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
[ 57, 10, 83, 46 ]
27
[ "57-46=11", "10*11=110", "110-83=27" ]
Current State: 27:[57, 10, 83, 46], Operations: [] Exploring Operation: 57-46=11, Resulting Numbers: [10, 83, 11] Generated Node #2: [10, 83, 11] from Operation: 57-46=11 Current State: 27:[10, 83, 11], Operations: ['57-46=11'] Exploring Operation: 10*11=110, Resulting Numbers: [83, 110] Generated Node #3: [83, 110] from Operation: 10*11=110 Current State: 27:[83, 110], Operations: ['57-46=11', '10*11=110'] Exploring Operation: 110-83=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[57, 10, 83, 46], Operations: [] Exploring Operation: 83-57=26, Resulting Numbers: [10, 46, 26] Generated Node #0,0: 27:[10, 46, 26] Operation: 83-57=26 Moving to Node #0,0 Current State: 27:[10, 46, 26], Operations: ['83-57=26'] Exploring Operation: 46-26=20, Resulting Numbers: [10, 20] Generated Node #0,0,0: 27:[10, 20] Operation: 46-26=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[10, 20], Operations: ['83-57=26', '46-26=20'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,27 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
[ 80, 11, 9, 83 ]
24
[ "83-80=3", "11*3=33", "33-9=24" ]
Current State: 24:[80, 11, 9, 83], Operations: [] Exploring Operation: 83-80=3, Resulting Numbers: [11, 9, 3] Generated Node #2: [11, 9, 3] from Operation: 83-80=3 Current State: 24:[11, 9, 3], Operations: ['83-80=3'] Exploring Operation: 11*3=33, Resulting Numbers: [9, 33] Generated Node #3: [9, 33] from Operation: 11*3=33 Current State: 24:[9, 33], Operations: ['83-80=3', '11*3=33'] Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[80, 11, 9, 83], Operations: [] Exploring Operation: 80-9=71, Resulting Numbers: [11, 83, 71] Generated Node #0,0: 24:[11, 83, 71] Operation: 80-9=71 Exploring Operation: 83-80=3, Resulting Numbers: [11, 9, 3] Generated Node #0,1: 24:[11, 9, 3] Operation: 83-80=3 Exploring Operation: 83-9=74, Resulting Numbers: [80, 11, 74] Generated Node #0,2: 24:[80, 11, 74] Operation: 83-9=74 Exploring Operation: 83-11=72, Resulting Numbers: [80, 9, 72] Generated Node #0,3: 24:[80, 9, 72] Operation: 83-11=72 Exploring Operation: 80-11=69, Resulting Numbers: [9, 83, 69] Generated Node #0,4: 24:[9, 83, 69] Operation: 80-11=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[11, 9, 3], Operations: ['83-80=3'] Exploring Operation: 9/3=3, Resulting Numbers: [11, 3] Generated Node #0,1,0: 24:[11, 3] Operation: 9/3=3 Exploring Operation: 9+3=12, Resulting Numbers: [11, 12] Generated Node #0,1,1: 24:[11, 12] Operation: 9+3=12 Exploring Operation: 9-3=6, Resulting Numbers: [11, 6] Generated Node #0,1,2: 24:[11, 6] Operation: 9-3=6 Exploring Operation: 11-3=8, Resulting Numbers: [9, 8] Generated Node #0,1,3: 24:[9, 8] Operation: 11-3=8 Exploring Operation: 11-9=2, Resulting Numbers: [3, 2] Generated Node #0,1,4: 24:[3, 2] Operation: 11-9=2 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 24:[3, 2], Operations: ['83-80=3', '11-9=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,24 unequal: No Solution No 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: 24:[11, 3], Operations: ['83-80=3', '9/3=3'] Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,24 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,24 unequal: No Solution No 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: 24:[11, 12], Operations: ['83-80=3', '9+3=12'] Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,24 unequal: No Solution No 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: 24:[11, 6], Operations: ['83-80=3', '9-3=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,24 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,24 unequal: No Solution No 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: 24:[9, 8], Operations: ['83-80=3', '11-3=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[80, 9, 72], Operations: ['83-11=72'] Exploring Operation: 72-9=63, Resulting Numbers: [80, 63] Generated Node #0,3,0: 24:[80, 63] Operation: 72-9=63 Exploring Operation: 80+9=89, Resulting Numbers: [72, 89] Generated Node #0,3,1: 24:[72, 89] Operation: 80+9=89 Exploring Operation: 80-9=71, Resulting Numbers: [72, 71] Generated Node #0,3,2: 24:[72, 71] Operation: 80-9=71 Exploring Operation: 72/9=8, Resulting Numbers: [80, 8] Generated Node #0,3,3: 24:[80, 8] Operation: 72/9=8 Exploring Operation: 80-72=8, Resulting Numbers: [9, 8] Generated Node #0,3,4: 24:[9, 8] Operation: 80-72=8 Moving to Node #0,3,4 Current State: 24:[9, 8], Operations: ['83-11=72', '80-72=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[80, 8], Operations: ['83-11=72', '72/9=8'] Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,24 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,24 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,24 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[80, 63], Operations: ['83-11=72', '72-9=63'] Exploring Operation: 80+63=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 80*63=5040, Resulting Numbers: [5040] 5040,24 unequal: No Solution Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[72, 71], Operations: ['83-11=72', '80-9=71'] Exploring Operation: 72+71=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 72*71=5112, Resulting Numbers: [5112] 5112,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[72, 89], Operations: ['83-11=72', '80+9=89'] Exploring Operation: 72+89=161, Resulting Numbers: [161] 161,24 unequal: No Solution Exploring Operation: 89-72=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 72*89=6408, Resulting Numbers: [6408] 6408,24 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 #0,4 Current State: 24:[9, 83, 69], Operations: ['80-11=69'] Exploring Operation: 83-69=14, Resulting Numbers: [9, 14] Generated Node #0,4,0: 24:[9, 14] Operation: 83-69=14 Exploring Operation: 9+69=78, Resulting Numbers: [83, 78] Generated Node #0,4,1: 24:[83, 78] Operation: 9+69=78 Exploring Operation: 9+83=92, Resulting Numbers: [69, 92] Generated Node #0,4,2: 24:[69, 92] Operation: 9+83=92 Exploring Operation: 69-9=60, Resulting Numbers: [83, 60] Generated Node #0,4,3: 24:[83, 60] Operation: 69-9=60 Exploring Operation: 83-9=74, Resulting Numbers: [69, 74] Generated Node #0,4,4: 24:[69, 74] Operation: 83-9=74 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 24:[9, 14], Operations: ['80-11=69', '83-69=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,24 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,24 unequal: No Solution No 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: 24:[83, 60], Operations: ['80-11=69', '69-9=60'] Exploring Operation: 83+60=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 83*60=4980, Resulting Numbers: [4980] 4980,24 unequal: No Solution No 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: 24:[69, 74], Operations: ['80-11=69', '83-9=74'] Exploring Operation: 69*74=5106, Resulting Numbers: [5106] 5106,24 unequal: No Solution Exploring Operation: 74-69=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 69+74=143, Resulting Numbers: [143] 143,24 unequal: No Solution No 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: 24:[83, 78], Operations: ['80-11=69', '9+69=78'] Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,24 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,24 unequal: No Solution No 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: 24:[69, 92], Operations: ['80-11=69', '9+83=92'] Exploring Operation: 92-69=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 69*92=6348, Resulting Numbers: [6348] 6348,24 unequal: No Solution Exploring Operation: 69+92=161, Resulting Numbers: [161] 161,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[11, 83, 71], Operations: ['80-9=71'] Exploring Operation: 11+71=82, Resulting Numbers: [83, 82] Generated Node #0,0,0: 24:[83, 82] Operation: 11+71=82 Exploring Operation: 11+83=94, Resulting Numbers: [71, 94] Generated Node #0,0,1: 24:[71, 94] Operation: 11+83=94 Exploring Operation: 71-11=60, Resulting Numbers: [83, 60] Generated Node #0,0,2: 24:[83, 60] Operation: 71-11=60 Exploring Operation: 83-71=12, Resulting Numbers: [11, 12] Generated Node #0,0,3: 24:[11, 12] Operation: 83-71=12 Exploring Operation: 83-11=72, Resulting Numbers: [71, 72] Generated Node #0,0,4: 24:[71, 72] Operation: 83-11=72 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 24:[11, 12], Operations: ['80-9=71', '83-71=12'] Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,24 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,24 unequal: No Solution No 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: 24:[83, 60], Operations: ['80-9=71', '71-11=60'] Exploring Operation: 83-60=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 83*60=4980, Resulting Numbers: [4980] 4980,24 unequal: No Solution Exploring Operation: 83+60=143, Resulting Numbers: [143] 143,24 unequal: No Solution No 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: 24:[71, 72], Operations: ['80-9=71', '83-11=72'] Exploring Operation: 71+72=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 71*72=5112, Resulting Numbers: [5112] 5112,24 unequal: No Solution Exploring Operation: 72-71=1, Resulting Numbers: [1] 1,24 unequal: No Solution No 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: 24:[83, 82], Operations: ['80-9=71', '11+71=82'] Exploring Operation: 83-82=1, Resulting Numbers: [1] 1,24 unequal: No Solution Exploring Operation: 83*82=6806, Resulting Numbers: [6806] 6806,24 unequal: No Solution Exploring Operation: 83+82=165, Resulting Numbers: [165] 165,24 unequal: No Solution No 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: 24:[71, 94], Operations: ['80-9=71', '11+83=94'] Exploring Operation: 94-71=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 71*94=6674, Resulting Numbers: [6674] 6674,24 unequal: No Solution Exploring Operation: 71+94=165, Resulting Numbers: [165] 165,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[80, 11, 74], Operations: ['83-9=74'] Exploring Operation: 80-74=6, Resulting Numbers: [11, 6] Generated Node #0,2,0: 24:[11, 6] Operation: 80-74=6 Exploring Operation: 74-11=63, Resulting Numbers: [80, 63] Generated Node #0,2,1: 24:[80, 63] Operation: 74-11=63 Exploring Operation: 80+11=91, Resulting Numbers: [74, 91] Generated Node #0,2,2: 24:[74, 91] Operation: 80+11=91 Exploring Operation: 80-11=69, Resulting Numbers: [74, 69] Generated Node #0,2,3: 24:[74, 69] Operation: 80-11=69 Exploring Operation: 11+74=85, Resulting Numbers: [80, 85] Generated Node #0,2,4: 24:[80, 85] Operation: 11+74=85 Moving to Node #0,2,0 Current State: 24:[11, 6], Operations: ['83-9=74', '80-74=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[74, 69], Operations: ['83-9=74', '80-11=69'] Exploring Operation: 74+69=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 74*69=5106, Resulting Numbers: [5106] 5106,24 unequal: No Solution Exploring Operation: 74-69=5, Resulting Numbers: [5] 5,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[80, 63], Operations: ['83-9=74', '74-11=63'] Exploring Operation: 80+63=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 80*63=5040, Resulting Numbers: [5040] 5040,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[74, 91], Operations: ['83-9=74', '80+11=91'] Exploring Operation: 91-74=17, Resulting Numbers: [17] 17,24 unequal: No Solution Exploring Operation: 74*91=6734, Resulting Numbers: [6734] 6734,24 unequal: No Solution Exploring Operation: 74+91=165, Resulting Numbers: [165] 165,24 unequal: No Solution Moving to Node #0,2,4 Current State: 24:[80, 85], Operations: ['83-9=74', '11+74=85'] Exploring Operation: 80*85=6800, Resulting Numbers: [6800] 6800,24 unequal: No Solution Exploring Operation: 80+85=165, Resulting Numbers: [165] 165,24 unequal: No Solution Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,24 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
[ 24, 16, 27, 93 ]
58
[ "24-16=8", "93-27=66", "66-8=58" ]
Current State: 58:[24, 16, 27, 93], Operations: [] Exploring Operation: 24-16=8, Resulting Numbers: [27, 93, 8] Generated Node #2: [27, 93, 8] from Operation: 24-16=8 Current State: 58:[27, 93, 8], Operations: ['24-16=8'] Exploring Operation: 93-27=66, Resulting Numbers: [8, 66] Generated Node #3: [8, 66] from Operation: 93-27=66 Current State: 58:[8, 66], Operations: ['24-16=8', '93-27=66'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[24, 16, 27, 93], Operations: [] Exploring Operation: 24-16=8, Resulting Numbers: [27, 93, 8] Generated Node #0,0: 58:[27, 93, 8] Operation: 24-16=8 Exploring Operation: 93-24=69, Resulting Numbers: [16, 27, 69] Generated Node #0,1: 58:[16, 27, 69] Operation: 93-24=69 Exploring Operation: 93-16=77, Resulting Numbers: [24, 27, 77] Generated Node #0,2: 58:[24, 27, 77] Operation: 93-16=77 Exploring Operation: 93-27=66, Resulting Numbers: [24, 16, 66] Generated Node #0,3: 58:[24, 16, 66] Operation: 93-27=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[16, 27, 69], Operations: ['93-24=69'] Exploring Operation: 16+27=43, Resulting Numbers: [69, 43] Generated Node #0,1,0: 58:[69, 43] Operation: 16+27=43 Exploring Operation: 69-16=53, Resulting Numbers: [27, 53] Generated Node #0,1,1: 58:[27, 53] Operation: 69-16=53 Exploring Operation: 27-16=11, Resulting Numbers: [69, 11] Generated Node #0,1,2: 58:[69, 11] Operation: 27-16=11 Exploring Operation: 69-27=42, Resulting Numbers: [16, 42] Generated Node #0,1,3: 58:[16, 42] Operation: 69-27=42 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[27, 53], Operations: ['93-24=69', '69-16=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,58 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 27*53=1431, Resulting Numbers: [1431] 1431,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 58:[69, 11], Operations: ['93-24=69', '27-16=11'] Exploring Operation: 69*11=759, Resulting Numbers: [759] 759,58 unequal: No Solution Exploring Operation: 69+11=80, Resulting Numbers: [80] 80,58 unequal: No Solution Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[24, 16, 27, 93], Operations: [] Exploring Operation: 93-24=69, Resulting Numbers: [16, 27, 69] Generated Node #0,1: 58:[16, 27, 69] Operation: 93-24=69 Moving to Node #0,1 Current State: 58:[16, 27, 69], Operations: ['93-24=69'] Exploring Operation: 27-16=11, Resulting Numbers: [69, 11] Generated Node #0,1,2: 58:[69, 11] Operation: 27-16=11 Moving to Node #0,1,2 Current State: 58:[69, 11], Operations: ['93-24=69', '27-16=11'] Exploring Operation: 69-11=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 66, 3, 61, 6 ]
