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
[ 5, 21, 2, 89 ]
63
[ "89-5=84", "84/2=42", "21+42=63" ]
Current State: 63:[5, 21, 2, 89], Operations: [] Exploring Operation: 89-5=84, Resulting Numbers: [21, 2, 84] Generated Node #2: [21, 2, 84] from Operation: 89-5=84 Current State: 63:[21, 2, 84], Operations: ['89-5=84'] Exploring Operation: 84/2=42, Resulting Numbers: [21, 42] Generated Node #3: [21, 42] from Operation: 84/2=42 Current State: 63:[21, 42], Operations: ['89-5=84', '84/2=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[5, 21, 2, 89], Operations: [] Exploring Operation: 89-21=68, Resulting Numbers: [5, 2, 68] Generated Node #0,0: 63:[5, 2, 68] Operation: 89-21=68 Exploring Operation: 89-5=84, Resulting Numbers: [21, 2, 84] Generated Node #0,1: 63:[21, 2, 84] Operation: 89-5=84 Exploring Operation: 5-2=3, Resulting Numbers: [21, 89, 3] Generated Node #0,2: 63:[21, 89, 3] Operation: 5-2=3 Exploring Operation: 5+2=7, Resulting Numbers: [21, 89, 7] Generated Node #0,3: 63:[21, 89, 7] Operation: 5+2=7 Moving to Node #0,0 Current State: 63:[5, 2, 68], Operations: ['89-21=68'] Exploring Operation: 5-2=3, Resulting Numbers: [68, 3] Generated Node #0,0,0: 63:[68, 3] Operation: 5-2=3 Exploring Operation: 68-2=66, Resulting Numbers: [5, 66] Generated Node #0,0,1: 63:[5, 66] Operation: 68-2=66 Exploring Operation: 68-5=63, Resulting Numbers: [2, 63] Generated Node #0,0,2: 63:[2, 63] Operation: 68-5=63 Exploring Operation: 5+2=7, Resulting Numbers: [68, 7] Generated Node #0,0,3: 63:[68, 7] Operation: 5+2=7 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[2, 63], Operations: ['89-21=68', '68-5=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,63 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[68, 3], Operations: ['89-21=68', '5-2=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,63 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[5, 66], Operations: ['89-21=68', '68-2=66'] Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 5*66=330, Resulting Numbers: [330] 330,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[68, 7], Operations: ['89-21=68', '5+2=7'] Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 68*7=476, Resulting Numbers: [476] 476,63 unequal: No Solution Exploring Operation: 68+7=75, Resulting Numbers: [75] 75,63 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: 63:[21, 2, 84], Operations: ['89-5=84'] Exploring Operation: 84/21=4, Resulting Numbers: [2, 4] Generated Node #0,1,0: 63:[2, 4] Operation: 84/21=4 Exploring Operation: 84-21=63, Resulting Numbers: [2, 63] Generated Node #0,1,1: 63:[2, 63] Operation: 84-21=63 Exploring Operation: 84-2=82, Resulting Numbers: [21, 82] Generated Node #0,1,2: 63:[21, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [21, 42] Generated Node #0,1,3: 63:[21, 42] Operation: 84/2=42 Moving to Node #0,3 Current State: 63:[21, 89, 7], Operations: ['5+2=7'] Exploring Operation: 89-21=68, Resulting Numbers: [7, 68] Generated Node #0,3,0: 63:[7, 68] Operation: 89-21=68 Exploring Operation: 89-7=82, Resulting Numbers: [21, 82] Generated Node #0,3,1: 63:[21, 82] Operation: 89-7=82 Exploring Operation: 21/7=3, Resulting Numbers: [89, 3] Generated Node #0,3,2: 63:[89, 3] Operation: 21/7=3 Exploring Operation: 21-7=14, Resulting Numbers: [89, 14] Generated Node #0,3,3: 63:[89, 14] Operation: 21-7=14 Moving to Node #0,2 Current State: 63:[21, 89, 3], Operations: ['5-2=3'] Exploring Operation: 21/3=7, Resulting Numbers: [89, 7] Generated Node #0,2,0: 63:[89, 7] Operation: 21/3=7 Exploring Operation: 89-3=86, Resulting Numbers: [21, 86] Generated Node #0,2,1: 63:[21, 86] Operation: 89-3=86 Exploring Operation: 89-21=68, Resulting Numbers: [3, 68] Generated Node #0,2,2: 63:[3, 68] Operation: 89-21=68 Exploring Operation: 21*3=63, Resulting Numbers: [89, 63] Generated Node #0,2,3: 63:[89, 63] Operation: 21*3=63 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[3, 68], Operations: ['5-2=3', '89-21=68'] Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,63 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,63 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[21, 86], Operations: ['5-2=3', '89-3=86'] Exploring Operation: 86-21=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 21*86=1806, Resulting Numbers: [1806] 1806,63 unequal: No Solution Exploring Operation: 21+86=107, Resulting Numbers: [107] 107,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[89, 7], Operations: ['5-2=3', '21/3=7'] Exploring Operation: 89+7=96, Resulting Numbers: [96] 96,63 unequal: No Solution Exploring Operation: 89*7=623, Resulting Numbers: [623] 623,63 unequal: No Solution Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 63:[89, 63], Operations: ['5-2=3', '21*3=63'] Exploring Operation: 89*63=5607, Resulting Numbers: [5607] 5607,63 unequal: No Solution Exploring Operation: 89+63=152, Resulting Numbers: [152] 152,63 unequal: No Solution Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 63:[2, 63], Operations: ['89-5=84', '84-21=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,63 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[2, 4], Operations: ['89-5=84', '84/21=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Moving to Node #0,3,0 Current State: 63:[7, 68], Operations: ['5+2=7', '89-21=68'] Exploring Operation: 7+68=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 7*68=476, Resulting Numbers: [476] 476,63 unequal: No Solution Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[21, 82], Operations: ['89-5=84', '84-2=82'] Exploring Operation: 21+82=103, Resulting Numbers: [103] 103,63 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,63 unequal: No Solution Exploring Operation: 21*82=1722, Resulting Numbers: [1722] 1722,63 unequal: No Solution Moving to Node #0,3,1 Current State: 63:[21, 82], Operations: ['5+2=7', '89-7=82'] Exploring Operation: 21*82=1722, Resulting Numbers: [1722] 1722,63 unequal: No Solution Exploring Operation: 21+82=103, Resulting Numbers: [103] 103,63 unequal: No Solution Exploring Operation: 82-21=61, Resulting Numbers: [61] 61,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[21, 42], Operations: ['89-5=84', '84/2=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[5, 21, 2, 89], Operations: [] Exploring Operation: 89-5=84, Resulting Numbers: [21, 2, 84] Generated Node #0,1: 63:[21, 2, 84] Operation: 89-5=84 Moving to Node #0,1 Current State: 63:[21, 2, 84], Operations: ['89-5=84'] Exploring Operation: 84/2=42, Resulting Numbers: [21, 42] Generated Node #0,1,3: 63:[21, 42] Operation: 84/2=42 Moving to Node #0,1,3 Current State: 63:[21, 42], Operations: ['89-5=84', '84/2=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
0.943576
hs_4
sum_heuristic
[ 25, 7, 56, 11 ]
63
[ "25-7=18", "56-11=45", "18+45=63" ]
Current State: 63:[25, 7, 56, 11], Operations: [] Exploring Operation: 25-7=18, Resulting Numbers: [56, 11, 18] Generated Node #2: [56, 11, 18] from Operation: 25-7=18 Current State: 63:[56, 11, 18], Operations: ['25-7=18'] Exploring Operation: 56-11=45, Resulting Numbers: [18, 45] Generated Node #3: [18, 45] from Operation: 56-11=45 Current State: 63:[18, 45], Operations: ['25-7=18', '56-11=45'] Exploring Operation: 18+45=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[25, 7, 56, 11], Operations: [] Exploring Operation: 25-7=18, Resulting Numbers: [56, 11, 18] Generated Node #0,0: 63:[56, 11, 18] Operation: 25-7=18 Exploring Operation: 7+56=63, Resulting Numbers: [25, 11, 63] Generated Node #0,1: 63:[25, 11, 63] Operation: 7+56=63 Exploring Operation: 56/7=8, Resulting Numbers: [25, 11, 8] Generated Node #0,2: 63:[25, 11, 8] Operation: 56/7=8 Exploring Operation: 56+11=67, Resulting Numbers: [25, 7, 67] Generated Node #0,3: 63:[25, 7, 67] Operation: 56+11=67 Exploring Operation: 56-25=31, Resulting Numbers: [7, 11, 31] Generated Node #0,4: 63:[7, 11, 31] Operation: 56-25=31 Moving to Node #0,1 Current State: 63:[25, 11, 63], Operations: ['7+56=63'] Exploring Operation: 25+11=36, Resulting Numbers: [63, 36] Generated Node #0,1,0: 63:[63, 36] Operation: 25+11=36 Exploring Operation: 11+63=74, Resulting Numbers: [25, 74] Generated Node #0,1,1: 63:[25, 74] Operation: 11+63=74 Exploring Operation: 63-11=52, Resulting Numbers: [25, 52] Generated Node #0,1,2: 63:[25, 52] Operation: 63-11=52 Exploring Operation: 25-11=14, Resulting Numbers: [63, 14] Generated Node #0,1,3: 63:[63, 14] Operation: 25-11=14 Exploring Operation: 63-25=38, Resulting Numbers: [11, 38] Generated Node #0,1,4: 63:[11, 38] Operation: 63-25=38 Moving to Node #0,2 Current State: 63:[25, 11, 8], Operations: ['56/7=8'] Exploring Operation: 25-8=17, Resulting Numbers: [11, 17] Generated Node #0,2,0: 63:[11, 17] Operation: 25-8=17 Exploring Operation: 25+8=33, Resulting Numbers: [11, 33] Generated Node #0,2,1: 63:[11, 33] Operation: 25+8=33 Exploring Operation: 11-8=3, Resulting Numbers: [25, 3] Generated Node #0,2,2: 63:[25, 3] Operation: 11-8=3 Exploring Operation: 25-11=14, Resulting Numbers: [8, 14] Generated Node #0,2,3: 63:[8, 14] Operation: 25-11=14 Exploring Operation: 11+8=19, Resulting Numbers: [25, 19] Generated Node #0,2,4: 63:[25, 19] Operation: 11+8=19 Moving to Node #0,3 Current State: 63:[25, 7, 67], Operations: ['56+11=67'] Exploring Operation: 67-25=42, Resulting Numbers: [7, 42] Generated Node #0,3,0: 63:[7, 42] Operation: 67-25=42 Exploring Operation: 25-7=18, Resulting Numbers: [67, 18] Generated Node #0,3,1: 63:[67, 18] Operation: 25-7=18 Exploring Operation: 25+7=32, Resulting Numbers: [67, 32] Generated Node #0,3,2: 63:[67, 32] Operation: 25+7=32 Exploring Operation: 7+67=74, Resulting Numbers: [25, 74] Generated Node #0,3,3: 63:[25, 74] Operation: 7+67=74 Exploring Operation: 67-7=60, Resulting Numbers: [25, 60] Generated Node #0,3,4: 63:[25, 60] Operation: 67-7=60 Moving to Node #0,0 Current State: 63:[56, 11, 18], Operations: ['25-7=18'] Exploring Operation: 11+18=29, Resulting Numbers: [56, 29] Generated Node #0,0,0: 63:[56, 29] Operation: 11+18=29 Exploring Operation: 18-11=7, Resulting Numbers: [56, 7] Generated Node #0,0,1: 63:[56, 7] Operation: 18-11=7 Exploring Operation: 56+11=67, Resulting Numbers: [18, 67] Generated Node #0,0,2: 63:[18, 67] Operation: 56+11=67 Exploring Operation: 56-18=38, Resulting Numbers: [11, 38] Generated Node #0,0,3: 63:[11, 38] Operation: 56-18=38 Exploring Operation: 56+18=74, Resulting Numbers: [11, 74] Generated Node #0,0,4: 63:[11, 74] Operation: 56+18=74 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[56, 7], Operations: ['25-7=18', '18-11=7'] Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,63 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,63 unequal: No Solution Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[25, 7, 56, 11], Operations: [] Exploring Operation: 25-7=18, Resulting Numbers: [56, 11, 18] Generated Node #0,0: 63:[56, 11, 18] Operation: 25-7=18 Moving to Node #0,0 Current State: 63:[56, 11, 18], Operations: ['25-7=18'] Exploring Operation: 18-11=7, Resulting Numbers: [56, 7] Generated Node #0,0,1: 63:[56, 7] Operation: 18-11=7 Moving to Node #0,0,1 Current State: 63:[56, 7], Operations: ['25-7=18', '18-11=7'] Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_5
sum_heuristic
[ 2, 4, 58, 42 ]
72
[ "2+58=60", "60-42=18", "4*18=72" ]
Current State: 72:[2, 4, 58, 42], Operations: [] Exploring Operation: 2+58=60, Resulting Numbers: [4, 42, 60] Generated Node #2: [4, 42, 60] from Operation: 2+58=60 Current State: 72:[4, 42, 60], Operations: ['2+58=60'] Exploring Operation: 60-42=18, Resulting Numbers: [4, 18] Generated Node #3: [4, 18] from Operation: 60-42=18 Current State: 72:[4, 18], Operations: ['2+58=60', '60-42=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[2, 4, 58, 42], Operations: [] Exploring Operation: 58-42=16, Resulting Numbers: [2, 4, 16] Generated Node #0,0: 72:[2, 4, 16] Operation: 58-42=16 Exploring Operation: 4+58=62, Resulting Numbers: [2, 42, 62] Generated Node #0,1: 72:[2, 42, 62] Operation: 4+58=62 Exploring Operation: 58/2=29, Resulting Numbers: [4, 42, 29] Generated Node #0,2: 72:[4, 42, 29] Operation: 58/2=29 Exploring Operation: 42-4=38, Resulting Numbers: [2, 58, 38] Generated Node #0,3: 72:[2, 58, 38] Operation: 42-4=38 Exploring Operation: 42/2=21, Resulting Numbers: [4, 58, 21] Generated Node #0,4: 72:[4, 58, 21] Operation: 42/2=21 Moving to Node #0,0 Current State: 72:[2, 4, 16], Operations: ['58-42=16'] Exploring Operation: 16/4=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 72:[2, 4] Operation: 16/4=4 Exploring Operation: 16/2=8, Resulting Numbers: [4, 8] Generated Node #0,0,1: 72:[4, 8] Operation: 16/2=8 Exploring Operation: 2+4=6, Resulting Numbers: [16, 6] Generated Node #0,0,2: 72:[16, 6] Operation: 2+4=6 Exploring Operation: 2+16=18, Resulting Numbers: [4, 18] Generated Node #0,0,3: 72:[4, 18] Operation: 2+16=18 Exploring Operation: 16-4=12, Resulting Numbers: [2, 12] Generated Node #0,0,4: 72:[2, 12] Operation: 16-4=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[2, 4], Operations: ['58-42=16', '16/4=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[4, 8], Operations: ['58-42=16', '16/2=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,72 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 72:[4, 18], Operations: ['58-42=16', '2+16=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[2, 4, 58, 42], Operations: [] Exploring Operation: 58-42=16, Resulting Numbers: [2, 4, 16] Generated Node #0,0: 72:[2, 4, 16] Operation: 58-42=16 Moving to Node #0,0 Current State: 72:[2, 4, 16], Operations: ['58-42=16'] Exploring Operation: 2+16=18, Resulting Numbers: [4, 18] Generated Node #0,0,3: 72:[4, 18] Operation: 2+16=18 Moving to Node #0,0,3 Current State: 72:[4, 18], Operations: ['58-42=16', '2+16=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 24, 29, 48, 69 ]
42
[ "48/24=2", "69-29=40", "2+40=42" ]
Current State: 42:[24, 29, 48, 69], Operations: [] Exploring Operation: 48/24=2, Resulting Numbers: [29, 69, 2] Generated Node #2: [29, 69, 2] from Operation: 48/24=2 Current State: 42:[29, 69, 2], Operations: ['48/24=2'] Exploring Operation: 69-29=40, Resulting Numbers: [2, 40] Generated Node #3: [2, 40] from Operation: 69-29=40 Current State: 42:[2, 40], Operations: ['48/24=2', '69-29=40'] Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[24, 29, 48, 69], Operations: [] Exploring Operation: 69-29=40, Resulting Numbers: [24, 48, 40] Generated Node #0,0: 42:[24, 48, 40] Operation: 69-29=40 Exploring Operation: 69-48=21, Resulting Numbers: [24, 29, 21] Generated Node #0,1: 42:[24, 29, 21] Operation: 69-48=21 Exploring Operation: 69-24=45, Resulting Numbers: [29, 48, 45] Generated Node #0,2: 42:[29, 48, 45] Operation: 69-24=45 Moving to Node #0,0 Current State: 42:[24, 48, 40], Operations: ['69-29=40'] Exploring Operation: 48-24=24, Resulting Numbers: [40, 24] Generated Node #0,0,0: 42:[40, 24] Operation: 48-24=24 Exploring Operation: 48-40=8, Resulting Numbers: [24, 8] Generated Node #0,0,1: 42:[24, 8] Operation: 48-40=8 Exploring Operation: 48/24=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 42:[40, 2] Operation: 48/24=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 42:[40, 2], Operations: ['69-29=40', '48/24=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[24, 29, 48, 69], Operations: [] Exploring Operation: 69-29=40, Resulting Numbers: [24, 48, 40] Generated Node #0,0: 42:[24, 48, 40] Operation: 69-29=40 Moving to Node #0,0 Current State: 42:[24, 48, 40], Operations: ['69-29=40'] Exploring Operation: 48/24=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 42:[40, 2] Operation: 48/24=2 Moving to Node #0,0,2 Current State: 42:[40, 2], Operations: ['69-29=40', '48/24=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 36, 65, 1, 41 ]
12
[ "65-36=29", "1*41=41", "41-29=12" ]
Current State: 12:[36, 65, 1, 41], Operations: [] Exploring Operation: 65-36=29, Resulting Numbers: [1, 41, 29] Generated Node #2: [1, 41, 29] from Operation: 65-36=29 Current State: 12:[1, 41, 29], Operations: ['65-36=29'] Exploring Operation: 1*41=41, Resulting Numbers: [29, 41] Generated Node #3: [29, 41] from Operation: 1*41=41 Current State: 12:[29, 41], Operations: ['65-36=29', '1*41=41'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[36, 65, 1, 41], Operations: [] Exploring Operation: 36-1=35, Resulting Numbers: [65, 41, 35] Generated Node #0,0: 12:[65, 41, 35] Operation: 36-1=35 Exploring Operation: 65-41=24, Resulting Numbers: [36, 1, 24] Generated Node #0,1: 12:[36, 1, 24] Operation: 65-41=24 Exploring Operation: 65-36=29, Resulting Numbers: [1, 41, 29] Generated Node #0,2: 12:[1, 41, 29] Operation: 65-36=29 Exploring Operation: 41-36=5, Resulting Numbers: [65, 1, 5] Generated Node #0,3: 12:[65, 1, 5] Operation: 41-36=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[36, 1, 24], Operations: ['65-41=24'] Exploring Operation: 36-1=35, Resulting Numbers: [24, 35] Generated Node #0,1,0: 12:[24, 35] Operation: 36-1=35 Exploring Operation: 36*1=36, Resulting Numbers: [24, 36] Generated Node #0,1,1: 12:[24, 36] Operation: 36*1=36 Exploring Operation: 24-1=23, Resulting Numbers: [36, 23] Generated Node #0,1,2: 12:[36, 23] Operation: 24-1=23 Exploring Operation: 36-24=12, Resulting Numbers: [1, 12] Generated Node #0,1,3: 12:[1, 12] Operation: 36-24=12 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 12:[1, 12], Operations: ['65-41=24', '36-24=12'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[36, 65, 1, 41], Operations: [] Exploring Operation: 65-41=24, Resulting Numbers: [36, 1, 24] Generated Node #0,1: 12:[36, 1, 24] Operation: 65-41=24 Moving to Node #0,1 Current State: 12:[36, 1, 24], Operations: ['65-41=24'] Exploring Operation: 36-24=12, Resulting Numbers: [1, 12] Generated Node #0,1,3: 12:[1, 12] Operation: 36-24=12 Moving to Node #0,1,3 Current State: 12:[1, 12], Operations: ['65-41=24', '36-24=12'] Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 3, 64, 21, 19 ]
38
[ "21/3=7", "64-19=45", "45-7=38" ]
Current State: 38:[3, 64, 21, 19], Operations: [] Exploring Operation: 21/3=7, Resulting Numbers: [64, 19, 7] Generated Node #2: [64, 19, 7] from Operation: 21/3=7 Current State: 38:[64, 19, 7], Operations: ['21/3=7'] Exploring Operation: 64-19=45, Resulting Numbers: [7, 45] Generated Node #3: [7, 45] from Operation: 64-19=45 Current State: 38:[7, 45], Operations: ['21/3=7', '64-19=45'] Exploring Operation: 45-7=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 64, 21, 19], Operations: [] Exploring Operation: 21-19=2, Resulting Numbers: [3, 64, 2] Generated Node #0,0: 38:[3, 64, 2] Operation: 21-19=2 Exploring Operation: 21-3=18, Resulting Numbers: [64, 19, 18] Generated Node #0,1: 38:[64, 19, 18] Operation: 21-3=18 Exploring Operation: 64-21=43, Resulting Numbers: [3, 19, 43] Generated Node #0,2: 38:[3, 19, 43] Operation: 64-21=43 Exploring Operation: 64-3=61, Resulting Numbers: [21, 19, 61] Generated Node #0,3: 38:[21, 19, 61] Operation: 64-3=61 Exploring Operation: 64-19=45, Resulting Numbers: [3, 21, 45] Generated Node #0,4: 38:[3, 21, 45] Operation: 64-19=45 Moving to Node #0,2 Current State: 38:[3, 19, 43], Operations: ['64-21=43'] Exploring Operation: 3+43=46, Resulting Numbers: [19, 46] Generated Node #0,2,0: 38:[19, 46] Operation: 3+43=46 Exploring Operation: 3+19=22, Resulting Numbers: [43, 22] Generated Node #0,2,1: 38:[43, 22] Operation: 3+19=22 Exploring Operation: 43-19=24, Resulting Numbers: [3, 24] Generated Node #0,2,2: 38:[3, 24] Operation: 43-19=24 Exploring Operation: 43-3=40, Resulting Numbers: [19, 40] Generated Node #0,2,3: 38:[19, 40] Operation: 43-3=40 Exploring Operation: 19-3=16, Resulting Numbers: [43, 16] Generated Node #0,2,4: 38:[43, 16] Operation: 19-3=16 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 38:[19, 40], Operations: ['64-21=43', '43-3=40'] Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 38:[3, 24], Operations: ['64-21=43', '43-19=24'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 38:[19, 46], Operations: ['64-21=43', '3+43=46'] Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 19+46=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 19*46=874, Resulting Numbers: [874] 874,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 38:[43, 22], Operations: ['64-21=43', '3+19=22'] Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,38 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 38:[43, 16], Operations: ['64-21=43', '19-3=16'] Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,38 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,38 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: 38:[3, 21, 45], Operations: ['64-19=45'] Exploring Operation: 45-3=42, Resulting Numbers: [21, 42] Generated Node #0,4,0: 38:[21, 42] Operation: 45-3=42 Exploring Operation: 21-3=18, Resulting Numbers: [45, 18] Generated Node #0,4,1: 38:[45, 18] Operation: 21-3=18 Exploring Operation: 3+21=24, Resulting Numbers: [45, 24] Generated Node #0,4,2: 38:[45, 24] Operation: 3+21=24 Exploring Operation: 45/3=15, Resulting Numbers: [21, 15] Generated Node #0,4,3: 38:[21, 15] Operation: 45/3=15 Exploring Operation: 45-21=24, Resulting Numbers: [3, 24] Generated Node #0,4,4: 38:[3, 24] Operation: 45-21=24 Moving to Node #0,3 Current State: 38:[21, 19, 61], Operations: ['64-3=61'] Exploring Operation: 21-19=2, Resulting Numbers: [61, 2] Generated Node #0,3,0: 38:[61, 2] Operation: 21-19=2 Exploring Operation: 61-19=42, Resulting Numbers: [21, 42] Generated Node #0,3,1: 38:[21, 42] Operation: 61-19=42 Exploring Operation: 21+61=82, Resulting Numbers: [19, 82] Generated Node #0,3,2: 38:[19, 82] Operation: 21+61=82 Exploring Operation: 61-21=40, Resulting Numbers: [19, 40] Generated Node #0,3,3: 38:[19, 40] Operation: 61-21=40 Exploring Operation: 21+19=40, Resulting Numbers: [61, 40] Generated Node #0,3,4: 38:[61, 40] Operation: 21+19=40 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[19, 40], Operations: ['64-3=61', '61-21=40'] Exploring Operation: 19+40=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 19*40=760, Resulting Numbers: [760] 760,38 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[21, 42], Operations: ['64-3=61', '61-19=42'] Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,38 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[61, 2], Operations: ['64-3=61', '21-19=2'] Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,38 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 38:[61, 40], Operations: ['64-3=61', '21+19=40'] Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 61*40=2440, Resulting Numbers: [2440] 2440,38 unequal: No Solution Exploring Operation: 61+40=101, Resulting Numbers: [101] 101,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[19, 82], Operations: ['64-3=61', '21+61=82'] Exploring Operation: 19*82=1558, Resulting Numbers: [1558] 1558,38 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 19+82=101, Resulting Numbers: [101] 101,38 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: 38:[3, 64, 2], Operations: ['21-19=2'] Exploring Operation: 64-3=61, Resulting Numbers: [2, 61] Generated Node #0,0,0: 38:[2, 61] Operation: 64-3=61 Exploring Operation: 3+64=67, Resulting Numbers: [2, 67] Generated Node #0,0,1: 38:[2, 67] Operation: 3+64=67 Exploring Operation: 3-2=1, Resulting Numbers: [64, 1] Generated Node #0,0,2: 38:[64, 1] Operation: 3-2=1 Exploring Operation: 64-2=62, Resulting Numbers: [3, 62] Generated Node #0,0,3: 38:[3, 62] Operation: 64-2=62 Exploring Operation: 64/2=32, Resulting Numbers: [3, 32] Generated Node #0,0,4: 38:[3, 32] Operation: 64/2=32 Moving to Node #0,1 Current State: 38:[64, 19, 18], Operations: ['21-3=18'] Exploring Operation: 64-19=45, Resulting Numbers: [18, 45] Generated Node #0,1,0: 38:[18, 45] Operation: 64-19=45 Exploring Operation: 19-18=1, Resulting Numbers: [64, 1] Generated Node #0,1,1: 38:[64, 1] Operation: 19-18=1 Exploring Operation: 19+18=37, Resulting Numbers: [64, 37] Generated Node #0,1,2: 38:[64, 37] Operation: 19+18=37 Exploring Operation: 64+18=82, Resulting Numbers: [19, 82] Generated Node #0,1,3: 38:[19, 82] Operation: 64+18=82 Exploring Operation: 64-18=46, Resulting Numbers: [19, 46] Generated Node #0,1,4: 38:[19, 46] Operation: 64-18=46 Moving to Node #0,4,0 Current State: 38:[21, 42], Operations: ['64-19=45', '45-3=42'] Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,38 unequal: No Solution Moving to Node #0,4,4 Current State: 38:[3, 24], Operations: ['64-19=45', '45-21=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,38 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,38 unequal: No Solution Moving to Node #0,4,3 Current State: 38:[21, 15], Operations: ['64-19=45', '45/3=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,38 unequal: No Solution Moving to Node #0,0,4 Current State: 38:[3, 32], Operations: ['21-19=2', '64/2=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,38 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,38 unequal: No Solution Moving to Node #0,1,4 Current State: 38:[19, 46], Operations: ['21-3=18', '64-18=46'] Exploring Operation: 19+46=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 19*46=874, Resulting Numbers: [874] 874,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[18, 45], Operations: ['21-3=18', '64-19=45'] Exploring Operation: 18*45=810, Resulting Numbers: [810] 810,38 unequal: No Solution Exploring Operation: 18+45=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,38 unequal: No Solution Moving to Node #0,4,1 Current State: 38:[45, 18], Operations: ['64-19=45', '21-3=18'] Exploring Operation: 45*18=810, Resulting Numbers: [810] 810,38 unequal: No Solution Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,38 unequal: No Solution Moving to Node #0,4,2 Current State: 38:[45, 24], Operations: ['64-19=45', '3+21=24'] Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,38 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 45*24=1080, Resulting Numbers: [1080] 1080,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[2, 61], Operations: ['21-19=2', '64-3=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,38 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[3, 62], Operations: ['21-19=2', '64-2=62'] Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,38 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[64, 1], Operations: ['21-3=18', '19-18=1'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,38 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,38 unequal: No Solution Exploring Operation: 64+1=65, Resulting Numbers: [65] 65,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[64, 1], Operations: ['21-19=2', '3-2=1'] Exploring Operation: 64+1=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,38 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[64, 37], Operations: ['21-3=18', '19+18=37'] Exploring Operation: 64-37=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 64+37=101, Resulting Numbers: [101] 101,38 unequal: No Solution Exploring Operation: 64*37=2368, Resulting Numbers: [2368] 2368,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[2, 67], Operations: ['21-19=2', '3+64=67'] Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,38 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[19, 82], Operations: ['21-3=18', '64+18=82'] Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,38 unequal: No Solution Exploring Operation: 19*82=1558, Resulting Numbers: [1558] 1558,38 unequal: No Solution Exploring Operation: 19+82=101, Resulting Numbers: [101] 101,38 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 97, 6, 29, 35 ]
96
[ "6+29=35", "35/35=1", "97-1=96" ]
Current State: 96:[97, 6, 29, 35], Operations: [] Exploring Operation: 6+29=35, Resulting Numbers: [97, 35, 35] Generated Node #2: [97, 35, 35] from Operation: 6+29=35 Current State: 96:[97, 35, 35], Operations: ['6+29=35'] Exploring Operation: 35/35=1, Resulting Numbers: [97, 1] Generated Node #3: [97, 1] from Operation: 35/35=1 Current State: 96:[97, 1], Operations: ['6+29=35', '35/35=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[97, 6, 29, 35], Operations: [] Exploring Operation: 6+29=35, Resulting Numbers: [97, 35, 35] Generated Node #0,0: 96:[97, 35, 35] Operation: 6+29=35 Exploring Operation: 35-29=6, Resulting Numbers: [97, 6, 6] Generated Node #0,1: 96:[97, 6, 6] Operation: 35-29=6 Exploring Operation: 29-6=23, Resulting Numbers: [97, 35, 23] Generated Node #0,2: 96:[97, 35, 23] Operation: 29-6=23 Moving to Node #0,1 Current State: 96:[97, 6, 6], Operations: ['35-29=6'] Exploring Operation: 6/6=1, Resulting Numbers: [97, 1] Generated Node #0,1,0: 96:[97, 1] Operation: 6/6=1 Exploring Operation: 6+6=12, Resulting Numbers: [97, 12] Generated Node #0,1,1: 96:[97, 12] Operation: 6+6=12 Exploring Operation: 6-6=0, Resulting Numbers: [97, 0] Generated Node #0,1,2: 96:[97, 0] Operation: 6-6=0 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[97, 12], Operations: ['35-29=6', '6+6=12'] Exploring Operation: 97*12=1164, Resulting Numbers: [1164] 1164,96 unequal: No Solution Exploring Operation: 97-12=85, Resulting Numbers: [85] 85,96 unequal: No Solution Exploring Operation: 97+12=109, Resulting Numbers: [109] 109,96 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 #0,1,0 Current State: 96:[97, 1], Operations: ['35-29=6', '6/6=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[97, 6, 29, 35], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [97, 6, 6] Generated Node #0,1: 96:[97, 6, 6] Operation: 35-29=6 Moving to Node #0,1 Current State: 96:[97, 6, 6], Operations: ['35-29=6'] Exploring Operation: 6/6=1, Resulting Numbers: [97, 1] Generated Node #0,1,0: 96:[97, 1] Operation: 6/6=1 Moving to Node #0,1,0 Current State: 96:[97, 1], Operations: ['35-29=6', '6/6=1'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 33, 14, 82, 89 ]
86
[ "89-33=56", "56/14=4", "82+4=86" ]
Current State: 86:[33, 14, 82, 89], Operations: [] Exploring Operation: 89-33=56, Resulting Numbers: [14, 82, 56] Generated Node #2: [14, 82, 56] from Operation: 89-33=56 Current State: 86:[14, 82, 56], Operations: ['89-33=56'] Exploring Operation: 56/14=4, Resulting Numbers: [82, 4] Generated Node #3: [82, 4] from Operation: 56/14=4 Current State: 86:[82, 4], Operations: ['89-33=56', '56/14=4'] Exploring Operation: 82+4=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[33, 14, 82, 89], Operations: [] Exploring Operation: 33+14=47, Resulting Numbers: [82, 89, 47] Generated Node #0,0: 86:[82, 89, 47] Operation: 33+14=47 Exploring Operation: 33-14=19, Resulting Numbers: [82, 89, 19] Generated Node #0,1: 86:[82, 89, 19] Operation: 33-14=19 Exploring Operation: 14+82=96, Resulting Numbers: [33, 89, 96] Generated Node #0,2: 86:[33, 89, 96] Operation: 14+82=96 Exploring Operation: 82-33=49, Resulting Numbers: [14, 89, 49] Generated Node #0,3: 86:[14, 89, 49] Operation: 82-33=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[82, 89, 47], Operations: ['33+14=47'] Exploring Operation: 89-82=7, Resulting Numbers: [47, 7] Generated Node #0,0,0: 86:[47, 7] Operation: 89-82=7 Exploring Operation: 89-47=42, Resulting Numbers: [82, 42] Generated Node #0,0,1: 86:[82, 42] Operation: 89-47=42 Exploring Operation: 82+47=129, Resulting Numbers: [89, 129] Generated Node #0,0,2: 86:[89, 129] Operation: 82+47=129 Exploring Operation: 82-47=35, Resulting Numbers: [89, 35] Generated Node #0,0,3: 86:[89, 35] Operation: 82-47=35 Moving to Node #0,0,1 Current State: 86:[82, 42], Operations: ['33+14=47', '89-47=42'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,86 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[47, 7], Operations: ['33+14=47', '89-82=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[89, 35], Operations: ['33+14=47', '82-47=35'] Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,86 unequal: No Solution Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,86 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[89, 129], Operations: ['33+14=47', '82+47=129'] Exploring Operation: 89*129=11481, Resulting Numbers: [11481] 11481,86 unequal: No Solution Exploring Operation: 129-89=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 89+129=218, Resulting Numbers: [218] 218,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[14, 89, 49], Operations: ['82-33=49'] Exploring Operation: 89-14=75, Resulting Numbers: [49, 75] Generated Node #0,3,0: 86:[49, 75] Operation: 89-14=75 Exploring Operation: 49-14=35, Resulting Numbers: [89, 35] Generated Node #0,3,1: 86:[89, 35] Operation: 49-14=35 Exploring Operation: 14+89=103, Resulting Numbers: [49, 103] Generated Node #0,3,2: 86:[49, 103] Operation: 14+89=103 Exploring Operation: 89-49=40, Resulting Numbers: [14, 40] Generated Node #0,3,3: 86:[14, 40] Operation: 89-49=40 Moving to Node #0,3,1 Current State: 86:[89, 35], Operations: ['82-33=49', '49-14=35'] Exploring Operation: 89*35=3115, Resulting Numbers: [3115] 3115,86 unequal: No Solution Exploring Operation: 89+35=124, Resulting Numbers: [124] 124,86 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[14, 40], Operations: ['82-33=49', '89-49=40'] Exploring Operation: 14*40=560, Resulting Numbers: [560] 560,86 unequal: No Solution Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[49, 75], Operations: ['82-33=49', '89-14=75'] Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 49*75=3675, Resulting Numbers: [3675] 3675,86 unequal: No Solution Exploring Operation: 49+75=124, Resulting Numbers: [124] 124,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[49, 103], Operations: ['82-33=49', '14+89=103'] Exploring Operation: 49+103=152, Resulting Numbers: [152] 152,86 unequal: No Solution Exploring Operation: 49*103=5047, Resulting Numbers: [5047] 5047,86 unequal: No Solution Exploring Operation: 103-49=54, Resulting Numbers: [54] 54,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[33, 89, 96], Operations: ['14+82=96'] Exploring Operation: 33+89=122, Resulting Numbers: [96, 122] Generated Node #0,2,0: 86:[96, 122] Operation: 33+89=122 Exploring Operation: 96-89=7, Resulting Numbers: [33, 7] Generated Node #0,2,1: 86:[33, 7] Operation: 96-89=7 Exploring Operation: 96-33=63, Resulting Numbers: [89, 63] Generated Node #0,2,2: 86:[89, 63] Operation: 96-33=63 Exploring Operation: 89-33=56, Resulting Numbers: [96, 56] Generated Node #0,2,3: 86:[96, 56] Operation: 89-33=56 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 86:[33, 7], Operations: ['14+82=96', '96-89=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,86 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,86 unequal: No Solution No 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: 86:[89, 63], Operations: ['14+82=96', '96-33=63'] Exploring Operation: 89+63=152, Resulting Numbers: [152] 152,86 unequal: No Solution Exploring Operation: 89*63=5607, Resulting Numbers: [5607] 5607,86 unequal: No Solution Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,86 unequal: No Solution No 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: 86:[96, 56], Operations: ['14+82=96', '89-33=56'] Exploring Operation: 96*56=5376, Resulting Numbers: [5376] 5376,86 unequal: No Solution Exploring Operation: 96+56=152, Resulting Numbers: [152] 152,86 unequal: No Solution Exploring Operation: 96-56=40, Resulting Numbers: [40] 40,86 unequal: No Solution No 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: 86:[96, 122], Operations: ['14+82=96', '33+89=122'] Exploring Operation: 96*122=11712, Resulting Numbers: [11712] 11712,86 unequal: No Solution Exploring Operation: 96+122=218, Resulting Numbers: [218] 218,86 unequal: No Solution Exploring Operation: 122-96=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[82, 89, 19], Operations: ['33-14=19'] Exploring Operation: 82-19=63, Resulting Numbers: [89, 63] Generated Node #0,1,0: 86:[89, 63] Operation: 82-19=63 Exploring Operation: 82+19=101, Resulting Numbers: [89, 101] Generated Node #0,1,1: 86:[89, 101] Operation: 82+19=101 Exploring Operation: 89-19=70, Resulting Numbers: [82, 70] Generated Node #0,1,2: 86:[82, 70] Operation: 89-19=70 Exploring Operation: 89-82=7, Resulting Numbers: [19, 7] Generated Node #0,1,3: 86:[19, 7] Operation: 89-82=7 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 86:[89, 101], Operations: ['33-14=19', '82+19=101'] Exploring Operation: 89*101=8989, Resulting Numbers: [8989] 8989,86 unequal: No Solution Exploring Operation: 89+101=190, Resulting Numbers: [190] 190,86 unequal: No Solution Exploring Operation: 101-89=12, Resulting Numbers: [12] 12,86 unequal: No Solution No 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: 86:[82, 70], Operations: ['33-14=19', '89-19=70'] Exploring Operation: 82*70=5740, Resulting Numbers: [5740] 5740,86 unequal: No Solution Exploring Operation: 82+70=152, Resulting Numbers: [152] 152,86 unequal: No Solution Exploring Operation: 82-70=12, Resulting Numbers: [12] 12,86 unequal: No Solution No 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: 86:[19, 7], Operations: ['33-14=19', '89-82=7'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,86 unequal: No Solution No 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: 86:[89, 63], Operations: ['33-14=19', '82-19=63'] Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 89*63=5607, Resulting Numbers: [5607] 5607,86 unequal: No Solution Exploring Operation: 89+63=152, Resulting Numbers: [152] 152,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 26, 71, 17, 34 ]
62
[ "71-26=45", "34-17=17", "45+17=62" ]
Current State: 62:[26, 71, 17, 34], Operations: [] Exploring Operation: 71-26=45, Resulting Numbers: [17, 34, 45] Generated Node #2: [17, 34, 45] from Operation: 71-26=45 Current State: 62:[17, 34, 45], Operations: ['71-26=45'] Exploring Operation: 34-17=17, Resulting Numbers: [45, 17] Generated Node #3: [45, 17] from Operation: 34-17=17 Current State: 62:[45, 17], Operations: ['71-26=45', '34-17=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[26, 71, 17, 34], Operations: [] Exploring Operation: 26+17=43, Resulting Numbers: [71, 34, 43] Generated Node #0,0: 62:[71, 34, 43] Operation: 26+17=43 Exploring Operation: 71-17=54, Resulting Numbers: [26, 34, 54] Generated Node #0,1: 62:[26, 34, 54] Operation: 71-17=54 Exploring Operation: 26-17=9, Resulting Numbers: [71, 34, 9] Generated Node #0,2: 62:[71, 34, 9] Operation: 26-17=9 Exploring Operation: 34/17=2, Resulting Numbers: [26, 71, 2] Generated Node #0,3: 62:[26, 71, 2] Operation: 34/17=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 62:[26, 71, 2], Operations: ['34/17=2'] Exploring Operation: 26+2=28, Resulting Numbers: [71, 28] Generated Node #0,3,0: 62:[71, 28] Operation: 26+2=28 Exploring Operation: 26-2=24, Resulting Numbers: [71, 24] Generated Node #0,3,1: 62:[71, 24] Operation: 26-2=24 Exploring Operation: 71-2=69, Resulting Numbers: [26, 69] Generated Node #0,3,2: 62:[26, 69] Operation: 71-2=69 Exploring Operation: 71-26=45, Resulting Numbers: [2, 45] Generated Node #0,3,3: 62:[2, 45] Operation: 71-26=45 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[71, 28], Operations: ['34/17=2', '26+2=28'] Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 71+28=99, Resulting Numbers: [99] 99,62 unequal: No Solution Exploring Operation: 71*28=1988, Resulting Numbers: [1988] 1988,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 62:[26, 69], Operations: ['34/17=2', '71-2=69'] Exploring Operation: 26+69=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 26*69=1794, Resulting Numbers: [1794] 1794,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 62:[2, 45], Operations: ['34/17=2', '71-26=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 62:[71, 24], Operations: ['34/17=2', '26-2=24'] Exploring Operation: 71+24=95, Resulting Numbers: [95] 95,62 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,62 unequal: No Solution Exploring Operation: 71*24=1704, Resulting Numbers: [1704] 1704,62 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:[26, 34, 54], Operations: ['71-17=54'] Exploring Operation: 34-26=8, Resulting Numbers: [54, 8] Generated Node #0,1,0: 62:[54, 8] Operation: 34-26=8 Exploring Operation: 54-34=20, Resulting Numbers: [26, 20] Generated Node #0,1,1: 62:[26, 20] Operation: 54-34=20 Exploring Operation: 26+34=60, Resulting Numbers: [54, 60] Generated Node #0,1,2: 62:[54, 60] Operation: 26+34=60 Exploring Operation: 54-26=28, Resulting Numbers: [34, 28] Generated Node #0,1,3: 62:[34, 28] Operation: 54-26=28 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 62:[34, 28], Operations: ['71-17=54', '54-26=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[26, 71, 17, 34], Operations: [] Exploring Operation: 71-17=54, Resulting Numbers: [26, 34, 54] Generated Node #0,1: 62:[26, 34, 54] Operation: 71-17=54 Moving to Node #0,1 Current State: 62:[26, 34, 54], Operations: ['71-17=54'] Exploring Operation: 54-26=28, Resulting Numbers: [34, 28] Generated Node #0,1,3: 62:[34, 28] Operation: 54-26=28 Moving to Node #0,1,3 Current State: 62:[34, 28], Operations: ['71-17=54', '54-26=28'] Exploring Operation: 34+28=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 16, 60, 71, 5 ]
49
[ "71-16=55", "55/5=11", "60-11=49" ]
Current State: 49:[16, 60, 71, 5], Operations: [] Exploring Operation: 71-16=55, Resulting Numbers: [60, 5, 55] Generated Node #2: [60, 5, 55] from Operation: 71-16=55 Current State: 49:[60, 5, 55], Operations: ['71-16=55'] Exploring Operation: 55/5=11, Resulting Numbers: [60, 11] Generated Node #3: [60, 11] from Operation: 55/5=11 Current State: 49:[60, 11], Operations: ['71-16=55', '55/5=11'] Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[16, 60, 71, 5], Operations: [] Exploring Operation: 71-60=11, Resulting Numbers: [16, 5, 11] Generated Node #0,0: 49:[16, 5, 11] Operation: 71-60=11 Exploring Operation: 60-16=44, Resulting Numbers: [71, 5, 44] Generated Node #0,1: 49:[71, 5, 44] Operation: 60-16=44 Exploring Operation: 16-5=11, Resulting Numbers: [60, 71, 11] Generated Node #0,2: 49:[60, 71, 11] Operation: 16-5=11 Exploring Operation: 60/5=12, Resulting Numbers: [16, 71, 12] Generated Node #0,3: 49:[16, 71, 12] Operation: 60/5=12 Exploring Operation: 71-16=55, Resulting Numbers: [60, 5, 55] Generated Node #0,4: 49:[60, 5, 55] Operation: 71-16=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[16, 5, 11], Operations: ['71-60=11'] Exploring Operation: 16-5=11, Resulting Numbers: [11, 11] Generated Node #0,0,0: 49:[11, 11] Operation: 16-5=11 Exploring Operation: 5*11=55, Resulting Numbers: [16, 55] Generated Node #0,0,1: 49:[16, 55] Operation: 5*11=55 Exploring Operation: 16+5=21, Resulting Numbers: [11, 21] Generated Node #0,0,2: 49:[11, 21] Operation: 16+5=21 Exploring Operation: 16-11=5, Resulting Numbers: [5, 5] Generated Node #0,0,3: 49:[5, 5] Operation: 16-11=5 Exploring Operation: 11-5=6, Resulting Numbers: [16, 6] Generated Node #0,0,4: 49:[16, 6] Operation: 11-5=6 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 49:[5, 5], Operations: ['71-60=11', '16-11=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,49 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[11, 11], Operations: ['71-60=11', '16-5=11'] Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,49 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,49 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 49:[16, 6], Operations: ['71-60=11', '11-5=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,49 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 49:[16, 55], Operations: ['71-60=11', '5*11=55'] Exploring Operation: 16*55=880, Resulting Numbers: [880] 880,49 unequal: No Solution Exploring Operation: 55-16=39, Resulting Numbers: [39] 39,49 unequal: No Solution Exploring Operation: 16+55=71, Resulting Numbers: [71] 71,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[11, 21], Operations: ['71-60=11', '16+5=21'] Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,49 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[60, 5, 55], Operations: ['71-16=55'] Exploring Operation: 60-5=55, Resulting Numbers: [55, 55] Generated Node #0,4,0: 49:[55, 55] Operation: 60-5=55 Exploring Operation: 55/5=11, Resulting Numbers: [60, 11] Generated Node #0,4,1: 49:[60, 11] Operation: 55/5=11 Exploring Operation: 60-55=5, Resulting Numbers: [5, 5] Generated Node #0,4,2: 49:[5, 5] Operation: 60-55=5 Exploring Operation: 60/5=12, Resulting Numbers: [55, 12] Generated Node #0,4,3: 49:[55, 12] Operation: 60/5=12 Exploring Operation: 55-5=50, Resulting Numbers: [60, 50] Generated Node #0,4,4: 49:[60, 50] Operation: 55-5=50 Moving to Node #0,4,2 Current State: 49:[5, 5], Operations: ['71-16=55', '60-55=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,49 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,49 unequal: No Solution Moving to Node #0,4,3 Current State: 49:[55, 12], Operations: ['71-16=55', '60/5=12'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,49 unequal: No Solution Exploring Operation: 55*12=660, Resulting Numbers: [660] 660,49 unequal: No Solution Exploring Operation: 55+12=67, Resulting Numbers: [67] 67,49 unequal: No Solution Moving to Node #0,4,0 Current State: 49:[55, 55], Operations: ['71-16=55', '60-5=55'] Exploring Operation: 55/55=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 55-55=0, Resulting Numbers: [0] 0,49 unequal: No Solution Exploring Operation: 55*55=3025, Resulting Numbers: [3025] 3025,49 unequal: No Solution Exploring Operation: 55+55=110, Resulting Numbers: [110] 110,49 unequal: No Solution Moving to Node #0,4,4 Current State: 49:[60, 50], Operations: ['71-16=55', '55-5=50'] Exploring Operation: 60+50=110, Resulting Numbers: [110] 110,49 unequal: No Solution Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,49 unequal: No Solution Exploring Operation: 60*50=3000, Resulting Numbers: [3000] 3000,49 unequal: No Solution Moving to Node #0,4,1 Current State: 49:[60, 11], Operations: ['71-16=55', '55/5=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,49 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[16, 60, 71, 5], Operations: [] Exploring Operation: 71-16=55, Resulting Numbers: [60, 5, 55] Generated Node #0,4: 49:[60, 5, 55] Operation: 71-16=55 Moving to Node #0,4 Current State: 49:[60, 5, 55], Operations: ['71-16=55'] Exploring Operation: 55/5=11, Resulting Numbers: [60, 11] Generated Node #0,4,1: 49:[60, 11] Operation: 55/5=11 Moving to Node #0,4,1 Current State: 49:[60, 11], Operations: ['71-16=55', '55/5=11'] Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.954861
hs_5
mult_heuristic
[ 23, 69, 92, 65 ]
81
[ "69/23=3", "92-65=27", "3*27=81" ]
