 6] Operation: 47-41=6 Moving to Node #0,1,2 Current State: 80:[74, 6], Operations: ['95-54=41', '47-41=6'] Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 9, 23, 70, 96 ]
67
[ "9+23=32", "96/32=3", "70-3=67" ]
Current State: 67:[9, 23, 70, 96], Operations: [] Exploring Operation: 9+23=32, Resulting Numbers: [70, 96, 32] Generated Node #2: [70, 96, 32] from Operation: 9+23=32 Current State: 67:[70, 96, 32], Operations: ['9+23=32'] Exploring Operation: 96/32=3, Resulting Numbers: [70, 3] Generated Node #3: [70, 3] from Operation: 96/32=3 Current State: 67:[70, 3], Operations: ['9+23=32', '96/32=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[9, 23, 70, 96], Operations: [] Exploring Operation: 96-9=87, Resulting Numbers: [23, 70, 87] Generated Node #0,0: 67:[23, 70, 87] Operation: 96-9=87 Exploring Operation: 9+23=32, Resulting Numbers: [70, 96, 32] Generated Node #0,1: 67:[70, 96, 32] Operation: 9+23=32 Moving to Node #0,0 Current State: 67:[23, 70, 87], Operations: ['96-9=87'] Exploring Operation: 87-23=64, Resulting Numbers: [70, 64] Generated Node #0,0,0: 67:[70, 64] Operation: 87-23=64 Exploring Operation: 70-23=47, Resulting Numbers: [87, 47] Generated Node #0,0,1: 67:[87, 47] Operation: 70-23=47 Moving to Node #0,1 Current State: 67:[70, 96, 32], Operations: ['9+23=32'] Exploring Operation: 70-32=38, Resulting Numbers: [96, 38] Generated Node #0,1,0: 67:[96, 38] Operation: 70-32=38 Exploring Operation: 96-32=64, Resulting Numbers: [70, 64] Generated Node #0,1,1: 67:[70, 64] Operation: 96-32=64 Moving to Node #0,0,0 Current State: 67:[70, 64], Operations: ['96-9=87', '87-23=64'] Exploring Operation: 70-64=6, Resulting Numbers: [6] 6,67 unequal: No Solution Exploring Operation: 70+64=134, Resulting Numbers: [134] 134,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[70, 64], Operations: ['9+23=32', '96-32=64'] Exploring Operation: 70+64=134, Resulting Numbers: [134] 134,67 unequal: No Solution Exploring Operation: 70-64=6, Resulting Numbers: [6] 6,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[87, 47], Operations: ['96-9=87', '70-23=47'] Exploring Operation: 87-47=40, Resulting Numbers: [40] 40,67 unequal: No Solution Exploring Operation: 87+47=134, Resulting Numbers: [134] 134,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[96, 38], Operations: ['9+23=32', '70-32=38'] Exploring Operation: 96+38=134, Resulting Numbers: [134] 134,67 unequal: No Solution Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,67 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 3, 21, 75, 1 ]
98
[ "3+21=24", "75-1=74", "24+74=98" ]
Current State: 98:[3, 21, 75, 1], Operations: [] Exploring Operation: 3+21=24, Resulting Numbers: [75, 1, 24] Generated Node #2: [75, 1, 24] from Operation: 3+21=24 Current State: 98:[75, 1, 24], Operations: ['3+21=24'] Exploring Operation: 75-1=74, Resulting Numbers: [24, 74] Generated Node #3: [24, 74] from Operation: 75-1=74 Current State: 98:[24, 74], Operations: ['3+21=24', '75-1=74'] Exploring Operation: 24+74=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[3, 21, 75, 1], Operations: [] Exploring Operation: 21+75=96, Resulting Numbers: [3, 1, 96] Generated Node #0,0: 98:[3, 1, 96] Operation: 21+75=96 Exploring Operation: 21/3=7, Resulting Numbers: [75, 1, 7] Generated Node #0,1: 98:[75, 1, 7] Operation: 21/3=7 Exploring Operation: 75/3=25, Resulting Numbers: [21, 1, 25] Generated Node #0,2: 98:[21, 1, 25] Operation: 75/3=25 Exploring Operation: 75-21=54, Resulting Numbers: [3, 1, 54] Generated Node #0,3: 98:[3, 1, 54] Operation: 75-21=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[3, 1, 96], Operations: ['21+75=96'] Exploring Operation: 1+96=97, Resulting Numbers: [3, 97] Generated Node #0,0,0: 98:[3, 97] Operation: 1+96=97 Exploring Operation: 3+96=99, Resulting Numbers: [1, 99] Generated Node #0,0,1: 98:[1, 99] Operation: 3+96=99 Exploring Operation: 3*1=3, Resulting Numbers: [96, 3] Generated Node #0,0,2: 98:[96, 3] Operation: 3*1=3 Exploring Operation: 3-1=2, Resulting Numbers: [96, 2] Generated Node #0,0,3: 98:[96, 2] Operation: 3-1=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[3, 97], Operations: ['21+75=96', '1+96=97'] Exploring Operation: 3+97=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,98 unequal: No Solution Exploring Operation: 3*97=291, Resulting Numbers: [291] 291,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[1, 99], Operations: ['21+75=96', '3+96=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[3, 21, 75, 1], Operations: [] Exploring Operation: 21+75=96, Resulting Numbers: [3, 1, 96] Generated Node #0,0: 98:[3, 1, 96] Operation: 21+75=96 Moving to Node #0,0 Current State: 98:[3, 1, 96], Operations: ['21+75=96'] Exploring Operation: 3+96=99, Resulting Numbers: [1, 99] Generated Node #0,0,1: 98:[1, 99] Operation: 3+96=99 Moving to Node #0,0,1 Current State: 98:[1, 99], Operations: ['21+75=96', '3+96=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 52, 91, 66, 74 ]
31
[ "91-52=39", "74-66=8", "39-8=31" ]
Current State: 31:[52, 91, 66, 74], Operations: [] Exploring Operation: 91-52=39, Resulting Numbers: [66, 74, 39] Generated Node #2: [66, 74, 39] from Operation: 91-52=39 Current State: 31:[66, 74, 39], Operations: ['91-52=39'] Exploring Operation: 74-66=8, Resulting Numbers: [39, 8] Generated Node #3: [39, 8] from Operation: 74-66=8 Current State: 31:[39, 8], Operations: ['91-52=39', '74-66=8'] Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[52, 91, 66, 74], Operations: [] Exploring Operation: 91-66=25, Resulting Numbers: [52, 74, 25] Generated Node #0,0: 31:[52, 74, 25] Operation: 91-66=25 Exploring Operation: 91-74=17, Resulting Numbers: [52, 66, 17] Generated Node #0,1: 31:[52, 66, 17] Operation: 91-74=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[52, 74, 25], Operations: ['91-66=25'] Exploring Operation: 74-52=22, Resulting Numbers: [25, 22] Generated Node #0,0,0: 31:[25, 22] Operation: 74-52=22 Exploring Operation: 74-25=49, Resulting Numbers: [52, 49] Generated Node #0,0,1: 31:[52, 49] Operation: 74-25=49 Moving to Node #0,0,0 Current State: 31:[25, 22], Operations: ['91-66=25', '74-52=22'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[52, 49], Operations: ['91-66=25', '74-25=49'] Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 52+49=101, Resulting Numbers: [101] 101,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[52, 66, 17], Operations: ['91-74=17'] Exploring Operation: 52-17=35, Resulting Numbers: [66, 35] Generated Node #0,1,0: 31:[66, 35] Operation: 52-17=35 Exploring Operation: 66-52=14, Resulting Numbers: [17, 14] Generated Node #0,1,1: 31:[17, 14] Operation: 66-52=14 Moving to Node #0,1,1 Current State: 31:[17, 14], Operations: ['91-74=17', '66-52=14'] Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[52, 91, 66, 74], Operations: [] Exploring Operation: 91-74=17, Resulting Numbers: [52, 66, 17] Generated Node #0,1: 31:[52, 66, 17] Operation: 91-74=17 Moving to Node #0,1 Current State: 31:[52, 66, 17], Operations: ['91-74=17'] Exploring Operation: 66-52=14, Resulting Numbers: [17, 14] Generated Node #0,1,1: 31:[17, 14] Operation: 66-52=14 Moving to Node #0,1,1 Current State: 31:[17, 14], Operations: ['91-74=17', '66-52=14'] Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 47, 33, 9, 90 ]
19
[ "47+33=80", "9+90=99", "99-80=19" ]
Current State: 19:[47, 33, 9, 90], Operations: [] Exploring Operation: 47+33=80, Resulting Numbers: [9, 90, 80] Generated Node #2: [9, 90, 80] from Operation: 47+33=80 Current State: 19:[9, 90, 80], Operations: ['47+33=80'] Exploring Operation: 9+90=99, Resulting Numbers: [80, 99] Generated Node #3: [80, 99] from Operation: 9+90=99 Current State: 19:[80, 99], Operations: ['47+33=80', '9+90=99'] Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[47, 33, 9, 90], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [47, 33, 10] Generated Node #0,0: 19:[47, 33, 10] Operation: 90/9=10 Exploring Operation: 90-33=57, Resulting Numbers: [47, 9, 57] Generated Node #0,1: 19:[47, 9, 57] Operation: 90-33=57 Exploring Operation: 90-47=43, Resulting Numbers: [33, 9, 43] Generated Node #0,2: 19:[33, 9, 43] Operation: 90-47=43 Exploring Operation: 47-33=14, Resulting Numbers: [9, 90, 14] Generated Node #0,3: 19:[9, 90, 14] Operation: 47-33=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[33, 9, 43], Operations: ['90-47=43'] Exploring Operation: 33-9=24, Resulting Numbers: [43, 24] Generated Node #0,2,0: 19:[43, 24] Operation: 33-9=24 Exploring Operation: 33+9=42, Resulting Numbers: [43, 42] Generated Node #0,2,1: 19:[43, 42] Operation: 33+9=42 Exploring Operation: 43-33=10, Resulting Numbers: [9, 10] Generated Node #0,2,2: 19:[9, 10] Operation: 43-33=10 Exploring Operation: 43-9=34, Resulting Numbers: [33, 34] Generated Node #0,2,3: 19:[33, 34] Operation: 43-9=34 Moving to Node #0,2,2 Current State: 19:[9, 10], Operations: ['90-47=43', '43-33=10'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,19 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[47, 33, 9, 90], Operations: [] Exploring Operation: 90-47=43, Resulting Numbers: [33, 9, 43] Generated Node #0,2: 19:[33, 9, 43] Operation: 90-47=43 Moving to Node #0,2 Current State: 19:[33, 9, 43], Operations: ['90-47=43'] Exploring Operation: 43-33=10, Resulting Numbers: [9, 10] Generated Node #0,2,2: 19:[9, 10] Operation: 43-33=10 Moving to Node #0,2,2 Current State: 19:[9, 10], Operations: ['90-47=43', '43-33=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 67, 11, 87, 86 ]
57
[ "67-11=56", "87-86=1", "56+1=57" ]
Current State: 57:[67, 11, 87, 86], Operations: [] Exploring Operation: 67-11=56, Resulting Numbers: [87, 86, 56] Generated Node #2: [87, 86, 56] from Operation: 67-11=56 Current State: 57:[87, 86, 56], Operations: ['67-11=56'] Exploring Operation: 87-86=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 87-86=1 Current State: 57:[56, 1], Operations: ['67-11=56', '87-86=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[67, 11, 87, 86], Operations: [] Exploring Operation: 87-86=1, Resulting Numbers: [67, 11, 1] Generated Node #0,0: 57:[67, 11, 1] Operation: 87-86=1 Exploring Operation: 87-67=20, Resulting Numbers: [11, 86, 20] Generated Node #0,1: 57:[11, 86, 20] Operation: 87-67=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[67, 11, 1], Operations: ['87-86=1'] Exploring Operation: 67-11=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 57:[1, 56] Operation: 67-11=56 Exploring Operation: 67-1=66, Resulting Numbers: [11, 66] Generated Node #0,0,1: 57:[11, 66] Operation: 67-1=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[1, 56], Operations: ['87-86=1', '67-11=56'] Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[67, 11, 87, 86], Operations: [] Exploring Operation: 87-86=1, Resulting Numbers: [67, 11, 1] Generated Node #0,0: 57:[67, 11, 1] Operation: 87-86=1 Moving to Node #0,0 Current State: 57:[67, 11, 1], Operations: ['87-86=1'] Exploring Operation: 67-11=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 57:[1, 56] Operation: 67-11=56 Moving to Node #0,0,0 Current State: 57:[1, 56], Operations: ['87-86=1', '67-11=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 8, 99, 54, 80 ]
27
[ "8+99=107", "54+80=134", "134-107=27" ]
Current State: 27:[8, 99, 54, 80], Operations: [] Exploring Operation: 8+99=107, Resulting Numbers: [54, 80, 107] Generated Node #2: [54, 80, 107] from Operation: 8+99=107 Current State: 27:[54, 80, 107], Operations: ['8+99=107'] Exploring Operation: 54+80=134, Resulting Numbers: [107, 134] Generated Node #3: [107, 134] from Operation: 54+80=134 Current State: 27:[107, 134], Operations: ['8+99=107', '54+80=134'] Exploring Operation: 134-107=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[8, 99, 54, 80], Operations: [] Exploring Operation: 99-54=45, Resulting Numbers: [8, 80, 45] Generated Node #0,0: 27:[8, 80, 45] Operation: 99-54=45 Exploring Operation: 80-54=26, Resulting Numbers: [8, 99, 26] Generated Node #0,1: 27:[8, 99, 26] Operation: 80-54=26 Exploring Operation: 99-80=19, Resulting Numbers: [8, 54, 19] Generated Node #0,2: 27:[8, 54, 19] Operation: 99-80=19 Moving to Node #0,2 Current State: 27:[8, 54, 19], Operations: ['99-80=19'] Exploring Operation: 54-8=46, Resulting Numbers: [19, 46] Generated Node #0,2,0: 27:[19, 46] Operation: 54-8=46 Exploring Operation: 8+19=27, Resulting Numbers: [54, 27] Generated Node #0,2,1: 27:[54, 27] Operation: 8+19=27 Exploring Operation: 54-19=35, Resulting Numbers: [8, 35] Generated Node #0,2,2: 27:[8, 35] Operation: 54-19=35 Moving to Node #0,0 Current State: 27:[8, 80, 45], Operations: ['99-54=45'] Exploring Operation: 80-45=35, Resulting Numbers: [8, 35] Generated Node #0,0,0: 27:[8, 35] Operation: 80-45=35 Exploring Operation: 80/8=10, Resulting Numbers: [45, 10] Generated Node #0,0,1: 27:[45, 10] Operation: 80/8=10 Exploring Operation: 80-8=72, Resulting Numbers: [45, 72] Generated Node #0,0,2: 27:[45, 72] Operation: 80-8=72 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[8, 35], Operations: ['99-54=45', '80-45=35'] Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,27 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[8, 99, 54, 80], Operations: [] Exploring Operation: 99-54=45, Resulting Numbers: [8, 80, 45] Generated Node #0,0: 27:[8, 80, 45] Operation: 99-54=45 Moving to Node #0,0 Current State: 27:[8, 80, 45], Operations: ['99-54=45'] Exploring Operation: 80-45=35, Resulting Numbers: [8, 35] Generated Node #0,0,0: 27:[8, 35] Operation: 80-45=35 Moving to Node #0,0,0 Current State: 27:[8, 35], Operations: ['99-54=45', '80-45=35'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 26, 79, 81, 81 ]
94
[ "81-79=2", "26/2=13", "81+13=94" ]
Current State: 94:[26, 79, 81, 81], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [26, 2] Generated Node #2: [26, 2] from Operation: 81-79=2 Current State: 94:[26, 2], Operations: ['81-79=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,94 equal: Goal Reached Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[26, 79, 81, 81], Operations: [] Exploring Operation: 81-26=55, Resulting Numbers: [79, 81, 55] Generated Node #0,0: 94:[79, 81, 55] Operation: 81-26=55 Exploring Operation: 81-26=55, Resulting Numbers: [79, 81, 55] Generated Node #0,1: 94:[79, 81, 55] Operation: 81-26=55 Exploring Operation: 79-26=53, Resulting Numbers: [81, 81, 53] Generated Node #0,2: 94:[81, 81, 53] Operation: 79-26=53 Exploring Operation: 81-79=2, Resulting Numbers: [26, 81, 2] Generated Node #0,3: 94:[26, 81, 2] Operation: 81-79=2 Exploring Operation: 81-79=2, Resulting Numbers: [26, 81, 2] Generated Node #0,4: 94:[26, 81, 2] Operation: 81-79=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[81, 81, 53], Operations: ['79-26=53'] Exploring Operation: 81/81=1, Resulting Numbers: [53, 1] Generated Node #0,2,0: 94:[53, 1] Operation: 81/81=1 Exploring Operation: 81+53=134, Resulting Numbers: [81, 134] Generated Node #0,2,1: 94:[81, 134] Operation: 81+53=134 Exploring Operation: 81-53=28, Resulting Numbers: [81, 28] Generated Node #0,2,2: 94:[81, 28] Operation: 81-53=28 Exploring Operation: 81-81=0, Resulting Numbers: [53, 0] Generated Node #0,2,3: 94:[53, 0] Operation: 81-81=0 Exploring Operation: 81-53=28, Resulting Numbers: [81, 28] Generated Node #0,2,4: 94:[81, 28] Operation: 81-53=28 Moving to Node #0,2,0 Current State: 94:[53, 1], Operations: ['79-26=53', '81/81=1'] Exploring Operation: 53-1=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[53, 0], Operations: ['79-26=53', '81-81=0'] Exploring Operation: 53*0=0, Resulting Numbers: [0] 0,94 unequal: No Solution Exploring Operation: 53+0=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 53-0=53, Resulting Numbers: [53] 53,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[81, 28], Operations: ['79-26=53', '81-53=28'] Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,94 unequal: No Solution Moving to Node #0,2,4 Current State: 94:[81, 28], Operations: ['79-26=53', '81-53=28'] Exploring Operation: 81-28=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 81+28=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 81*28=2268, Resulting Numbers: [2268] 2268,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[81, 134], Operations: ['79-26=53', '81+53=134'] Exploring Operation: 81*134=10854, Resulting Numbers: [10854] 10854,94 unequal: No Solution Exploring Operation: 134-81=53, Resulting Numbers: [53] 53,94 unequal: No Solution Exploring Operation: 81+134=215, Resulting Numbers: [215] 215,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[26, 81, 2], Operations: ['81-79=2'] Exploring Operation: 26+81=107, Resulting Numbers: [2, 107] Generated Node #0,3,0: 94:[2, 107] Operation: 26+81=107 Exploring Operation: 26/2=13, Resulting Numbers: [81, 13] Generated Node #0,3,1: 94:[81, 13] Operation: 26/2=13 Exploring Operation: 81-26=55, Resulting Numbers: [2, 55] Generated Node #0,3,2: 94:[2, 55] Operation: 81-26=55 Exploring Operation: 26*2=52, Resulting Numbers: [81, 52] Generated Node #0,3,3: 94:[81, 52] Operation: 26*2=52 Exploring Operation: 26+2=28, Resulting Numbers: [81, 28] Generated Node #0,3,4: 94:[81, 28] Operation: 26+2=28 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 94:[2, 55], Operations: ['81-79=2', '81-26=55'] Exploring Operation: 2+55=57, Resulting Numbers: [57] 57,94 unequal: No Solution Exploring Operation: 2*55=110, Resulting Numbers: [110] 110,94 unequal: No Solution Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 94:[2, 107], Operations: ['81-79=2', '26+81=107'] Exploring Operation: 2+107=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 107-2=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 2*107=214, Resulting Numbers: [214] 214,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 94:[81, 52], Operations: ['81-79=2', '26*2=52'] Exploring Operation: 81*52=4212, Resulting Numbers: [4212] 4212,94 unequal: No Solution Exploring Operation: 81+52=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 81-52=29, Resulting Numbers: [29] 29,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[81, 13], Operations: ['81-79=2', '26/2=13'] Exploring Operation: 81*13=1053, Resulting Numbers: [1053] 1053,94 unequal: No Solution Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[26, 79, 81, 81], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [26, 81, 2] Generated Node #0,3: 94:[26, 81, 2] Operation: 81-79=2 Moving to Node #0,3 Current State: 94:[26, 81, 2], Operations: ['81-79=2'] Exploring Operation: 26/2=13, Resulting Numbers: [81, 13] Generated Node #0,3,1: 94:[81, 13] Operation: 26/2=13 Moving to Node #0,3,1 Current State: 94:[81, 13], Operations: ['81-79=2', '26/2=13'] Exploring Operation: 81+13=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_5
sum_heuristic
[ 1, 22, 3, 3 ]
72
[ "1+22=23", "3*23=69", "3+69=72" ]