23
[ "66-61=5", "3*6=18", "5+18=23" ]
Current State: 23:[66, 3, 61, 6], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [3, 6, 5] Generated Node #2: [3, 6, 5] from Operation: 66-61=5 Current State: 23:[3, 6, 5], Operations: ['66-61=5'] Exploring Operation: 3*6=18, Resulting Numbers: [5, 18] Generated Node #3: [5, 18] from Operation: 3*6=18 Current State: 23:[5, 18], Operations: ['66-61=5', '3*6=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[66, 3, 61, 6], Operations: [] Exploring Operation: 3*6=18, Resulting Numbers: [66, 61, 18] Generated Node #0,0: 23:[66, 61, 18] Operation: 3*6=18 Exploring Operation: 66/6=11, Resulting Numbers: [3, 61, 11] Generated Node #0,1: 23:[3, 61, 11] Operation: 66/6=11 Exploring Operation: 66/3=22, Resulting Numbers: [61, 6, 22] Generated Node #0,2: 23:[61, 6, 22] Operation: 66/3=22 Exploring Operation: 66-61=5, Resulting Numbers: [3, 6, 5] Generated Node #0,3: 23:[3, 6, 5] Operation: 66-61=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[3, 6, 5], Operations: ['66-61=5'] Exploring Operation: 3*6=18, Resulting Numbers: [5, 18] Generated Node #0,3,0: 23:[5, 18] Operation: 3*6=18 Exploring Operation: 6*5=30, Resulting Numbers: [3, 30] Generated Node #0,3,1: 23:[3, 30] Operation: 6*5=30 Exploring Operation: 3*5=15, Resulting Numbers: [6, 15] Generated Node #0,3,2: 23:[6, 15] Operation: 3*5=15 Exploring Operation: 3+6=9, Resulting Numbers: [5, 9] Generated Node #0,3,3: 23:[5, 9] Operation: 3+6=9 Moving to Node #0,3,0 Current State: 23:[5, 18], Operations: ['66-61=5', '3*6=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[66, 3, 61, 6], Operations: [] Exploring Operation: 66-61=5, Resulting Numbers: [3, 6, 5] Generated Node #0,3: 23:[3, 6, 5] Operation: 66-61=5 Moving to Node #0,3 Current State: 23:[3, 6, 5], Operations: ['66-61=5'] Exploring Operation: 3*6=18, Resulting Numbers: [5, 18] Generated Node #0,3,0: 23:[5, 18] Operation: 3*6=18 Moving to Node #0,3,0 Current State: 23:[5, 18], Operations: ['66-61=5', '3*6=18'] Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 84, 36, 8, 12 ]
17
[ "36*8=288", "288-84=204", "204/12=17" ]
Current State: 17:[84, 36, 8, 12], Operations: [] Exploring Operation: 36*8=288, Resulting Numbers: [84, 12, 288] Generated Node #2: [84, 12, 288] from Operation: 36*8=288 Current State: 17:[84, 12, 288], Operations: ['36*8=288'] Exploring Operation: 288-84=204, Resulting Numbers: [12, 204] Generated Node #3: [12, 204] from Operation: 288-84=204 Current State: 17:[12, 204], Operations: ['36*8=288', '288-84=204'] Exploring Operation: 204/12=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[84, 36, 8, 12], Operations: [] Exploring Operation: 84/12=7, Resulting Numbers: [36, 8, 7] Generated Node #0,0: 17:[36, 8, 7] Operation: 84/12=7 Moving to Node #0,0 Current State: 17:[36, 8, 7], Operations: ['84/12=7'] Exploring Operation: 36-8=28, Resulting Numbers: [7, 28] Generated Node #0,0,0: 17:[7, 28] Operation: 36-8=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[7, 28], Operations: ['84/12=7', '36-8=28'] Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,17 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
[ 97, 21, 17, 24 ]
69
[ "97-21=76", "24-17=7", "76-7=69" ]
Current State: 69:[97, 21, 17, 24], Operations: [] Exploring Operation: 97-21=76, Resulting Numbers: [17, 24, 76] Generated Node #2: [17, 24, 76] from Operation: 97-21=76 Current State: 69:[17, 24, 76], Operations: ['97-21=76'] Exploring Operation: 24-17=7, Resulting Numbers: [76, 7] Generated Node #3: [76, 7] from Operation: 24-17=7 Current State: 69:[76, 7], Operations: ['97-21=76', '24-17=7'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[97, 21, 17, 24], Operations: [] Exploring Operation: 97-17=80, Resulting Numbers: [21, 24, 80] Generated Node #0,0: 69:[21, 24, 80] Operation: 97-17=80 Exploring Operation: 97-24=73, Resulting Numbers: [21, 17, 73] Generated Node #0,1: 69:[21, 17, 73] Operation: 97-24=73 Exploring Operation: 97-21=76, Resulting Numbers: [17, 24, 76] Generated Node #0,2: 69:[17, 24, 76] Operation: 97-21=76 Moving to Node #0,1 Current State: 69:[21, 17, 73], Operations: ['97-24=73'] Exploring Operation: 21+17=38, Resulting Numbers: [73, 38] Generated Node #0,1,0: 69:[73, 38] Operation: 21+17=38 Exploring Operation: 21-17=4, Resulting Numbers: [73, 4] Generated Node #0,1,1: 69:[73, 4] Operation: 21-17=4 Exploring Operation: 73-17=56, Resulting Numbers: [21, 56] Generated Node #0,1,2: 69:[21, 56] Operation: 73-17=56 Moving to Node #0,0 Current State: 69:[21, 24, 80], Operations: ['97-17=80'] Exploring Operation: 24-21=3, Resulting Numbers: [80, 3] Generated Node #0,0,0: 69:[80, 3] Operation: 24-21=3 Exploring Operation: 80-24=56, Resulting Numbers: [21, 56] Generated Node #0,0,1: 69:[21, 56] Operation: 80-24=56 Exploring Operation: 80-21=59, Resulting Numbers: [24, 59] Generated Node #0,0,2: 69:[24, 59] Operation: 80-21=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[80, 3], Operations: ['97-17=80', '24-21=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 80*3=240, Resulting Numbers: [240] 240,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[24, 59], Operations: ['97-17=80', '80-21=59'] Exploring Operation: 24+59=83, Resulting Numbers: [83] 83,69 unequal: No Solution Exploring Operation: 24*59=1416, Resulting Numbers: [1416] 1416,69 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[21, 56], Operations: ['97-17=80', '80-24=56'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,69 unequal: No Solution Exploring Operation: 21*56=1176, Resulting Numbers: [1176] 1176,69 unequal: No Solution Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[17, 24, 76], Operations: ['97-21=76'] Exploring Operation: 76-17=59, Resulting Numbers: [24, 59] Generated Node #0,2,0: 69:[24, 59] Operation: 76-17=59 Exploring Operation: 24-17=7, Resulting Numbers: [76, 7] Generated Node #0,2,1: 69:[76, 7] Operation: 24-17=7 Exploring Operation: 76-24=52, Resulting Numbers: [17, 52] Generated Node #0,2,2: 69:[17, 52] Operation: 76-24=52 Moving to Node #0,1,1 Current State: 69:[73, 4], Operations: ['97-24=73', '21-17=4'] Exploring Operation: 73*4=292, Resulting Numbers: [292] 292,69 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[97, 21, 17, 24], Operations: [] Exploring Operation: 97-24=73, Resulting Numbers: [21, 17, 73] Generated Node #0,1: 69:[21, 17, 73] Operation: 97-24=73 Moving to Node #0,1 Current State: 69:[21, 17, 73], Operations: ['97-24=73'] Exploring Operation: 21-17=4, Resulting Numbers: [73, 4] Generated Node #0,1,1: 69:[73, 4] Operation: 21-17=4 Moving to Node #0,1,1 Current State: 69:[73, 4], Operations: ['97-24=73', '21-17=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 18, 29, 56, 22 ]
58
[ "29-18=11", "22/11=2", "56+2=58" ]
Current State: 58:[18, 29, 56, 22], Operations: [] Exploring Operation: 29-18=11, Resulting Numbers: [56, 22, 11] Generated Node #2: [56, 22, 11] from Operation: 29-18=11 Current State: 58:[56, 22, 11], Operations: ['29-18=11'] Exploring Operation: 22/11=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 22/11=2 Current State: 58:[56, 2], Operations: ['29-18=11', '22/11=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[18, 29, 56, 22], Operations: [] Exploring Operation: 56-22=34, Resulting Numbers: [18, 29, 34] Generated Node #0,0: 58:[18, 29, 34] Operation: 56-22=34 Exploring Operation: 18+22=40, Resulting Numbers: [29, 56, 40] Generated Node #0,1: 58:[29, 56, 40] Operation: 18+22=40 Exploring Operation: 22-18=4, Resulting Numbers: [29, 56, 4] Generated Node #0,2: 58:[29, 56, 4] Operation: 22-18=4 Exploring Operation: 56-18=38, Resulting Numbers: [29, 22, 38] Generated Node #0,3: 58:[29, 22, 38] Operation: 56-18=38 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[29, 56, 4], Operations: ['22-18=4'] Exploring Operation: 29-4=25, Resulting Numbers: [56, 25] Generated Node #0,2,0: 58:[56, 25] Operation: 29-4=25 Exploring Operation: 29+4=33, Resulting Numbers: [56, 33] Generated Node #0,2,1: 58:[56, 33] Operation: 29+4=33 Exploring Operation: 56-29=27, Resulting Numbers: [4, 27] Generated Node #0,2,2: 58:[4, 27] Operation: 56-29=27 Exploring Operation: 56+4=60, Resulting Numbers: [29, 60] Generated Node #0,2,3: 58:[29, 60] Operation: 56+4=60 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 58:[29, 60], Operations: ['22-18=4', '56+4=60'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,58 unequal: No Solution Exploring Operation: 29*60=1740, Resulting Numbers: [1740] 1740,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 58:[4, 27], Operations: ['22-18=4', '56-29=27'] Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[56, 25], Operations: ['22-18=4', '29-4=25'] Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,58 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 58:[56, 33], Operations: ['22-18=4', '29+4=33'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 56*33=1848, Resulting Numbers: [1848] 1848,58 unequal: No Solution Exploring Operation: 56+33=89, Resulting Numbers: [89] 89,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[29, 56, 40], Operations: ['18+22=40'] Exploring Operation: 56-40=16, Resulting Numbers: [29, 16] Generated Node #0,1,0: 58:[29, 16] Operation: 56-40=16 Exploring Operation: 56-29=27, Resulting Numbers: [40, 27] Generated Node #0,1,1: 58:[40, 27] Operation: 56-29=27 Exploring Operation: 29+40=69, Resulting Numbers: [56, 69] Generated Node #0,1,2: 58:[56, 69] Operation: 29+40=69 Exploring Operation: 40-29=11, Resulting Numbers: [56, 11] Generated Node #0,1,3: 58:[56, 11] Operation: 40-29=11 Moving to Node #0,1,3 Current State: 58:[56, 11], Operations: ['18+22=40', '40-29=11'] Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 56*11=616, Resulting Numbers: [616] 616,58 unequal: No Solution Exploring Operation: 56+11=67, Resulting Numbers: [67] 67,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[40, 27], Operations: ['18+22=40', '56-29=27'] Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,58 unequal: No Solution Exploring Operation: 40*27=1080, Resulting Numbers: [1080] 1080,58 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[29, 16], Operations: ['18+22=40', '56-40=16'] Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[56, 69], Operations: ['18+22=40', '29+40=69'] Exploring Operation: 56+69=125, Resulting Numbers: [125] 125,58 unequal: No Solution Exploring Operation: 56*69=3864, Resulting Numbers: [3864] 3864,58 unequal: No Solution Exploring Operation: 69-56=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[18, 29, 34], Operations: ['56-22=34'] Exploring Operation: 34-18=16, Resulting Numbers: [29, 16] Generated Node #0,0,0: 58:[29, 16] Operation: 34-18=16 Exploring Operation: 18+34=52, Resulting Numbers: [29, 52] Generated Node #0,0,1: 58:[29, 52] Operation: 18+34=52 Exploring Operation: 29-18=11, Resulting Numbers: [34, 11] Generated Node #0,0,2: 58:[34, 11] Operation: 29-18=11 Exploring Operation: 34-29=5, Resulting Numbers: [18, 5] Generated Node #0,0,3: 58:[18, 5] Operation: 34-29=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 58:[29, 52], Operations: ['56-22=34', '18+34=52'] Exploring Operation: 29+52=81, Resulting Numbers: [81] 81,58 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 29*52=1508, Resulting Numbers: [1508] 1508,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[29, 16], Operations: ['56-22=34', '34-18=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,58 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 58:[34, 11], Operations: ['56-22=34', '29-18=11'] Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,58 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 58:[18, 5], Operations: ['56-22=34', '34-29=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,58 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,58 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[29, 22, 38], Operations: ['56-18=38'] Exploring Operation: 29-22=7, Resulting Numbers: [38, 7] Generated Node #0,3,0: 58:[38, 7] Operation: 29-22=7 Exploring Operation: 38-29=9, Resulting Numbers: [22, 9] Generated Node #0,3,1: 58:[22, 9] Operation: 38-29=9 Exploring Operation: 22+38=60, Resulting Numbers: [29, 60] Generated Node #0,3,2: 58:[29, 60] Operation: 22+38=60 Exploring Operation: 38-22=16, Resulting Numbers: [29, 16] Generated Node #0,3,3: 58:[29, 16] Operation: 38-22=16 Moving to Node #0,3,2 Current State: 58:[29, 60], Operations: ['56-18=38', '22+38=60'] Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,58 unequal: No Solution Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 29*60=1740, Resulting Numbers: [1740] 1740,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[29, 16], Operations: ['56-18=38', '38-22=16'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,58 unequal: No Solution Moving to Node #0,3,1 Current State: 58:[22, 9], Operations: ['56-18=38', '38-29=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,58 unequal: No Solution Moving to Node #0,3,0 Current State: 58:[38, 7], Operations: ['56-18=38', '29-22=7'] Exploring Operation: 38-7=31, Resulting Numbers: [31] 31,58 unequal: No Solution Exploring Operation: 38*7=266, Resulting Numbers: [266] 266,58 unequal: No Solution Exploring Operation: 38+7=45, Resulting Numbers: [45] 45,58 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
[ 7, 49, 9, 3 ]
92
[ "9-7=2", "49-3=46", "2*46=92" ]