Current State: 81:[23, 69, 92, 65], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [92, 65, 3] Generated Node #2: [92, 65, 3] from Operation: 69/23=3 Current State: 81:[92, 65, 3], Operations: ['69/23=3'] Exploring Operation: 92-65=27, Resulting Numbers: [3, 27] Generated Node #3: [3, 27] from Operation: 92-65=27 Current State: 81:[3, 27], Operations: ['69/23=3', '92-65=27'] Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[23, 69, 92, 65], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [23, 92, 4] Generated Node #0,0: 81:[23, 92, 4] Operation: 69-65=4 Exploring Operation: 92-69=23, Resulting Numbers: [23, 65, 23] Generated Node #0,1: 81:[23, 65, 23] Operation: 92-69=23 Exploring Operation: 92-65=27, Resulting Numbers: [23, 69, 27] Generated Node #0,2: 81:[23, 69, 27] Operation: 92-65=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[23, 92, 4], Operations: ['69-65=4'] Exploring Operation: 23+4=27, Resulting Numbers: [92, 27] Generated Node #0,0,0: 81:[92, 27] Operation: 23+4=27 Exploring Operation: 92/4=23, Resulting Numbers: [23, 23] Generated Node #0,0,1: 81:[23, 23] Operation: 92/4=23 Exploring Operation: 92/23=4, Resulting Numbers: [4, 4] Generated Node #0,0,2: 81:[4, 4] Operation: 92/23=4 Moving to Node #0,0,2 Current State: 81:[4, 4], Operations: ['69-65=4', '92/23=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,81 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[23, 23], Operations: ['69-65=4', '92/4=23'] Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,81 unequal: No Solution Exploring Operation: 23/23=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 23-23=0, Resulting Numbers: [0] 0,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[92, 27], Operations: ['69-65=4', '23+4=27'] Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,81 unequal: No Solution Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,81 unequal: No Solution Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,81 unequal: No Solution No 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: 81:[23, 69, 27], Operations: ['92-65=27'] Exploring Operation: 27-23=4, Resulting Numbers: [69, 4] Generated Node #0,2,0: 81:[69, 4] Operation: 27-23=4 Exploring Operation: 23+69=92, Resulting Numbers: [27, 92] Generated Node #0,2,1: 81:[27, 92] Operation: 23+69=92 Exploring Operation: 69/23=3, Resulting Numbers: [27, 3] Generated Node #0,2,2: 81:[27, 3] Operation: 69/23=3 Moving to Node #0,2,2 Current State: 81:[27, 3], Operations: ['92-65=27', '69/23=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[23, 69, 92, 65], Operations: [] Exploring Operation: 92-65=27, Resulting Numbers: [23, 69, 27] Generated Node #0,2: 81:[23, 69, 27] Operation: 92-65=27 Moving to Node #0,2 Current State: 81:[23, 69, 27], Operations: ['92-65=27'] Exploring Operation: 69/23=3, Resulting Numbers: [27, 3] Generated Node #0,2,2: 81:[27, 3] Operation: 69/23=3 Moving to Node #0,2,2 Current State: 81:[27, 3], Operations: ['92-65=27', '69/23=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 60, 66, 53, 74 ]
56
[ "60-53=7", "74-66=8", "7*8=56" ]
Current State: 56:[60, 66, 53, 74], Operations: [] Exploring Operation: 60-53=7, Resulting Numbers: [66, 74, 7] Generated Node #2: [66, 74, 7] from Operation: 60-53=7 Current State: 56:[66, 74, 7], Operations: ['60-53=7'] Exploring Operation: 74-66=8, Resulting Numbers: [7, 8] Generated Node #3: [7, 8] from Operation: 74-66=8 Current State: 56:[7, 8], Operations: ['60-53=7', '74-66=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[60, 66, 53, 74], Operations: [] Exploring Operation: 66-60=6, Resulting Numbers: [53, 74, 6] Generated Node #0,0: 56:[53, 74, 6] Operation: 66-60=6 Exploring Operation: 74-66=8, Resulting Numbers: [60, 53, 8] Generated Node #0,1: 56:[60, 53, 8] Operation: 74-66=8 Exploring Operation: 74-53=21, Resulting Numbers: [60, 66, 21] Generated Node #0,2: 56:[60, 66, 21] Operation: 74-53=21 Exploring Operation: 74-60=14, Resulting Numbers: [66, 53, 14] Generated Node #0,3: 56:[66, 53, 14] Operation: 74-60=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[60, 53, 8], Operations: ['74-66=8'] Exploring Operation: 60+8=68, Resulting Numbers: [53, 68] Generated Node #0,1,0: 56:[53, 68] Operation: 60+8=68 Exploring Operation: 53+8=61, Resulting Numbers: [60, 61] Generated Node #0,1,1: 56:[60, 61] Operation: 53+8=61 Exploring Operation: 60-53=7, Resulting Numbers: [8, 7] Generated Node #0,1,2: 56:[8, 7] Operation: 60-53=7 Exploring Operation: 60-8=52, Resulting Numbers: [53, 52] Generated Node #0,1,3: 56:[53, 52] Operation: 60-8=52 Moving to Node #0,1,2 Current State: 56:[8, 7], Operations: ['74-66=8', '60-53=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[60, 66, 53, 74], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [60, 53, 8] Generated Node #0,1: 56:[60, 53, 8] Operation: 74-66=8 Moving to Node #0,1 Current State: 56:[60, 53, 8], Operations: ['74-66=8'] Exploring Operation: 60-53=7, Resulting Numbers: [8, 7] Generated Node #0,1,2: 56:[8, 7] Operation: 60-53=7 Moving to Node #0,1,2 Current State: 56:[8, 7], Operations: ['74-66=8', '60-53=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 26, 68, 97, 86 ]
83
[ "26+68=94", "97-86=11", "94-11=83" ]
Current State: 83:[26, 68, 97, 86], Operations: [] Exploring Operation: 26+68=94, Resulting Numbers: [97, 86, 94] Generated Node #2: [97, 86, 94] from Operation: 26+68=94 Current State: 83:[97, 86, 94], Operations: ['26+68=94'] Exploring Operation: 97-86=11, Resulting Numbers: [94, 11] Generated Node #3: [94, 11] from Operation: 97-86=11 Current State: 83:[94, 11], Operations: ['26+68=94', '97-86=11'] Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[26, 68, 97, 86], Operations: [] Exploring Operation: 86-26=60, Resulting Numbers: [68, 97, 60] Generated Node #0,0: 83:[68, 97, 60] Operation: 86-26=60 Exploring Operation: 26+68=94, Resulting Numbers: [97, 86, 94] Generated Node #0,1: 83:[97, 86, 94] Operation: 26+68=94 Exploring Operation: 68-26=42, Resulting Numbers: [97, 86, 42] Generated Node #0,2: 83:[97, 86, 42] Operation: 68-26=42 Exploring Operation: 97-26=71, Resulting Numbers: [68, 86, 71] Generated Node #0,3: 83:[68, 86, 71] Operation: 97-26=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[97, 86, 94], Operations: ['26+68=94'] Exploring Operation: 97-94=3, Resulting Numbers: [86, 3] Generated Node #0,1,0: 83:[86, 3] Operation: 97-94=3 Exploring Operation: 97+86=183, Resulting Numbers: [94, 183] Generated Node #0,1,1: 83:[94, 183] Operation: 97+86=183 Exploring Operation: 94-86=8, Resulting Numbers: [97, 8] Generated Node #0,1,2: 83:[97, 8] Operation: 94-86=8 Exploring Operation: 97-86=11, Resulting Numbers: [94, 11] Generated Node #0,1,3: 83:[94, 11] Operation: 97-86=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[86, 3], Operations: ['26+68=94', '97-94=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,83 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[26, 68, 97, 86], Operations: [] Exploring Operation: 26+68=94, Resulting Numbers: [97, 86, 94] Generated Node #0,1: 83:[97, 86, 94] Operation: 26+68=94 Moving to Node #0,1 Current State: 83:[97, 86, 94], Operations: ['26+68=94'] Exploring Operation: 97-94=3, Resulting Numbers: [86, 3] Generated Node #0,1,0: 83:[86, 3] Operation: 97-94=3 Moving to Node #0,1,0 Current State: 83:[86, 3], Operations: ['26+68=94', '97-94=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 34, 72, 52, 85 ]
89
[ "52-34=18", "72/18=4", "85+4=89" ]
Current State: 89:[34, 72, 52, 85], Operations: [] Exploring Operation: 52-34=18, Resulting Numbers: [72, 85, 18] Generated Node #2: [72, 85, 18] from Operation: 52-34=18 Current State: 89:[72, 85, 18], Operations: ['52-34=18'] Exploring Operation: 72/18=4, Resulting Numbers: [85, 4] Generated Node #3: [85, 4] from Operation: 72/18=4 Current State: 89:[85, 4], Operations: ['52-34=18', '72/18=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[34, 72, 52, 85], Operations: [] Exploring Operation: 34+72=106, Resulting Numbers: [52, 85, 106] Generated Node #0,0: 89:[52, 85, 106] Operation: 34+72=106 Exploring Operation: 34+85=119, Resulting Numbers: [72, 52, 119] Generated Node #0,1: 89:[72, 52, 119] Operation: 34+85=119 Exploring Operation: 52-34=18, Resulting Numbers: [72, 85, 18] Generated Node #0,2: 89:[72, 85, 18] Operation: 52-34=18 Exploring Operation: 72-34=38, Resulting Numbers: [52, 85, 38] Generated Node #0,3: 89:[52, 85, 38] Operation: 72-34=38 Exploring Operation: 34+52=86, Resulting Numbers: [72, 85, 86] Generated Node #0,4: 89:[72, 85, 86] Operation: 34+52=86 Start Sub Search at level 1: Moving to Node #0,4 Current State: 89:[72, 85, 86], Operations: ['34+52=86'] Exploring Operation: 72+86=158, Resulting Numbers: [85, 158] Generated Node #0,4,0: 89:[85, 158] Operation: 72+86=158 Exploring Operation: 86-72=14, Resulting Numbers: [85, 14] Generated Node #0,4,1: 89:[85, 14] Operation: 86-72=14 Exploring Operation: 85-72=13, Resulting Numbers: [86, 13] Generated Node #0,4,2: 89:[86, 13] Operation: 85-72=13 Exploring Operation: 85+86=171, Resulting Numbers: [72, 171] Generated Node #0,4,3: 89:[72, 171] Operation: 85+86=171 Exploring Operation: 72+85=157, Resulting Numbers: [86, 157] Generated Node #0,4,4: 89:[86, 157] Operation: 72+85=157 Moving to Node #0,4,4 Current State: 89:[86, 157], Operations: ['34+52=86', '72+85=157'] Exploring Operation: 86+157=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 86*157=13502, Resulting Numbers: [13502] 13502,89 unequal: No Solution Exploring Operation: 157-86=71, Resulting Numbers: [71] 71,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[85, 158], Operations: ['34+52=86', '72+86=158'] Exploring Operation: 85*158=13430, Resulting Numbers: [13430] 13430,89 unequal: No Solution Exploring Operation: 85+158=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 158-85=73, Resulting Numbers: [73] 73,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[85, 14], Operations: ['34+52=86', '86-72=14'] Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,89 unequal: No Solution Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,89 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[86, 13], Operations: ['34+52=86', '85-72=13'] Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,89 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[72, 171], Operations: ['34+52=86', '85+86=171'] Exploring Operation: 72*171=12312, Resulting Numbers: [12312] 12312,89 unequal: No Solution Exploring Operation: 72+171=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 171-72=99, Resulting Numbers: [99] 99,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[52, 85, 106], Operations: ['34+72=106'] Exploring Operation: 52+85=137, Resulting Numbers: [106, 137] Generated Node #0,0,0: 89:[106, 137] Operation: 52+85=137 Exploring Operation: 106-85=21, Resulting Numbers: [52, 21] Generated Node #0,0,1: 89:[52, 21] Operation: 106-85=21 Exploring Operation: 106-52=54, Resulting Numbers: [85, 54] Generated Node #0,0,2: 89:[85, 54] Operation: 106-52=54 Exploring Operation: 85-52=33, Resulting Numbers: [106, 33] Generated Node #0,0,3: 89:[106, 33] Operation: 85-52=33 Exploring Operation: 52+106=158, Resulting Numbers: [85, 158] Generated Node #0,0,4: 89:[85, 158] Operation: 52+106=158 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[85, 54], Operations: ['34+72=106', '106-52=54'] Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 85*54=4590, Resulting Numbers: [4590] 4590,89 unequal: No Solution Exploring Operation: 85+54=139, Resulting Numbers: [139] 139,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[106, 137], Operations: ['34+72=106', '52+85=137'] Exploring Operation: 106+137=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 106*137=14522, Resulting Numbers: [14522] 14522,89 unequal: No Solution Exploring Operation: 137-106=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 89:[106, 33], Operations: ['34+72=106', '85-52=33'] Exploring Operation: 106+33=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 106*33=3498, Resulting Numbers: [3498] 3498,89 unequal: No Solution Exploring Operation: 106-33=73, Resulting Numbers: [73] 73,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 89:[85, 158], Operations: ['34+72=106', '52+106=158'] Exploring Operation: 85+158=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 158-85=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 85*158=13430, Resulting Numbers: [13430] 13430,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[52, 21], Operations: ['34+72=106', '106-85=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[72, 52, 119], Operations: ['34+85=119'] Exploring Operation: 119-72=47, Resulting Numbers: [52, 47] Generated Node #0,1,0: 89:[52, 47] Operation: 119-72=47 Exploring Operation: 52+119=171, Resulting Numbers: [72, 171] Generated Node #0,1,1: 89:[72, 171] Operation: 52+119=171 Exploring Operation: 72-52=20, Resulting Numbers: [119, 20] Generated Node #0,1,2: 89:[119, 20] Operation: 72-52=20 Exploring Operation: 119-52=67, Resulting Numbers: [72, 67] Generated Node #0,1,3: 89:[72, 67] Operation: 119-52=67 Exploring Operation: 72+52=124, Resulting Numbers: [119, 124] Generated Node #0,1,4: 89:[119, 124] Operation: 72+52=124 Moving to Node #0,1,3 Current State: 89:[72, 67], Operations: ['34+85=119', '119-52=67'] Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 72+67=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 72*67=4824, Resulting Numbers: [4824] 4824,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[119, 124], Operations: ['34+85=119', '72+52=124'] Exploring Operation: 124-119=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 119*124=14756, Resulting Numbers: [14756] 14756,89 unequal: No Solution Exploring Operation: 119+124=243, Resulting Numbers: [243] 243,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[52, 47], Operations: ['34+85=119', '119-72=47'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 52+47=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 52*47=2444, Resulting Numbers: [2444] 2444,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[72, 171], Operations: ['34+85=119', '52+119=171'] Exploring Operation: 171-72=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 72+171=243, Resulting Numbers: [243] 243,89 unequal: No Solution Exploring Operation: 72*171=12312, Resulting Numbers: [12312] 12312,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[119, 20], Operations: ['34+85=119', '72-52=20'] Exploring Operation: 119+20=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 119*20=2380, Resulting Numbers: [2380] 2380,89 unequal: No Solution Exploring Operation: 119-20=99, Resulting Numbers: [99] 99,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[72, 85, 18], Operations: ['52-34=18'] Exploring Operation: 85+18=103, Resulting Numbers: [72, 103] Generated Node #0,2,0: 89:[72, 103] Operation: 85+18=103 Exploring Operation: 72-18=54, Resulting Numbers: [85, 54] Generated Node #0,2,1: 89:[85, 54] Operation: 72-18=54 Exploring Operation: 72+18=90, Resulting Numbers: [85, 90] Generated Node #0,2,2: 89:[85, 90] Operation: 72+18=90 Exploring Operation: 72/18=4, Resulting Numbers: [85, 4] Generated Node #0,2,3: 89:[85, 4] Operation: 72/18=4 Exploring Operation: 85-18=67, Resulting Numbers: [72, 67] Generated Node #0,2,4: 89:[72, 67] Operation: 85-18=67 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[85, 90], Operations: ['52-34=18', '72+18=90'] Exploring Operation: 85*90=7650, Resulting Numbers: [7650] 7650,89 unequal: No Solution Exploring Operation: 90-85=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 85+90=175, Resulting Numbers: [175] 175,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[72, 103], Operations: ['52-34=18', '85+18=103'] Exploring Operation: 72+103=175, Resulting Numbers: [175] 175,89 unequal: No Solution Exploring Operation: 103-72=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 72*103=7416, Resulting Numbers: [7416] 7416,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 89:[85, 54], Operations: ['52-34=18', '72-18=54'] Exploring Operation: 85*54=4590, Resulting Numbers: [4590] 4590,89 unequal: No Solution Exploring Operation: 85+54=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 89:[72, 67], Operations: ['52-34=18', '85-18=67'] Exploring Operation: 72+67=139, Resulting Numbers: [139] 139,89 unequal: No Solution Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 72*67=4824, Resulting Numbers: [4824] 4824,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 89:[85, 4], Operations: ['52-34=18', '72/18=4'] Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[34, 72, 52, 85], Operations: [] Exploring Operation: 52-34=18, Resulting Numbers: [72, 85, 18] Generated Node #0,2: 89:[72, 85, 18] Operation: 52-34=18 Moving to Node #0,2 Current State: 89:[72, 85, 18], Operations: ['52-34=18'] Exploring Operation: 72/18=4, Resulting Numbers: [85, 4] Generated Node #0,2,3: 89:[85, 4] Operation: 72/18=4 Moving to Node #0,2,3 Current State: 89:[85, 4], Operations: ['52-34=18', '72/18=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.923611
hs_5
mult_heuristic
[ 30, 64, 63, 45 ]
52
[ "64-30=34", "63-45=18", "34+18=52" ]
Current State: 52:[30, 64, 63, 45], Operations: [] Exploring Operation: 64-30=34, Resulting Numbers: [63, 45, 34] Generated Node #2: [63, 45, 34] from Operation: 64-30=34 Current State: 52:[63, 45, 34], Operations: ['64-30=34'] Exploring Operation: 63-45=18, Resulting Numbers: [34, 18] Generated Node #3: [34, 18] from Operation: 63-45=18 Current State: 52:[34, 18], Operations: ['64-30=34', '63-45=18'] Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[30, 64, 63, 45], Operations: [] Exploring Operation: 63-45=18, Resulting Numbers: [30, 64, 18] Generated Node #0,0: 52:[30, 64, 18] Operation: 63-45=18 Exploring Operation: 64-45=19, Resulting Numbers: [30, 63, 19] Generated Node #0,1: 52:[30, 63, 19] Operation: 64-45=19 Exploring Operation: 64-30=34, Resulting Numbers: [63, 45, 34] Generated Node #0,2: 52:[63, 45, 34] Operation: 64-30=34 Exploring Operation: 45-30=15, Resulting Numbers: [64, 63, 15] Generated Node #0,3: 52:[64, 63, 15] Operation: 45-30=15 Exploring Operation: 64-63=1, Resulting Numbers: [30, 45, 1] Generated Node #0,4: 52:[30, 45, 1] Operation: 64-63=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 52:[30, 45, 1], Operations: ['64-63=1'] Exploring Operation: 45-30=15, Resulting Numbers: [1, 15] Generated Node #0,4,0: 52:[1, 15] Operation: 45-30=15 Exploring Operation: 30/1=30, Resulting Numbers: [45, 30] Generated Node #0,4,1: 52:[45, 30] Operation: 30/1=30 Exploring Operation: 30*1=30, Resulting Numbers: [45, 30] Generated Node #0,4,2: 52:[45, 30] Operation: 30*1=30 Exploring Operation: 30-1=29, Resulting Numbers: [45, 29] Generated Node #0,4,3: 52:[45, 29] Operation: 30-1=29 Exploring Operation: 45+1=46, Resulting Numbers: [30, 46] Generated Node #0,4,4: 52:[30, 46] Operation: 45+1=46 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 52:[1, 15], Operations: ['64-63=1', '45-30=15'] Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,52 unequal: No Solution Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,52 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 #0,4,3 Current State: 52:[45, 29], Operations: ['64-63=1', '30-1=29'] Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 45+29=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 45*29=1305, Resulting Numbers: [1305] 1305,52 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 #0,4,4 Current State: 52:[30, 46], Operations: ['64-63=1', '45+1=46'] Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,52 unequal: No Solution Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,52 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 #0,4,1 Current State: 52:[45, 30], Operations: ['64-63=1', '30/1=30'] Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,52 unequal: No Solution Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,52 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 #0,4,2 Current State: 52:[45, 30], Operations: ['64-63=1', '30*1=30'] Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,52 unequal: No Solution Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,52 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:[30, 64, 18], Operations: ['63-45=18'] Exploring Operation: 30-18=12, Resulting Numbers: [64, 12] Generated Node #0,0,0: 52:[64, 12] Operation: 30-18=12 Exploring Operation: 30+18=48, Resulting Numbers: [64, 48] Generated Node #0,0,1: 52:[64, 48] Operation: 30+18=48 Exploring Operation: 64-30=34, Resulting Numbers: [18, 34] Generated Node #0,0,2: 52:[18, 34] Operation: 64-30=34 Exploring Operation: 64+18=82, Resulting Numbers: [30, 82] Generated Node #0,0,3: 52:[30, 82] Operation: 64+18=82 Exploring Operation: 64-18=46, Resulting Numbers: [30, 46] Generated Node #0,0,4: 52:[30, 46] Operation: 64-18=46 Moving to Node #0,0,4 Current State: 52:[30, 46], Operations: ['63-45=18', '64-18=46'] Exploring Operation: 30*46=1380, Resulting Numbers: [1380] 1380,52 unequal: No Solution Exploring Operation: 30+46=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[18, 34], Operations: ['63-45=18', '64-30=34'] Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,52 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[30, 64, 63, 45], Operations: [] Exploring Operation: 63-45=18, Resulting Numbers: [30, 64, 18] Generated Node #0,0: 52:[30, 64, 18] Operation: 63-45=18 Moving to Node #0,0 Current State: 52:[30, 64, 18], Operations: ['63-45=18'] Exploring Operation: 64-30=34, Resulting Numbers: [18, 34] Generated Node #0,0,2: 52:[18, 34] Operation: 64-30=34 Moving to Node #0,0,2 Current State: 52:[18, 34], Operations: ['63-45=18', '64-30=34'] Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 86, 81, 31, 13 ]
13
[ "86-81=5", "31-13=18", "18-5=13" ]
Current State: 13:[86, 81, 31, 13], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [31, 13, 5] Generated Node #2: [31, 13, 5] from Operation: 86-81=5 Current State: 13:[31, 13, 5], Operations: ['86-81=5'] Exploring Operation: 31-13=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 31-13=18 Current State: 13:[5, 18], Operations: ['86-81=5', '31-13=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[86, 81, 31, 13], Operations: [] Exploring Operation: 81-31=50, Resulting Numbers: [86, 13, 50] Generated Node #0,0: 13:[86, 13, 50] Operation: 81-31=50 Exploring Operation: 86-31=55, Resulting Numbers: [81, 13, 55] Generated Node #0,1: 13:[81, 13, 55] Operation: 86-31=55 Exploring Operation: 81-13=68, Resulting Numbers: [86, 31, 68] Generated Node #0,2: 13:[86, 31, 68] Operation: 81-13=68 Exploring Operation: 86-81=5, Resulting Numbers: [31, 13, 5] Generated Node #0,3: 13:[31, 13, 5] Operation: 86-81=5 Exploring Operation: 86-13=73, Resulting Numbers: [81, 31, 73] Generated Node #0,4: 13:[81, 31, 73] Operation: 86-13=73 Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[31, 13, 5], Operations: ['86-81=5'] Exploring Operation: 13+5=18, Resulting Numbers: [31, 18] Generated Node #0,3,0: 13:[31, 18] Operation: 13+5=18 Exploring Operation: 31-5=26, Resulting Numbers: [13, 26] Generated Node #0,3,1: 13:[13, 26] Operation: 31-5=26 Exploring Operation: 31-13=18, Resulting Numbers: [5, 18] Generated Node #0,3,2: 13:[5, 18] Operation: 31-13=18 Exploring Operation: 13-5=8, Resulting Numbers: [31, 8] Generated Node #0,3,3: 13:[31, 8] Operation: 13-5=8 Exploring Operation: 31+5=36, Resulting Numbers: [13, 36] Generated Node #0,3,4: 13:[13, 36] Operation: 31+5=36 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 13:[13, 26], Operations: ['86-81=5', '31-5=26'] Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,13 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[86, 81, 31, 13], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [31, 13, 5] Generated Node #0,3: 13:[31, 13, 5] Operation: 86-81=5 Moving to Node #0,3 Current State: 13:[31, 13, 5], Operations: ['86-81=5'] Exploring Operation: 31-5=26, Resulting Numbers: [13, 26] Generated Node #0,3,1: 13:[13, 26] Operation: 31-5=26 Moving to Node #0,3,1 Current State: 13:[13, 26], Operations: ['86-81=5', '31-5=26'] Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 93, 6, 72, 52 ]
27
[ "72-52=20", "6*20=120", "120-93=27" ]
Current State: 27:[93, 6, 72, 52], Operations: [] Exploring Operation: 72-52=20, Resulting Numbers: [93, 6, 20] Generated Node #2: [93, 6, 20] from Operation: 72-52=20 Current State: 27:[93, 6, 20], Operations: ['72-52=20'] Exploring Operation: 6*20=120, Resulting Numbers: [93, 120] Generated Node #3: [93, 120] from Operation: 6*20=120 Current State: 27:[93, 120], Operations: ['72-52=20', '6*20=120'] Exploring Operation: 120-93=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[93, 6, 72, 52], Operations: [] Exploring Operation: 93-72=21, Resulting Numbers: [6, 52, 21] Generated Node #0,0: 27:[6, 52, 21] Operation: 93-72=21 Exploring Operation: 93-6=87, Resulting Numbers: [72, 52, 87] Generated Node #0,1: 27:[72, 52, 87] Operation: 93-6=87 Exploring Operation: 93-52=41, Resulting Numbers: [6, 72, 41] Generated Node #0,2: 27:[6, 72, 41] Operation: 93-52=41 Exploring Operation: 72-52=20, Resulting Numbers: [93, 6, 20] Generated Node #0,3: 27:[93, 6, 20] Operation: 72-52=20 Exploring Operation: 72/6=12, Resulting Numbers: [93, 52, 12] Generated Node #0,4: 27:[93, 52, 12] Operation: 72/6=12 Moving to Node #0,0 Current State: 27:[6, 52, 21], Operations: ['93-72=21'] Exploring Operation: 21-6=15, Resulting Numbers: [52, 15] Generated Node #0,0,0: 27:[52, 15] Operation: 21-6=15 Exploring Operation: 6+21=27, Resulting Numbers: [52, 27] Generated Node #0,0,1: 27:[52, 27] Operation: 6+21=27 Exploring Operation: 6+52=58, Resulting Numbers: [21, 58] Generated Node #0,0,2: 27:[21, 58] Operation: 6+52=58 Exploring Operation: 52-21=31, Resulting Numbers: [6, 31] Generated Node #0,0,3: 27:[6, 31] Operation: 52-21=31 Exploring Operation: 52-6=46, Resulting Numbers: [21, 46] Generated Node #0,0,4: 27:[21, 46] Operation: 52-6=46 Moving to Node #0,2 Current State: 27:[6, 72, 41], Operations: ['93-52=41'] Exploring Operation: 72-41=31, Resulting Numbers: [6, 31] Generated Node #0,2,0: 27:[6, 31] Operation: 72-41=31 Exploring Operation: 72-6=66, Resulting Numbers: [41, 66] Generated Node #0,2,1: 27:[41, 66] Operation: 72-6=66 Exploring Operation: 72/6=12, Resulting Numbers: [41, 12] Generated Node #0,2,2: 27:[41, 12] Operation: 72/6=12 Exploring Operation: 6+72=78, Resulting Numbers: [41, 78] Generated Node #0,2,3: 27:[41, 78] Operation: 6+72=78 Exploring Operation: 41-6=35, Resulting Numbers: [72, 35] Generated Node #0,2,4: 27:[72, 35] Operation: 41-6=35 Moving to Node #0,3 Current State: 27:[93, 6, 20], Operations: ['72-52=20'] Exploring Operation: 6+20=26, Resulting Numbers: [93, 26] Generated Node #0,3,0: 27:[93, 26] Operation: 6+20=26 Exploring Operation: 93-6=87, Resulting Numbers: [20, 87] Generated Node #0,3,1: 27:[20, 87] Operation: 93-6=87 Exploring Operation: 20-6=14, Resulting Numbers: [93, 14] Generated Node #0,3,2: 27:[93, 14] Operation: 20-6=14 Exploring Operation: 93+6=99, Resulting Numbers: [20, 99] Generated Node #0,3,3: 27:[20, 99] Operation: 93+6=99 Exploring Operation: 93-20=73, Resulting Numbers: [6, 73] Generated Node #0,3,4: 27:[6, 73] Operation: 93-20=73 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 27:[6, 73], Operations: ['72-52=20', '93-20=73'] Exploring Operation: 6*73=438, Resulting Numbers: [438] 438,27 unequal: No Solution Exploring Operation: 6+73=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 27:[93, 26], Operations: ['72-52=20', '6+20=26'] Exploring Operation: 93*26=2418, Resulting Numbers: [2418] 2418,27 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 93+26=119, Resulting Numbers: [119] 119,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 27:[20, 87], Operations: ['72-52=20', '93-6=87'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 20+87=107, Resulting Numbers: [107] 107,27 unequal: No Solution Exploring Operation: 20*87=1740, Resulting Numbers: [1740] 1740,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 27:[93, 14], Operations: ['72-52=20', '20-6=14'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,27 unequal: No Solution Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 27:[20, 99], Operations: ['72-52=20', '93+6=99'] Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 20*99=1980, Resulting Numbers: [1980] 1980,27 unequal: No Solution Exploring Operation: 20+99=119, Resulting Numbers: [119] 119,27 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: 27:[93, 52, 12], Operations: ['72/6=12'] Exploring Operation: 52-12=40, Resulting Numbers: [93, 40] Generated Node #0,4,0: 27:[93, 40] Operation: 52-12=40 Exploring Operation: 93-12=81, Resulting Numbers: [52, 81] Generated Node #0,4,1: 27:[52, 81] Operation: 93-12=81 Exploring Operation: 93-52=41, Resulting Numbers: [12, 41] Generated Node #0,4,2: 27:[12, 41] Operation: 93-52=41 Exploring Operation: 52+12=64, Resulting Numbers: [93, 64] Generated Node #0,4,3: 27:[93, 64] Operation: 52+12=64 Exploring Operation: 93+12=105, Resulting Numbers: [52, 105] Generated Node #0,4,4: 27:[52, 105] Operation: 93+12=105 Moving to Node #0,1 Current State: 27:[72, 52, 87], Operations: ['93-6=87'] Exploring Operation: 72+87=159, Resulting Numbers: [52, 159] Generated Node #0,1,0: 27:[52, 159] Operation: 72+87=159 Exploring Operation: 87-52=35, Resulting Numbers: [72, 35] Generated Node #0,1,1: 27:[72, 35] Operation: 87-52=35 Exploring Operation: 87-72=15, Resulting Numbers: [52, 15] Generated Node #0,1,2: 27:[52, 15] Operation: 87-72=15 Exploring Operation: 72-52=20, Resulting Numbers: [87, 20] Generated Node #0,1,3: 27:[87, 20] Operation: 72-52=20 Exploring Operation: 72+52=124, Resulting Numbers: [87, 124] Generated Node #0,1,4: 27:[87, 124] Operation: 72+52=124 Moving to Node #0,0,3 Current State: 27:[6, 31], Operations: ['93-72=21', '52-21=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,27 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[6, 31], Operations: ['93-52=41', '72-41=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,27 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[41, 12], Operations: ['93-52=41', '72/6=12'] Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,27 unequal: No Solution Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,27 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,27 unequal: No Solution Moving to Node #0,4,2 Current State: 27:[12, 41], Operations: ['72/6=12', '93-52=41'] Exploring Operation: 12*41=492, Resulting Numbers: [492] 492,27 unequal: No Solution Exploring Operation: 12+41=53, Resulting Numbers: [53] 53,27 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,27 unequal: No Solution Moving to Node #0,0,4 Current State: 27:[21, 46], Operations: ['93-72=21', '52-6=46'] Exploring Operation: 21+46=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 21*46=966, Resulting Numbers: [966] 966,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[52, 27], Operations: ['93-72=21', '6+21=27'] Exploring Operation: 52+27=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 52*27=1404, Resulting Numbers: [1404] 1404,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[52, 15], Operations: ['93-72=21', '21-6=15'] Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,27 unequal: No Solution Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[52, 15], Operations: ['93-6=87', '87-72=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 52*15=780, Resulting Numbers: [780] 780,27 unequal: No Solution Exploring Operation: 52-15=37, Resulting Numbers: [37] 37,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[21, 58], Operations: ['93-72=21', '6+52=58'] Exploring Operation: 58-21=37, Resulting Numbers: [37] 37,27 unequal: No Solution Exploring Operation: 21*58=1218, Resulting Numbers: [1218] 1218,27 unequal: No Solution Exploring Operation: 21+58=79, Resulting Numbers: [79] 79,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[72, 35], Operations: ['93-6=87', '87-52=35'] Exploring Operation: 72+35=107, Resulting Numbers: [107] 107,27 unequal: No Solution Exploring Operation: 72*35=2520, Resulting Numbers: [2520] 2520,27 unequal: No Solution Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,27 unequal: No Solution Moving to Node #0,2,4 Current State: 27:[72, 35], Operations: ['93-52=41', '41-6=35'] Exploring Operation: 72*35=2520, Resulting Numbers: [2520] 2520,27 unequal: No Solution Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,27 unequal: No Solution Exploring Operation: 72+35=107, Resulting Numbers: [107] 107,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[41, 66], Operations: ['93-52=41', '72-6=66'] Exploring Operation: 41*66=2706, Resulting Numbers: [2706] 2706,27 unequal: No Solution Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 41+66=107, Resulting Numbers: [107] 107,27 unequal: No Solution Moving to Node #0,2,3 Current State: 27:[41, 78], Operations: ['93-52=41', '6+72=78'] Exploring Operation: 41*78=3198, Resulting Numbers: [3198] 3198,27 unequal: No Solution Exploring Operation: 41+78=119, Resulting Numbers: [119] 119,27 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[87, 20], Operations: ['93-6=87', '72-52=20'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,27 unequal: No Solution Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,27 unequal: No Solution Exploring Operation: 87+20=107, Resulting Numbers: [107] 107,27 unequal: No Solution Moving to Node #0,4,1 Current State: 27:[52, 81], Operations: ['72/6=12', '93-12=81'] Exploring Operation: 52+81=133, Resulting Numbers: [133] 133,27 unequal: No Solution Exploring Operation: 81-52=29, Resulting Numbers: [29] 29,27 unequal: No Solution Exploring Operation: 52*81=4212, Resulting Numbers: [4212] 4212,27 unequal: No Solution Moving to Node #0,4,0 Current State: 27:[93, 40], Operations: ['72/6=12', '52-12=40'] Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,27 unequal: No Solution Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,27 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,27 unequal: No Solution Moving to Node #0,4,4 Current State: 27:[52, 105], Operations: ['72/6=12', '93+12=105'] Exploring Operation: 52+105=157, Resulting Numbers: [157] 157,27 unequal: No Solution Exploring Operation: 52*105=5460, Resulting Numbers: [5460] 5460,27 unequal: No Solution Exploring Operation: 105-52=53, Resulting Numbers: [53] 53,27 unequal: No Solution Moving to Node #0,4,3 Current State: 27:[93, 64], Operations: ['72/6=12', '52+12=64'] Exploring Operation: 93+64=157, Resulting Numbers: [157] 157,27 unequal: No Solution Exploring Operation: 93*64=5952, Resulting Numbers: [5952] 5952,27 unequal: No Solution Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[52, 159], Operations: ['93-6=87', '72+87=159'] Exploring Operation: 52+159=211, Resulting Numbers: [211] 211,27 unequal: No Solution Exploring Operation: 159-52=107, Resulting Numbers: [107] 107,27 unequal: No Solution Exploring Operation: 52*159=8268, Resulting Numbers: [8268] 8268,27 unequal: No Solution Moving to Node #0,1,4 Current State: 27:[87, 124], Operations: ['93-6=87', '72+52=124'] Exploring Operation: 87+124=211, Resulting Numbers: [211] 211,27 unequal: No Solution Exploring Operation: 87*124=10788, Resulting Numbers: [10788] 10788,27 unequal: No Solution Exploring Operation: 124-87=37, Resulting Numbers: [37] 37,27 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 46, 6, 13, 9 ]
74
[ "46+6=52", "13+9=22", "52+22=74" ]
Current State: 74:[46, 6, 13, 9], Operations: [] Exploring Operation: 46+6=52, Resulting Numbers: [13, 9, 52] Generated Node #2: [13, 9, 52] from Operation: 46+6=52 Current State: 74:[13, 9, 52], Operations: ['46+6=52'] Exploring Operation: 13+9=22, Resulting Numbers: [52, 22] Generated Node #3: [52, 22] from Operation: 13+9=22 Current State: 74:[52, 22], Operations: ['46+6=52', '13+9=22'] Exploring Operation: 52+22=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[46, 6, 13, 9], Operations: [] Exploring Operation: 46-13=33, Resulting Numbers: [6, 9, 33] Generated Node #0,0: 74:[6, 9, 33] Operation: 46-13=33 Exploring Operation: 6*13=78, Resulting Numbers: [46, 9, 78] Generated Node #0,1: 74:[46, 9, 78] Operation: 6*13=78 Exploring Operation: 13-9=4, Resulting Numbers: [46, 6, 4] Generated Node #0,2: 74:[46, 6, 4] Operation: 13-9=4 Exploring Operation: 46-9=37, Resulting Numbers: [6, 13, 37] Generated Node #0,3: 74:[6, 13, 37] Operation: 46-9=37 Moving to Node #0,0 Current State: 74:[6, 9, 33], Operations: ['46-13=33'] Exploring Operation: 9-6=3, Resulting Numbers: [33, 3] Generated Node #0,0,0: 74:[33, 3] Operation: 9-6=3 Exploring Operation: 6+33=39, Resulting Numbers: [9, 39] Generated Node #0,0,1: 74:[9, 39] Operation: 6+33=39 Exploring Operation: 9+33=42, Resulting Numbers: [6, 42] Generated Node #0,0,2: 74:[6, 42] Operation: 9+33=42 Exploring Operation: 6+9=15, Resulting Numbers: [33, 15] Generated Node #0,0,3: 74:[33, 15] Operation: 6+9=15 Moving to Node #0,3 Current State: 74:[6, 13, 37], Operations: ['46-9=37'] Exploring Operation: 6+13=19, Resulting Numbers: [37, 19] Generated Node #0,3,0: 74:[37, 19] Operation: 6+13=19 Exploring Operation: 6*13=78, Resulting Numbers: [37, 78] Generated Node #0,3,1: 74:[37, 78] Operation: 6*13=78 Exploring Operation: 6+37=43, Resulting Numbers: [13, 43] Generated Node #0,3,2: 74:[13, 43] Operation: 6+37=43 Exploring Operation: 13-6=7, Resulting Numbers: [37, 7] Generated Node #0,3,3: 74:[37, 7] Operation: 13-6=7 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[37, 78], Operations: ['46-9=37', '6*13=78'] Exploring Operation: 37*78=2886, Resulting Numbers: [2886] 2886,74 unequal: No Solution Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 37+78=115, Resulting Numbers: [115] 115,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[37, 7], Operations: ['46-9=37', '13-6=7'] Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,74 unequal: No Solution Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[37, 19], Operations: ['46-9=37', '6+13=19'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[13, 43], Operations: ['46-9=37', '6+37=43'] Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,74 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 74:[46, 6, 4], Operations: ['13-9=4'] Exploring Operation: 46+6=52, Resulting Numbers: [4, 52] Generated Node #0,2,0: 74:[4, 52] Operation: 46+6=52 Exploring Operation: 46-6=40, Resulting Numbers: [4, 40] Generated Node #0,2,1: 74:[4, 40] Operation: 46-6=40 Exploring Operation: 46-4=42, Resulting Numbers: [6, 42] Generated Node #0,2,2: 74:[6, 42] Operation: 46-4=42 Exploring Operation: 6-4=2, Resulting Numbers: [46, 2] Generated Node #0,2,3: 74:[46, 2] Operation: 6-4=2 Moving to Node #0,1 Current State: 74:[46, 9, 78], Operations: ['6*13=78'] Exploring Operation: 46-9=37, Resulting Numbers: [78, 37] Generated Node #0,1,0: 74:[78, 37] Operation: 46-9=37 Exploring Operation: 46+9=55, Resulting Numbers: [78, 55] Generated Node #0,1,1: 74:[78, 55] Operation: 46+9=55 Exploring Operation: 78-46=32, Resulting Numbers: [9, 32] Generated Node #0,1,2: 74:[9, 32] Operation: 78-46=32 Exploring Operation: 78-9=69, Resulting Numbers: [46, 69] Generated Node #0,1,3: 74:[46, 69] Operation: 78-9=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[78, 37], Operations: ['6*13=78', '46-9=37'] Exploring Operation: 78*37=2886, Resulting Numbers: [2886] 2886,74 unequal: No Solution Exploring Operation: 78+37=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[9, 32], Operations: ['6*13=78', '78-46=32'] Exploring Operation: 9+32=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,74 unequal: No Solution Exploring Operation: 9*32=288, Resulting Numbers: [288] 288,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 74:[46, 69], Operations: ['6*13=78', '78-9=69'] Exploring Operation: 46*69=3174, Resulting Numbers: [3174] 3174,74 unequal: No Solution Exploring Operation: 46+69=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[78, 55], Operations: ['6*13=78', '46+9=55'] Exploring Operation: 78*55=4290, Resulting Numbers: [4290] 4290,74 unequal: No Solution Exploring Operation: 78+55=133, Resulting Numbers: [133] 133,74 unequal: No Solution Exploring Operation: 78-55=23, Resulting Numbers: [23] 23,74 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: 74:[33, 3], Operations: ['46-13=33', '9-6=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,74 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,74 unequal: No Solution Moving to Node #0,2,1 Current State: 74:[4, 40], Operations: ['13-9=4', '46-6=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,74 unequal: No Solution Exploring Operation: 4*40=160, Resulting Numbers: [160] 160,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[6, 42], Operations: ['46-13=33', '9+33=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,74 unequal: No Solution Moving to Node #0,2,2 Current State: 74:[6, 42], Operations: ['13-9=4', '46-4=42'] Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 6+42=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 6*42=252, Resulting Numbers: [252] 252,74 unequal: No Solution Moving to Node #0,2,3 Current State: 74:[46, 2], Operations: ['13-9=4', '6-4=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,74 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,74 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[9, 39], Operations: ['46-13=33', '6+33=39'] Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 9*39=351, Resulting Numbers: [351] 351,74 unequal: No Solution Exploring Operation: 9+39=48, Resulting Numbers: [48] 48,74 unequal: No Solution Moving to Node #0,0,3 Current State: 74:[33, 15], Operations: ['46-13=33', '6+9=15'] Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,74 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,74 unequal: No Solution Moving to Node #0,2,0 Current State: 74:[4, 52], Operations: ['13-9=4', '46+6=52'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,74 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,74 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,74 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 33, 64, 50, 16 ]
97
[ "64-33=31", "50+16=66", "31+66=97" ]
Current State: 97:[33, 64, 50, 16], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [50, 16, 31] Generated Node #2: [50, 16, 31] from Operation: 64-33=31 Current State: 97:[50, 16, 31], Operations: ['64-33=31'] Exploring Operation: 50+16=66, Resulting Numbers: [31, 66] Generated Node #3: [31, 66] from Operation: 50+16=66 Current State: 97:[31, 66], Operations: ['64-33=31', '50+16=66'] Exploring Operation: 31+66=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[33, 64, 50, 16], Operations: [] Exploring Operation: 33+50=83, Resulting Numbers: [64, 16, 83] Generated Node #0,0: 97:[64, 16, 83] Operation: 33+50=83 Exploring Operation: 64+16=80, Resulting Numbers: [33, 50, 80] Generated Node #0,1: 97:[33, 50, 80] Operation: 64+16=80 Exploring Operation: 33+64=97, Resulting Numbers: [50, 16, 97] Generated Node #0,2: 97:[50, 16, 97] Operation: 33+64=97 Exploring Operation: 33+16=49, Resulting Numbers: [64, 50, 49] Generated Node #0,3: 97:[64, 50, 49] Operation: 33+16=49 Moving to Node #0,0 Current State: 97:[64, 16, 83], Operations: ['33+50=83'] Exploring Operation: 64-16=48, Resulting Numbers: [83, 48] Generated Node #0,0,0: 97:[83, 48] Operation: 64-16=48 Exploring Operation: 64+16=80, Resulting Numbers: [83, 80] Generated Node #0,0,1: 97:[83, 80] Operation: 64+16=80 Exploring Operation: 83-16=67, Resulting Numbers: [64, 67] Generated Node #0,0,2: 97:[64, 67] Operation: 83-16=67 Exploring Operation: 16+83=99, Resulting Numbers: [64, 99] Generated Node #0,0,3: 97:[64, 99] Operation: 16+83=99 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[83, 80], Operations: ['33+50=83', '64+16=80'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 83+80=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 83*80=6640, Resulting Numbers: [6640] 6640,97 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 #0,0,3 Current State: 97:[64, 99], Operations: ['33+50=83', '16+83=99'] Exploring Operation: 64*99=6336, Resulting Numbers: [6336] 6336,97 unequal: No Solution Exploring Operation: 64+99=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 99-64=35, Resulting Numbers: [35] 35,97 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 #0,0,0 Current State: 97:[83, 48], Operations: ['33+50=83', '64-16=48'] Exploring Operation: 83*48=3984, Resulting Numbers: [3984] 3984,97 unequal: No Solution Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 83+48=131, Resulting Numbers: [131] 131,97 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 #0,0,2 Current State: 97:[64, 67], Operations: ['33+50=83', '83-16=67'] Exploring Operation: 67-64=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 64*67=4288, Resulting Numbers: [4288] 4288,97 unequal: No Solution Exploring Operation: 64+67=131, Resulting Numbers: [131] 131,97 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: 97:[50, 16, 97], Operations: ['33+64=97'] Exploring Operation: 97-16=81, Resulting Numbers: [50, 81] Generated Node #0,2,0: 97:[50, 81] Operation: 97-16=81 Exploring Operation: 50-16=34, Resulting Numbers: [97, 34] Generated Node #0,2,1: 97:[97, 34] Operation: 50-16=34 Exploring Operation: 16+97=113, Resulting Numbers: [50, 113] Generated Node #0,2,2: 97:[50, 113] Operation: 16+97=113 Exploring Operation: 50+16=66, Resulting Numbers: [97, 66] Generated Node #0,2,3: 97:[97, 66] Operation: 50+16=66 Moving to Node #0,1 Current State: 97:[33, 50, 80], Operations: ['64+16=80'] Exploring Operation: 80-33=47, Resulting Numbers: [50, 47] Generated Node #0,1,0: 97:[50, 47] Operation: 80-33=47 Exploring Operation: 33+50=83, Resulting Numbers: [80, 83] Generated Node #0,1,1: 97:[80, 83] Operation: 33+50=83 Exploring Operation: 50-33=17, Resulting Numbers: [80, 17] Generated Node #0,1,2: 97:[80, 17] Operation: 50-33=17 Exploring Operation: 33+80=113, Resulting Numbers: [50, 113] Generated Node #0,1,3: 97:[50, 113] Operation: 33+80=113 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[80, 83], Operations: ['64+16=80', '33+50=83'] Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,97 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 #0,1,3 Current State: 97:[50, 113], Operations: ['64+16=80', '33+80=113'] Exploring Operation: 50+113=163, Resulting Numbers: [163] 163,97 unequal: No Solution Exploring Operation: 50*113=5650, Resulting Numbers: [5650] 5650,97 unequal: No Solution Exploring Operation: 113-50=63, Resulting Numbers: [63] 63,97 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 #0,1,0 Current State: 97:[50, 47], Operations: ['64+16=80', '80-33=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[33, 64, 50, 16], Operations: [] Exploring Operation: 64+16=80, Resulting Numbers: [33, 50, 80] Generated Node #0,1: 97:[33, 50, 80] Operation: 64+16=80 Moving to Node #0,1 Current State: 97:[33, 50, 80], Operations: ['64+16=80'] Exploring Operation: 80-33=47, Resulting Numbers: [50, 47] Generated Node #0,1,0: 97:[50, 47] Operation: 80-33=47 Moving to Node #0,1,0 Current State: 97:[50, 47], Operations: ['64+16=80', '80-33=47'] Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 5, 47, 46, 89 ]