Current State: 72:[1, 22, 3, 3], Operations: [] Exploring Operation: 1+22=23, Resulting Numbers: [3, 3, 23] Generated Node #2: [3, 3, 23] from Operation: 1+22=23 Current State: 72:[3, 3, 23], Operations: ['1+22=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,72 equal: Goal Reached Exploring Operation: 3+69=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[1, 22, 3, 3], Operations: [] Exploring Operation: 1+3=4, Resulting Numbers: [22, 3, 4] Generated Node #0,0: 72:[22, 3, 4] Operation: 1+3=4 Exploring Operation: 1*22=22, Resulting Numbers: [3, 3, 22] Generated Node #0,1: 72:[3, 3, 22] Operation: 1*22=22 Exploring Operation: 22/1=22, Resulting Numbers: [3, 3, 22] Generated Node #0,2: 72:[3, 3, 22] Operation: 22/1=22 Exploring Operation: 1+22=23, Resulting Numbers: [3, 3, 23] Generated Node #0,3: 72:[3, 3, 23] Operation: 1+22=23 Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[3, 3, 23], Operations: ['1+22=23'] Exploring Operation: 3/3=1, Resulting Numbers: [23, 1] Generated Node #0,3,0: 72:[23, 1] Operation: 3/3=1 Exploring Operation: 3+23=26, Resulting Numbers: [3, 26] Generated Node #0,3,1: 72:[3, 26] Operation: 3+23=26 Exploring Operation: 3+3=6, Resulting Numbers: [23, 6] Generated Node #0,3,2: 72:[23, 6] Operation: 3+3=6 Exploring Operation: 3*3=9, Resulting Numbers: [23, 9] Generated Node #0,3,3: 72:[23, 9] Operation: 3*3=9 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 72:[23, 6], Operations: ['1+22=23', '3+3=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,72 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 72:[23, 9], Operations: ['1+22=23', '3*3=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 23*9=207, Resulting Numbers: [207] 207,72 unequal: No Solution Exploring Operation: 23+9=32, Resulting Numbers: [32] 32,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[23, 1], Operations: ['1+22=23', '3/3=1'] Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,72 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[3, 26], Operations: ['1+22=23', '3+23=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[22, 3, 4], Operations: ['1+3=4'] Exploring Operation: 22-4=18, Resulting Numbers: [3, 18] Generated Node #0,0,0: 72:[3, 18] Operation: 22-4=18 Exploring Operation: 22-3=19, Resulting Numbers: [4, 19] Generated Node #0,0,1: 72:[4, 19] Operation: 22-3=19 Exploring Operation: 22+3=25, Resulting Numbers: [4, 25] Generated Node #0,0,2: 72:[4, 25] Operation: 22+3=25 Exploring Operation: 22+4=26, Resulting Numbers: [3, 26] Generated Node #0,0,3: 72:[3, 26] Operation: 22+4=26 Moving to Node #0,0,0 Current State: 72:[3, 18], Operations: ['1+3=4', '22-4=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,72 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[4, 25], Operations: ['1+3=4', '22+3=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,72 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,72 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[4, 19], Operations: ['1+3=4', '22-3=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,72 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[3, 26], Operations: ['1+3=4', '22+4=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,72 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[3, 3, 22], Operations: ['1*22=22'] Exploring Operation: 22-3=19, Resulting Numbers: [3, 19] Generated Node #0,1,0: 72:[3, 19] Operation: 22-3=19 Exploring Operation: 3+22=25, Resulting Numbers: [3, 25] Generated Node #0,1,1: 72:[3, 25] Operation: 3+22=25 Exploring Operation: 3+22=25, Resulting Numbers: [3, 25] Generated Node #0,1,2: 72:[3, 25] Operation: 3+22=25 Exploring Operation: 22-3=19, Resulting Numbers: [3, 19] Generated Node #0,1,3: 72:[3, 19] Operation: 22-3=19 Moving to Node #0,1,0 Current State: 72:[3, 19], Operations: ['1*22=22', '22-3=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[3, 25], Operations: ['1*22=22', '3+22=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,72 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[3, 25], Operations: ['1*22=22', '3+22=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[3, 19], Operations: ['1*22=22', '22-3=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[3, 3, 22], Operations: ['22/1=22'] Exploring Operation: 22-3=19, Resulting Numbers: [3, 19] Generated Node #0,2,0: 72:[3, 19] Operation: 22-3=19 Exploring Operation: 3+22=25, Resulting Numbers: [3, 25] Generated Node #0,2,1: 72:[3, 25] Operation: 3+22=25 Exploring Operation: 3+22=25, Resulting Numbers: [3, 25] Generated Node #0,2,2: 72:[3, 25] Operation: 3+22=25 Exploring Operation: 22-3=19, Resulting Numbers: [3, 19] Generated Node #0,2,3: 72:[3, 19] Operation: 22-3=19 Moving to Node #0,2,0 Current State: 72:[3, 19], Operations: ['22/1=22', '22-3=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[3, 25], Operations: ['22/1=22', '3+22=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,72 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[3, 25], Operations: ['22/1=22', '3+22=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[3, 19], Operations: ['22/1=22', '22-3=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 36, 92, 74, 24 ]
30
[ "36+92=128", "74+24=98", "128-98=30" ]
Current State: 30:[36, 92, 74, 24], Operations: [] Exploring Operation: 36+92=128, Resulting Numbers: [74, 24, 128] Generated Node #2: [74, 24, 128] from Operation: 36+92=128 Current State: 30:[74, 24, 128], Operations: ['36+92=128'] Exploring Operation: 74+24=98, Resulting Numbers: [128, 98] Generated Node #3: [128, 98] from Operation: 74+24=98 Current State: 30:[128, 98], Operations: ['36+92=128', '74+24=98'] Exploring Operation: 128-98=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[36, 92, 74, 24], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [36, 24, 18] Generated Node #0,0: 30:[36, 24, 18] Operation: 92-74=18 Exploring Operation: 74-36=38, Resulting Numbers: [92, 24, 38] Generated Node #0,1: 30:[92, 24, 38] Operation: 74-36=38 Exploring Operation: 92-36=56, Resulting Numbers: [74, 24, 56] Generated Node #0,2: 30:[74, 24, 56] Operation: 92-36=56 Exploring Operation: 74-24=50, Resulting Numbers: [36, 92, 50] Generated Node #0,3: 30:[36, 92, 50] Operation: 74-24=50 Exploring Operation: 92-24=68, Resulting Numbers: [36, 74, 68] Generated Node #0,4: 30:[36, 74, 68] Operation: 92-24=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[36, 24, 18], Operations: ['92-74=18'] Exploring Operation: 24+18=42, Resulting Numbers: [36, 42] Generated Node #0,0,0: 30:[36, 42] Operation: 24+18=42 Exploring Operation: 24-18=6, Resulting Numbers: [36, 6] Generated Node #0,0,1: 30:[36, 6] Operation: 24-18=6 Exploring Operation: 36-18=18, Resulting Numbers: [24, 18] Generated Node #0,0,2: 30:[24, 18] Operation: 36-18=18 Exploring Operation: 36-24=12, Resulting Numbers: [18, 12] Generated Node #0,0,3: 30:[18, 12] Operation: 36-24=12 Exploring Operation: 36/18=2, Resulting Numbers: [24, 2] Generated Node #0,0,4: 30:[24, 2] Operation: 36/18=2 Moving to Node #0,0,3 Current State: 30:[18, 12], Operations: ['92-74=18', '36-24=12'] Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,30 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[36, 92, 74, 24], Operations: [] Exploring Operation: 92-74=18, Resulting Numbers: [36, 24, 18] Generated Node #0,0: 30:[36, 24, 18] Operation: 92-74=18 Moving to Node #0,0 Current State: 30:[36, 24, 18], Operations: ['92-74=18'] Exploring Operation: 36-24=12, Resulting Numbers: [18, 12] Generated Node #0,0,3: 30:[18, 12] Operation: 36-24=12 Moving to Node #0,0,3 Current State: 30:[18, 12], Operations: ['92-74=18', '36-24=12'] Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 66, 60, 15, 22 ]
22
[ "66+22=88", "60/15=4", "88/4=22" ]
Current State: 22:[66, 60, 15, 22], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [60, 15, 88] Generated Node #2: [60, 15, 88] from Operation: 66+22=88 Current State: 22:[60, 15, 88], Operations: ['66+22=88'] Exploring Operation: 60/15=4, Resulting Numbers: [88, 4] Generated Node #3: [88, 4] from Operation: 60/15=4 Current State: 22:[88, 4], Operations: ['66+22=88', '60/15=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[66, 60, 15, 22], Operations: [] Exploring Operation: 60-22=38, Resulting Numbers: [66, 15, 38] Generated Node #0,0: 22:[66, 15, 38] Operation: 60-22=38 Exploring Operation: 66-60=6, Resulting Numbers: [15, 22, 6] Generated Node #0,1: 22:[15, 22, 6] Operation: 66-60=6 Exploring Operation: 60/15=4, Resulting Numbers: [66, 22, 4] Generated Node #0,2: 22:[66, 22, 4] Operation: 60/15=4 Exploring Operation: 66-22=44, Resulting Numbers: [60, 15, 44] Generated Node #0,3: 22:[60, 15, 44] Operation: 66-22=44 Exploring Operation: 66/22=3, Resulting Numbers: [60, 15, 3] Generated Node #0,4: 22:[60, 15, 3] Operation: 66/22=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[15, 22, 6], Operations: ['66-60=6'] Exploring Operation: 22-6=16, Resulting Numbers: [15, 16] Generated Node #0,1,0: 22:[15, 16] Operation: 22-6=16 Exploring Operation: 15+6=21, Resulting Numbers: [22, 21] Generated Node #0,1,1: 22:[22, 21] Operation: 15+6=21 Exploring Operation: 15-6=9, Resulting Numbers: [22, 9] Generated Node #0,1,2: 22:[22, 9] Operation: 15-6=9 Exploring Operation: 22+6=28, Resulting Numbers: [15, 28] Generated Node #0,1,3: 22:[15, 28] Operation: 22+6=28 Exploring Operation: 22-15=7, Resulting Numbers: [6, 7] Generated Node #0,1,4: 22:[6, 7] Operation: 22-15=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[22, 21], Operations: ['66-60=6', '15+6=21'] Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 22:[22, 9], Operations: ['66-60=6', '15-6=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,22 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 22:[6, 7], Operations: ['66-60=6', '22-15=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[15, 16], Operations: ['66-60=6', '22-6=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,22 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 22:[15, 28], Operations: ['66-60=6', '22+6=28'] Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 22:[60, 15, 3], Operations: ['66/22=3'] Exploring Operation: 60-15=45, Resulting Numbers: [3, 45] Generated Node #0,4,0: 22:[3, 45] Operation: 60-15=45 Exploring Operation: 60-3=57, Resulting Numbers: [15, 57] Generated Node #0,4,1: 22:[15, 57] Operation: 60-3=57 Exploring Operation: 60/3=20, Resulting Numbers: [15, 20] Generated Node #0,4,2: 22:[15, 20] Operation: 60/3=20 Exploring Operation: 15-3=12, Resulting Numbers: [60, 12] Generated Node #0,4,3: 22:[60, 12] Operation: 15-3=12 Exploring Operation: 60/15=4, Resulting Numbers: [3, 4] Generated Node #0,4,4: 22:[3, 4] Operation: 60/15=4 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 22:[3, 4], Operations: ['66/22=3', '60/15=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 22:[15, 20], Operations: ['66/22=3', '60/3=20'] Exploring Operation: 20-15=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 15*20=300, Resulting Numbers: [300] 300,22 unequal: No Solution Exploring Operation: 15+20=35, Resulting Numbers: [35] 35,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 22:[3, 45], Operations: ['66/22=3', '60-15=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 3*45=135, Resulting Numbers: [135] 135,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 22:[15, 57], Operations: ['66/22=3', '60-3=57'] Exploring Operation: 15+57=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 15*57=855, Resulting Numbers: [855] 855,22 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 22:[60, 12], Operations: ['66/22=3', '15-3=12'] Exploring Operation: 60+12=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 60*12=720, Resulting Numbers: [720] 720,22 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[66, 22, 4], Operations: ['60/15=4'] Exploring Operation: 22+4=26, Resulting Numbers: [66, 26] Generated Node #0,2,0: 22:[66, 26] Operation: 22+4=26 Exploring Operation: 66/22=3, Resulting Numbers: [4, 3] Generated Node #0,2,1: 22:[4, 3] Operation: 66/22=3 Exploring Operation: 66-4=62, Resulting Numbers: [22, 62] Generated Node #0,2,2: 22:[22, 62] Operation: 66-4=62 Exploring Operation: 66-22=44, Resulting Numbers: [4, 44] Generated Node #0,2,3: 22:[4, 44] Operation: 66-22=44 Exploring Operation: 66+4=70, Resulting Numbers: [22, 70] Generated Node #0,2,4: 22:[22, 70] Operation: 66+4=70 Moving to Node #0,2,1 Current State: 22:[4, 3], Operations: ['60/15=4', '66/22=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[4, 44], Operations: ['60/15=4', '66-22=44'] Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,22 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[22, 62], Operations: ['60/15=4', '66-4=62'] Exploring Operation: 22*62=1364, Resulting Numbers: [1364] 1364,22 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[66, 26], Operations: ['60/15=4', '22+4=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,22 unequal: No Solution Exploring Operation: 66*26=1716, Resulting Numbers: [1716] 1716,22 unequal: No Solution Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[22, 70], Operations: ['60/15=4', '66+4=70'] Exploring Operation: 70-22=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 22+70=92, Resulting Numbers: [92] 92,22 unequal: No Solution Exploring Operation: 22*70=1540, Resulting Numbers: [1540] 1540,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[66, 15, 38], Operations: ['60-22=38'] Exploring Operation: 66-15=51, Resulting Numbers: [38, 51] Generated Node #0,0,0: 22:[38, 51] Operation: 66-15=51 Exploring Operation: 38-15=23, Resulting Numbers: [66, 23] Generated Node #0,0,1: 22:[66, 23] Operation: 38-15=23 Exploring Operation: 15+38=53, Resulting Numbers: [66, 53] Generated Node #0,0,2: 22:[66, 53] Operation: 15+38=53 Exploring Operation: 66-38=28, Resulting Numbers: [15, 28] Generated Node #0,0,3: 22:[15, 28] Operation: 66-38=28 Exploring Operation: 66+15=81, Resulting Numbers: [38, 81] Generated Node #0,0,4: 22:[38, 81] Operation: 66+15=81 Moving to Node #0,0,3 Current State: 22:[15, 28], Operations: ['60-22=38', '66-38=28'] Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,22 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[66, 23], Operations: ['60-22=38', '38-15=23'] Exploring Operation: 66+23=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 66*23=1518, Resulting Numbers: [1518] 1518,22 unequal: No Solution Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[38, 51], Operations: ['60-22=38', '66-15=51'] Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,22 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[66, 53], Operations: ['60-22=38', '15+38=53'] Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,22 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[38, 81], Operations: ['60-22=38', '66+15=81'] Exploring Operation: 38+81=119, Resulting Numbers: [119] 119,22 unequal: No Solution Exploring Operation: 38*81=3078, Resulting Numbers: [3078] 3078,22 unequal: No Solution Exploring Operation: 81-38=43, Resulting Numbers: [43] 43,22 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 #0,3 Current State: 22:[60, 15, 44], Operations: ['66-22=44'] Exploring Operation: 44-15=29, Resulting Numbers: [60, 29] Generated Node #0,3,0: 22:[60, 29] Operation: 44-15=29 Exploring Operation: 60+15=75, Resulting Numbers: [44, 75] Generated Node #0,3,1: 22:[44, 75] Operation: 60+15=75 Exploring Operation: 60-44=16, Resulting Numbers: [15, 16] Generated Node #0,3,2: 22:[15, 16] Operation: 60-44=16 Exploring Operation: 60-15=45, Resulting Numbers: [44, 45] Generated Node #0,3,3: 22:[44, 45] Operation: 60-15=45 Exploring Operation: 60/15=4, Resulting Numbers: [44, 4] Generated Node #0,3,4: 22:[44, 4] Operation: 60/15=4 Moving to Node #0,3,2 Current State: 22:[15, 16], Operations: ['66-22=44', '60-44=16'] Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,22 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[44, 4], Operations: ['66-22=44', '60/15=4'] Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,22 unequal: No Solution Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,22 unequal: No Solution Exploring Operation: 44*4=176, Resulting Numbers: [176] 176,22 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[60, 29], Operations: ['66-22=44', '44-15=29'] Exploring Operation: 60+29=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 60*29=1740, Resulting Numbers: [1740] 1740,22 unequal: No Solution Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[44, 45], Operations: ['66-22=44', '60-15=45'] Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 44+45=89, Resulting Numbers: [89] 89,22 unequal: No Solution Exploring Operation: 44*45=1980, Resulting Numbers: [1980] 1980,22 unequal: No Solution Moving to Node #0,3,1 Current State: 22:[44, 75], Operations: ['66-22=44', '60+15=75'] Exploring Operation: 44+75=119, Resulting Numbers: [119] 119,22 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,22 unequal: No Solution Exploring Operation: 44*75=3300, Resulting Numbers: [3300] 3300,22 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
[ 60, 90, 14, 10 ]
95
[ "60+10=70", "70/14=5", "90+5=95" ]
Current State: 95:[60, 90, 14, 10], Operations: [] Exploring Operation: 60+10=70, Resulting Numbers: [90, 14, 70] Generated Node #2: [90, 14, 70] from Operation: 60+10=70 Current State: 95:[90, 14, 70], Operations: ['60+10=70'] Exploring Operation: 70/14=5, Resulting Numbers: [90, 5] Generated Node #3: [90, 5] from Operation: 70/14=5 Current State: 95:[90, 5], Operations: ['60+10=70', '70/14=5'] Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[60, 90, 14, 10], Operations: [] Exploring Operation: 60/10=6, Resulting Numbers: [90, 14, 6] Generated Node #0,0: 95:[90, 14, 6] Operation: 60/10=6 Exploring Operation: 90-60=30, Resulting Numbers: [14, 10, 30] Generated Node #0,1: 95:[14, 10, 30] Operation: 90-60=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[90, 14, 6], Operations: ['60/10=6'] Exploring Operation: 14+6=20, Resulting Numbers: [90, 20] Generated Node #0,0,0: 95:[90, 20] Operation: 14+6=20 Exploring Operation: 90+6=96, Resulting Numbers: [14, 96] Generated Node #0,0,1: 95:[14, 96] Operation: 90+6=96 Moving to Node #0,0,0 Current State: 95:[90, 20], Operations: ['60/10=6', '14+6=20'] Exploring Operation: 90-20=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 90+20=110, Resulting Numbers: [110] 110,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[14, 96], Operations: ['60/10=6', '90+6=96'] Exploring Operation: 14+96=110, Resulting Numbers: [110] 110,95 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[14, 10, 30], Operations: ['90-60=30'] Exploring Operation: 30/10=3, Resulting Numbers: [14, 3] Generated Node #0,1,0: 95:[14, 3] Operation: 30/10=3 Exploring Operation: 30-10=20, Resulting Numbers: [14, 20] Generated Node #0,1,1: 95:[14, 20] Operation: 30-10=20 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 95:[14, 20], Operations: ['90-60=30', '30-10=20'] Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[14, 3], Operations: ['90-60=30', '30/10=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,95 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,95 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 7, 6, 35, 49 ]
22
[ "49/7=7", "35-6=29", "29-7=22" ]
Current State: 22:[7, 6, 35, 49], Operations: [] Exploring Operation: 49/7=7, Resulting Numbers: [6, 35, 7] Generated Node #2: [6, 35, 7] from Operation: 49/7=7 Current State: 22:[6, 35, 7], Operations: ['49/7=7'] Exploring Operation: 35-6=29, Resulting Numbers: [7, 29] Generated Node #3: [7, 29] from Operation: 35-6=29 Current State: 22:[7, 29], Operations: ['49/7=7', '35-6=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[7, 6, 35, 49], Operations: [] Exploring Operation: 35/7=5, Resulting Numbers: [6, 49, 5] Generated Node #0,0: 22:[6, 49, 5] Operation: 35/7=5 Exploring Operation: 35-7=28, Resulting Numbers: [6, 49, 28] Generated Node #0,1: 22:[6, 49, 28] Operation: 35-7=28 Exploring Operation: 49/7=7, Resulting Numbers: [6, 35, 7] Generated Node #0,2: 22:[6, 35, 7] Operation: 49/7=7 Exploring Operation: 49-35=14, Resulting Numbers: [7, 6, 14] Generated Node #0,3: 22:[7, 6, 14] Operation: 49-35=14 Moving to Node #0,3 Current State: 22:[7, 6, 14], Operations: ['49-35=14'] Exploring Operation: 7+14=21, Resulting Numbers: [6, 21] Generated Node #0,3,0: 22:[6, 21] Operation: 7+14=21 Exploring Operation: 7+6=13, Resulting Numbers: [14, 13] Generated Node #0,3,1: 22:[14, 13] Operation: 7+6=13 Exploring Operation: 14/7=2, Resulting Numbers: [6, 2] Generated Node #0,3,2: 22:[6, 2] Operation: 14/7=2 Exploring Operation: 7-6=1, Resulting Numbers: [14, 1] Generated Node #0,3,3: 22:[14, 1] Operation: 7-6=1 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 22:[6, 2], Operations: ['49-35=14', '14/7=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,22 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,22 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,22 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 #0,3,3 Current State: 22:[14, 1], Operations: ['49-35=14', '7-6=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,22 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 #0,3,0 Current State: 22:[6, 21], Operations: ['49-35=14', '7+14=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,22 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,22 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 #0,3,1 Current State: 22:[14, 13], Operations: ['49-35=14', '7+6=13'] Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,22 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,22 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,22 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: 22:[6, 35, 7], Operations: ['49/7=7'] Exploring Operation: 7-6=1, Resulting Numbers: [35, 1] Generated Node #0,2,0: 22:[35, 1] Operation: 7-6=1 Exploring Operation: 35-7=28, Resulting Numbers: [6, 28] Generated Node #0,2,1: 22:[6, 28] Operation: 35-7=28 Exploring Operation: 35-6=29, Resulting Numbers: [7, 29] Generated Node #0,2,2: 22:[7, 29] Operation: 35-6=29 Exploring Operation: 35/7=5, Resulting Numbers: [6, 5] Generated Node #0,2,3: 22:[6, 5] Operation: 35/7=5 Moving to Node #0,0 Current State: 22:[6, 49, 5], Operations: ['35/7=5'] Exploring Operation: 6-5=1, Resulting Numbers: [49, 1] Generated Node #0,0,0: 22:[49, 1] Operation: 6-5=1 Exploring Operation: 49-5=44, Resulting Numbers: [6, 44] Generated Node #0,0,1: 22:[6, 44] Operation: 49-5=44 Exploring Operation: 49-6=43, Resulting Numbers: [5, 43] Generated Node #0,0,2: 22:[5, 43] Operation: 49-6=43 Exploring Operation: 6+5=11, Resulting Numbers: [49, 11] Generated Node #0,0,3: 22:[49, 11] Operation: 6+5=11 Moving to Node #0,1 Current State: 22:[6, 49, 28], Operations: ['35-7=28'] Exploring Operation: 49-6=43, Resulting Numbers: [28, 43] Generated Node #0,1,0: 22:[28, 43] Operation: 49-6=43 Exploring Operation: 28-6=22, Resulting Numbers: [49, 22] Generated Node #0,1,1: 22:[49, 22] Operation: 28-6=22 Exploring Operation: 6+49=55, Resulting Numbers: [28, 55] Generated Node #0,1,2: 22:[28, 55] Operation: 6+49=55 Exploring Operation: 49-28=21, Resulting Numbers: [6, 21] Generated Node #0,1,3: 22:[6, 21] Operation: 49-28=21 Moving to Node #0,1,3 Current State: 22:[6, 21], Operations: ['35-7=28', '49-28=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,22 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[6, 5], Operations: ['49/7=7', '35/7=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,22 unequal: No Solution Moving to Node #0,2,1 Current State: 22:[6, 28], Operations: ['49/7=7', '35-7=28'] Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,22 unequal: No Solution Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,22 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[7, 6, 35, 49], Operations: [] Exploring Operation: 49/7=7, Resulting Numbers: [6, 35, 7] Generated Node #0,2: 22:[6, 35, 7] Operation: 49/7=7 Moving to Node #0,2 Current State: 22:[6, 35, 7], Operations: ['49/7=7'] Exploring Operation: 35-7=28, Resulting Numbers: [6, 28] Generated Node #0,2,1: 22:[6, 28] Operation: 35-7=28 Moving to Node #0,2,1 Current State: 22:[6, 28], Operations: ['49/7=7', '35-7=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.959201