Current State: 92:[7, 49, 9, 3], Operations: [] Exploring Operation: 9-7=2, Resulting Numbers: [49, 3, 2] Generated Node #2: [49, 3, 2] from Operation: 9-7=2 Current State: 92:[49, 3, 2], Operations: ['9-7=2'] Exploring Operation: 49-3=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 49-3=46 Current State: 92:[2, 46], Operations: ['9-7=2', '49-3=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[7, 49, 9, 3], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [7, 49, 3] Generated Node #0,0: 92:[7, 49, 3] Operation: 9/3=3 Exploring Operation: 9-7=2, Resulting Numbers: [49, 3, 2] Generated Node #0,1: 92:[49, 3, 2] Operation: 9-7=2 Exploring Operation: 7-3=4, Resulting Numbers: [49, 9, 4] Generated Node #0,2: 92:[49, 9, 4] Operation: 7-3=4 Moving to Node #0,1 Current State: 92:[49, 3, 2], Operations: ['9-7=2'] Exploring Operation: 3+2=5, Resulting Numbers: [49, 5] Generated Node #0,1,0: 92:[49, 5] Operation: 3+2=5 Exploring Operation: 49-2=47, Resulting Numbers: [3, 47] Generated Node #0,1,1: 92:[3, 47] Operation: 49-2=47 Exploring Operation: 49-3=46, Resulting Numbers: [2, 46] Generated Node #0,1,2: 92:[2, 46] Operation: 49-3=46 Moving to Node #0,0 Current State: 92:[7, 49, 3], Operations: ['9/3=3'] Exploring Operation: 7-3=4, Resulting Numbers: [49, 4] Generated Node #0,0,0: 92:[49, 4] Operation: 7-3=4 Exploring Operation: 49-3=46, Resulting Numbers: [7, 46] Generated Node #0,0,1: 92:[7, 46] Operation: 49-3=46 Exploring Operation: 49/7=7, Resulting Numbers: [3, 7] Generated Node #0,0,2: 92:[3, 7] Operation: 49/7=7 Moving to Node #0,2 Current State: 92:[49, 9, 4], Operations: ['7-3=4'] Exploring Operation: 9-4=5, Resulting Numbers: [49, 5] Generated Node #0,2,0: 92:[49, 5] Operation: 9-4=5 Exploring Operation: 49-9=40, Resulting Numbers: [4, 40] Generated Node #0,2,1: 92:[4, 40] Operation: 49-9=40 Exploring Operation: 49-4=45, Resulting Numbers: [9, 45] Generated Node #0,2,2: 92:[9, 45] Operation: 49-4=45 Moving to Node #0,1,2 Current State: 92:[2, 46], Operations: ['9-7=2', '49-3=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,92 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[7, 49, 9, 3], Operations: [] Exploring Operation: 9-7=2, Resulting Numbers: [49, 3, 2] Generated Node #0,1: 92:[49, 3, 2] Operation: 9-7=2 Moving to Node #0,1 Current State: 92:[49, 3, 2], Operations: ['9-7=2'] Exploring Operation: 49-3=46, Resulting Numbers: [2, 46] Generated Node #0,1,2: 92:[2, 46] Operation: 49-3=46 Moving to Node #0,1,2 Current State: 92:[2, 46], Operations: ['9-7=2', '49-3=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
0.984375
hs_3
sum_heuristic
[ 46, 31, 62, 46 ]
31
[ "46+31=77", "62+46=108", "108-77=31" ]
Current State: 31:[46, 31, 62, 46], Operations: [] Exploring Operation: 46+31=77, Resulting Numbers: [62, 77] Generated Node #2: [62, 77] from Operation: 46+31=77 Current State: 31:[62, 77], Operations: ['46+31=77'] Exploring Operation: 62+46=108, Resulting Numbers: [77, 108] Generated Node #3: [77, 108] from Operation: 62+46=108 Current State: 31:[77, 108], Operations: ['46+31=77', '62+46=108'] Exploring Operation: 108-77=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[46, 31, 62, 46], Operations: [] Exploring Operation: 62-31=31, Resulting Numbers: [46, 46, 31] Generated Node #0,0: 31:[46, 46, 31] Operation: 62-31=31 Exploring Operation: 62-46=16, Resulting Numbers: [46, 31, 16] Generated Node #0,1: 31:[46, 31, 16] Operation: 62-46=16 Exploring Operation: 62-46=16, Resulting Numbers: [31, 46, 16] Generated Node #0,2: 31:[31, 46, 16] Operation: 62-46=16 Moving to Node #0,0 Current State: 31:[46, 46, 31], Operations: ['62-31=31'] Exploring Operation: 46/46=1, Resulting Numbers: [31, 1] Generated Node #0,0,0: 31:[31, 1] Operation: 46/46=1 Exploring Operation: 46-46=0, Resulting Numbers: [31, 0] Generated Node #0,0,1: 31:[31, 0] Operation: 46-46=0 Exploring Operation: 46-31=15, Resulting Numbers: [46, 15] Generated Node #0,0,2: 31:[46, 15] Operation: 46-31=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[31, 1], Operations: ['62-31=31', '46/46=1'] Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[46, 31, 62, 46], Operations: [] Exploring Operation: 62-31=31, Resulting Numbers: [46, 46, 31] Generated Node #0,0: 31:[46, 46, 31] Operation: 62-31=31 Moving to Node #0,0 Current State: 31:[46, 46, 31], Operations: ['62-31=31'] Exploring Operation: 46/46=1, Resulting Numbers: [31, 1] Generated Node #0,0,0: 31:[31, 1] Operation: 46/46=1 Moving to Node #0,0,0 Current State: 31:[31, 1], Operations: ['62-31=31', '46/46=1'] Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 93, 3, 26, 95 ]
25
[ "93+3=96", "26+95=121", "121-96=25" ]
Current State: 25:[93, 3, 26, 95], Operations: [] Exploring Operation: 93+3=96, Resulting Numbers: [26, 95, 96] Generated Node #2: [26, 95, 96] from Operation: 93+3=96 Current State: 25:[26, 95, 96], Operations: ['93+3=96'] Exploring Operation: 26+95=121, Resulting Numbers: [96, 121] Generated Node #3: [96, 121] from Operation: 26+95=121 Current State: 25:[96, 121], Operations: ['93+3=96', '26+95=121'] Exploring Operation: 121-96=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[93, 3, 26, 95], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [26, 95, 31] Generated Node #0,0: 25:[26, 95, 31] Operation: 93/3=31 Exploring Operation: 95-93=2, Resulting Numbers: [3, 26, 2] Generated Node #0,1: 25:[3, 26, 2] Operation: 95-93=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[3, 26, 2], Operations: ['95-93=2'] Exploring Operation: 3+2=5, Resulting Numbers: [26, 5] Generated Node #0,1,0: 25:[26, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [26, 6] Generated Node #0,1,1: 25:[26, 6] Operation: 3*2=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[26, 5], Operations: ['95-93=2', '3+2=5'] Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,25 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,25 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:[26, 6], Operations: ['95-93=2', '3*2=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[26, 95, 31], Operations: ['93/3=31'] Exploring Operation: 95-26=69, Resulting Numbers: [31, 69] Generated Node #0,0,0: 25:[31, 69] Operation: 95-26=69 Exploring Operation: 95-31=64, Resulting Numbers: [26, 64] Generated Node #0,0,1: 25:[26, 64] Operation: 95-31=64 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[26, 64], Operations: ['93/3=31', '95-31=64'] Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,25 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[31, 69], Operations: ['93/3=31', '95-26=69'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,25 unequal: No Solution Exploring Operation: 31+69=100, Resulting Numbers: [100] 100,25 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_2
mult_heuristic
[ 86, 25, 12, 97 ]
80
[ "97-25=72", "72/12=6", "86-6=80" ]
Current State: 80:[86, 25, 12, 97], Operations: [] Exploring Operation: 97-25=72, Resulting Numbers: [86, 12, 72] Generated Node #2: [86, 12, 72] from Operation: 97-25=72 Current State: 80:[86, 12, 72], Operations: ['97-25=72'] Exploring Operation: 72/12=6, Resulting Numbers: [86, 6] Generated Node #3: [86, 6] from Operation: 72/12=6 Current State: 80:[86, 6], Operations: ['97-25=72', '72/12=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[86, 25, 12, 97], Operations: [] Exploring Operation: 97-86=11, Resulting Numbers: [25, 12, 11] Generated Node #0,0: 80:[25, 12, 11] Operation: 97-86=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[25, 12, 11], Operations: ['97-86=11'] Exploring Operation: 25+12=37, Resulting Numbers: [11, 37] Generated Node #0,0,0: 80:[11, 37] Operation: 25+12=37 Moving to Node #0,0,0 Current State: 80:[11, 37], Operations: ['97-86=11', '25+12=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,80 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
[ 87, 4, 64, 41 ]
96
[ "87+41=128", "128/4=32", "64+32=96" ]
Current State: 96:[87, 4, 64, 41], Operations: [] Exploring Operation: 87+41=128, Resulting Numbers: [4, 64, 128] Generated Node #2: [4, 64, 128] from Operation: 87+41=128 Current State: 96:[4, 64, 128], Operations: ['87+41=128'] Exploring Operation: 128/4=32, Resulting Numbers: [64, 32] Generated Node #3: [64, 32] from Operation: 128/4=32 Current State: 96:[64, 32], Operations: ['87+41=128', '128/4=32'] Exploring Operation: 64+32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[87, 4, 64, 41], Operations: [] Exploring Operation: 87-64=23, Resulting Numbers: [4, 41, 23] Generated Node #0,0: 96:[4, 41, 23] Operation: 87-64=23 Exploring Operation: 64-41=23, Resulting Numbers: [87, 4, 23] Generated Node #0,1: 96:[87, 4, 23] Operation: 64-41=23 Exploring Operation: 64/4=16, Resulting Numbers: [87, 41, 16] Generated Node #0,2: 96:[87, 41, 16] Operation: 64/4=16 Exploring Operation: 64+41=105, Resulting Numbers: [87, 4, 105] Generated Node #0,3: 96:[87, 4, 105] Operation: 64+41=105 Exploring Operation: 87-41=46, Resulting Numbers: [4, 64, 46] Generated Node #0,4: 96:[4, 64, 46] Operation: 87-41=46 Moving to Node #0,0 Current State: 96:[4, 41, 23], Operations: ['87-64=23'] Exploring Operation: 41-4=37, Resulting Numbers: [23, 37] Generated Node #0,0,0: 96:[23, 37] Operation: 41-4=37 Exploring Operation: 4+41=45, Resulting Numbers: [23, 45] Generated Node #0,0,1: 96:[23, 45] Operation: 4+41=45 Exploring Operation: 4+23=27, Resulting Numbers: [41, 27] Generated Node #0,0,2: 96:[41, 27] Operation: 4+23=27 Exploring Operation: 23-4=19, Resulting Numbers: [41, 19] Generated Node #0,0,3: 96:[41, 19] Operation: 23-4=19 Exploring Operation: 41-23=18, Resulting Numbers: [4, 18] Generated Node #0,0,4: 96:[4, 18] Operation: 41-23=18 Moving to Node #0,1 Current State: 96:[87, 4, 23], Operations: ['64-41=23'] Exploring Operation: 87+4=91, Resulting Numbers: [23, 91] Generated Node #0,1,0: 96:[23, 91] Operation: 87+4=91 Exploring Operation: 4*23=92, Resulting Numbers: [87, 92] Generated Node #0,1,1: 96:[87, 92] Operation: 4*23=92 Exploring Operation: 4+23=27, Resulting Numbers: [87, 27] Generated Node #0,1,2: 96:[87, 27] Operation: 4+23=27 Exploring Operation: 23-4=19, Resulting Numbers: [87, 19] Generated Node #0,1,3: 96:[87, 19] Operation: 23-4=19 Exploring Operation: 87-4=83, Resulting Numbers: [23, 83] Generated Node #0,1,4: 96:[23, 83] Operation: 87-4=83 Moving to Node #0,2 Current State: 96:[87, 41, 16], Operations: ['64/4=16'] Exploring Operation: 41+16=57, Resulting Numbers: [87, 57] Generated Node #0,2,0: 96:[87, 57] Operation: 41+16=57 Exploring Operation: 41-16=25, Resulting Numbers: [87, 25] Generated Node #0,2,1: 96:[87, 25] Operation: 41-16=25 Exploring Operation: 87+16=103, Resulting Numbers: [41, 103] Generated Node #0,2,2: 96:[41, 103] Operation: 87+16=103 Exploring Operation: 87-41=46, Resulting Numbers: [16, 46] Generated Node #0,2,3: 96:[16, 46] Operation: 87-41=46 Exploring Operation: 87-16=71, Resulting Numbers: [41, 71] Generated Node #0,2,4: 96:[41, 71] Operation: 87-16=71 Moving to Node #0,3 Current State: 96:[87, 4, 105], Operations: ['64+41=105'] Exploring Operation: 87+4=91, Resulting Numbers: [105, 91] Generated Node #0,3,0: 96:[105, 91] Operation: 87+4=91 Exploring Operation: 4+105=109, Resulting Numbers: [87, 109] Generated Node #0,3,1: 96:[87, 109] Operation: 4+105=109 Exploring Operation: 105-4=101, Resulting Numbers: [87, 101] Generated Node #0,3,2: 96:[87, 101] Operation: 105-4=101 Exploring Operation: 87-4=83, Resulting Numbers: [105, 83] Generated Node #0,3,3: 96:[105, 83] Operation: 87-4=83 Exploring Operation: 105-87=18, Resulting Numbers: [4, 18] Generated Node #0,3,4: 96:[4, 18] Operation: 105-87=18 Moving to Node #0,4 Current State: 96:[4, 64, 46], Operations: ['87-41=46'] Exploring Operation: 64-4=60, Resulting Numbers: [46, 60] Generated Node #0,4,0: 96:[46, 60] Operation: 64-4=60 Exploring Operation: 4+46=50, Resulting Numbers: [64, 50] Generated Node #0,4,1: 96:[64, 50] Operation: 4+46=50 Exploring Operation: 64/4=16, Resulting Numbers: [46, 16] Generated Node #0,4,2: 96:[46, 16] Operation: 64/4=16 Exploring Operation: 64+46=110, Resulting Numbers: [4, 110] Generated Node #0,4,3: 96:[4, 110] Operation: 64+46=110 Exploring Operation: 64-46=18, Resulting Numbers: [4, 18] Generated Node #0,4,4: 96:[4, 18] Operation: 64-46=18 Moving to Node #0,0,4 Current State: 96:[4, 18], Operations: ['87-64=23', '41-23=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,2,3 Current State: 96:[16, 46], Operations: ['64/4=16', '87-41=46'] Exploring Operation: 16*46=736, Resulting Numbers: [736] 736,96 unequal: No Solution Exploring Operation: 16+46=62, Resulting Numbers: [62] 62,96 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,96 unequal: No Solution Moving to Node #0,4,2 Current State: 96:[46, 16], Operations: ['87-41=46', '64/4=16'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,96 unequal: No Solution Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,96 unequal: No Solution Moving to Node #0,4,4 Current State: 96:[4, 18], Operations: ['87-41=46', '64-46=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[4, 18], Operations: ['64+41=105', '105-87=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,96 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[23, 45], Operations: ['87-64=23', '4+41=45'] Exploring Operation: 23+45=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 23*45=1035, Resulting Numbers: [1035] 1035,96 unequal: No Solution Exploring Operation: 45-23=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[23, 37], Operations: ['87-64=23', '41-4=37'] Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,96 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[23, 91], Operations: ['64-41=23', '87+4=91'] Exploring Operation: 91-23=68, Resulting Numbers: [68] 68,96 unequal: No Solution Exploring Operation: 23*91=2093, Resulting Numbers: [2093] 2093,96 unequal: No Solution Exploring Operation: 23+91=114, Resulting Numbers: [114] 114,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[87, 25], Operations: ['64/4=16', '41-16=25'] Exploring Operation: 87*25=2175, Resulting Numbers: [2175] 2175,96 unequal: No Solution Exploring Operation: 87+25=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[41, 19], Operations: ['87-64=23', '23-4=19'] Exploring Operation: 41+19=60, Resulting Numbers: [60] 60,96 unequal: No Solution Exploring Operation: 41*19=779, Resulting Numbers: [779] 779,96 unequal: No Solution Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[41, 27], Operations: ['87-64=23', '4+23=27'] Exploring Operation: 41*27=1107, Resulting Numbers: [1107] 1107,96 unequal: No