20
[ "47+46=93", "93-89=4", "5*4=20" ]
Current State: 20:[5, 47, 46, 89], Operations: [] Exploring Operation: 47+46=93, Resulting Numbers: [5, 89, 93] Generated Node #2: [5, 89, 93] from Operation: 47+46=93 Current State: 20:[5, 89, 93], Operations: ['47+46=93'] Exploring Operation: 93-89=4, Resulting Numbers: [5, 4] Generated Node #3: [5, 4] from Operation: 93-89=4 Current State: 20:[5, 4], Operations: ['47+46=93', '93-89=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[5, 47, 46, 89], Operations: [] Exploring Operation: 47-5=42, Resulting Numbers: [46, 89, 42] Generated Node #0,0: 20:[46, 89, 42] Operation: 47-5=42 Exploring Operation: 89-47=42, Resulting Numbers: [5, 46, 42] Generated Node #0,1: 20:[5, 46, 42] Operation: 89-47=42 Exploring Operation: 89-46=43, Resulting Numbers: [5, 47, 43] Generated Node #0,2: 20:[5, 47, 43] Operation: 89-46=43 Exploring Operation: 47-46=1, Resulting Numbers: [5, 89, 1] Generated Node #0,3: 20:[5, 89, 1] Operation: 47-46=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[5, 46, 42], Operations: ['89-47=42'] Exploring Operation: 5+46=51, Resulting Numbers: [42, 51] Generated Node #0,1,0: 20:[42, 51] Operation: 5+46=51 Exploring Operation: 46-5=41, Resulting Numbers: [42, 41] Generated Node #0,1,1: 20:[42, 41] Operation: 46-5=41 Exploring Operation: 46-42=4, Resulting Numbers: [5, 4] Generated Node #0,1,2: 20:[5, 4] Operation: 46-42=4 Exploring Operation: 42-5=37, Resulting Numbers: [46, 37] Generated Node #0,1,3: 20:[46, 37] Operation: 42-5=37 Moving to Node #0,1,2 Current State: 20:[5, 4], Operations: ['89-47=42', '46-42=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[5, 47, 46, 89], Operations: [] Exploring Operation: 89-47=42, Resulting Numbers: [5, 46, 42] Generated Node #0,1: 20:[5, 46, 42] Operation: 89-47=42 Moving to Node #0,1 Current State: 20:[5, 46, 42], Operations: ['89-47=42'] Exploring Operation: 46-42=4, Resulting Numbers: [5, 4] Generated Node #0,1,2: 20:[5, 4] Operation: 46-42=4 Moving to Node #0,1,2 Current State: 20:[5, 4], Operations: ['89-47=42', '46-42=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 35, 84, 42, 13 ]
83
[ "35*84=2940", "2940/42=70", "13+70=83" ]
Current State: 83:[35, 84, 42, 13], Operations: [] Exploring Operation: 35*84=2940, Resulting Numbers: [42, 13, 2940] Generated Node #2: [42, 13, 2940] from Operation: 35*84=2940 Current State: 83:[42, 13, 2940], Operations: ['35*84=2940'] Exploring Operation: 2940/42=70, Resulting Numbers: [13, 70] Generated Node #3: [13, 70] from Operation: 2940/42=70 Current State: 83:[13, 70], Operations: ['35*84=2940', '2940/42=70'] Exploring Operation: 13+70=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[35, 84, 42, 13], Operations: [] Exploring Operation: 35+42=77, Resulting Numbers: [84, 13, 77] Generated Node #0,0: 83:[84, 13, 77] Operation: 35+42=77 Exploring Operation: 35+13=48, Resulting Numbers: [84, 42, 48] Generated Node #0,1: 83:[84, 42, 48] Operation: 35+13=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[84, 13, 77], Operations: ['35+42=77'] Exploring Operation: 13+77=90, Resulting Numbers: [84, 90] Generated Node #0,0,0: 83:[84, 90] Operation: 13+77=90 Exploring Operation: 84-13=71, Resulting Numbers: [77, 71] Generated Node #0,0,1: 83:[77, 71] Operation: 84-13=71 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[84, 90], Operations: ['35+42=77', '13+77=90'] Exploring Operation: 84+90=174, Resulting Numbers: [174] 174,83 unequal: No Solution Exploring Operation: 90-84=6, Resulting Numbers: [6] 6,83 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:[77, 71], Operations: ['35+42=77', '84-13=71'] Exploring Operation: 77+71=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 77-71=6, Resulting Numbers: [6] 6,83 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:[84, 42, 48], Operations: ['35+13=48'] Exploring Operation: 84-42=42, Resulting Numbers: [48, 42] Generated Node #0,1,0: 83:[48, 42] Operation: 84-42=42 Exploring Operation: 42+48=90, Resulting Numbers: [84, 90] Generated Node #0,1,1: 83:[84, 90] Operation: 42+48=90 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[84, 90], Operations: ['35+13=48', '42+48=90'] Exploring Operation: 84+90=174, Resulting Numbers: [174] 174,83 unequal: No Solution Exploring Operation: 90-84=6, Resulting Numbers: [6] 6,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[48, 42], Operations: ['35+13=48', '84-42=42'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,83 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,83 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
mult_heuristic
[ 58, 81, 43, 35 ]
41
[ "81+35=116", "116/58=2", "43-2=41" ]
Current State: 41:[58, 81, 43, 35], Operations: [] Exploring Operation: 81+35=116, Resulting Numbers: [58, 43, 116] Generated Node #2: [58, 43, 116] from Operation: 81+35=116 Current State: 41:[58, 43, 116], Operations: ['81+35=116'] Exploring Operation: 116/58=2, Resulting Numbers: [43, 2] Generated Node #3: [43, 2] from Operation: 116/58=2 Current State: 41:[43, 2], Operations: ['81+35=116', '116/58=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[58, 81, 43, 35], Operations: [] Exploring Operation: 81-43=38, Resulting Numbers: [58, 35, 38] Generated Node #0,0: 41:[58, 35, 38] Operation: 81-43=38 Exploring Operation: 81-35=46, Resulting Numbers: [58, 43, 46] Generated Node #0,1: 41:[58, 43, 46] Operation: 81-35=46 Exploring Operation: 81-58=23, Resulting Numbers: [43, 35, 23] Generated Node #0,2: 41:[43, 35, 23] Operation: 81-58=23 Exploring Operation: 58-35=23, Resulting Numbers: [81, 43, 23] Generated Node #0,3: 41:[81, 43, 23] Operation: 58-35=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[58, 43, 46], Operations: ['81-35=46'] Exploring Operation: 58+43=101, Resulting Numbers: [46, 101] Generated Node #0,1,0: 41:[46, 101] Operation: 58+43=101 Exploring Operation: 58-43=15, Resulting Numbers: [46, 15] Generated Node #0,1,1: 41:[46, 15] Operation: 58-43=15 Exploring Operation: 58-46=12, Resulting Numbers: [43, 12] Generated Node #0,1,2: 41:[43, 12] Operation: 58-46=12 Exploring Operation: 46-43=3, Resulting Numbers: [58, 3] Generated Node #0,1,3: 41:[58, 3] Operation: 46-43=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[46, 15], Operations: ['81-35=46', '58-43=15'] Exploring Operation: 46*15=690, Resulting Numbers: [690] 690,41 unequal: No Solution Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,41 unequal: No Solution No 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: 41:[43, 12], Operations: ['81-35=46', '58-46=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,41 unequal: No Solution No 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: 41:[58, 3], Operations: ['81-35=46', '46-43=3'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,41 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,41 unequal: No Solution No 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: 41:[46, 101], Operations: ['81-35=46', '58+43=101'] Exploring Operation: 46*101=4646, Resulting Numbers: [4646] 4646,41 unequal: No Solution Exploring Operation: 101-46=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 46+101=147, Resulting Numbers: [147] 147,41 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: 41:[58, 35, 38], Operations: ['81-43=38'] Exploring Operation: 58-38=20, Resulting Numbers: [35, 20] Generated Node #0,0,0: 41:[35, 20] Operation: 58-38=20 Exploring Operation: 35+38=73, Resulting Numbers: [58, 73] Generated Node #0,0,1: 41:[58, 73] Operation: 35+38=73 Exploring Operation: 58+35=93, Resulting Numbers: [38, 93] Generated Node #0,0,2: 41:[38, 93] Operation: 58+35=93 Exploring Operation: 58-35=23, Resulting Numbers: [38, 23] Generated Node #0,0,3: 41:[38, 23] Operation: 58-35=23 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[38, 23], Operations: ['81-43=38', '58-35=23'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 38*23=874, Resulting Numbers: [874] 874,41 unequal: No Solution No 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: 41:[35, 20], Operations: ['81-43=38', '58-38=20'] Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,41 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,41 unequal: No Solution No 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: 41:[58, 73], Operations: ['81-43=38', '35+38=73'] Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 58+73=131, Resulting Numbers: [131] 131,41 unequal: No Solution Exploring Operation: 58*73=4234, Resulting Numbers: [4234] 4234,41 unequal: No Solution No 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: 41:[38, 93], Operations: ['81-43=38', '58+35=93'] Exploring Operation: 93-38=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 38*93=3534, Resulting Numbers: [3534] 3534,41 unequal: No Solution Exploring Operation: 38+93=131, Resulting Numbers: [131] 131,41 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: 41:[43, 35, 23], Operations: ['81-58=23'] Exploring Operation: 43+23=66, Resulting Numbers: [35, 66] Generated Node #0,2,0: 41:[35, 66] Operation: 43+23=66 Exploring Operation: 35+23=58, Resulting Numbers: [43, 58] Generated Node #0,2,1: 41:[43, 58] Operation: 35+23=58 Exploring Operation: 35-23=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 41:[43, 12] Operation: 35-23=12 Exploring Operation: 43-23=20, Resulting Numbers: [35, 20] Generated Node #0,2,3: 41:[35, 20] Operation: 43-23=20 Moving to Node #0,2,1 Current State: 41:[43, 58], Operations: ['81-58=23', '35+23=58'] Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 43+58=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 43*58=2494, Resulting Numbers: [2494] 2494,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[35, 20], Operations: ['81-58=23', '43-23=20'] Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,41 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[43, 12], Operations: ['81-58=23', '35-23=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,41 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[35, 66], Operations: ['81-58=23', '43+23=66'] Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 35+66=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 35*66=2310, Resulting Numbers: [2310] 2310,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[81, 43, 23], Operations: ['58-35=23'] Exploring Operation: 81-43=38, Resulting Numbers: [23, 38] Generated Node #0,3,0: 41:[23, 38] Operation: 81-43=38 Exploring Operation: 81+23=104, Resulting Numbers: [43, 104] Generated Node #0,3,1: 41:[43, 104] Operation: 81+23=104 Exploring Operation: 81-23=58, Resulting Numbers: [43, 58] Generated Node #0,3,2: 41:[43, 58] Operation: 81-23=58 Exploring Operation: 43-23=20, Resulting Numbers: [81, 20] Generated Node #0,3,3: 41:[81, 20] Operation: 43-23=20 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 41:[43, 58], Operations: ['58-35=23', '81-23=58'] Exploring Operation: 43+58=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 43*58=2494, Resulting Numbers: [2494] 2494,41 unequal: No Solution Exploring Operation: 58-43=15, Resulting Numbers: [15] 15,41 unequal: No Solution No 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: 41:[23, 38], Operations: ['58-35=23', '81-43=38'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,41 unequal: No Solution No 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: 41:[81, 20], Operations: ['58-35=23', '43-23=20'] Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 81+20=101, Resulting Numbers: [101] 101,41 unequal: No Solution Exploring Operation: 81*20=1620, Resulting Numbers: [1620] 1620,41 unequal: No Solution No 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: 41:[43, 104], Operations: ['58-35=23', '81+23=104'] Exploring Operation: 104-43=61, Resulting Numbers: [61] 61,41 unequal: No Solution Exploring Operation: 43+104=147, Resulting Numbers: [147] 147,41 unequal: No Solution Exploring Operation: 43*104=4472, Resulting Numbers: [4472] 4472,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 47, 70, 19, 14 ]
33
[ "47-19=28", "70/14=5", "28+5=33" ]
Current State: 33:[47, 70, 19, 14], Operations: [] Exploring Operation: 47-19=28, Resulting Numbers: [70, 14, 28] Generated Node #2: [70, 14, 28] from Operation: 47-19=28 Current State: 33:[70, 14, 28], Operations: ['47-19=28'] Exploring Operation: 70/14=5, Resulting Numbers: [28, 5] Generated Node #3: [28, 5] from Operation: 70/14=5 Current State: 33:[28, 5], Operations: ['47-19=28', '70/14=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[47, 70, 19, 14], Operations: [] Exploring Operation: 70-47=23, Resulting Numbers: [19, 14, 23] Generated Node #0,0: 33:[19, 14, 23] Operation: 70-47=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[19, 14, 23], Operations: ['70-47=23'] Exploring Operation: 23-19=4, Resulting Numbers: [14, 4] Generated Node #0,0,0: 33:[14, 4] Operation: 23-19=4 Moving to Node #0,0,0 Current State: 33:[14, 4], Operations: ['70-47=23', '23-19=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 10, 53, 48 ]
14
[ "53-48=5", "28*5=140", "140/10=14" ]
Current State: 14:[28, 10, 53, 48], Operations: [] Exploring Operation: 53-48=5, Resulting Numbers: [28, 10, 5] Generated Node #2: [28, 10, 5] from Operation: 53-48=5 Current State: 14:[28, 10, 5], Operations: ['53-48=5'] Exploring Operation: 28*5=140, Resulting Numbers: [10, 140] Generated Node #3: [10, 140] from Operation: 28*5=140 Current State: 14:[10, 140], Operations: ['53-48=5', '28*5=140'] Exploring Operation: 140/10=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[28, 10, 53, 48], Operations: [] Exploring Operation: 28-10=18, Resulting Numbers: [53, 48, 18] Generated Node #0,0: 14:[53, 48, 18] Operation: 28-10=18 Exploring Operation: 48-28=20, Resulting Numbers: [10, 53, 20] Generated Node #0,1: 14:[10, 53, 20] Operation: 48-28=20 Exploring Operation: 53-28=25, Resulting Numbers: [10, 48, 25] Generated Node #0,2: 14:[10, 48, 25] Operation: 53-28=25 Exploring Operation: 53-48=5, Resulting Numbers: [28, 10, 5] Generated Node #0,3: 14:[28, 10, 5] Operation: 53-48=5 Moving to Node #0,3 Current State: 14:[28, 10, 5], Operations: ['53-48=5'] Exploring Operation: 28-5=23, Resulting Numbers: [10, 23] Generated Node #0,3,0: 14:[10, 23] Operation: 28-5=23 Exploring Operation: 10+5=15, Resulting Numbers: [28, 15] Generated Node #0,3,1: 14:[28, 15] Operation: 10+5=15 Exploring Operation: 10/5=2, Resulting Numbers: [28, 2] Generated Node #0,3,2: 14:[28, 2] Operation: 10/5=2 Exploring Operation: 28-10=18, Resulting Numbers: [5, 18] Generated Node #0,3,3: 14:[5, 18] Operation: 28-10=18 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 14:[5, 18], Operations: ['53-48=5', '28-10=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,14 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,14 unequal: No Solution No 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: 14:[10, 23], Operations: ['53-48=5', '28-5=23'] Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,14 unequal: No Solution Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,14 unequal: No Solution No 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: 14:[28, 2], Operations: ['53-48=5', '10/5=2'] Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[28, 10, 53, 48], Operations: [] Exploring Operation: 53-48=5, Resulting Numbers: [28, 10, 5] Generated Node #0,3: 14:[28, 10, 5] Operation: 53-48=5 Moving to Node #0,3 Current State: 14:[28, 10, 5], Operations: ['53-48=5'] Exploring Operation: 10/5=2, Resulting Numbers: [28, 2] Generated Node #0,3,2: 14:[28, 2] Operation: 10/5=2 Moving to Node #0,3,2 Current State: 14:[28, 2], Operations: ['53-48=5', '10/5=2'] Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 81, 71, 7, 25 ]
42
[ "81-71=10", "7+25=32", "10+32=42" ]
Current State: 42:[81, 71, 7, 25], Operations: [] Exploring Operation: 81-71=10, Resulting Numbers: [7, 25, 10] Generated Node #2: [7, 25, 10] from Operation: 81-71=10 Current State: 42:[7, 25, 10], Operations: ['81-71=10'] Exploring Operation: 7+25=32, Resulting Numbers: [10, 32] Generated Node #3: [10, 32] from Operation: 7+25=32 Current State: 42:[10, 32], Operations: ['81-71=10', '7+25=32'] Exploring Operation: 10+32=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[81, 71, 7, 25], Operations: [] Exploring Operation: 81-71=10, Resulting Numbers: [7, 25, 10] Generated Node #0,0: 42:[7, 25, 10] Operation: 81-71=10 Exploring Operation: 81-25=56, Resulting Numbers: [71, 7, 56] Generated Node #0,1: 42:[71, 7, 56] Operation: 81-25=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[7, 25, 10], Operations: ['81-71=10'] Exploring Operation: 10-7=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 42:[25, 3] Operation: 10-7=3 Exploring Operation: 25-10=15, Resulting Numbers: [7, 15] Generated Node #0,0,1: 42:[7, 15] Operation: 25-10=15 Moving to Node #0,0,1 Current State: 42:[7, 15], Operations: ['81-71=10', '25-10=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[25, 3], Operations: ['81-71=10', '10-7=3'] Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,42 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[71, 7, 56], Operations: ['81-25=56'] Exploring Operation: 56/7=8, Resulting Numbers: [71, 8] Generated Node #0,1,0: 42:[71, 8] Operation: 56/7=8 Exploring Operation: 71-56=15, Resulting Numbers: [7, 15] Generated Node #0,1,1: 42:[7, 15] Operation: 71-56=15 Moving to Node #0,1,1 Current State: 42:[7, 15], Operations: ['81-25=56', '71-56=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[71, 8], Operations: ['81-25=56', '56/7=8'] Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,42 unequal: No Solution Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 19, 81, 12, 40 ]
72
[ "19+81=100", "40-12=28", "100-28=72" ]
Current State: 72:[19, 81, 12, 40], Operations: [] Exploring Operation: 19+81=100, Resulting Numbers: [12, 40, 100] Generated Node #2: [12, 40, 100] from Operation: 19+81=100 Current State: 72:[12, 40, 100], Operations: ['19+81=100'] Exploring Operation: 40-12=28, Resulting Numbers: [100, 28] Generated Node #3: [100, 28] from Operation: 40-12=28 Current State: 72:[100, 28], Operations: ['19+81=100', '40-12=28'] Exploring Operation: 100-28=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[19, 81, 12, 40], Operations: [] Exploring Operation: 19-12=7, Resulting Numbers: [81, 40, 7] Generated Node #0,0: 72:[81, 40, 7] Operation: 19-12=7 Exploring Operation: 81-19=62, Resulting Numbers: [12, 40, 62] Generated Node #0,1: 72:[12, 40, 62] Operation: 81-19=62 Exploring Operation: 40-19=21, Resulting Numbers: [81, 12, 21] Generated Node #0,2: 72:[81, 12, 21] Operation: 40-19=21 Exploring Operation: 81-12=69, Resulting Numbers: [19, 40, 69] Generated Node #0,3: 72:[19, 40, 69] Operation: 81-12=69 Exploring Operation: 81-40=41, Resulting Numbers: [19, 12, 41] Generated Node #0,4: 72:[19, 12, 41] Operation: 81-40=41 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[19, 12, 41], Operations: ['81-40=41'] Exploring Operation: 19+41=60, Resulting Numbers: [12, 60] Generated Node #0,4,0: 72:[12, 60] Operation: 19+41=60 Exploring Operation: 19-12=7, Resulting Numbers: [41, 7] Generated Node #0,4,1: 72:[41, 7] Operation: 19-12=7 Exploring Operation: 19+12=31, Resulting Numbers: [41, 31] Generated Node #0,4,2: 72:[41, 31] Operation: 19+12=31 Exploring Operation: 41-12=29, Resulting Numbers: [19, 29] Generated Node #0,4,3: 72:[19, 29] Operation: 41-12=29 Exploring Operation: 41-19=22, Resulting Numbers: [12, 22] Generated Node #0,4,4: 72:[12, 22] Operation: 41-19=22 Moving to Node #0,4,4 Current State: 72:[12, 22], Operations: ['81-40=41', '41-19=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,72 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,72 unequal: No Solution Moving to Node #0,4,3 Current State: 72:[19, 29], Operations: ['81-40=41', '41-12=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,72 unequal: No Solution Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,72 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,72 unequal: No Solution Moving to Node #0,4,1 Current State: 72:[41, 7], Operations: ['81-40=41', '19-12=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,72 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,72 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,72 unequal: No Solution Moving to Node #0,4,2 Current State: 72:[41, 31], Operations: ['81-40=41', '19+12=31'] Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[19, 81, 12, 40], Operations: [] Exploring Operation: 81-40=41, Resulting Numbers: [19, 12, 41] Generated Node #0,4: 72:[19, 12, 41] Operation: 81-40=41 Moving to Node #0,4 Current State: 72:[19, 12, 41], Operations: ['81-40=41'] Exploring Operation: 19+12=31, Resulting Numbers: [41, 31] Generated Node #0,4,2: 72:[41, 31] Operation: 19+12=31 Moving to Node #0,4,2 Current State: 72:[41, 31], Operations: ['81-40=41', '19+12=31'] Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_5
mult_heuristic
[ 75, 13, 14, 92 ]
39
[ "75+14=89", "92-89=3", "13*3=39" ]
Current State: 39:[75, 13, 14, 92], Operations: [] Exploring Operation: 75+14=89, Resulting Numbers: [13, 92, 89] Generated Node #2: [13, 92, 89] from Operation: 75+14=89 Current State: 39:[13, 92, 89], Operations: ['75+14=89'] Exploring Operation: 92-89=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 92-89=3 Current State: 39:[13, 3], Operations: ['75+14=89', '92-89=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[75, 13, 14, 92], Operations: [] Exploring Operation: 92-13=79, Resulting Numbers: [75, 14, 79] Generated Node #0,0: 39:[75, 14, 79] Operation: 92-13=79 Exploring Operation: 75-14=61, Resulting Numbers: [13, 92, 61] Generated Node #0,1: 39:[13, 92, 61] Operation: 75-14=61 Exploring Operation: 75-13=62, Resulting Numbers: [14, 92, 62] Generated Node #0,2: 39:[14, 92, 62] Operation: 75-13=62 Exploring Operation: 92-75=17, Resulting Numbers: [13, 14, 17] Generated Node #0,3: 39:[13, 14, 17] Operation: 92-75=17 Exploring Operation: 92-14=78, Resulting Numbers: [75, 13, 78] Generated Node #0,4: 39:[75, 13, 78] Operation: 92-14=78 Moving to Node #0,3 Current State: 39:[13, 14, 17], Operations: ['92-75=17'] Exploring Operation: 17-14=3, Resulting Numbers: [13, 3] Generated Node #0,3,0: 39:[13, 3] Operation: 17-14=3 Exploring Operation: 14-13=1, Resulting Numbers: [17, 1] Generated Node #0,3,1: 39:[17, 1] Operation: 14-13=1 Exploring Operation: 17-13=4, Resulting Numbers: [14, 4] Generated Node #0,3,2: 39:[14, 4] Operation: 17-13=4 Exploring Operation: 14+17=31, Resulting Numbers: [13, 31] Generated Node #0,3,3: 39:[13, 31] Operation: 14+17=31 Exploring Operation: 13+17=30, Resulting Numbers: [14, 30] Generated Node #0,3,4: 39:[14, 30] Operation: 13+17=30 Moving to Node #0,4 Current State: 39:[75, 13, 78], Operations: ['92-14=78'] Exploring Operation: 78-13=65, Resulting Numbers: [75, 65] Generated Node #0,4,0: 39:[75, 65] Operation: 78-13=65 Exploring Operation: 78/13=6, Resulting Numbers: [75, 6] Generated Node #0,4,1: 39:[75, 6] Operation: 78/13=6 Exploring Operation: 78-75=3, Resulting Numbers: [13, 3] Generated Node #0,4,2: 39:[13, 3] Operation: 78-75=3 Exploring Operation: 75-13=62, Resulting Numbers: [78, 62] Generated Node #0,4,3: 39:[78, 62] Operation: 75-13=62 Exploring Operation: 75+13=88, Resulting Numbers: [78, 88] Generated Node #0,4,4: 39:[78, 88] Operation: 75+13=88 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 39:[13, 3], Operations: ['92-14=78', '78-75=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[75, 13, 14, 92], Operations: [] Exploring Operation: 92-14=78, Resulting Numbers: [75, 13, 78] Generated Node #0,4: 39:[75, 13, 78] Operation: 92-14=78 Moving to Node #0,4 Current State: 39:[75, 13, 78], Operations: ['92-14=78'] Exploring Operation: 78-75=3, Resulting Numbers: [13, 3] Generated Node #0,4,2: 39:[13, 3] Operation: 78-75=3 Moving to Node #0,4,2 Current State: 39:[13, 3], Operations: ['92-14=78', '78-75=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 85, 9, 54, 55 ]
24
[ "85-55=30", "54/9=6", "30-6=24" ]
Current State: 24:[85, 9, 54, 55], Operations: [] Exploring Operation: 85-55=30, Resulting Numbers: [9, 54, 30] Generated Node #2: [9, 54, 30] from Operation: 85-55=30 Current State: 24:[9, 54, 30], Operations: ['85-55=30'] Exploring Operation: 54/9=6, Resulting Numbers: [30, 6] Generated Node #3: [30, 6] from Operation: 54/9=6 Current State: 24:[30, 6], Operations: ['85-55=30', '54/9=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[85, 9, 54, 55], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [85, 55, 6] Generated Node #0,0: 24:[85, 55, 6] Operation: 54/9=6 Exploring Operation: 55-54=1, Resulting Numbers: [85, 9, 1] Generated Node #0,1: 24:[85, 9, 1] Operation: 55-54=1 Exploring Operation: 85-55=30, Resulting Numbers: [9, 54, 30] Generated Node #0,2: 24:[9, 54, 30] Operation: 85-55=30 Exploring Operation: 85-54=31, Resulting Numbers: [9, 55, 31] Generated Node #0,3: 24:[9, 55, 31] Operation: 85-54=31 Exploring Operation: 85-9=76, Resulting Numbers: [54, 55, 76] Generated Node #0,4: 24:[54, 55, 76] Operation: 85-9=76 Moving to Node #0,2 Current State: 24:[9, 54, 30], Operations: ['85-55=30'] Exploring Operation: 54-9=45, Resulting Numbers: [30, 45] Generated Node #0,2,0: 24:[30, 45] Operation: 54-9=45 Exploring Operation: 54-30=24, Resulting Numbers: [9, 24] Generated Node #0,2,1: 24:[9, 24] Operation: 54-30=24 Exploring Operation: 9+54=63, Resulting Numbers: [30, 63] Generated Node #0,2,2: 24:[30, 63] Operation: 9+54=63 Exploring Operation: 54/9=6, Resulting Numbers: [30, 6] Generated Node #0,2,3: 24:[30, 6] Operation: 54/9=6 Exploring Operation: 30-9=21, Resulting Numbers: [54, 21] Generated Node #0,2,4: 24:[54, 21] Operation: 30-9=21 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 24:[9, 24], Operations: ['85-55=30', '54-30=24'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,24 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,24 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 24:[30, 6], Operations: ['85-55=30', '54/9=6'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[85, 9, 54, 55], Operations: [] Exploring Operation: 85-55=30, Resulting Numbers: [9, 54, 30] Generated Node #0,2: 24:[9, 54, 30] Operation: 85-55=30 Moving to Node #0,2 Current State: 24:[9, 54, 30], Operations: ['85-55=30'] Exploring Operation: 54/9=6, Resulting Numbers: [30, 6] Generated Node #0,2,3: 24:[30, 6] Operation: 54/9=6 Moving to Node #0,2,3 Current State: 24:[30, 6], Operations: ['85-55=30', '54/9=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 46, 4, 97, 92 ]
47
[ "46-4=42", "97-92=5", "42+5=47" ]
Current State: 47:[46, 4, 97, 92], Operations: [] Exploring Operation: 46-4=42, Resulting Numbers: [97, 92, 42] Generated Node #2: [97, 92, 42] from Operation: 46-4=42 Current State: 47:[97, 92, 42], Operations: ['46-4=42'] Exploring Operation: 97-92=5, Resulting Numbers: [42, 5] Generated Node #3: [42, 5] from Operation: 97-92=5 Current State: 47:[42, 5], Operations: ['46-4=42', '97-92=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[46, 4, 97, 92], Operations: [] Exploring Operation: 97-4=93, Resulting Numbers: [46, 92, 93] Generated Node #0,0: 47:[46, 92, 93] Operation: 97-4=93 Exploring Operation: 92/4=23, Resulting Numbers: [46, 97, 23] Generated Node #0,1: 47:[46, 97, 23] Operation: 92/4=23 Exploring Operation: 92-4=88, Resulting Numbers: [46, 97, 88] Generated Node #0,2: 47:[46, 97, 88] Operation: 92-4=88 Exploring Operation: 97-46=51, Resulting Numbers: [4, 92, 51] Generated Node #0,3: 47:[4, 92, 51] Operation: 97-46=51 Exploring Operation: 97-92=5, Resulting Numbers: [46, 4, 5] Generated Node #0,4: 47:[46, 4, 5] Operation: 97-92=5 Moving to Node #0,1 Current State: 47:[46, 97, 23], Operations: ['92/4=23'] Exploring Operation: 46-23=23, Resulting Numbers: [97, 23] Generated Node #0,1,0: 47:[97, 23] Operation: 46-23=23 Exploring Operation: 97-46=51, Resulting Numbers: [23, 51] Generated Node #0,1,1: 47:[23, 51] Operation: 97-46=51 Exploring Operation: 46+23=69, Resulting Numbers: [97, 69] Generated Node #0,1,2: 47:[97, 69] Operation: 46+23=69 Exploring Operation: 97+23=120, Resulting Numbers: [46, 120] Generated Node #0,1,3: 47:[46, 120] Operation: 97+23=120 Exploring Operation: 97-23=74, Resulting Numbers: [46, 74] Generated Node #0,1,4: 47:[46, 74] Operation: 97-23=74 Moving to Node #0,4 Current State: 47:[46, 4, 5], Operations: ['97-92=5'] Exploring Operation: 46-4=42, Resulting Numbers: [5, 42] Generated Node #0,4,0: 47:[5, 42] Operation: 46-4=42 Exploring Operation: 46+4=50, Resulting Numbers: [5, 50] Generated Node #0,4,1: 47:[5, 50] Operation: 46+4=50 Exploring Operation: 4+5=9, Resulting Numbers: [46, 9] Generated Node #0,4,2: 47:[46, 9] Operation: 4+5=9 Exploring Operation: 4*5=20, Resulting Numbers: [46, 20] Generated Node #0,4,3: 47:[46, 20] Operation: 4*5=20 Exploring Operation: 46+5=51, Resulting Numbers: [4, 51] Generated Node #0,4,4: 47:[4, 51] Operation: 46+5=51 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 47:[46, 20], Operations: ['97-92=5', '4*5=20'] Exploring Operation: 46*20=920, Resulting Numbers: [920] 920,47 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,47 unequal: No Solution Exploring Operation: 46+20=66, Resulting Numbers: [66] 66,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 47:[46, 9], Operations: ['97-92=5', '4+5=9'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,47 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 47:[5, 50], Operations: ['97-92=5', '46+4=50'] Exploring Operation: 5+50=55, Resulting Numbers: [55] 55,47 unequal: No Solution Exploring Operation: 5*50=250, Resulting Numbers: [250] 250,47 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,47 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 47:[5, 42], Operations: ['97-92=5', '46-4=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[46, 4, 97, 92], Operations: [] Exploring Operation: 97-92=5, Resulting Numbers: [46, 4, 5] Generated Node #0,4: 47:[46, 4, 5] Operation: 97-92=5 Moving to Node #0,4 Current State: 47:[46, 4, 5], Operations: ['97-92=5'] Exploring Operation: 46-4=42, Resulting Numbers: [5, 42] Generated Node #0,4,0: 47:[5, 42] Operation: 46-4=42 Moving to Node #0,4,0 Current State: 47:[5, 42], Operations: ['97-92=5', '46-4=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
sum_heuristic
[ 60, 19, 49, 91 ]
99
[ "60-19=41", "49+91=140", "140-41=99" ]
Current State: 99:[60, 19, 49, 91], Operations: [] Exploring Operation: 60-19=41, Resulting Numbers: [49, 91, 41] Generated Node #2: [49, 91, 41] from Operation: 60-19=41 Current State: 99:[49, 91, 41], Operations: ['60-19=41'] Exploring Operation: 49+91=140, Resulting Numbers: [41, 140] Generated Node #3: [41, 140] from Operation: 49+91=140 Current State: 99:[41, 140], Operations: ['60-19=41', '49+91=140'] Exploring Operation: 140-41=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[60, 19, 49, 91], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [19, 91, 11] Generated Node #0,0: 99:[19, 91, 11] Operation: 60-49=11 Exploring Operation: 91-60=31, Resulting Numbers: [19, 49, 31] Generated Node #0,1: 99:[19, 49, 31] Operation: 91-60=31 Exploring Operation: 60-19=41, Resulting Numbers: [49, 91, 41] Generated Node #0,2: 99:[49, 91, 41] Operation: 60-19=41 Exploring Operation: 60+49=109, Resulting Numbers: [19, 91, 109] Generated Node #0,3: 99:[19, 91, 109] Operation: 60+49=109 Moving to Node #0,0 Current State: 99:[19, 91, 11], Operations: ['60-49=11'] Exploring Operation: 91+11=102, Resulting Numbers: [19, 102] Generated Node #0,0,0: 99:[19, 102] Operation: 91+11=102 Exploring Operation: 19+11=30, Resulting Numbers: [91, 30] Generated Node #0,0,1: 99:[91, 30] Operation: 19+11=30 Exploring Operation: 19-11=8, Resulting Numbers: [91, 8] Generated Node #0,0,2: 99:[91, 8] Operation: 19-11=8 Exploring Operation: 19+91=110, Resulting Numbers: [11, 110] Generated Node #0,0,3: 99:[11, 110] Operation: 19+91=110 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[91, 8], Operations: ['60-49=11', '19-11=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,99 unequal: No Solution Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[60, 19, 49, 91], Operations: [] Exploring Operation: 60-49=11, Resulting Numbers: [19, 91, 11] Generated Node #0,0: 99:[19, 91, 11] Operation: 60-49=11 Moving to Node #0,0 Current State: 99:[19, 91, 11], Operations: ['60-49=11'] Exploring Operation: 19-11=8, Resulting Numbers: [91, 8] Generated Node #0,0,2: 99:[91, 8] Operation: 19-11=8 Moving to Node #0,0,2 Current State: 99:[91, 8], Operations: ['60-49=11', '19-11=8'] Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 8, 82, 88, 34 ]
59
[ "88/8=11", "82-34=48", "11+48=59" ]
Current State: 59:[8, 82, 88, 34], Operations: [] Exploring Operation: 88/8=11, Resulting Numbers: [82, 34, 11] Generated Node #2: [82, 34, 11] from Operation: 88/8=11 Current State: 59:[82, 34, 11], Operations: ['88/8=11'] Exploring Operation: 82-34=48, Resulting Numbers: [11, 48] Generated Node #3: [11, 48] from Operation: 82-34=48 Current State: 59:[11, 48], Operations: ['88/8=11', '82-34=48'] Exploring Operation: 11+48=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[8, 82, 88, 34], Operations: [] Exploring Operation: 82-8=74, Resulting Numbers: [88, 34, 74] Generated Node #0,0: 59:[88, 34, 74] Operation: 82-8=74 Exploring Operation: 88-8=80, Resulting Numbers: [82, 34, 80] Generated Node #0,1: 59:[82, 34, 80] Operation: 88-8=80 Exploring Operation: 8+34=42, Resulting Numbers: [82, 88, 42] Generated Node #0,2: 59:[82, 88, 42] Operation: 8+34=42 Moving to Node #0,0 Current State: 59:[88, 34, 74], Operations: ['82-8=74'] Exploring Operation: 88-34=54, Resulting Numbers: [74, 54] Generated Node #0,0,0: 59:[74, 54] Operation: 88-34=54 Exploring Operation: 88-74=14, Resulting Numbers: [34, 14] Generated Node #0,0,1: 59:[34, 14] Operation: 88-74=14 Exploring Operation: 74-34=40, Resulting Numbers: [88, 40] Generated Node #0,0,2: 59:[88, 40] Operation: 74-34=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[74, 54], Operations: ['82-8=74', '88-34=54'] Exploring Operation: 74+54=128, Resulting Numbers: [128] 128,59 unequal: No Solution Exploring Operation: 74*54=3996, Resulting Numbers: [3996] 3996,59 unequal: No Solution Exploring Operation: 74-54=20, Resulting Numbers: [20] 20,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 59:[88, 40], Operations: ['82-8=74', '74-34=40'] Exploring Operation: 88+40=128, Resulting Numbers: [128] 128,59 unequal: No Solution Exploring Operation: 88-40=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 88*40=3520, Resulting Numbers: [3520] 3520,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[34, 14], Operations: ['82-8=74', '88-74=14'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,59 unequal: No Solution Exploring Operation: 34*14=476, Resulting Numbers: [476] 476,59 unequal: No Solution Exploring Operation: 34+14=48, Resulting Numbers: [48] 48,59 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: 59:[82, 34, 80], Operations: ['88-8=80'] Exploring Operation: 82-34=48, Resulting Numbers: [80, 48] Generated Node #0,1,0: 59:[80, 48] Operation: 82-34=48 Exploring Operation: 80-34=46, Resulting Numbers: [82, 46] Generated Node #0,1,1: 59:[82, 46] Operation: 80-34=46 Exploring Operation: 82+34=116, Resulting Numbers: [80, 116] Generated Node #0,1,2: 59:[80, 116] Operation: 82+34=116 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[80, 48], Operations: ['88-8=80', '82-34=48'] Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,59 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,59 unequal: No Solution Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[82, 46], Operations: ['88-8=80', '80-34=46'] Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 82+46=128, Resulting Numbers: [128] 128,59 unequal: No Solution Exploring Operation: 82*46=3772, Resulting Numbers: [3772] 3772,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[80, 116], Operations: ['88-8=80', '82+34=116'] Exploring Operation: 116-80=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 80+116=196, Resulting Numbers: [196] 196,59 unequal: No Solution Exploring Operation: 80*116=9280, Resulting Numbers: [9280] 9280,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[82, 88, 42], Operations: ['8+34=42'] Exploring Operation: 88-82=6, Resulting Numbers: [42, 6] Generated Node #0,2,0: 59:[42, 6] Operation: 88-82=6 Exploring Operation: 82-42=40, Resulting Numbers: [88, 40] Generated Node #0,2,1: 59:[88, 40] Operation: 82-42=40 Exploring Operation: 88-42=46, Resulting Numbers: [82, 46] Generated Node #0,2,2: 59:[82, 46] Operation: 88-42=46 Moving to Node #0,2,2 Current State: 59:[82, 46], Operations: ['8+34=42', '88-42=46'] Exploring Operation: 82-46=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 82*46=3772, Resulting Numbers: [3772] 3772,59 unequal: No Solution Exploring Operation: 82+46=128, Resulting Numbers: [128] 128,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[88, 40], Operations: ['8+34=42', '82-42=40'] Exploring Operation: 88+40=128, Resulting Numbers: [128] 128,59 unequal: No Solution Exploring Operation: 88-40=48, Resulting Numbers: [48] 48,59 unequal: No Solution Exploring Operation: 88*40=3520, Resulting Numbers: [3520] 3520,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[42, 6], Operations: ['8+34=42', '88-82=6'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 52, 11, 5, 67 ]
86
[ "67-52=15", "5*15=75", "11+75=86" ]
Current State: 86:[52, 11, 5, 67], Operations: [] Exploring Operation: 67-52=15, Resulting Numbers: [11, 5, 15] Generated Node #2: [11, 5, 15] from Operation: 67-52=15 Current State: 86:[11, 5, 15], Operations: ['67-52=15'] Exploring Operation: 5*15=75, Resulting Numbers: [11, 75] Generated Node #3: [11, 75] from Operation: 5*15=75 Current State: 86:[11, 75], Operations: ['67-52=15', '5*15=75'] Exploring Operation: 11+75=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[52, 11, 5, 67], Operations: [] Exploring Operation: 11+67=78, Resulting Numbers: [52, 5, 78] Generated Node #0,0: 86:[52, 5, 78] Operation: 11+67=78 Exploring Operation: 52-11=41, Resulting Numbers: [5, 67, 41] Generated Node #0,1: 86:[5, 67, 41] Operation: 52-11=41 Moving to Node #0,0 Current State: 86:[52, 5, 78], Operations: ['11+67=78'] Exploring Operation: 52-5=47, Resulting Numbers: [78, 47] Generated Node #0,0,0: 86:[78, 47] Operation: 52-5=47 Exploring Operation: 5+78=83, Resulting Numbers: [52, 83] Generated Node #0,0,1: 86:[52, 83] Operation: 5+78=83 Moving to Node #0,1 Current State: 86:[5, 67, 41], Operations: ['52-11=41'] Exploring Operation: 67-41=26, Resulting Numbers: [5, 26] Generated Node #0,1,0: 86:[5, 26] Operation: 67-41=26 Exploring Operation: 5+67=72, Resulting Numbers: [41, 72] Generated Node #0,1,1: 86:[41, 72] Operation: 5+67=72 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[41, 72], Operations: ['52-11=41', '5+67=72'] Exploring Operation: 72-41=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 41+72=113, Resulting Numbers: [113] 113,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[5, 26], Operations: ['52-11=41', '67-41=26'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,86 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,86 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: 86:[78, 47], Operations: ['11+67=78', '52-5=47'] Exploring Operation: 78+47=125, Resulting Numbers: [125] 125,86 unequal: No Solution Exploring Operation: 78-47=31, Resulting Numbers: [31] 31,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[52, 83], Operations: ['11+67=78', '5+78=83'] Exploring Operation: 83-52=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 52+83=135, Resulting Numbers: [135] 135,86 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 28, 58, 11, 37 ]
56
[ "58-28=30", "37-11=26", "30+26=56" ]
Current State: 56:[28, 58, 11, 37], Operations: [] Exploring Operation: 58-28=30, Resulting Numbers: [11, 37, 30] Generated Node #2: [11, 37, 30] from Operation: 58-28=30 Current State: 56:[11, 37, 30], Operations: ['58-28=30'] Exploring Operation: 37-11=26, Resulting Numbers: [30, 26] Generated Node #3: [30, 26] from Operation: 37-11=26 Current State: 56:[30, 26], Operations: ['58-28=30', '37-11=26'] Exploring Operation: 30+26=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[28, 58, 11, 37], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [28, 58, 26] Generated Node #0,0: 56:[28, 58, 26] Operation: 37-11=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[28, 58, 26], Operations: ['37-11=26'] Exploring Operation: 28-26=2, Resulting Numbers: [58, 2] Generated Node #0,0,0: 56:[58, 2] Operation: 28-26=2 Moving to Node #0,0,0 Current State: 56:[58, 2], Operations: ['37-11=26', '28-26=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[28, 58, 11, 37], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [28, 58, 26] Generated Node #0,0: 56:[28, 58, 26] Operation: 37-11=26 Moving to Node #0,0 Current State: 56:[28, 58, 26], Operations: ['37-11=26'] Exploring Operation: 28-26=2, Resulting Numbers: [58, 2] Generated Node #0,0,0: 56:[58, 2] Operation: 28-26=2 Moving to Node #0,0,0 Current State: 56:[58, 2], Operations: ['37-11=26', '28-26=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 82, 9, 59 ]
29
[ "15+82=97", "9+59=68", "97-68=29" ]
Current State: 29:[15, 82, 9, 59], Operations: [] Exploring Operation: 15+82=97, Resulting Numbers: [9, 59, 97] Generated Node #2: [9, 59, 97] from Operation: 15+82=97 Current State: 29:[9, 59, 97], Operations: ['15+82=97'] Exploring Operation: 9+59=68, Resulting Numbers: [97, 68] Generated Node #3: [97, 68] from Operation: 9+59=68 Current State: 29:[97, 68], Operations: ['15+82=97', '9+59=68'] Exploring Operation: 97-68=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[15, 82, 9, 59], Operations: [] Exploring Operation: 82-15=67, Resulting Numbers: [9, 59, 67] Generated Node #0,0: 29:[9, 59, 67] Operation: 82-15=67 Exploring Operation: 82-59=23, Resulting Numbers: [15, 9, 23] Generated Node #0,1: 29:[15, 9, 23] Operation: 82-59=23 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[15, 9, 23], Operations: ['82-59=23'] Exploring Operation: 15+9=24, Resulting Numbers: [23, 24] Generated Node #0,1,0: 29:[23, 24] Operation: 15+9=24 Exploring Operation: 9+23=32, Resulting Numbers: [15, 32] Generated Node #0,1,1: 29:[15, 32] Operation: 9+23=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[23, 24], Operations: ['82-59=23', '15+9=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,29 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 29:[15, 32], Operations: ['82-59=23', '9+23=32'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 15+32=47, Resulting Numbers: [47] 47,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[9, 59, 67], Operations: ['82-15=67'] Exploring Operation: 67-59=8, Resulting Numbers: [9, 8] Generated Node #0,0,0: 29:[9, 8] Operation: 67-59=8 Exploring Operation: 59-9=50, Resulting Numbers: [67, 50] Generated Node #0,0,1: 29:[67, 50] Operation: 59-9=50 Moving to Node #0,0,0 Current State: 29:[9, 8], Operations: ['82-15=67', '67-59=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[67, 50], Operations: ['82-15=67', '59-9=50'] Exploring Operation: 67+50=117, Resulting Numbers: [117] 117,29 unequal: No Solution Exploring Operation: 67-50=17, Resulting Numbers: [17] 17,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 37, 92, 36, 47 ]
28
[ "92-37=55", "36+47=83", "83-55=28" ]
Current State: 28:[37, 92, 36, 47], Operations: [] Exploring Operation: 92-37=55, Resulting Numbers: [36, 47, 55] Generated Node #2: [36, 47, 55] from Operation: 92-37=55 Current State: 28:[36, 47, 55], Operations: ['92-37=55'] Exploring Operation: 36+47=83, Resulting Numbers: [55, 83] Generated Node #3: [55, 83] from Operation: 36+47=83 Current State: 28:[55, 83], Operations: ['92-37=55', '36+47=83'] Exploring Operation: 83-55=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[37, 92, 36, 47], Operations: [] Exploring Operation: 92-37=55, Resulting Numbers: [36, 47, 55] Generated Node #0,0: 28:[36, 47, 55] Operation: 92-37=55 Exploring Operation: 92-36=56, Resulting Numbers: [37, 47, 56] Generated Node #0,1: 28:[37, 47, 56] Operation: 92-36=56 Exploring Operation: 92-47=45, Resulting Numbers: [37, 36, 45] Generated Node #0,2: 28:[37, 36, 45] Operation: 92-47=45 Moving to Node #0,2 Current State: 28:[37, 36, 45], Operations: ['92-47=45'] Exploring Operation: 45-36=9, Resulting Numbers: [37, 9] Generated Node #0,2,0: 28:[37, 9] Operation: 45-36=9 Exploring Operation: 45-37=8, Resulting Numbers: [36, 8] Generated Node #0,2,1: 28:[36, 8] Operation: 45-37=8 Exploring Operation: 37-36=1, Resulting Numbers: [45, 1] Generated Node #0,2,2: 28:[45, 1] Operation: 37-36=1 Moving to Node #0,0 Current State: 28:[36, 47, 55], Operations: ['92-37=55'] Exploring Operation: 47-36=11, Resulting Numbers: [55, 11] Generated Node #0,0,0: 28:[55, 11] Operation: 47-36=11 Exploring Operation: 55-36=19, Resulting Numbers: [47, 19] Generated Node #0,0,1: 28:[47, 19] Operation: 55-36=19 Exploring Operation: 55-47=8, Resulting Numbers: [36, 8] Generated Node #0,0,2: 28:[36, 8] Operation: 55-47=8 Moving to Node #0,1 Current State: 28:[37, 47, 56], Operations: ['92-36=56'] Exploring Operation: 56-37=19, Resulting Numbers: [47, 19] Generated Node #0,1,0: 28:[47, 19] Operation: 56-37=19 Exploring Operation: 47-37=10, Resulting Numbers: [56, 10] Generated Node #0,1,1: 28:[56, 10] Operation: 47-37=10 Exploring Operation: 56-47=9, Resulting Numbers: [37, 9] Generated Node #0,1,2: 28:[37, 9] Operation: 56-47=9 Moving to Node #0,2,1 Current State: 28:[36, 8], Operations: ['92-47=45', '45-37=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[37, 92, 36, 47], Operations: [] Exploring Operation: 92-47=45, Resulting Numbers: [37, 36, 45] Generated Node #0,2: 28:[37, 36, 45] Operation: 92-47=45 Moving to Node #0,2 Current State: 28:[37, 36, 45], Operations: ['92-47=45'] Exploring Operation: 45-37=8, Resulting Numbers: [36, 8] Generated Node #0,2,1: 28:[36, 8] Operation: 45-37=8 Moving to Node #0,2,1 Current State: 28:[36, 8], Operations: ['92-47=45', '45-37=8'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
0.984375
hs_3
mult_heuristic
[ 35, 66, 66, 51 ]
16
[ "35+66=101", "66+51=117", "117-101=16" ]