hs_4
mult_heuristic
[ 95, 34, 72, 89 ]
22
[ "95-89=6", "72/6=12", "34-12=22" ]
Current State: 22:[95, 34, 72, 89], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [34, 72, 6] Generated Node #2: [34, 72, 6] from Operation: 95-89=6 Current State: 22:[34, 72, 6], Operations: ['95-89=6'] Exploring Operation: 72/6=12, Resulting Numbers: [34, 12] Generated Node #3: [34, 12] from Operation: 72/6=12 Current State: 22:[34, 12], Operations: ['95-89=6', '72/6=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[95, 34, 72, 89], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [34, 72, 6] Generated Node #0,0: 22:[34, 72, 6] Operation: 95-89=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[34, 72, 6], Operations: ['95-89=6'] Exploring Operation: 72/6=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 22:[34, 12] Operation: 72/6=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[34, 12], Operations: ['95-89=6', '72/6=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[95, 34, 72, 89], Operations: [] Exploring Operation: 95-89=6, Resulting Numbers: [34, 72, 6] Generated Node #0,0: 22:[34, 72, 6] Operation: 95-89=6 Moving to Node #0,0 Current State: 22:[34, 72, 6], Operations: ['95-89=6'] Exploring Operation: 72/6=12, Resulting Numbers: [34, 12] Generated Node #0,0,0: 22:[34, 12] Operation: 72/6=12 Moving to Node #0,0,0 Current State: 22:[34, 12], Operations: ['95-89=6', '72/6=12'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 34, 82, 3, 95 ]
25
[ "82+95=177", "177/3=59", "59-34=25" ]
Current State: 25:[34, 82, 3, 95], Operations: [] Exploring Operation: 82+95=177, Resulting Numbers: [34, 3, 177] Generated Node #2: [34, 3, 177] from Operation: 82+95=177 Current State: 25:[34, 3, 177], Operations: ['82+95=177'] Exploring Operation: 177/3=59, Resulting Numbers: [34, 59] Generated Node #3: [34, 59] from Operation: 177/3=59 Current State: 25:[34, 59], Operations: ['82+95=177', '177/3=59'] Exploring Operation: 59-34=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[34, 82, 3, 95], Operations: [] Exploring Operation: 82-3=79, Resulting Numbers: [34, 95, 79] Generated Node #0,0: 25:[34, 95, 79] Operation: 82-3=79 Exploring Operation: 95-34=61, Resulting Numbers: [82, 3, 61] Generated Node #0,1: 25:[82, 3, 61] Operation: 95-34=61 Exploring Operation: 34-3=31, Resulting Numbers: [82, 95, 31] Generated Node #0,2: 25:[82, 95, 31] Operation: 34-3=31 Exploring Operation: 95-82=13, Resulting Numbers: [34, 3, 13] Generated Node #0,3: 25:[34, 3, 13] Operation: 95-82=13 Exploring Operation: 82-34=48, Resulting Numbers: [3, 95, 48] Generated Node #0,4: 25:[3, 95, 48] Operation: 82-34=48 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[34, 3, 13], Operations: ['95-82=13'] Exploring Operation: 3+13=16, Resulting Numbers: [34, 16] Generated Node #0,3,0: 25:[34, 16] Operation: 3+13=16 Exploring Operation: 34-13=21, Resulting Numbers: [3, 21] Generated Node #0,3,1: 25:[3, 21] Operation: 34-13=21 Exploring Operation: 34-3=31, Resulting Numbers: [13, 31] Generated Node #0,3,2: 25:[13, 31] Operation: 34-3=31 Exploring Operation: 13-3=10, Resulting Numbers: [34, 10] Generated Node #0,3,3: 25:[34, 10] Operation: 13-3=10 Exploring Operation: 34+3=37, Resulting Numbers: [13, 37] Generated Node #0,3,4: 25:[13, 37] Operation: 34+3=37 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 25:[3, 21], Operations: ['95-82=13', '34-13=21'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,25 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,25 unequal: No Solution No 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: 25:[13, 31], Operations: ['95-82=13', '34-3=31'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 13*31=403, Resulting Numbers: [403] 403,25 unequal: No Solution Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,25 unequal: No Solution No 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: 25:[34, 10], Operations: ['95-82=13', '13-3=10'] Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,25 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,25 unequal: No Solution No 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: 25:[34, 16], Operations: ['95-82=13', '3+13=16'] Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,25 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,25 unequal: No Solution No 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: 25:[13, 37], Operations: ['95-82=13', '34+3=37'] Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,25 unequal: No Solution Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[82, 3, 61], Operations: ['95-34=61'] Exploring Operation: 61-3=58, Resulting Numbers: [82, 58] Generated Node #0,1,0: 25:[82, 58] Operation: 61-3=58 Exploring Operation: 82+3=85, Resulting Numbers: [61, 85] Generated Node #0,1,1: 25:[61, 85] Operation: 82+3=85 Exploring Operation: 82-3=79, Resulting Numbers: [61, 79] Generated Node #0,1,2: 25:[61, 79] Operation: 82-3=79 Exploring Operation: 3+61=64, Resulting Numbers: [82, 64] Generated Node #0,1,3: 25:[82, 64] Operation: 3+61=64 Exploring Operation: 82-61=21, Resulting Numbers: [3, 21] Generated Node #0,1,4: 25:[3, 21] Operation: 82-61=21 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 25:[3, 21], Operations: ['95-34=61', '82-61=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,25 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,25 unequal: No Solution No 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: 25:[82, 58], Operations: ['95-34=61', '61-3=58'] Exploring Operation: 82+58=140, Resulting Numbers: [140] 140,25 unequal: No Solution Exploring Operation: 82-58=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 82*58=4756, Resulting Numbers: [4756] 4756,25 unequal: No Solution No 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: 25:[61, 79], Operations: ['95-34=61', '82-3=79'] Exploring Operation: 79-61=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 61*79=4819, Resulting Numbers: [4819] 4819,25 unequal: No Solution Exploring Operation: 61+79=140, Resulting Numbers: [140] 140,25 unequal: No Solution No 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: 25:[61, 85], Operations: ['95-34=61', '82+3=85'] Exploring Operation: 61+85=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 61*85=5185, Resulting Numbers: [5185] 5185,25 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,25 unequal: No Solution No 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: 25:[82, 64], Operations: ['95-34=61', '3+61=64'] Exploring Operation: 82*64=5248, Resulting Numbers: [5248] 5248,25 unequal: No Solution Exploring Operation: 82-64=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 82+64=146, Resulting Numbers: [146] 146,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 25:[3, 95, 48], Operations: ['82-34=48'] Exploring Operation: 48-3=45, Resulting Numbers: [95, 45] Generated Node #0,4,0: 25:[95, 45] Operation: 48-3=45 Exploring Operation: 95-3=92, Resulting Numbers: [48, 92] Generated Node #0,4,1: 25:[48, 92] Operation: 95-3=92 Exploring Operation: 48/3=16, Resulting Numbers: [95, 16] Generated Node #0,4,2: 25:[95, 16] Operation: 48/3=16 Exploring Operation: 3+95=98, Resulting Numbers: [48, 98] Generated Node #0,4,3: 25:[48, 98] Operation: 3+95=98 Exploring Operation: 95-48=47, Resulting Numbers: [3, 47] Generated Node #0,4,4: 25:[3, 47] Operation: 95-48=47 Moving to Node #0,4,4 Current State: 25:[3, 47], Operations: ['82-34=48', '95-48=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,25 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,25 unequal: No Solution Moving to Node #0,4,2 Current State: 25:[95, 16], Operations: ['82-34=48', '48/3=16'] Exploring Operation: 95+16=111, Resulting Numbers: [111] 111,25 unequal: No Solution Exploring Operation: 95-16=79, Resulting Numbers: [79] 79,25 unequal: No Solution Exploring Operation: 95*16=1520, Resulting Numbers: [1520] 1520,25 unequal: No Solution Moving to Node #0,4,0 Current State: 25:[95, 45], Operations: ['82-34=48', '48-3=45'] Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,25 unequal: No Solution Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,25 unequal: No Solution Moving to Node #0,4,1 Current State: 25:[48, 92], Operations: ['82-34=48', '95-3=92'] Exploring Operation: 48+92=140, Resulting Numbers: [140] 140,25 unequal: No Solution Exploring Operation: 48*92=4416, Resulting Numbers: [4416] 4416,25 unequal: No Solution Exploring Operation: 92-48=44, Resulting Numbers: [44] 44,25 unequal: No Solution Moving to Node #0,4,3 Current State: 25:[48, 98], Operations: ['82-34=48', '3+95=98'] Exploring Operation: 48+98=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 48*98=4704, Resulting Numbers: [4704] 4704,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[34, 95, 79], Operations: ['82-3=79'] Exploring Operation: 95-34=61, Resulting Numbers: [79, 61] Generated Node #0,0,0: 25:[79, 61] Operation: 95-34=61 Exploring Operation: 34+79=113, Resulting Numbers: [95, 113] Generated Node #0,0,1: 25:[95, 113] Operation: 34+79=113 Exploring Operation: 34+95=129, Resulting Numbers: [79, 129] Generated Node #0,0,2: 25:[79, 129] Operation: 34+95=129 Exploring Operation: 95-79=16, Resulting Numbers: [34, 16] Generated Node #0,0,3: 25:[34, 16] Operation: 95-79=16 Exploring Operation: 79-34=45, Resulting Numbers: [95, 45] Generated Node #0,0,4: 25:[95, 45] Operation: 79-34=45 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 25:[34, 16], Operations: ['82-3=79', '95-79=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,25 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,25 unequal: No Solution No 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: 25:[79, 61], Operations: ['82-3=79', '95-34=61'] Exploring Operation: 79*61=4819, Resulting Numbers: [4819] 4819,25 unequal: No Solution Exploring Operation: 79-61=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 79+61=140, Resulting Numbers: [140] 140,25 unequal: No Solution No 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: 25:[95, 45], Operations: ['82-3=79', '79-34=45'] Exploring Operation: 95-45=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 95*45=4275, Resulting Numbers: [4275] 4275,25 unequal: No Solution Exploring Operation: 95+45=140, Resulting Numbers: [140] 140,25 unequal: No Solution No 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: 25:[95, 113], Operations: ['82-3=79', '34+79=113'] Exploring Operation: 113-95=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 95+113=208, Resulting Numbers: [208] 208,25 unequal: No Solution Exploring Operation: 95*113=10735, Resulting Numbers: [10735] 10735,25 unequal: No Solution No 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: 25:[79, 129], Operations: ['82-3=79', '34+95=129'] Exploring Operation: 129-79=50, Resulting Numbers: [50] 50,25 unequal: No Solution Exploring Operation: 79*129=10191, Resulting Numbers: [10191] 10191,25 unequal: No Solution Exploring Operation: 79+129=208, Resulting Numbers: [208] 208,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[82, 95, 31], Operations: ['34-3=31'] Exploring Operation: 82-31=51, Resulting Numbers: [95, 51] Generated Node #0,2,0: 25:[95, 51] Operation: 82-31=51 Exploring Operation: 95-82=13, Resulting Numbers: [31, 13] Generated Node #0,2,1: 25:[31, 13] Operation: 95-82=13 Exploring Operation: 82+95=177, Resulting Numbers: [31, 177] Generated Node #0,2,2: 25:[31, 177] Operation: 82+95=177 Exploring Operation: 95-31=64, Resulting Numbers: [82, 64] Generated Node #0,2,3: 25:[82, 64] Operation: 95-31=64 Exploring Operation: 82+31=113, Resulting Numbers: [95, 113] Generated Node #0,2,4: 25:[95, 113] Operation: 82+31=113 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[31, 13], Operations: ['34-3=31', '95-82=13'] Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 31+13=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 31*13=403, Resulting Numbers: [403] 403,25 unequal: No Solution No 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: 25:[95, 51], Operations: ['34-3=31', '82-31=51'] Exploring Operation: 95-51=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 95+51=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 95*51=4845, Resulting Numbers: [4845] 4845,25 unequal: No Solution No 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: 25:[82, 64], Operations: ['34-3=31', '95-31=64'] Exploring Operation: 82*64=5248, Resulting Numbers: [5248] 5248,25 unequal: No Solution Exploring Operation: 82-64=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 82+64=146, Resulting Numbers: [146] 146,25 unequal: No Solution No 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: 25:[31, 177], Operations: ['34-3=31', '82+95=177'] Exploring Operation: 177-31=146, Resulting Numbers: [146] 146,25 unequal: No Solution Exploring Operation: 31+177=208, Resulting Numbers: [208] 208,25 unequal: No Solution Exploring Operation: 31*177=5487, Resulting Numbers: [5487] 5487,25 unequal: No Solution No 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: 25:[95, 113], Operations: ['34-3=31', '82+31=113'] Exploring Operation: 95*113=10735, Resulting Numbers: [10735] 10735,25 unequal: No Solution Exploring Operation: 113-95=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 95+113=208, Resulting Numbers: [208] 208,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 2, 76, 16, 36 ]
14
[ "76/2=38", "16+36=52", "52-38=14" ]
Current State: 14:[2, 76, 16, 36], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [16, 36, 38] Generated Node #2: [16, 36, 38] from Operation: 76/2=38 Current State: 14:[16, 36, 38], Operations: ['76/2=38'] Exploring Operation: 16+36=52, Resulting Numbers: [38, 52] Generated Node #3: [38, 52] from Operation: 16+36=52 Current State: 14:[38, 52], Operations: ['76/2=38', '16+36=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[2, 76, 16, 36], Operations: [] Exploring Operation: 36/2=18, Resulting Numbers: [76, 16, 18] Generated Node #0,0: 14:[76, 16, 18] Operation: 36/2=18 Exploring Operation: 76/2=38, Resulting Numbers: [16, 36, 38] Generated Node #0,1: 14:[16, 36, 38] Operation: 76/2=38 Exploring Operation: 76-36=40, Resulting Numbers: [2, 16, 40] Generated Node #0,2: 14:[2, 16, 40] Operation: 76-36=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[2, 16, 40], Operations: ['76-36=40'] Exploring Operation: 16-2=14, Resulting Numbers: [40, 14] Generated Node #0,2,0: 14:[40, 14] Operation: 16-2=14 Exploring Operation: 40/2=20, Resulting Numbers: [16, 20] Generated Node #0,2,1: 14:[16, 20] Operation: 40/2=20 Exploring Operation: 40-16=24, Resulting Numbers: [2, 24] Generated Node #0,2,2: 14:[2, 24] Operation: 40-16=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 14:[16, 20], Operations: ['76-36=40', '40/2=20'] Exploring Operation: 16*20=320, Resulting Numbers: [320] 320,14 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,14 unequal: No Solution No 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: 14:[2, 24], Operations: ['76-36=40', '40-16=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,14 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,14 unequal: No Solution No 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: 14:[40, 14], Operations: ['76-36=40', '16-2=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 40*14=560, Resulting Numbers: [560] 560,14 unequal: No Solution Exploring Operation: 40+14=54, Resulting Numbers: [54] 54,14 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: 14:[16, 36, 38], Operations: ['76/2=38'] Exploring Operation: 38-16=22, Resulting Numbers: [36, 22] Generated Node #0,1,0: 14:[36, 22] Operation: 38-16=22 Exploring Operation: 36-16=20, Resulting Numbers: [38, 20] Generated Node #0,1,1: 14:[38, 20] Operation: 36-16=20 Exploring Operation: 38-36=2, Resulting Numbers: [16, 2] Generated Node #0,1,2: 14:[16, 2] Operation: 38-36=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 14:[16, 2], Operations: ['76/2=38', '38-36=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[2, 76, 16, 36], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [16, 36, 38] Generated Node #0,1: 14:[16, 36, 38] Operation: 76/2=38 Moving to Node #0,1 Current State: 14:[16, 36, 38], Operations: ['76/2=38'] Exploring Operation: 38-36=2, Resulting Numbers: [16, 2] Generated Node #0,1,2: 14:[16, 2] Operation: 38-36=2 Moving to Node #0,1,2 Current State: 14:[16, 2], Operations: ['76/2=38', '38-36=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 3, 8, 41, 2 ]
81
[ "3+2=5", "8*5=40", "41+40=81" ]
Current State: 81:[3, 8, 41, 2], Operations: [] Exploring Operation: 3+2=5, Resulting Numbers: [8, 41, 5] Generated Node #2: [8, 41, 5] from Operation: 3+2=5 Current State: 81:[8, 41, 5], Operations: ['3+2=5'] Exploring Operation: 8*5=40, Resulting Numbers: [41, 40] Generated Node #3: [41, 40] from Operation: 8*5=40 Current State: 81:[41, 40], Operations: ['3+2=5', '8*5=40'] Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[3, 8, 41, 2], Operations: [] Exploring Operation: 41*2=82, Resulting Numbers: [3, 8, 82] Generated Node #0,0: 81:[3, 8, 82] Operation: 41*2=82 Moving to Node #0,0 Current State: 81:[3, 8, 82], Operations: ['41*2=82'] Exploring Operation: 3+8=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 81:[82, 11] Operation: 3+8=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[82, 11], Operations: ['41*2=82', '3+8=11'] Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,81 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
[ 2, 91, 29, 35 ]
37
[ "29+35=64", "2*64=128", "128-91=37" ]