Solution Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 41+27=68, Resulting Numbers: [68] 68,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[87, 27], Operations: ['64-41=23', '4+23=27'] Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,96 unequal: No Solution Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,96 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[87, 19], Operations: ['64-41=23', '23-4=19'] Exploring Operation: 87*19=1653, Resulting Numbers: [1653] 1653,96 unequal: No Solution Exploring Operation: 87+19=106, Resulting Numbers: [106] 106,96 unequal: No Solution Exploring Operation: 87-19=68, Resulting Numbers: [68] 68,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[87, 92], Operations: ['64-41=23', '4*23=92'] Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,96 unequal: No Solution Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[87, 101], Operations: ['64+41=105', '105-4=101'] Exploring Operation: 87*101=8787, Resulting Numbers: [8787] 8787,96 unequal: No Solution Exploring Operation: 87+101=188, Resulting Numbers: [188] 188,96 unequal: No Solution Exploring Operation: 101-87=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[41, 103], Operations: ['64/4=16', '87+16=103'] Exploring Operation: 41+103=144, Resulting Numbers: [144] 144,96 unequal: No Solution Exploring Operation: 103-41=62, Resulting Numbers: [62] 62,96 unequal: No Solution Exploring Operation: 41*103=4223, Resulting Numbers: [4223] 4223,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[23, 83], Operations: ['64-41=23', '87-4=83'] Exploring Operation: 23+83=106, Resulting Numbers: [106] 106,96 unequal: No Solution Exploring Operation: 23*83=1909, Resulting Numbers: [1909] 1909,96 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,96 unequal: No Solution Moving to Node #0,4,3 Current State: 96:[4, 110], Operations: ['87-41=46', '64+46=110'] Exploring Operation: 110-4=106, Resulting Numbers: [106] 106,96 unequal: No Solution Exploring Operation: 4*110=440, Resulting Numbers: [440] 440,96 unequal: No Solution Exploring Operation: 4+110=114, Resulting Numbers: [114] 114,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[105, 91], Operations: ['64+41=105', '87+4=91'] Exploring Operation: 105+91=196, Resulting Numbers: [196] 196,96 unequal: No Solution Exploring Operation: 105*91=9555, Resulting Numbers: [9555] 9555,96 unequal: No Solution Exploring Operation: 105-91=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,4,0 Current State: 96:[46, 60], Operations: ['87-41=46', '64-4=60'] Exploring Operation: 60-46=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 46*60=2760, Resulting Numbers: [2760] 2760,96 unequal: No Solution Exploring Operation: 46+60=106, Resulting Numbers: [106] 106,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[87, 57], Operations: ['64/4=16', '41+16=57'] Exploring Operation: 87+57=144, Resulting Numbers: [144] 144,96 unequal: No Solution Exploring Operation: 87*57=4959, Resulting Numbers: [4959] 4959,96 unequal: No Solution Exploring Operation: 87-57=30, Resulting Numbers: [30] 30,96 unequal: No Solution Moving to Node #0,4,1 Current State: 96:[64, 50], Operations: ['87-41=46', '4+46=50'] Exploring Operation: 64+50=114, Resulting Numbers: [114] 114,96 unequal: No Solution Exploring Operation: 64*50=3200, Resulting Numbers: [3200] 3200,96 unequal: No Solution Exploring Operation: 64-50=14, Resulting Numbers: [14] 14,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[105, 83], Operations: ['64+41=105', '87-4=83'] Exploring Operation: 105*83=8715, Resulting Numbers: [8715] 8715,96 unequal: No Solution Exploring Operation: 105+83=188, Resulting Numbers: [188] 188,96 unequal: No Solution Exploring Operation: 105-83=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[87, 109], Operations: ['64+41=105', '4+105=109'] Exploring Operation: 87+109=196, Resulting Numbers: [196] 196,96 unequal: No Solution Exploring Operation: 87*109=9483, Resulting Numbers: [9483] 9483,96 unequal: No Solution Exploring Operation: 109-87=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,2,4 Current State: 96:[41, 71], Operations: ['64/4=16', '87-16=71'] Exploring Operation: 41*71=2911, Resulting Numbers: [2911] 2911,96 unequal: No Solution Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 41+71=112, Resulting Numbers: [112] 112,96 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 13, 46, 24, 98 ]
96
[ "98-46=52", "52/13=4", "24*4=96" ]
Current State: 96:[13, 46, 24, 98], Operations: [] Exploring Operation: 98-46=52, Resulting Numbers: [13, 24, 52] Generated Node #2: [13, 24, 52] from Operation: 98-46=52 Current State: 96:[13, 24, 52], Operations: ['98-46=52'] Exploring Operation: 52/13=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 52/13=4 Current State: 96:[24, 4], Operations: ['98-46=52', '52/13=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[13, 46, 24, 98], Operations: [] Exploring Operation: 46-13=33, Resulting Numbers: [24, 98, 33] Generated Node #0,0: 96:[24, 98, 33] Operation: 46-13=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[24, 98, 33], Operations: ['46-13=33'] Exploring Operation: 33-24=9, Resulting Numbers: [98, 9] Generated Node #0,0,0: 96:[98, 9] Operation: 33-24=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[98, 9], Operations: ['46-13=33', '33-24=9'] Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 53, 29, 51, 47 ]
65
[ "53-51=2", "47*2=94", "94-29=65" ]
Current State: 65:[53, 29, 51, 47], Operations: [] Exploring Operation: 53-51=2, Resulting Numbers: [29, 47, 2] Generated Node #2: [29, 47, 2] from Operation: 53-51=2 Current State: 65:[29, 47, 2], Operations: ['53-51=2'] Exploring Operation: 47*2=94, Resulting Numbers: [29, 94] Generated Node #3: [29, 94] from Operation: 47*2=94 Current State: 65:[29, 94], Operations: ['53-51=2', '47*2=94'] Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[53, 29, 51, 47], Operations: [] Exploring Operation: 51-47=4, Resulting Numbers: [53, 29, 4] Generated Node #0,0: 65:[53, 29, 4] Operation: 51-47=4 Exploring Operation: 53-47=6, Resulting Numbers: [29, 51, 6] Generated Node #0,1: 65:[29, 51, 6] Operation: 53-47=6 Exploring Operation: 47-29=18, Resulting Numbers: [53, 51, 18] Generated Node #0,2: 65:[53, 51, 18] Operation: 47-29=18 Moving to Node #0,0 Current State: 65:[53, 29, 4], Operations: ['51-47=4'] Exploring Operation: 53+29=82, Resulting Numbers: [4, 82] Generated Node #0,0,0: 65:[4, 82] Operation: 53+29=82 Exploring Operation: 53-29=24, Resulting Numbers: [4, 24] Generated Node #0,0,1: 65:[4, 24] Operation: 53-29=24 Exploring Operation: 53+4=57, Resulting Numbers: [29, 57] Generated Node #0,0,2: 65:[29, 57] Operation: 53+4=57 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[4, 24], Operations: ['51-47=4', '53-29=24'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,65 unequal: No Solution No 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: 65:[4, 82], Operations: ['51-47=4', '53+29=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,65 unequal: No Solution Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,65 unequal: No Solution Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,65 unequal: No Solution No 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: 65:[29, 57], Operations: ['51-47=4', '53+4=57'] Exploring Operation: 29*57=1653, Resulting Numbers: [1653] 1653,65 unequal: No Solution Exploring Operation: 57-29=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 29+57=86, Resulting Numbers: [86] 86,65 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: 65:[29, 51, 6], Operations: ['53-47=6'] Exploring Operation: 51-29=22, Resulting Numbers: [6, 22] Generated Node #0,1,0: 65:[6, 22] Operation: 51-29=22 Exploring Operation: 29+51=80, Resulting Numbers: [6, 80] Generated Node #0,1,1: 65:[6, 80] Operation: 29+51=80 Exploring Operation: 29-6=23, Resulting Numbers: [51, 23] Generated Node #0,1,2: 65:[51, 23] Operation: 29-6=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[6, 22], Operations: ['53-47=6', '51-29=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,65 unequal: No Solution No 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: 65:[6, 80], Operations: ['53-47=6', '29+51=80'] Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,65 unequal: No Solution Exploring Operation: 6*80=480, Resulting Numbers: [480] 480,65 unequal: No Solution Exploring Operation: 6+80=86, Resulting Numbers: [86] 86,65 unequal: No Solution No 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: 65:[51, 23], Operations: ['53-47=6', '29-6=23'] Exploring Operation: 51*23=1173, Resulting Numbers: [1173] 1173,65 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 51+23=74, Resulting Numbers: [74] 74,65 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: 65:[53, 51, 18], Operations: ['47-29=18'] Exploring Operation: 53-51=2, Resulting Numbers: [18, 2] Generated Node #0,2,0: 65:[18, 2] Operation: 53-51=2 Exploring Operation: 51+18=69, Resulting Numbers: [53, 69] Generated Node #0,2,1: 65:[53, 69] Operation: 51+18=69 Exploring Operation: 53+18=71, Resulting Numbers: [51, 71] Generated Node #0,2,2: 65:[51, 71] Operation: 53+18=71 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[18, 2], Operations: ['47-29=18', '53-51=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,65 unequal: No Solution No 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: 65:[53, 69], Operations: ['47-29=18', '51+18=69'] Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 53*69=3657, Resulting Numbers: [3657] 3657,65 unequal: No Solution Exploring Operation: 53+69=122, Resulting Numbers: [122] 122,65 unequal: No Solution No 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: 65:[51, 71], Operations: ['47-29=18', '53+18=71'] Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,65 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,65 unequal: No Solution Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 23, 48, 56, 76 ]
16
[ "23+56=79", "79-76=3", "48/3=16" ]
Current State: 16:[23, 48, 56, 76], Operations: [] Exploring Operation: 23+56=79, Resulting Numbers: [48, 76, 79] Generated Node #2: [48, 76, 79] from Operation: 23+56=79 Current State: 16:[48, 76, 79], Operations: ['23+56=79'] Exploring Operation: 79-76=3, Resulting Numbers: [48, 3] Generated Node #3: [48, 3] from Operation: 79-76=3 Current State: 16:[48, 3], Operations: ['23+56=79', '79-76=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[23, 48, 56, 76], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [23, 56, 28] Generated Node #0,0: 16:[23, 56, 28] Operation: 76-48=28 Exploring Operation: 56-48=8, Resulting Numbers: [23, 76, 8] Generated Node #0,1: 16:[23, 76, 8] Operation: 56-48=8 Exploring Operation: 76-56=20, Resulting Numbers: [23, 48, 20] Generated Node #0,2: 16:[23, 48, 20] Operation: 76-56=20 Exploring Operation: 48-23=25, Resulting Numbers: [56, 76, 25] Generated Node #0,3: 16:[56, 76, 25] Operation: 48-23=25 Exploring Operation: 56-23=33, Resulting Numbers: [48, 76, 33] Generated Node #0,4: 16:[48, 76, 33] Operation: 56-23=33 Moving to Node #0,2 Current State: 16:[23, 48, 20], Operations: ['76-56=20'] Exploring Operation: 23-20=3, Resulting Numbers: [48, 3] Generated Node #0,2,0: 16:[48, 3] Operation: 23-20=3 Exploring Operation: 48-20=28, Resulting Numbers: [23, 28] Generated Node #0,2,1: 16:[23, 28] Operation: 48-20=28 Exploring Operation: 48-23=25, Resulting Numbers: [20, 25] Generated Node #0,2,2: 16:[20, 25] Operation: 48-23=25 Exploring Operation: 23+20=43, Resulting Numbers: [48, 43] Generated Node #0,2,3: 16:[48, 43] Operation: 23+20=43 Exploring Operation: 23+48=71, Resulting Numbers: [20, 71] Generated Node #0,2,4: 16:[20, 71] Operation: 23+48=71 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[20, 25], Operations: ['76-56=20', '48-23=25'] Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,16 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[23, 28], Operations: ['76-56=20', '48-20=28'] Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,16 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[48, 3], Operations: ['76-56=20', '23-20=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[23, 48, 56, 76], Operations: [] Exploring Operation: 76-56=20, Resulting Numbers: [23, 48, 20] Generated Node #0,2: 16:[23, 48, 20] Operation: 76-56=20 Moving to Node #0,2 Current State: 16:[23, 48, 20], Operations: ['76-56=20'] Exploring Operation: 23-20=3, Resulting Numbers: [48, 3] Generated Node #0,2,0: 16:[48, 3] Operation: 23-20=3 Moving to Node #0,2,0 Current State: 16:[48, 3], Operations: ['76-56=20', '23-20=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 4, 25, 73, 35 ]
62
[ "4*25=100", "73-35=38", "100-38=62" ]
Current State: 62:[4, 25, 73, 35], Operations: [] Exploring Operation: 4*25=100, Resulting Numbers: [73, 35, 100] Generated Node #2: [73, 35, 100] from Operation: 4*25=100 Current State: 62:[73, 35, 100], Operations: ['4*25=100'] Exploring Operation: 73-35=38, Resulting Numbers: [100, 38] Generated Node #3: [100, 38] from Operation: 73-35=38 Current State: 62:[100, 38], Operations: ['4*25=100', '73-35=38'] Exploring Operation: 100-38=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[4, 25, 73, 35], Operations: [] Exploring Operation: 25+35=60, Resulting Numbers: [4, 73, 60] Generated Node #0,0: 62:[4, 73, 60] Operation: 25+35=60 Moving to Node #0,0 Current State: 62:[4, 73, 60], Operations: ['25+35=60'] Exploring Operation: 73-4=69, Resulting Numbers: [60, 69] Generated Node #0,0,0: 62:[60, 69] Operation: 73-4=69 Moving to Node #0,0,0 Current State: 62:[60, 69], Operations: ['25+35=60', '73-4=69'] Exploring Operation: 69-60=9, Resulting Numbers: [9] 9,62 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 50, 55, 1, 56 ]
60
[ "55-50=5", "56-1=55", "5+55=60" ]