Current State: 16:[35, 66, 66, 51], Operations: [] Exploring Operation: 35+66=101, Resulting Numbers: [51, 101] Generated Node #2: [51, 101] from Operation: 35+66=101 Current State: 16:[51, 101], Operations: ['35+66=101'] Exploring Operation: 66+51=117, Resulting Numbers: [101, 117] Generated Node #3: [101, 117] from Operation: 66+51=117 Current State: 16:[101, 117], Operations: ['35+66=101', '66+51=117'] Exploring Operation: 117-101=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[35, 66, 66, 51], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [35, 66, 15] Generated Node #0,0: 16:[35, 66, 15] Operation: 66-51=15 Exploring Operation: 66-66=0, Resulting Numbers: [35, 51, 0] Generated Node #0,1: 16:[35, 51, 0] Operation: 66-66=0 Exploring Operation: 66-35=31, Resulting Numbers: [66, 51, 31] Generated Node #0,2: 16:[66, 51, 31] Operation: 66-35=31 Exploring Operation: 66/66=1, Resulting Numbers: [35, 51, 1] Generated Node #0,3: 16:[35, 51, 1] Operation: 66/66=1 Exploring Operation: 66-51=15, Resulting Numbers: [35, 66, 15] Generated Node #0,4: 16:[35, 66, 15] Operation: 66-51=15 Moving to Node #0,3 Current State: 16:[35, 51, 1], Operations: ['66/66=1'] Exploring Operation: 35-1=34, Resulting Numbers: [51, 34] Generated Node #0,3,0: 16:[51, 34] Operation: 35-1=34 Exploring Operation: 35*1=35, Resulting Numbers: [51, 35] Generated Node #0,3,1: 16:[51, 35] Operation: 35*1=35 Exploring Operation: 35/1=35, Resulting Numbers: [51, 35] Generated Node #0,3,2: 16:[51, 35] Operation: 35/1=35 Exploring Operation: 51-1=50, Resulting Numbers: [35, 50] Generated Node #0,3,3: 16:[35, 50] Operation: 51-1=50 Exploring Operation: 51-35=16, Resulting Numbers: [1, 16] Generated Node #0,3,4: 16:[1, 16] Operation: 51-35=16 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 16:[1, 16], Operations: ['66/66=1', '51-35=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[35, 66, 66, 51], Operations: [] Exploring Operation: 66/66=1, Resulting Numbers: [35, 51, 1] Generated Node #0,3: 16:[35, 51, 1] Operation: 66/66=1 Moving to Node #0,3 Current State: 16:[35, 51, 1], Operations: ['66/66=1'] Exploring Operation: 51-35=16, Resulting Numbers: [1, 16] Generated Node #0,3,4: 16:[1, 16] Operation: 51-35=16 Moving to Node #0,3,4 Current State: 16:[1, 16], Operations: ['66/66=1', '51-35=16'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 17, 64, 11, 4 ]
32
[ "64-17=47", "11+4=15", "47-15=32" ]
Current State: 32:[17, 64, 11, 4], Operations: [] Exploring Operation: 64-17=47, Resulting Numbers: [11, 4, 47] Generated Node #2: [11, 4, 47] from Operation: 64-17=47 Current State: 32:[11, 4, 47], Operations: ['64-17=47'] Exploring Operation: 11+4=15, Resulting Numbers: [47, 15] Generated Node #3: [47, 15] from Operation: 11+4=15 Current State: 32:[47, 15], Operations: ['64-17=47', '11+4=15'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[17, 64, 11, 4], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [17, 11, 16] Generated Node #0,0: 32:[17, 11, 16] Operation: 64/4=16 Exploring Operation: 64-17=47, Resulting Numbers: [11, 4, 47] Generated Node #0,1: 32:[11, 4, 47] Operation: 64-17=47 Moving to Node #0,0 Current State: 32:[17, 11, 16], Operations: ['64/4=16'] Exploring Operation: 17-11=6, Resulting Numbers: [16, 6] Generated Node #0,0,0: 32:[16, 6] Operation: 17-11=6 Exploring Operation: 16-11=5, Resulting Numbers: [17, 5] Generated Node #0,0,1: 32:[17, 5] Operation: 16-11=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[16, 6], Operations: ['64/4=16', '17-11=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[17, 5], Operations: ['64/4=16', '16-11=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,32 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: 32:[11, 4, 47], Operations: ['64-17=47'] Exploring Operation: 47-11=36, Resulting Numbers: [4, 36] Generated Node #0,1,0: 32:[4, 36] Operation: 47-11=36 Exploring Operation: 47-4=43, Resulting Numbers: [11, 43] Generated Node #0,1,1: 32:[11, 43] Operation: 47-4=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[4, 36], Operations: ['64-17=47', '47-11=36'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[17, 64, 11, 4], Operations: [] Exploring Operation: 64-17=47, Resulting Numbers: [11, 4, 47] Generated Node #0,1: 32:[11, 4, 47] Operation: 64-17=47 Moving to Node #0,1 Current State: 32:[11, 4, 47], Operations: ['64-17=47'] Exploring Operation: 47-11=36, Resulting Numbers: [4, 36] Generated Node #0,1,0: 32:[4, 36] Operation: 47-11=36 Moving to Node #0,1,0 Current State: 32:[4, 36], Operations: ['64-17=47', '47-11=36'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 5, 80, 32, 58 ]
15
[ "80-5=75", "32+58=90", "90-75=15" ]
Current State: 15:[5, 80, 32, 58], Operations: [] Exploring Operation: 80-5=75, Resulting Numbers: [32, 58, 75] Generated Node #2: [32, 58, 75] from Operation: 80-5=75 Current State: 15:[32, 58, 75], Operations: ['80-5=75'] Exploring Operation: 32+58=90, Resulting Numbers: [75, 90] Generated Node #3: [75, 90] from Operation: 32+58=90 Current State: 15:[75, 90], Operations: ['80-5=75', '32+58=90'] Exploring Operation: 90-75=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[5, 80, 32, 58], Operations: [] Exploring Operation: 58-32=26, Resulting Numbers: [5, 80, 26] Generated Node #0,0: 15:[5, 80, 26] Operation: 58-32=26 Exploring Operation: 80-5=75, Resulting Numbers: [32, 58, 75] Generated Node #0,1: 15:[32, 58, 75] Operation: 80-5=75 Exploring Operation: 80-32=48, Resulting Numbers: [5, 58, 48] Generated Node #0,2: 15:[5, 58, 48] Operation: 80-32=48 Exploring Operation: 80-58=22, Resulting Numbers: [5, 32, 22] Generated Node #0,3: 15:[5, 32, 22] Operation: 80-58=22 Exploring Operation: 80/5=16, Resulting Numbers: [32, 58, 16] Generated Node #0,4: 15:[32, 58, 16] Operation: 80/5=16 Start Sub Search at level 1: Moving to Node #0,3 Current State: 15:[5, 32, 22], Operations: ['80-58=22'] Exploring Operation: 32-22=10, Resulting Numbers: [5, 10] Generated Node #0,3,0: 15:[5, 10] Operation: 32-22=10 Exploring Operation: 5+32=37, Resulting Numbers: [22, 37] Generated Node #0,3,1: 15:[22, 37] Operation: 5+32=37 Exploring Operation: 22-5=17, Resulting Numbers: [32, 17] Generated Node #0,3,2: 15:[32, 17] Operation: 22-5=17 Exploring Operation: 32-5=27, Resulting Numbers: [22, 27] Generated Node #0,3,3: 15:[22, 27] Operation: 32-5=27 Exploring Operation: 5+22=27, Resulting Numbers: [32, 27] Generated Node #0,3,4: 15:[32, 27] Operation: 5+22=27 Moving to Node #0,3,0 Current State: 15:[5, 10], Operations: ['80-58=22', '32-22=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[5, 80, 32, 58], Operations: [] Exploring Operation: 80-58=22, Resulting Numbers: [5, 32, 22] Generated Node #0,3: 15:[5, 32, 22] Operation: 80-58=22 Moving to Node #0,3 Current State: 15:[5, 32, 22], Operations: ['80-58=22'] Exploring Operation: 32-22=10, Resulting Numbers: [5, 10] Generated Node #0,3,0: 15:[5, 10] Operation: 32-22=10 Moving to Node #0,3,0 Current State: 15:[5, 10], Operations: ['80-58=22', '32-22=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 34, 41, 37, 20 ]
18
[ "34+41=75", "37+20=57", "75-57=18" ]
Current State: 18:[34, 41, 37, 20], Operations: [] Exploring Operation: 34+41=75, Resulting Numbers: [37, 20, 75] Generated Node #2: [37, 20, 75] from Operation: 34+41=75 Current State: 18:[37, 20, 75], Operations: ['34+41=75'] Exploring Operation: 37+20=57, Resulting Numbers: [75, 57] Generated Node #3: [75, 57] from Operation: 37+20=57 Current State: 18:[75, 57], Operations: ['34+41=75', '37+20=57'] Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[34, 41, 37, 20], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [34, 20, 4] Generated Node #0,0: 18:[34, 20, 4] Operation: 41-37=4 Moving to Node #0,0 Current State: 18:[34, 20, 4], Operations: ['41-37=4'] Exploring Operation: 34-20=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 18:[4, 14] Operation: 34-20=14 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[4, 14], Operations: ['41-37=4', '34-20=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[34, 41, 37, 20], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [34, 20, 4] Generated Node #0,0: 18:[34, 20, 4] Operation: 41-37=4 Moving to Node #0,0 Current State: 18:[34, 20, 4], Operations: ['41-37=4'] Exploring Operation: 34-20=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 18:[4, 14] Operation: 34-20=14 Moving to Node #0,0,0 Current State: 18:[4, 14], Operations: ['41-37=4', '34-20=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 21, 51, 82, 19 ]
17
[ "21*51=1071", "82-19=63", "1071/63=17" ]
Current State: 17:[21, 51, 82, 19], Operations: [] Exploring Operation: 21*51=1071, Resulting Numbers: [82, 19, 1071] Generated Node #2: [82, 19, 1071] from Operation: 21*51=1071 Current State: 17:[82, 19, 1071], Operations: ['21*51=1071'] Exploring Operation: 82-19=63, Resulting Numbers: [1071, 63] Generated Node #3: [1071, 63] from Operation: 82-19=63 Current State: 17:[1071, 63], Operations: ['21*51=1071', '82-19=63'] Exploring Operation: 1071/63=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[21, 51, 82, 19], Operations: [] Exploring Operation: 51-21=30, Resulting Numbers: [82, 19, 30] Generated Node #0,0: 17:[82, 19, 30] Operation: 51-21=30 Exploring Operation: 82-51=31, Resulting Numbers: [21, 19, 31] Generated Node #0,1: 17:[21, 19, 31] Operation: 82-51=31 Exploring Operation: 82-21=61, Resulting Numbers: [51, 19, 61] Generated Node #0,2: 17:[51, 19, 61] Operation: 82-21=61 Moving to Node #0,1 Current State: 17:[21, 19, 31], Operations: ['82-51=31'] Exploring Operation: 31-21=10, Resulting Numbers: [19, 10] Generated Node #0,1,0: 17:[19, 10] Operation: 31-21=10 Exploring Operation: 21-19=2, Resulting Numbers: [31, 2] Generated Node #0,1,1: 17:[31, 2] Operation: 21-19=2 Exploring Operation: 31-19=12, Resulting Numbers: [21, 12] Generated Node #0,1,2: 17:[21, 12] Operation: 31-19=12 Moving to Node #0,0 Current State: 17:[82, 19, 30], Operations: ['51-21=30'] Exploring Operation: 30-19=11, Resulting Numbers: [82, 11] Generated Node #0,0,0: 17:[82, 11] Operation: 30-19=11 Exploring Operation: 82-19=63, Resulting Numbers: [30, 63] Generated Node #0,0,1: 17:[30, 63] Operation: 82-19=63 Exploring Operation: 82-30=52, Resulting Numbers: [19, 52] Generated Node #0,0,2: 17:[19, 52] Operation: 82-30=52 Moving to Node #0,2 Current State: 17:[51, 19, 61], Operations: ['82-21=61'] Exploring Operation: 51-19=32, Resulting Numbers: [61, 32] Generated Node #0,2,0: 17:[61, 32] Operation: 51-19=32 Exploring Operation: 61-19=42, Resulting Numbers: [51, 42] Generated Node #0,2,1: 17:[51, 42] Operation: 61-19=42 Exploring Operation: 61-51=10, Resulting Numbers: [19, 10] Generated Node #0,2,2: 17:[19, 10] Operation: 61-51=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 17:[19, 10], Operations: ['82-21=61', '61-51=10'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,17 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,17 unequal: No Solution No 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: 17:[61, 32], Operations: ['82-21=61', '51-19=32'] Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,17 unequal: No Solution Exploring Operation: 61*32=1952, Resulting Numbers: [1952] 1952,17 unequal: No Solution Exploring Operation: 61-32=29, Resulting Numbers: [29] 29,17 unequal: No Solution No 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: 17:[51, 42], Operations: ['82-21=61', '61-19=42'] Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,17 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,17 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: 17:[19, 10], Operations: ['82-51=31', '31-21=10'] Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,17 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[21, 12], Operations: ['82-51=31', '31-19=12'] Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[31, 2], Operations: ['82-51=31', '21-19=2'] Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,17 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[19, 52], Operations: ['51-21=30', '82-30=52'] Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,17 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,17 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[30, 63], Operations: ['51-21=30', '82-19=63'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 30*63=1890, Resulting Numbers: [1890] 1890,17 unequal: No Solution Exploring Operation: 30+63=93, Resulting Numbers: [93] 93,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[82, 11], Operations: ['51-21=30', '30-19=11'] Exploring Operation: 82*11=902, Resulting Numbers: [902] 902,17 unequal: No Solution Exploring Operation: 82+11=93, Resulting Numbers: [93] 93,17 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,17 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 84, 34, 55, 33 ]
72
[ "84-34=50", "55-33=22", "50+22=72" ]
Current State: 72:[84, 34, 55, 33], Operations: [] Exploring Operation: 84-34=50, Resulting Numbers: [55, 33, 50] Generated Node #2: [55, 33, 50] from Operation: 84-34=50 Current State: 72:[55, 33, 50], Operations: ['84-34=50'] Exploring Operation: 55-33=22, Resulting Numbers: [50, 22] Generated Node #3: [50, 22] from Operation: 55-33=22 Current State: 72:[50, 22], Operations: ['84-34=50', '55-33=22'] Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[84, 34, 55, 33], Operations: [] Exploring Operation: 34-33=1, Resulting Numbers: [84, 55, 1] Generated Node #0,0: 72:[84, 55, 1] Operation: 34-33=1 Exploring Operation: 55-34=21, Resulting Numbers: [84, 33, 21] Generated Node #0,1: 72:[84, 33, 21] Operation: 55-34=21 Exploring Operation: 84-55=29, Resulting Numbers: [34, 33, 29] Generated Node #0,2: 72:[34, 33, 29] Operation: 84-55=29 Exploring Operation: 55-33=22, Resulting Numbers: [84, 34, 22] Generated Node #0,3: 72:[84, 34, 22] Operation: 55-33=22 Moving to Node #0,2 Current State: 72:[34, 33, 29], Operations: ['84-55=29'] Exploring Operation: 34-29=5, Resulting Numbers: [33, 5] Generated Node #0,2,0: 72:[33, 5] Operation: 34-29=5 Exploring Operation: 34-33=1, Resulting Numbers: [29, 1] Generated Node #0,2,1: 72:[29, 1] Operation: 34-33=1 Exploring Operation: 34+33=67, Resulting Numbers: [29, 67] Generated Node #0,2,2: 72:[29, 67] Operation: 34+33=67 Exploring Operation: 33-29=4, Resulting Numbers: [34, 4] Generated Node #0,2,3: 72:[34, 4] Operation: 33-29=4 Moving to Node #0,3 Current State: 72:[84, 34, 22], Operations: ['55-33=22'] Exploring Operation: 34+22=56, Resulting Numbers: [84, 56] Generated Node #0,3,0: 72:[84, 56] Operation: 34+22=56 Exploring Operation: 34-22=12, Resulting Numbers: [84, 12] Generated Node #0,3,1: 72:[84, 12] Operation: 34-22=12 Exploring Operation: 84-22=62, Resulting Numbers: [34, 62] Generated Node #0,3,2: 72:[34, 62] Operation: 84-22=62 Exploring Operation: 84-34=50, Resulting Numbers: [22, 50] Generated Node #0,3,3: 72:[22, 50] Operation: 84-34=50 Moving to Node #0,1 Current State: 72:[84, 33, 21], Operations: ['55-34=21'] Exploring Operation: 33-21=12, Resulting Numbers: [84, 12] Generated Node #0,1,0: 72:[84, 12] Operation: 33-21=12 Exploring Operation: 84-21=63, Resulting Numbers: [33, 63] Generated Node #0,1,1: 72:[33, 63] Operation: 84-21=63 Exploring Operation: 84-33=51, Resulting Numbers: [21, 51] Generated Node #0,1,2: 72:[21, 51] Operation: 84-33=51 Exploring Operation: 84/21=4, Resulting Numbers: [33, 4] Generated Node #0,1,3: 72:[33, 4] Operation: 84/21=4 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 72:[33, 4], Operations: ['55-34=21', '84/21=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,72 unequal: No Solution Exploring Operation: 33-4=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 #0,1,0 Current State: 72:[84, 12], Operations: ['55-34=21', '33-21=12'] Exploring Operation: 84+12=96, Resulting Numbers: [96] 96,72 unequal: No Solution Exploring Operation: 84*12=1008, Resulting Numbers: [1008] 1008,72 unequal: No Solution Exploring Operation: 84-12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[84, 34, 55, 33], Operations: [] Exploring Operation: 55-34=21, Resulting Numbers: [84, 33, 21] Generated Node #0,1: 72:[84, 33, 21] Operation: 55-34=21 Moving to Node #0,1 Current State: 72:[84, 33, 21], Operations: ['55-34=21'] Exploring Operation: 33-21=12, Resulting Numbers: [84, 12] Generated Node #0,1,0: 72:[84, 12] Operation: 33-21=12 Moving to Node #0,1,0 Current State: 72:[84, 12], Operations: ['55-34=21', '33-21=12'] Exploring Operation: 84-12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_4
sum_heuristic
[ 65, 67, 21, 17 ]
69
[ "67+17=84", "84/21=4", "65+4=69" ]
Current State: 69:[65, 67, 21, 17], Operations: [] Exploring Operation: 67+17=84, Resulting Numbers: [65, 21, 84] Generated Node #2: [65, 21, 84] from Operation: 67+17=84 Current State: 69:[65, 21, 84], Operations: ['67+17=84'] Exploring Operation: 84/21=4, Resulting Numbers: [65, 4] Generated Node #3: [65, 4] from Operation: 84/21=4 Current State: 69:[65, 4], Operations: ['67+17=84', '84/21=4'] Exploring Operation: 65+4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[65, 67, 21, 17], Operations: [] Exploring Operation: 21-17=4, Resulting Numbers: [65, 67, 4] Generated Node #0,0: 69:[65, 67, 4] Operation: 21-17=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[65, 67, 4], Operations: ['21-17=4'] Exploring Operation: 67-65=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 69:[4, 2] Operation: 67-65=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[4, 2], Operations: ['21-17=4', '67-65=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 30, 99, 16, 16 ]
69
[ "99-30=69", "16-16=0", "69+0=69" ]
Current State: 69:[30, 99, 16, 16], Operations: [] Exploring Operation: 99-30=69, Resulting Numbers: [16, 16, 69] Generated Node #2: [16, 16, 69] from Operation: 99-30=69 Current State: 69:[16, 16, 69], Operations: ['99-30=69'] Exploring Operation: 16-16=0, Resulting Numbers: [69, 0] Generated Node #3: [69, 0] from Operation: 16-16=0 Current State: 69:[69, 0], Operations: ['99-30=69', '16-16=0'] Exploring Operation: 69+0=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[30, 99, 16, 16], Operations: [] Exploring Operation: 99-16=83, Resulting Numbers: [30, 16, 83] Generated Node #0,0: 69:[30, 16, 83] Operation: 99-16=83 Exploring Operation: 99-16=83, Resulting Numbers: [30, 16, 83] Generated Node #0,1: 69:[30, 16, 83] Operation: 99-16=83 Exploring Operation: 16/16=1, Resulting Numbers: [30, 99, 1] Generated Node #0,2: 69:[30, 99, 1] Operation: 16/16=1 Exploring Operation: 99-30=69, Resulting Numbers: [16, 16, 69] Generated Node #0,3: 69:[16, 16, 69] Operation: 99-30=69 Moving to Node #0,3 Current State: 69:[16, 16, 69], Operations: ['99-30=69'] Exploring Operation: 16-16=0, Resulting Numbers: [69, 0] Generated Node #0,3,0: 69:[69, 0] Operation: 16-16=0 Exploring Operation: 16+69=85, Resulting Numbers: [16, 85] Generated Node #0,3,1: 69:[16, 85] Operation: 16+69=85 Exploring Operation: 16+16=32, Resulting Numbers: [69, 32] Generated Node #0,3,2: 69:[69, 32] Operation: 16+16=32 Exploring Operation: 16/16=1, Resulting Numbers: [69, 1] Generated Node #0,3,3: 69:[69, 1] Operation: 16/16=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[69, 1], Operations: ['99-30=69', '16/16=1'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[30, 99, 16, 16], Operations: [] Exploring Operation: 99-30=69, Resulting Numbers: [16, 16, 69] Generated Node #0,3: 69:[16, 16, 69] Operation: 99-30=69 Moving to Node #0,3 Current State: 69:[16, 16, 69], Operations: ['99-30=69'] Exploring Operation: 16/16=1, Resulting Numbers: [69, 1] Generated Node #0,3,3: 69:[69, 1] Operation: 16/16=1 Moving to Node #0,3,3 Current State: 69:[69, 1], Operations: ['99-30=69', '16/16=1'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 4, 94, 68, 89 ]
12
[ "68/4=17", "94-89=5", "17-5=12" ]
Current State: 12:[4, 94, 68, 89], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [94, 89, 17] Generated Node #2: [94, 89, 17] from Operation: 68/4=17 Current State: 12:[94, 89, 17], Operations: ['68/4=17'] Exploring Operation: 94-89=5, Resulting Numbers: [17, 5] Generated Node #3: [17, 5] from Operation: 94-89=5 Current State: 12:[17, 5], Operations: ['68/4=17', '94-89=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[4, 94, 68, 89], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [4, 89, 26] Generated Node #0,0: 12:[4, 89, 26] Operation: 94-68=26 Exploring Operation: 94-89=5, Resulting Numbers: [4, 68, 5] Generated Node #0,1: 12:[4, 68, 5] Operation: 94-89=5 Moving to Node #0,1 Current State: 12:[4, 68, 5], Operations: ['94-89=5'] Exploring Operation: 68-5=63, Resulting Numbers: [4, 63] Generated Node #0,1,0: 12:[4, 63] Operation: 68-5=63 Exploring Operation: 68/4=17, Resulting Numbers: [5, 17] Generated Node #0,1,1: 12:[5, 17] Operation: 68/4=17 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[5, 17], Operations: ['94-89=5', '68/4=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[4, 94, 68, 89], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [4, 68, 5] Generated Node #0,1: 12:[4, 68, 5] Operation: 94-89=5 Moving to Node #0,1 Current State: 12:[4, 68, 5], Operations: ['94-89=5'] Exploring Operation: 68/4=17, Resulting Numbers: [5, 17] Generated Node #0,1,1: 12:[5, 17] Operation: 68/4=17 Moving to Node #0,1,1 Current State: 12:[5, 17], Operations: ['94-89=5', '68/4=17'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 31, 36, 5, 52 ]
10
[ "31+36=67", "5+52=57", "67-57=10" ]
Current State: 10:[31, 36, 5, 52], Operations: [] Exploring Operation: 31+36=67, Resulting Numbers: [5, 52, 67] Generated Node #2: [5, 52, 67] from Operation: 31+36=67 Current State: 10:[5, 52, 67], Operations: ['31+36=67'] Exploring Operation: 5+52=57, Resulting Numbers: [67, 57] Generated Node #3: [67, 57] from Operation: 5+52=57 Current State: 10:[67, 57], Operations: ['31+36=67', '5+52=57'] Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[31, 36, 5, 52], Operations: [] Exploring Operation: 52-36=16, Resulting Numbers: [31, 5, 16] Generated Node #0,0: 10:[31, 5, 16] Operation: 52-36=16 Exploring Operation: 36-31=5, Resulting Numbers: [5, 52, 5] Generated Node #0,1: 10:[5, 52, 5] Operation: 36-31=5 Exploring Operation: 52-31=21, Resulting Numbers: [36, 5, 21] Generated Node #0,2: 10:[36, 5, 21] Operation: 52-31=21 Moving to Node #0,0 Current State: 10:[31, 5, 16], Operations: ['52-36=16'] Exploring Operation: 31-16=15, Resulting Numbers: [5, 15] Generated Node #0,0,0: 10:[5, 15] Operation: 31-16=15 Exploring Operation: 31-5=26, Resulting Numbers: [16, 26] Generated Node #0,0,1: 10:[16, 26] Operation: 31-5=26 Exploring Operation: 16-5=11, Resulting Numbers: [31, 11] Generated Node #0,0,2: 10:[31, 11] Operation: 16-5=11 Moving to Node #0,2 Current State: 10:[36, 5, 21], Operations: ['52-31=21'] Exploring Operation: 36-5=31, Resulting Numbers: [21, 31] Generated Node #0,2,0: 10:[21, 31] Operation: 36-5=31 Exploring Operation: 36-21=15, Resulting Numbers: [5, 15] Generated Node #0,2,1: 10:[5, 15] Operation: 36-21=15 Exploring Operation: 21-5=16, Resulting Numbers: [36, 16] Generated Node #0,2,2: 10:[36, 16] Operation: 21-5=16 Moving to Node #0,1 Current State: 10:[5, 52, 5], Operations: ['36-31=5'] Exploring Operation: 5+5=10, Resulting Numbers: [52, 10] Generated Node #0,1,0: 10:[52, 10] Operation: 5+5=10 Exploring Operation: 52-5=47, Resulting Numbers: [5, 47] Generated Node #0,1,1: 10:[5, 47] Operation: 52-5=47 Exploring Operation: 52-5=47, Resulting Numbers: [5, 47] Generated Node #0,1,2: 10:[5, 47] Operation: 52-5=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[5, 47], Operations: ['36-31=5', '52-5=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,10 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,10 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[5, 47], Operations: ['36-31=5', '52-5=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,10 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,10 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[52, 10], Operations: ['36-31=5', '5+5=10'] Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,10 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,10 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: 10:[5, 15], Operations: ['52-36=16', '31-16=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[31, 36, 5, 52], Operations: [] Exploring Operation: 52-36=16, Resulting Numbers: [31, 5, 16] Generated Node #0,0: 10:[31, 5, 16] Operation: 52-36=16 Moving to Node #0,0 Current State: 10:[31, 5, 16], Operations: ['52-36=16'] Exploring Operation: 31-16=15, Resulting Numbers: [5, 15] Generated Node #0,0,0: 10:[5, 15] Operation: 31-16=15 Moving to Node #0,0,0 Current State: 10:[5, 15], Operations: ['52-36=16', '31-16=15'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.975694
hs_3
sum_heuristic
[ 80, 96, 30, 4 ]
46
[ "80/4=20", "96-30=66", "66-20=46" ]
Current State: 46:[80, 96, 30, 4], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [96, 30, 20] Generated Node #2: [96, 30, 20] from Operation: 80/4=20 Current State: 46:[96, 30, 20], Operations: ['80/4=20'] Exploring Operation: 96-30=66, Resulting Numbers: [20, 66] Generated Node #3: [20, 66] from Operation: 96-30=66 Current State: 46:[20, 66], Operations: ['80/4=20', '96-30=66'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[80, 96, 30, 4], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [96, 30, 20] Generated Node #0,0: 46:[96, 30, 20] Operation: 80/4=20 Exploring Operation: 80-30=50, Resulting Numbers: [96, 4, 50] Generated Node #0,1: 46:[96, 4, 50] Operation: 80-30=50 Exploring Operation: 96-80=16, Resulting Numbers: [30, 4, 16] Generated Node #0,2: 46:[30, 4, 16] Operation: 96-80=16 Exploring Operation: 96-30=66, Resulting Numbers: [80, 4, 66] Generated Node #0,3: 46:[80, 4, 66] Operation: 96-30=66 Exploring Operation: 96/4=24, Resulting Numbers: [80, 30, 24] Generated Node #0,4: 46:[80, 30, 24] Operation: 96/4=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[30, 4, 16], Operations: ['96-80=16'] Exploring Operation: 30-4=26, Resulting Numbers: [16, 26] Generated Node #0,2,0: 46:[16, 26] Operation: 30-4=26 Exploring Operation: 30+16=46, Resulting Numbers: [4, 46] Generated Node #0,2,1: 46:[4, 46] Operation: 30+16=46 Exploring Operation: 16/4=4, Resulting Numbers: [30, 4] Generated Node #0,2,2: 46:[30, 4] Operation: 16/4=4 Exploring Operation: 4+16=20, Resulting Numbers: [30, 20] Generated Node #0,2,3: 46:[30, 20] Operation: 4+16=20 Exploring Operation: 30-16=14, Resulting Numbers: [4, 14] Generated Node #0,2,4: 46:[4, 14] Operation: 30-16=14 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[4, 46], Operations: ['96-80=16', '30+16=46'] Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,46 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,46 unequal: No Solution No 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: 46:[30, 4], Operations: ['96-80=16', '16/4=4'] Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,46 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,46 unequal: No Solution No 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: 46:[16, 26], Operations: ['96-80=16', '30-4=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,46 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,46 unequal: No Solution No 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: 46:[30, 20], Operations: ['96-80=16', '4+16=20'] Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,46 unequal: No Solution Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,46 unequal: No Solution No 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: 46:[4, 14], Operations: ['96-80=16', '30-16=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,46 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,46 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,46 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: 46:[80, 30, 24], Operations: ['96/4=24'] Exploring Operation: 80-30=50, Resulting Numbers: [24, 50] Generated Node #0,4,0: 46:[24, 50] Operation: 80-30=50 Exploring Operation: 80-24=56, Resulting Numbers: [30, 56] Generated Node #0,4,1: 46:[30, 56] Operation: 80-24=56 Exploring Operation: 30-24=6, Resulting Numbers: [80, 6] Generated Node #0,4,2: 46:[80, 6] Operation: 30-24=6 Exploring Operation: 30+24=54, Resulting Numbers: [80, 54] Generated Node #0,4,3: 46:[80, 54] Operation: 30+24=54 Exploring Operation: 80+30=110, Resulting Numbers: [24, 110] Generated Node #0,4,4: 46:[24, 110] Operation: 80+30=110 Moving to Node #0,4,0 Current State: 46:[24, 50], Operations: ['96/4=24', '80-30=50'] Exploring Operation: 24*50=1200, Resulting Numbers: [1200] 1200,46 unequal: No Solution Exploring Operation: 24+50=74, Resulting Numbers: [74] 74,46 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[30, 56], Operations: ['96/4=24', '80-24=56'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 30*56=1680, Resulting Numbers: [1680] 1680,46 unequal: No Solution Exploring Operation: 30+56=86, Resulting Numbers: [86] 86,46 unequal: No Solution Moving to Node #0,4,2 Current State: 46:[80, 6], Operations: ['96/4=24', '30-24=6'] Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,46 unequal: No Solution Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,46 unequal: No Solution Moving to Node #0,4,3 Current State: 46:[80, 54], Operations: ['96/4=24', '30+24=54'] Exploring Operation: 80-54=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 80+54=134, Resulting Numbers: [134] 134,46 unequal: No Solution Exploring Operation: 80*54=4320, Resulting Numbers: [4320] 4320,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[24, 110], Operations: ['96/4=24', '80+30=110'] Exploring Operation: 24+110=134, Resulting Numbers: [134] 134,46 unequal: No Solution Exploring Operation: 24*110=2640, Resulting Numbers: [2640] 2640,46 unequal: No Solution Exploring Operation: 110-24=86, Resulting Numbers: [86] 86,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[96, 4, 50], Operations: ['80-30=50'] Exploring Operation: 96-4=92, Resulting Numbers: [50, 92] Generated Node #0,1,0: 46:[50, 92] Operation: 96-4=92 Exploring Operation: 96/4=24, Resulting Numbers: [50, 24] Generated Node #0,1,1: 46:[50, 24] Operation: 96/4=24 Exploring Operation: 50-4=46, Resulting Numbers: [96, 46] Generated Node #0,1,2: 46:[96, 46] Operation: 50-4=46 Exploring Operation: 96-50=46, Resulting Numbers: [4, 46] Generated Node #0,1,3: 46:[4, 46] Operation: 96-50=46 Exploring Operation: 96+4=100, Resulting Numbers: [50, 100] Generated Node #0,1,4: 46:[50, 100] Operation: 96+4=100 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[4, 46], Operations: ['80-30=50', '96-50=46'] Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,46 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,46 unequal: No Solution No 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: 46:[50, 24], Operations: ['80-30=50', '96/4=24'] Exploring Operation: 50*24=1200, Resulting Numbers: [1200] 1200,46 unequal: No Solution Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,46 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,46 unequal: No Solution No 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: 46:[50, 92], Operations: ['80-30=50', '96-4=92'] Exploring Operation: 50+92=142, Resulting Numbers: [142] 142,46 unequal: No Solution Exploring Operation: 92-50=42, Resulting Numbers: [42] 42,46 unequal: No Solution Exploring Operation: 50*92=4600, Resulting Numbers: [4600] 4600,46 unequal: No Solution No 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: 46:[96, 46], Operations: ['80-30=50', '50-4=46'] Exploring Operation: 96*46=4416, Resulting Numbers: [4416] 4416,46 unequal: No Solution Exploring Operation: 96-46=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 96+46=142, Resulting Numbers: [142] 142,46 unequal: No Solution No 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: 46:[50, 100], Operations: ['80-30=50', '96+4=100'] Exploring Operation: 50*100=5000, Resulting Numbers: [5000] 5000,46 unequal: No Solution Exploring Operation: 100-50=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 100/50=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 50+100=150, Resulting Numbers: [150] 150,46 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: 46:[80, 4, 66], Operations: ['96-30=66'] Exploring Operation: 80/4=20, Resulting Numbers: [66, 20] Generated Node #0,3,0: 46:[66, 20] Operation: 80/4=20 Exploring Operation: 66-4=62, Resulting Numbers: [80, 62] Generated Node #0,3,1: 46:[80, 62] Operation: 66-4=62 Exploring Operation: 80+4=84, Resulting Numbers: [66, 84] Generated Node #0,3,2: 46:[66, 84] Operation: 80+4=84 Exploring Operation: 80-66=14, Resulting Numbers: [4, 14] Generated Node #0,3,3: 46:[4, 14] Operation: 80-66=14 Exploring Operation: 80-4=76, Resulting Numbers: [66, 76] Generated Node #0,3,4: 46:[66, 76] Operation: 80-4=76 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 46:[4, 14], Operations: ['96-30=66', '80-66=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,46 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,46 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,46 unequal: No Solution No 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: 46:[66, 20], Operations: ['96-30=66', '80/4=20'] Exploring Operation: 66*20=1320, Resulting Numbers: [1320] 1320,46 unequal: No Solution Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[80, 96, 30, 4], Operations: [] Exploring Operation: 96-30=66, Resulting Numbers: [80, 4, 66] Generated Node #0,3: 46:[80, 4, 66] Operation: 96-30=66 Moving to Node #0,3 Current State: 46:[80, 4, 66], Operations: ['96-30=66'] Exploring Operation: 80/4=20, Resulting Numbers: [66, 20] Generated Node #0,3,0: 46:[66, 20] Operation: 80/4=20 Moving to Node #0,3,0 Current State: 46:[66, 20], Operations: ['96-30=66', '80/4=20'] Exploring Operation: 66-20=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.930556
hs_5
mult_heuristic
[ 67, 51, 52, 70 ]
35
[ "70-67=3", "51/3=17", "52-17=35" ]
Current State: 35:[67, 51, 52, 70], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [51, 52, 3] Generated Node #2: [51, 52, 3] from Operation: 70-67=3 Current State: 35:[51, 52, 3], Operations: ['70-67=3'] Exploring Operation: 51/3=17, Resulting Numbers: [52, 17] Generated Node #3: [52, 17] from Operation: 51/3=17 Current State: 35:[52, 17], Operations: ['70-67=3', '51/3=17'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[67, 51, 52, 70], Operations: [] Exploring Operation: 70-67=3, Resulting Numbers: [51, 52, 3] Generated Node #0,0: 35:[51, 52, 3] Operation: 70-67=3 Moving to Node #0,0 Current State: 35:[51, 52, 3], Operations: ['70-67=3'] Exploring Operation: 52-51=1, Resulting Numbers: [3, 1] Generated Node #0,0,0: 35:[3, 1] Operation: 52-51=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[3, 1], Operations: ['70-67=3', '52-51=1'] Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 71, 55, 96, 62 ]
56
[ "71-55=16", "96/16=6", "62-6=56" ]
Current State: 56:[71, 55, 96, 62], Operations: [] Exploring Operation: 71-55=16, Resulting Numbers: [96, 62, 16] Generated Node #2: [96, 62, 16] from Operation: 71-55=16 Current State: 56:[96, 62, 16], Operations: ['71-55=16'] Exploring Operation: 96/16=6, Resulting Numbers: [62, 6] Generated Node #3: [62, 6] from Operation: 96/16=6 Current State: 56:[62, 6], Operations: ['71-55=16', '96/16=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[71, 55, 96, 62], Operations: [] Exploring Operation: 71-62=9, Resulting Numbers: [55, 96, 9] Generated Node #0,0: 56:[55, 96, 9] Operation: 71-62=9 Exploring Operation: 96-62=34, Resulting Numbers: [71, 55, 34] Generated Node #0,1: 56:[71, 55, 34] Operation: 96-62=34 Exploring Operation: 96-55=41, Resulting Numbers: [71, 62, 41] Generated Node #0,2: 56:[71, 62, 41] Operation: 96-55=41 Exploring Operation: 96-71=25, Resulting Numbers: [55, 62, 25] Generated Node #0,3: 56:[55, 62, 25] Operation: 96-71=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[55, 62, 25], Operations: ['96-71=25'] Exploring Operation: 62-55=7, Resulting Numbers: [25, 7] Generated Node #0,3,0: 56:[25, 7] Operation: 62-55=7 Exploring Operation: 62-25=37, Resulting Numbers: [55, 37] Generated Node #0,3,1: 56:[55, 37] Operation: 62-25=37 Exploring Operation: 55+25=80, Resulting Numbers: [62, 80] Generated Node #0,3,2: 56:[62, 80] Operation: 55+25=80 Exploring Operation: 55-25=30, Resulting Numbers: [62, 30] Generated Node #0,3,3: 56:[62, 30] Operation: 55-25=30 Moving to Node #0,3,0 Current State: 56:[25, 7], Operations: ['96-71=25', '62-55=7'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,56 unequal: No Solution Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[62, 30], Operations: ['96-71=25', '55-25=30'] Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,56 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[55, 37], Operations: ['96-71=25', '62-25=37'] Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[62, 80], Operations: ['96-71=25', '55+25=80'] Exploring Operation: 80-62=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 62*80=4960, Resulting Numbers: [4960] 4960,56 unequal: No Solution Exploring Operation: 62+80=142, Resulting Numbers: [142] 142,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[71, 55, 34], Operations: ['96-62=34'] Exploring Operation: 71-55=16, Resulting Numbers: [34, 16] Generated Node #0,1,0: 56:[34, 16] Operation: 71-55=16 Exploring Operation: 71-34=37, Resulting Numbers: [55, 37] Generated Node #0,1,1: 56:[55, 37] Operation: 71-34=37 Exploring Operation: 55+34=89, Resulting Numbers: [71, 89] Generated Node #0,1,2: 56:[71, 89] Operation: 55+34=89 Exploring Operation: 55-34=21, Resulting Numbers: [71, 21] Generated Node #0,1,3: 56:[71, 21] Operation: 55-34=21 Moving to Node #0,1,0 Current State: 56:[34, 16], Operations: ['96-62=34', '71-55=16'] Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,56 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[55, 37], Operations: ['96-62=34', '71-34=37'] Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,56 unequal: No Solution Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[71, 21], Operations: ['96-62=34', '55-34=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,56 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[71, 89], Operations: ['96-62=34', '55+34=89'] Exploring Operation: 71*89=6319, Resulting Numbers: [6319] 6319,56 unequal: No Solution Exploring Operation: 71+89=160, Resulting Numbers: [160] 160,56 unequal: No Solution Exploring Operation: 89-71=18, Resulting Numbers: [18] 18,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[71, 62, 41], Operations: ['96-55=41'] Exploring Operation: 71-41=30, Resulting Numbers: [62, 30] Generated Node #0,2,0: 56:[62, 30] Operation: 71-41=30 Exploring Operation: 71+41=112, Resulting Numbers: [62, 112] Generated Node #0,2,1: 56:[62, 112] Operation: 71+41=112 Exploring Operation: 62-41=21, Resulting Numbers: [71, 21] Generated Node #0,2,2: 56:[71, 21] Operation: 62-41=21 Exploring Operation: 71-62=9, Resulting Numbers: [41, 9] Generated Node #0,2,3: 56:[41, 9] Operation: 71-62=9 Moving to Node #0,2,0 Current State: 56:[62, 30], Operations: ['96-55=41', '71-41=30'] Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,56 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,2,3 Current State: 56:[41, 9], Operations: ['96-55=41', '71-62=9'] Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,56 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[71, 21], Operations: ['96-55=41', '62-41=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,56 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,56 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[62, 112], Operations: ['96-55=41', '71+41=112'] Exploring Operation: 62+112=174, Resulting Numbers: [174] 174,56 unequal: No Solution Exploring Operation: 112-62=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 62*112=6944, Resulting Numbers: [6944] 6944,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[55, 96, 9], Operations: ['71-62=9'] Exploring Operation: 55+9=64, Resulting Numbers: [96, 64] Generated Node #0,0,0: 56:[96, 64] Operation: 55+9=64 Exploring Operation: 55-9=46, Resulting Numbers: [96, 46] Generated Node #0,0,1: 56:[96, 46] Operation: 55-9=46 Exploring Operation: 96-55=41, Resulting Numbers: [9, 41] Generated Node #0,0,2: 56:[9, 41] Operation: 96-55=41 Exploring Operation: 96-9=87, Resulting Numbers: [55, 87] Generated Node #0,0,3: 56:[55, 87] Operation: 96-9=87 Moving to Node #0,0,2 Current State: 56:[9, 41], Operations: ['71-62=9', '96-55=41'] Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 9+41=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 9*41=369, Resulting Numbers: [369] 369,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[55, 87], Operations: ['71-62=9', '96-9=87'] Exploring Operation: 55*87=4785, Resulting Numbers: [4785] 4785,56 unequal: No Solution Exploring Operation: 55+87=142, Resulting Numbers: [142] 142,56 unequal: No Solution Exploring Operation: 87-55=32, Resulting Numbers: [32] 32,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[96, 64], Operations: ['71-62=9', '55+9=64'] Exploring Operation: 96-64=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 96*64=6144, Resulting Numbers: [6144] 6144,56 unequal: No Solution Exploring Operation: 96+64=160, Resulting Numbers: [160] 160,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[96, 46], Operations: ['71-62=9', '55-9=46'] Exploring Operation: 96*46=4416, Resulting Numbers: [4416] 4416,56 unequal: No Solution Exploring Operation: 96-46=50, Resulting Numbers: [50] 50,56 unequal: No Solution Exploring Operation: 96+46=142, Resulting Numbers: [142] 142,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 69, 81, 37, 79 ]
77
[ "69+79=148", "148/37=4", "81-4=77" ]
Current State: 77:[69, 81, 37, 79], Operations: [] Exploring Operation: 69+79=148, Resulting Numbers: [81, 37, 148] Generated Node #2: [81, 37, 148] from Operation: 69+79=148 Current State: 77:[81, 37, 148], Operations: ['69+79=148'] Exploring Operation: 148/37=4, Resulting Numbers: [81, 4] Generated Node #3: [81, 4] from Operation: 148/37=4 Current State: 77:[81, 4], Operations: ['69+79=148', '148/37=4'] Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[69, 81, 37, 79], Operations: [] Exploring Operation: 69-37=32, Resulting Numbers: [81, 79, 32] Generated Node #0,0: 77:[81, 79, 32] Operation: 69-37=32 Exploring Operation: 81-69=12, Resulting Numbers: [37, 79, 12] Generated Node #0,1: 77:[37, 79, 12] Operation: 81-69=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[81, 79, 32], Operations: ['69-37=32'] Exploring Operation: 81-32=49, Resulting Numbers: [79, 49] Generated Node #0,0,0: 77:[79, 49] Operation: 81-32=49 Exploring Operation: 81-79=2, Resulting Numbers: [32, 2] Generated Node #0,0,1: 77:[32, 2] Operation: 81-79=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[32, 2], Operations: ['69-37=32', '81-79=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,77 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,77 unequal: No Solution No 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: 77:[79, 49], Operations: ['69-37=32', '81-32=49'] Exploring Operation: 79-49=30, Resulting Numbers: [30] 30,77 unequal: No Solution Exploring Operation: 79+49=128, Resulting Numbers: [128] 128,77 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: 77:[37, 79, 12], Operations: ['81-69=12'] Exploring Operation: 37+12=49, Resulting Numbers: [79, 49] Generated Node #0,1,0: 77:[79, 49] Operation: 37+12=49 Exploring Operation: 37-12=25, Resulting Numbers: [79, 25] Generated Node #0,1,1: 77:[79, 25] Operation: 37-12=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[79, 25], Operations: ['81-69=12', '37-12=25'] Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,77 unequal: No Solution Exploring Operation: 79+25=104, Resulting Numbers: [104] 104,77 unequal: No Solution No 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: 77:[79, 49], Operations: ['81-69=12', '37+12=49'] Exploring Operation: 79+49=128, Resulting Numbers: [128] 128,77 unequal: No Solution Exploring Operation: 79-49=30, Resulting Numbers: [30] 30,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 14, 63, 42, 41 ]
49
[ "63-14=49", "42-41=1", "49*1=49" ]
Current State: 49:[14, 63, 42, 41], Operations: [] Exploring Operation: 63-14=49, Resulting Numbers: [42, 41, 49] Generated Node #2: [42, 41, 49] from Operation: 63-14=49 Current State: 49:[42, 41, 49], Operations: ['63-14=49'] Exploring Operation: 42-41=1, Resulting Numbers: [49, 1] Generated Node #3: [49, 1] from Operation: 42-41=1 Current State: 49:[49, 1], Operations: ['63-14=49', '42-41=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[14, 63, 42, 41], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [63, 41, 3] Generated Node #0,0: 49:[63, 41, 3] Operation: 42/14=3 Exploring Operation: 14+41=55, Resulting Numbers: [63, 42, 55] Generated Node #0,1: 49:[63, 42, 55] Operation: 14+41=55 Exploring Operation: 63-14=49, Resulting Numbers: [42, 41, 49] Generated Node #0,2: 49:[42, 41, 49] Operation: 63-14=49 Exploring Operation: 42-41=1, Resulting Numbers: [14, 63, 1] Generated Node #0,3: 49:[14, 63, 1] Operation: 42-41=1 Moving to Node #0,2 Current State: 49:[42, 41, 49], Operations: ['63-14=49'] Exploring Operation: 42+41=83, Resulting Numbers: [49, 83] Generated Node #0,2,0: 49:[49, 83] Operation: 42+41=83 Exploring Operation: 49-41=8, Resulting Numbers: [42, 8] Generated Node #0,2,1: 49:[42, 8] Operation: 49-41=8 Exploring Operation: 49-42=7, Resulting Numbers: [41, 7] Generated Node #0,2,2: 49:[41, 7] Operation: 49-42=7 Exploring Operation: 42-41=1, Resulting Numbers: [49, 1] Generated Node #0,2,3: 49:[49, 1] Operation: 42-41=1 Moving to Node #0,0 Current State: 49:[63, 41, 3], Operations: ['42/14=3'] Exploring Operation: 63-41=22, Resulting Numbers: [3, 22] Generated Node #0,0,0: 49:[3, 22] Operation: 63-41=22 Exploring Operation: 41+3=44, Resulting Numbers: [63, 44] Generated Node #0,0,1: 49:[63, 44] Operation: 41+3=44 Exploring Operation: 63-3=60, Resulting Numbers: [41, 60] Generated Node #0,0,2: 49:[41, 60] Operation: 63-3=60 Exploring Operation: 63/3=21, Resulting Numbers: [41, 21] Generated Node #0,0,3: 49:[41, 21] Operation: 63/3=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[3, 22], Operations: ['42/14=3', '63-41=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,49 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,49 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 49:[63, 44], Operations: ['42/14=3', '41+3=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,49 unequal: No Solution Exploring Operation: 63+44=107, Resulting Numbers: [107] 107,49 unequal: No Solution Exploring Operation: 63*44=2772, Resulting Numbers: [2772] 2772,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 49:[41, 60], Operations: ['42/14=3', '63-3=60'] Exploring Operation: 41*60=2460, Resulting Numbers: [2460] 2460,49 unequal: No Solution Exploring Operation: 41+60=101, Resulting Numbers: [101] 101,49 unequal: No Solution Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 49:[41, 21], Operations: ['42/14=3', '63/3=21'] Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,49 unequal: No Solution Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 49:[14, 63, 1], Operations: ['42-41=1'] Exploring Operation: 63-14=49, Resulting Numbers: [1, 49] Generated Node #0,3,0: 49:[1, 49] Operation: 63-14=49 Exploring Operation: 63-1=62, Resulting Numbers: [14, 62] Generated Node #0,3,1: 49:[14, 62] Operation: 63-1=62 Exploring Operation: 14-1=13, Resulting Numbers: [63, 13] Generated Node #0,3,2: 49:[63, 13] Operation: 14-1=13 Exploring Operation: 14*1=14, Resulting Numbers: [63, 14] Generated Node #0,3,3: 49:[63, 14] Operation: 14*1=14 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 49:[1, 49], Operations: ['42-41=1', '63-14=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[14, 63, 42, 41], Operations: [] Exploring Operation: 42-41=1, Resulting Numbers: [14, 63, 1] Generated Node #0,3: 49:[14, 63, 1] Operation: 42-41=1 Moving to Node #0,3 Current State: 49:[14, 63, 1], Operations: ['42-41=1'] Exploring Operation: 63-14=49, Resulting Numbers: [1, 49] Generated Node #0,3,0: 49:[1, 49] Operation: 63-14=49 Moving to Node #0,3,0 Current State: 49:[1, 49], Operations: ['42-41=1', '63-14=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 15, 52, 5, 50 ]