Current State: 37:[2, 91, 29, 35], Operations: [] Exploring Operation: 29+35=64, Resulting Numbers: [2, 91, 64] Generated Node #2: [2, 91, 64] from Operation: 29+35=64 Current State: 37:[2, 91, 64], Operations: ['29+35=64'] Exploring Operation: 2*64=128, Resulting Numbers: [91, 128] Generated Node #3: [91, 128] from Operation: 2*64=128 Current State: 37:[91, 128], Operations: ['29+35=64', '2*64=128'] Exploring Operation: 128-91=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[2, 91, 29, 35], Operations: [] Exploring Operation: 91-29=62, Resulting Numbers: [2, 35, 62] Generated Node #0,0: 37:[2, 35, 62] Operation: 91-29=62 Exploring Operation: 2+35=37, Resulting Numbers: [91, 29, 37] Generated Node #0,1: 37:[91, 29, 37] Operation: 2+35=37 Exploring Operation: 91-2=89, Resulting Numbers: [29, 35, 89] Generated Node #0,2: 37:[29, 35, 89] Operation: 91-2=89 Exploring Operation: 2+29=31, Resulting Numbers: [91, 35, 31] Generated Node #0,3: 37:[91, 35, 31] Operation: 2+29=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[2, 35, 62], Operations: ['91-29=62'] Exploring Operation: 62/2=31, Resulting Numbers: [35, 31] Generated Node #0,0,0: 37:[35, 31] Operation: 62/2=31 Exploring Operation: 35-2=33, Resulting Numbers: [62, 33] Generated Node #0,0,1: 37:[62, 33] Operation: 35-2=33 Exploring Operation: 62-2=60, Resulting Numbers: [35, 60] Generated Node #0,0,2: 37:[35, 60] Operation: 62-2=60 Exploring Operation: 2+35=37, Resulting Numbers: [62, 37] Generated Node #0,0,3: 37:[62, 37] Operation: 2+35=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[35, 31], Operations: ['91-29=62', '62/2=31'] Exploring Operation: 35+31=66, Resulting Numbers: [66] 66,37 unequal: No Solution Exploring Operation: 35-31=4, Resulting Numbers: [4] 4,37 unequal: No Solution Exploring Operation: 35*31=1085, Resulting Numbers: [1085] 1085,37 unequal: No Solution No 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: 37:[35, 60], Operations: ['91-29=62', '62-2=60'] Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,37 unequal: No Solution Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,37 unequal: No Solution No 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: 37:[62, 37], Operations: ['91-29=62', '2+35=37'] Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 62*37=2294, Resulting Numbers: [2294] 2294,37 unequal: No Solution Exploring Operation: 62+37=99, Resulting Numbers: [99] 99,37 unequal: No Solution No 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: 37:[62, 33], Operations: ['91-29=62', '35-2=33'] Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 62*33=2046, Resulting Numbers: [2046] 2046,37 unequal: No Solution Exploring Operation: 62+33=95, Resulting Numbers: [95] 95,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[91, 29, 37], Operations: ['2+35=37'] Exploring Operation: 29+37=66, Resulting Numbers: [91, 66] Generated Node #0,1,0: 37:[91, 66] Operation: 29+37=66 Exploring Operation: 91-37=54, Resulting Numbers: [29, 54] Generated Node #0,1,1: 37:[29, 54] Operation: 91-37=54 Exploring Operation: 91+29=120, Resulting Numbers: [37, 120] Generated Node #0,1,2: 37:[37, 120] Operation: 91+29=120 Exploring Operation: 91-29=62, Resulting Numbers: [37, 62] Generated Node #0,1,3: 37:[37, 62] Operation: 91-29=62 Moving to Node #0,1,1 Current State: 37:[29, 54], Operations: ['2+35=37', '91-37=54'] Exploring Operation: 29*54=1566, Resulting Numbers: [1566] 1566,37 unequal: No Solution Exploring Operation: 29+54=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,37 unequal: No Solution Moving to Node #0,1,3 Current State: 37:[37, 62], Operations: ['2+35=37', '91-29=62'] Exploring Operation: 37*62=2294, Resulting Numbers: [2294] 2294,37 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,37 unequal: No Solution Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,37 unequal: No Solution Moving to Node #0,1,2 Current State: 37:[37, 120], Operations: ['2+35=37', '91+29=120'] Exploring Operation: 120-37=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 37+120=157, Resulting Numbers: [157] 157,37 unequal: No Solution Exploring Operation: 37*120=4440, Resulting Numbers: [4440] 4440,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[91, 66], Operations: ['2+35=37', '29+37=66'] Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 91+66=157, Resulting Numbers: [157] 157,37 unequal: No Solution Exploring Operation: 91*66=6006, Resulting Numbers: [6006] 6006,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[29, 35, 89], Operations: ['91-2=89'] Exploring Operation: 89-35=54, Resulting Numbers: [29, 54] Generated Node #0,2,0: 37:[29, 54] Operation: 89-35=54 Exploring Operation: 29+35=64, Resulting Numbers: [89, 64] Generated Node #0,2,1: 37:[89, 64] Operation: 29+35=64 Exploring Operation: 35-29=6, Resulting Numbers: [89, 6] Generated Node #0,2,2: 37:[89, 6] Operation: 35-29=6 Exploring Operation: 89-29=60, Resulting Numbers: [35, 60] Generated Node #0,2,3: 37:[35, 60] Operation: 89-29=60 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 37:[29, 54], Operations: ['91-2=89', '89-35=54'] Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 29+54=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 29*54=1566, Resulting Numbers: [1566] 1566,37 unequal: No Solution No 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: 37:[35, 60], Operations: ['91-2=89', '89-29=60'] Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,37 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,37 unequal: No Solution No 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: 37:[89, 64], Operations: ['91-2=89', '29+35=64'] Exploring Operation: 89-64=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 89+64=153, Resulting Numbers: [153] 153,37 unequal: No Solution Exploring Operation: 89*64=5696, Resulting Numbers: [5696] 5696,37 unequal: No Solution No 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: 37:[89, 6], Operations: ['91-2=89', '35-29=6'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,37 unequal: No Solution Exploring Operation: 89*6=534, Resulting Numbers: [534] 534,37 unequal: No Solution Exploring Operation: 89+6=95, Resulting Numbers: [95] 95,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[91, 35, 31], Operations: ['2+29=31'] Exploring Operation: 91-35=56, Resulting Numbers: [31, 56] Generated Node #0,3,0: 37:[31, 56] Operation: 91-35=56 Exploring Operation: 35+31=66, Resulting Numbers: [91, 66] Generated Node #0,3,1: 37:[91, 66] Operation: 35+31=66 Exploring Operation: 91+31=122, Resulting Numbers: [35, 122] Generated Node #0,3,2: 37:[35, 122] Operation: 91+31=122 Exploring Operation: 91-31=60, Resulting Numbers: [35, 60] Generated Node #0,3,3: 37:[35, 60] Operation: 91-31=60 Moving to Node #0,3,0 Current State: 37:[31, 56], Operations: ['2+29=31', '91-35=56'] Exploring Operation: 56-31=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 31+56=87, Resulting Numbers: [87] 87,37 unequal: No Solution Exploring Operation: 31*56=1736, Resulting Numbers: [1736] 1736,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[35, 60], Operations: ['2+29=31', '91-31=60'] Exploring Operation: 35+60=95, Resulting Numbers: [95] 95,37 unequal: No Solution Exploring Operation: 35*60=2100, Resulting Numbers: [2100] 2100,37 unequal: No Solution Exploring Operation: 60-35=25, Resulting Numbers: [25] 25,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[91, 66], Operations: ['2+29=31', '35+31=66'] Exploring Operation: 91*66=6006, Resulting Numbers: [6006] 6006,37 unequal: No Solution Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 91+66=157, Resulting Numbers: [157] 157,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[35, 122], Operations: ['2+29=31', '91+31=122'] Exploring Operation: 122-35=87, Resulting Numbers: [87] 87,37 unequal: No Solution Exploring Operation: 35*122=4270, Resulting Numbers: [4270] 4270,37 unequal: No Solution Exploring Operation: 35+122=157, Resulting Numbers: [157] 157,37 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, 9, 91, 25 ]
97
[ "91-83=8", "9*8=72", "25+72=97" ]
Current State: 97:[83, 9, 91, 25], Operations: [] Exploring Operation: 91-83=8, Resulting Numbers: [9, 25, 8] Generated Node #2: [9, 25, 8] from Operation: 91-83=8 Current State: 97:[9, 25, 8], Operations: ['91-83=8'] Exploring Operation: 9*8=72, Resulting Numbers: [25, 72] Generated Node #3: [25, 72] from Operation: 9*8=72 Current State: 97:[25, 72], Operations: ['91-83=8', '9*8=72'] Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[83, 9, 91, 25], Operations: [] Exploring Operation: 9+25=34, Resulting Numbers: [83, 91, 34] Generated Node #0,0: 97:[83, 91, 34] Operation: 9+25=34 Exploring Operation: 9+91=100, Resulting Numbers: [83, 25, 100] Generated Node #0,1: 97:[83, 25, 100] Operation: 9+91=100 Exploring Operation: 91-9=82, Resulting Numbers: [83, 25, 82] Generated Node #0,2: 97:[83, 25, 82] Operation: 91-9=82 Exploring Operation: 83-9=74, Resulting Numbers: [91, 25, 74] Generated Node #0,3: 97:[91, 25, 74] Operation: 83-9=74 Exploring Operation: 83+9=92, Resulting Numbers: [91, 25, 92] Generated Node #0,4: 97:[91, 25, 92] Operation: 83+9=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[83, 91, 34], Operations: ['9+25=34'] Exploring Operation: 91+34=125, Resulting Numbers: [83, 125] Generated Node #0,0,0: 97:[83, 125] Operation: 91+34=125 Exploring Operation: 83+91=174, Resulting Numbers: [34, 174] Generated Node #0,0,1: 97:[34, 174] Operation: 83+91=174 Exploring Operation: 83+34=117, Resulting Numbers: [91, 117] Generated Node #0,0,2: 97:[91, 117] Operation: 83+34=117 Exploring Operation: 83-34=49, Resulting Numbers: [91, 49] Generated Node #0,0,3: 97:[91, 49] Operation: 83-34=49 Exploring Operation: 91-34=57, Resulting Numbers: [83, 57] Generated Node #0,0,4: 97:[83, 57] Operation: 91-34=57 Moving to Node #0,0,2 Current State: 97:[91, 117], Operations: ['9+25=34', '83+34=117'] Exploring Operation: 91*117=10647, Resulting Numbers: [10647] 10647,97 unequal: No Solution Exploring Operation: 91+117=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 117-91=26, Resulting Numbers: [26] 26,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[83, 125], Operations: ['9+25=34', '91+34=125'] Exploring Operation: 83*125=10375, Resulting Numbers: [10375] 10375,97 unequal: No Solution Exploring Operation: 83+125=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 125-83=42, Resulting Numbers: [42] 42,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[91, 49], Operations: ['9+25=34', '83-34=49'] Exploring Operation: 91*49=4459, Resulting Numbers: [4459] 4459,97 unequal: No Solution Exploring Operation: 91-49=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 91+49=140, Resulting Numbers: [140] 140,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[83, 57], Operations: ['9+25=34', '91-34=57'] Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[34, 174], Operations: ['9+25=34', '83+91=174'] Exploring Operation: 174-34=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 34+174=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 34*174=5916, Resulting Numbers: [5916] 5916,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 97:[91, 25, 92], Operations: ['83+9=92'] Exploring Operation: 92-25=67, Resulting Numbers: [91, 67] Generated Node #0,4,0: 97:[91, 67] Operation: 92-25=67 Exploring Operation: 91+25=116, Resulting Numbers: [92, 116] Generated Node #0,4,1: 97:[92, 116] Operation: 91+25=116 Exploring Operation: 25+92=117, Resulting Numbers: [91, 117] Generated Node #0,4,2: 97:[91, 117] Operation: 25+92=117 Exploring Operation: 91+92=183, Resulting Numbers: [25, 183] Generated Node #0,4,3: 97:[25, 183] Operation: 91+92=183 Exploring Operation: 91-25=66, Resulting Numbers: [92, 66] Generated Node #0,4,4: 97:[92, 66] Operation: 91-25=66 Moving to Node #0,4,1 Current State: 97:[92, 116], Operations: ['83+9=92', '91+25=116'] Exploring Operation: 116-92=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 92+116=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 92*116=10672, Resulting Numbers: [10672] 10672,97 unequal: No Solution Moving to Node #0,4,2 Current State: 97:[91, 117], Operations: ['83+9=92', '25+92=117'] Exploring Operation: 117-91=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 91*117=10647, Resulting Numbers: [10647] 10647,97 unequal: No Solution Exploring Operation: 91+117=208, Resulting Numbers: [208] 208,97 unequal: No Solution Moving to Node #0,4,0 Current State: 97:[91, 67], Operations: ['83+9=92', '92-25=67'] Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 91*67=6097, Resulting Numbers: [6097] 6097,97 unequal: No Solution Exploring Operation: 91+67=158, Resulting Numbers: [158] 158,97 unequal: No Solution Moving to Node #0,4,4 Current State: 97:[92, 66], Operations: ['83+9=92', '91-25=66'] Exploring Operation: 92-66=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 92*66=6072, Resulting Numbers: [6072] 6072,97 unequal: No Solution Exploring Operation: 92+66=158, Resulting Numbers: [158] 158,97 unequal: No Solution Moving to Node #0,4,3 Current State: 97:[25, 183], Operations: ['83+9=92', '91+92=183'] Exploring Operation: 25*183=4575, Resulting Numbers: [4575] 4575,97 unequal: No Solution Exploring Operation: 183-25=158, Resulting Numbers: [158] 158,97 unequal: No Solution Exploring Operation: 25+183=208, Resulting Numbers: [208] 208,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[83, 25, 100], Operations: ['9+91=100'] Exploring Operation: 100/25=4, Resulting Numbers: [83, 4] Generated Node #0,1,0: 97:[83, 4] Operation: 100/25=4 Exploring Operation: 83+25=108, Resulting Numbers: [100, 108] Generated Node #0,1,1: 97:[100, 108] Operation: 83+25=108 Exploring Operation: 83-25=58, Resulting Numbers: [100, 58] Generated Node #0,1,2: 97:[100, 58] Operation: 83-25=58 Exploring Operation: 25+100=125, Resulting Numbers: [83, 125] Generated Node #0,1,3: 97:[83, 125] Operation: 25+100=125 Exploring Operation: 100-25=75, Resulting Numbers: [83, 75] Generated Node #0,1,4: 97:[83, 75] Operation: 100-25=75 Moving to Node #0,1,1 Current State: 97:[100, 108], Operations: ['9+91=100', '83+25=108'] Exploring Operation: 108-100=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 100+108=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 100*108=10800, Resulting Numbers: [10800] 10800,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[83, 75], Operations: ['9+91=100', '100-25=75'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,97 unequal: No Solution Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[100, 58], Operations: ['9+91=100', '83-25=58'] Exploring Operation: 100*58=5800, Resulting Numbers: [5800] 5800,97 unequal: No Solution Exploring Operation: 100-58=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 100+58=158, Resulting Numbers: [158] 158,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[83, 125], Operations: ['9+91=100', '25+100=125'] Exploring Operation: 83+125=208, Resulting Numbers: [208] 208,97 unequal: No Solution Exploring Operation: 83*125=10375, Resulting Numbers: [10375] 10375,97 unequal: No Solution Exploring Operation: 125-83=42, Resulting Numbers: [42] 42,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[83, 4], Operations: ['9+91=100', '100/25=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,97 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[83, 25, 82], Operations: ['91-9=82'] Exploring Operation: 25+82=107, Resulting Numbers: [83, 107] Generated Node #0,2,0: 97:[83, 107] Operation: 25+82=107 Exploring Operation: 83+25=108, Resulting Numbers: [82, 108] Generated Node #0,2,1: 97:[82, 108] Operation: 83+25=108 Exploring Operation: 83+82=165, Resulting Numbers: [25, 165] Generated Node #0,2,2: 97:[25, 165] Operation: 83+82=165 Exploring Operation: 82-25=57, Resulting Numbers: [83, 57] Generated Node #0,2,3: 97:[83, 57] Operation: 82-25=57 Exploring Operation: 83-25=58, Resulting Numbers: [82, 58] Generated Node #0,2,4: 97:[82, 58] Operation: 83-25=58 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[83, 107], Operations: ['91-9=82', '25+82=107'] Exploring Operation: 83*107=8881, Resulting Numbers: [8881] 8881,97 unequal: No Solution Exploring Operation: 83+107=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 107-83=24, Resulting Numbers: [24] 24,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[82, 108], Operations: ['91-9=82', '83+25=108'] Exploring Operation: 108-82=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 82*108=8856, Resulting Numbers: [8856] 8856,97 unequal: No Solution Exploring Operation: 82+108=190, Resulting Numbers: [190] 190,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 97:[83, 57], Operations: ['91-9=82', '82-25=57'] Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,97 unequal: No Solution Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 97:[82, 58], Operations: ['91-9=82', '83-25=58'] Exploring Operation: 82-58=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 82*58=4756, Resulting Numbers: [4756] 4756,97 unequal: No Solution Exploring Operation: 82+58=140, Resulting Numbers: [140] 140,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[25, 165], Operations: ['91-9=82', '83+82=165'] Exploring Operation: 25*165=4125, Resulting Numbers: [4125] 4125,97 unequal: No Solution Exploring Operation: 25+165=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 165-25=140, Resulting Numbers: [140] 140,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[91, 25, 74], Operations: ['83-9=74'] Exploring Operation: 91+25=116, Resulting Numbers: [74, 116] Generated Node #0,3,0: 97:[74, 116] Operation: 91+25=116 Exploring Operation: 91-25=66, Resulting Numbers: [74, 66] Generated Node #0,3,1: 97:[74, 66] Operation: 91-25=66 Exploring Operation: 91+74=165, Resulting Numbers: [25, 165] Generated Node #0,3,2: 97:[25, 165] Operation: 91+74=165 Exploring Operation: 25+74=99, Resulting Numbers: [91, 99] Generated Node #0,3,3: 97:[91, 99] Operation: 25+74=99 Exploring Operation: 74-25=49, Resulting Numbers: [91, 49] Generated Node #0,3,4: 97:[91, 49] Operation: 74-25=49 Moving to Node #0,3,3 Current State: 97:[91, 99], Operations: ['83-9=74', '25+74=99'] Exploring Operation: 91*99=9009, Resulting Numbers: [9009] 9009,97 unequal: No Solution Exploring Operation: 91+99=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 99-91=8, Resulting Numbers: [8] 8,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[74, 116], Operations: ['83-9=74', '91+25=116'] Exploring Operation: 74*116=8584, Resulting Numbers: [8584] 8584,97 unequal: No Solution Exploring Operation: 74+116=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 116-74=42, Resulting Numbers: [42] 42,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[74, 66], Operations: ['83-9=74', '91-25=66'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 74*66=4884, Resulting Numbers: [4884] 4884,97 unequal: No Solution Exploring Operation: 74+66=140, Resulting Numbers: [140] 140,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[91, 49], Operations: ['83-9=74', '74-25=49'] Exploring Operation: 91+49=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 91-49=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 91*49=4459, Resulting Numbers: [4459] 4459,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[25, 165], Operations: ['83-9=74', '91+74=165'] Exploring Operation: 165-25=140, Resulting Numbers: [140] 140,97 unequal: No Solution Exploring Operation: 25*165=4125, Resulting Numbers: [4125] 4125,97 unequal: No Solution Exploring Operation: 25+165=190, Resulting Numbers: [190] 190,97 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
[ 1, 6, 90, 67 ]
83
[ "1+67=68", "90/6=15", "68+15=83" ]