Current State: 60:[50, 55, 1, 56], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [1, 56, 5] Generated Node #2: [1, 56, 5] from Operation: 55-50=5 Current State: 60:[1, 56, 5], Operations: ['55-50=5'] Exploring Operation: 56-1=55, Resulting Numbers: [5, 55] Generated Node #3: [5, 55] from Operation: 56-1=55 Current State: 60:[5, 55], Operations: ['55-50=5', '56-1=55'] Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[50, 55, 1, 56], Operations: [] Exploring Operation: 55+1=56, Resulting Numbers: [50, 56, 56] Generated Node #0,0: 60:[50, 56, 56] Operation: 55+1=56 Exploring Operation: 55-50=5, Resulting Numbers: [1, 56, 5] Generated Node #0,1: 60:[1, 56, 5] Operation: 55-50=5 Exploring Operation: 50+1=51, Resulting Numbers: [55, 56, 51] Generated Node #0,2: 60:[55, 56, 51] Operation: 50+1=51 Exploring Operation: 56-55=1, Resulting Numbers: [50, 1, 1] Generated Node #0,3: 60:[50, 1, 1] Operation: 56-55=1 Exploring Operation: 56-50=6, Resulting Numbers: [55, 1, 6] Generated Node #0,4: 60:[55, 1, 6] Operation: 56-50=6 Moving to Node #0,1 Current State: 60:[1, 56, 5], Operations: ['55-50=5'] Exploring Operation: 56+5=61, Resulting Numbers: [1, 61] Generated Node #0,1,0: 60:[1, 61] Operation: 56+5=61 Exploring Operation: 1+5=6, Resulting Numbers: [56, 6] Generated Node #0,1,1: 60:[56, 6] Operation: 1+5=6 Exploring Operation: 1*56=56, Resulting Numbers: [5, 56] Generated Node #0,1,2: 60:[5, 56] Operation: 1*56=56 Exploring Operation: 1+56=57, Resulting Numbers: [5, 57] Generated Node #0,1,3: 60:[5, 57] Operation: 1+56=57 Exploring Operation: 56/1=56, Resulting Numbers: [5, 56] Generated Node #0,1,4: 60:[5, 56] Operation: 56/1=56 Moving to Node #0,4 Current State: 60:[55, 1, 6], Operations: ['56-50=6'] Exploring Operation: 55+1=56, Resulting Numbers: [6, 56] Generated Node #0,4,0: 60:[6, 56] Operation: 55+1=56 Exploring Operation: 55+6=61, Resulting Numbers: [1, 61] Generated Node #0,4,1: 60:[1, 61] Operation: 55+6=61 Exploring Operation: 55*1=55, Resulting Numbers: [6, 55] Generated Node #0,4,2: 60:[6, 55] Operation: 55*1=55 Exploring Operation: 55/1=55, Resulting Numbers: [6, 55] Generated Node #0,4,3: 60:[6, 55] Operation: 55/1=55 Exploring Operation: 1*6=6, Resulting Numbers: [55, 6] Generated Node #0,4,4: 60:[55, 6] Operation: 1*6=6 Moving to Node #0,3 Current State: 60:[50, 1, 1], Operations: ['56-55=1'] Exploring Operation: 50/1=50, Resulting Numbers: [1, 50] Generated Node #0,3,0: 60:[1, 50] Operation: 50/1=50 Exploring Operation: 1+1=2, Resulting Numbers: [50, 2] Generated Node #0,3,1: 60:[50, 2] Operation: 1+1=2 Exploring Operation: 50*1=50, Resulting Numbers: [1, 50] Generated Node #0,3,2: 60:[1, 50] Operation: 50*1=50 Exploring Operation: 50+1=51, Resulting Numbers: [1, 51] Generated Node #0,3,3: 60:[1, 51] Operation: 50+1=51 Exploring Operation: 50+1=51, Resulting Numbers: [1, 51] Generated Node #0,3,4: 60:[1, 51] Operation: 50+1=51 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 60:[50, 2], Operations: ['56-55=1', '1+1=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,60 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 #0,3,3 Current State: 60:[1, 51], Operations: ['56-55=1', '50+1=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,60 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 #0,3,4 Current State: 60:[1, 51], Operations: ['56-55=1', '50+1=51'] Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,60 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 #0,3,0 Current State: 60:[1, 50], Operations: ['56-55=1', '50/1=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,60 unequal: No Solution Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,60 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 #0,3,2 Current State: 60:[1, 50], Operations: ['56-55=1', '50*1=50'] Exploring Operation: 50/1=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 1+50=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,60 unequal: No Solution Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 60:[50, 56, 56], Operations: ['55+1=56'] Exploring Operation: 56-50=6, Resulting Numbers: [56, 6] Generated Node #0,0,0: 60:[56, 6] Operation: 56-50=6 Exploring Operation: 56/56=1, Resulting Numbers: [50, 1] Generated Node #0,0,1: 60:[50, 1] Operation: 56/56=1 Exploring Operation: 56-50=6, Resulting Numbers: [56, 6] Generated Node #0,0,2: 60:[56, 6] Operation: 56-50=6 Exploring Operation: 50+56=106, Resulting Numbers: [56, 106] Generated Node #0,0,3: 60:[56, 106] Operation: 50+56=106 Exploring Operation: 56-56=0, Resulting Numbers: [50, 0] Generated Node #0,0,4: 60:[50, 0] Operation: 56-56=0 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[56, 6], Operations: ['55+1=56', '56-50=6'] Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,60 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,60 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:[56, 6], Operations: ['55+1=56', '56-50=6'] Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,60 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,60 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:[50, 1], Operations: ['55+1=56', '56/56=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 50+1=51, Resulting Numbers: [51] 51,60 unequal: No Solution Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,60 unequal: No Solution Exploring Operation: 50/1=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 #0,0,4 Current State: 60:[50, 0], Operations: ['55+1=56', '56-56=0'] Exploring Operation: 50-0=50, Resulting Numbers: [50] 50,60 unequal: No Solution Exploring Operation: 50*0=0, Resulting Numbers: [0] 0,60 unequal: No Solution Exploring Operation: 50+0=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 #0,0,3 Current State: 60:[56, 106], Operations: ['55+1=56', '50+56=106'] Exploring Operation: 56*106=5936, Resulting Numbers: [5936] 5936,60 unequal: No Solution Exploring Operation: 56+106=162, Resulting Numbers: [162] 162,60 unequal: No Solution Exploring Operation: 106-56=50, Resulting Numbers: [50] 50,60 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:[55, 56, 51], Operations: ['50+1=51'] Exploring Operation: 55-51=4, Resulting Numbers: [56, 4] Generated Node #0,2,0: 60:[56, 4] Operation: 55-51=4 Exploring Operation: 55+51=106, Resulting Numbers: [56, 106] Generated Node #0,2,1: 60:[56, 106] Operation: 55+51=106 Exploring Operation: 56-51=5, Resulting Numbers: [55, 5] Generated Node #0,2,2: 60:[55, 5] Operation: 56-51=5 Exploring Operation: 56-55=1, Resulting Numbers: [51, 1] Generated Node #0,2,3: 60:[51, 1] Operation: 56-55=1 Exploring Operation: 56+51=107, Resulting Numbers: [55, 107] Generated Node #0,2,4: 60:[55, 107] Operation: 56+51=107 Moving to Node #0,1,0 Current State: 60:[1, 61], Operations: ['55-50=5', '56+5=61'] Exploring Operation: 1*61=61, Resulting Numbers: [61] 61,60 unequal: No Solution Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,60 unequal: No Solution Exploring Operation: 61/1=61, Resulting Numbers: [61] 61,60 unequal: No Solution Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[50, 55, 1, 56], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [1, 56, 5] Generated Node #0,1: 60:[1, 56, 5] Operation: 55-50=5 Moving to Node #0,1 Current State: 60:[1, 56, 5], Operations: ['55-50=5'] Exploring Operation: 56+5=61, Resulting Numbers: [1, 61] Generated Node #0,1,0: 60:[1, 61] Operation: 56+5=61 Moving to Node #0,1,0 Current State: 60:[1, 61], Operations: ['55-50=5', '56+5=61'] Exploring Operation: 61-1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.935764
hs_5
sum_heuristic
[ 18, 10, 45, 46 ]
43
[ "46-10=36", "36/18=2", "45-2=43" ]
Current State: 43:[18, 10, 45, 46], Operations: [] Exploring Operation: 46-10=36, Resulting Numbers: [18, 45, 36] Generated Node #2: [18, 45, 36] from Operation: 46-10=36 Current State: 43:[18, 45, 36], Operations: ['46-10=36'] Exploring Operation: 36/18=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 36/18=2 Current State: 43:[45, 2], Operations: ['46-10=36', '36/18=2'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[18, 10, 45, 46], Operations: [] Exploring Operation: 46-10=36, Resulting Numbers: [18, 45, 36] Generated Node #0,0: 43:[18, 45, 36] Operation: 46-10=36 Exploring Operation: 45-10=35, Resulting Numbers: [18, 46, 35] Generated Node #0,1: 43:[18, 46, 35] Operation: 45-10=35 Exploring Operation: 18+10=28, Resulting Numbers: [45, 46, 28] Generated Node #0,2: 43:[45, 46, 28] Operation: 18+10=28 Moving to Node #0,2 Current State: 43:[45, 46, 28], Operations: ['18+10=28'] Exploring Operation: 45+28=73, Resulting Numbers: [46, 73] Generated Node #0,2,0: 43:[46, 73] Operation: 45+28=73 Exploring Operation: 46-28=18, Resulting Numbers: [45, 18] Generated Node #0,2,1: 43:[45, 18] Operation: 46-28=18 Exploring Operation: 45-28=17, Resulting Numbers: [46, 17] Generated Node #0,2,2: 43:[46, 17] Operation: 45-28=17 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[45, 18], Operations: ['18+10=28', '46-28=18'] Exploring Operation: 45+18=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 45*18=810, Resulting Numbers: [810] 810,43 unequal: No Solution Exploring Operation: 45-18=27, Resulting Numbers: [27] 27,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[46, 17], Operations: ['18+10=28', '45-28=17'] Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,43 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,43 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[46, 73], Operations: ['18+10=28', '45+28=73'] Exploring Operation: 46+73=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 46*73=3358, Resulting Numbers: [3358] 3358,43 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 43:[18, 45, 36], Operations: ['46-10=36'] Exploring Operation: 18+36=54, Resulting Numbers: [45, 54] Generated Node #0,0,0: 43:[45, 54] Operation: 18+36=54 Exploring Operation: 18+45=63, Resulting Numbers: [36, 63] Generated Node #0,0,1: 43:[36, 63] Operation: 18+45=63 Exploring Operation: 45-18=27, Resulting Numbers: [36, 27] Generated Node #0,0,2: 43:[36, 27] Operation: 45-18=27 Moving to Node #0,1 Current State: 43:[18, 46, 35], Operations: ['45-10=35'] Exploring Operation: 18+46=64, Resulting Numbers: [35, 64] Generated Node #0,1,0: 43:[35, 64] Operation: 18+46=64 Exploring Operation: 18+35=53, Resulting Numbers: [46, 53] Generated Node #0,1,1: 43:[46, 53] Operation: 18+35=53 Exploring Operation: 46-18=28, Resulting Numbers: [35, 28] Generated Node #0,1,2: 43:[35, 28] Operation: 46-18=28 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[46, 53], Operations: ['45-10=35', '18+35=53'] Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,43 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[35, 28], Operations: ['45-10=35', '46-18=28'] Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[35, 64], Operations: ['45-10=35', '18+46=64'] Exploring Operation: 35+64=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,43 unequal: No Solution Exploring Operation: 35*64=2240, Resulting Numbers: [2240] 2240,43 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: 43:[45, 54], Operations: ['46-10=36', '18+36=54'] Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,43 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[36, 27], Operations: ['46-10=36', '45-18=27'] Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,43 unequal: No Solution Exploring Operation: 36*27=972, Resulting Numbers: [972] 972,43 unequal: No Solution Exploring Operation: 36+27=63, Resulting Numbers: [63] 63,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[36, 63], Operations: ['46-10=36', '18+45=63'] Exploring Operation: 36*63=2268, Resulting Numbers: [2268] 2268,43 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 36+63=99, Resulting Numbers: [99] 99,43 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 60, 50, 1, 51 ]
42
[ "60-50=10", "1+51=52", "52-10=42" ]
Current State: 42:[60, 50, 1, 51], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [1, 51, 10] Generated Node #2: [1, 51, 10] from Operation: 60-50=10 Current State: 42:[1, 51, 10], Operations: ['60-50=10'] Exploring Operation: 1+51=52, Resulting Numbers: [10, 52] Generated Node #3: [10, 52] from Operation: 1+51=52 Current State: 42:[10, 52], Operations: ['60-50=10', '1+51=52'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[60, 50, 1, 51], Operations: [] Exploring Operation: 60-1=59, Resulting Numbers: [50, 51, 59] Generated Node #0,0: 42:[50, 51, 59] Operation: 60-1=59 Exploring Operation: 51-50=1, Resulting Numbers: [60, 1, 1] Generated Node #0,1: 42:[60, 1, 1] Operation: 51-50=1 Exploring Operation: 60-50=10, Resulting Numbers: [1, 51, 10] Generated Node #0,2: 42:[1, 51, 10] Operation: 60-50=10 Exploring Operation: 60-51=9, Resulting Numbers: [50, 1, 9] Generated Node #0,3: 42:[50, 1, 9] Operation: 60-51=9 Moving to Node #0,3 Current State: 42:[50, 1, 9], Operations: ['60-51=9'] Exploring Operation: 50-9=41, Resulting Numbers: [1, 41] Generated Node #0,3,0: 42:[1, 41] Operation: 50-9=41 Exploring Operation: 9-1=8, Resulting Numbers: [50, 8] Generated Node #0,3,1: 42:[50, 8] Operation: 9-1=8 Exploring Operation: 50*1=50, Resulting Numbers: [9, 50] Generated Node #0,3,2: 42:[9, 50] Operation: 50*1=50 Exploring Operation: 50-1=49, Resulting Numbers: [9, 49] Generated Node #0,3,3: 42:[9, 49] Operation: 50-1=49 Moving to Node #0,2 Current State: 42:[1, 51, 10], Operations: ['60-50=10'] Exploring Operation: 1*51=51, Resulting Numbers: [10, 51] Generated Node #0,2,0: 42:[10, 51] Operation: 1*51=51 Exploring Operation: 51-10=41, Resulting Numbers: [1, 41] Generated Node #0,2,1: 42:[1, 41] Operation: 51-10=41 Exploring Operation: 10-1=9, Resulting Numbers: [51, 9] Generated Node #0,2,2: 42:[51, 9] Operation: 10-1=9 Exploring Operation: 51-1=50, Resulting Numbers: [10, 50] Generated Node #0,2,3: 42:[10, 50] Operation: 51-1=50 Moving to Node #0,1 Current State: 42:[60, 1, 1], Operations: ['51-50=1'] Exploring Operation: 1+1=2, Resulting Numbers: [60, 2] Generated Node #0,1,0: 42:[60, 2] Operation: 1+1=2 Exploring Operation: 60-1=59, Resulting Numbers: [1, 59] Generated Node #0,1,1: 42:[1, 59] Operation: 60-1=59 Exploring Operation: 60*1=60, Resulting Numbers: [1, 60] Generated Node #0,1,2: 42:[1, 60] Operation: 60*1=60 Exploring Operation: 60-1=59, Resulting Numbers: [1, 59] Generated Node #0,1,3: 42:[1, 59] Operation: 60-1=59 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 42:[60, 2], Operations: ['51-50=1', '1+1=2'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 60*2=120, Resulting Numbers: [120] 120,42 unequal: No Solution Exploring Operation: 60+2=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[1, 59], Operations: ['51-50=1', '60-1=59'] Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 1*59=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 42:[1, 59], Operations: ['51-50=1', '60-1=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 1*59=59, Resulting Numbers: [59] 59,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[1, 60], Operations: ['51-50=1', '60*1=60'] Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 1+60=61, Resulting Numbers: [61] 61,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 42:[50, 51, 59], Operations: ['60-1=59'] Exploring Operation: 59-50=9, Resulting Numbers: [51, 9] Generated Node #0,0,0: 42:[51, 9] Operation: 59-50=9 Exploring Operation: 59-51=8, Resulting Numbers: [50, 8] Generated Node #0,0,1: 42:[50, 8] Operation: 59-51=8 Exploring Operation: 51-50=1, Resulting Numbers: [59, 1] Generated Node #0,0,2: 42:[59, 1] Operation: 51-50=1 Exploring Operation: 50+51=101, Resulting Numbers: [59, 101] Generated Node #0,0,3: 42:[59, 101] Operation: 50+51=101 Moving to Node #0,3,0 Current State: 42:[1, 41], Operations: ['60-51=9', '50-9=41'] Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[60, 50, 1, 51], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [50, 1, 9] Generated Node #0,3: 42:[50, 1, 9] Operation: 60-51=9 Moving to Node #0,3 Current State: 42:[50, 1, 9], Operations: ['60-51=9'] Exploring Operation: 50-9=41, Resulting Numbers: [1, 41] Generated Node #0,3,0: 42:[1, 41] Operation: 50-9=41 Moving to Node #0,3,0 Current State: 42:[1, 41], Operations: ['60-51=9', '50-9=41'] Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.96441