82
[ "52-15=37", "50-5=45", "37+45=82" ]
Current State: 82:[15, 52, 5, 50], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [5, 50, 37] Generated Node #2: [5, 50, 37] from Operation: 52-15=37 Current State: 82:[5, 50, 37], Operations: ['52-15=37'] Exploring Operation: 50-5=45, Resulting Numbers: [37, 45] Generated Node #3: [37, 45] from Operation: 50-5=45 Current State: 82:[37, 45], Operations: ['52-15=37', '50-5=45'] Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[15, 52, 5, 50], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [15, 5, 2] Generated Node #0,0: 82:[15, 5, 2] Operation: 52-50=2 Exploring Operation: 52-15=37, Resulting Numbers: [5, 50, 37] Generated Node #0,1: 82:[5, 50, 37] Operation: 52-15=37 Moving to Node #0,0 Current State: 82:[15, 5, 2], Operations: ['52-50=2'] Exploring Operation: 15*5=75, Resulting Numbers: [2, 75] Generated Node #0,0,0: 82:[2, 75] Operation: 15*5=75 Exploring Operation: 15/5=3, Resulting Numbers: [2, 3] Generated Node #0,0,1: 82:[2, 3] Operation: 15/5=3 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 82:[2, 3], Operations: ['52-50=2', '15/5=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,82 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,82 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:[2, 75], Operations: ['52-50=2', '15*5=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,82 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,82 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:[5, 50, 37], Operations: ['52-15=37'] Exploring Operation: 50-5=45, Resulting Numbers: [37, 45] Generated Node #0,1,0: 82:[37, 45] Operation: 50-5=45 Exploring Operation: 50+37=87, Resulting Numbers: [5, 87] Generated Node #0,1,1: 82:[5, 87] Operation: 50+37=87 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[37, 45], Operations: ['52-15=37', '50-5=45'] Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[15, 52, 5, 50], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [5, 50, 37] Generated Node #0,1: 82:[5, 50, 37] Operation: 52-15=37 Moving to Node #0,1 Current State: 82:[5, 50, 37], Operations: ['52-15=37'] Exploring Operation: 50-5=45, Resulting Numbers: [37, 45] Generated Node #0,1,0: 82:[37, 45] Operation: 50-5=45 Moving to Node #0,1,0 Current State: 82:[37, 45], Operations: ['52-15=37', '50-5=45'] Exploring Operation: 37+45=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 11, 57, 2, 37 ]
88
[ "37-11=26", "57*2=114", "114-26=88" ]
Current State: 88:[11, 57, 2, 37], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [57, 2, 26] Generated Node #2: [57, 2, 26] from Operation: 37-11=26 Current State: 88:[57, 2, 26], Operations: ['37-11=26'] Exploring Operation: 57*2=114, Resulting Numbers: [26, 114] Generated Node #3: [26, 114] from Operation: 57*2=114 Current State: 88:[26, 114], Operations: ['37-11=26', '57*2=114'] Exploring Operation: 114-26=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[11, 57, 2, 37], Operations: [] Exploring Operation: 57-37=20, Resulting Numbers: [11, 2, 20] Generated Node #0,0: 88:[11, 2, 20] Operation: 57-37=20 Moving to Node #0,0 Current State: 88:[11, 2, 20], Operations: ['57-37=20'] Exploring Operation: 2+20=22, Resulting Numbers: [11, 22] Generated Node #0,0,0: 88:[11, 22] Operation: 2+20=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[11, 22], Operations: ['57-37=20', '2+20=22'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,88 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
[ 35, 30, 36, 51 ]
96
[ "51-35=16", "36-30=6", "16*6=96" ]
Current State: 96:[35, 30, 36, 51], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [30, 36, 16] Generated Node #2: [30, 36, 16] from Operation: 51-35=16 Current State: 96:[30, 36, 16], Operations: ['51-35=16'] Exploring Operation: 36-30=6, Resulting Numbers: [16, 6] Generated Node #3: [16, 6] from Operation: 36-30=6 Current State: 96:[16, 6], Operations: ['51-35=16', '36-30=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[35, 30, 36, 51], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [35, 30, 15] Generated Node #0,0: 96:[35, 30, 15] Operation: 51-36=15 Exploring Operation: 36-35=1, Resulting Numbers: [30, 51, 1] Generated Node #0,1: 96:[30, 51, 1] Operation: 36-35=1 Exploring Operation: 51-35=16, Resulting Numbers: [30, 36, 16] Generated Node #0,2: 96:[30, 36, 16] Operation: 51-35=16 Exploring Operation: 36-30=6, Resulting Numbers: [35, 51, 6] Generated Node #0,3: 96:[35, 51, 6] Operation: 36-30=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[35, 30, 15], Operations: ['51-36=15'] Exploring Operation: 35-30=5, Resulting Numbers: [15, 5] Generated Node #0,0,0: 96:[15, 5] Operation: 35-30=5 Exploring Operation: 30/15=2, Resulting Numbers: [35, 2] Generated Node #0,0,1: 96:[35, 2] Operation: 30/15=2 Exploring Operation: 35+15=50, Resulting Numbers: [30, 50] Generated Node #0,0,2: 96:[30, 50] Operation: 35+15=50 Exploring Operation: 30-15=15, Resulting Numbers: [35, 15] Generated Node #0,0,3: 96:[35, 15] Operation: 30-15=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[15, 5], Operations: ['51-36=15', '35-30=5'] Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,96 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,96 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[35, 2], Operations: ['51-36=15', '30/15=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[30, 50], Operations: ['51-36=15', '35+15=50'] Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,96 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[35, 15], Operations: ['51-36=15', '30-15=15'] 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 Exploring Operation: 35*15=525, Resulting Numbers: [525] 525,96 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 #0,1 Current State: 96:[30, 51, 1], Operations: ['36-35=1'] Exploring Operation: 30*1=30, Resulting Numbers: [51, 30] Generated Node #0,1,0: 96:[51, 30] Operation: 30*1=30 Exploring Operation: 51-30=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 96:[1, 21] Operation: 51-30=21 Exploring Operation: 51-1=50, Resulting Numbers: [30, 50] Generated Node #0,1,2: 96:[30, 50] Operation: 51-1=50 Exploring Operation: 30+1=31, Resulting Numbers: [51, 31] Generated Node #0,1,3: 96:[51, 31] Operation: 30+1=31 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[1, 21], Operations: ['36-35=1', '51-30=21'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,96 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:[30, 50], Operations: ['36-35=1', '51-1=50'] Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,96 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,96 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:[51, 31], Operations: ['36-35=1', '30+1=31'] Exploring Operation: 51+31=82, Resulting Numbers: [82] 82,96 unequal: No Solution Exploring Operation: 51-31=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 51*31=1581, Resulting Numbers: [1581] 1581,96 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 #0,1,0 Current State: 96:[51, 30], Operations: ['36-35=1', '30*1=30'] Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,96 unequal: No Solution Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,96 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[30, 36, 16], Operations: ['51-35=16'] Exploring Operation: 36+16=52, Resulting Numbers: [30, 52] Generated Node #0,2,0: 96:[30, 52] Operation: 36+16=52 Exploring Operation: 30+16=46, Resulting Numbers: [36, 46] Generated Node #0,2,1: 96:[36, 46] Operation: 30+16=46 Exploring Operation: 30-16=14, Resulting Numbers: [36, 14] Generated Node #0,2,2: 96:[36, 14] Operation: 30-16=14 Exploring Operation: 36-30=6, Resulting Numbers: [16, 6] Generated Node #0,2,3: 96:[16, 6] Operation: 36-30=6 Moving to Node #0,2,3 Current State: 96:[16, 6], Operations: ['51-35=16', '36-30=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,96 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[35, 30, 36, 51], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [30, 36, 16] Generated Node #0,2: 96:[30, 36, 16] Operation: 51-35=16 Moving to Node #0,2 Current State: 96:[30, 36, 16], Operations: ['51-35=16'] Exploring Operation: 36-30=6, Resulting Numbers: [16, 6] Generated Node #0,2,3: 96:[16, 6] Operation: 36-30=6 Moving to Node #0,2,3 Current State: 96:[16, 6], Operations: ['51-35=16', '36-30=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 20, 34, 60, 2 ]
97
[ "20+60=80", "34/2=17", "80+17=97" ]
Current State: 97:[20, 34, 60, 2], Operations: [] Exploring Operation: 20+60=80, Resulting Numbers: [34, 2, 80] Generated Node #2: [34, 2, 80] from Operation: 20+60=80 Current State: 97:[34, 2, 80], Operations: ['20+60=80'] Exploring Operation: 34/2=17, Resulting Numbers: [80, 17] Generated Node #3: [80, 17] from Operation: 34/2=17 Current State: 97:[80, 17], Operations: ['20+60=80', '34/2=17'] Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[20, 34, 60, 2], Operations: [] Exploring Operation: 34*2=68, Resulting Numbers: [20, 60, 68] Generated Node #0,0: 97:[20, 60, 68] Operation: 34*2=68 Exploring Operation: 20*2=40, Resulting Numbers: [34, 60, 40] Generated Node #0,1: 97:[34, 60, 40] Operation: 20*2=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[20, 60, 68], Operations: ['34*2=68'] Exploring Operation: 20+68=88, Resulting Numbers: [60, 88] Generated Node #0,0,0: 97:[60, 88] Operation: 20+68=88 Exploring Operation: 20+60=80, Resulting Numbers: [68, 80] Generated Node #0,0,1: 97:[68, 80] Operation: 20+60=80 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[60, 88], Operations: ['34*2=68', '20+68=88'] Exploring Operation: 60+88=148, Resulting Numbers: [148] 148,97 unequal: No Solution Exploring Operation: 88-60=28, Resulting Numbers: [28] 28,97 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:[68, 80], Operations: ['34*2=68', '20+60=80'] Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,97 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[34, 60, 40], Operations: ['20*2=40'] Exploring Operation: 34+60=94, Resulting Numbers: [40, 94] Generated Node #0,1,0: 97:[40, 94] Operation: 34+60=94 Exploring Operation: 34+40=74, Resulting Numbers: [60, 74] Generated Node #0,1,1: 97:[60, 74] Operation: 34+40=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[40, 94], Operations: ['20*2=40', '34+60=94'] Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 40+94=134, Resulting Numbers: [134] 134,97 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 #0,1,1 Current State: 97:[60, 74], Operations: ['20*2=40', '34+40=74'] Exploring Operation: 60+74=134, Resulting Numbers: [134] 134,97 unequal: No Solution Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,97 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
[ 3, 66, 44, 71 ]
88
[ "3+66=69", "71-69=2", "44*2=88" ]
Current State: 88:[3, 66, 44, 71], Operations: [] Exploring Operation: 3+66=69, Resulting Numbers: [44, 71, 69] Generated Node #2: [44, 71, 69] from Operation: 3+66=69 Current State: 88:[44, 71, 69], Operations: ['3+66=69'] Exploring Operation: 71-69=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 71-69=2 Current State: 88:[44, 2], Operations: ['3+66=69', '71-69=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[3, 66, 44, 71], Operations: [] Exploring Operation: 66-44=22, Resulting Numbers: [3, 71, 22] Generated Node #0,0: 88:[3, 71, 22] Operation: 66-44=22 Exploring Operation: 66/3=22, Resulting Numbers: [44, 71, 22] Generated Node #0,1: 88:[44, 71, 22] Operation: 66/3=22 Exploring Operation: 71-44=27, Resulting Numbers: [3, 66, 27] Generated Node #0,2: 88:[3, 66, 27] Operation: 71-44=27 Exploring Operation: 71-66=5, Resulting Numbers: [3, 44, 5] Generated Node #0,3: 88:[3, 44, 5] Operation: 71-66=5 Moving to Node #0,3 Current State: 88:[3, 44, 5], Operations: ['71-66=5'] Exploring Operation: 5-3=2, Resulting Numbers: [44, 2] Generated Node #0,3,0: 88:[44, 2] Operation: 5-3=2 Exploring Operation: 44-3=41, Resulting Numbers: [5, 41] Generated Node #0,3,1: 88:[5, 41] Operation: 44-3=41 Exploring Operation: 3+44=47, Resulting Numbers: [5, 47] Generated Node #0,3,2: 88:[5, 47] Operation: 3+44=47 Exploring Operation: 3+5=8, Resulting Numbers: [44, 8] Generated Node #0,3,3: 88:[44, 8] Operation: 3+5=8 Moving to Node #0,1 Current State: 88:[44, 71, 22], Operations: ['66/3=22'] Exploring Operation: 71-22=49, Resulting Numbers: [44, 49] Generated Node #0,1,0: 88:[44, 49] Operation: 71-22=49 Exploring Operation: 71-44=27, Resulting Numbers: [22, 27] Generated Node #0,1,1: 88:[22, 27] Operation: 71-44=27 Exploring Operation: 71+22=93, Resulting Numbers: [44, 93] Generated Node #0,1,2: 88:[44, 93] Operation: 71+22=93 Exploring Operation: 44-22=22, Resulting Numbers: [71, 22] Generated Node #0,1,3: 88:[71, 22] Operation: 44-22=22 Moving to Node #0,0 Current State: 88:[3, 71, 22], Operations: ['66-44=22'] Exploring Operation: 71-3=68, Resulting Numbers: [22, 68] Generated Node #0,0,0: 88:[22, 68] Operation: 71-3=68 Exploring Operation: 71+22=93, Resulting Numbers: [3, 93] Generated Node #0,0,1: 88:[3, 93] Operation: 71+22=93 Exploring Operation: 71-22=49, Resulting Numbers: [3, 49] Generated Node #0,0,2: 88:[3, 49] Operation: 71-22=49 Exploring Operation: 3+71=74, Resulting Numbers: [22, 74] Generated Node #0,0,3: 88:[22, 74] Operation: 3+71=74 Moving to Node #0,2 Current State: 88:[3, 66, 27], Operations: ['71-44=27'] Exploring Operation: 66+27=93, Resulting Numbers: [3, 93] Generated Node #0,2,0: 88:[3, 93] Operation: 66+27=93 Exploring Operation: 66/3=22, Resulting Numbers: [27, 22] Generated Node #0,2,1: 88:[27, 22] Operation: 66/3=22 Exploring Operation: 66-27=39, Resulting Numbers: [3, 39] Generated Node #0,2,2: 88:[3, 39] Operation: 66-27=39 Exploring Operation: 27/3=9, Resulting Numbers: [66, 9] Generated Node #0,2,3: 88:[66, 9] Operation: 27/3=9 Moving to Node #0,3,0 Current State: 88:[44, 2], Operations: ['71-66=5', '5-3=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,88 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[3, 66, 44, 71], Operations: [] Exploring Operation: 71-66=5, Resulting Numbers: [3, 44, 5] Generated Node #0,3: 88:[3, 44, 5] Operation: 71-66=5 Moving to Node #0,3 Current State: 88:[3, 44, 5], Operations: ['71-66=5'] Exploring Operation: 5-3=2, Resulting Numbers: [44, 2] Generated Node #0,3,0: 88:[44, 2] Operation: 5-3=2 Moving to Node #0,3,0 Current State: 88:[44, 2], Operations: ['71-66=5', '5-3=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.975694
hs_4
sum_heuristic
[ 15, 81, 41, 75 ]
20
[ "15+81=96", "41+75=116", "116-96=20" ]
Current State: 20:[15, 81, 41, 75], Operations: [] Exploring Operation: 15+81=96, Resulting Numbers: [41, 75, 96] Generated Node #2: [41, 75, 96] from Operation: 15+81=96 Current State: 20:[41, 75, 96], Operations: ['15+81=96'] Exploring Operation: 41+75=116, Resulting Numbers: [96, 116] Generated Node #3: [96, 116] from Operation: 41+75=116 Current State: 20:[96, 116], Operations: ['15+81=96', '41+75=116'] Exploring Operation: 116-96=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[15, 81, 41, 75], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [15, 41, 6] Generated Node #0,0: 20:[15, 41, 6] Operation: 81-75=6 Exploring Operation: 75-41=34, Resulting Numbers: [15, 81, 34] Generated Node #0,1: 20:[15, 81, 34] Operation: 75-41=34 Exploring Operation: 81-41=40, Resulting Numbers: [15, 75, 40] Generated Node #0,2: 20:[15, 75, 40] Operation: 81-41=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[15, 41, 6], Operations: ['81-75=6'] Exploring Operation: 15+6=21, Resulting Numbers: [41, 21] Generated Node #0,0,0: 20:[41, 21] Operation: 15+6=21 Exploring Operation: 41-15=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 20:[6, 26] Operation: 41-15=26 Exploring Operation: 41-6=35, Resulting Numbers: [15, 35] Generated Node #0,0,2: 20:[15, 35] Operation: 41-6=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[6, 26], Operations: ['81-75=6', '41-15=26'] Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[15, 81, 41, 75], Operations: [] Exploring Operation: 81-75=6, Resulting Numbers: [15, 41, 6] Generated Node #0,0: 20:[15, 41, 6] Operation: 81-75=6 Moving to Node #0,0 Current State: 20:[15, 41, 6], Operations: ['81-75=6'] Exploring Operation: 41-15=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 20:[6, 26] Operation: 41-15=26 Moving to Node #0,0,1 Current State: 20:[6, 26], Operations: ['81-75=6', '41-15=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 79, 16, 61, 2 ]
25
[ "79-61=18", "18/2=9", "16+9=25" ]
Current State: 25:[79, 16, 61, 2], Operations: [] Exploring Operation: 79-61=18, Resulting Numbers: [16, 2, 18] Generated Node #2: [16, 2, 18] from Operation: 79-61=18 Current State: 25:[16, 2, 18], Operations: ['79-61=18'] Exploring Operation: 18/2=9, Resulting Numbers: [16, 9] Generated Node #3: [16, 9] from Operation: 18/2=9 Current State: 25:[16, 9], Operations: ['79-61=18', '18/2=9'] Exploring Operation: 16+9=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[79, 16, 61, 2], Operations: [] Exploring Operation: 61-16=45, Resulting Numbers: [79, 2, 45] Generated Node #0,0: 25:[79, 2, 45] Operation: 61-16=45 Exploring Operation: 79-16=63, Resulting Numbers: [61, 2, 63] Generated Node #0,1: 25:[61, 2, 63] Operation: 79-16=63 Exploring Operation: 79-61=18, Resulting Numbers: [16, 2, 18] Generated Node #0,2: 25:[16, 2, 18] Operation: 79-61=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[16, 2, 18], Operations: ['79-61=18'] Exploring Operation: 16/2=8, Resulting Numbers: [18, 8] Generated Node #0,2,0: 25:[18, 8] Operation: 16/2=8 Exploring Operation: 16+18=34, Resulting Numbers: [2, 34] Generated Node #0,2,1: 25:[2, 34] Operation: 16+18=34 Exploring Operation: 18-16=2, Resulting Numbers: [2, 2] Generated Node #0,2,2: 25:[2, 2] Operation: 18-16=2 Moving to Node #0,2,2 Current State: 25:[2, 2], Operations: ['79-61=18', '18-16=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[18, 8], Operations: ['79-61=18', '16/2=8'] Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,25 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[2, 34], Operations: ['79-61=18', '16+18=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,25 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:[79, 2, 45], Operations: ['61-16=45'] Exploring Operation: 79-45=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 25:[2, 34] Operation: 79-45=34 Exploring Operation: 79-2=77, Resulting Numbers: [45, 77] Generated Node #0,0,1: 25:[45, 77] Operation: 79-2=77 Exploring Operation: 45-2=43, Resulting Numbers: [79, 43] Generated Node #0,0,2: 25:[79, 43] Operation: 45-2=43 Moving to Node #0,0,0 Current State: 25:[2, 34], Operations: ['61-16=45', '79-45=34'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,25 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[45, 77], Operations: ['61-16=45', '79-2=77'] Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,25 unequal: No Solution Exploring Operation: 45+77=122, Resulting Numbers: [122] 122,25 unequal: No Solution Exploring Operation: 45*77=3465, Resulting Numbers: [3465] 3465,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[79, 43], Operations: ['61-16=45', '45-2=43'] Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,25 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,25 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 #0,1 Current State: 25:[61, 2, 63], Operations: ['79-16=63'] Exploring Operation: 63-61=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 25:[2, 2] Operation: 63-61=2 Exploring Operation: 63-2=61, Resulting Numbers: [61, 61] Generated Node #0,1,1: 25:[61, 61] Operation: 63-2=61 Exploring Operation: 61-2=59, Resulting Numbers: [63, 59] Generated Node #0,1,2: 25:[63, 59] Operation: 61-2=59 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[2, 2], Operations: ['79-16=63', '63-61=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,25 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, 61], Operations: ['79-16=63', '63-2=61'] Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,25 unequal: No Solution Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,25 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:[63, 59], Operations: ['79-16=63', '61-2=59'] Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 63+59=122, Resulting Numbers: [122] 122,25 unequal: No Solution Exploring Operation: 63*59=3717, Resulting Numbers: [3717] 3717,25 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_3
mult_heuristic
[ 8, 71, 14, 25 ]
17
[ "25-14=11", "8*11=88", "88-71=17" ]
Current State: 17:[8, 71, 14, 25], Operations: [] Exploring Operation: 25-14=11, Resulting Numbers: [8, 71, 11] Generated Node #2: [8, 71, 11] from Operation: 25-14=11 Current State: 17:[8, 71, 11], Operations: ['25-14=11'] Exploring Operation: 8*11=88, Resulting Numbers: [71, 88] Generated Node #3: [71, 88] from Operation: 8*11=88 Current State: 17:[71, 88], Operations: ['25-14=11', '8*11=88'] Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[8, 71, 14, 25], Operations: [] Exploring Operation: 71-8=63, Resulting Numbers: [14, 25, 63] Generated Node #0,0: 17:[14, 25, 63] Operation: 71-8=63 Exploring Operation: 71-25=46, Resulting Numbers: [8, 14, 46] Generated Node #0,1: 17:[8, 14, 46] Operation: 71-25=46 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[8, 14, 46], Operations: ['71-25=46'] Exploring Operation: 46-14=32, Resulting Numbers: [8, 32] Generated Node #0,1,0: 17:[8, 32] Operation: 46-14=32 Exploring Operation: 46-8=38, Resulting Numbers: [14, 38] Generated Node #0,1,1: 17:[14, 38] Operation: 46-8=38 Moving to Node #0,1,0 Current State: 17:[8, 32], Operations: ['71-25=46', '46-14=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[14, 38], Operations: ['71-25=46', '46-8=38'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,17 unequal: No Solution No 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: 17:[14, 25, 63], Operations: ['71-8=63'] Exploring Operation: 63-25=38, Resulting Numbers: [14, 38] Generated Node #0,0,0: 17:[14, 38] Operation: 63-25=38 Exploring Operation: 63-14=49, Resulting Numbers: [25, 49] Generated Node #0,0,1: 17:[25, 49] Operation: 63-14=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[14, 38], Operations: ['71-8=63', '63-25=38'] Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,17 unequal: No Solution No 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: 17:[25, 49], Operations: ['71-8=63', '63-14=49'] Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,17 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,17 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
[ 35, 65, 25, 26 ]
31
[ "65-35=30", "26-25=1", "30+1=31" ]
Current State: 31:[35, 65, 25, 26], Operations: [] Exploring Operation: 65-35=30, Resulting Numbers: [25, 26, 30] Generated Node #2: [25, 26, 30] from Operation: 65-35=30 Current State: 31:[25, 26, 30], Operations: ['65-35=30'] Exploring Operation: 26-25=1, Resulting Numbers: [30, 1] Generated Node #3: [30, 1] from Operation: 26-25=1 Current State: 31:[30, 1], Operations: ['65-35=30', '26-25=1'] Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[35, 65, 25, 26], Operations: [] Exploring Operation: 65-26=39, Resulting Numbers: [35, 25, 39] Generated Node #0,0: 31:[35, 25, 39] Operation: 65-26=39 Exploring Operation: 65-35=30, Resulting Numbers: [25, 26, 30] Generated Node #0,1: 31:[25, 26, 30] Operation: 65-35=30 Exploring Operation: 65-25=40, Resulting Numbers: [35, 26, 40] Generated Node #0,2: 31:[35, 26, 40] Operation: 65-25=40 Moving to Node #0,1 Current State: 31:[25, 26, 30], Operations: ['65-35=30'] Exploring Operation: 25+26=51, Resulting Numbers: [30, 51] Generated Node #0,1,0: 31:[30, 51] Operation: 25+26=51 Exploring Operation: 26-25=1, Resulting Numbers: [30, 1] Generated Node #0,1,1: 31:[30, 1] Operation: 26-25=1 Exploring Operation: 25+30=55, Resulting Numbers: [26, 55] Generated Node #0,1,2: 31:[26, 55] Operation: 25+30=55 Moving to Node #0,0 Current State: 31:[35, 25, 39], Operations: ['65-26=39'] Exploring Operation: 39-35=4, Resulting Numbers: [25, 4] Generated Node #0,0,0: 31:[25, 4] Operation: 39-35=4 Exploring Operation: 35-25=10, Resulting Numbers: [39, 10] Generated Node #0,0,1: 31:[39, 10] Operation: 35-25=10 Exploring Operation: 39-25=14, Resulting Numbers: [35, 14] Generated Node #0,0,2: 31:[35, 14] Operation: 39-25=14 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[35, 14], Operations: ['65-26=39', '39-25=14'] Exploring Operation: 35*14=490, Resulting Numbers: [490] 490,31 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[39, 10], Operations: ['65-26=39', '35-25=10'] Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,31 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[25, 4], Operations: ['65-26=39', '39-35=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,31 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,31 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,31 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:[35, 26, 40], Operations: ['65-25=40'] Exploring Operation: 35-26=9, Resulting Numbers: [40, 9] Generated Node #0,2,0: 31:[40, 9] Operation: 35-26=9 Exploring Operation: 40-26=14, Resulting Numbers: [35, 14] Generated Node #0,2,1: 31:[35, 14] Operation: 40-26=14 Exploring Operation: 40-35=5, Resulting Numbers: [26, 5] Generated Node #0,2,2: 31:[26, 5] Operation: 40-35=5 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[35, 14], Operations: ['65-25=40', '40-26=14'] Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,31 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,31 unequal: No Solution Exploring Operation: 35*14=490, Resulting Numbers: [490] 490,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[40, 9], Operations: ['65-25=40', '35-26=9'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[35, 65, 25, 26], Operations: [] Exploring Operation: 65-25=40, Resulting Numbers: [35, 26, 40] Generated Node #0,2: 31:[35, 26, 40] Operation: 65-25=40 Moving to Node #0,2 Current State: 31:[35, 26, 40], Operations: ['65-25=40'] Exploring Operation: 35-26=9, Resulting Numbers: [40, 9] Generated Node #0,2,0: 31:[40, 9] Operation: 35-26=9 Moving to Node #0,2,0 Current State: 31:[40, 9], Operations: ['65-25=40', '35-26=9'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 52, 86, 6, 52 ]
24
[ "86-52=34", "6+52=58", "58-34=24" ]
Current State: 24:[52, 86, 6, 52], Operations: [] Exploring Operation: 86-52=34, Resulting Numbers: [6, 34] Generated Node #2: [6, 34] from Operation: 86-52=34 Current State: 24:[6, 34], Operations: ['86-52=34'] Exploring Operation: 6+52=58, Resulting Numbers: [34, 58] Generated Node #3: [34, 58] from Operation: 6+52=58 Current State: 24:[34, 58], Operations: ['86-52=34', '6+52=58'] Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[52, 86, 6, 52], Operations: [] Exploring Operation: 86-52=34, Resulting Numbers: [52, 6, 34] Generated Node #0,0: 24:[52, 6, 34] Operation: 86-52=34 Exploring Operation: 52/52=1, Resulting Numbers: [86, 6, 1] Generated Node #0,1: 24:[86, 6, 1] Operation: 52/52=1 Exploring Operation: 86-52=34, Resulting Numbers: [6, 52, 34] Generated Node #0,2: 24:[6, 52, 34] Operation: 86-52=34 Moving to Node #0,0 Current State: 24:[52, 6, 34], Operations: ['86-52=34'] Exploring Operation: 34-6=28, Resulting Numbers: [52, 28] Generated Node #0,0,0: 24:[52, 28] Operation: 34-6=28 Exploring Operation: 52-34=18, Resulting Numbers: [6, 18] Generated Node #0,0,1: 24:[6, 18] Operation: 52-34=18 Exploring Operation: 52-6=46, Resulting Numbers: [34, 46] Generated Node #0,0,2: 24:[34, 46] Operation: 52-6=46 Moving to Node #0,2 Current State: 24:[6, 52, 34], Operations: ['86-52=34'] Exploring Operation: 52-6=46, Resulting Numbers: [34, 46] Generated Node #0,2,0: 24:[34, 46] Operation: 52-6=46 Exploring Operation: 34-6=28, Resulting Numbers: [52, 28] Generated Node #0,2,1: 24:[52, 28] Operation: 34-6=28 Exploring Operation: 52-34=18, Resulting Numbers: [6, 18] Generated Node #0,2,2: 24:[6, 18] Operation: 52-34=18 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 24:[6, 18], Operations: ['86-52=34', '52-34=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[52, 86, 6, 52], Operations: [] Exploring Operation: 86-52=34, Resulting Numbers: [6, 52, 34] Generated Node #0,2: 24:[6, 52, 34] Operation: 86-52=34 Moving to Node #0,2 Current State: 24:[6, 52, 34], Operations: ['86-52=34'] Exploring Operation: 52-34=18, Resulting Numbers: [6, 18] Generated Node #0,2,2: 24:[6, 18] Operation: 52-34=18 Moving to Node #0,2,2 Current State: 24:[6, 18], Operations: ['86-52=34', '52-34=18'] Exploring Operation: 6+18=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 26, 45, 76, 12 ]
69
[ "45-26=19", "76+12=88", "88-19=69" ]
Current State: 69:[26, 45, 76, 12], Operations: [] Exploring Operation: 45-26=19, Resulting Numbers: [76, 12, 19] Generated Node #2: [76, 12, 19] from Operation: 45-26=19 Current State: 69:[76, 12, 19], Operations: ['45-26=19'] Exploring Operation: 76+12=88, Resulting Numbers: [19, 88] Generated Node #3: [19, 88] from Operation: 76+12=88 Current State: 69:[19, 88], Operations: ['45-26=19', '76+12=88'] Exploring Operation: 88-19=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[26, 45, 76, 12], Operations: [] Exploring Operation: 26+45=71, Resulting Numbers: [76, 12, 71] Generated Node #0,0: 69:[76, 12, 71] Operation: 26+45=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[76, 12, 71], Operations: ['26+45=71'] Exploring Operation: 76-12=64, Resulting Numbers: [71, 64] Generated Node #0,0,0: 69:[71, 64] Operation: 76-12=64 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[71, 64], Operations: ['26+45=71', '76-12=64'] Exploring Operation: 71-64=7, Resulting Numbers: [7] 7,69 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
[ 33, 44, 34, 86 ]
25
[ "33+44=77", "86-34=52", "77-52=25" ]
Current State: 25:[33, 44, 34, 86], Operations: [] Exploring Operation: 33+44=77, Resulting Numbers: [34, 86, 77] Generated Node #2: [34, 86, 77] from Operation: 33+44=77 Current State: 25:[34, 86, 77], Operations: ['33+44=77'] Exploring Operation: 86-34=52, Resulting Numbers: [77, 52] Generated Node #3: [77, 52] from Operation: 86-34=52 Current State: 25:[77, 52], Operations: ['33+44=77', '86-34=52'] Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[33, 44, 34, 86], Operations: [] Exploring Operation: 86-44=42, Resulting Numbers: [33, 34, 42] Generated Node #0,0: 25:[33, 34, 42] Operation: 86-44=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[33, 34, 42], Operations: ['86-44=42'] Exploring Operation: 42-34=8, Resulting Numbers: [33, 8] Generated Node #0,0,0: 25:[33, 8] Operation: 42-34=8 Moving to Node #0,0,0 Current State: 25:[33, 8], Operations: ['86-44=42', '42-34=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[33, 44, 34, 86], Operations: [] Exploring Operation: 86-44=42, Resulting Numbers: [33, 34, 42] Generated Node #0,0: 25:[33, 34, 42] Operation: 86-44=42 Moving to Node #0,0 Current State: 25:[33, 34, 42], Operations: ['86-44=42'] Exploring Operation: 42-34=8, Resulting Numbers: [33, 8] Generated Node #0,0,0: 25:[33, 8] Operation: 42-34=8 Moving to Node #0,0,0 Current State: 25:[33, 8], Operations: ['86-44=42', '42-34=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 44, 11, 21, 24 ]
100
[ "44+11=55", "21+24=45", "55+45=100" ]
Current State: 100:[44, 11, 21, 24], Operations: [] Exploring Operation: 44+11=55, Resulting Numbers: [21, 24, 55] Generated Node #2: [21, 24, 55] from Operation: 44+11=55 Current State: 100:[21, 24, 55], Operations: ['44+11=55'] Exploring Operation: 21+24=45, Resulting Numbers: [55, 45] Generated Node #3: [55, 45] from Operation: 21+24=45 Current State: 100:[55, 45], Operations: ['44+11=55', '21+24=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[44, 11, 21, 24], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [11, 21, 20] Generated Node #0,0: 100:[11, 21, 20] Operation: 44-24=20 Exploring Operation: 44/11=4, Resulting Numbers: [21, 24, 4] Generated Node #0,1: 100:[21, 24, 4] Operation: 44/11=4 Exploring Operation: 44+11=55, Resulting Numbers: [21, 24, 55] Generated Node #0,2: 100:[21, 24, 55] Operation: 44+11=55 Exploring Operation: 44-21=23, Resulting Numbers: [11, 24, 23] Generated Node #0,3: 100:[11, 24, 23] Operation: 44-21=23 Moving to Node #0,0 Current State: 100:[11, 21, 20], Operations: ['44-24=20'] Exploring Operation: 21-11=10, Resulting Numbers: [20, 10] Generated Node #0,0,0: 100:[20, 10] Operation: 21-11=10 Exploring Operation: 21-20=1, Resulting Numbers: [11, 1] Generated Node #0,0,1: 100:[11, 1] Operation: 21-20=1 Exploring Operation: 20-11=9, Resulting Numbers: [21, 9] Generated Node #0,0,2: 100:[21, 9] Operation: 20-11=9 Exploring Operation: 11+21=32, Resulting Numbers: [20, 32] Generated Node #0,0,3: 100:[20, 32] Operation: 11+21=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[20, 10], Operations: ['44-24=20', '21-11=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,100 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,100 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:[11, 1], Operations: ['44-24=20', '21-20=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,100 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,100 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 #0,0,2 Current State: 100:[21, 9], Operations: ['44-24=20', '20-11=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,100 unequal: No Solution Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,100 unequal: No Solution Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,100 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 #0,0,3 Current State: 100:[20, 32], Operations: ['44-24=20', '11+21=32'] Exploring Operation: 20+32=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 20*32=640, Resulting Numbers: [640] 640,100 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,100 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: 100:[21, 24, 4], Operations: ['44/11=4'] Exploring Operation: 21+4=25, Resulting Numbers: [24, 25] Generated Node #0,1,0: 100:[24, 25] Operation: 21+4=25 Exploring Operation: 24/4=6, Resulting Numbers: [21, 6] Generated Node #0,1,1: 100:[21, 6] Operation: 24/4=6 Exploring Operation: 24-21=3, Resulting Numbers: [4, 3] Generated Node #0,1,2: 100:[4, 3] Operation: 24-21=3 Exploring Operation: 24-4=20, Resulting Numbers: [21, 20] Generated Node #0,1,3: 100:[21, 20] Operation: 24-4=20 Moving to Node #0,3 Current State: 100:[11, 24, 23], Operations: ['44-21=23'] Exploring Operation: 24-11=13, Resulting Numbers: [23, 13] Generated Node #0,3,0: 100:[23, 13] Operation: 24-11=13 Exploring Operation: 24+23=47, Resulting Numbers: [11, 47] Generated Node #0,3,1: 100:[11, 47] Operation: 24+23=47 Exploring Operation: 23-11=12, Resulting Numbers: [24, 12] Generated Node #0,3,2: 100:[24, 12] Operation: 23-11=12 Exploring Operation: 24-23=1, Resulting Numbers: [11, 1] Generated Node #0,3,3: 100:[11, 1] Operation: 24-23=1 Moving to Node #0,2 Current State: 100:[21, 24, 55], Operations: ['44+11=55'] Exploring Operation: 21+24=45, Resulting Numbers: [55, 45] Generated Node #0,2,0: 100:[55, 45] Operation: 21+24=45 Exploring Operation: 55-24=31, Resulting Numbers: [21, 31] Generated Node #0,2,1: 100:[21, 31] Operation: 55-24=31 Exploring Operation: 24-21=3, Resulting Numbers: [55, 3] Generated Node #0,2,2: 100:[55, 3] Operation: 24-21=3 Exploring Operation: 55-21=34, Resulting Numbers: [24, 34] Generated Node #0,2,3: 100:[24, 34] Operation: 55-21=34 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[55, 3], Operations: ['44+11=55', '24-21=3'] Exploring Operation: 55*3=165, Resulting Numbers: [165] 165,100 unequal: No Solution Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[21, 31], Operations: ['44+11=55', '55-24=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,100 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[55, 45], Operations: ['44+11=55', '21+24=45'] Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,100 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[44, 11, 21, 24], Operations: [] Exploring Operation: 44+11=55, Resulting Numbers: [21, 24, 55] Generated Node #0,2: 100:[21, 24, 55] Operation: 44+11=55 Moving to Node #0,2 Current State: 100:[21, 24, 55], Operations: ['44+11=55'] Exploring Operation: 21+24=45, Resulting Numbers: [55, 45] Generated Node #0,2,0: 100:[55, 45] Operation: 21+24=45 Moving to Node #0,2,0 Current State: 100:[55, 45], Operations: ['44+11=55', '21+24=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_4
mult_heuristic
[ 40, 47, 20, 30 ]
77
[ "40+47=87", "30-20=10", "87-10=77" ]
Current State: 77:[40, 47, 20, 30], Operations: [] Exploring Operation: 40+47=87, Resulting Numbers: [20, 30, 87] Generated Node #2: [20, 30, 87] from Operation: 40+47=87 Current State: 77:[20, 30, 87], Operations: ['40+47=87'] Exploring Operation: 30-20=10, Resulting Numbers: [87, 10] Generated Node #3: [87, 10] from Operation: 30-20=10 Current State: 77:[87, 10], Operations: ['40+47=87', '30-20=10'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[40, 47, 20, 30], Operations: [] Exploring Operation: 40+47=87, Resulting Numbers: [20, 30, 87] Generated Node #0,0: 77:[20, 30, 87] Operation: 40+47=87 Exploring Operation: 47+30=77, Resulting Numbers: [40, 20, 77] Generated Node #0,1: 77:[40, 20, 77] Operation: 47+30=77 Exploring Operation: 47-40=7, Resulting Numbers: [20, 30, 7] Generated Node #0,2: 77:[20, 30, 7] Operation: 47-40=7 Moving to Node #0,2 Current State: 77:[20, 30, 7], Operations: ['47-40=7'] Exploring Operation: 20-7=13, Resulting Numbers: [30, 13] Generated Node #0,2,0: 77:[30, 13] Operation: 20-7=13 Exploring Operation: 30-20=10, Resulting Numbers: [7, 10] Generated Node #0,2,1: 77:[7, 10] Operation: 30-20=10 Exploring Operation: 30-7=23, Resulting Numbers: [20, 23] Generated Node #0,2,2: 77:[20, 23] Operation: 30-7=23 Moving to Node #0,0 Current State: 77:[20, 30, 87], Operations: ['40+47=87'] Exploring Operation: 87-20=67, Resulting Numbers: [30, 67] Generated Node #0,0,0: 77:[30, 67] Operation: 87-20=67 Exploring Operation: 30-20=10, Resulting Numbers: [87, 10] Generated Node #0,0,1: 77:[87, 10] Operation: 30-20=10 Exploring Operation: 87-30=57, Resulting Numbers: [20, 57] Generated Node #0,0,2: 77:[20, 57] Operation: 87-30=57 Moving to Node #0,1 Current State: 77:[40, 20, 77], Operations: ['47+30=77'] Exploring Operation: 40+20=60, Resulting Numbers: [77, 60] Generated Node #0,1,0: 77:[77, 60] Operation: 40+20=60 Exploring Operation: 40/20=2, Resulting Numbers: [77, 2] Generated Node #0,1,1: 77:[77, 2] Operation: 40/20=2 Exploring Operation: 40-20=20, Resulting Numbers: [77, 20] Generated Node #0,1,2: 77:[77, 20] Operation: 40-20=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[77, 2], Operations: ['47+30=77', '40/20=2'] Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,77 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,77 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[77, 20], Operations: ['47+30=77', '40-20=20'] Exploring Operation: 77+20=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,77 unequal: No Solution Exploring Operation: 77*20=1540, Resulting Numbers: [1540] 1540,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[77, 60], Operations: ['47+30=77', '40+20=60'] Exploring Operation: 77-60=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 77+60=137, Resulting Numbers: [137] 137,77 unequal: No Solution Exploring Operation: 77*60=4620, Resulting Numbers: [4620] 4620,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 77:[7, 10], Operations: ['47-40=7', '30-20=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[87, 10], Operations: ['40+47=87', '30-20=10'] Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[40, 47, 20, 30], Operations: [] Exploring Operation: 40+47=87, Resulting Numbers: [20, 30, 87] Generated Node #0,0: 77:[20, 30, 87] Operation: 40+47=87 Moving to Node #0,0 Current State: 77:[20, 30, 87], Operations: ['40+47=87'] Exploring Operation: 30-20=10, Resulting Numbers: [87, 10] Generated Node #0,0,1: 77:[87, 10] Operation: 30-20=10 Moving to Node #0,0,1 Current State: 77:[87, 10], Operations: ['40+47=87', '30-20=10'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 14, 5, 44, 47 ]
29
[ "47-44=3", "5*3=15", "14+15=29" ]
Current State: 29:[14, 5, 44, 47], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [14, 5, 3] Generated Node #2: [14, 5, 3] from Operation: 47-44=3 Current State: 29:[14, 5, 3], Operations: ['47-44=3'] Exploring Operation: 5*3=15, Resulting Numbers: [14, 15] Generated Node #3: [14, 15] from Operation: 5*3=15 Current State: 29:[14, 15], Operations: ['47-44=3', '5*3=15'] Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[14, 5, 44, 47], Operations: [] Exploring Operation: 44-5=39, Resulting Numbers: [14, 47, 39] Generated Node #0,0: 29:[14, 47, 39] Operation: 44-5=39 Exploring Operation: 47-14=33, Resulting Numbers: [5, 44, 33] Generated Node #0,1: 29:[5, 44, 33] Operation: 47-14=33 Exploring Operation: 44-14=30, Resulting Numbers: [5, 47, 30] Generated Node #0,2: 29:[5, 47, 30] Operation: 44-14=30 Exploring Operation: 14+5=19, Resulting Numbers: [44, 47, 19] Generated Node #0,3: 29:[44, 47, 19] Operation: 14+5=19 Moving to Node #0,0 Current State: 29:[14, 47, 39], Operations: ['44-5=39'] Exploring Operation: 47-39=8, Resulting Numbers: [14, 8] Generated Node #0,0,0: 29:[14, 8] Operation: 47-39=8 Exploring Operation: 39-14=25, Resulting Numbers: [47, 25] Generated Node #0,0,1: 29:[47, 25] Operation: 39-14=25 Exploring Operation: 47-14=33, Resulting Numbers: [39, 33] Generated Node #0,0,2: 29:[39, 33] Operation: 47-14=33 Exploring Operation: 14+47=61, Resulting Numbers: [39, 61] Generated Node #0,0,3: 29:[39, 61] Operation: 14+47=61 Moving to Node #0,2 Current State: 29:[5, 47, 30], Operations: ['44-14=30'] Exploring Operation: 5+30=35, Resulting Numbers: [47, 35] Generated Node #0,2,0: 29:[47, 35] Operation: 5+30=35 Exploring Operation: 47-5=42, Resulting Numbers: [30, 42] Generated Node #0,2,1: 29:[30, 42] Operation: 47-5=42 Exploring Operation: 5+47=52, Resulting Numbers: [30, 52] Generated Node #0,2,2: 29:[30, 52] Operation: 5+47=52 Exploring Operation: 30-5=25, Resulting Numbers: [47, 25] Generated Node #0,2,3: 29:[47, 25] Operation: 30-5=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[30, 42], Operations: ['44-14=30', '47-5=42'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,29 unequal: No Solution Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[47, 25], Operations: ['44-14=30', '30-5=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[47, 35], Operations: ['44-14=30', '5+30=35'] Exploring Operation: 47+35=82, Resulting Numbers: [82] 82,29 unequal: No Solution Exploring Operation: 47*35=1645, Resulting Numbers: [1645] 1645,29 unequal: No Solution Exploring Operation: 47-35=12, Resulting Numbers: [12] 12,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[30, 52], Operations: ['44-14=30', '5+47=52'] Exploring Operation: 52-30=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 30+52=82, Resulting Numbers: [82] 82,29 unequal: No Solution Exploring Operation: 30*52=1560, Resulting Numbers: [1560] 1560,29 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: 29:[5, 44, 33], Operations: ['47-14=33'] Exploring Operation: 5+33=38, Resulting Numbers: [44, 38] Generated Node #0,1,0: 29:[44, 38] Operation: 5+33=38 Exploring Operation: 33-5=28, Resulting Numbers: [44, 28] Generated Node #0,1,1: 29:[44, 28] Operation: 33-5=28 Exploring Operation: 44-5=39, Resulting Numbers: [33, 39] Generated Node #0,1,2: 29:[33, 39] Operation: 44-5=39 Exploring Operation: 5+44=49, Resulting Numbers: [33, 49] Generated Node #0,1,3: 29:[33, 49] Operation: 5+44=49 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 29:[33, 39], Operations: ['47-14=33', '44-5=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,29 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[44, 28], Operations: ['47-14=33', '33-5=28'] Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,29 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[44, 38], Operations: ['47-14=33', '5+33=38'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 44*38=1672, Resulting Numbers: [1672] 1672,29 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 29:[33, 49], Operations: ['47-14=33', '5+44=49'] Exploring Operation: 33*49=1617, Resulting Numbers: [1617] 1617,29 unequal: No Solution Exploring Operation: 49-33=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 33+49=82, Resulting Numbers: [82] 82,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 29:[44, 47, 19], Operations: ['14+5=19'] Exploring Operation: 44-19=25, Resulting Numbers: [47, 25] Generated Node #0,3,0: 29:[47, 25] Operation: 44-19=25 Exploring Operation: 44+19=63, Resulting Numbers: [47, 63] Generated Node #0,3,1: 29:[47, 63] Operation: 44+19=63 Exploring Operation: 47-19=28, Resulting Numbers: [44, 28] Generated Node #0,3,2: 29:[44, 28] Operation: 47-19=28 Exploring Operation: 47-44=3, Resulting Numbers: [19, 3] Generated Node #0,3,3: 29:[19, 3] Operation: 47-44=3 Moving to Node #0,0,2 Current State: 29:[39, 33], Operations: ['44-5=39', '47-14=33'] Exploring Operation: 39*33=1287, Resulting Numbers: [1287] 1287,29 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 39+33=72, Resulting Numbers: [72] 72,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[44, 28], Operations: ['14+5=19', '47-19=28'] Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,29 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,29 unequal: No Solution Moving to Node #0,3,0 Current State: 29:[47, 25], Operations: ['14+5=19', '44-19=25'] Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[47, 25], Operations: ['44-5=39', '39-14=25'] Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,29 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,29 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[14, 8], Operations: ['44-5=39', '47-39=8'] Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,29 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[19, 3], Operations: ['14+5=19', '47-44=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,29 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[39, 61], Operations: ['44-5=39', '14+47=61'] Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 39+61=100, Resulting Numbers: [100] 100,29 unequal: No Solution Exploring Operation: 39*61=2379, Resulting Numbers: [2379] 2379,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[47, 63], Operations: ['14+5=19', '44+19=63'] Exploring Operation: 47+63=110, Resulting Numbers: [110] 110,29 unequal: No Solution Exploring Operation: 47*63=2961, Resulting Numbers: [2961] 2961,29 unequal: No Solution Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,29 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 71, 3, 19, 45 ]