Current State: 83:[1, 6, 90, 67], Operations: [] Exploring Operation: 1+67=68, Resulting Numbers: [6, 90, 68] Generated Node #2: [6, 90, 68] from Operation: 1+67=68 Current State: 83:[6, 90, 68], Operations: ['1+67=68'] Exploring Operation: 90/6=15, Resulting Numbers: [68, 15] Generated Node #3: [68, 15] from Operation: 90/6=15 Current State: 83:[68, 15], Operations: ['1+67=68', '90/6=15'] Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[1, 6, 90, 67], Operations: [] Exploring Operation: 1+6=7, Resulting Numbers: [90, 67, 7] Generated Node #0,0: 83:[90, 67, 7] Operation: 1+6=7 Exploring Operation: 90-1=89, Resulting Numbers: [6, 67, 89] Generated Node #0,1: 83:[6, 67, 89] Operation: 90-1=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[90, 67, 7], Operations: ['1+6=7'] Exploring Operation: 67+7=74, Resulting Numbers: [90, 74] Generated Node #0,0,0: 83:[90, 74] Operation: 67+7=74 Exploring Operation: 90-7=83, Resulting Numbers: [67, 83] Generated Node #0,0,1: 83:[67, 83] Operation: 90-7=83 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[90, 74], Operations: ['1+6=7', '67+7=74'] Exploring Operation: 90+74=164, Resulting Numbers: [164] 164,83 unequal: No Solution Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,83 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:[67, 83], Operations: ['1+6=7', '90-7=83'] Exploring Operation: 67+83=150, Resulting Numbers: [150] 150,83 unequal: No Solution Exploring Operation: 83-67=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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[6, 67, 89], Operations: ['90-1=89'] Exploring Operation: 89-6=83, Resulting Numbers: [67, 83] Generated Node #0,1,0: 83:[67, 83] Operation: 89-6=83 Exploring Operation: 6+67=73, Resulting Numbers: [89, 73] Generated Node #0,1,1: 83:[89, 73] Operation: 6+67=73 Moving to Node #0,1,0 Current State: 83:[67, 83], Operations: ['90-1=89', '89-6=83'] Exploring Operation: 67+83=150, Resulting Numbers: [150] 150,83 unequal: No Solution Exploring Operation: 83-67=16, Resulting Numbers: [16] 16,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[89, 73], Operations: ['90-1=89', '6+67=73'] Exploring Operation: 89+73=162, Resulting Numbers: [162] 162,83 unequal: No Solution Exploring Operation: 89-73=16, Resulting Numbers: [16] 16,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 2, 69, 68, 69 ]
33
[ "68/2=34", "69/69=1", "34-1=33" ]
Current State: 33:[2, 69, 68, 69], Operations: [] Exploring Operation: 68/2=34, Resulting Numbers: [69, 69, 34] Generated Node #2: [69, 69, 34] from Operation: 68/2=34 Current State: 33:[69, 69, 34], Operations: ['68/2=34'] Exploring Operation: 69/69=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 69/69=1 Current State: 33:[34, 1], Operations: ['68/2=34', '69/69=1'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[2, 69, 68, 69], Operations: [] Exploring Operation: 69/69=1, Resulting Numbers: [2, 68, 1] Generated Node #0,0: 33:[2, 68, 1] Operation: 69/69=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[2, 68, 1], Operations: ['69/69=1'] Exploring Operation: 68/2=34, Resulting Numbers: [1, 34] Generated Node #0,0,0: 33:[1, 34] Operation: 68/2=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[1, 34], Operations: ['69/69=1', '68/2=34'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[2, 69, 68, 69], Operations: [] Exploring Operation: 69/69=1, Resulting Numbers: [2, 68, 1] Generated Node #0,0: 33:[2, 68, 1] Operation: 69/69=1 Moving to Node #0,0 Current State: 33:[2, 68, 1], Operations: ['69/69=1'] Exploring Operation: 68/2=34, Resulting Numbers: [1, 34] Generated Node #0,0,0: 33:[1, 34] Operation: 68/2=34 Moving to Node #0,0,0 Current State: 33:[1, 34], Operations: ['69/69=1', '68/2=34'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 56, 73, 3, 49 ]
69
[ "73-56=17", "3+49=52", "17+52=69" ]
Current State: 69:[56, 73, 3, 49], Operations: [] Exploring Operation: 73-56=17, Resulting Numbers: [3, 49, 17] Generated Node #2: [3, 49, 17] from Operation: 73-56=17 Current State: 69:[3, 49, 17], Operations: ['73-56=17'] Exploring Operation: 3+49=52, Resulting Numbers: [17, 52] Generated Node #3: [17, 52] from Operation: 3+49=52 Current State: 69:[17, 52], Operations: ['73-56=17', '3+49=52'] Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[56, 73, 3, 49], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [56, 3, 24] Generated Node #0,0: 69:[56, 3, 24] Operation: 73-49=24 Exploring Operation: 73-56=17, Resulting Numbers: [3, 49, 17] Generated Node #0,1: 69:[3, 49, 17] Operation: 73-56=17 Exploring Operation: 56-49=7, Resulting Numbers: [73, 3, 7] Generated Node #0,2: 69:[73, 3, 7] Operation: 56-49=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[73, 3, 7], Operations: ['56-49=7'] Exploring Operation: 73-3=70, Resulting Numbers: [7, 70] Generated Node #0,2,0: 69:[7, 70] Operation: 73-3=70 Exploring Operation: 73-7=66, Resulting Numbers: [3, 66] Generated Node #0,2,1: 69:[3, 66] Operation: 73-7=66 Exploring Operation: 7-3=4, Resulting Numbers: [73, 4] Generated Node #0,2,2: 69:[73, 4] Operation: 7-3=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 69:[3, 66], Operations: ['56-49=7', '73-7=66'] Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,69 unequal: No Solution Exploring Operation: 3+66=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[56, 73, 3, 49], Operations: [] Exploring Operation: 56-49=7, Resulting Numbers: [73, 3, 7] Generated Node #0,2: 69:[73, 3, 7] Operation: 56-49=7 Moving to Node #0,2 Current State: 69:[73, 3, 7], Operations: ['56-49=7'] Exploring Operation: 73-7=66, Resulting Numbers: [3, 66] Generated Node #0,2,1: 69:[3, 66] Operation: 73-7=66 Moving to Node #0,2,1 Current State: 69:[3, 66], Operations: ['56-49=7', '73-7=66'] Exploring Operation: 3+66=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 43, 41, 51, 67 ]
83
[ "43-41=2", "67*2=134", "134-51=83" ]
Current State: 83:[43, 41, 51, 67], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [51, 67, 2] Generated Node #2: [51, 67, 2] from Operation: 43-41=2 Current State: 83:[51, 67, 2], Operations: ['43-41=2'] Exploring Operation: 67*2=134, Resulting Numbers: [51, 134] Generated Node #3: [51, 134] from Operation: 67*2=134 Current State: 83:[51, 134], Operations: ['43-41=2', '67*2=134'] Exploring Operation: 134-51=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[43, 41, 51, 67], Operations: [] Exploring Operation: 43+41=84, Resulting Numbers: [51, 67, 84] Generated Node #0,0: 83:[51, 67, 84] Operation: 43+41=84 Exploring Operation: 41+51=92, Resulting Numbers: [43, 67, 92] Generated Node #0,1: 83:[43, 67, 92] Operation: 41+51=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[51, 67, 84], Operations: ['43+41=84'] Exploring Operation: 84-51=33, Resulting Numbers: [67, 33] Generated Node #0,0,0: 83:[67, 33] Operation: 84-51=33 Exploring Operation: 51+67=118, Resulting Numbers: [84, 118] Generated Node #0,0,1: 83:[84, 118] Operation: 51+67=118 Moving to Node #0,0,1 Current State: 83:[84, 118], Operations: ['43+41=84', '51+67=118'] Exploring Operation: 118-84=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 84+118=202, Resulting Numbers: [202] 202,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[67, 33], Operations: ['43+41=84', '84-51=33'] Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,83 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,83 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:[43, 67, 92], Operations: ['41+51=92'] Exploring Operation: 43+67=110, Resulting Numbers: [92, 110] Generated Node #0,1,0: 83:[92, 110] Operation: 43+67=110 Exploring Operation: 92-43=49, Resulting Numbers: [67, 49] Generated Node #0,1,1: 83:[67, 49] Operation: 92-43=49 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[92, 110], Operations: ['41+51=92', '43+67=110'] Exploring Operation: 92+110=202, Resulting Numbers: [202] 202,83 unequal: No Solution Exploring Operation: 110-92=18, Resulting Numbers: [18] 18,83 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:[67, 49], Operations: ['41+51=92', '92-43=49'] Exploring Operation: 67+49=116, Resulting Numbers: [116] 116,83 unequal: No Solution Exploring Operation: 67-49=18, Resulting Numbers: [18] 18,83 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
[ 46, 73, 52, 36 ]
79
[ "52-46=6", "36/6=6", "73+6=79" ]
Current State: 79:[46, 73, 52, 36], Operations: [] Exploring Operation: 52-46=6, Resulting Numbers: [73, 36, 6] Generated Node #2: [73, 36, 6] from Operation: 52-46=6 Current State: 79:[73, 36, 6], Operations: ['52-46=6'] Exploring Operation: 36/6=6, Resulting Numbers: [73, 6] Generated Node #3: [73, 6] from Operation: 36/6=6 Current State: 79:[73, 6], Operations: ['52-46=6', '36/6=6'] Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[46, 73, 52, 36], Operations: [] Exploring Operation: 46+52=98, Resulting Numbers: [73, 36, 98] Generated Node #0,0: 79:[73, 36, 98] Operation: 46+52=98 Exploring Operation: 73+36=109, Resulting Numbers: [46, 52, 109] Generated Node #0,1: 79:[46, 52, 109] Operation: 73+36=109 Exploring Operation: 46-36=10, Resulting Numbers: [73, 52, 10] Generated Node #0,2: 79:[73, 52, 10] Operation: 46-36=10 Exploring Operation: 46+36=82, Resulting Numbers: [73, 52, 82] Generated Node #0,3: 79:[73, 52, 82] Operation: 46+36=82 Exploring Operation: 52+36=88, Resulting Numbers: [46, 73, 88] Generated Node #0,4: 79:[46, 73, 88] Operation: 52+36=88 Moving to Node #0,3 Current State: 79:[73, 52, 82], Operations: ['46+36=82'] Exploring Operation: 52+82=134, Resulting Numbers: [73, 134] Generated Node #0,3,0: 79:[73, 134] Operation: 52+82=134 Exploring Operation: 82-52=30, Resulting Numbers: [73, 30] Generated Node #0,3,1: 79:[73, 30] Operation: 82-52=30 Exploring Operation: 82-73=9, Resulting Numbers: [52, 9] Generated Node #0,3,2: 79:[52, 9] Operation: 82-73=9 Exploring Operation: 73+52=125, Resulting Numbers: [82, 125] Generated Node #0,3,3: 79:[82, 125] Operation: 73+52=125 Exploring Operation: 73-52=21, Resulting Numbers: [82, 21] Generated Node #0,3,4: 79:[82, 21] Operation: 73-52=21 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[82, 125], Operations: ['46+36=82', '73+52=125'] Exploring Operation: 125-82=43, Resulting Numbers: [43] 43,79 unequal: No Solution Exploring Operation: 82*125=10250, Resulting Numbers: [10250] 10250,79 unequal: No Solution Exploring Operation: 82+125=207, Resulting Numbers: [207] 207,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[73, 30], Operations: ['46+36=82', '82-52=30'] Exploring Operation: 73*30=2190, Resulting Numbers: [2190] 2190,79 unequal: No Solution Exploring Operation: 73+30=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 73-30=43, Resulting Numbers: [43] 43,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[73, 134], Operations: ['46+36=82', '52+82=134'] Exploring Operation: 134-73=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 73*134=9782, Resulting Numbers: [9782] 9782,79 unequal: No Solution Exploring Operation: 73+134=207, Resulting Numbers: [207] 207,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 79:[82, 21], Operations: ['46+36=82', '73-52=21'] Exploring Operation: 82+21=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 82*21=1722, Resulting Numbers: [1722] 1722,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[52, 9], Operations: ['46+36=82', '82-73=9'] Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,79 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,79 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: 79:[46, 73, 88], Operations: ['52+36=88'] Exploring Operation: 46+88=134, Resulting Numbers: [73, 134] Generated Node #0,4,0: 79:[73, 134] Operation: 46+88=134 Exploring Operation: 88-46=42, Resulting Numbers: [73, 42] Generated Node #0,4,1: 79:[73, 42] Operation: 88-46=42 Exploring Operation: 88-73=15, Resulting Numbers: [46, 15] Generated Node #0,4,2: 79:[46, 15] Operation: 88-73=15 Exploring Operation: 73-46=27, Resulting Numbers: [88, 27] Generated Node #0,4,3: 79:[88, 27] Operation: 73-46=27 Exploring Operation: 46+73=119, Resulting Numbers: [88, 119] Generated Node #0,4,4: 79:[88, 119] Operation: 46+73=119 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 79:[73, 42], Operations: ['52+36=88', '88-46=42'] Exploring Operation: 73*42=3066, Resulting Numbers: [3066] 3066,79 unequal: No Solution Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 73+42=115, Resulting Numbers: [115] 115,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 79:[88, 119], Operations: ['52+36=88', '46+73=119'] Exploring Operation: 119-88=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 88*119=10472, Resulting Numbers: [10472] 10472,79 unequal: No Solution Exploring Operation: 88+119=207, Resulting Numbers: [207] 207,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 79:[73, 134], Operations: ['52+36=88', '46+88=134'] Exploring Operation: 134-73=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 73*134=9782, Resulting Numbers: [9782] 9782,79 unequal: No Solution Exploring Operation: 73+134=207, Resulting Numbers: [207] 207,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 79:[88, 27], Operations: ['52+36=88', '73-46=27'] Exploring Operation: 88-27=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 88+27=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 88*27=2376, Resulting Numbers: [2376] 2376,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 79:[46, 15], Operations: ['52+36=88', '88-73=15'] Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,79 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 79:[73, 36, 98], Operations: ['46+52=98'] Exploring Operation: 73+36=109, Resulting Numbers: [98, 109] Generated Node #0,0,0: 79:[98, 109] Operation: 73+36=109 Exploring Operation: 98-36=62, Resulting Numbers: [73, 62] Generated Node #0,0,1: 79:[73, 62] Operation: 98-36=62 Exploring Operation: 36+98=134, Resulting Numbers: [73, 134] Generated Node #0,0,2: 79:[73, 134] Operation: 36+98=134 Exploring Operation: 98-73=25, Resulting Numbers: [36, 25] Generated Node #0,0,3: 79:[36, 25] Operation: 98-73=25 Exploring Operation: 73-36=37, Resulting Numbers: [98, 37] Generated Node #0,0,4: 79:[98, 37] Operation: 73-36=37 Moving to Node #0,1 Current State: 79:[46, 52, 109], Operations: ['73+36=109'] Exploring Operation: 46+52=98, Resulting Numbers: [109, 98] Generated Node #0,1,0: 79:[109, 98] Operation: 46+52=98 Exploring Operation: 52-46=6, Resulting Numbers: [109, 6] Generated Node #0,1,1: 79:[109, 6] Operation: 52-46=6 Exploring Operation: 109-52=57, Resulting Numbers: [46, 57] Generated Node #0,1,2: 79:[46, 57] Operation: 109-52=57 Exploring Operation: 109-46=63, Resulting Numbers: [52, 63] Generated Node #0,1,3: 79:[52, 63] Operation: 109-46=63 Exploring Operation: 46+109=155, Resulting Numbers: [52, 155] Generated Node #0,1,4: 79:[52, 155] Operation: 46+109=155 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[52, 63], Operations: ['73+36=109', '109-46=63'] Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 52*63=3276, Resulting Numbers: [3276] 3276,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[109, 98], Operations: ['73+36=109', '46+52=98'] Exploring Operation: 109+98=207, Resulting Numbers: [207] 207,79 unequal: No Solution Exploring Operation: 109-98=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 109*98=10682, Resulting Numbers: [10682] 10682,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[46, 57], Operations: ['73+36=109', '109-52=57'] Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 46+57=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 46*57=2622, Resulting Numbers: [2622] 2622,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[109, 6], Operations: ['73+36=109', '52-46=6'] Exploring Operation: 109-6=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 109*6=654, Resulting Numbers: [654] 654,79 unequal: No Solution Exploring Operation: 109+6=115, Resulting Numbers: [115] 115,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 79:[52, 155], Operations: ['73+36=109', '46+109=155'] Exploring Operation: 155-52=103, Resulting Numbers: [103] 103,79 unequal: No Solution Exploring Operation: 52*155=8060, Resulting Numbers: [8060] 8060,79 unequal: No Solution Exploring Operation: 52+155=207, Resulting Numbers: [207] 207,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 79:[73, 52, 10], Operations: ['46-36=10'] Exploring Operation: 73+52=125, Resulting Numbers: [10, 125] Generated Node #0,2,0: 79:[10, 125] Operation: 73+52=125 Exploring Operation: 73+10=83, Resulting Numbers: [52, 83] Generated Node #0,2,1: 79:[52, 83] Operation: 73+10=83 Exploring Operation: 73-10=63, Resulting Numbers: [52, 63] Generated Node #0,2,2: 79:[52, 63] Operation: 73-10=63 Exploring Operation: 52+10=62, Resulting Numbers: [73, 62] Generated Node #0,2,3: 79:[73, 62] Operation: 52+10=62 Exploring Operation: 52-10=42, Resulting Numbers: [73, 42] Generated Node #0,2,4: 79:[73, 42] Operation: 52-10=42 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[73, 62], Operations: ['46-36=10', '52+10=62'] Exploring Operation: 73*62=4526, Resulting Numbers: [4526] 4526,79 unequal: No Solution Exploring Operation: 73+62=135, Resulting Numbers: [135] 135,79 unequal: No Solution Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[52, 83], Operations: ['46-36=10', '73+10=83'] Exploring Operation: 52+83=135, Resulting Numbers: [135] 135,79 unequal: No Solution Exploring Operation: 52*83=4316, Resulting Numbers: [4316] 4316,79 unequal: No Solution Exploring Operation: 83-52=31, Resulting Numbers: [31] 31,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[52, 63], Operations: ['46-36=10', '73-10=63'] Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 52*63=3276, Resulting Numbers: [3276] 3276,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 79:[73, 42], Operations: ['46-36=10', '52-10=42'] Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 73+42=115, Resulting Numbers: [115] 115,79 unequal: No Solution Exploring Operation: 73*42=3066, Resulting Numbers: [3066] 3066,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[10, 125], Operations: ['46-36=10', '73+52=125'] Exploring Operation: 10+125=135, Resulting Numbers: [135] 135,79 unequal: No Solution Exploring Operation: 10*125=1250, Resulting Numbers: [1250] 1250,79 unequal: No Solution Exploring Operation: 125-10=115, Resulting Numbers: [115] 115,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 79:[73, 62], Operations: ['46+52=98', '98-36=62'] Exploring Operation: 73*62=4526, Resulting Numbers: [4526] 4526,79 unequal: No Solution Exploring Operation: 73-62=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 73+62=135, Resulting Numbers: [135] 135,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[98, 109], Operations: ['46+52=98', '73+36=109'] Exploring Operation: 98+109=207, Resulting Numbers: [207] 207,79 unequal: No Solution Exploring Operation: 98*109=10682, Resulting Numbers: [10682] 10682,79 unequal: No Solution Exploring Operation: 109-98=11, Resulting Numbers: [11] 11,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[73, 134], Operations: ['46+52=98', '36+98=134'] Exploring Operation: 73*134=9782, Resulting Numbers: [9782] 9782,79 unequal: No Solution Exploring Operation: 134-73=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 73+134=207, Resulting Numbers: [207] 207,79 unequal: No Solution Moving to Node #0,0,4 Current State: 79:[98, 37], Operations: ['46+52=98', '73-36=37'] Exploring Operation: 98-37=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 98*37=3626, Resulting Numbers: [3626] 3626,79 unequal: No Solution Exploring Operation: 98+37=135, Resulting Numbers: [135] 135,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[36, 25], Operations: ['46+52=98', '98-73=25'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,79 unequal: No Solution Exploring Operation: 36+25=61, Resulting Numbers: [61] 61,79 unequal: No Solution Exploring Operation: 36*25=900, Resulting Numbers: [900] 900,79 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 79, 19, 7, 89 ]
16
[ "79+19=98", "89-7=82", "98-82=16" ]
Current State: 16:[79, 19, 7, 89], Operations: [] Exploring Operation: 79+19=98, Resulting Numbers: [7, 89, 98] Generated Node #2: [7, 89, 98] from Operation: 79+19=98 Current State: 16:[7, 89, 98], Operations: ['79+19=98'] Exploring Operation: 89-7=82, Resulting Numbers: [98, 82] Generated Node #3: [98, 82] from Operation: 89-7=82 Current State: 16:[98, 82], Operations: ['79+19=98', '89-7=82'] Exploring Operation: 98-82=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[79, 19, 7, 89], Operations: [] Exploring Operation: 89-79=10, Resulting Numbers: [19, 7, 10] Generated Node #0,0: 16:[19, 7, 10] Operation: 89-79=10 Exploring Operation: 79-19=60, Resulting Numbers: [7, 89, 60] Generated Node #0,1: 16:[7, 89, 60] Operation: 79-19=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[19, 7, 10], Operations: ['89-79=10'] Exploring Operation: 7+10=17, Resulting Numbers: [19, 17] Generated Node #0,0,0: 16:[19, 17] Operation: 7+10=17 Exploring Operation: 19-10=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 16:[7, 9] Operation: 19-10=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[7, 9], Operations: ['89-79=10', '19-10=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[79, 19, 7, 89], Operations: [] Exploring Operation: 89-79=10, Resulting Numbers: [19, 7, 10] Generated Node #0,0: 16:[19, 7, 10] Operation: 89-79=10 Moving to Node #0,0 Current State: 16:[19, 7, 10], Operations: ['89-79=10'] Exploring Operation: 19-10=9, Resulting Numbers: [7, 9] Generated Node #0,0,1: 16:[7, 9] Operation: 19-10=9 Moving to Node #0,0,1 Current State: 16:[7, 9], Operations: ['89-79=10', '19-10=9'] Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 81, 7, 89, 95 ]