hs_4
sum_heuristic
[ 28, 28, 48, 51 ]
98
[ "28/28=1", "48+51=99", "99-1=98" ]
Current State: 98:[28, 28, 48, 51], Operations: [] Exploring Operation: 28/28=1, Resulting Numbers: [48, 51, 1] Generated Node #2: [48, 51, 1] from Operation: 28/28=1 Current State: 98:[48, 51, 1], Operations: ['28/28=1'] Exploring Operation: 48+51=99, Resulting Numbers: [1, 99] Generated Node #3: [1, 99] from Operation: 48+51=99 Current State: 98:[1, 99], Operations: ['28/28=1', '48+51=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[28, 28, 48, 51], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [28, 51, 20] Generated Node #0,0: 98:[28, 51, 20] Operation: 48-28=20 Exploring Operation: 48-28=20, Resulting Numbers: [28, 51, 20] Generated Node #0,1: 98:[28, 51, 20] Operation: 48-28=20 Exploring Operation: 28+28=56, Resulting Numbers: [48, 51, 56] Generated Node #0,2: 98:[48, 51, 56] Operation: 28+28=56 Exploring Operation: 28-28=0, Resulting Numbers: [48, 51, 0] Generated Node #0,3: 98:[48, 51, 0] Operation: 28-28=0 Exploring Operation: 28/28=1, Resulting Numbers: [48, 51, 1] Generated Node #0,4: 98:[48, 51, 1] Operation: 28/28=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 98:[48, 51, 1], Operations: ['28/28=1'] Exploring Operation: 48+51=99, Resulting Numbers: [1, 99] Generated Node #0,4,0: 98:[1, 99] Operation: 48+51=99 Exploring Operation: 48*1=48, Resulting Numbers: [51, 48] Generated Node #0,4,1: 98:[51, 48] Operation: 48*1=48 Exploring Operation: 48+1=49, Resulting Numbers: [51, 49] Generated Node #0,4,2: 98:[51, 49] Operation: 48+1=49 Exploring Operation: 51-48=3, Resulting Numbers: [1, 3] Generated Node #0,4,3: 98:[1, 3] Operation: 51-48=3 Exploring Operation: 51-1=50, Resulting Numbers: [48, 50] Generated Node #0,4,4: 98:[48, 50] Operation: 51-1=50 Moving to Node #0,4,0 Current State: 98:[1, 99], Operations: ['28/28=1', '48+51=99'] Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[28, 28, 48, 51], Operations: [] Exploring Operation: 28/28=1, Resulting Numbers: [48, 51, 1] Generated Node #0,4: 98:[48, 51, 1] Operation: 28/28=1 Moving to Node #0,4 Current State: 98:[48, 51, 1], Operations: ['28/28=1'] Exploring Operation: 48+51=99, Resulting Numbers: [1, 99] Generated Node #0,4,0: 98:[1, 99] Operation: 48+51=99 Moving to Node #0,4,0 Current State: 98:[1, 99], Operations: ['28/28=1', '48+51=99'] Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 21, 16, 44, 89 ]
50
[ "21-16=5", "89-44=45", "5+45=50" ]
Current State: 50:[21, 16, 44, 89], Operations: [] Exploring Operation: 21-16=5, Resulting Numbers: [44, 89, 5] Generated Node #2: [44, 89, 5] from Operation: 21-16=5 Current State: 50:[44, 89, 5], Operations: ['21-16=5'] Exploring Operation: 89-44=45, Resulting Numbers: [5, 45] Generated Node #3: [5, 45] from Operation: 89-44=45 Current State: 50:[5, 45], Operations: ['21-16=5', '89-44=45'] Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[21, 16, 44, 89], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [21, 16, 45] Generated Node #0,0: 50:[21, 16, 45] Operation: 89-44=45 Moving to Node #0,0 Current State: 50:[21, 16, 45], Operations: ['89-44=45'] Exploring Operation: 21-16=5, Resulting Numbers: [45, 5] Generated Node #0,0,0: 50:[45, 5] Operation: 21-16=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 50:[45, 5], Operations: ['89-44=45', '21-16=5'] Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[21, 16, 44, 89], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [21, 16, 45] Generated Node #0,0: 50:[21, 16, 45] Operation: 89-44=45 Moving to Node #0,0 Current State: 50:[21, 16, 45], Operations: ['89-44=45'] Exploring Operation: 21-16=5, Resulting Numbers: [45, 5] Generated Node #0,0,0: 50:[45, 5] Operation: 21-16=5 Moving to Node #0,0,0 Current State: 50:[45, 5], Operations: ['89-44=45', '21-16=5'] Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 18, 81, 6, 65 ]
40
[ "18+81=99", "65-6=59", "99-59=40" ]
Current State: 40:[18, 81, 6, 65], Operations: [] Exploring Operation: 18+81=99, Resulting Numbers: [6, 65, 99] Generated Node #2: [6, 65, 99] from Operation: 18+81=99 Current State: 40:[6, 65, 99], Operations: ['18+81=99'] Exploring Operation: 65-6=59, Resulting Numbers: [99, 59] Generated Node #3: [99, 59] from Operation: 65-6=59 Current State: 40:[99, 59], Operations: ['18+81=99', '65-6=59'] Exploring Operation: 99-59=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[18, 81, 6, 65], Operations: [] Exploring Operation: 81-18=63, Resulting Numbers: [6, 65, 63] Generated Node #0,0: 40:[6, 65, 63] Operation: 81-18=63 Exploring Operation: 81-65=16, Resulting Numbers: [18, 6, 16] Generated Node #0,1: 40:[18, 6, 16] Operation: 81-65=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[18, 6, 16], Operations: ['81-65=16'] Exploring Operation: 16-6=10, Resulting Numbers: [18, 10] Generated Node #0,1,0: 40:[18, 10] Operation: 16-6=10 Exploring Operation: 18-16=2, Resulting Numbers: [6, 2] Generated Node #0,1,1: 40:[6, 2] Operation: 18-16=2 Moving to Node #0,1,1 Current State: 40:[6, 2], Operations: ['81-65=16', '18-16=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[18, 10], Operations: ['81-65=16', '16-6=10'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[6, 65, 63], Operations: ['81-18=63'] Exploring Operation: 65-63=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 40:[6, 2] Operation: 65-63=2 Exploring Operation: 65-6=59, Resulting Numbers: [63, 59] Generated Node #0,0,1: 40:[63, 59] Operation: 65-6=59 Moving to Node #0,0,0 Current State: 40:[6, 2], Operations: ['81-18=63', '65-63=2'] Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[63, 59], Operations: ['81-18=63', '65-6=59'] Exploring Operation: 63+59=122, Resulting Numbers: [122] 122,40 unequal: No Solution Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,40 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
[ 58, 24, 13, 12 ]
81
[ "58+24=82", "13-12=1", "82-1=81" ]
Current State: 81:[58, 24, 13, 12], Operations: [] Exploring Operation: 58+24=82, Resulting Numbers: [13, 12, 82] Generated Node #2: [13, 12, 82] from Operation: 58+24=82 Current State: 81:[13, 12, 82], Operations: ['58+24=82'] Exploring Operation: 13-12=1, Resulting Numbers: [82, 1] Generated Node #3: [82, 1] from Operation: 13-12=1 Current State: 81:[82, 1], Operations: ['58+24=82', '13-12=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[58, 24, 13, 12], Operations: [] Exploring Operation: 58+13=71, Resulting Numbers: [24, 12, 71] Generated Node #0,0: 81:[24, 12, 71] Operation: 58+13=71 Exploring Operation: 58-13=45, Resulting Numbers: [24, 12, 45] Generated Node #0,1: 81:[24, 12, 45] Operation: 58-13=45 Exploring Operation: 58+24=82, Resulting Numbers: [13, 12, 82] Generated Node #0,2: 81:[13, 12, 82] Operation: 58+24=82 Exploring Operation: 58+12=70, Resulting Numbers: [24, 13, 70] Generated Node #0,3: 81:[24, 13, 70] Operation: 58+12=70 Exploring Operation: 58-24=34, Resulting Numbers: [13, 12, 34] Generated Node #0,4: 81:[13, 12, 34] Operation: 58-24=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[13, 12, 82], Operations: ['58+24=82'] Exploring Operation: 13+82=95, Resulting Numbers: [12, 95] Generated Node #0,2,0: 81:[12, 95] Operation: 13+82=95 Exploring Operation: 13+12=25, Resulting Numbers: [82, 25] Generated Node #0,2,1: 81:[82, 25] Operation: 13+12=25 Exploring Operation: 13-12=1, Resulting Numbers: [82, 1] Generated Node #0,2,2: 81:[82, 1] Operation: 13-12=1 Exploring Operation: 82-12=70, Resulting Numbers: [13, 70] Generated Node #0,2,3: 81:[13, 70] Operation: 82-12=70 Exploring Operation: 82-13=69, Resulting Numbers: [12, 69] Generated Node #0,2,4: 81:[12, 69] Operation: 82-13=69 Moving to Node #0,2,1 Current State: 81:[82, 25], Operations: ['58+24=82', '13+12=25'] Exploring Operation: 82+25=107, Resulting Numbers: [107] 107,81 unequal: No Solution Exploring Operation: 82*25=2050, Resulting Numbers: [2050] 2050,81 unequal: No Solution Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[82, 1], Operations: ['58+24=82', '13-12=1'] Exploring Operation: 82+1=83, Resulting Numbers: [83] 83,81 unequal: No Solution Exploring Operation: 82/1=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[58, 24, 13, 12], Operations: [] Exploring Operation: 58+24=82, Resulting Numbers: [13, 12, 82] Generated Node #0,2: 81:[13, 12, 82] Operation: 58+24=82 Moving to Node #0,2 Current State: 81:[13, 12, 82], Operations: ['58+24=82'] Exploring Operation: 13-12=1, Resulting Numbers: [82, 1] Generated Node #0,2,2: 81:[82, 1] Operation: 13-12=1 Moving to Node #0,2,2 Current State: 81:[82, 1], Operations: ['58+24=82', '13-12=1'] Exploring Operation: 82-1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 5, 25, 63, 55 ]
13
[ "25/5=5", "63-55=8", "5+8=13" ]
Current State: 13:[5, 25, 63, 55], Operations: [] Exploring Operation: 25/5=5, Resulting Numbers: [63, 55, 5] Generated Node #2: [63, 55, 5] from Operation: 25/5=5 Current State: 13:[63, 55, 5], Operations: ['25/5=5'] Exploring Operation: 63-55=8, Resulting Numbers: [5, 8] Generated Node #3: [5, 8] from Operation: 63-55=8 Current State: 13:[5, 8], Operations: ['25/5=5', '63-55=8'] Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[5, 25, 63, 55], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [5, 25, 8] Generated Node #0,0: 13:[5, 25, 8] Operation: 63-55=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[5, 25, 8], Operations: ['63-55=8'] Exploring Operation: 25-5=20, Resulting Numbers: [8, 20] Generated Node #0,0,0: 13:[8, 20] Operation: 25-5=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[8, 20], Operations: ['63-55=8', '25-5=20'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 93, 29, 19, 86 ]
96
[ "86-29=57", "57/19=3", "93+3=96" ]
Current State: 96:[93, 29, 19, 86], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [93, 19, 57] Generated Node #2: [93, 19, 57] from Operation: 86-29=57 Current State: 96:[93, 19, 57], Operations: ['86-29=57'] Exploring Operation: 57/19=3, Resulting Numbers: [93, 3] Generated Node #3: [93, 3] from Operation: 57/19=3 Current State: 96:[93, 3], Operations: ['86-29=57', '57/19=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[93, 29, 19, 86], Operations: [] Exploring Operation: 93-86=7, Resulting Numbers: [29, 19, 7] Generated Node #0,0: 96:[29, 19, 7] Operation: 93-86=7 Exploring Operation: 29+19=48, Resulting Numbers: [93, 86, 48] Generated Node #0,1: 96:[93, 86, 48] Operation: 29+19=48 Exploring Operation: 86-29=57, Resulting Numbers: [93, 19, 57] Generated Node #0,2: 96:[93, 19, 57] Operation: 86-29=57 Exploring Operation: 29-19=10, Resulting Numbers: [93, 86, 10] Generated Node #0,3: 96:[93, 86, 10] Operation: 29-19=10 Moving to Node #0,0 Current State: 96:[29, 19, 7], Operations: ['93-86=7'] Exploring Operation: 29+19=48, Resulting Numbers: [7, 48] Generated Node #0,0,0: 96:[7, 48] Operation: 29+19=48 Exploring Operation: 19-7=12, Resulting Numbers: [29, 12] Generated Node #0,0,1: 96:[29, 12] Operation: 19-7=12 Exploring Operation: 29-19=10, Resulting Numbers: [7, 10] Generated Node #0,0,2: 96:[7, 10] Operation: 29-19=10 Exploring Operation: 29-7=22, Resulting Numbers: [19, 22] Generated Node #0,0,3: 96:[19, 22] Operation: 29-7=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[7, 48], Operations: ['93-86=7', '29+19=48'] Exploring Operation: 7*48=336, Resulting Numbers: [336] 336,96 unequal: No Solution Exploring Operation: 48-7=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 7+48=55, Resulting Numbers: [55] 55,96 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 #0,0,1 Current State: 96:[29, 12], Operations: ['93-86=7', '19-7=12'] Exploring Operation: 29*12=348, Resulting Numbers: [348] 348,96 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,96 unequal: No Solution Exploring Operation: 29+12=41, Resulting Numbers: [41] 41,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[7, 10], Operations: ['93-86=7', '29-19=10'] Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,96 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 #0,0,3 Current State: 96:[19, 22], Operations: ['93-86=7', '29-7=22'] Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,96 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,96 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,96 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: 96:[93, 86, 48], Operations: ['29+19=48'] Exploring Operation: 93-86=7, Resulting Numbers: [48, 7] Generated Node #0,1,0: 96:[48, 7] Operation: 