83
[ "71-19=52", "3*45=135", "135-52=83" ]
Current State: 83:[71, 3, 19, 45], Operations: [] Exploring Operation: 71-19=52, Resulting Numbers: [3, 45, 52] Generated Node #2: [3, 45, 52] from Operation: 71-19=52 Current State: 83:[3, 45, 52], Operations: ['71-19=52'] Exploring Operation: 3*45=135, Resulting Numbers: [52, 135] Generated Node #3: [52, 135] from Operation: 3*45=135 Current State: 83:[52, 135], Operations: ['71-19=52', '3*45=135'] Exploring Operation: 135-52=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[71, 3, 19, 45], Operations: [] Exploring Operation: 3+19=22, Resulting Numbers: [71, 45, 22] Generated Node #0,0: 83:[71, 45, 22] Operation: 3+19=22 Exploring Operation: 3*19=57, Resulting Numbers: [71, 45, 57] Generated Node #0,1: 83:[71, 45, 57] Operation: 3*19=57 Exploring Operation: 3+45=48, Resulting Numbers: [71, 19, 48] Generated Node #0,2: 83:[71, 19, 48] Operation: 3+45=48 Exploring Operation: 71+3=74, Resulting Numbers: [19, 45, 74] Generated Node #0,3: 83:[19, 45, 74] Operation: 71+3=74 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[71, 45, 57], Operations: ['3*19=57'] Exploring Operation: 71+45=116, Resulting Numbers: [57, 116] Generated Node #0,1,0: 83:[57, 116] Operation: 71+45=116 Exploring Operation: 71-45=26, Resulting Numbers: [57, 26] Generated Node #0,1,1: 83:[57, 26] Operation: 71-45=26 Exploring Operation: 71+57=128, Resulting Numbers: [45, 128] Generated Node #0,1,2: 83:[45, 128] Operation: 71+57=128 Exploring Operation: 45+57=102, Resulting Numbers: [71, 102] Generated Node #0,1,3: 83:[71, 102] Operation: 45+57=102 Moving to Node #0,1,3 Current State: 83:[71, 102], Operations: ['3*19=57', '45+57=102'] Exploring Operation: 102-71=31, Resulting Numbers: [31] 31,83 unequal: No Solution Exploring Operation: 71*102=7242, Resulting Numbers: [7242] 7242,83 unequal: No Solution Exploring Operation: 71+102=173, Resulting Numbers: [173] 173,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[57, 116], Operations: ['3*19=57', '71+45=116'] Exploring Operation: 57*116=6612, Resulting Numbers: [6612] 6612,83 unequal: No Solution Exploring Operation: 57+116=173, Resulting Numbers: [173] 173,83 unequal: No Solution Exploring Operation: 116-57=59, Resulting Numbers: [59] 59,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[45, 128], Operations: ['3*19=57', '71+57=128'] Exploring Operation: 45+128=173, Resulting Numbers: [173] 173,83 unequal: No Solution Exploring Operation: 128-45=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[71, 3, 19, 45], Operations: [] Exploring Operation: 3*19=57, Resulting Numbers: [71, 45, 57] Generated Node #0,1: 83:[71, 45, 57] Operation: 3*19=57 Moving to Node #0,1 Current State: 83:[71, 45, 57], Operations: ['3*19=57'] Exploring Operation: 71+57=128, Resulting Numbers: [45, 128] Generated Node #0,1,2: 83:[45, 128] Operation: 71+57=128 Moving to Node #0,1,2 Current State: 83:[45, 128], Operations: ['3*19=57', '71+57=128'] Exploring Operation: 128-45=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 98, 40, 48, 16 ]
30
[ "48-40=8", "16*8=128", "128-98=30" ]
Current State: 30:[98, 40, 48, 16], Operations: [] Exploring Operation: 48-40=8, Resulting Numbers: [98, 16, 8] Generated Node #2: [98, 16, 8] from Operation: 48-40=8 Current State: 30:[98, 16, 8], Operations: ['48-40=8'] Exploring Operation: 16*8=128, Resulting Numbers: [98, 128] Generated Node #3: [98, 128] from Operation: 16*8=128 Current State: 30:[98, 128], Operations: ['48-40=8', '16*8=128'] Exploring Operation: 128-98=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[98, 40, 48, 16], Operations: [] Exploring Operation: 98-16=82, Resulting Numbers: [40, 48, 82] Generated Node #0,0: 30:[40, 48, 82] Operation: 98-16=82 Exploring Operation: 98-40=58, Resulting Numbers: [48, 16, 58] Generated Node #0,1: 30:[48, 16, 58] Operation: 98-40=58 Exploring Operation: 48-40=8, Resulting Numbers: [98, 16, 8] Generated Node #0,2: 30:[98, 16, 8] Operation: 48-40=8 Exploring Operation: 48/16=3, Resulting Numbers: [98, 40, 3] Generated Node #0,3: 30:[98, 40, 3] Operation: 48/16=3 Exploring Operation: 98-48=50, Resulting Numbers: [40, 16, 50] Generated Node #0,4: 30:[40, 16, 50] Operation: 98-48=50 Moving to Node #0,4 Current State: 30:[40, 16, 50], Operations: ['98-48=50'] Exploring Operation: 40-16=24, Resulting Numbers: [50, 24] Generated Node #0,4,0: 30:[50, 24] Operation: 40-16=24 Exploring Operation: 40+16=56, Resulting Numbers: [50, 56] Generated Node #0,4,1: 30:[50, 56] Operation: 40+16=56 Exploring Operation: 16+50=66, Resulting Numbers: [40, 66] Generated Node #0,4,2: 30:[40, 66] Operation: 16+50=66 Exploring Operation: 50-40=10, Resulting Numbers: [16, 10] Generated Node #0,4,3: 30:[16, 10] Operation: 50-40=10 Exploring Operation: 50-16=34, Resulting Numbers: [40, 34] Generated Node #0,4,4: 30:[40, 34] Operation: 50-16=34 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 30:[16, 10], Operations: ['98-48=50', '50-40=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,30 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,30 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 #0,4,4 Current State: 30:[40, 34], Operations: ['98-48=50', '50-16=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,30 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,30 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 #0,4,0 Current State: 30:[50, 24], Operations: ['98-48=50', '40-16=24'] Exploring Operation: 50*24=1200, Resulting Numbers: [1200] 1200,30 unequal: No Solution Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,30 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 #0,4,1 Current State: 30:[50, 56], Operations: ['98-48=50', '40+16=56'] Exploring Operation: 56-50=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 50*56=2800, Resulting Numbers: [2800] 2800,30 unequal: No Solution Exploring Operation: 50+56=106, Resulting Numbers: [106] 106,30 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 #0,4,2 Current State: 30:[40, 66], Operations: ['98-48=50', '16+50=66'] Exploring Operation: 40*66=2640, Resulting Numbers: [2640] 2640,30 unequal: No Solution Exploring Operation: 66-40=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 40+66=106, Resulting Numbers: [106] 106,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[48, 16, 58], Operations: ['98-40=58'] Exploring Operation: 48/16=3, Resulting Numbers: [58, 3] Generated Node #0,1,0: 30:[58, 3] Operation: 48/16=3 Exploring Operation: 48+16=64, Resulting Numbers: [58, 64] Generated Node #0,1,1: 30:[58, 64] Operation: 48+16=64 Exploring Operation: 58-16=42, Resulting Numbers: [48, 42] Generated Node #0,1,2: 30:[48, 42] Operation: 58-16=42 Exploring Operation: 48-16=32, Resulting Numbers: [58, 32] Generated Node #0,1,3: 30:[58, 32] Operation: 48-16=32 Exploring Operation: 58-48=10, Resulting Numbers: [16, 10] Generated Node #0,1,4: 30:[16, 10] Operation: 58-48=10 Moving to Node #0,2 Current State: 30:[98, 16, 8], Operations: ['48-40=8'] Exploring Operation: 16-8=8, Resulting Numbers: [98, 8] Generated Node #0,2,0: 30:[98, 8] Operation: 16-8=8 Exploring Operation: 16+8=24, Resulting Numbers: [98, 24] Generated Node #0,2,1: 30:[98, 24] Operation: 16+8=24 Exploring Operation: 98-8=90, Resulting Numbers: [16, 90] Generated Node #0,2,2: 30:[16, 90] Operation: 98-8=90 Exploring Operation: 98-16=82, Resulting Numbers: [8, 82] Generated Node #0,2,3: 30:[8, 82] Operation: 98-16=82 Exploring Operation: 16/8=2, Resulting Numbers: [98, 2] Generated Node #0,2,4: 30:[98, 2] Operation: 16/8=2 Moving to Node #0,3 Current State: 30:[98, 40, 3], Operations: ['48/16=3'] Exploring Operation: 40+3=43, Resulting Numbers: [98, 43] Generated Node #0,3,0: 30:[98, 43] Operation: 40+3=43 Exploring Operation: 98+3=101, Resulting Numbers: [40, 101] Generated Node #0,3,1: 30:[40, 101] Operation: 98+3=101 Exploring Operation: 40-3=37, Resulting Numbers: [98, 37] Generated Node #0,3,2: 30:[98, 37] Operation: 40-3=37 Exploring Operation: 98-3=95, Resulting Numbers: [40, 95] Generated Node #0,3,3: 30:[40, 95] Operation: 98-3=95 Exploring Operation: 98-40=58, Resulting Numbers: [3, 58] Generated Node #0,3,4: 30:[3, 58] Operation: 98-40=58 Moving to Node #0,0 Current State: 30:[40, 48, 82], Operations: ['98-16=82'] Exploring Operation: 48-40=8, Resulting Numbers: [82, 8] Generated Node #0,0,0: 30:[82, 8] Operation: 48-40=8 Exploring Operation: 82-48=34, Resulting Numbers: [40, 34] Generated Node #0,0,1: 30:[40, 34] Operation: 82-48=34 Exploring Operation: 82-40=42, Resulting Numbers: [48, 42] Generated Node #0,0,2: 30:[48, 42] Operation: 82-40=42 Exploring Operation: 40+48=88, Resulting Numbers: [82, 88] Generated Node #0,0,3: 30:[82, 88] Operation: 40+48=88 Exploring Operation: 40+82=122, Resulting Numbers: [48, 122] Generated Node #0,0,4: 30:[48, 122] Operation: 40+82=122 Moving to Node #0,1,4 Current State: 30:[16, 10], Operations: ['98-40=58', '58-48=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[40, 34], Operations: ['98-16=82', '82-48=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,30 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[3, 58], Operations: ['48/16=3', '98-40=58'] Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[58, 3], Operations: ['98-40=58', '48/16=3'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,30 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[48, 42], Operations: ['98-40=58', '58-16=42'] Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,30 unequal: No Solution Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,30 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[58, 32], Operations: ['98-40=58', '48-16=32'] Exploring Operation: 58+32=90, Resulting Numbers: [90] 90,30 unequal: No Solution Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 58*32=1856, Resulting Numbers: [1856] 1856,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[48, 42], Operations: ['98-16=82', '82-40=42'] Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,30 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,30 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,30 unequal: No Solution Moving to Node #0,2,3 Current State: 30:[8, 82], Operations: ['48-40=8', '98-16=82'] Exploring Operation: 8*82=656, Resulting Numbers: [656] 656,30 unequal: No Solution Exploring Operation: 8+82=90, Resulting Numbers: [90] 90,30 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[82, 8], Operations: ['98-16=82', '48-40=8'] Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,30 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[16, 90], Operations: ['48-40=8', '98-8=90'] Exploring Operation: 16*90=1440, Resulting Numbers: [1440] 1440,30 unequal: No Solution Exploring Operation: 16+90=106, Resulting Numbers: [106] 106,30 unequal: No Solution Exploring Operation: 90-16=74, Resulting Numbers: [74] 74,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[58, 64], Operations: ['98-40=58', '48+16=64'] Exploring Operation: 58*64=3712, Resulting Numbers: [3712] 3712,30 unequal: No Solution Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 58+64=122, Resulting Numbers: [122] 122,30 unequal: No Solution Moving to Node #0,2,4 Current State: 30:[98, 2], Operations: ['48-40=8', '16/8=2'] Exploring Operation: 98*2=196, Resulting Numbers: [196] 196,30 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,30 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,30 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[98, 8], Operations: ['48-40=8', '16-8=8'] Exploring Operation: 98*8=784, Resulting Numbers: [784] 784,30 unequal: No Solution Exploring Operation: 98+8=106, Resulting Numbers: [106] 106,30 unequal: No Solution Exploring Operation: 98-8=90, Resulting Numbers: [90] 90,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[98, 24], Operations: ['48-40=8', '16+8=24'] Exploring Operation: 98+24=122, Resulting Numbers: [122] 122,30 unequal: No Solution Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 98*24=2352, Resulting Numbers: [2352] 2352,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[40, 95], Operations: ['48/16=3', '98-3=95'] Exploring Operation: 40+95=135, Resulting Numbers: [135] 135,30 unequal: No Solution Exploring Operation: 40*95=3800, Resulting Numbers: [3800] 3800,30 unequal: No Solution Exploring Operation: 95-40=55, Resulting Numbers: [55] 55,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[98, 37], Operations: ['48/16=3', '40-3=37'] Exploring Operation: 98+37=135, Resulting Numbers: [135] 135,30 unequal: No Solution Exploring Operation: 98-37=61, Resulting Numbers: [61] 61,30 unequal: No Solution Exploring Operation: 98*37=3626, Resulting Numbers: [3626] 3626,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[98, 43], Operations: ['48/16=3', '40+3=43'] Exploring Operation: 98+43=141, Resulting Numbers: [141] 141,30 unequal: No Solution Exploring Operation: 98*43=4214, Resulting Numbers: [4214] 4214,30 unequal: No Solution Exploring Operation: 98-43=55, Resulting Numbers: [55] 55,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[40, 101], Operations: ['48/16=3', '98+3=101'] Exploring Operation: 40+101=141, Resulting Numbers: [141] 141,30 unequal: No Solution Exploring Operation: 40*101=4040, Resulting Numbers: [4040] 4040,30 unequal: No Solution Exploring Operation: 101-40=61, Resulting Numbers: [61] 61,30 unequal: No Solution Moving to Node #0,0,3 Current State: 30:[82, 88], Operations: ['98-16=82', '40+48=88'] Exploring Operation: 82*88=7216, Resulting Numbers: [7216] 7216,30 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 82+88=170, Resulting Numbers: [170] 170,30 unequal: No Solution Moving to Node #0,0,4 Current State: 30:[48, 122], Operations: ['98-16=82', '40+82=122'] Exploring Operation: 122-48=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 48*122=5856, Resulting Numbers: [5856] 5856,30 unequal: No Solution Exploring Operation: 48+122=170, Resulting Numbers: [170] 170,30 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 76, 6, 11, 22 ]
49
[ "76+6=82", "11+22=33", "82-33=49" ]
Current State: 49:[76, 6, 11, 22], Operations: [] Exploring Operation: 76+6=82, Resulting Numbers: [11, 22, 82] Generated Node #2: [11, 22, 82] from Operation: 76+6=82 Current State: 49:[11, 22, 82], Operations: ['76+6=82'] Exploring Operation: 11+22=33, Resulting Numbers: [82, 33] Generated Node #3: [82, 33] from Operation: 11+22=33 Current State: 49:[82, 33], Operations: ['76+6=82', '11+22=33'] Exploring Operation: 82-33=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[76, 6, 11, 22], Operations: [] Exploring Operation: 76-22=54, Resulting Numbers: [6, 11, 54] Generated Node #0,0: 49:[6, 11, 54] Operation: 76-22=54 Exploring Operation: 22-11=11, Resulting Numbers: [76, 6, 11] Generated Node #0,1: 49:[76, 6, 11] Operation: 22-11=11 Exploring Operation: 22/11=2, Resulting Numbers: [76, 6, 2] Generated Node #0,2: 49:[76, 6, 2] Operation: 22/11=2 Exploring Operation: 76-6=70, Resulting Numbers: [11, 22, 70] Generated Node #0,3: 49:[11, 22, 70] Operation: 76-6=70 Exploring Operation: 76-11=65, Resulting Numbers: [6, 22, 65] Generated Node #0,4: 49:[6, 22, 65] Operation: 76-11=65 Moving to Node #0,0 Current State: 49:[6, 11, 54], Operations: ['76-22=54'] Exploring Operation: 11-6=5, Resulting Numbers: [54, 5] Generated Node #0,0,0: 49:[54, 5] Operation: 11-6=5 Exploring Operation: 54/6=9, Resulting Numbers: [11, 9] Generated Node #0,0,1: 49:[11, 9] Operation: 54/6=9 Exploring Operation: 54-11=43, Resulting Numbers: [6, 43] Generated Node #0,0,2: 49:[6, 43] Operation: 54-11=43 Exploring Operation: 54-6=48, Resulting Numbers: [11, 48] Generated Node #0,0,3: 49:[11, 48] Operation: 54-6=48 Exploring Operation: 6+11=17, Resulting Numbers: [54, 17] Generated Node #0,0,4: 49:[54, 17] Operation: 6+11=17 Moving to Node #0,4 Current State: 49:[6, 22, 65], Operations: ['76-11=65'] Exploring Operation: 22-6=16, Resulting Numbers: [65, 16] Generated Node #0,4,0: 49:[65, 16] Operation: 22-6=16 Exploring Operation: 65-6=59, Resulting Numbers: [22, 59] Generated Node #0,4,1: 49:[22, 59] Operation: 65-6=59 Exploring Operation: 6+65=71, Resulting Numbers: [22, 71] Generated Node #0,4,2: 49:[22, 71] Operation: 6+65=71 Exploring Operation: 65-22=43, Resulting Numbers: [6, 43] Generated Node #0,4,3: 49:[6, 43] Operation: 65-22=43 Exploring Operation: 6+22=28, Resulting Numbers: [65, 28] Generated Node #0,4,4: 49:[65, 28] Operation: 6+22=28 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 49:[6, 43], Operations: ['76-11=65', '65-22=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[76, 6, 11, 22], Operations: [] Exploring Operation: 76-11=65, Resulting Numbers: [6, 22, 65] Generated Node #0,4: 49:[6, 22, 65] Operation: 76-11=65 Moving to Node #0,4 Current State: 49:[6, 22, 65], Operations: ['76-11=65'] Exploring Operation: 65-22=43, Resulting Numbers: [6, 43] Generated Node #0,4,3: 49:[6, 43] Operation: 65-22=43 Moving to Node #0,4,3 Current State: 49:[6, 43], Operations: ['76-11=65', '65-22=43'] Exploring Operation: 6+43=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 49, 20, 64, 45 ]
60
[ "64-49=15", "20*45=900", "900/15=60" ]
Current State: 60:[49, 20, 64, 45], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [20, 45, 15] Generated Node #2: [20, 45, 15] from Operation: 64-49=15 Current State: 60:[20, 45, 15], Operations: ['64-49=15'] Exploring Operation: 20*45=900, Resulting Numbers: [15, 900] Generated Node #3: [15, 900] from Operation: 20*45=900 Current State: 60:[15, 900], Operations: ['64-49=15', '20*45=900'] Exploring Operation: 900/15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[49, 20, 64, 45], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [20, 64, 4] Generated Node #0,0: 60:[20, 64, 4] Operation: 49-45=4 Exploring Operation: 64-45=19, Resulting Numbers: [49, 20, 19] Generated Node #0,1: 60:[49, 20, 19] Operation: 64-45=19 Exploring Operation: 64-49=15, Resulting Numbers: [20, 45, 15] Generated Node #0,2: 60:[20, 45, 15] Operation: 64-49=15 Moving to Node #0,0 Current State: 60:[20, 64, 4], Operations: ['49-45=4'] Exploring Operation: 64-4=60, Resulting Numbers: [20, 60] Generated Node #0,0,0: 60:[20, 60] Operation: 64-4=60 Exploring Operation: 20/4=5, Resulting Numbers: [64, 5] Generated Node #0,0,1: 60:[64, 5] Operation: 20/4=5 Exploring Operation: 64/4=16, Resulting Numbers: [20, 16] Generated Node #0,0,2: 60:[20, 16] Operation: 64/4=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[20, 60], Operations: ['49-45=4', '64-4=60'] Exploring Operation: 20+60=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 60-20=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 60/20=3, Resulting Numbers: [3] 3,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[20, 16], Operations: ['49-45=4', '64/4=16'] Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,60 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[64, 5], Operations: ['49-45=4', '20/4=5'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 64*5=320, Resulting Numbers: [320] 320,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 60:[49, 20, 19], Operations: ['64-45=19'] Exploring Operation: 49-20=29, Resulting Numbers: [19, 29] Generated Node #0,1,0: 60:[19, 29] Operation: 49-20=29 Exploring Operation: 49-19=30, Resulting Numbers: [20, 30] Generated Node #0,1,1: 60:[20, 30] Operation: 49-19=30 Exploring Operation: 49+19=68, Resulting Numbers: [20, 68] Generated Node #0,1,2: 60:[20, 68] Operation: 49+19=68 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[20, 30], Operations: ['64-45=19', '49-19=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,60 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[19, 29], Operations: ['64-45=19', '49-20=29'] Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,60 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[20, 68], Operations: ['64-45=19', '49+19=68'] Exploring Operation: 20*68=1360, Resulting Numbers: [1360] 1360,60 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 20+68=88, Resulting Numbers: [88] 88,60 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: 60:[20, 45, 15], Operations: ['64-49=15'] Exploring Operation: 45-15=30, Resulting Numbers: [20, 30] Generated Node #0,2,0: 60:[20, 30] Operation: 45-15=30 Exploring Operation: 45/15=3, Resulting Numbers: [20, 3] Generated Node #0,2,1: 60:[20, 3] Operation: 45/15=3 Exploring Operation: 45+15=60, Resulting Numbers: [20, 60] Generated Node #0,2,2: 60:[20, 60] Operation: 45+15=60 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[20, 30], Operations: ['64-49=15', '45-15=30'] Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,60 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[20, 3], Operations: ['64-49=15', '45/15=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[49, 20, 64, 45], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [20, 45, 15] Generated Node #0,2: 60:[20, 45, 15] Operation: 64-49=15 Moving to Node #0,2 Current State: 60:[20, 45, 15], Operations: ['64-49=15'] Exploring Operation: 45/15=3, Resulting Numbers: [20, 3] Generated Node #0,2,1: 60:[20, 3] Operation: 45/15=3 Moving to Node #0,2,1 Current State: 60:[20, 3], Operations: ['64-49=15', '45/15=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_3
mult_heuristic
[ 78, 50, 88, 27 ]
87
[ "78-50=28", "88+27=115", "115-28=87" ]
Current State: 87:[78, 50, 88, 27], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [88, 27, 28] Generated Node #2: [88, 27, 28] from Operation: 78-50=28 Current State: 87:[88, 27, 28], Operations: ['78-50=28'] Exploring Operation: 88+27=115, Resulting Numbers: [28, 115] Generated Node #3: [28, 115] from Operation: 88+27=115 Current State: 87:[28, 115], Operations: ['78-50=28', '88+27=115'] Exploring Operation: 115-28=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[78, 50, 88, 27], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [88, 27, 28] Generated Node #0,0: 87:[88, 27, 28] Operation: 78-50=28 Moving to Node #0,0 Current State: 87:[88, 27, 28], Operations: ['78-50=28'] Exploring Operation: 28-27=1, Resulting Numbers: [88, 1] Generated Node #0,0,0: 87:[88, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[88, 1], Operations: ['78-50=28', '28-27=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[78, 50, 88, 27], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [88, 27, 28] Generated Node #0,0: 87:[88, 27, 28] Operation: 78-50=28 Moving to Node #0,0 Current State: 87:[88, 27, 28], Operations: ['78-50=28'] Exploring Operation: 28-27=1, Resulting Numbers: [88, 1] Generated Node #0,0,0: 87:[88, 1] Operation: 28-27=1 Moving to Node #0,0,0 Current State: 87:[88, 1], Operations: ['78-50=28', '28-27=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 35, 2, 25, 51 ]
68
[ "35+51=86", "86/2=43", "25+43=68" ]
Current State: 68:[35, 2, 25, 51], Operations: [] Exploring Operation: 35+51=86, Resulting Numbers: [2, 25, 86] Generated Node #2: [2, 25, 86] from Operation: 35+51=86 Current State: 68:[2, 25, 86], Operations: ['35+51=86'] Exploring Operation: 86/2=43, Resulting Numbers: [25, 43] Generated Node #3: [25, 43] from Operation: 86/2=43 Current State: 68:[25, 43], Operations: ['35+51=86', '86/2=43'] Exploring Operation: 25+43=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[35, 2, 25, 51], Operations: [] Exploring Operation: 25+51=76, Resulting Numbers: [35, 2, 76] Generated Node #0,0: 68:[35, 2, 76] Operation: 25+51=76 Exploring Operation: 35-25=10, Resulting Numbers: [2, 51, 10] Generated Node #0,1: 68:[2, 51, 10] Operation: 35-25=10 Exploring Operation: 51-25=26, Resulting Numbers: [35, 2, 26] Generated Node #0,2: 68:[35, 2, 26] Operation: 51-25=26 Exploring Operation: 51-35=16, Resulting Numbers: [2, 25, 16] Generated Node #0,3: 68:[2, 25, 16] Operation: 51-35=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[35, 2, 76], Operations: ['25+51=76'] Exploring Operation: 35-2=33, Resulting Numbers: [76, 33] Generated Node #0,0,0: 68:[76, 33] Operation: 35-2=33 Exploring Operation: 76/2=38, Resulting Numbers: [35, 38] Generated Node #0,0,1: 68:[35, 38] Operation: 76/2=38 Exploring Operation: 76-35=41, Resulting Numbers: [2, 41] Generated Node #0,0,2: 68:[2, 41] Operation: 76-35=41 Exploring Operation: 76-2=74, Resulting Numbers: [35, 74] Generated Node #0,0,3: 68:[35, 74] Operation: 76-2=74 Moving to Node #0,0,1 Current State: 68:[35, 38], Operations: ['25+51=76', '76/2=38'] Exploring Operation: 35*38=1330, Resulting Numbers: [1330] 1330,68 unequal: No Solution Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[35, 74], Operations: ['25+51=76', '76-2=74'] Exploring Operation: 35*74=2590, Resulting Numbers: [2590] 2590,68 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 35+74=109, Resulting Numbers: [109] 109,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[2, 41], Operations: ['25+51=76', '76-35=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,68 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[76, 33], Operations: ['25+51=76', '35-2=33'] Exploring Operation: 76+33=109, Resulting Numbers: [109] 109,68 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,68 unequal: No Solution Exploring Operation: 76*33=2508, Resulting Numbers: [2508] 2508,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[35, 2, 26], Operations: ['51-25=26'] Exploring Operation: 35+26=61, Resulting Numbers: [2, 61] Generated Node #0,2,0: 68:[2, 61] Operation: 35+26=61 Exploring Operation: 2+26=28, Resulting Numbers: [35, 28] Generated Node #0,2,1: 68:[35, 28] Operation: 2+26=28 Exploring Operation: 35-26=9, Resulting Numbers: [2, 9] Generated Node #0,2,2: 68:[2, 9] Operation: 35-26=9 Exploring Operation: 26/2=13, Resulting Numbers: [35, 13] Generated Node #0,2,3: 68:[35, 13] Operation: 26/2=13 Moving to Node #0,2,2 Current State: 68:[2, 9], Operations: ['51-25=26', '35-26=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[35, 13], Operations: ['51-25=26', '26/2=13'] Exploring Operation: 35*13=455, Resulting Numbers: [455] 455,68 unequal: No Solution Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 35+13=48, Resulting Numbers: [48] 48,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[35, 28], Operations: ['51-25=26', '2+26=28'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[2, 61], Operations: ['51-25=26', '35+26=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,68 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[2, 25, 16], Operations: ['51-35=16'] Exploring Operation: 2+25=27, Resulting Numbers: [16, 27] Generated Node #0,3,0: 68:[16, 27] Operation: 2+25=27 Exploring Operation: 25+16=41, Resulting Numbers: [2, 41] Generated Node #0,3,1: 68:[2, 41] Operation: 25+16=41 Exploring Operation: 25-2=23, Resulting Numbers: [16, 23] Generated Node #0,3,2: 68:[16, 23] Operation: 25-2=23 Exploring Operation: 25-16=9, Resulting Numbers: [2, 9] Generated Node #0,3,3: 68:[2, 9] Operation: 25-16=9 Moving to Node #0,3,3 Current State: 68:[2, 9], Operations: ['51-35=16', '25-16=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,68 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[16, 23], Operations: ['51-35=16', '25-2=23'] Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,68 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[2, 41], Operations: ['51-35=16', '25+16=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,68 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[16, 27], Operations: ['51-35=16', '2+25=27'] Exploring Operation: 16+27=43, Resulting Numbers: [43] 43,68 unequal: No Solution Exploring Operation: 16*27=432, Resulting Numbers: [432] 432,68 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[2, 51, 10], Operations: ['35-25=10'] Exploring Operation: 2*10=20, Resulting Numbers: [51, 20] Generated Node #0,1,0: 68:[51, 20] Operation: 2*10=20 Exploring Operation: 51+10=61, Resulting Numbers: [2, 61] Generated Node #0,1,1: 68:[2, 61] Operation: 51+10=61 Exploring Operation: 51-10=41, Resulting Numbers: [2, 41] Generated Node #0,1,2: 68:[2, 41] Operation: 51-10=41 Exploring Operation: 10/2=5, Resulting Numbers: [51, 5] Generated Node #0,1,3: 68:[51, 5] Operation: 10/2=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[2, 61], Operations: ['35-25=10', '51+10=61'] Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,68 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,68 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[2, 41], Operations: ['35-25=10', '51-10=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,68 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,68 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 68:[51, 5], Operations: ['35-25=10', '10/2=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,68 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[51, 20], Operations: ['35-25=10', '2*10=20'] Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,68 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,68 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 72, 11, 33, 66 ]
45
[ "72*11=792", "792/66=12", "33+12=45" ]
Current State: 45:[72, 11, 33, 66], Operations: [] Exploring Operation: 72*11=792, Resulting Numbers: [33, 66, 792] Generated Node #2: [33, 66, 792] from Operation: 72*11=792 Current State: 45:[33, 66, 792], Operations: ['72*11=792'] Exploring Operation: 792/66=12, Resulting Numbers: [33, 12] Generated Node #3: [33, 12] from Operation: 792/66=12 Current State: 45:[33, 12], Operations: ['72*11=792', '792/66=12'] Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[72, 11, 33, 66], Operations: [] Exploring Operation: 66-33=33, Resulting Numbers: [72, 11, 33] Generated Node #0,0: 45:[72, 11, 33] Operation: 66-33=33 Exploring Operation: 66/33=2, Resulting Numbers: [72, 11, 2] Generated Node #0,1: 45:[72, 11, 2] Operation: 66/33=2 Exploring Operation: 66/11=6, Resulting Numbers: [72, 33, 6] Generated Node #0,2: 45:[72, 33, 6] Operation: 66/11=6 Exploring Operation: 72-66=6, Resulting Numbers: [11, 33, 6] Generated Node #0,3: 45:[11, 33, 6] Operation: 72-66=6 Exploring Operation: 72-33=39, Resulting Numbers: [11, 66, 39] Generated Node #0,4: 45:[11, 66, 39] Operation: 72-33=39 Moving to Node #0,3 Current State: 45:[11, 33, 6], Operations: ['72-66=6'] Exploring Operation: 11+33=44, Resulting Numbers: [6, 44] Generated Node #0,3,0: 45:[6, 44] Operation: 11+33=44 Exploring Operation: 33/11=3, Resulting Numbers: [6, 3] Generated Node #0,3,1: 45:[6, 3] Operation: 33/11=3 Exploring Operation: 33+6=39, Resulting Numbers: [11, 39] Generated Node #0,3,2: 45:[11, 39] Operation: 33+6=39 Exploring Operation: 11-6=5, Resulting Numbers: [33, 5] Generated Node #0,3,3: 45:[33, 5] Operation: 11-6=5 Exploring Operation: 33-11=22, Resulting Numbers: [6, 22] Generated Node #0,3,4: 45:[6, 22] Operation: 33-11=22 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[6, 3], Operations: ['72-66=6', '33/11=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,45 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 45:[6, 44], Operations: ['72-66=6', '11+33=44'] Exploring Operation: 6*44=264, Resulting Numbers: [264] 264,45 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 45:[11, 39], Operations: ['72-66=6', '33+6=39'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,45 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 45:[6, 22], Operations: ['72-66=6', '33-11=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[33, 5], Operations: ['72-66=6', '11-6=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,45 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,45 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,45 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: 45:[11, 66, 39], Operations: ['72-33=39'] Exploring Operation: 66-11=55, Resulting Numbers: [39, 55] Generated Node #0,4,0: 45:[39, 55] Operation: 66-11=55 Exploring Operation: 66/11=6, Resulting Numbers: [39, 6] Generated Node #0,4,1: 45:[39, 6] Operation: 66/11=6 Exploring Operation: 11+39=50, Resulting Numbers: [66, 50] Generated Node #0,4,2: 45:[66, 50] Operation: 11+39=50 Exploring Operation: 39-11=28, Resulting Numbers: [66, 28] Generated Node #0,4,3: 45:[66, 28] Operation: 39-11=28 Exploring Operation: 66-39=27, Resulting Numbers: [11, 27] Generated Node #0,4,4: 45:[11, 27] Operation: 66-39=27 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 45:[39, 6], Operations: ['72-33=39', '66/11=6'] Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,45 unequal: No Solution Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[72, 11, 33, 66], Operations: [] Exploring Operation: 72-33=39, Resulting Numbers: [11, 66, 39] Generated Node #0,4: 45:[11, 66, 39] Operation: 72-33=39 Moving to Node #0,4 Current State: 45:[11, 66, 39], Operations: ['72-33=39'] Exploring Operation: 66/11=6, Resulting Numbers: [39, 6] Generated Node #0,4,1: 45:[39, 6] Operation: 66/11=6 Moving to Node #0,4,1 Current State: 45:[39, 6], Operations: ['72-33=39', '66/11=6'] Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 54, 73, 48, 75 ]
42
[ "75-73=2", "48*2=96", "96-54=42" ]
Current State: 42:[54, 73, 48, 75], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [54, 48, 2] Generated Node #2: [54, 48, 2] from Operation: 75-73=2 Current State: 42:[54, 48, 2], Operations: ['75-73=2'] Exploring Operation: 48*2=96, Resulting Numbers: [54, 96] Generated Node #3: [54, 96] from Operation: 48*2=96 Current State: 42:[54, 96], Operations: ['75-73=2', '48*2=96'] Exploring Operation: 96-54=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[54, 73, 48, 75], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [54, 73, 27] Generated Node #0,0: 42:[54, 73, 27] Operation: 75-48=27 Exploring Operation: 73-54=19, Resulting Numbers: [48, 75, 19] Generated Node #0,1: 42:[48, 75, 19] Operation: 73-54=19 Exploring Operation: 75-54=21, Resulting Numbers: [73, 48, 21] Generated Node #0,2: 42:[73, 48, 21] Operation: 75-54=21 Exploring Operation: 75-73=2, Resulting Numbers: [54, 48, 2] Generated Node #0,3: 42:[54, 48, 2] Operation: 75-73=2 Exploring Operation: 73-48=25, Resulting Numbers: [54, 75, 25] Generated Node #0,4: 42:[54, 75, 25] Operation: 73-48=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[54, 48, 2], Operations: ['75-73=2'] Exploring Operation: 54-2=52, Resulting Numbers: [48, 52] Generated Node #0,3,0: 42:[48, 52] Operation: 54-2=52 Exploring Operation: 54-48=6, Resulting Numbers: [2, 6] Generated Node #0,3,1: 42:[2, 6] Operation: 54-48=6 Exploring Operation: 48/2=24, Resulting Numbers: [54, 24] Generated Node #0,3,2: 42:[54, 24] Operation: 48/2=24 Exploring Operation: 54/2=27, Resulting Numbers: [48, 27] Generated Node #0,3,3: 42:[48, 27] Operation: 54/2=27 Exploring Operation: 48-2=46, Resulting Numbers: [54, 46] Generated Node #0,3,4: 42:[54, 46] Operation: 48-2=46 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 42:[2, 6], Operations: ['75-73=2', '54-48=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,42 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 42:[48, 27], Operations: ['75-73=2', '54/2=27'] Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,42 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,42 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 42:[54, 24], Operations: ['75-73=2', '48/2=24'] Exploring Operation: 54+24=78, Resulting Numbers: [78] 78,42 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 54*24=1296, Resulting Numbers: [1296] 1296,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 42:[48, 52], Operations: ['75-73=2', '54-2=52'] Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 42:[54, 46], Operations: ['75-73=2', '48-2=46'] Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[73, 48, 21], Operations: ['75-54=21'] Exploring Operation: 73+21=94, Resulting Numbers: [48, 94] Generated Node #0,2,0: 42:[48, 94] Operation: 73+21=94 Exploring Operation: 73-21=52, Resulting Numbers: [48, 52] Generated Node #0,2,1: 42:[48, 52] Operation: 73-21=52 Exploring Operation: 73-48=25, Resulting Numbers: [21, 25] Generated Node #0,2,2: 42:[21, 25] Operation: 73-48=25 Exploring Operation: 48-21=27, Resulting Numbers: [73, 27] Generated Node #0,2,3: 42:[73, 27] Operation: 48-21=27 Exploring Operation: 48+21=69, Resulting Numbers: [73, 69] Generated Node #0,2,4: 42:[73, 69] Operation: 48+21=69 Moving to Node #0,2,2 Current State: 42:[21, 25], Operations: ['75-54=21', '73-48=25'] Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 21*25=525, Resulting Numbers: [525] 525,42 unequal: No Solution Exploring Operation: 21+25=46, Resulting Numbers: [46] 46,42 unequal: No Solution Moving to Node #0,2,1 Current State: 42:[48, 52], Operations: ['75-54=21', '73-21=52'] Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,42 unequal: No Solution Moving to Node #0,2,3 Current State: 42:[73, 27], Operations: ['75-54=21', '48-21=27'] Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[48, 94], Operations: ['75-54=21', '73+21=94'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 48*94=4512, Resulting Numbers: [4512] 4512,42 unequal: No Solution Exploring Operation: 48+94=142, Resulting Numbers: [142] 142,42 unequal: No Solution Moving to Node #0,2,4 Current State: 42:[73, 69], Operations: ['75-54=21', '48+21=69'] Exploring Operation: 73-69=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 73+69=142, Resulting Numbers: [142] 142,42 unequal: No Solution Exploring Operation: 73*69=5037, Resulting Numbers: [5037] 5037,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[48, 75, 19], Operations: ['73-54=19'] Exploring Operation: 48+19=67, Resulting Numbers: [75, 67] Generated Node #0,1,0: 42:[75, 67] Operation: 48+19=67 Exploring Operation: 75+19=94, Resulting Numbers: [48, 94] Generated Node #0,1,1: 42:[48, 94] Operation: 75+19=94 Exploring Operation: 75-48=27, Resulting Numbers: [19, 27] Generated Node #0,1,2: 42:[19, 27] Operation: 75-48=27 Exploring Operation: 75-19=56, Resulting Numbers: [48, 56] Generated Node #0,1,3: 42:[48, 56] Operation: 75-19=56 Exploring Operation: 48-19=29, Resulting Numbers: [75, 29] Generated Node #0,1,4: 42:[75, 29] Operation: 48-19=29 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[19, 27], Operations: ['73-54=19', '75-48=27'] Exploring Operation: 19*27=513, Resulting Numbers: [513] 513,42 unequal: No Solution Exploring Operation: 19+27=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 42:[48, 56], Operations: ['73-54=19', '75-19=56'] Exploring Operation: 56-48=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 48+56=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 48*56=2688, Resulting Numbers: [2688] 2688,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 42:[75, 29], Operations: ['73-54=19', '48-19=29'] Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,42 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[75, 67], Operations: ['73-54=19', '48+19=67'] Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 75+67=142, Resulting Numbers: [142] 142,42 unequal: No Solution Exploring Operation: 75*67=5025, Resulting Numbers: [5025] 5025,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[48, 94], Operations: ['73-54=19', '75+19=94'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 48*94=4512, Resulting Numbers: [4512] 4512,42 unequal: No Solution Exploring Operation: 48+94=142, Resulting Numbers: [142] 142,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[54, 73, 27], Operations: ['75-48=27'] Exploring Operation: 54/27=2, Resulting Numbers: [73, 2] Generated Node #0,0,0: 42:[73, 2] Operation: 54/27=2 Exploring Operation: 73-27=46, Resulting Numbers: [54, 46] Generated Node #0,0,1: 42:[54, 46] Operation: 73-27=46 Exploring Operation: 54-27=27, Resulting Numbers: [73, 27] Generated Node #0,0,2: 42:[73, 27] Operation: 54-27=27 Exploring Operation: 54+27=81, Resulting Numbers: [73, 81] Generated Node #0,0,3: 42:[73, 81] Operation: 54+27=81 Exploring Operation: 73-54=19, Resulting Numbers: [27, 19] Generated Node #0,0,4: 42:[27, 19] Operation: 73-54=19 Moving to Node #0,0,4 Current State: 42:[27, 19], Operations: ['75-48=27', '73-54=19'] Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 27+19=46, Resulting Numbers: [46] 46,42 unequal: No Solution Exploring Operation: 27*19=513, Resulting Numbers: [513] 513,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[54, 46], Operations: ['75-48=27', '73-27=46'] Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[73, 2], Operations: ['75-48=27', '54/27=2'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,42 unequal: No Solution Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,42 unequal: No Solution Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,42 unequal: No Solution Moving to Node #0,0,2 Current State: 42:[73, 27], Operations: ['75-48=27', '54-27=27'] Exploring Operation: 73+27=100, Resulting Numbers: [100] 100,42 unequal: No Solution Exploring Operation: 73*27=1971, Resulting Numbers: [1971] 1971,42 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,42 unequal: No Solution Moving to Node #0,0,3 Current State: 42:[73, 81], Operations: ['75-48=27', '54+27=81'] Exploring Operation: 73+81=154, Resulting Numbers: [154] 154,42 unequal: No Solution Exploring Operation: 81-73=8, Resulting Numbers: [8] 8,42 unequal: No Solution Exploring Operation: 73*81=5913, Resulting Numbers: [5913] 5913,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 42:[54, 75, 25], Operations: ['73-48=25'] Exploring Operation: 75/25=3, Resulting Numbers: [54, 3] Generated Node #0,4,0: 42:[54, 3] Operation: 75/25=3 Exploring Operation: 75-54=21, Resulting Numbers: [25, 21] Generated Node #0,4,1: 42:[25, 21] Operation: 75-54=21 Exploring Operation: 54-25=29, Resulting Numbers: [75, 29] Generated Node #0,4,2: 42:[75, 29] Operation: 54-25=29 Exploring Operation: 54+25=79, Resulting Numbers: [75, 79] Generated Node #0,4,3: 42:[75, 79] Operation: 54+25=79 Exploring Operation: 75-25=50, Resulting Numbers: [54, 50] Generated Node #0,4,4: 42:[54, 50] Operation: 75-25=50 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 42:[25, 21], Operations: ['73-48=25', '75-54=21'] Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,42 unequal: No Solution Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 42:[54, 3], Operations: ['73-48=25', '75/25=3'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,42 unequal: No Solution Exploring Operation: 54+3=57, Resulting Numbers: [57] 57,42 unequal: No Solution Exploring Operation: 54*3=162, Resulting Numbers: [162] 162,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 42:[54, 50], Operations: ['73-48=25', '75-25=50'] Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,42 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 42:[75, 29], Operations: ['73-48=25', '54-25=29'] Exploring Operation: 75*29=2175, Resulting Numbers: [2175] 2175,42 unequal: No Solution Exploring Operation: 75+29=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 42:[75, 79], Operations: ['73-48=25', '54+25=79'] Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 75+79=154, Resulting Numbers: [154] 154,42 unequal: No Solution Exploring Operation: 75*79=5925, Resulting Numbers: [5925] 5925,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 61, 30, 59, 42 ]
54
[ "61-59=2", "42*2=84", "84-30=54" ]
Current State: 54:[61, 30, 59, 42], Operations: [] Exploring Operation: 61-59=2, Resulting Numbers: [30, 42, 2] Generated Node #2: [30, 42, 2] from Operation: 61-59=2 Current State: 54:[30, 42, 2], Operations: ['61-59=2'] Exploring Operation: 42*2=84, Resulting Numbers: [30, 84] Generated Node #3: [30, 84] from Operation: 42*2=84 Current State: 54:[30, 84], Operations: ['61-59=2', '42*2=84'] Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[61, 30, 59, 42], Operations: [] Exploring Operation: 61-42=19, Resulting Numbers: [30, 59, 19] Generated Node #0,0: 54:[30, 59, 19] Operation: 61-42=19 Exploring Operation: 59-42=17, Resulting Numbers: [61, 30, 17] Generated Node #0,1: 54:[61, 30, 17] Operation: 59-42=17 Moving to Node #0,0 Current State: 54:[30, 59, 19], Operations: ['61-42=19'] Exploring Operation: 59-30=29, Resulting Numbers: [19, 29] Generated Node #0,0,0: 54:[19, 29] Operation: 59-30=29 Exploring Operation: 30-19=11, Resulting Numbers: [59, 11] Generated Node #0,0,1: 54:[59, 11] Operation: 30-19=11 Moving to Node #0,1 Current State: 54:[61, 30, 17], Operations: ['59-42=17'] Exploring Operation: 61-30=31, Resulting Numbers: [17, 31] Generated Node #0,1,0: 54:[17, 31] Operation: 61-30=31 Exploring Operation: 30-17=13, Resulting Numbers: [61, 13] Generated Node #0,1,1: 54:[61, 13] Operation: 30-17=13 Moving to Node #0,0,0 Current State: 54:[19, 29], Operations: ['61-42=19', '59-30=29'] Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[17, 31], Operations: ['59-42=17', '61-30=31'] Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[59, 11], Operations: ['61-42=19', '30-19=11'] Exploring Operation: 59+11=70, Resulting Numbers: [70] 70,54 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[61, 13], Operations: ['59-42=17', '30-17=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,54 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,54 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 46, 60, 3, 20 ]
86
[ "46+20=66", "60/3=20", "66+20=86" ]