96
[ "81+7=88", "89+95=184", "184-88=96" ]
Current State: 96:[81, 7, 89, 95], Operations: [] Exploring Operation: 81+7=88, Resulting Numbers: [89, 95, 88] Generated Node #2: [89, 95, 88] from Operation: 81+7=88 Current State: 96:[89, 95, 88], Operations: ['81+7=88'] Exploring Operation: 89+95=184, Resulting Numbers: [88, 184] Generated Node #3: [88, 184] from Operation: 89+95=184 Current State: 96:[88, 184], Operations: ['81+7=88', '89+95=184'] Exploring Operation: 184-88=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[81, 7, 89, 95], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [7, 89, 14] Generated Node #0,0: 96:[7, 89, 14] Operation: 95-81=14 Exploring Operation: 81+7=88, Resulting Numbers: [89, 95, 88] Generated Node #0,1: 96:[89, 95, 88] Operation: 81+7=88 Exploring Operation: 95-89=6, Resulting Numbers: [81, 7, 6] Generated Node #0,2: 96:[81, 7, 6] Operation: 95-89=6 Exploring Operation: 89-81=8, Resulting Numbers: [7, 95, 8] Generated Node #0,3: 96:[7, 95, 8] Operation: 89-81=8 Exploring Operation: 7+89=96, Resulting Numbers: [81, 95, 96] Generated Node #0,4: 96:[81, 95, 96] Operation: 7+89=96 Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[7, 95, 8], Operations: ['89-81=8'] Exploring Operation: 7+95=102, Resulting Numbers: [8, 102] Generated Node #0,3,0: 96:[8, 102] Operation: 7+95=102 Exploring Operation: 7+8=15, Resulting Numbers: [95, 15] Generated Node #0,3,1: 96:[95, 15] Operation: 7+8=15 Exploring Operation: 8-7=1, Resulting Numbers: [95, 1] Generated Node #0,3,2: 96:[95, 1] Operation: 8-7=1 Exploring Operation: 95-7=88, Resulting Numbers: [8, 88] Generated Node #0,3,3: 96:[8, 88] Operation: 95-7=88 Exploring Operation: 95+8=103, Resulting Numbers: [7, 103] Generated Node #0,3,4: 96:[7, 103] Operation: 95+8=103 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 96:[95, 15], Operations: ['89-81=8', '7+8=15'] Exploring Operation: 95-15=80, Resulting Numbers: [80] 80,96 unequal: No Solution Exploring Operation: 95+15=110, Resulting Numbers: [110] 110,96 unequal: No Solution Exploring Operation: 95*15=1425, Resulting Numbers: [1425] 1425,96 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:[95, 1], Operations: ['89-81=8', '8-7=1'] Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[81, 7, 89, 95], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [7, 95, 8] Generated Node #0,3: 96:[7, 95, 8] Operation: 89-81=8 Moving to Node #0,3 Current State: 96:[7, 95, 8], Operations: ['89-81=8'] Exploring Operation: 8-7=1, Resulting Numbers: [95, 1] Generated Node #0,3,2: 96:[95, 1] Operation: 8-7=1 Moving to Node #0,3,2 Current State: 96:[95, 1], Operations: ['89-81=8', '8-7=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 16, 48, 1, 17 ]
80
[ "16+48=64", "17-1=16", "64+16=80" ]
Current State: 80:[16, 48, 1, 17], Operations: [] Exploring Operation: 16+48=64, Resulting Numbers: [1, 17, 64] Generated Node #2: [1, 17, 64] from Operation: 16+48=64 Current State: 80:[1, 17, 64], Operations: ['16+48=64'] Exploring Operation: 17-1=16, Resulting Numbers: [64, 16] Generated Node #3: [64, 16] from Operation: 17-1=16 Current State: 80:[64, 16], Operations: ['16+48=64', '17-1=16'] Exploring Operation: 64+16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[16, 48, 1, 17], Operations: [] Exploring Operation: 48-1=47, Resulting Numbers: [16, 17, 47] Generated Node #0,0: 80:[16, 17, 47] Operation: 48-1=47 Exploring Operation: 48/16=3, Resulting Numbers: [1, 17, 3] Generated Node #0,1: 80:[1, 17, 3] Operation: 48/16=3 Moving to Node #0,1 Current State: 80:[1, 17, 3], Operations: ['48/16=3'] Exploring Operation: 17-1=16, Resulting Numbers: [3, 16] Generated Node #0,1,0: 80:[3, 16] Operation: 17-1=16 Exploring Operation: 1+3=4, Resulting Numbers: [17, 4] Generated Node #0,1,1: 80:[17, 4] Operation: 1+3=4 Moving to Node #0,0 Current State: 80:[16, 17, 47], Operations: ['48-1=47'] Exploring Operation: 47-16=31, Resulting Numbers: [17, 31] Generated Node #0,0,0: 80:[17, 31] Operation: 47-16=31 Exploring Operation: 17-16=1, Resulting Numbers: [47, 1] Generated Node #0,0,1: 80:[47, 1] Operation: 17-16=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[47, 1], Operations: ['48-1=47', '17-16=1'] Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,80 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[17, 31], Operations: ['48-1=47', '47-16=31'] Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,80 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: 80:[3, 16], Operations: ['48/16=3', '17-1=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,80 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[17, 4], Operations: ['48/16=3', '1+3=4'] Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,80 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 69, 14, 25, 84 ]
88
[ "69+25=94", "84/14=6", "94-6=88" ]
Current State: 88:[69, 14, 25, 84], Operations: [] Exploring Operation: 69+25=94, Resulting Numbers: [14, 84, 94] Generated Node #2: [14, 84, 94] from Operation: 69+25=94 Current State: 88:[14, 84, 94], Operations: ['69+25=94'] Exploring Operation: 84/14=6, Resulting Numbers: [94, 6] Generated Node #3: [94, 6] from Operation: 84/14=6 Current State: 88:[94, 6], Operations: ['69+25=94', '84/14=6'] Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[69, 14, 25, 84], Operations: [] Exploring Operation: 69+14=83, Resulting Numbers: [25, 84, 83] Generated Node #0,0: 88:[25, 84, 83] Operation: 69+14=83 Exploring Operation: 69-25=44, Resulting Numbers: [14, 84, 44] Generated Node #0,1: 88:[14, 84, 44] Operation: 69-25=44 Exploring Operation: 84-69=15, Resulting Numbers: [14, 25, 15] Generated Node #0,2: 88:[14, 25, 15] Operation: 84-69=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[14, 84, 44], Operations: ['69-25=44'] Exploring Operation: 84-44=40, Resulting Numbers: [14, 40] Generated Node #0,1,0: 88:[14, 40] Operation: 84-44=40 Exploring Operation: 84/14=6, Resulting Numbers: [44, 6] Generated Node #0,1,1: 88:[44, 6] Operation: 84/14=6 Exploring Operation: 14+84=98, Resulting Numbers: [44, 98] Generated Node #0,1,2: 88:[44, 98] Operation: 14+84=98 Moving to Node #0,1,1 Current State: 88:[44, 6], Operations: ['69-25=44', '84/14=6'] Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,88 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[14, 40], Operations: ['69-25=44', '84-44=40'] Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,88 unequal: No Solution Exploring Operation: 14*40=560, Resulting Numbers: [560] 560,88 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[44, 98], Operations: ['69-25=44', '14+84=98'] Exploring Operation: 44*98=4312, Resulting Numbers: [4312] 4312,88 unequal: No Solution Exploring Operation: 98-44=54, Resulting Numbers: [54] 54,88 unequal: No Solution Exploring Operation: 44+98=142, Resulting Numbers: [142] 142,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[14, 25, 15], Operations: ['84-69=15'] Exploring Operation: 25-14=11, Resulting Numbers: [15, 11] Generated Node #0,2,0: 88:[15, 11] Operation: 25-14=11 Exploring Operation: 15-14=1, Resulting Numbers: [25, 1] Generated Node #0,2,1: 88:[25, 1] Operation: 15-14=1 Exploring Operation: 25-15=10, Resulting Numbers: [14, 10] Generated Node #0,2,2: 88:[14, 10] Operation: 25-15=10 Moving to Node #0,2,0 Current State: 88:[15, 11], Operations: ['84-69=15', '25-14=11'] Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[25, 1], Operations: ['84-69=15', '15-14=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[14, 10], Operations: ['84-69=15', '25-15=10'] Exploring Operation: 14*10=140, Resulting Numbers: [140] 140,88 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[25, 84, 83], Operations: ['69+14=83'] Exploring Operation: 83-25=58, Resulting Numbers: [84, 58] Generated Node #0,0,0: 88:[84, 58] Operation: 83-25=58 Exploring Operation: 84-25=59, Resulting Numbers: [83, 59] Generated Node #0,0,1: 88:[83, 59] Operation: 84-25=59 Exploring Operation: 84-83=1, Resulting Numbers: [25, 1] Generated Node #0,0,2: 88:[25, 1] Operation: 84-83=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[25, 1], Operations: ['69+14=83', '84-83=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[84, 58], Operations: ['69+14=83', '83-25=58'] Exploring Operation: 84*58=4872, Resulting Numbers: [4872] 4872,88 unequal: No Solution Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 84+58=142, Resulting Numbers: [142] 142,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[83, 59], Operations: ['69+14=83', '84-25=59'] Exploring Operation: 83-59=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 83*59=4897, Resulting Numbers: [4897] 4897,88 unequal: No Solution Exploring Operation: 83+59=142, Resulting Numbers: [142] 142,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 24, 22, 64, 68 ]
66
[ "24-22=2", "64+68=132", "132/2=66" ]
Current State: 66:[24, 22, 64, 68], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [64, 68, 2] Generated Node #2: [64, 68, 2] from Operation: 24-22=2 Current State: 66:[64, 68, 2], Operations: ['24-22=2'] Exploring Operation: 64+68=132, Resulting Numbers: [2, 132] Generated Node #3: [2, 132] from Operation: 64+68=132 Current State: 66:[2, 132], Operations: ['24-22=2', '64+68=132'] Exploring Operation: 132/2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[24, 22, 64, 68], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [24, 22, 4] Generated Node #0,0: 66:[24, 22, 4] Operation: 68-64=4 Moving to Node #0,0 Current State: 66:[24, 22, 4], Operations: ['68-64=4'] Exploring Operation: 24/4=6, Resulting Numbers: [22, 6] Generated Node #0,0,0: 66:[22, 6] Operation: 24/4=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 66:[22, 6], Operations: ['68-64=4', '24/4=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 46, 2, 30, 85 ]
67
[ "46+2=48", "30+85=115", "115-48=67" ]
Current State: 67:[46, 2, 30, 85], Operations: [] Exploring Operation: 46+2=48, Resulting Numbers: [30, 85, 48] Generated Node #2: [30, 85, 48] from Operation: 46+2=48 Current State: 67:[30, 85, 48], Operations: ['46+2=48'] Exploring Operation: 30+85=115, Resulting Numbers: [48, 115] Generated Node #3: [48, 115] from Operation: 30+85=115 Current State: 67:[48, 115], Operations: ['46+2=48', '30+85=115'] Exploring Operation: 115-48=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[46, 2, 30, 85], Operations: [] Exploring Operation: 46+2=48, Resulting Numbers: [30, 85, 48] Generated Node #0,0: 67:[30, 85, 48] Operation: 46+2=48 Exploring Operation: 2*30=60, Resulting Numbers: [46, 85, 60] Generated Node #0,1: 67:[46, 85, 60] Operation: 2*30=60 Exploring Operation: 85-2=83, Resulting Numbers: [46, 30, 83] Generated Node #0,2: 67:[46, 30, 83] Operation: 85-2=83 Exploring Operation: 2+30=32, Resulting Numbers: [46, 85, 32] Generated Node #0,3: 67:[46, 85, 32] Operation: 2+30=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[46, 85, 60], Operations: ['2*30=60'] Exploring Operation: 85-60=25, Resulting Numbers: [46, 25] Generated Node #0,1,0: 67:[46, 25] Operation: 85-60=25 Exploring Operation: 46+85=131, Resulting Numbers: [60, 131] Generated Node #0,1,1: 67:[60, 131] Operation: 46+85=131 Exploring Operation: 85-46=39, Resulting Numbers: [60, 39] Generated Node #0,1,2: 67:[60, 39] Operation: 85-46=39 Exploring Operation: 46+60=106, Resulting Numbers: [85, 106] Generated Node #0,1,3: 67:[85, 106] Operation: 46+60=106 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 67:[60, 39], Operations: ['2*30=60', '85-46=39'] Exploring Operation: 60-39=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 60*39=2340, Resulting Numbers: [2340] 2340,67 unequal: No Solution Exploring Operation: 60+39=99, Resulting Numbers: [99] 99,67 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:[85, 106], Operations: ['2*30=60', '46+60=106'] Exploring Operation: 85+106=191, Resulting Numbers: [191] 191,67 unequal: No Solution Exploring Operation: 106-85=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 85*106=9010, Resulting Numbers: [9010] 9010,67 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 #0,1,0 Current State: 67:[46, 25], Operations: ['2*30=60', '85-60=25'] Exploring Operation: 46+25=71, Resulting Numbers: [71] 71,67 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 46*25=1150, Resulting Numbers: [1150] 1150,67 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:[60, 131], Operations: ['2*30=60', '46+85=131'] Exploring Operation: 131-60=71, Resulting Numbers: [71] 71,67 unequal: No Solution Exploring Operation: 60+131=191, Resulting Numbers: [191] 191,67 unequal: No Solution Exploring Operation: 60*131=7860, Resulting Numbers: [7860] 7860,67 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 #0,0 Current State: 67:[30, 85, 48], Operations: ['46+2=48'] Exploring Operation: 30+85=115, Resulting Numbers: [48, 115] Generated Node #0,0,0: 67:[48, 115] Operation: 30+85=115 Exploring Operation: 85-30=55, Resulting Numbers: [48, 55] Generated Node #0,0,1: 67:[48, 55] Operation: 85-30=55 Exploring Operation: 48-30=18, Resulting Numbers: [85, 18] Generated Node #0,0,2: 67:[85, 18] Operation: 48-30=18 Exploring Operation: 30+48=78, Resulting Numbers: [85, 78] Generated Node #0,0,3: 67:[85, 78] Operation: 30+48=78 Moving to Node #0,0,3 Current State: 67:[85, 78], Operations: ['46+2=48', '30+48=78'] Exploring Operation: 85-78=7, Resulting Numbers: [7] 7,67 unequal: No Solution Exploring Operation: 85*78=6630, Resulting Numbers: [6630] 6630,67 unequal: No Solution Exploring Operation: 85+78=163, Resulting Numbers: [163] 163,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[48, 55], Operations: ['46+2=48', '85-30=55'] Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,67 unequal: No Solution Exploring Operation: 48*55=2640, Resulting Numbers: [2640] 2640,67 unequal: No Solution Exploring Operation: 48+55=103, Resulting Numbers: [103] 103,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[85, 18], Operations: ['46+2=48', '48-30=18'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[46, 2, 30, 85], Operations: [] Exploring Operation: 46+2=48, Resulting Numbers: [30, 85, 48] Generated Node #0,0: 67:[30, 85, 48] Operation: 46+2=48 Moving to Node #0,0 Current State: 67:[30, 85, 48], Operations: ['46+2=48'] Exploring Operation: 48-30=18, Resulting Numbers: [85, 18] Generated Node #0,0,2: 67:[85, 18] Operation: 48-30=18 Moving to Node #0,0,2 Current State: 67:[85, 18], Operations: ['46+2=48', '48-30=18'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_4
mult_heuristic
[ 5, 4, 72, 18 ]
22
[ "5*18=90", "72-4=68", "90-68=22" ]
Current State: 22:[5, 4, 72, 18], Operations: [] Exploring Operation: 5*18=90, Resulting Numbers: [4, 72, 90] Generated Node #2: [4, 72, 90] from Operation: 5*18=90 Current State: 22:[4, 72, 90], Operations: ['5*18=90'] Exploring Operation: 72-4=68, Resulting Numbers: [90, 68] Generated Node #3: [90, 68] from Operation: 72-4=68 Current State: 22:[90, 68], Operations: ['5*18=90', '72-4=68'] Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[5, 4, 72, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [5, 4, 4] Generated Node #0,0: 22:[5, 4, 4] Operation: 72/18=4 Exploring Operation: 72/4=18, Resulting Numbers: [5, 18, 18] Generated Node #0,1: 22:[5, 18, 18] Operation: 72/4=18 Moving to Node #0,0 Current State: 22:[5, 4, 4], Operations: ['72/18=4'] Exploring Operation: 5-4=1, Resulting Numbers: [4, 1] Generated Node #0,0,0: 22:[4, 1] Operation: 5-4=1 Exploring Operation: 5-4=1, Resulting Numbers: [4, 1] Generated Node #0,0,1: 22:[4, 1] Operation: 5-4=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[4, 1], Operations: ['72/18=4', '5-4=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,22 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:[4, 1], Operations: ['72/18=4', '5-4=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,22 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:[5, 18, 18], Operations: ['72/4=18'] Exploring Operation: 18/18=1, Resulting Numbers: [5, 1] Generated Node #0,1,0: 22:[5, 1] Operation: 18/18=1 Exploring Operation: 5+18=23, Resulting Numbers: [18, 23] Generated Node #0,1,1: 22:[18, 23] Operation: 5+18=23 Moving to Node #0,1,0 Current State: 22:[5, 1], Operations: ['72/4=18', '18/18=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[18, 23], Operations: ['72/4=18', '5+18=23'] Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,22 unequal: No Solution Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,22 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 5, 67, 83, 19 ]
55
[ "5*19=95", "67+83=150", "150-95=55" ]
Current State: 55:[5, 67, 83, 19], Operations: [] Exploring Operation: 5*19=95, Resulting Numbers: [67, 83, 95] Generated Node #2: [67, 83, 95] from Operation: 5*19=95 Current State: 55:[67, 83, 95], Operations: ['5*19=95'] Exploring Operation: 67+83=150, Resulting Numbers: [95, 150] Generated Node #3: [95, 150] from Operation: 67+83=150 Current State: 55:[95, 150], Operations: ['5*19=95', '67+83=150'] Exploring Operation: 150-95=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 67, 83, 19], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [5, 19, 16] Generated Node #0,0: 55:[5, 19, 16] Operation: 83-67=16 Exploring Operation: 83-19=64, Resulting Numbers: [5, 67, 64] Generated Node #0,1: 55:[5, 67, 64] Operation: 83-19=64 Moving to Node #0,0 Current State: 55:[5, 19, 16], Operations: ['83-67=16'] Exploring Operation: 19-16=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 55:[5, 3] Operation: 19-16=3 Exploring Operation: 19-5=14, Resulting Numbers: [16, 14] Generated Node #0,0,1: 55:[16, 14] Operation: 19-5=14 Moving to Node #0,1 Current State: 55:[5, 67, 64], Operations: ['83-19=64'] Exploring Operation: 67-5=62, Resulting Numbers: [64, 62] Generated Node #0,1,0: 55:[64, 62] Operation: 67-5=62 Exploring Operation: 67-64=3, Resulting Numbers: [5, 3] Generated Node #0,1,1: 55:[5, 3] Operation: 67-64=3 Moving to Node #0,0,0 Current State: 55:[5, 3], Operations: ['83-67=16', '19-16=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[5, 3], Operations: ['83-19=64', '67-64=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[16, 14], Operations: ['83-67=16', '19-5=14'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[64, 62], Operations: ['83-19=64', '67-5=62'] Exploring Operation: 64-62=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 64+62=126, Resulting Numbers: [126] 126,55 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 48, 24, 26, 11 ]
57
[ "48+24=72", "26-11=15", "72-15=57" ]