93-86=7 Exploring Operation: 86+48=134, Resulting Numbers: [93, 134] Generated Node #0,1,1: 96:[93, 134] Operation: 86+48=134 Exploring Operation: 86-48=38, Resulting Numbers: [93, 38] Generated Node #0,1,2: 96:[93, 38] Operation: 86-48=38 Exploring Operation: 93-48=45, Resulting Numbers: [86, 45] Generated Node #0,1,3: 96:[86, 45] Operation: 93-48=45 Moving to Node #0,3 Current State: 96:[93, 86, 10], Operations: ['29-19=10'] Exploring Operation: 93-86=7, Resulting Numbers: [10, 7] Generated Node #0,3,0: 96:[10, 7] Operation: 93-86=7 Exploring Operation: 93-10=83, Resulting Numbers: [86, 83] Generated Node #0,3,1: 96:[86, 83] Operation: 93-10=83 Exploring Operation: 86+10=96, Resulting Numbers: [93, 96] Generated Node #0,3,2: 96:[93, 96] Operation: 86+10=96 Exploring Operation: 93+10=103, Resulting Numbers: [86, 103] Generated Node #0,3,3: 96:[86, 103] Operation: 93+10=103 Moving to Node #0,2 Current State: 96:[93, 19, 57], Operations: ['86-29=57'] Exploring Operation: 57/19=3, Resulting Numbers: [93, 3] Generated Node #0,2,0: 96:[93, 3] Operation: 57/19=3 Exploring Operation: 93-57=36, Resulting Numbers: [19, 36] Generated Node #0,2,1: 96:[19, 36] Operation: 93-57=36 Exploring Operation: 19+57=76, Resulting Numbers: [93, 76] Generated Node #0,2,2: 96:[93, 76] Operation: 19+57=76 Exploring Operation: 57-19=38, Resulting Numbers: [93, 38] Generated Node #0,2,3: 96:[93, 38] Operation: 57-19=38 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[93, 3], Operations: ['86-29=57', '57/19=3'] Exploring Operation: 93-3=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,96 unequal: No Solution Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[93, 29, 19, 86], Operations: [] Exploring Operation: 86-29=57, Resulting Numbers: [93, 19, 57] Generated Node #0,2: 96:[93, 19, 57] Operation: 86-29=57 Moving to Node #0,2 Current State: 96:[93, 19, 57], Operations: ['86-29=57'] Exploring Operation: 57/19=3, Resulting Numbers: [93, 3] Generated Node #0,2,0: 96:[93, 3] Operation: 57/19=3 Moving to Node #0,2,0 Current State: 96:[93, 3], Operations: ['86-29=57', '57/19=3'] Exploring Operation: 93+3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
mult_heuristic
[ 52, 72, 78, 95 ]
47
[ "52*72=3744", "3744/78=48", "95-48=47" ]
Current State: 47:[52, 72, 78, 95], Operations: [] Exploring Operation: 52*72=3744, Resulting Numbers: [78, 95, 3744] Generated Node #2: [78, 95, 3744] from Operation: 52*72=3744 Current State: 47:[78, 95, 3744], Operations: ['52*72=3744'] Exploring Operation: 3744/78=48, Resulting Numbers: [95, 48] Generated Node #3: [95, 48] from Operation: 3744/78=48 Current State: 47:[95, 48], Operations: ['52*72=3744', '3744/78=48'] Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[52, 72, 78, 95], Operations: [] Exploring Operation: 95-52=43, Resulting Numbers: [72, 78, 43] Generated Node #0,0: 47:[72, 78, 43] Operation: 95-52=43 Moving to Node #0,0 Current State: 47:[72, 78, 43], Operations: ['95-52=43'] Exploring Operation: 78-43=35, Resulting Numbers: [72, 35] Generated Node #0,0,0: 47:[72, 35] Operation: 78-43=35 Moving to Node #0,0,0 Current State: 47:[72, 35], Operations: ['95-52=43', '78-43=35'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,47 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 31, 2, 46, 54 ]
24
[ "46-31=15", "2*15=30", "54-30=24" ]
Current State: 24:[31, 2, 46, 54], Operations: [] Exploring Operation: 46-31=15, Resulting Numbers: [2, 54, 15] Generated Node #2: [2, 54, 15] from Operation: 46-31=15 Current State: 24:[2, 54, 15], Operations: ['46-31=15'] Exploring Operation: 2*15=30, Resulting Numbers: [54, 30] Generated Node #3: [54, 30] from Operation: 2*15=30 Current State: 24:[54, 30], Operations: ['46-31=15', '2*15=30'] Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[31, 2, 46, 54], Operations: [] Exploring Operation: 54-31=23, Resulting Numbers: [2, 46, 23] Generated Node #0,0: 24:[2, 46, 23] Operation: 54-31=23 Exploring Operation: 54-46=8, Resulting Numbers: [31, 2, 8] Generated Node #0,1: 24:[31, 2, 8] Operation: 54-46=8 Moving to Node #0,1 Current State: 24:[31, 2, 8], Operations: ['54-46=8'] Exploring Operation: 31-8=23, Resulting Numbers: [2, 23] Generated Node #0,1,0: 24:[2, 23] Operation: 31-8=23 Exploring Operation: 31-2=29, Resulting Numbers: [8, 29] Generated Node #0,1,1: 24:[8, 29] Operation: 31-2=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[2, 23], Operations: ['54-46=8', '31-8=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,24 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,24 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 #0,1,1 Current State: 24:[8, 29], Operations: ['54-46=8', '31-2=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,24 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,24 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: 24:[2, 46, 23], Operations: ['54-31=23'] Exploring Operation: 46/23=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 24:[2, 2] Operation: 46/23=2 Exploring Operation: 46-23=23, Resulting Numbers: [2, 23] Generated Node #0,0,1: 24:[2, 23] Operation: 46-23=23 Moving to Node #0,0,0 Current State: 24:[2, 2], Operations: ['54-31=23', '46/23=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[2, 23], Operations: ['54-31=23', '46-23=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,24 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,24 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 26, 87, 20, 4 ]
85
[ "87-26=61", "20+4=24", "61+24=85" ]
Current State: 85:[26, 87, 20, 4], Operations: [] Exploring Operation: 87-26=61, Resulting Numbers: [20, 4, 61] Generated Node #2: [20, 4, 61] from Operation: 87-26=61 Current State: 85:[20, 4, 61], Operations: ['87-26=61'] Exploring Operation: 20+4=24, Resulting Numbers: [61, 24] Generated Node #3: [61, 24] from Operation: 20+4=24 Current State: 85:[61, 24], Operations: ['87-26=61', '20+4=24'] Exploring Operation: 61+24=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[26, 87, 20, 4], Operations: [] Exploring Operation: 26-4=22, Resulting Numbers: [87, 20, 22] Generated Node #0,0: 85:[87, 20, 22] Operation: 26-4=22 Exploring Operation: 26-20=6, Resulting Numbers: [87, 4, 6] Generated Node #0,1: 85:[87, 4, 6] Operation: 26-20=6 Moving to Node #0,1 Current State: 85:[87, 4, 6], Operations: ['26-20=6'] Exploring Operation: 87-6=81, Resulting Numbers: [4, 81] Generated Node #0,1,0: 85:[4, 81] Operation: 87-6=81 Exploring Operation: 87-4=83, Resulting Numbers: [6, 83] Generated Node #0,1,1: 85:[6, 83] Operation: 87-4=83 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[6, 83], Operations: ['26-20=6', '87-4=83'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,85 unequal: No Solution Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[4, 81], Operations: ['26-20=6', '87-6=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[26, 87, 20, 4], Operations: [] Exploring Operation: 26-20=6, Resulting Numbers: [87, 4, 6] Generated Node #0,1: 85:[87, 4, 6] Operation: 26-20=6 Moving to Node #0,1 Current State: 85:[87, 4, 6], Operations: ['26-20=6'] Exploring Operation: 87-6=81, Resulting Numbers: [4, 81] Generated Node #0,1,0: 85:[4, 81] Operation: 87-6=81 Moving to Node #0,1,0 Current State: 85:[4, 81], Operations: ['26-20=6', '87-6=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 89, 44, 71, 90 ]
49
[ "89-71=18", "90/18=5", "44+5=49" ]
Current State: 49:[89, 44, 71, 90], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [44, 90, 18] Generated Node #2: [44, 90, 18] from Operation: 89-71=18 Current State: 49:[44, 90, 18], Operations: ['89-71=18'] Exploring Operation: 90/18=5, Resulting Numbers: [44, 5] Generated Node #3: [44, 5] from Operation: 90/18=5 Current State: 49:[44, 5], Operations: ['89-71=18', '90/18=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[89, 44, 71, 90], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [44, 90, 18] Generated Node #0,0: 49:[44, 90, 18] Operation: 89-71=18 Exploring Operation: 90-89=1, Resulting Numbers: [44, 71, 1] Generated Node #0,1: 49:[44, 71, 1] Operation: 90-89=1 Moving to Node #0,1 Current State: 49:[44, 71, 1], Operations: ['90-89=1'] Exploring Operation: 71-44=27, Resulting Numbers: [1, 27] Generated Node #0,1,0: 49:[1, 27] Operation: 71-44=27 Exploring Operation: 44+1=45, Resulting Numbers: [71, 45] Generated Node #0,1,1: 49:[71, 45] Operation: 44+1=45 Moving to Node #0,0 Current State: 49:[44, 90, 18], Operations: ['89-71=18'] Exploring Operation: 90/18=5, Resulting Numbers: [44, 5] Generated Node #0,0,0: 49:[44, 5] Operation: 90/18=5 Exploring Operation: 90-44=46, Resulting Numbers: [18, 46] Generated Node #0,0,1: 49:[18, 46] Operation: 90-44=46 Moving to Node #0,0,0 Current State: 49:[44, 5], Operations: ['89-71=18', '90/18=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[89, 44, 71, 90], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [44, 90, 18] Generated Node #0,0: 49:[44, 90, 18] Operation: 89-71=18 Moving to Node #0,0 Current State: 49:[44, 90, 18], Operations: ['89-71=18'] Exploring Operation: 90/18=5, Resulting Numbers: [44, 5] Generated Node #0,0,0: 49:[44, 5] Operation: 90/18=5 Moving to Node #0,0,0 Current State: 49:[44, 5], Operations: ['89-71=18', '90/18=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 56, 31, 99, 20 ]
54
[ "56-31=25", "99-20=79", "79-25=54" ]
Current State: 54:[56, 31, 99, 20], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [99, 20, 25] Generated Node #2: [99, 20, 25] from Operation: 56-31=25 Current State: 54:[99, 20, 25], Operations: ['56-31=25'] Exploring Operation: 99-20=79, Resulting Numbers: [25, 79] Generated Node #3: [25, 79] from Operation: 99-20=79 Current State: 54:[25, 79], Operations: ['56-31=25', '99-20=79'] Exploring Operation: 79-25=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[56, 31, 99, 20], Operations: [] Exploring Operation: 99-31=68, Resulting Numbers: [56, 20, 68] Generated Node #0,0: 54:[56, 20, 68] Operation: 99-31=68 Exploring Operation: 99-56=43, Resulting Numbers: [31, 20, 43] Generated Node #0,1: 54:[31, 20, 43] Operation: 99-56=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[31, 20, 43], Operations: ['99-56=43'] Exploring Operation: 43-20=23, Resulting Numbers: [31, 23] Generated Node #0,1,0: 54:[31, 23] Operation: 43-20=23 Exploring Operation: 43-31=12, Resulting Numbers: [20, 12] Generated Node #0,1,1: 54:[20, 12] Operation: 43-31=12 Moving to Node #0,1,1 Current State: 54:[20, 12], Operations: ['99-56=43', '43-31=12'] Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[31, 23], Operations: ['99-56=43', '43-20=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[56, 31, 99, 20], Operations: [] Exploring Operation: 99-56=43, Resulting Numbers: [31, 20, 43] Generated Node #0,1: 54:[31, 20, 43] Operation: 99-56=43 Moving to Node #0,1 Current State: 54:[31, 20, 43], Operations: ['99-56=43'] Exploring Operation: 43-20=23, Resulting Numbers: [31, 23] Generated Node #0,1,0: 54:[31, 23] Operation: 43-20=23 Moving to Node #0,1,0 Current State: 54:[31, 23], Operations: ['99-56=43', '43-20=23'] Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 74, 67, 23, 67 ]
74
[ "67-67=0", "23*0=0", "74+0=74" ]
Current State: 74:[74, 67, 23, 67], Operations: [] Exploring Operation: 67-67=0, Resulting Numbers: [74, 23, 0] Generated Node #2: [74, 23, 0] from Operation: 67-67=0 Current State: 74:[74, 23, 0], Operations: ['67-67=0'] Exploring Operation: 23*0=0, Resulting Numbers: [74, 0] Generated Node #3: [74, 0] from Operation: 23*0=0 Current State: 74:[74, 0], Operations: ['67-67=0', '23*0=0'] Exploring Operation: 74+0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[74, 67, 23, 67], Operations: [] Exploring Operation: 67-67=0, Resulting Numbers: [74, 23, 0] Generated Node #0,0: 74:[74, 23, 0] Operation: 67-67=0 Exploring Operation: 67-23=44, Resulting Numbers: [74, 67, 44] Generated Node #0,1: 74:[74, 67, 44] Operation: 67-23=44 Exploring Operation: 67/67=1, Resulting Numbers: [74, 23, 1] Generated Node #0,2: 74:[74, 23, 1] Operation: 67/67=1 Exploring Operation: 67-23=44, Resulting Numbers: [74, 67, 44] Generated Node #0,3: 74:[74, 67, 44] Operation: 67-23=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[74, 67, 44], Operations: ['67-23=44'] Exploring Operation: 67-44=23, Resulting Numbers: [74, 23] Generated Node #0,1,0: 74:[74, 23] Operation: 67-44=23 Exploring Operation: 74-67=7, Resulting Numbers: [44, 7] Generated Node #0,1,1: 74:[44, 7] Operation: 74-67=7 Exploring Operation: 74-44=30, Resulting Numbers: [67, 30] Generated Node #0,1,2: 74:[67, 30] Operation: 74-44=30 Exploring Operation: 67+44=111, Resulting Numbers: [74, 111] Generated Node #0,1,3: 74:[74, 111] Operation: 67+44=111 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 74:[44, 7], Operations: ['67-23=44', '74-67=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,74 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,74 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[74, 23], Operations: ['67-23=44', '67-44=23'] Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,74 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 74:[67, 30], Operations: ['67-23=44', '74-44=30'] Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,74 unequal: No Solution Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 74:[74, 111], Operations: ['67-23=44', '67+44=111'] Exploring Operation: 74*111=8214, Resulting Numbers: [8214] 8214,74 unequal: No Solution Exploring Operation: 74+111=185, Resulting Numbers: [185] 185,74 unequal: No Solution Exploring Operation: 111-74=37, Resulting Numbers: [37] 37,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 74:[74, 67, 44], Operations: ['67-23=44'] Exploring Operation: 74-44=30, Resulting Numbers: [67, 30] Generated Node #0,3,0: 74:[67, 30] Operation: 74-44=30 Exploring Operation: 74-67=7, Resulting Numbers: [44, 7] Generated Node #0,3,1: 74:[44, 7] Operation: 74-67=7 Exploring Operation: 67-44=23, Resulting Numbers: [74, 23] Generated Node #0,3,2: 74:[74, 23] Operation: 67-44=23 Exploring Operation: 67+44=111, Resulting Numbers: [74, 111] Generated Node #0,3,3: 74:[74, 111] Operation: 67+44=111 Moving to Node #0,3,1 