Current State: 86:[46, 60, 3, 20], Operations: [] Exploring Operation: 46+20=66, Resulting Numbers: [60, 3, 66] Generated Node #2: [60, 3, 66] from Operation: 46+20=66 Current State: 86:[60, 3, 66], Operations: ['46+20=66'] Exploring Operation: 60/3=20, Resulting Numbers: [66, 20] Generated Node #3: [66, 20] from Operation: 60/3=20 Current State: 86:[66, 20], Operations: ['46+20=66', '60/3=20'] Exploring Operation: 66+20=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[46, 60, 3, 20], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [46, 3, 3] Generated Node #0,0: 86:[46, 3, 3] Operation: 60/20=3 Exploring Operation: 60+20=80, Resulting Numbers: [46, 3, 80] Generated Node #0,1: 86:[46, 3, 80] Operation: 60+20=80 Exploring Operation: 60-46=14, Resulting Numbers: [3, 20, 14] Generated Node #0,2: 86:[3, 20, 14] Operation: 60-46=14 Exploring Operation: 60-20=40, Resulting Numbers: [46, 3, 40] Generated Node #0,3: 86:[46, 3, 40] Operation: 60-20=40 Moving to Node #0,0 Current State: 86:[46, 3, 3], Operations: ['60/20=3'] Exploring Operation: 3/3=1, Resulting Numbers: [46, 1] Generated Node #0,0,0: 86:[46, 1] Operation: 3/3=1 Exploring Operation: 46-3=43, Resulting Numbers: [3, 43] Generated Node #0,0,1: 86:[3, 43] Operation: 46-3=43 Exploring Operation: 3-3=0, Resulting Numbers: [46, 0] Generated Node #0,0,2: 86:[46, 0] Operation: 3-3=0 Exploring Operation: 46-3=43, Resulting Numbers: [3, 43] Generated Node #0,0,3: 86:[3, 43] Operation: 46-3=43 Moving to Node #0,3 Current State: 86:[46, 3, 40], Operations: ['60-20=40'] Exploring Operation: 46+40=86, Resulting Numbers: [3, 86] Generated Node #0,3,0: 86:[3, 86] Operation: 46+40=86 Exploring Operation: 3+40=43, Resulting Numbers: [46, 43] Generated Node #0,3,1: 86:[46, 43] Operation: 3+40=43 Exploring Operation: 46-40=6, Resulting Numbers: [3, 6] Generated Node #0,3,2: 86:[3, 6] Operation: 46-40=6 Exploring Operation: 46-3=43, Resulting Numbers: [40, 43] Generated Node #0,3,3: 86:[40, 43] Operation: 46-3=43 Moving to Node #0,1 Current State: 86:[46, 3, 80], Operations: ['60+20=80'] Exploring Operation: 46-3=43, Resulting Numbers: [80, 43] Generated Node #0,1,0: 86:[80, 43] Operation: 46-3=43 Exploring Operation: 46+3=49, Resulting Numbers: [80, 49] Generated Node #0,1,1: 86:[80, 49] Operation: 46+3=49 Exploring Operation: 3+80=83, Resulting Numbers: [46, 83] Generated Node #0,1,2: 86:[46, 83] Operation: 3+80=83 Exploring Operation: 80-46=34, Resulting Numbers: [3, 34] Generated Node #0,1,3: 86:[3, 34] Operation: 80-46=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[80, 43], Operations: ['60+20=80', '46-3=43'] Exploring Operation: 80+43=123, Resulting Numbers: [123] 123,86 unequal: No Solution Exploring Operation: 80*43=3440, Resulting Numbers: [3440] 3440,86 unequal: No Solution Exploring Operation: 80-43=37, Resulting Numbers: [37] 37,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[46, 83], Operations: ['60+20=80', '3+80=83'] Exploring Operation: 46*83=3818, Resulting Numbers: [3818] 3818,86 unequal: No Solution Exploring Operation: 83-46=37, Resulting Numbers: [37] 37,86 unequal: No Solution Exploring Operation: 46+83=129, Resulting Numbers: [129] 129,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[3, 34], Operations: ['60+20=80', '80-46=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[80, 49], Operations: ['60+20=80', '46+3=49'] Exploring Operation: 80+49=129, Resulting Numbers: [129] 129,86 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 80*49=3920, Resulting Numbers: [3920] 3920,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[3, 20, 14], Operations: ['60-46=14'] Exploring Operation: 3*14=42, Resulting Numbers: [20, 42] Generated Node #0,2,0: 86:[20, 42] Operation: 3*14=42 Exploring Operation: 20+14=34, Resulting Numbers: [3, 34] Generated Node #0,2,1: 86:[3, 34] Operation: 20+14=34 Exploring Operation: 20-3=17, Resulting Numbers: [14, 17] Generated Node #0,2,2: 86:[14, 17] Operation: 20-3=17 Exploring Operation: 20-14=6, Resulting Numbers: [3, 6] Generated Node #0,2,3: 86:[3, 6] Operation: 20-14=6 Moving to Node #0,0,1 Current State: 86:[3, 43], Operations: ['60/20=3', '46-3=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,86 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,0,3 Current State: 86:[3, 43], Operations: ['60/20=3', '46-3=43'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 3*43=129, Resulting Numbers: [129] 129,86 unequal: No Solution Exploring Operation: 3+43=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,3,0 Current State: 86:[3, 86], Operations: ['60-20=40', '46+40=86'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 3+86=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 3*86=258, Resulting Numbers: [258] 258,86 unequal: No Solution Moving to Node #0,3,1 Current State: 86:[46, 43], Operations: ['60-20=40', '3+40=43'] Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,86 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,86 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,3,3 Current State: 86:[40, 43], Operations: ['60-20=40', '46-3=43'] Exploring Operation: 40*43=1720, Resulting Numbers: [1720] 1720,86 unequal: No Solution Exploring Operation: 40+43=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 43-40=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[46, 1], Operations: ['60/20=3', '3/3=1'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,86 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,86 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,3,2 Current State: 86:[3, 6], Operations: ['60-20=40', '46-40=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[46, 0], Operations: ['60/20=3', '3-3=0'] Exploring Operation: 46-0=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 46*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 46+0=46, Resulting Numbers: [46] 46,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[3, 6], Operations: ['60-46=14', '20-14=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[3, 34], Operations: ['60-46=14', '20+14=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[20, 42], Operations: ['60-46=14', '3*14=42'] Exploring Operation: 20+42=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,86 unequal: No Solution Exploring Operation: 20*42=840, Resulting Numbers: [840] 840,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[14, 17], Operations: ['60-46=14', '20-3=17'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,86 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,86 unequal: No Solution Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,86 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 63, 41, 94, 70 ]
80
[ "63+41=104", "94-70=24", "104-24=80" ]
Current State: 80:[63, 41, 94, 70], Operations: [] Exploring Operation: 63+41=104, Resulting Numbers: [94, 70, 104] Generated Node #2: [94, 70, 104] from Operation: 63+41=104 Current State: 80:[94, 70, 104], Operations: ['63+41=104'] Exploring Operation: 94-70=24, Resulting Numbers: [104, 24] Generated Node #3: [104, 24] from Operation: 94-70=24 Current State: 80:[104, 24], Operations: ['63+41=104', '94-70=24'] Exploring Operation: 104-24=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[63, 41, 94, 70], Operations: [] Exploring Operation: 94-41=53, Resulting Numbers: [63, 70, 53] Generated Node #0,0: 80:[63, 70, 53] Operation: 94-41=53 Exploring Operation: 70-63=7, Resulting Numbers: [41, 94, 7] Generated Node #0,1: 80:[41, 94, 7] Operation: 70-63=7 Exploring Operation: 94-63=31, Resulting Numbers: [41, 70, 31] Generated Node #0,2: 80:[41, 70, 31] Operation: 94-63=31 Exploring Operation: 94-70=24, Resulting Numbers: [63, 41, 24] Generated Node #0,3: 80:[63, 41, 24] Operation: 94-70=24 Exploring Operation: 63-41=22, Resulting Numbers: [94, 70, 22] Generated Node #0,4: 80:[94, 70, 22] Operation: 63-41=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[41, 94, 7], Operations: ['70-63=7'] Exploring Operation: 41+7=48, Resulting Numbers: [94, 48] Generated Node #0,1,0: 80:[94, 48] Operation: 41+7=48 Exploring Operation: 94-41=53, Resulting Numbers: [7, 53] Generated Node #0,1,1: 80:[7, 53] Operation: 94-41=53 Exploring Operation: 41-7=34, Resulting Numbers: [94, 34] Generated Node #0,1,2: 80:[94, 34] Operation: 41-7=34 Exploring Operation: 94-7=87, Resulting Numbers: [41, 87] Generated Node #0,1,3: 80:[41, 87] Operation: 94-7=87 Exploring Operation: 94+7=101, Resulting Numbers: [41, 101] Generated Node #0,1,4: 80:[41, 101] Operation: 94+7=101 Moving to Node #0,1,3 Current State: 80:[41, 87], Operations: ['70-63=7', '94-7=87'] Exploring Operation: 41*87=3567, Resulting Numbers: [3567] 3567,80 unequal: No Solution Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 41+87=128, Resulting Numbers: [128] 128,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[7, 53], Operations: ['70-63=7', '94-41=53'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[94, 34], Operations: ['70-63=7', '41-7=34'] Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,80 unequal: No Solution Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[94, 48], Operations: ['70-63=7', '41+7=48'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,80 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,80 unequal: No Solution Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,80 unequal: No Solution Moving to Node #0,1,4 Current State: 80:[41, 101], Operations: ['70-63=7', '94+7=101'] Exploring Operation: 101-41=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 41*101=4141, Resulting Numbers: [4141] 4141,80 unequal: No Solution Exploring Operation: 41+101=142, Resulting Numbers: [142] 142,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[41, 70, 31], Operations: ['94-63=31'] Exploring Operation: 41+31=72, Resulting Numbers: [70, 72] Generated Node #0,2,0: 80:[70, 72] Operation: 41+31=72 Exploring Operation: 70-31=39, Resulting Numbers: [41, 39] Generated Node #0,2,1: 80:[41, 39] Operation: 70-31=39 Exploring Operation: 70+31=101, Resulting Numbers: [41, 101] Generated Node #0,2,2: 80:[41, 101] Operation: 70+31=101 Exploring Operation: 41-31=10, Resulting Numbers: [70, 10] Generated Node #0,2,3: 80:[70, 10] Operation: 41-31=10 Exploring Operation: 70-41=29, Resulting Numbers: [31, 29] Generated Node #0,2,4: 80:[31, 29] Operation: 70-41=29 Moving to Node #0,2,1 Current State: 80:[41, 39], Operations: ['94-63=31', '70-31=39'] Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[63, 41, 94, 70], Operations: [] Exploring Operation: 94-63=31, Resulting Numbers: [41, 70, 31] Generated Node #0,2: 80:[41, 70, 31] Operation: 94-63=31 Moving to Node #0,2 Current State: 80:[41, 70, 31], Operations: ['94-63=31'] Exploring Operation: 70-31=39, Resulting Numbers: [41, 39] Generated Node #0,2,1: 80:[41, 39] Operation: 70-31=39 Moving to Node #0,2,1 Current State: 80:[41, 39], Operations: ['94-63=31', '70-31=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 70, 18, 39, 30 ]
35
[ "39-30=9", "70*9=630", "630/18=35" ]
Current State: 35:[70, 18, 39, 30], Operations: [] Exploring Operation: 39-30=9, Resulting Numbers: [70, 18, 9] Generated Node #2: [70, 18, 9] from Operation: 39-30=9 Current State: 35:[70, 18, 9], Operations: ['39-30=9'] Exploring Operation: 70*9=630, Resulting Numbers: [18, 630] Generated Node #3: [18, 630] from Operation: 70*9=630 Current State: 35:[18, 630], Operations: ['39-30=9', '70*9=630'] Exploring Operation: 630/18=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[70, 18, 39, 30], Operations: [] Exploring Operation: 70-39=31, Resulting Numbers: [18, 30, 31] Generated Node #0,0: 35:[18, 30, 31] Operation: 70-39=31 Exploring Operation: 70-30=40, Resulting Numbers: [18, 39, 40] Generated Node #0,1: 35:[18, 39, 40] Operation: 70-30=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[18, 30, 31], Operations: ['70-39=31'] Exploring Operation: 31-18=13, Resulting Numbers: [30, 13] Generated Node #0,0,0: 35:[30, 13] Operation: 31-18=13 Exploring Operation: 30-18=12, Resulting Numbers: [31, 12] Generated Node #0,0,1: 35:[31, 12] Operation: 30-18=12 Moving to Node #0,0,1 Current State: 35:[31, 12], Operations: ['70-39=31', '30-18=12'] Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[30, 13], Operations: ['70-39=31', '31-18=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[18, 39, 40], Operations: ['70-30=40'] Exploring Operation: 40-39=1, Resulting Numbers: [18, 1] Generated Node #0,1,0: 35:[18, 1] Operation: 40-39=1 Exploring Operation: 40-18=22, Resulting Numbers: [39, 22] Generated Node #0,1,1: 35:[39, 22] Operation: 40-18=22 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[18, 1], Operations: ['70-30=40', '40-39=1'] Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,35 unequal: No Solution Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,35 unequal: No Solution No 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: 35:[39, 22], Operations: ['70-30=40', '40-18=22'] Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,35 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 33, 21, 85, 99 ]
26
[ "33-21=12", "99-85=14", "12+14=26" ]
Current State: 26:[33, 21, 85, 99], Operations: [] Exploring Operation: 33-21=12, Resulting Numbers: [85, 99, 12] Generated Node #2: [85, 99, 12] from Operation: 33-21=12 Current State: 26:[85, 99, 12], Operations: ['33-21=12'] Exploring Operation: 99-85=14, Resulting Numbers: [12, 14] Generated Node #3: [12, 14] from Operation: 99-85=14 Current State: 26:[12, 14], Operations: ['33-21=12', '99-85=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[33, 21, 85, 99], Operations: [] Exploring Operation: 99-85=14, Resulting Numbers: [33, 21, 14] Generated Node #0,0: 26:[33, 21, 14] Operation: 99-85=14 Moving to Node #0,0 Current State: 26:[33, 21, 14], Operations: ['99-85=14'] Exploring Operation: 33-21=12, Resulting Numbers: [14, 12] Generated Node #0,0,0: 26:[14, 12] Operation: 33-21=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[14, 12], Operations: ['99-85=14', '33-21=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[33, 21, 85, 99], Operations: [] Exploring Operation: 99-85=14, Resulting Numbers: [33, 21, 14] Generated Node #0,0: 26:[33, 21, 14] Operation: 99-85=14 Moving to Node #0,0 Current State: 26:[33, 21, 14], Operations: ['99-85=14'] Exploring Operation: 33-21=12, Resulting Numbers: [14, 12] Generated Node #0,0,0: 26:[14, 12] Operation: 33-21=12 Moving to Node #0,0,0 Current State: 26:[14, 12], Operations: ['99-85=14', '33-21=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 53, 86, 67, 98 ]
79
[ "67-53=14", "98/14=7", "86-7=79" ]
Current State: 79:[53, 86, 67, 98], Operations: [] Exploring Operation: 67-53=14, Resulting Numbers: [86, 98, 14] Generated Node #2: [86, 98, 14] from Operation: 67-53=14 Current State: 79:[86, 98, 14], Operations: ['67-53=14'] Exploring Operation: 98/14=7, Resulting Numbers: [86, 7] Generated Node #3: [86, 7] from Operation: 98/14=7 Current State: 79:[86, 7], Operations: ['67-53=14', '98/14=7'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[53, 86, 67, 98], Operations: [] Exploring Operation: 98-67=31, Resulting Numbers: [53, 86, 31] Generated Node #0,0: 79:[53, 86, 31] Operation: 98-67=31 Exploring Operation: 53+86=139, Resulting Numbers: [67, 98, 139] Generated Node #0,1: 79:[67, 98, 139] Operation: 53+86=139 Exploring Operation: 53+67=120, Resulting Numbers: [86, 98, 120] Generated Node #0,2: 79:[86, 98, 120] Operation: 53+67=120 Exploring Operation: 86-53=33, Resulting Numbers: [67, 98, 33] Generated Node #0,3: 79:[67, 98, 33] Operation: 86-53=33 Exploring Operation: 98-53=45, Resulting Numbers: [86, 67, 45] Generated Node #0,4: 79:[86, 67, 45] Operation: 98-53=45 Start Sub Search at level 1: Moving to Node #0,4 Current State: 79:[86, 67, 45], Operations: ['98-53=45'] Exploring Operation: 86-67=19, Resulting Numbers: [45, 19] Generated Node #0,4,0: 79:[45, 19] Operation: 86-67=19 Exploring Operation: 86-45=41, Resulting Numbers: [67, 41] Generated Node #0,4,1: 79:[67, 41] Operation: 86-45=41 Exploring Operation: 86+45=131, Resulting Numbers: [67, 131] Generated Node #0,4,2: 79:[67, 131] Operation: 86+45=131 Exploring Operation: 67-45=22, Resulting Numbers: [86, 22] Generated Node #0,4,3: 79:[86, 22] Operation: 67-45=22 Exploring Operation: 67+45=112, Resulting Numbers: [86, 112] Generated Node #0,4,4: 79:[86, 112] Operation: 67+45=112 Moving to Node #0,4,4 Current State: 79:[86, 112], Operations: ['98-53=45', '67+45=112'] Exploring Operation: 86+112=198, Resulting Numbers: [198] 198,79 unequal: No Solution Exploring Operation: 86*112=9632, Resulting Numbers: [9632] 9632,79 unequal: No Solution Exploring Operation: 112-86=26, Resulting Numbers: [26] 26,79 unequal: No Solution Moving to Node #0,4,1 Current State: 79:[67, 41], Operations: ['98-53=45', '86-45=41'] Exploring Operation: 67+41=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 67*41=2747, Resulting Numbers: [2747] 2747,79 unequal: No Solution Moving to Node #0,4,2 Current State: 79:[67, 131], Operations: ['98-53=45', '86+45=131'] Exploring Operation: 131-67=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 67+131=198, Resulting Numbers: [198] 198,79 unequal: No Solution Exploring Operation: 67*131=8777, Resulting Numbers: [8777] 8777,79 unequal: No Solution Moving to Node #0,4,3 Current State: 79:[86, 22], Operations: ['98-53=45', '67-45=22'] Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,79 unequal: No Solution Moving to Node #0,4,0 Current State: 79:[45, 19], Operations: ['98-53=45', '86-67=19'] Exploring Operation: 45*19=855, Resulting Numbers: [855] 855,79 unequal: No Solution Exploring Operation: 45+19=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,79 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 Current State: 79:[86, 98, 120], Operations: ['53+67=120'] Exploring Operation: 98-86=12, Resulting Numbers: [120, 12] Generated Node #0,2,0: 79:[120, 12] Operation: 98-86=12 Exploring Operation: 120-98=22, Resulting Numbers: [86, 22] Generated Node #0,2,1: 79:[86, 22] Operation: 120-98=22 Exploring Operation: 86+120=206, Resulting Numbers: [98, 206] Generated Node #0,2,2: 79:[98, 206] Operation: 86+120=206 Exploring Operation: 120-86=34, Resulting Numbers: [98, 34] Generated Node #0,2,3: 79:[98, 34] Operation: 120-86=34 Exploring Operation: 86+98=184, Resulting Numbers: [120, 184] Generated Node #0,2,4: 79:[120, 184] Operation: 86+98=184 Moving to Node #0,2,1 Current State: 79:[86, 22], Operations: ['53+67=120', '120-98=22'] Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,79 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[98, 34], Operations: ['53+67=120', '120-86=34'] Exploring Operation: 98+34=132, Resulting Numbers: [132] 132,79 unequal: No Solution Exploring Operation: 98-34=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 98*34=3332, Resulting Numbers: [3332] 3332,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[120, 12], Operations: ['53+67=120', '98-86=12'] Exploring Operation: 120-12=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 120/12=10, Resulting Numbers: [10] 10,79 unequal: No Solution Exploring Operation: 120*12=1440, Resulting Numbers: [1440] 1440,79 unequal: No Solution Exploring Operation: 120+12=132, Resulting Numbers: [132] 132,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[98, 206], Operations: ['53+67=120', '86+120=206'] Exploring Operation: 98*206=20188, Resulting Numbers: [20188] 20188,79 unequal: No Solution Exploring Operation: 206-98=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 98+206=304, Resulting Numbers: [304] 304,79 unequal: No Solution Moving to Node #0,2,4 Current State: 79:[120, 184], Operations: ['53+67=120', '86+98=184'] Exploring Operation: 120+184=304, Resulting Numbers: [304] 304,79 unequal: No Solution Exploring Operation: 184-120=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 120*184=22080, Resulting Numbers: [22080] 22080,79 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 Current State: 79:[67, 98, 33], Operations: ['86-53=33'] Exploring Operation: 67-33=34, Resulting Numbers: [98, 34] Generated Node #0,3,0: 79:[98, 34] Operation: 67-33=34 Exploring Operation: 67+33=100, Resulting Numbers: [98, 100] Generated Node #0,3,1: 79:[98, 100] Operation: 67+33=100 Exploring Operation: 98-33=65, Resulting Numbers: [67, 65] Generated Node #0,3,2: 79:[67, 65] Operation: 98-33=65 Exploring Operation: 98+33=131, Resulting Numbers: [67, 131] Generated Node #0,3,3: 79:[67, 131] Operation: 98+33=131 Exploring Operation: 98-67=31, Resulting Numbers: [33, 31] Generated Node #0,3,4: 79:[33, 31] Operation: 98-67=31 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 79:[67, 65], Operations: ['86-53=33', '98-33=65'] Exploring Operation: 67+65=132, Resulting Numbers: [132] 132,79 unequal: No Solution Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 67*65=4355, Resulting Numbers: [4355] 4355,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 79:[98, 100], Operations: ['86-53=33', '67+33=100'] Exploring Operation: 100-98=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 98*100=9800, Resulting Numbers: [9800] 9800,79 unequal: No Solution Exploring Operation: 98+100=198, Resulting Numbers: [198] 198,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 79:[98, 34], Operations: ['86-53=33', '67-33=34'] Exploring Operation: 98+34=132, Resulting Numbers: [132] 132,79 unequal: No Solution Exploring Operation: 98-34=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 98*34=3332, Resulting Numbers: [3332] 3332,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 79:[67, 131], Operations: ['86-53=33', '98+33=131'] Exploring Operation: 67*131=8777, Resulting Numbers: [8777] 8777,79 unequal: No Solution Exploring Operation: 67+131=198, Resulting Numbers: [198] 198,79 unequal: No Solution Exploring Operation: 131-67=64, Resulting Numbers: [64] 64,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 79:[33, 31], Operations: ['86-53=33', '98-67=31'] Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,79 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[53, 86, 31], Operations: ['98-67=31'] Exploring Operation: 53+31=84, Resulting Numbers: [86, 84] Generated Node #0,0,0: 79:[86, 84] Operation: 53+31=84 Exploring Operation: 86-31=55, Resulting Numbers: [53, 55] Generated Node #0,0,1: 79:[53, 55] Operation: 86-31=55 Exploring Operation: 86+31=117, Resulting Numbers: [53, 117] Generated Node #0,0,2: 79:[53, 117] Operation: 86+31=117 Exploring Operation: 53-31=22, Resulting Numbers: [86, 22] Generated Node #0,0,3: 79:[86, 22] Operation: 53-31=22 Exploring Operation: 86-53=33, Resulting Numbers: [31, 33] Generated Node #0,0,4: 79:[31, 33] Operation: 86-53=33 Moving to Node #0,0,0 Current State: 79:[86, 84], Operations: ['98-67=31', '53+31=84'] Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 86+84=170, Resulting Numbers: [170] 170,79 unequal: No Solution Exploring Operation: 86*84=7224, Resulting Numbers: [7224] 7224,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[53, 55], Operations: ['98-67=31', '86-31=55'] Exploring Operation: 53*55=2915, Resulting Numbers: [2915] 2915,79 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 53+55=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[53, 117], Operations: ['98-67=31', '86+31=117'] Exploring Operation: 53+117=170, Resulting Numbers: [170] 170,79 unequal: No Solution Exploring Operation: 53*117=6201, Resulting Numbers: [6201] 6201,79 unequal: No Solution Exploring Operation: 117-53=64, Resulting Numbers: [64] 64,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[86, 22], Operations: ['98-67=31', '53-31=22'] Exploring Operation: 86*22=1892, Resulting Numbers: [1892] 1892,79 unequal: No Solution Exploring Operation: 86+22=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 86-22=64, Resulting Numbers: [64] 64,79 unequal: No Solution Moving to Node #0,0,4 Current State: 79:[31, 33], Operations: ['98-67=31', '86-53=33'] Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 31+33=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 31*33=1023, Resulting Numbers: [1023] 1023,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[67, 98, 139], Operations: ['53+86=139'] Exploring Operation: 139-98=41, Resulting Numbers: [67, 41] Generated Node #0,1,0: 79:[67, 41] Operation: 139-98=41 Exploring Operation: 67+139=206, Resulting Numbers: [98, 206] Generated Node #0,1,1: 79:[98, 206] Operation: 67+139=206 Exploring Operation: 139-67=72, Resulting Numbers: [98, 72] Generated Node #0,1,2: 79:[98, 72] Operation: 139-67=72 Exploring Operation: 98-67=31, Resulting Numbers: [139, 31] Generated Node #0,1,3: 79:[139, 31] Operation: 98-67=31 Exploring Operation: 67+98=165, Resulting Numbers: [139, 165] Generated Node #0,1,4: 79:[139, 165] Operation: 67+98=165 Moving to Node #0,1,2 Current State: 79:[98, 72], Operations: ['53+86=139', '139-67=72'] Exploring Operation: 98-72=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 98*72=7056, Resulting Numbers: [7056] 7056,79 unequal: No Solution Exploring Operation: 98+72=170, Resulting Numbers: [170] 170,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[67, 41], Operations: ['53+86=139', '139-98=41'] Exploring Operation: 67-41=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 67*41=2747, Resulting Numbers: [2747] 2747,79 unequal: No Solution Exploring Operation: 67+41=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[139, 31], Operations: ['53+86=139', '98-67=31'] Exploring Operation: 139-31=108, Resulting Numbers: [108] 108,79 unequal: No Solution Exploring Operation: 139*31=4309, Resulting Numbers: [4309] 4309,79 unequal: No Solution Exploring Operation: 139+31=170, Resulting Numbers: [170] 170,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[98, 206], Operations: ['53+86=139', '67+139=206'] Exploring Operation: 98*206=20188, Resulting Numbers: [20188] 20188,79 unequal: No Solution Exploring Operation: 98+206=304, Resulting Numbers: [304] 304,79 unequal: No Solution Exploring Operation: 206-98=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,1,4 Current State: 79:[139, 165], Operations: ['53+86=139', '67+98=165'] Exploring Operation: 139+165=304, Resulting Numbers: [304] 304,79 unequal: No Solution Exploring Operation: 165-139=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 139*165=22935, Resulting Numbers: [22935] 22935,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 2, 80, 32, 34 ]
79
[ "2+32=34", "34/34=1", "80-1=79" ]
Current State: 79:[2, 80, 32, 34], Operations: [] Exploring Operation: 2+32=34, Resulting Numbers: [80, 34, 34] Generated Node #2: [80, 34, 34] from Operation: 2+32=34 Current State: 79:[80, 34, 34], Operations: ['2+32=34'] Exploring Operation: 34/34=1, Resulting Numbers: [80, 1] Generated Node #3: [80, 1] from Operation: 34/34=1 Current State: 79:[80, 1], Operations: ['2+32=34', '34/34=1'] Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[2, 80, 32, 34], Operations: [] Exploring Operation: 2*34=68, Resulting Numbers: [80, 32, 68] Generated Node #0,0: 79:[80, 32, 68] Operation: 2*34=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[80, 32, 68], Operations: ['2*34=68'] Exploring Operation: 32+68=100, Resulting Numbers: [80, 100] Generated Node #0,0,0: 79:[80, 100] Operation: 32+68=100 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[80, 100], Operations: ['2*34=68', '32+68=100'] Exploring Operation: 100-80=20, Resulting Numbers: [20] 20,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 24, 58, 76, 82 ]
62
[ "82-76=6", "24/6=4", "58+4=62" ]
Current State: 62:[24, 58, 76, 82], Operations: [] Exploring Operation: 82-76=6, Resulting Numbers: [24, 58, 6] Generated Node #2: [24, 58, 6] from Operation: 82-76=6 Current State: 62:[24, 58, 6], Operations: ['82-76=6'] Exploring Operation: 24/6=4, Resulting Numbers: [58, 4] Generated Node #3: [58, 4] from Operation: 24/6=4 Current State: 62:[58, 4], Operations: ['82-76=6', '24/6=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[24, 58, 76, 82], Operations: [] Exploring Operation: 76-24=52, Resulting Numbers: [58, 82, 52] Generated Node #0,0: 62:[58, 82, 52] Operation: 76-24=52 Exploring Operation: 82-58=24, Resulting Numbers: [24, 76, 24] Generated Node #0,1: 62:[24, 76, 24] Operation: 82-58=24 Exploring Operation: 82-76=6, Resulting Numbers: [24, 58, 6] Generated Node #0,2: 62:[24, 58, 6] Operation: 82-76=6 Exploring Operation: 82-24=58, Resulting Numbers: [58, 76, 58] Generated Node #0,3: 62:[58, 76, 58] Operation: 82-24=58 Moving to Node #0,2 Current State: 62:[24, 58, 6], Operations: ['82-76=6'] Exploring Operation: 24+6=30, Resulting Numbers: [58, 30] Generated Node #0,2,0: 62:[58, 30] Operation: 24+6=30 Exploring Operation: 58+6=64, Resulting Numbers: [24, 64] Generated Node #0,2,1: 62:[24, 64] Operation: 58+6=64 Exploring Operation: 24/6=4, Resulting Numbers: [58, 4] Generated Node #0,2,2: 62:[58, 4] Operation: 24/6=4 Exploring Operation: 58-24=34, Resulting Numbers: [6, 34] Generated Node #0,2,3: 62:[6, 34] Operation: 58-24=34 Moving to Node #0,3 Current State: 62:[58, 76, 58], Operations: ['82-24=58'] Exploring Operation: 76-58=18, Resulting Numbers: [58, 18] Generated Node #0,3,0: 62:[58, 18] Operation: 76-58=18 Exploring Operation: 58-58=0, Resulting Numbers: [76, 0] Generated Node #0,3,1: 62:[76, 0] Operation: 58-58=0 Exploring Operation: 76-58=18, Resulting Numbers: [58, 18] Generated Node #0,3,2: 62:[58, 18] Operation: 76-58=18 Exploring Operation: 58/58=1, Resulting Numbers: [76, 1] Generated Node #0,3,3: 62:[76, 1] Operation: 58/58=1 Moving to Node #0,1 Current State: 62:[24, 76, 24], Operations: ['82-58=24'] Exploring Operation: 76-24=52, Resulting Numbers: [24, 52] Generated Node #0,1,0: 62:[24, 52] Operation: 76-24=52 Exploring Operation: 24/24=1, Resulting Numbers: [76, 1] Generated Node #0,1,1: 62:[76, 1] Operation: 24/24=1 Exploring Operation: 76-24=52, Resulting Numbers: [24, 52] Generated Node #0,1,2: 62:[24, 52] Operation: 76-24=52 Exploring Operation: 24-24=0, Resulting Numbers: [76, 0] Generated Node #0,1,3: 62:[76, 0] Operation: 24-24=0 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[76, 1], Operations: ['82-58=24', '24/24=1'] Exploring Operation: 76*1=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 76-1=75, Resulting Numbers: [75] 75,62 unequal: No Solution Exploring Operation: 76/1=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[76, 0], Operations: ['82-58=24', '24-24=0'] Exploring Operation: 76-0=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 76+0=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 76*0=0, Resulting Numbers: [0] 0,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[24, 52], Operations: ['82-58=24', '76-24=52'] Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,62 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[24, 52], Operations: ['82-58=24', '76-24=52'] Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,62 unequal: No Solution Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,62 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,62 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: 62:[58, 82, 52], Operations: ['76-24=52'] Exploring Operation: 58-52=6, Resulting Numbers: [82, 6] Generated Node #0,0,0: 62:[82, 6] Operation: 58-52=6 Exploring Operation: 82-52=30, Resulting Numbers: [58, 30] Generated Node #0,0,1: 62:[58, 30] Operation: 82-52=30 Exploring Operation: 82-58=24, Resulting Numbers: [52, 24] Generated Node #0,0,2: 62:[52, 24] Operation: 82-58=24 Exploring Operation: 58+52=110, Resulting Numbers: [82, 110] Generated Node #0,0,3: 62:[82, 110] Operation: 58+52=110 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[58, 30], Operations: ['76-24=52', '82-52=30'] Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,62 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,62 unequal: No Solution Exploring Operation: 58*30=1740, Resulting Numbers: [1740] 1740,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[52, 24], Operations: ['76-24=52', '82-58=24'] Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,62 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,62 unequal: No Solution Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[82, 6], Operations: ['76-24=52', '58-52=6'] Exploring Operation: 82+6=88, Resulting Numbers: [88] 88,62 unequal: No Solution Exploring Operation: 82*6=492, Resulting Numbers: [492] 492,62 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 62:[82, 110], Operations: ['76-24=52', '58+52=110'] Exploring Operation: 82*110=9020, Resulting Numbers: [9020] 9020,62 unequal: No Solution Exploring Operation: 110-82=28, Resulting Numbers: [28] 28,62 unequal: No Solution Exploring Operation: 82+110=192, Resulting Numbers: [192] 192,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 62:[58, 30], Operations: ['82-76=6', '24+6=30'] Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,62 unequal: No Solution Exploring Operation: 58*30=1740, Resulting Numbers: [1740] 1740,62 unequal: No Solution Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[58, 4], Operations: ['82-76=6', '24/6=4'] Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,62 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,62 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[24, 58, 76, 82], Operations: [] Exploring Operation: 82-76=6, Resulting Numbers: [24, 58, 6] Generated Node #0,2: 62:[24, 58, 6] Operation: 82-76=6 Moving to Node #0,2 Current State: 62:[24, 58, 6], Operations: ['82-76=6'] Exploring Operation: 24/6=4, Resulting Numbers: [58, 4] Generated Node #0,2,2: 62:[58, 4] Operation: 24/6=4 Moving to Node #0,2,2 Current State: 62:[58, 4], Operations: ['82-76=6', '24/6=4'] Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.952257
hs_4
sum_heuristic
[ 67, 95, 57, 43 ]
40
[ "67-43=24", "95*24=2280", "2280/57=40" ]
Current State: 40:[67, 95, 57, 43], Operations: [] Exploring Operation: 67-43=24, Resulting Numbers: [95, 57, 24] Generated Node #2: [95, 57, 24] from Operation: 67-43=24 Current State: 40:[95, 57, 24], Operations: ['67-43=24'] Exploring Operation: 95*24=2280, Resulting Numbers: [57, 2280] Generated Node #3: [57, 2280] from Operation: 95*24=2280 Current State: 40:[57, 2280], Operations: ['67-43=24', '95*24=2280'] Exploring Operation: 2280/57=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[67, 95, 57, 43], Operations: [] Exploring Operation: 95-57=38, Resulting Numbers: [67, 43, 38] Generated Node #0,0: 40:[67, 43, 38] Operation: 95-57=38 Exploring Operation: 95-43=52, Resulting Numbers: [67, 57, 52] Generated Node #0,1: 40:[67, 57, 52] Operation: 95-43=52 Exploring Operation: 95-67=28, Resulting Numbers: [57, 43, 28] Generated Node #0,2: 40:[57, 43, 28] Operation: 95-67=28 Moving to Node #0,2 Current State: 40:[57, 43, 28], Operations: ['95-67=28'] Exploring Operation: 43-28=15, Resulting Numbers: [57, 15] Generated Node #0,2,0: 40:[57, 15] Operation: 43-28=15 Exploring Operation: 57-43=14, Resulting Numbers: [28, 14] Generated Node #0,2,1: 40:[28, 14] Operation: 57-43=14 Exploring Operation: 57-28=29, Resulting Numbers: [43, 29] Generated Node #0,2,2: 40:[43, 29] Operation: 57-28=29 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[28, 14], Operations: ['95-67=28', '57-43=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 28+14=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[43, 29], Operations: ['95-67=28', '57-28=29'] Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,40 unequal: No Solution Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[57, 15], Operations: ['95-67=28', '43-28=15'] Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,40 unequal: No Solution Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,40 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: 40:[67, 43, 38], Operations: ['95-57=38'] Exploring Operation: 67-38=29, Resulting Numbers: [43, 29] Generated Node #0,0,0: 40:[43, 29] Operation: 67-38=29 Exploring Operation: 43-38=5, Resulting Numbers: [67, 5] Generated Node #0,0,1: 40:[67, 5] Operation: 43-38=5 Exploring Operation: 67-43=24, Resulting Numbers: [38, 24] Generated Node #0,0,2: 40:[38, 24] Operation: 67-43=24 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[38, 24], Operations: ['95-57=38', '67-43=24'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 38*24=912, Resulting Numbers: [912] 912,40 unequal: No Solution Exploring Operation: 38+24=62, Resulting Numbers: [62] 62,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[43, 29], Operations: ['95-57=38', '67-38=29'] Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,40 unequal: No Solution Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[67, 5], Operations: ['95-57=38', '43-38=5'] Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,40 unequal: No Solution Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,40 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,40 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: 40:[67, 57, 52], Operations: ['95-43=52'] Exploring Operation: 57-52=5, Resulting Numbers: [67, 5] Generated Node #0,1,0: 40:[67, 5] Operation: 57-52=5 Exploring Operation: 67-57=10, Resulting Numbers: [52, 10] Generated Node #0,1,1: 40:[52, 10] Operation: 67-57=10 Exploring Operation: 67-52=15, Resulting Numbers: [57, 15] Generated Node #0,1,2: 40:[57, 15] Operation: 67-52=15 Moving to Node #0,1,1 Current State: 40:[52, 10], Operations: ['95-43=52', '67-57=10'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,40 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[57, 15], Operations: ['95-43=52', '67-52=15'] Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,40 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[67, 5], Operations: ['95-43=52', '57-52=5'] Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,40 unequal: No Solution Exploring Operation: 67*5=335, Resulting Numbers: [335] 335,40 unequal: No Solution Exploring Operation: 67+5=72, Resulting Numbers: [72] 72,40 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 46, 1, 51 ]
56
[ "46-40=6", "51-1=50", "6+50=56" ]
Current State: 56:[40, 46, 1, 51], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [1, 51, 6] Generated Node #2: [1, 51, 6] from Operation: 46-40=6 Current State: 56:[1, 51, 6], Operations: ['46-40=6'] Exploring Operation: 51-1=50, Resulting Numbers: [6, 50] Generated Node #3: [6, 50] from Operation: 51-1=50 Current State: 56:[6, 50], Operations: ['46-40=6', '51-1=50'] Exploring Operation: 6+50=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[40, 46, 1, 51], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [1, 51, 6] Generated Node #0,0: 56:[1, 51, 6] Operation: 46-40=6 Exploring Operation: 51-40=11, Resulting Numbers: [46, 1, 11] Generated Node #0,1: 56:[46, 1, 11] Operation: 51-40=11 Moving to Node #0,0 Current State: 56:[1, 51, 6], Operations: ['46-40=6'] Exploring Operation: 51+6=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 56:[1, 57] Operation: 51+6=57 Exploring Operation: 1+51=52, Resulting Numbers: [6, 52] Generated Node #0,0,1: 56:[6, 52] Operation: 1+51=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[1, 57], Operations: ['46-40=6', '51+6=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[40, 46, 1, 51], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [1, 51, 6] Generated Node #0,0: 56:[1, 51, 6] Operation: 46-40=6 Moving to Node #0,0 Current State: 56:[1, 51, 6], Operations: ['46-40=6'] Exploring Operation: 51+6=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 56:[1, 57] Operation: 51+6=57 Moving to Node #0,0,0 Current State: 56:[1, 57], Operations: ['46-40=6', '51+6=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 72, 29, 58, 27 ]
97
[ "72+27=99", "58/29=2", "99-2=97" ]
Current State: 97:[72, 29, 58, 27], Operations: [] Exploring Operation: 72+27=99, Resulting Numbers: [29, 58, 99] Generated Node #2: [29, 58, 99] from Operation: 72+27=99 Current State: 97:[29, 58, 99], Operations: ['72+27=99'] Exploring Operation: 58/29=2, Resulting Numbers: [99, 2] Generated Node #3: [99, 2] from Operation: 58/29=2 Current State: 97:[99, 2], Operations: ['72+27=99', '58/29=2'] Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[72, 29, 58, 27], Operations: [] Exploring Operation: 29+27=56, Resulting Numbers: [72, 58, 56] Generated Node #0,0: 97:[72, 58, 56] Operation: 29+27=56 Exploring Operation: 29+58=87, Resulting Numbers: [72, 27, 87] Generated Node #0,1: 97:[72, 27, 87] Operation: 29+58=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[72, 58, 56], Operations: ['29+27=56'] Exploring Operation: 58+56=114, Resulting Numbers: [72, 114] Generated Node #0,0,0: 97:[72, 114] Operation: 58+56=114 Exploring Operation: 72+56=128, Resulting Numbers: [58, 128] Generated Node #0,0,1: 97:[58, 128] Operation: 72+56=128 Moving to Node #0,0,0 Current State: 97:[72, 114], Operations: ['29+27=56', '58+56=114'] Exploring Operation: 72+114=186, Resulting Numbers: [186] 186,97 unequal: No Solution Exploring Operation: 114-72=42, Resulting Numbers: [42] 42,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[58, 128], Operations: ['29+27=56', '72+56=128'] Exploring Operation: 128-58=70, Resulting Numbers: [70] 70,97 unequal: No Solution Exploring Operation: 58+128=186, Resulting Numbers: [186] 186,97 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:[72, 27, 87], Operations: ['29+58=87'] Exploring Operation: 72+27=99, Resulting Numbers: [87, 99] Generated Node #0,1,0: 97:[87, 99] Operation: 72+27=99 Exploring Operation: 27+87=114, Resulting Numbers: [72, 114] Generated Node #0,1,1: 97:[72, 114] Operation: 27+87=114 Moving to Node #0,1,0 Current State: 97:[87, 99], Operations: ['29+58=87', '72+27=99'] Exploring Operation: 87+99=186, Resulting Numbers: [186] 186,97 unequal: No Solution Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[72, 114], Operations: ['29+58=87', '27+87=114'] Exploring Operation: 72+114=186, Resulting Numbers: [186] 186,97 unequal: No Solution Exploring Operation: 114-72=42, Resulting Numbers: [42] 42,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 19, 53, 38, 34 ]
89
[ "38/19=2", "53+34=87", "2+87=89" ]
Current State: 89:[19, 53, 38, 34], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [53, 34, 2] Generated Node #2: [53, 34, 2] from Operation: 38/19=2 Current State: 89:[53, 34, 2], Operations: ['38/19=2'] Exploring Operation: 53+34=87, Resulting Numbers: [2, 87] Generated Node #3: [2, 87] from Operation: 53+34=87 Current State: 89:[2, 87], Operations: ['38/19=2', '53+34=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[19, 53, 38, 34], Operations: [] Exploring Operation: 19+38=57, Resulting Numbers: [53, 34, 57] Generated Node #0,0: 89:[53, 34, 57] Operation: 19+38=57 Exploring Operation: 19+34=53, Resulting Numbers: [53, 38, 53] Generated Node #0,1: 89:[53, 38, 53] Operation: 19+34=53 Exploring Operation: 53+34=87, Resulting Numbers: [19, 38, 87] Generated Node #0,2: 89:[19, 38, 87] Operation: 53+34=87 Exploring Operation: 19+53=72, Resulting Numbers: [38, 34, 72] Generated Node #0,3: 89:[38, 34, 72] Operation: 19+53=72 Moving to Node #0,0 Current State: 89:[53, 34, 57], Operations: ['19+38=57'] Exploring Operation: 34+57=91, Resulting Numbers: [53, 91] Generated Node #0,0,0: 89:[53, 91] Operation: 34+57=91 Exploring Operation: 53+34=87, Resulting Numbers: [57, 87] Generated Node #0,0,1: 89:[57, 87] Operation: 53+34=87 Exploring Operation: 53-34=19, Resulting Numbers: [57, 19] Generated Node #0,0,2: 89:[57, 19] Operation: 53-34=19 Exploring Operation: 53+57=110, Resulting Numbers: [34, 110] Generated Node #0,0,3: 89:[34, 110] Operation: 53+57=110 Moving to Node #0,2 Current State: 89:[19, 38, 87], Operations: ['53+34=87'] Exploring Operation: 19+87=106, Resulting Numbers: [38, 106] Generated Node #0,2,0: 89:[38, 106] Operation: 19+87=106 Exploring Operation: 19+38=57, Resulting Numbers: [87, 57] Generated Node #0,2,1: 89:[87, 57] Operation: 19+38=57 Exploring Operation: 87-19=68, Resulting Numbers: [38, 68] Generated Node #0,2,2: 89:[38, 68] Operation: 87-19=68 Exploring Operation: 38-19=19, Resulting Numbers: [87, 19] Generated Node #0,2,3: 89:[87, 19] Operation: 38-19=19 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[87, 57], Operations: ['53+34=87', '19+38=57'] Exploring Operation: 87-57=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 87+57=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 87*57=4959, Resulting Numbers: [4959] 4959,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[38, 106], Operations: ['53+34=87', '19+87=106'] Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[38, 68], Operations: ['53+34=87', '87-19=68'] Exploring Operation: 38+68=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 38*68=2584, Resulting Numbers: [2584] 2584,89 unequal: No Solution Exploring Operation: 68-38=30, Resulting Numbers: [30] 30,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[87, 19], Operations: ['53+34=87', '38-19=19'] Exploring Operation: 87+19=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 87*19=1653, Resulting Numbers: [1653] 1653,89 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: 89:[53, 38, 53], Operations: ['19+34=53'] Exploring Operation: 53+53=106, Resulting Numbers: [38, 106] Generated Node #0,1,0: 89:[38, 106] Operation: 53+53=106 Exploring Operation: 53-38=15, Resulting Numbers: [53, 15] Generated Node #0,1,1: 89:[53, 15] Operation: 53-38=15 Exploring Operation: 38+53=91, Resulting Numbers: [53, 91] Generated Node #0,1,2: 89:[53, 91] Operation: 38+53=91 Exploring Operation: 53+38=91, Resulting Numbers: [53, 91] Generated Node #0,1,3: 89:[53, 91] Operation: 53+38=91 Moving to Node #0,3 Current State: 89:[38, 34, 72], Operations: ['19+53=72'] Exploring Operation: 34+72=106, Resulting Numbers: [38, 106] Generated Node #0,3,0: 89:[38, 106] Operation: 34+72=106 Exploring Operation: 38-34=4, Resulting Numbers: [72, 4] Generated Node #0,3,1: 89:[72, 4] Operation: 38-34=4 Exploring Operation: 38+72=110, Resulting Numbers: [34, 110] Generated Node #0,3,2: 89:[34, 110] Operation: 38+72=110 Exploring Operation: 38+34=72, Resulting Numbers: [72, 72] Generated Node #0,3,3: 89:[72, 72] Operation: 38+34=72 Moving to Node #0,0,1 Current State: 89:[57, 87], Operations: ['19+38=57', '53+34=87'] Exploring Operation: 87-57=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 57*87=4959, Resulting Numbers: [4959] 4959,89 unequal: No Solution Exploring Operation: 57+87=144, Resulting Numbers: [144] 144,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[72, 72], Operations: ['19+53=72', '38+34=72'] Exploring Operation: 72+72=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 72/72=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 72-72=0, Resulting Numbers: [0] 0,89 unequal: No Solution Exploring Operation: 72*72=5184, Resulting Numbers: [5184] 5184,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[53, 91], Operations: ['19+34=53', '53+38=91'] Exploring Operation: 53+91=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 53*91=4823, Resulting Numbers: [4823] 4823,89 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[53, 91], Operations: ['19+34=53', '38+53=91'] Exploring Operation: 53+91=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 53*91=4823, Resulting Numbers: [4823] 4823,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[53, 91], Operations: ['19+38=57', '34+57=91'] Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 53*91=4823, Resulting Numbers: [4823] 4823,89 unequal: No Solution Exploring Operation: 53+91=144, Resulting Numbers: [144] 144,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[38, 106], Operations: ['19+34=53', '53+53=106'] Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,89 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[38, 106], Operations: ['19+53=72', '34+72=106'] Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[34, 110], Operations: ['19+53=72', '38+72=110'] Exploring Operation: 34+110=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 34*110=3740, Resulting Numbers: [3740] 3740,89 unequal: No Solution Exploring Operation: 110-34=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[34, 110], Operations: ['19+38=57', '53+57=110'] Exploring Operation: 34*110=3740, Resulting Numbers: [3740] 3740,89 unequal: No Solution Exploring Operation: 34+110=144, Resulting Numbers: [144] 144,89 unequal: No Solution Exploring Operation: 110-34=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[72, 4], Operations: ['19+53=72', '38-34=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,89 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,89 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[57, 19], Operations: ['19+38=57', '53-34=19'] Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,89 unequal: No Solution Exploring Operation: 57*19=1083, Resulting Numbers: [1083] 1083,89 unequal: No Solution Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,89 unequal: No Solution Exploring Operation: 57+19=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[53, 15], Operations: ['19+34=53', '53-38=15'] Exploring Operation: 53*15=795, Resulting Numbers: [795] 795,89 unequal: No Solution Exploring Operation: 53+15=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,89 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 72, 25, 56, 10 ]