Current State: 57:[48, 24, 26, 11], Operations: [] Exploring Operation: 48+24=72, Resulting Numbers: [26, 11, 72] Generated Node #2: [26, 11, 72] from Operation: 48+24=72 Current State: 57:[26, 11, 72], Operations: ['48+24=72'] Exploring Operation: 26-11=15, Resulting Numbers: [72, 15] Generated Node #3: [72, 15] from Operation: 26-11=15 Current State: 57:[72, 15], Operations: ['48+24=72', '26-11=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[48, 24, 26, 11], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [24, 11, 22] Generated Node #0,0: 57:[24, 11, 22] Operation: 48-26=22 Exploring Operation: 26-24=2, Resulting Numbers: [48, 11, 2] Generated Node #0,1: 57:[48, 11, 2] Operation: 26-24=2 Exploring Operation: 48/24=2, Resulting Numbers: [26, 11, 2] Generated Node #0,2: 57:[26, 11, 2] Operation: 48/24=2 Exploring Operation: 48+11=59, Resulting Numbers: [24, 26, 59] Generated Node #0,3: 57:[24, 26, 59] Operation: 48+11=59 Exploring Operation: 26-11=15, Resulting Numbers: [48, 24, 15] Generated Node #0,4: 57:[48, 24, 15] Operation: 26-11=15 Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[24, 26, 59], Operations: ['48+11=59'] Exploring Operation: 59-26=33, Resulting Numbers: [24, 33] Generated Node #0,3,0: 57:[24, 33] Operation: 59-26=33 Exploring Operation: 24+26=50, Resulting Numbers: [59, 50] Generated Node #0,3,1: 57:[59, 50] Operation: 24+26=50 Exploring Operation: 24+59=83, Resulting Numbers: [26, 83] Generated Node #0,3,2: 57:[26, 83] Operation: 24+59=83 Exploring Operation: 59-24=35, Resulting Numbers: [26, 35] Generated Node #0,3,3: 57:[26, 35] Operation: 59-24=35 Exploring Operation: 26-24=2, Resulting Numbers: [59, 2] Generated Node #0,3,4: 57:[59, 2] Operation: 26-24=2 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 57:[59, 2], Operations: ['48+11=59', '26-24=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 59*2=118, Resulting Numbers: [118] 118,57 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[48, 24, 26, 11], Operations: [] Exploring Operation: 48+11=59, Resulting Numbers: [24, 26, 59] Generated Node #0,3: 57:[24, 26, 59] Operation: 48+11=59 Moving to Node #0,3 Current State: 57:[24, 26, 59], Operations: ['48+11=59'] Exploring Operation: 26-24=2, Resulting Numbers: [59, 2] Generated Node #0,3,4: 57:[59, 2] Operation: 26-24=2 Moving to Node #0,3,4 Current State: 57:[59, 2], Operations: ['48+11=59', '26-24=2'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 14, 42, 9, 45 ]
82
[ "42-14=28", "9+45=54", "28+54=82" ]
Current State: 82:[14, 42, 9, 45], Operations: [] Exploring Operation: 42-14=28, Resulting Numbers: [9, 45, 28] Generated Node #2: [9, 45, 28] from Operation: 42-14=28 Current State: 82:[9, 45, 28], Operations: ['42-14=28'] Exploring Operation: 9+45=54, Resulting Numbers: [28, 54] Generated Node #3: [28, 54] from Operation: 9+45=54 Current State: 82:[28, 54], Operations: ['42-14=28', '9+45=54'] Exploring Operation: 28+54=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[14, 42, 9, 45], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [9, 45, 3] Generated Node #0,0: 82:[9, 45, 3] Operation: 42/14=3 Exploring Operation: 45/9=5, Resulting Numbers: [14, 42, 5] Generated Node #0,1: 82:[14, 42, 5] Operation: 45/9=5 Exploring Operation: 45-9=36, Resulting Numbers: [14, 42, 36] Generated Node #0,2: 82:[14, 42, 36] Operation: 45-9=36 Exploring Operation: 14-9=5, Resulting Numbers: [42, 45, 5] Generated Node #0,3: 82:[42, 45, 5] Operation: 14-9=5 Exploring Operation: 45-14=31, Resulting Numbers: [42, 9, 31] Generated Node #0,4: 82:[42, 9, 31] Operation: 45-14=31 Moving to Node #0,3 Current State: 82:[42, 45, 5], Operations: ['14-9=5'] Exploring Operation: 45-5=40, Resulting Numbers: [42, 40] Generated Node #0,3,0: 82:[42, 40] Operation: 45-5=40 Exploring Operation: 42-5=37, Resulting Numbers: [45, 37] Generated Node #0,3,1: 82:[45, 37] Operation: 42-5=37 Exploring Operation: 42+45=87, Resulting Numbers: [5, 87] Generated Node #0,3,2: 82:[5, 87] Operation: 42+45=87 Exploring Operation: 45-42=3, Resulting Numbers: [5, 3] Generated Node #0,3,3: 82:[5, 3] Operation: 45-42=3 Exploring Operation: 45/5=9, Resulting Numbers: [42, 9] Generated Node #0,3,4: 82:[42, 9] Operation: 45/5=9 Moving to Node #0,0 Current State: 82:[9, 45, 3], Operations: ['42/14=3'] Exploring Operation: 9/3=3, Resulting Numbers: [45, 3] Generated Node #0,0,0: 82:[45, 3] Operation: 9/3=3 Exploring Operation: 45-9=36, Resulting Numbers: [3, 36] Generated Node #0,0,1: 82:[3, 36] Operation: 45-9=36 Exploring Operation: 9-3=6, Resulting Numbers: [45, 6] Generated Node #0,0,2: 82:[45, 6] Operation: 9-3=6 Exploring Operation: 45/9=5, Resulting Numbers: [3, 5] Generated Node #0,0,3: 82:[3, 5] Operation: 45/9=5 Exploring Operation: 45-3=42, Resulting Numbers: [9, 42] Generated Node #0,0,4: 82:[9, 42] Operation: 45-3=42 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 82:[3, 5], Operations: ['42/14=3', '45/9=5'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,82 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,82 unequal: No Solution No 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: 82:[45, 3], Operations: ['42/14=3', '9/3=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,82 unequal: No Solution Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,82 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,82 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,82 unequal: No Solution No 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: 82:[3, 36], Operations: ['42/14=3', '45-9=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,82 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,82 unequal: No Solution No 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: 82:[45, 6], Operations: ['42/14=3', '9-3=6'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,82 unequal: No Solution Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,82 unequal: No Solution No 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: 82:[9, 42], Operations: ['42/14=3', '45-3=42'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,82 unequal: No Solution Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,82 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: 82:[14, 42, 5], Operations: ['45/9=5'] Exploring Operation: 14-5=9, Resulting Numbers: [42, 9] Generated Node #0,1,0: 82:[42, 9] Operation: 14-5=9 Exploring Operation: 42-14=28, Resulting Numbers: [5, 28] Generated Node #0,1,1: 82:[5, 28] Operation: 42-14=28 Exploring Operation: 14*5=70, Resulting Numbers: [42, 70] Generated Node #0,1,2: 82:[42, 70] Operation: 14*5=70 Exploring Operation: 42-5=37, Resulting Numbers: [14, 37] Generated Node #0,1,3: 82:[14, 37] Operation: 42-5=37 Exploring Operation: 42/14=3, Resulting Numbers: [5, 3] Generated Node #0,1,4: 82:[5, 3] Operation: 42/14=3 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 82:[5, 3], Operations: ['45/9=5', '42/14=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,82 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,82 unequal: No Solution No 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: 82:[42, 9], Operations: ['45/9=5', '14-5=9'] Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,82 unequal: No Solution Exploring Operation: 42*9=378, Resulting Numbers: [378] 378,82 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,82 unequal: No Solution No 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: 82:[42, 70], Operations: ['45/9=5', '14*5=70'] Exploring Operation: 42*70=2940, Resulting Numbers: [2940] 2940,82 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,82 unequal: No Solution Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,82 unequal: No Solution No 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: 82:[5, 28], Operations: ['45/9=5', '42-14=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,82 unequal: No Solution No 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: 82:[14, 37], Operations: ['45/9=5', '42-5=37'] Exploring Operation: 14*37=518, Resulting Numbers: [518] 518,82 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,82 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: 82:[14, 42, 36], Operations: ['45-9=36'] Exploring Operation: 42+36=78, Resulting Numbers: [14, 78] Generated Node #0,2,0: 82:[14, 78] Operation: 42+36=78 Exploring Operation: 42-14=28, Resulting Numbers: [36, 28] Generated Node #0,2,1: 82:[36, 28] Operation: 42-14=28 Exploring Operation: 42/14=3, Resulting Numbers: [36, 3] Generated Node #0,2,2: 82:[36, 3] Operation: 42/14=3 Exploring Operation: 14+36=50, Resulting Numbers: [42, 50] Generated Node #0,2,3: 82:[42, 50] Operation: 14+36=50 Exploring Operation: 42-36=6, Resulting Numbers: [14, 6] Generated Node #0,2,4: 82:[14, 6] Operation: 42-36=6 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 82:[36, 3], Operations: ['45-9=36', '42/14=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,82 unequal: No Solution No 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: 82:[42, 50], Operations: ['45-9=36', '14+36=50'] Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,82 unequal: No Solution No 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: 82:[14, 78], Operations: ['45-9=36', '42+36=78'] Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 14*78=1092, Resulting Numbers: [1092] 1092,82 unequal: No Solution Exploring Operation: 14+78=92, Resulting Numbers: [92] 92,82 unequal: No Solution No 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: 82:[14, 6], Operations: ['45-9=36', '42-36=6'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,82 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,82 unequal: No Solution No 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: 82:[36, 28], Operations: ['45-9=36', '42-14=28'] Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,82 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,82 unequal: No Solution Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,82 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: 82:[42, 9, 31], Operations: ['45-14=31'] Exploring Operation: 9+31=40, Resulting Numbers: [42, 40] Generated Node #0,4,0: 82:[42, 40] Operation: 9+31=40 Exploring Operation: 42+31=73, Resulting Numbers: [9, 73] Generated Node #0,4,1: 82:[9, 73] Operation: 42+31=73 Exploring Operation: 42-9=33, Resulting Numbers: [31, 33] Generated Node #0,4,2: 82:[31, 33] Operation: 42-9=33 Exploring Operation: 42+9=51, Resulting Numbers: [31, 51] Generated Node #0,4,3: 82:[31, 51] Operation: 42+9=51 Exploring Operation: 42-31=11, Resulting Numbers: [9, 11] Generated Node #0,4,4: 82:[9, 11] Operation: 42-31=11 Moving to Node #0,3,0 Current State: 82:[42, 40], Operations: ['14-9=5', '45-5=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[14, 42, 9, 45], Operations: [] Exploring Operation: 14-9=5, Resulting Numbers: [42, 45, 5] Generated Node #0,3: 82:[42, 45, 5] Operation: 14-9=5 Moving to Node #0,3 Current State: 82:[42, 45, 5], Operations: ['14-9=5'] Exploring Operation: 45-5=40, Resulting Numbers: [42, 40] Generated Node #0,3,0: 82:[42, 40] Operation: 45-5=40 Moving to Node #0,3,0 Current State: 82:[42, 40], Operations: ['14-9=5', '45-5=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
0.927951
hs_5
mult_heuristic
[ 51, 49, 34, 78 ]
46
[ "51-49=2", "78-34=44", "2+44=46" ]
Current State: 46:[51, 49, 34, 78], Operations: [] Exploring Operation: 51-49=2, Resulting Numbers: [34, 78, 2] Generated Node #2: [34, 78, 2] from Operation: 51-49=2 Current State: 46:[34, 78, 2], Operations: ['51-49=2'] Exploring Operation: 78-34=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 78-34=44 Current State: 46:[2, 44], Operations: ['51-49=2', '78-34=44'] Exploring Operation: 2+44=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[51, 49, 34, 78], Operations: [] Exploring Operation: 78-34=44, Resulting Numbers: [51, 49, 44] Generated Node #0,0: 46:[51, 49, 44] Operation: 78-34=44 Exploring Operation: 78-51=27, Resulting Numbers: [49, 34, 27] Generated Node #0,1: 46:[49, 34, 27] Operation: 78-51=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[51, 49, 44], Operations: ['78-34=44'] Exploring Operation: 51-49=2, Resulting Numbers: [44, 2] Generated Node #0,0,0: 46:[44, 2] Operation: 51-49=2 Exploring Operation: 51-44=7, Resulting Numbers: [49, 7] Generated Node #0,0,1: 46:[49, 7] Operation: 51-44=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[44, 2], Operations: ['78-34=44', '51-49=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[51, 49, 34, 78], Operations: [] Exploring Operation: 78-34=44, Resulting Numbers: [51, 49, 44] Generated Node #0,0: 46:[51, 49, 44] Operation: 78-34=44 Moving to Node #0,0 Current State: 46:[51, 49, 44], Operations: ['78-34=44'] Exploring Operation: 51-49=2, Resulting Numbers: [44, 2] Generated Node #0,0,0: 46:[44, 2] Operation: 51-49=2 Moving to Node #0,0,0 Current State: 46:[44, 2], Operations: ['78-34=44', '51-49=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 19, 4, 33, 18 ]
61
[ "19*4=76", "33-18=15", "76-15=61" ]
Current State: 61:[19, 4, 33, 18], Operations: [] Exploring Operation: 19*4=76, Resulting Numbers: [33, 18, 76] Generated Node #2: [33, 18, 76] from Operation: 19*4=76 Current State: 61:[33, 18, 76], Operations: ['19*4=76'] Exploring Operation: 33-18=15, Resulting Numbers: [76, 15] Generated Node #3: [76, 15] from Operation: 33-18=15 Current State: 61:[76, 15], Operations: ['19*4=76', '33-18=15'] Exploring Operation: 76-15=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[19, 4, 33, 18], Operations: [] Exploring Operation: 4*18=72, Resulting Numbers: [19, 33, 72] Generated Node #0,0: 61:[19, 33, 72] Operation: 4*18=72 Moving to Node #0,0 Current State: 61:[19, 33, 72], Operations: ['4*18=72'] Exploring Operation: 19+33=52, Resulting Numbers: [72, 52] Generated Node #0,0,0: 61:[72, 52] Operation: 19+33=52 Moving to Node #0,0,0 Current State: 61:[72, 52], Operations: ['4*18=72', '19+33=52'] Exploring Operation: 72-52=20, Resulting Numbers: [20] 20,61 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 3, 45, 18, 10 ]
84
[ "45*18=810", "810/10=81", "3+81=84" ]
Current State: 84:[3, 45, 18, 10], Operations: [] Exploring Operation: 45*18=810, Resulting Numbers: [3, 10, 810] Generated Node #2: [3, 10, 810] from Operation: 45*18=810 Current State: 84:[3, 10, 810], Operations: ['45*18=810'] Exploring Operation: 810/10=81, Resulting Numbers: [3, 81] Generated Node #3: [3, 81] from Operation: 810/10=81 Current State: 84:[3, 81], Operations: ['45*18=810', '810/10=81'] Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[3, 45, 18, 10], Operations: [] Exploring Operation: 3+18=21, Resulting Numbers: [45, 10, 21] Generated Node #0,0: 84:[45, 10, 21] Operation: 3+18=21 Exploring Operation: 18-10=8, Resulting Numbers: [3, 45, 8] Generated Node #0,1: 84:[3, 45, 8] Operation: 18-10=8 Exploring Operation: 45-3=42, Resulting Numbers: [18, 10, 42] Generated Node #0,2: 84:[18, 10, 42] Operation: 45-3=42 Exploring Operation: 18+10=28, Resulting Numbers: [3, 45, 28] Generated Node #0,3: 84:[3, 45, 28] Operation: 18+10=28 Exploring Operation: 45-18=27, Resulting Numbers: [3, 10, 27] Generated Node #0,4: 84:[3, 10, 27] Operation: 45-18=27 Moving to Node #0,3 Current State: 84:[3, 45, 28], Operations: ['18+10=28'] Exploring Operation: 45-3=42, Resulting Numbers: [28, 42] Generated Node #0,3,0: 84:[28, 42] Operation: 45-3=42 Exploring Operation: 3+45=48, Resulting Numbers: [28, 48] Generated Node #0,3,1: 84:[28, 48] Operation: 3+45=48 Exploring Operation: 45/3=15, Resulting Numbers: [28, 15] Generated Node #0,3,2: 84:[28, 15] Operation: 45/3=15 Exploring Operation: 45-28=17, Resulting Numbers: [3, 17] Generated Node #0,3,3: 84:[3, 17] Operation: 45-28=17 Exploring Operation: 3*28=84, Resulting Numbers: [45, 84] Generated Node #0,3,4: 84:[45, 84] Operation: 3*28=84 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[28, 42], Operations: ['18+10=28', '45-3=42'] Exploring Operation: 28*42=1176, Resulting Numbers: [1176] 1176,84 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 28+42=70, Resulting Numbers: [70] 70,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[28, 15], Operations: ['18+10=28', '45/3=15'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,84 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[3, 17], Operations: ['18+10=28', '45-28=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 84:[45, 84], Operations: ['18+10=28', '3*28=84'] Exploring Operation: 45+84=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 45*84=3780, Resulting Numbers: [3780] 3780,84 unequal: No Solution Exploring Operation: 84-45=39, Resulting Numbers: [39] 39,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[28, 48], Operations: ['18+10=28', '3+45=48'] Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 28*48=1344, Resulting Numbers: [1344] 1344,84 unequal: No Solution Exploring Operation: 28+48=76, Resulting Numbers: [76] 76,84 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: 84:[3, 10, 27], Operations: ['45-18=27'] Exploring Operation: 10-3=7, Resulting Numbers: [27, 7] Generated Node #0,4,0: 84:[27, 7] Operation: 10-3=7 Exploring Operation: 3+10=13, Resulting Numbers: [27, 13] Generated Node #0,4,1: 84:[27, 13] Operation: 3+10=13 Exploring Operation: 3+27=30, Resulting Numbers: [10, 30] Generated Node #0,4,2: 84:[10, 30] Operation: 3+27=30 Exploring Operation: 27-10=17, Resulting Numbers: [3, 17] Generated Node #0,4,3: 84:[3, 17] Operation: 27-10=17 Exploring Operation: 3*10=30, Resulting Numbers: [27, 30] Generated Node #0,4,4: 84:[27, 30] Operation: 3*10=30 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 84:[27, 7], Operations: ['45-18=27', '10-3=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 84:[27, 13], Operations: ['45-18=27', '3+10=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,84 unequal: No Solution Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 84:[3, 17], Operations: ['45-18=27', '27-10=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 84:[27, 30], Operations: ['45-18=27', '3*10=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,84 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 84:[10, 30], Operations: ['45-18=27', '3+27=30'] Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,84 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 84:[3, 45, 8], Operations: ['18-10=8'] Exploring Operation: 8-3=5, Resulting Numbers: [45, 5] Generated Node #0,1,0: 84:[45, 5] Operation: 8-3=5 Exploring Operation: 45-8=37, Resulting Numbers: [3, 37] Generated Node #0,1,1: 84:[3, 37] Operation: 45-8=37 Exploring Operation: 45-3=42, Resulting Numbers: [8, 42] Generated Node #0,1,2: 84:[8, 42] Operation: 45-3=42 Exploring Operation: 3+8=11, Resulting Numbers: [45, 11] Generated Node #0,1,3: 84:[45, 11] Operation: 3+8=11 Exploring Operation: 45/3=15, Resulting Numbers: [8, 15] Generated Node #0,1,4: 84:[8, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[8, 42], Operations: ['18-10=8', '45-3=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 84:[8, 15], Operations: ['18-10=8', '45/3=15'] Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,84 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[45, 5], Operations: ['18-10=8', '8-3=5'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,84 unequal: No Solution Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[45, 11], Operations: ['18-10=8', '3+8=11'] Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,84 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[3, 37], Operations: ['18-10=8', '45-8=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,84 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,84 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: 84:[45, 10, 21], Operations: ['3+18=21'] Exploring Operation: 10+21=31, Resulting Numbers: [45, 31] Generated Node #0,0,0: 84:[45, 31] Operation: 10+21=31 Exploring Operation: 21-10=11, Resulting Numbers: [45, 11] Generated Node #0,0,1: 84:[45, 11] Operation: 21-10=11 Exploring Operation: 45+10=55, Resulting Numbers: [21, 55] Generated Node #0,0,2: 84:[21, 55] Operation: 45+10=55 Exploring Operation: 45-21=24, Resulting Numbers: [10, 24] Generated Node #0,0,3: 84:[10, 24] Operation: 45-21=24 Exploring Operation: 45-10=35, Resulting Numbers: [21, 35] Generated Node #0,0,4: 84:[21, 35] Operation: 45-10=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[45, 11], Operations: ['3+18=21', '21-10=11'] Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,84 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[10, 24], Operations: ['3+18=21', '45-21=24'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,84 unequal: No Solution Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[45, 31], Operations: ['3+18=21', '10+21=31'] Exploring Operation: 45*31=1395, Resulting Numbers: [1395] 1395,84 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 45+31=76, Resulting Numbers: [76] 76,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 84:[21, 35], Operations: ['3+18=21', '45-10=35'] Exploring Operation: 21+35=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 21*35=735, Resulting Numbers: [735] 735,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[21, 55], Operations: ['3+18=21', '45+10=55'] Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 21+55=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 21*55=1155, Resulting Numbers: [1155] 1155,84 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: 84:[18, 10, 42], Operations: ['45-3=42'] Exploring Operation: 42-18=24, Resulting Numbers: [10, 24] Generated Node #0,2,0: 84:[10, 24] Operation: 42-18=24 Exploring Operation: 42-10=32, Resulting Numbers: [18, 32] Generated Node #0,2,1: 84:[18, 32] Operation: 42-10=32 Exploring Operation: 18-10=8, Resulting Numbers: [42, 8] Generated Node #0,2,2: 84:[42, 8] Operation: 18-10=8 Exploring Operation: 18+10=28, Resulting Numbers: [42, 28] Generated Node #0,2,3: 84:[42, 28] Operation: 18+10=28 Exploring Operation: 10+42=52, Resulting Numbers: [18, 52] Generated Node #0,2,4: 84:[18, 52] Operation: 10+42=52 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[42, 28], Operations: ['45-3=42', '18+10=28'] Exploring Operation: 42+28=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 42-28=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 42*28=1176, Resulting Numbers: [1176] 1176,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[42, 8], Operations: ['45-3=42', '18-10=8'] Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,84 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,84 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[10, 24], Operations: ['45-3=42', '42-18=24'] Exploring Operation: 10*24=240, Resulting Numbers: [240] 240,84 unequal: No Solution Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[18, 32], Operations: ['45-3=42', '42-10=32'] Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,84 unequal: No Solution Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 84:[18, 52], Operations: ['45-3=42', '10+42=52'] Exploring Operation: 18+52=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 52-18=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 18*52=936, Resulting Numbers: [936] 936,84 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
[ 52, 34, 82, 17 ]
68
[ "52+34=86", "86-82=4", "17*4=68" ]
Current State: 68:[52, 34, 82, 17], Operations: [] Exploring Operation: 52+34=86, Resulting Numbers: [82, 17, 86] Generated Node #2: [82, 17, 86] from Operation: 52+34=86 Current State: 68:[82, 17, 86], Operations: ['52+34=86'] Exploring Operation: 86-82=4, Resulting Numbers: [17, 4] Generated Node #3: [17, 4] from Operation: 86-82=4 Current State: 68:[17, 4], Operations: ['52+34=86', '86-82=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[52, 34, 82, 17], Operations: [] Exploring Operation: 52-34=18, Resulting Numbers: [82, 17, 18] Generated Node #0,0: 68:[82, 17, 18] Operation: 52-34=18 Exploring Operation: 82-52=30, Resulting Numbers: [34, 17, 30] Generated Node #0,1: 68:[34, 17, 30] Operation: 82-52=30 Exploring Operation: 52-17=35, Resulting Numbers: [34, 82, 35] Generated Node #0,2: 68:[34, 82, 35] Operation: 52-17=35 Exploring Operation: 52+17=69, Resulting Numbers: [34, 82, 69] Generated Node #0,3: 68:[34, 82, 69] Operation: 52+17=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[34, 17, 30], Operations: ['82-52=30'] Exploring Operation: 34+30=64, Resulting Numbers: [17, 64] Generated Node #0,1,0: 68:[17, 64] Operation: 34+30=64 Exploring Operation: 34/17=2, Resulting Numbers: [30, 2] Generated Node #0,1,1: 68:[30, 2] Operation: 34/17=2 Exploring Operation: 34-30=4, Resulting Numbers: [17, 4] Generated Node #0,1,2: 68:[17, 4] Operation: 34-30=4 Exploring Operation: 34-17=17, Resulting Numbers: [30, 17] Generated Node #0,1,3: 68:[30, 17] Operation: 34-17=17 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[17, 4], Operations: ['82-52=30', '34-30=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[52, 34, 82, 17], Operations: [] Exploring Operation: 82-52=30, Resulting Numbers: [34, 17, 30] Generated Node #0,1: 68:[34, 17, 30] Operation: 82-52=30 Moving to Node #0,1 Current State: 68:[34, 17, 30], Operations: ['82-52=30'] Exploring Operation: 34-30=4, Resulting Numbers: [17, 4] Generated Node #0,1,2: 68:[17, 4] Operation: 34-30=4 Moving to Node #0,1,2 Current State: 68:[17, 4], Operations: ['82-52=30', '34-30=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 13, 67, 60, 56 ]
62
[ "67-13=54", "60+56=116", "116-54=62" ]
Current State: 62:[13, 67, 60, 56], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [60, 56, 54] Generated Node #2: [60, 56, 54] from Operation: 67-13=54 Current State: 62:[60, 56, 54], Operations: ['67-13=54'] Exploring Operation: 60+56=116, Resulting Numbers: [54, 116] Generated Node #3: [54, 116] from Operation: 60+56=116 Current State: 62:[54, 116], Operations: ['67-13=54', '60+56=116'] Exploring Operation: 116-54=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[13, 67, 60, 56], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [60, 56, 54] Generated Node #0,0: 62:[60, 56, 54] Operation: 67-13=54 Exploring Operation: 60-56=4, Resulting Numbers: [13, 67, 4] Generated Node #0,1: 62:[13, 67, 4] Operation: 60-56=4 Exploring Operation: 13+60=73, Resulting Numbers: [67, 56, 73] Generated Node #0,2: 62:[67, 56, 73] Operation: 13+60=73 Exploring Operation: 56-13=43, Resulting Numbers: [67, 60, 43] Generated Node #0,3: 62:[67, 60, 43] Operation: 56-13=43 Exploring Operation: 13+56=69, Resulting Numbers: [67, 60, 69] Generated Node #0,4: 62:[67, 60, 69] Operation: 13+56=69 Start Sub Search at level 1: Moving to Node #0,4 Current State: 62:[67, 60, 69], Operations: ['13+56=69'] Exploring Operation: 69-67=2, Resulting Numbers: [60, 2] Generated Node #0,4,0: 62:[60, 2] Operation: 69-67=2 Exploring Operation: 67-60=7, Resulting Numbers: [69, 7] Generated Node #0,4,1: 62:[69, 7] Operation: 67-60=7 Exploring Operation: 67+60=127, Resulting Numbers: [69, 127] Generated Node #0,4,2: 62:[69, 127] Operation: 67+60=127 Exploring Operation: 69-60=9, Resulting Numbers: [67, 9] Generated Node #0,4,3: 62:[67, 9] Operation: 69-60=9 Exploring Operation: 60+69=129, Resulting Numbers: [67, 129] Generated Node #0,4,4: 62:[67, 129] Operation: 60+69=129 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 62:[60, 2], Operations: ['13+56=69', '69-67=2'] Exploring Operation: 60*2=120, Resulting Numbers: [120] 120,62 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,62 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[13, 67, 60, 56], Operations: [] Exploring Operation: 13+56=69, Resulting Numbers: [67, 60, 69] Generated Node #0,4: 62:[67, 60, 69] Operation: 13+56=69 Moving to Node #0,4 Current State: 62:[67, 60, 69], Operations: ['13+56=69'] Exploring Operation: 69-67=2, Resulting Numbers: [60, 2] Generated Node #0,4,0: 62:[60, 2] Operation: 69-67=2 Moving to Node #0,4,0 Current State: 62:[60, 2], Operations: ['13+56=69', '69-67=2'] Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 65, 64, 38, 13 ]
31
[ "65/13=5", "64-38=26", "5+26=31" ]
Current State: 31:[65, 64, 38, 13], Operations: [] Exploring Operation: 65/13=5, Resulting Numbers: [64, 38, 5] Generated Node #2: [64, 38, 5] from Operation: 65/13=5 Current State: 31:[64, 38, 5], Operations: ['65/13=5'] Exploring Operation: 64-38=26, Resulting Numbers: [5, 26] Generated Node #3: [5, 26] from Operation: 64-38=26 Current State: 31:[5, 26], Operations: ['65/13=5', '64-38=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[65, 64, 38, 13], Operations: [] Exploring Operation: 64-38=26, Resulting Numbers: [65, 13, 26] Generated Node #0,0: 31:[65, 13, 26] Operation: 64-38=26 Exploring Operation: 65-64=1, Resulting Numbers: [38, 13, 1] Generated Node #0,1: 31:[38, 13, 1] Operation: 65-64=1 Exploring Operation: 65-38=27, Resulting Numbers: [64, 13, 27] Generated Node #0,2: 31:[64, 13, 27] Operation: 65-38=27 Moving to Node #0,1 Current State: 31:[38, 13, 1], Operations: ['65-64=1'] Exploring Operation: 38*1=38, Resulting Numbers: [13, 38] Generated Node #0,1,0: 31:[13, 38] Operation: 38*1=38 Exploring Operation: 13+1=14, Resulting Numbers: [38, 14] Generated Node #0,1,1: 31:[38, 14] Operation: 13+1=14 Exploring Operation: 38-1=37, Resulting Numbers: [13, 37] Generated Node #0,1,2: 31:[13, 37] Operation: 38-1=37 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[38, 14], Operations: ['65-64=1', '13+1=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,31 unequal: No Solution Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[13, 37], Operations: ['65-64=1', '38-1=37'] Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,31 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 13+37=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 #0,1,0 Current State: 31:[13, 38], Operations: ['65-64=1', '38*1=38'] Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,31 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 31:[64, 13, 27], Operations: ['65-38=27'] Exploring Operation: 64-27=37, Resulting Numbers: [13, 37] Generated Node #0,2,0: 31:[13, 37] Operation: 64-27=37 Exploring Operation: 13+27=40, Resulting Numbers: [64, 40] Generated Node #0,2,1: 31:[64, 40] Operation: 13+27=40 Exploring Operation: 64-13=51, Resulting Numbers: [27, 51] Generated Node #0,2,2: 31:[27, 51] Operation: 64-13=51 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[13, 37], Operations: ['65-38=27', '64-27=37'] Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,31 unequal: No Solution Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,31 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:[27, 51], Operations: ['65-38=27', '64-13=51'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,31 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:[64, 40], Operations: ['65-38=27', '13+27=40'] Exploring Operation: 64+40=104, Resulting Numbers: [104] 104,31 unequal: No Solution Exploring Operation: 64*40=2560, Resulting Numbers: [2560] 2560,31 unequal: No Solution Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 31:[65, 13, 26], Operations: ['64-38=26'] Exploring Operation: 65/13=5, Resulting Numbers: [26, 5] Generated Node #0,0,0: 31:[26, 5] Operation: 65/13=5 Exploring Operation: 65-26=39, Resulting Numbers: [13, 39] Generated Node #0,0,1: 31:[13, 39] Operation: 65-26=39 Exploring Operation: 65-13=52, Resulting Numbers: [26, 52] Generated Node #0,0,2: 31:[26, 52] Operation: 65-13=52 Moving to Node #0,0,1 Current State: 31:[13, 39], Operations: ['64-38=26', '65-26=39'] Exploring Operation: 13+39=52, Resulting Numbers: [52] 52,31 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[26, 52], Operations: ['64-38=26', '65-13=52'] Exploring Operation: 26+52=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,31 unequal: No Solution Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[26, 5], Operations: ['64-38=26', '65/13=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,31 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[65, 64, 38, 13], Operations: [] Exploring Operation: 64-38=26, Resulting Numbers: [65, 13, 26] Generated Node #0,0: 31:[65, 13, 26] Operation: 64-38=26 Moving to Node #0,0 Current State: 31:[65, 13, 26], Operations: ['64-38=26'] Exploring Operation: 65/13=5, Resulting Numbers: [26, 5] Generated Node #0,0,0: 31:[26, 5] Operation: 65/13=5 Moving to Node #0,0,0 Current State: 31:[26, 5], Operations: ['64-38=26', '65/13=5'] Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.962674
hs_3
sum_heuristic
[ 4, 44, 27, 41 ]
26
[ "44-4=40", "41-27=14", "40-14=26" ]
Current State: 26:[4, 44, 27, 41], Operations: [] Exploring Operation: 44-4=40, Resulting Numbers: [27, 41, 40] Generated Node #2: [27, 41, 40] from Operation: 44-4=40 Current State: 26:[27, 41, 40], Operations: ['44-4=40'] Exploring Operation: 41-27=14, Resulting Numbers: [40, 14] Generated Node #3: [40, 14] from Operation: 41-27=14 Current State: 26:[40, 14], Operations: ['44-4=40', '41-27=14'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[4, 44, 27, 41], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [4, 27, 3] Generated Node #0,0: 26:[4, 27, 3] Operation: 44-41=3 Exploring Operation: 44/4=11, Resulting Numbers: [27, 41, 11] Generated Node #0,1: 26:[27, 41, 11] Operation: 44/4=11 Exploring Operation: 44-27=17, Resulting Numbers: [4, 41, 17] Generated Node #0,2: 26:[4, 41, 17] Operation: 44-27=17 Moving to Node #0,0 Current State: 26:[4, 27, 3], Operations: ['44-41=3'] Exploring Operation: 4-3=1, Resulting Numbers: [27, 1] Generated Node #0,0,0: 26:[27, 1] Operation: 4-3=1 Exploring Operation: 4*3=12, Resulting Numbers: [27, 12] Generated Node #0,0,1: 26:[27, 12] Operation: 4*3=12 Exploring Operation: 27-4=23, Resulting Numbers: [3, 23] Generated Node #0,0,2: 26:[3, 23] Operation: 27-4=23 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[27, 1], Operations: ['44-41=3', '4-3=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[4, 44, 27, 41], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [4, 27, 3] Generated Node #0,0: 26:[4, 27, 3] Operation: 44-41=3 Moving to Node #0,0 Current State: 26:[4, 27, 3], Operations: ['44-41=3'] Exploring Operation: 4-3=1, Resulting Numbers: [27, 1] Generated Node #0,0,0: 26:[27, 1] Operation: 4-3=1 Moving to Node #0,0,0 Current State: 26:[27, 1], Operations: ['44-41=3', '4-3=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 56, 69, 86, 2 ]
75
[ "69-56=13", "86+2=88", "88-13=75" ]
Current State: 75:[56, 69, 86, 2], Operations: [] Exploring Operation: 69-56=13, Resulting Numbers: [86, 2, 13] Generated Node #2: [86, 2, 13] from Operation: 69-56=13 Current State: 75:[86, 2, 13], Operations: ['69-56=13'] Exploring Operation: 86+2=88, Resulting Numbers: [13, 88] Generated Node #3: [13, 88] from Operation: 86+2=88 Current State: 75:[13, 88], Operations: ['69-56=13', '86+2=88'] Exploring Operation: 88-13=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[56, 69, 86, 2], Operations: [] Exploring Operation: 86-56=30, Resulting Numbers: [69, 2, 30] Generated Node #0,0: 75:[69, 2, 30] Operation: 86-56=30 Exploring Operation: 56/2=28, Resulting Numbers: [69, 86, 28] Generated Node #0,1: 75:[69, 86, 28] Operation: 56/2=28 Exploring Operation: 56+2=58, Resulting Numbers: [69, 86, 58] Generated Node #0,2: 75:[69, 86, 58] Operation: 56+2=58 Exploring Operation: 86-69=17, Resulting Numbers: [56, 2, 17] Generated Node #0,3: 75:[56, 2, 17] Operation: 86-69=17 Exploring Operation: 69-56=13, Resulting Numbers: [86, 2, 13] Generated Node #0,4: 75:[86, 2, 13] Operation: 69-56=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[69, 2, 30], Operations: ['86-56=30'] Exploring Operation: 69+2=71, Resulting Numbers: [30, 71] Generated Node #0,0,0: 75:[30, 71] Operation: 69+2=71 Exploring Operation: 30/2=15, Resulting Numbers: [69, 15] Generated Node #0,0,1: 75:[69, 15] Operation: 30/2=15 Exploring Operation: 69-2=67, Resulting Numbers: [30, 67] Generated Node #0,0,2: 75:[30, 67] Operation: 69-2=67 Exploring Operation: 30-2=28, Resulting Numbers: [69, 28] Generated Node #0,0,3: 75:[69, 28] Operation: 30-2=28 Exploring Operation: 2+30=32, Resulting Numbers: [69, 32] Generated Node #0,0,4: 75:[69, 32] Operation: 2+30=32 Moving to Node #0,0,1 Current State: 75:[69, 15], Operations: ['86-56=30', '30/2=15'] Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,75 unequal: No Solution Exploring Operation: 69*15=1035, Resulting Numbers: [1035] 1035,75 unequal: No Solution Exploring Operation: 69+15=84, Resulting Numbers: [84] 84,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[69, 28], Operations: ['86-56=30', '30-2=28'] Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,75 unequal: No Solution Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,75 unequal: No Solution Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[30, 71], Operations: ['86-56=30', '69+2=71'] Exploring Operation: 30*71=2130, Resulting Numbers: [2130] 2130,75 unequal: No Solution Exploring Operation: 30+71=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[30, 67], Operations: ['86-56=30', '69-2=67'] Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,75 unequal: No Solution Exploring Operation: 30*67=2010, Resulting Numbers: [2010] 2010,75 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,75 unequal: No Solution Moving to Node #0,0,4 Current State: 75:[69, 32], Operations: ['86-56=30', '2+30=32'] Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,75 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,75 unequal: No Solution No 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: 75:[86, 2, 13], Operations: ['69-56=13'] Exploring Operation: 2+13=15, Resulting Numbers: [86, 15] Generated Node #0,4,0: 75:[86, 15] Operation: 2+13=15 Exploring Operation: 2*13=26, Resulting Numbers: [86, 26] Generated Node #0,4,1: 75:[86, 26] Operation: 2*13=26 Exploring Operation: 86-13=73, Resulting Numbers: [2, 73] Generated Node #0,4,2: 75:[2, 73] Operation: 86-13=73 Exploring Operation: 86+2=88, Resulting Numbers: [13, 88] Generated Node #0,4,3: 75:[13, 88] Operation: 86+2=88 Exploring Operation: 86-2=84, Resulting Numbers: [13, 84] Generated Node #0,4,4: 75:[13, 84] Operation: 86-2=84 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 75:[2, 73], Operations: ['69-56=13', '86-13=73'] Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,75 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,75 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[56, 69, 86, 2], Operations: [] Exploring Operation: 69-56=13, Resulting Numbers: [86, 2, 13] Generated Node #0,4: 75:[86, 2, 13] Operation: 69-56=13 Moving to Node #0,4 Current State: 75:[86, 2, 13], Operations: ['69-56=13'] Exploring Operation: 86-13=73, Resulting Numbers: [2, 73] Generated Node #0,4,2: 75:[2, 73] Operation: 86-13=73 Moving to Node #0,4,2 Current State: 75:[2, 73], Operations: ['69-56=13', '86-13=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 17, 49, 56, 67 ]
21
[ "49-17=32", "67-56=11", "32-11=21" ]
Current State: 21:[17, 49, 56, 67], Operations: [] Exploring Operation: 49-17=32, Resulting Numbers: [56, 67, 32] Generated Node #2: [56, 67, 32] from Operation: 49-17=32 Current State: 21:[56, 67, 32], Operations: ['49-17=32'] Exploring Operation: 67-56=11, Resulting Numbers: [32, 11] Generated Node #3: [32, 11] from Operation: 67-56=11 Current State: 21:[32, 11], Operations: ['49-17=32', '67-56=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[17, 49, 56, 67], Operations: [] Exploring Operation: 67-56=11, Resulting Numbers: [17, 49, 11] Generated Node #0,0: 21:[17, 49, 11] Operation: 67-56=11 Exploring Operation: 56-49=7, Resulting Numbers: [17, 67, 7] Generated Node #0,1: 21:[17, 67, 7] Operation: 56-49=7 Exploring Operation: 67-49=18, Resulting Numbers: [17, 56, 18] Generated Node #0,2: 21:[17, 56, 18] Operation: 67-49=18 Moving to Node #0,0 Current State: 21:[17, 49, 11], Operations: ['67-56=11'] Exploring Operation: 17-11=6, Resulting Numbers: [49, 6] Generated Node #0,0,0: 21:[49, 6] Operation: 17-11=6 Exploring Operation: 49-11=38, Resulting Numbers: [17, 38] Generated Node #0,0,1: 21:[17, 38] Operation: 49-11=38 Exploring Operation: 49-17=32, Resulting Numbers: [11, 32] Generated Node #0,0,2: 21:[11, 32] Operation: 49-17=32 Moving to Node #0,2 Current State: 21:[17, 56, 18], Operations: ['67-49=18'] Exploring Operation: 56-18=38, Resulting Numbers: [17, 38] Generated Node #0,2,0: 21:[17, 38] Operation: 56-18=38 Exploring Operation: 56-17=39, Resulting Numbers: [18, 39] Generated Node #0,2,1: 21:[18, 39] Operation: 56-17=39 Exploring Operation: 18-17=1, Resulting Numbers: [56, 1] Generated Node #0,2,2: 21:[56, 1] Operation: 18-17=1 Moving to Node #0,1 Current State: 21:[17, 67, 7], Operations: ['56-49=7'] Exploring Operation: 17+7=24, Resulting Numbers: [67, 24] Generated Node #0,1,0: 21:[67, 24] Operation: 17+7=24 Exploring Operation: 67-17=50, Resulting Numbers: [7, 50] Generated Node #0,1,1: 21:[7, 50] Operation: 67-17=50 Exploring Operation: 67-7=60, Resulting Numbers: [17, 60] Generated Node #0,1,2: 21:[17, 60] Operation: 67-7=60 Moving to Node #0,0,2 Current State: 21:[11, 32], Operations: ['67-56=11', '49-17=32'] Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,21 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[17, 49, 56, 67], Operations: [] Exploring Operation: 67-56=11, Resulting Numbers: [17, 49, 11] Generated Node #0,0: 21:[17, 49, 11] Operation: 67-56=11 Moving to Node #0,0 Current State: 21:[17, 49, 11], Operations: ['67-56=11'] Exploring Operation: 49-17=32, Resulting Numbers: [11, 32] Generated Node #0,0,2: 21:[11, 32] Operation: 49-17=32 Moving to Node #0,0,2 Current State: 21:[11, 32], Operations: ['67-56=11', '49-17=32'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.983507
hs_3
mult_heuristic