93
[ "72-25=47", "56-10=46", "47+46=93" ]
Current State: 93:[72, 25, 56, 10], Operations: [] Exploring Operation: 72-25=47, Resulting Numbers: [56, 10, 47] Generated Node #2: [56, 10, 47] from Operation: 72-25=47 Current State: 93:[56, 10, 47], Operations: ['72-25=47'] Exploring Operation: 56-10=46, Resulting Numbers: [47, 46] Generated Node #3: [47, 46] from Operation: 56-10=46 Current State: 93:[47, 46], Operations: ['72-25=47', '56-10=46'] Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[72, 25, 56, 10], Operations: [] Exploring Operation: 25+56=81, Resulting Numbers: [72, 10, 81] Generated Node #0,0: 93:[72, 10, 81] Operation: 25+56=81 Exploring Operation: 72-56=16, Resulting Numbers: [25, 10, 16] Generated Node #0,1: 93:[25, 10, 16] Operation: 72-56=16 Exploring Operation: 72+25=97, Resulting Numbers: [56, 10, 97] Generated Node #0,2: 93:[56, 10, 97] Operation: 72+25=97 Exploring Operation: 56-25=31, Resulting Numbers: [72, 10, 31] Generated Node #0,3: 93:[72, 10, 31] Operation: 56-25=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[25, 10, 16], Operations: ['72-56=16'] Exploring Operation: 25-16=9, Resulting Numbers: [10, 9] Generated Node #0,1,0: 93:[10, 9] Operation: 25-16=9 Exploring Operation: 16-10=6, Resulting Numbers: [25, 6] Generated Node #0,1,1: 93:[25, 6] Operation: 16-10=6 Exploring Operation: 25+10=35, Resulting Numbers: [16, 35] Generated Node #0,1,2: 93:[16, 35] Operation: 25+10=35 Exploring Operation: 10+16=26, Resulting Numbers: [25, 26] Generated Node #0,1,3: 93:[25, 26] Operation: 10+16=26 Moving to Node #0,1,1 Current State: 93:[25, 6], Operations: ['72-56=16', '16-10=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,93 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,93 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[25, 26], Operations: ['72-56=16', '10+16=26'] Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 25*26=650, Resulting Numbers: [650] 650,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[10, 9], Operations: ['72-56=16', '25-16=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,93 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,93 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[16, 35], Operations: ['72-56=16', '25+10=35'] Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,93 unequal: No Solution Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,93 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,93 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 #0,3 Current State: 93:[72, 10, 31], Operations: ['56-25=31'] Exploring Operation: 72+10=82, Resulting Numbers: [31, 82] Generated Node #0,3,0: 93:[31, 82] Operation: 72+10=82 Exploring Operation: 72-31=41, Resulting Numbers: [10, 41] Generated Node #0,3,1: 93:[10, 41] Operation: 72-31=41 Exploring Operation: 72-10=62, Resulting Numbers: [31, 62] Generated Node #0,3,2: 93:[31, 62] Operation: 72-10=62 Exploring Operation: 72+31=103, Resulting Numbers: [10, 103] Generated Node #0,3,3: 93:[10, 103] Operation: 72+31=103 Moving to Node #0,3,0 Current State: 93:[31, 82], Operations: ['56-25=31', '72+10=82'] Exploring Operation: 31*82=2542, Resulting Numbers: [2542] 2542,93 unequal: No Solution Exploring Operation: 31+82=113, Resulting Numbers: [113] 113,93 unequal: No Solution Exploring Operation: 82-31=51, Resulting Numbers: [51] 51,93 unequal: No Solution Moving to Node #0,3,3 Current State: 93:[10, 103], Operations: ['56-25=31', '72+31=103'] Exploring Operation: 10*103=1030, Resulting Numbers: [1030] 1030,93 unequal: No Solution Exploring Operation: 10+103=113, Resulting Numbers: [113] 113,93 unequal: No Solution Exploring Operation: 103-10=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[72, 25, 56, 10], Operations: [] Exploring Operation: 56-25=31, Resulting Numbers: [72, 10, 31] Generated Node #0,3: 93:[72, 10, 31] Operation: 56-25=31 Moving to Node #0,3 Current State: 93:[72, 10, 31], Operations: ['56-25=31'] Exploring Operation: 72+31=103, Resulting Numbers: [10, 103] Generated Node #0,3,3: 93:[10, 103] Operation: 72+31=103 Moving to Node #0,3,3 Current State: 93:[10, 103], Operations: ['56-25=31', '72+31=103'] Exploring Operation: 103-10=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 16, 96, 19, 11 ]
98
[ "19-11=8", "16/8=2", "96+2=98" ]
Current State: 98:[16, 96, 19, 11], Operations: [] Exploring Operation: 19-11=8, Resulting Numbers: [16, 96, 8] Generated Node #2: [16, 96, 8] from Operation: 19-11=8 Current State: 98:[16, 96, 8], Operations: ['19-11=8'] Exploring Operation: 16/8=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 16/8=2 Current State: 98:[96, 2], Operations: ['19-11=8', '16/8=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[16, 96, 19, 11], Operations: [] Exploring Operation: 16-11=5, Resulting Numbers: [96, 19, 5] Generated Node #0,0: 98:[96, 19, 5] Operation: 16-11=5 Exploring Operation: 96+11=107, Resulting Numbers: [16, 19, 107] Generated Node #0,1: 98:[16, 19, 107] Operation: 96+11=107 Exploring Operation: 96/16=6, Resulting Numbers: [19, 11, 6] Generated Node #0,2: 98:[19, 11, 6] Operation: 96/16=6 Exploring Operation: 19-16=3, Resulting Numbers: [96, 11, 3] Generated Node #0,3: 98:[96, 11, 3] Operation: 19-16=3 Exploring Operation: 19-11=8, Resulting Numbers: [16, 96, 8] Generated Node #0,4: 98:[16, 96, 8] Operation: 19-11=8 Start Sub Search at level 1: Moving to Node #0,4 Current State: 98:[16, 96, 8], Operations: ['19-11=8'] Exploring Operation: 16-8=8, Resulting Numbers: [96, 8] Generated Node #0,4,0: 98:[96, 8] Operation: 16-8=8 Exploring Operation: 96/8=12, Resulting Numbers: [16, 12] Generated Node #0,4,1: 98:[16, 12] Operation: 96/8=12 Exploring Operation: 96+8=104, Resulting Numbers: [16, 104] Generated Node #0,4,2: 98:[16, 104] Operation: 96+8=104 Exploring Operation: 16/8=2, Resulting Numbers: [96, 2] Generated Node #0,4,3: 98:[96, 2] Operation: 16/8=2 Exploring Operation: 96/16=6, Resulting Numbers: [8, 6] Generated Node #0,4,4: 98:[8, 6] Operation: 96/16=6 Moving to Node #0,4,3 Current State: 98:[96, 2], Operations: ['19-11=8', '16/8=2'] Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,98 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[16, 96, 19, 11], Operations: [] Exploring Operation: 19-11=8, Resulting Numbers: [16, 96, 8] Generated Node #0,4: 98:[16, 96, 8] Operation: 19-11=8 Moving to Node #0,4 Current State: 98:[16, 96, 8], Operations: ['19-11=8'] Exploring Operation: 16/8=2, Resulting Numbers: [96, 2] Generated Node #0,4,3: 98:[96, 2] Operation: 16/8=2 Moving to Node #0,4,3 Current State: 98:[96, 2], Operations: ['19-11=8', '16/8=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 6, 39, 41, 72 ]
84
[ "41-39=2", "6*2=12", "72+12=84" ]
Current State: 84:[6, 39, 41, 72], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [6, 72, 2] Generated Node #2: [6, 72, 2] from Operation: 41-39=2 Current State: 84:[6, 72, 2], Operations: ['41-39=2'] Exploring Operation: 6*2=12, Resulting Numbers: [72, 12] Generated Node #3: [72, 12] from Operation: 6*2=12 Current State: 84:[72, 12], Operations: ['41-39=2', '6*2=12'] Exploring Operation: 72+12=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[6, 39, 41, 72], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [6, 41, 33] Generated Node #0,0: 84:[6, 41, 33] Operation: 72-39=33 Exploring Operation: 72/6=12, Resulting Numbers: [39, 41, 12] Generated Node #0,1: 84:[39, 41, 12] Operation: 72/6=12 Exploring Operation: 6+72=78, Resulting Numbers: [39, 41, 78] Generated Node #0,2: 84:[39, 41, 78] Operation: 6+72=78 Exploring Operation: 72-41=31, Resulting Numbers: [6, 39, 31] Generated Node #0,3: 84:[6, 39, 31] Operation: 72-41=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[39, 41, 12], Operations: ['72/6=12'] Exploring Operation: 39-12=27, Resulting Numbers: [41, 27] Generated Node #0,1,0: 84:[41, 27] Operation: 39-12=27 Exploring Operation: 41-12=29, Resulting Numbers: [39, 29] Generated Node #0,1,1: 84:[39, 29] Operation: 41-12=29 Exploring Operation: 41-39=2, Resulting Numbers: [12, 2] Generated Node #0,1,2: 84:[12, 2] Operation: 41-39=2 Exploring Operation: 39+41=80, Resulting Numbers: [12, 80] Generated Node #0,1,3: 84:[12, 80] Operation: 39+41=80 Moving to Node #0,1,2 Current State: 84:[12, 2], Operations: ['72/6=12', '41-39=2'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[41, 27], Operations: ['72/6=12', '39-12=27'] Exploring Operation: 41+27=68, Resulting Numbers: [68] 68,84 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 41*27=1107, Resulting Numbers: [1107] 1107,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[12, 80], Operations: ['72/6=12', '39+41=80'] Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,84 unequal: No Solution Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[39, 29], Operations: ['72/6=12', '41-12=29'] Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,84 unequal: No Solution Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,84 unequal: No Solution Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,84 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 Current State: 84:[6, 41, 33], Operations: ['72-39=33'] Exploring Operation: 6+33=39, Resulting Numbers: [41, 39] Generated Node #0,0,0: 84:[41, 39] Operation: 6+33=39 Exploring Operation: 41-33=8, Resulting Numbers: [6, 8] Generated Node #0,0,1: 84:[6, 8] Operation: 41-33=8 Exploring Operation: 6+41=47, Resulting Numbers: [33, 47] Generated Node #0,0,2: 84:[33, 47] Operation: 6+41=47 Exploring Operation: 33-6=27, Resulting Numbers: [41, 27] Generated Node #0,0,3: 84:[41, 27] Operation: 33-6=27 Moving to Node #0,0,1 Current State: 84:[6, 8], Operations: ['72-39=33', '41-33=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[41, 27], Operations: ['72-39=33', '33-6=27'] Exploring Operation: 41+27=68, Resulting Numbers: [68] 68,84 unequal: No Solution Exploring Operation: 41*27=1107, Resulting Numbers: [1107] 1107,84 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[41, 39], Operations: ['72-39=33', '6+33=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[33, 47], Operations: ['72-39=33', '6+41=47'] Exploring Operation: 33*47=1551, Resulting Numbers: [1551] 1551,84 unequal: No Solution Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 33+47=80, Resulting Numbers: [80] 80,84 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 Current State: 84:[6, 39, 31], Operations: ['72-41=31'] Exploring Operation: 6+39=45, Resulting Numbers: [31, 45] Generated Node #0,3,0: 84:[31, 45] Operation: 6+39=45 Exploring Operation: 39-6=33, Resulting Numbers: [31, 33] Generated Node #0,3,1: 84:[31, 33] Operation: 39-6=33 Exploring Operation: 39-31=8, Resulting Numbers: [6, 8] Generated Node #0,3,2: 84:[6, 8] Operation: 39-31=8 Exploring Operation: 31-6=25, Resulting Numbers: [39, 25] Generated Node #0,3,3: 84:[39, 25] Operation: 31-6=25 Moving to Node #0,3,2 Current State: 84:[6, 8], Operations: ['72-41=31', '39-31=8'] Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[39, 25], Operations: ['72-41=31', '31-6=25'] Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,84 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[31, 45], Operations: ['72-41=31', '6+39=45'] Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 31*45=1395, Resulting Numbers: [1395] 1395,84 unequal: No Solution Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[31, 33], Operations: ['72-41=31', '39-6=33'] Exploring Operation: 31*33=1023, Resulting Numbers: [1023] 1023,84 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 31+33=64, Resulting Numbers: [64] 64,84 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 Current State: 84:[39, 41, 78], Operations: ['6+72=78'] Exploring Operation: 78-41=37, Resulting Numbers: [39, 37] Generated Node #0,2,0: 84:[39, 37] Operation: 78-41=37 Exploring Operation: 41-39=2, Resulting Numbers: [78, 2] Generated Node #0,2,1: 84:[78, 2] Operation: 41-39=2 Exploring Operation: 78-39=39, Resulting Numbers: [41, 39] Generated Node #0,2,2: 84:[41, 39] Operation: 78-39=39 Exploring Operation: 78/39=2, Resulting Numbers: [41, 2] Generated Node #0,2,3: 84:[41, 2] Operation: 78/39=2 Moving to Node #0,2,3 Current State: 84:[41, 2], Operations: ['6+72=78', '78/39=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,84 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[41, 39], Operations: ['6+72=78', '78-39=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,84 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[78, 2], Operations: ['6+72=78', '41-39=2'] Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,84 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[39, 37], Operations: ['6+72=78', '78-41=37'] Exploring Operation: 39+37=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 39*37=1443, Resulting Numbers: [1443] 1443,84 unequal: No Solution Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,84 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
[ 38, 56, 5, 48 ]
28
[ "48-38=10", "56*5=280", "280/10=28" ]
Current State: 28:[38, 56, 5, 48], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [56, 5, 10] Generated Node #2: [56, 5, 10] from Operation: 48-38=10 Current State: 28:[56, 5, 10], Operations: ['48-38=10'] Exploring Operation: 56*5=280, Resulting Numbers: [10, 280] Generated Node #3: [10, 280] from Operation: 56*5=280 Current State: 28:[10, 280], Operations: ['48-38=10', '56*5=280'] Exploring Operation: 280/10=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[38, 56, 5, 48], Operations: [] Exploring Operation: 56-38=18, Resulting Numbers: [5, 48, 18] Generated Node #0,0: 28:[5, 48, 18] Operation: 56-38=18 Exploring Operation: 48-38=10, Resulting Numbers: [56, 5, 10] Generated Node #0,1: 28:[56, 5, 10] Operation: 48-38=10 Exploring Operation: 56-48=8, Resulting Numbers: [38, 5, 8] Generated Node #0,2: 28:[38, 5, 8] Operation: 56-48=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[38, 5, 8], Operations: ['56-48=8'] Exploring Operation: 5+8=13, Resulting Numbers: [38, 13] Generated Node #0,2,0: 28:[38, 13] Operation: 5+8=13 Exploring Operation: 38-5=33, Resulting Numbers: [8, 33] Generated Node #0,2,1: 28:[8, 33] Operation: 38-5=33 Exploring Operation: 38-8=30, Resulting Numbers: [5, 30] Generated Node #0,2,2: 28:[5, 30] Operation: 38-8=30 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[5, 30], Operations: ['56-48=8', '38-8=30'] Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,28 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,28 unequal: No Solution No 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: 28:[8, 33], Operations: ['56-48=8', '38-5=33'] Exploring Operation: 8*33=264, Resulting Numbers: [264] 264,28 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,28 unequal: No Solution Exploring Operation: 8+33=41, Resulting Numbers: [41] 41,28 unequal: No Solution No 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: 28:[38, 13], Operations: ['56-48=8', '5+8=13'] Exploring Operation: 38*13=494, Resulting Numbers: [494] 494,28 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,28 unequal: No Solution Exploring Operation: 38+13=51, Resulting Numbers: [51] 51,28 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: 28:[5, 48, 18], Operations: ['56-38=18'] Exploring Operation: 48-18=30, Resulting Numbers: [5, 30] Generated Node #0,0,0: 28:[5, 30] Operation: 48-18=30 Exploring Operation: 18-5=13, Resulting Numbers: [48, 13] Generated Node #0,0,1: 28:[48, 13] Operation: 18-5=13 Exploring Operation: 48-5=43, Resulting Numbers: [18, 43] Generated Node #0,0,2: 28:[18, 43] Operation: 48-5=43 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[5, 30], Operations: ['56-38=18', '48-18=30'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,28 unequal: No Solution No 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: 28:[18, 43], Operations: ['56-38=18', '48-5=43'] Exploring Operation: 18+43=61, Resulting Numbers: [61] 61,28 unequal: No Solution Exploring Operation: 18*43=774, Resulting Numbers: [774] 774,28 unequal: No Solution Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,28 unequal: No Solution No 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: 28:[48, 13], Operations: ['56-38=18', '18-5=13'] Exploring Operation: 48+13=61, Resulting Numbers: [61] 61,28 unequal: No Solution Exploring Operation: 48*13=624, Resulting Numbers: [624] 624,28 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,28 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: 28:[56, 5, 10], Operations: ['48-38=10'] Exploring Operation: 56-10=46, Resulting Numbers: [5, 46] Generated Node #0,1,0: 28:[5, 46] Operation: 56-10=46 Exploring Operation: 56-5=51, Resulting Numbers: [10, 51] Generated Node #0,1,1: 28:[10, 51] Operation: 56-5=51 Exploring Operation: 10/5=2, Resulting Numbers: [56, 2] Generated Node #0,1,2: 28:[56, 2] Operation: 10/5=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[5, 46], Operations: ['48-38=10', '56-10=46'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,28 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,28 unequal: No Solution No 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: 28:[10, 51], Operations: ['48-38=10', '56-5=51'] Exploring Operation: 10*51=510, Resulting Numbers: [510] 510,28 unequal: No Solution Exploring Operation: 10+51=61, Resulting Numbers: [61] 61,28 unequal: No Solution Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,28 unequal: No Solution No 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: 28:[56, 2], Operations: ['48-38=10', '10/5=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[38, 56, 5, 48], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [56, 5, 10] Generated Node #0,1: 28:[56, 5, 10] Operation: 48-38=10 Moving to Node #0,1 Current State: 28:[56, 5, 10], Operations: ['48-38=10'] Exploring Operation: 10/5=2, Resulting Numbers: [56, 2] Generated Node #0,1,2: 28:[56, 2] Operation: 10/5=2 Moving to Node #0,1,2 Current State: 28:[56, 2], Operations: ['48-38=10', '10/5=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_3
mult_heuristic
[ 49, 32, 64, 15 ]
33
[ "64-49=15", "15/15=1", "32+1=33" ]
Current State: 33:[49, 32, 64, 15], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [32, 15, 15] Generated Node #2: [32, 15, 15] from Operation: 64-49=15 Current State: 33:[32, 15, 15], Operations: ['64-49=15'] Exploring Operation: 15/15=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 15/15=1 Current State: 33:[32, 1], Operations: ['64-49=15', '15/15=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[49, 32, 64, 15], Operations: [] Exploring Operation: 64-32=32, Resulting Numbers: [49, 15, 32] Generated Node #0,0: 33:[49, 15, 32] Operation: 64-32=32 Exploring Operation: 64-49=15, Resulting Numbers: [32, 15, 15] Generated Node #0,1: 33:[32, 15, 15] Operation: 64-49=15 Exploring Operation: 49-15=34, Resulting Numbers: [32, 64, 34] Generated Node #0,2: 33:[32, 64, 34] Operation: 49-15=34 Exploring Operation: 64/32=2, Resulting Numbers: [49, 15, 2] Generated Node #0,3: 33:[49, 15, 2] Operation: 64/32=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[32, 15, 15], Operations: ['64-49=15'] Exploring Operation: 15/15=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 33:[32, 1] Operation: 15/15=1 Exploring Operation: 32-15=17, Resulting Numbers: [15, 17] Generated Node #0,1,1: 33:[15, 17] Operation: 32-15=17 Exploring Operation: 15+15=30, Resulting Numbers: [32, 30] Generated Node #0,1,2: 33:[32, 30] Operation: 15+15=30 Exploring Operation: 15-15=0, Resulting Numbers: [32, 0] Generated Node #0,1,3: 33:[32, 0] Operation: 15-15=0 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[32, 1], Operations: ['64-49=15', '15/15=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[49, 32, 64, 15], Operations: [] Exploring Operation: 64-49=15, Resulting Numbers: [32, 15, 15] Generated Node #0,1: 33:[32, 15, 15] Operation: 64-49=15 Moving to Node #0,1 Current State: 33:[32, 15, 15], Operations: ['64-49=15'] Exploring Operation: 15/15=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 33:[32, 1] Operation: 15/15=1 Moving to Node #0,1,0 Current State: 33:[32, 1], Operations: ['64-49=15', '15/15=1'] Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 12, 21, 42, 57 ]
14
[ "12*42=504", "57-21=36", "504/36=14" ]
Current State: 14:[12, 21, 42, 57], Operations: [] Exploring Operation: 12*42=504, Resulting Numbers: [21, 57, 504] Generated Node #2: [21, 57, 504] from Operation: 12*42=504 Current State: 14:[21, 57, 504], Operations: ['12*42=504'] Exploring Operation: 57-21=36, Resulting Numbers: [504, 36] Generated Node #3: [504, 36] from Operation: 57-21=36 Current State: 14:[504, 36], Operations: ['12*42=504', '57-21=36'] Exploring Operation: 504/36=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[12, 21, 42, 57], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [12, 57, 2] Generated Node #0,0: 14:[12, 57, 2] Operation: 42/21=2 Exploring Operation: 57-42=15, Resulting Numbers: [12, 21, 15] Generated Node #0,1: 14:[12, 21, 15] Operation: 57-42=15 Exploring Operation: 42-21=21, Resulting Numbers: [12, 57, 21] Generated Node #0,2: 14:[12, 57, 21] Operation: 42-21=21 Moving to Node #0,1 Current State: 14:[12, 21, 15], Operations: ['57-42=15'] Exploring Operation: 21-12=9, Resulting Numbers: [15, 9] Generated Node #0,1,0: 14:[15, 9] Operation: 21-12=9 Exploring Operation: 21-15=6, Resulting Numbers: [12, 6] Generated Node #0,1,1: 14:[12, 6] Operation: 21-15=6 Exploring Operation: 15-12=3, Resulting Numbers: [21, 3] Generated Node #0,1,2: 14:[21, 3] Operation: 15-12=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[15, 9], Operations: ['57-42=15', '21-12=9'] Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 15*9=135, Resulting Numbers: [135] 135,14 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,14 unequal: No Solution No 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: 14:[12, 6], Operations: ['57-42=15', '21-15=6'] Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,14 unequal: No Solution No 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: 14:[21, 3], Operations: ['57-42=15', '15-12=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,14 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: 14:[12, 57, 2], Operations: ['42/21=2'] Exploring Operation: 57-2=55, Resulting Numbers: [12, 55] Generated Node #0,0,0: 14:[12, 55] Operation: 57-2=55 Exploring Operation: 57-12=45, Resulting Numbers: [2, 45] Generated Node #0,0,1: 14:[2, 45] Operation: 57-12=45 Exploring Operation: 12+2=14, Resulting Numbers: [57, 14] Generated Node #0,0,2: 14:[57, 14] Operation: 12+2=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[2, 45], Operations: ['42/21=2', '57-12=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,14 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,14 unequal: No Solution No 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: 14:[12, 55], Operations: ['42/21=2', '57-2=55'] Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,14 unequal: No Solution Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,14 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,14 unequal: No Solution No 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: 14:[57, 14], Operations: ['42/21=2', '12+2=14'] Exploring Operation: 57*14=798, Resulting Numbers: [798] 798,14 unequal: No Solution Exploring Operation: 57+14=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,14 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: 14:[12, 57, 21], Operations: ['42-21=21'] Exploring Operation: 21-12=9, Resulting Numbers: [57, 9] Generated Node #0,2,0: 14:[57, 9] Operation: 21-12=9 Exploring Operation: 57-12=45, Resulting Numbers: [21, 45] Generated Node #0,2,1: 14:[21, 45] Operation: 57-12=45 Exploring Operation: 57-21=36, Resulting Numbers: [12, 36] Generated Node #0,2,2: 14:[12, 36] Operation: 57-21=36 Moving to Node #0,2,2 Current State: 14:[12, 36], Operations: ['42-21=21', '57-21=36'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,14 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[21, 45], Operations: ['42-21=21', '57-12=45'] Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,14 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[57, 9], Operations: ['42-21=21', '21-12=9'] Exploring Operation: 57*9=513, Resulting Numbers: [513] 513,14 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,14 unequal: No Solution Exploring Operation: 57+9=66, Resulting Numbers: [66] 66,14 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 6, 58, 14, 12 ]
86
[ "12/6=2", "14*2=28", "58+28=86" ]
Current State: 86:[6, 58, 14, 12], Operations: [] Exploring Operation: 12/6=2, Resulting Numbers: [58, 14, 2] Generated Node #2: [58, 14, 2] from Operation: 12/6=2 Current State: 86:[58, 14, 2], Operations: ['12/6=2'] Exploring Operation: 14*2=28, Resulting Numbers: [58, 28] Generated Node #3: [58, 28] from Operation: 14*2=28 Current State: 86:[58, 28], Operations: ['12/6=2', '14*2=28'] Exploring Operation: 58+28=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[6, 58, 14, 12], Operations: [] Exploring Operation: 58-14=44, Resulting Numbers: [6, 12, 44] Generated Node #0,0: 86:[6, 12, 44] Operation: 58-14=44 Exploring Operation: 14-12=2, Resulting Numbers: [6, 58, 2] Generated Node #0,1: 86:[6, 58, 2] Operation: 14-12=2 Exploring Operation: 58-12=46, Resulting Numbers: [6, 14, 46] Generated Node #0,2: 86:[6, 14, 46] Operation: 58-12=46 Moving to Node #0,0 Current State: 86:[6, 12, 44], Operations: ['58-14=44'] Exploring Operation: 6*12=72, Resulting Numbers: [44, 72] Generated Node #0,0,0: 86:[44, 72] Operation: 6*12=72 Exploring Operation: 12-6=6, Resulting Numbers: [44, 6] Generated Node #0,0,1: 86:[44, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [44, 2] Generated Node #0,0,2: 86:[44, 2] Operation: 12/6=2 Moving to Node #0,1 Current State: 86:[6, 58, 2], Operations: ['14-12=2'] Exploring Operation: 6/2=3, Resulting Numbers: [58, 3] Generated Node #0,1,0: 86:[58, 3] Operation: 6/2=3 Exploring Operation: 58-6=52, Resulting Numbers: [2, 52] Generated Node #0,1,1: 86:[2, 52] Operation: 58-6=52 Exploring Operation: 6-2=4, Resulting Numbers: [58, 4] Generated Node #0,1,2: 86:[58, 4] Operation: 6-2=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[2, 52], Operations: ['14-12=2', '58-6=52'] Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,86 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[58, 3], Operations: ['14-12=2', '6/2=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,86 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,86 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[58, 4], Operations: ['14-12=2', '6-2=4'] Exploring Operation: 58*4=232, Resulting Numbers: [232] 232,86 unequal: No Solution Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[6, 14, 46], Operations: ['58-12=46'] Exploring Operation: 6*14=84, Resulting Numbers: [46, 84] Generated Node #0,2,0: 86:[46, 84] Operation: 6*14=84 Exploring Operation: 46-6=40, Resulting Numbers: [14, 40] Generated Node #0,2,1: 86:[14, 40] Operation: 46-6=40 Exploring Operation: 14-6=8, Resulting Numbers: [46, 8] Generated Node #0,2,2: 86:[46, 8] Operation: 14-6=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[46, 84], Operations: ['58-12=46', '6*14=84'] Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 46+84=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 46*84=3864, Resulting Numbers: [3864] 3864,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[46, 8], Operations: ['58-12=46', '14-6=8'] Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,86 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[14, 40], Operations: ['58-12=46', '46-6=40'] Exploring Operation: 40-14=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 14+40=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 14*40=560, Resulting Numbers: [560] 560,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 86:[44, 2], Operations: ['58-14=44', '12/6=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[44, 6], Operations: ['58-14=44', '12-6=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,86 unequal: No Solution Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[44, 72], Operations: ['58-14=44', '6*12=72'] Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,86 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,86 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 20, 80, 34, 63 ]
31
[ "80-20=60", "63-34=29", "60-29=31" ]
Current State: 31:[20, 80, 34, 63], Operations: [] Exploring Operation: 80-20=60, Resulting Numbers: [34, 63, 60] Generated Node #2: [34, 63, 60] from Operation: 80-20=60 Current State: 31:[34, 63, 60], Operations: ['80-20=60'] Exploring Operation: 63-34=29, Resulting Numbers: [60, 29] Generated Node #3: [60, 29] from Operation: 63-34=29 Current State: 31:[60, 29], Operations: ['80-20=60', '63-34=29'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[20, 80, 34, 63], Operations: [] Exploring Operation: 80-20=60, Resulting Numbers: [34, 63, 60] Generated Node #0,0: 31:[34, 63, 60] Operation: 80-20=60 Exploring Operation: 80/20=4, Resulting Numbers: [34, 63, 4] Generated Node #0,1: 31:[34, 63, 4] Operation: 80/20=4 Exploring Operation: 63-34=29, Resulting Numbers: [20, 80, 29] Generated Node #0,2: 31:[20, 80, 29] Operation: 63-34=29 Exploring Operation: 80-63=17, Resulting Numbers: [20, 34, 17] Generated Node #0,3: 31:[20, 34, 17] Operation: 80-63=17 Exploring Operation: 80-34=46, Resulting Numbers: [20, 63, 46] Generated Node #0,4: 31:[20, 63, 46] Operation: 80-34=46 Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[20, 34, 17], Operations: ['80-63=17'] Exploring Operation: 34+17=51, Resulting Numbers: [20, 51] Generated Node #0,3,0: 31:[20, 51] Operation: 34+17=51 Exploring Operation: 34-20=14, Resulting Numbers: [17, 14] Generated Node #0,3,1: 31:[17, 14] Operation: 34-20=14 Exploring Operation: 34-17=17, Resulting Numbers: [20, 17] Generated Node #0,3,2: 31:[20, 17] Operation: 34-17=17 Exploring Operation: 20-17=3, Resulting Numbers: [34, 3] Generated Node #0,3,3: 31:[34, 3] Operation: 20-17=3 Exploring Operation: 20+17=37, Resulting Numbers: [34, 37] Generated Node #0,3,4: 31:[34, 37] Operation: 20+17=37 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 31:[34, 37], Operations: ['80-63=17', '20+17=37'] Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 34*37=1258, Resulting Numbers: [1258] 1258,31 unequal: No Solution Exploring Operation: 34+37=71, Resulting Numbers: [71] 71,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 31:[20, 17], Operations: ['80-63=17', '34-17=17'] Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,31 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,31 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[20, 51], Operations: ['80-63=17', '34+17=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[20, 80, 34, 63], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [20, 34, 17] Generated Node #0,3: 31:[20, 34, 17] Operation: 80-63=17 Moving to Node #0,3 Current State: 31:[20, 34, 17], Operations: ['80-63=17'] Exploring Operation: 34+17=51, Resulting Numbers: [20, 51] Generated Node #0,3,0: 31:[20, 51] Operation: 34+17=51 Moving to Node #0,3,0 Current State: 31:[20, 51], Operations: ['80-63=17', '34+17=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 93, 3, 45, 57 ]
43
[ "93/3=31", "57-45=12", "31+12=43" ]
Current State: 43:[93, 3, 45, 57], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [45, 57, 31] Generated Node #2: [45, 57, 31] from Operation: 93/3=31 Current State: 43:[45, 57, 31], Operations: ['93/3=31'] Exploring Operation: 57-45=12, Resulting Numbers: [31, 12] Generated Node #3: [31, 12] from Operation: 57-45=12 Current State: 43:[31, 12], Operations: ['93/3=31', '57-45=12'] Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[93, 3, 45, 57], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [45, 57, 31] Generated Node #0,0: 43:[45, 57, 31] Operation: 93/3=31 Moving to Node #0,0 Current State: 43:[45, 57, 31], Operations: ['93/3=31'] Exploring Operation: 57-31=26, Resulting Numbers: [45, 26] Generated Node #0,0,0: 43:[45, 26] Operation: 57-31=26 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[45, 26], Operations: ['93/3=31', '57-31=26'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 11, 30, 25, 60 ]
61
[ "30*60=1800", "1800/25=72", "72-11=61" ]
Current State: 61:[11, 30, 25, 60], Operations: [] Exploring Operation: 30*60=1800, Resulting Numbers: [11, 25, 1800] Generated Node #2: [11, 25, 1800] from Operation: 30*60=1800 Current State: 61:[11, 25, 1800], Operations: ['30*60=1800'] Exploring Operation: 1800/25=72, Resulting Numbers: [11, 72] Generated Node #3: [11, 72] from Operation: 1800/25=72 Current State: 61:[11, 72], Operations: ['30*60=1800', '1800/25=72'] Exploring Operation: 72-11=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[11, 30, 25, 60], Operations: [] Exploring Operation: 11+30=41, Resulting Numbers: [25, 60, 41] Generated Node #0,0: 61:[25, 60, 41] Operation: 11+30=41 Moving to Node #0,0 Current State: 61:[25, 60, 41], Operations: ['11+30=41'] Exploring Operation: 25+41=66, Resulting Numbers: [60, 66] Generated Node #0,0,0: 61:[60, 66] Operation: 25+41=66 Moving to Node #0,0,0 Current State: 61:[60, 66], Operations: ['11+30=41', '25+41=66'] Exploring Operation: 66-60=6, Resulting Numbers: [6] 6,61 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 44, 14, 45, 16 ]
30
[ "45-44=1", "14+16=30", "1*30=30" ]
Current State: 30:[44, 14, 45, 16], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [14, 16, 1] Generated Node #2: [14, 16, 1] from Operation: 45-44=1 Current State: 30:[14, 16, 1], Operations: ['45-44=1'] Exploring Operation: 14+16=30, Resulting Numbers: [1, 30] Generated Node #3: [1, 30] from Operation: 14+16=30 Current State: 30:[1, 30], Operations: ['45-44=1', '14+16=30'] Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[44, 14, 45, 16], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [14, 16, 1] Generated Node #0,0: 30:[14, 16, 1] Operation: 45-44=1 Exploring Operation: 44-14=30, Resulting Numbers: [45, 16, 30] Generated Node #0,1: 30:[45, 16, 30] Operation: 44-14=30 Exploring Operation: 45-14=31, Resulting Numbers: [44, 16, 31] Generated Node #0,2: 30:[44, 16, 31] Operation: 45-14=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[14, 16, 1], Operations: ['45-44=1'] Exploring Operation: 14+16=30, Resulting Numbers: [1, 30] Generated Node #0,0,0: 30:[1, 30] Operation: 14+16=30 Exploring Operation: 16-14=2, Resulting Numbers: [1, 2] Generated Node #0,0,1: 30:[1, 2] Operation: 16-14=2 Exploring Operation: 14+1=15, Resulting Numbers: [16, 15] Generated Node #0,0,2: 30:[16, 15] Operation: 14+1=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[1, 30], Operations: ['45-44=1', '14+16=30'] Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[44, 14, 45, 16], Operations: [] Exploring Operation: 45-44=1, Resulting Numbers: [14, 16, 1] Generated Node #0,0: 30:[14, 16, 1] Operation: 45-44=1 Moving to Node #0,0 Current State: 30:[14, 16, 1], Operations: ['45-44=1'] Exploring Operation: 14+16=30, Resulting Numbers: [1, 30] Generated Node #0,0,0: 30:[1, 30] Operation: 14+16=30 Moving to Node #0,0,0 Current State: 30:[1, 30], Operations: ['45-44=1', '14+16=30'] Exploring Operation: 30/1=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 37, 79, 47, 60 ]
73
[ "47-37=10", "60/10=6", "79-6=73" ]
Current State: 73:[37, 79, 47, 60], Operations: [] Exploring Operation: 47-37=10, Resulting Numbers: [79, 60, 10] Generated Node #2: [79, 60, 10] from Operation: 47-37=10 Current State: 73:[79, 60, 10], Operations: ['47-37=10'] Exploring Operation: 60/10=6, Resulting Numbers: [79, 6] Generated Node #3: [79, 6] from Operation: 60/10=6 Current State: 73:[79, 6], Operations: ['47-37=10', '60/10=6'] Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[37, 79, 47, 60], Operations: [] Exploring Operation: 79-37=42, Resulting Numbers: [47, 60, 42] Generated Node #0,0: 73:[47, 60, 42] Operation: 79-37=42 Exploring Operation: 37+47=84, Resulting Numbers: [79, 60, 84] Generated Node #0,1: 73:[79, 60, 84] Operation: 37+47=84 Exploring Operation: 37+60=97, Resulting Numbers: [79, 47, 97] Generated Node #0,2: 73:[79, 47, 97] Operation: 37+60=97 Moving to Node #0,1 Current State: 73:[79, 60, 84], Operations: ['37+47=84'] Exploring Operation: 84-60=24, Resulting Numbers: [79, 24] Generated Node #0,1,0: 73:[79, 24] Operation: 84-60=24 Exploring Operation: 79+60=139, Resulting Numbers: [84, 139] Generated Node #0,1,1: 73:[84, 139] Operation: 79+60=139 Exploring Operation: 79-60=19, Resulting Numbers: [84, 19] Generated Node #0,1,2: 73:[84, 19] Operation: 79-60=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[79, 24], Operations: ['37+47=84', '84-60=24'] Exploring Operation: 79+24=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 79-24=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 79*24=1896, Resulting Numbers: [1896] 1896,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[84, 19], Operations: ['37+47=84', '79-60=19'] Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,73 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[84, 139], Operations: ['37+47=84', '79+60=139'] Exploring Operation: 84*139=11676, Resulting Numbers: [11676] 11676,73 unequal: No Solution Exploring Operation: 139-84=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 84+139=223, Resulting Numbers: [223] 223,73 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: 73:[79, 47, 97], Operations: ['37+60=97'] Exploring Operation: 97-47=50, Resulting Numbers: [79, 50] Generated Node #0,2,0: 73:[79, 50] Operation: 97-47=50 Exploring Operation: 79-47=32, Resulting Numbers: [97, 32] Generated Node #0,2,1: 73:[97, 32] Operation: 79-47=32 Exploring Operation: 79+47=126, Resulting Numbers: [97, 126] Generated Node #0,2,2: 73:[97, 126] Operation: 79+47=126 Moving to Node #0,0 Current State: 73:[47, 60, 42], Operations: ['79-37=42'] Exploring Operation: 60+42=102, Resulting Numbers: [47, 102] Generated Node #0,0,0: 73:[47, 102] Operation: 60+42=102 Exploring Operation: 47+60=107, Resulting Numbers: [42, 107] Generated Node #0,0,1: 73:[42, 107] Operation: 47+60=107 Exploring Operation: 47+42=89, Resulting Numbers: [60, 89] Generated Node #0,0,2: 73:[60, 89] Operation: 47+42=89 Moving to Node #0,2,0 Current State: 73:[79, 50], Operations: ['37+60=97', '97-47=50'] Exploring Operation: 79*50=3950, Resulting Numbers: [3950] 3950,73 unequal: No Solution Exploring Operation: 79-50=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 79+50=129, Resulting Numbers: [129] 129,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[60, 89], Operations: ['79-37=42', '47+42=89'] Exploring Operation: 60*89=5340, Resulting Numbers: [5340] 5340,73 unequal: No Solution Exploring Operation: 60+89=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 89-60=29, Resulting Numbers: [29] 29,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[47, 102], Operations: ['79-37=42', '60+42=102'] Exploring Operation: 47+102=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 102-47=55, Resulting Numbers: [55] 55,73 unequal: No Solution Exploring Operation: 47*102=4794, Resulting Numbers: [4794] 4794,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[42, 107], Operations: ['79-37=42', '47+60=107'] Exploring Operation: 42+107=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 107-42=65, Resulting Numbers: [65] 65,73 unequal: No Solution Exploring Operation: 42*107=4494, Resulting Numbers: [4494] 4494,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[97, 32], Operations: ['37+60=97', '79-47=32'] Exploring Operation: 97*32=3104, Resulting Numbers: [3104] 3104,73 unequal: No Solution Exploring Operation: 97+32=129, Resulting Numbers: [129] 129,73 unequal: No Solution Exploring Operation: 97-32=65, Resulting Numbers: [65] 65,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[97, 126], Operations: ['37+60=97', '79+47=126'] Exploring Operation: 97+126=223, Resulting Numbers: [223] 223,73 unequal: No Solution Exploring Operation: 126-97=29, Resulting Numbers: [29] 29,73 unequal: No Solution Exploring Operation: 97*126=12222, Resulting Numbers: [12222] 12222,73 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 34, 45, 49, 39 ]
58
[ "39-34=5", "45/5=9", "49+9=58" ]
Current State: 58:[34, 45, 49, 39], Operations: [] Exploring Operation: 39-34=5, Resulting Numbers: [45, 49, 5] Generated Node #2: [45, 49, 5] from Operation: 39-34=5 Current State: 58:[45, 49, 5], Operations: ['39-34=5'] Exploring Operation: 45/5=9, Resulting Numbers: [49, 9] Generated Node #3: [49, 9] from Operation: 45/5=9 Current State: 58:[49, 9], Operations: ['39-34=5', '45/5=9'] Exploring Operation: 49+9=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[34, 45, 49, 39], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [34, 49, 6] Generated Node #0,0: 58:[34, 49, 6] Operation: 45-39=6 Exploring Operation: 49-45=4, Resulting Numbers: [34, 39, 4] Generated Node #0,1: 58:[34, 39, 4] Operation: 49-45=4 Moving to Node #0,1 Current State: 58:[34, 39, 4], Operations: ['49-45=4'] Exploring Operation: 39-34=5, Resulting Numbers: [4, 5] Generated Node #0,1,0: 58:[4, 5] Operation: 39-34=5 Exploring Operation: 34-4=30, Resulting Numbers: [39, 30] Generated Node #0,1,1: 58:[39, 30] Operation: 34-4=30 Moving to Node #0,0 Current State: 58:[34, 49, 6], Operations: ['45-39=6'] Exploring Operation: 49+6=55, Resulting Numbers: [34, 55] Generated Node #0,0,0: 58:[34, 55] Operation: 49+6=55 Exploring Operation: 34-6=28, Resulting Numbers: [49, 28] Generated Node #0,0,1: 58:[49, 28] Operation: 34-6=28 Moving to Node #0,1,0 Current State: 58:[4, 5], Operations: ['49-45=4', '39-34=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[34, 55], Operations: ['45-39=6', '49+6=55'] Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,58 unequal: No Solution Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[49, 28], Operations: ['45-39=6', '34-6=28'] Exploring Operation: 49+28=77, Resulting Numbers: [77] 77,58 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[39, 30], Operations: ['49-45=4', '34-4=30'] Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,58 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 4, 87, 42, 92 ]
42
[ "4+87=91", "92-91=1", "42*1=42" ]
Current State: 42:[4, 87, 42, 92], Operations: [] Exploring Operation: 4+87=91, Resulting Numbers: [42, 92, 91] Generated Node #2: [42, 92, 91] from Operation: 4+87=91 Current State: 42:[42, 92, 91], Operations: ['4+87=91'] Exploring Operation: 92-91=1, Resulting Numbers: [42, 1] Generated Node #3: [42, 1] from Operation: 92-91=1 Current State: 42:[42, 1], Operations: ['4+87=91', '92-91=1'] Exploring Operation: 42*1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[4, 87, 42, 92], Operations: [] Exploring Operation: 92-87=5, Resulting Numbers: [4, 42, 5] Generated Node #0,0: 42:[4, 42, 5] Operation: 92-87=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[4, 42, 5], Operations: ['92-87=5'] Exploring Operation: 4*5=20, Resulting Numbers: [42, 20] Generated Node #0,0,0: 42:[42, 20] Operation: 4*5=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[42, 20], Operations: ['92-87=5', '4*5=20'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 45, 80, 98 ]
100
[ "10+80=90", "90/45=2", "98+2=100" ]
Current State: 100:[10, 45, 80, 98], Operations: [] Exploring Operation: 10+80=90, Resulting Numbers: [45, 98, 90] Generated Node #2: [45, 98, 90] from Operation: 10+80=90 Current State: 100:[45, 98, 90], Operations: ['10+80=90'] Exploring Operation: 90/45=2, Resulting Numbers: [98, 2] Generated Node #3: [98, 2] from Operation: 90/45=2 Current State: 100:[98, 2], Operations: ['10+80=90', '90/45=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[10, 45, 80, 98], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [10, 45, 18] Generated Node #0,0: 100:[10, 45, 18] Operation: 98-80=18 Moving to Node #0,0 Current State: 100:[10, 45, 18], Operations: ['98-80=18'] Exploring Operation: 45-18=27, Resulting Numbers: [10, 27] Generated Node #0,0,0: 100:[10, 27] Operation: 45-18=27 Moving to Node #0,0,0 Current State: 100:[10, 27], Operations: ['98-80=18', '45-18=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,100 unequal: No Solution No solution found.
0
hs_1
sum_heuristic