Current State: 74:[44, 7], Operations: ['67-23=44', '74-67=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,74 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,74 unequal: No Solution Moving to Node #0,3,2 Current State: 74:[74, 23], Operations: ['67-23=44', '67-44=23'] Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,74 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,74 unequal: No Solution Moving to Node #0,3,0 Current State: 74:[67, 30], Operations: ['67-23=44', '74-44=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,74 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,74 unequal: No Solution Moving to Node #0,3,3 Current State: 74:[74, 111], Operations: ['67-23=44', '67+44=111'] Exploring Operation: 74*111=8214, Resulting Numbers: [8214] 8214,74 unequal: No Solution Exploring Operation: 74+111=185, Resulting Numbers: [185] 185,74 unequal: No Solution Exploring Operation: 111-74=37, Resulting Numbers: [37] 37,74 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 #0,2 Current State: 74:[74, 23, 1], Operations: ['67/67=1'] Exploring Operation: 23*1=23, Resulting Numbers: [74, 23] Generated Node #0,2,0: 74:[74, 23] Operation: 23*1=23 Exploring Operation: 74/1=74, Resulting Numbers: [23, 74] Generated Node #0,2,1: 74:[23, 74] Operation: 74/1=74 Exploring Operation: 74*1=74, Resulting Numbers: [23, 74] Generated Node #0,2,2: 74:[23, 74] Operation: 74*1=74 Exploring Operation: 23+1=24, Resulting Numbers: [74, 24] Generated Node #0,2,3: 74:[74, 24] Operation: 23+1=24 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 74:[74, 24], Operations: ['67/67=1', '23+1=24'] Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,74 unequal: No Solution Exploring Operation: 74*24=1776, Resulting Numbers: [1776] 1776,74 unequal: No Solution Exploring Operation: 74+24=98, Resulting Numbers: [98] 98,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[74, 23], Operations: ['67/67=1', '23*1=23'] Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,74 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[23, 74], Operations: ['67/67=1', '74/1=74'] Exploring Operation: 23*74=1702, Resulting Numbers: [1702] 1702,74 unequal: No Solution Exploring Operation: 23+74=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[23, 74], Operations: ['67/67=1', '74*1=74'] Exploring Operation: 23+74=97, Resulting Numbers: [97] 97,74 unequal: No Solution Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 23*74=1702, Resulting Numbers: [1702] 1702,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[74, 23, 0], Operations: ['67-67=0'] Exploring Operation: 74+0=74, Resulting Numbers: [23, 74] Generated Node #0,0,0: 74:[23, 74] Operation: 74+0=74 Exploring Operation: 23+0=23, Resulting Numbers: [74, 23] Generated Node #0,0,1: 74:[74, 23] Operation: 23+0=23 Exploring Operation: 23*0=0, Resulting Numbers: [74, 0] Generated Node #0,0,2: 74:[74, 0] Operation: 23*0=0 Exploring Operation: 74-0=74, Resulting Numbers: [23, 74] Generated Node #0,0,3: 74:[23, 74] Operation: 74-0=74 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 74:[74, 0], Operations: ['67-67=0', '23*0=0'] Exploring Operation: 74*0=0, Resulting Numbers: [0] 0,74 unequal: No Solution Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[74, 67, 23, 67], Operations: [] Exploring Operation: 67-67=0, Resulting Numbers: [74, 23, 0] Generated Node #0,0: 74:[74, 23, 0] Operation: 67-67=0 Moving to Node #0,0 Current State: 74:[74, 23, 0], Operations: ['67-67=0'] Exploring Operation: 23*0=0, Resulting Numbers: [74, 0] Generated Node #0,0,2: 74:[74, 0] Operation: 23*0=0 Moving to Node #0,0,2 Current State: 74:[74, 0], Operations: ['67-67=0', '23*0=0'] Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.946181
hs_4
sum_heuristic
[ 74, 4, 37, 37 ]
37
[ "74+37=111", "4*37=148", "148-111=37" ]
Current State: 37:[74, 4, 37, 37], Operations: [] Exploring Operation: 74+37=111, Resulting Numbers: [4, 111] Generated Node #2: [4, 111] from Operation: 74+37=111 Current State: 37:[4, 111], Operations: ['74+37=111'] Exploring Operation: 4*37=148, Resulting Numbers: [111, 148] Generated Node #3: [111, 148] from Operation: 4*37=148 Current State: 37:[111, 148], Operations: ['74+37=111', '4*37=148'] Exploring Operation: 148-111=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[74, 4, 37, 37], Operations: [] Exploring Operation: 74-4=70, Resulting Numbers: [37, 37, 70] Generated Node #0,0: 37:[37, 37, 70] Operation: 74-4=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[37, 37, 70], Operations: ['74-4=70'] Exploring Operation: 70-37=33, Resulting Numbers: [37, 33] Generated Node #0,0,0: 37:[37, 33] Operation: 70-37=33 Moving to Node #0,0,0 Current State: 37:[37, 33], Operations: ['74-4=70', '70-37=33'] Exploring Operation: 37+33=70, Resulting Numbers: [70] 70,37 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
[ 66, 98, 51, 33 ]
45
[ "66/33=2", "98-51=47", "47-2=45" ]
Current State: 45:[66, 98, 51, 33], Operations: [] Exploring Operation: 66/33=2, Resulting Numbers: [98, 51, 2] Generated Node #2: [98, 51, 2] from Operation: 66/33=2 Current State: 45:[98, 51, 2], Operations: ['66/33=2'] Exploring Operation: 98-51=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 98-51=47 Current State: 45:[2, 47], Operations: ['66/33=2', '98-51=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[66, 98, 51, 33], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [66, 33, 47] Generated Node #0,0: 45:[66, 33, 47] Operation: 98-51=47 Exploring Operation: 98-66=32, Resulting Numbers: [51, 33, 32] Generated Node #0,1: 45:[51, 33, 32] Operation: 98-66=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[51, 33, 32], Operations: ['98-66=32'] Exploring Operation: 33-32=1, Resulting Numbers: [51, 1] Generated Node #0,1,0: 45:[51, 1] Operation: 33-32=1 Exploring Operation: 51-33=18, Resulting Numbers: [32, 18] Generated Node #0,1,1: 45:[32, 18] Operation: 51-33=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[51, 1], Operations: ['98-66=32', '33-32=1'] Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,45 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 45:[32, 18], Operations: ['98-66=32', '51-33=18'] Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[66, 33, 47], Operations: ['98-51=47'] Exploring Operation: 66-33=33, Resulting Numbers: [47, 33] Generated Node #0,0,0: 45:[47, 33] Operation: 66-33=33 Exploring Operation: 66/33=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 45:[47, 2] Operation: 66/33=2 Moving to Node #0,0,1 Current State: 45:[47, 2], Operations: ['98-51=47', '66/33=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[66, 98, 51, 33], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [66, 33, 47] Generated Node #0,0: 45:[66, 33, 47] Operation: 98-51=47 Moving to Node #0,0 Current State: 45:[66, 33, 47], Operations: ['98-51=47'] Exploring Operation: 66/33=2, Resulting Numbers: [47, 2] Generated Node #0,0,1: 45:[47, 2] Operation: 66/33=2 Moving to Node #0,0,1 Current State: 45:[47, 2], Operations: ['98-51=47', '66/33=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 80, 72, 11, 5 ]
97
[ "80+72=152", "11*5=55", "152-55=97" ]
Current State: 97:[80, 72, 11, 5], Operations: [] Exploring Operation: 80+72=152, Resulting Numbers: [11, 5, 152] Generated Node #2: [11, 5, 152] from Operation: 80+72=152 Current State: 97:[11, 5, 152], Operations: ['80+72=152'] Exploring Operation: 11*5=55, Resulting Numbers: [152, 55] Generated Node #3: [152, 55] from Operation: 11*5=55 Current State: 97:[152, 55], Operations: ['80+72=152', '11*5=55'] Exploring Operation: 152-55=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[80, 72, 11, 5], Operations: [] Exploring Operation: 11*5=55, Resulting Numbers: [80, 72, 55] Generated Node #0,0: 97:[80, 72, 55] Operation: 11*5=55 Exploring Operation: 72+11=83, Resulting Numbers: [80, 5, 83] Generated Node #0,1: 97:[80, 5, 83] Operation: 72+11=83 Exploring Operation: 80+5=85, Resulting Numbers: [72, 11, 85] Generated Node #0,2: 97:[72, 11, 85] Operation: 80+5=85 Exploring Operation: 80+11=91, Resulting Numbers: [72, 5, 91] Generated Node #0,3: 97:[72, 5, 91] Operation: 80+11=91 Moving to Node #0,0 Current State: 97:[80, 72, 55], Operations: ['11*5=55'] Exploring Operation: 80+55=135, Resulting Numbers: [72, 135] Generated Node #0,0,0: 97:[72, 135] Operation: 80+55=135 Exploring Operation: 80+72=152, Resulting Numbers: [55, 152] Generated Node #0,0,1: 97:[55, 152] Operation: 80+72=152 Exploring Operation: 72+55=127, Resulting Numbers: [80, 127] Generated Node #0,0,2: 97:[80, 127] Operation: 72+55=127 Exploring Operation: 80-55=25, Resulting Numbers: [72, 25] Generated Node #0,0,3: 97:[72, 25] Operation: 80-55=25 Moving to Node #0,2 Current State: 97:[72, 11, 85], Operations: ['80+5=85'] Exploring Operation: 11+85=96, Resulting Numbers: [72, 96] Generated Node #0,2,0: 97:[72, 96] Operation: 11+85=96 Exploring Operation: 72+11=83, Resulting Numbers: [85, 83] Generated Node #0,2,1: 97:[85, 83] Operation: 72+11=83 Exploring Operation: 85-11=74, Resulting Numbers: [72, 74] Generated Node #0,2,2: 97:[72, 74] Operation: 85-11=74 Exploring Operation: 72-11=61, Resulting Numbers: [85, 61] Generated Node #0,2,3: 97:[85, 61] Operation: 72-11=61 Moving to Node #0,1 Current State: 97:[80, 5, 83], Operations: ['72+11=83'] Exploring Operation: 5+83=88, Resulting Numbers: [80, 88] Generated Node #0,1,0: 97:[80, 88] Operation: 5+83=88 Exploring Operation: 83-5=78, Resulting Numbers: [80, 78] Generated Node #0,1,1: 97:[80, 78] Operation: 83-5=78 Exploring Operation: 80+5=85, Resulting Numbers: [83, 85] Generated Node #0,1,2: 97:[83, 85] Operation: 80+5=85 Exploring Operation: 80-5=75, Resulting Numbers: [83, 75] Generated Node #0,1,3: 97:[83, 75] Operation: 80-5=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[80, 88], Operations: ['72+11=83', '5+83=88'] Exploring Operation: 80+88=168, Resulting Numbers: [168] 168,97 unequal: No Solution Exploring Operation: 88-80=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 80*88=7040, Resulting Numbers: [7040] 7040,97 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 #0,1,2 Current State: 97:[83, 85], Operations: ['72+11=83', '80+5=85'] Exploring Operation: 83*85=7055, Resulting Numbers: [7055] 7055,97 unequal: No Solution Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 83+85=168, Resulting Numbers: [168] 168,97 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 #0,1,1 Current State: 97:[80, 78], Operations: ['72+11=83', '83-5=78'] Exploring Operation: 80*78=6240, Resulting Numbers: [6240] 6240,97 unequal: No Solution Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 80+78=158, Resulting Numbers: [158] 158,97 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:[83, 75], Operations: ['72+11=83', '80-5=75'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,97 unequal: No Solution Exploring Operation: 83*75=6225, Resulting Numbers: [6225] 6225,97 unequal: No Solution Exploring Operation: 83+75=158, Resulting Numbers: [158] 158,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 97:[72, 5, 91], Operations: ['80+11=91'] Exploring Operation: 91-5=86, Resulting Numbers: [72, 86] Generated Node #0,3,0: 97:[72, 86] Operation: 91-5=86 Exploring Operation: 72-5=67, Resulting Numbers: [91, 67] Generated Node #0,3,1: 97:[91, 67] Operation: 72-5=67 Exploring Operation: 5+91=96, Resulting Numbers: [72, 96] Generated Node #0,3,2: 97:[72, 96] Operation: 5+91=96 Exploring Operation: 72+5=77, Resulting Numbers: [91, 77] Generated Node #0,3,3: 97:[91, 77] Operation: 72+5=77 Moving to Node #0,2,0 Current State: 97:[72, 96], Operations: ['80+5=85', '11+85=96'] Exploring Operation: 96-72=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 72*96=6912, Resulting Numbers: [6912] 6912,97 unequal: No Solution Exploring Operation: 72+96=168, Resulting Numbers: [168] 168,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[85, 83], Operations: ['80+5=85', '72+11=83'] Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 85+83=168, Resulting Numbers: [168] 168,97 unequal: No Solution Exploring Operation: 85*83=7055, Resulting Numbers: [7055] 7055,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[72, 96], Operations: ['80+11=91', '5+91=96'] Exploring Operation: 96-72=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 72*96=6912, Resulting Numbers: [6912] 6912,97 unequal: No Solution Exploring Operation: 72+96=168, Resulting Numbers: [168] 168,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[91, 77], Operations: ['80+11=91', '72+5=77'] Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,97 unequal: No Solution Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,97 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[91, 67], Operations: ['80+11=91', '72-5=67'] Exploring Operation: 91+67=158, Resulting Numbers: [158] 158,97 unequal: No Solution Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 91*67=6097, Resulting Numbers: [6097] 6097,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[72, 86], Operations: ['80+11=91', '91-5=86'] Exploring Operation: 86-72=14, Resulting Numbers: [14] 14,97 unequal: No Solution Exploring Operation: 72*86=6192, Resulting Numbers: [6192] 6192,97 unequal: No Solution Exploring Operation: 72+86=158, Resulting Numbers: [158] 158,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[80, 127], Operations: ['11*5=55', '72+55=127'] Exploring Operation: 80+127=207, Resulting Numbers: [207] 207,97 unequal: No Solution Exploring Operation: 80*127=10160, Resulting Numbers: [10160] 10160,97 unequal: No Solution Exploring Operation: 127-80=47, Resulting Numbers: [47] 47,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[72, 74], Operations: ['80+5=85', '85-11=74'] Exploring Operation: 72+74=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,97 unequal: No Solution Exploring Operation: 72*74=5328, Resulting Numbers: [5328] 5328,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[85, 61], Operations: ['80+5=85', '72-11=61'] Exploring Operation: 85*61=5185, Resulting Numbers: [5185] 5185,97 unequal: No Solution Exploring Operation: 85-61=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 85+61=146, Resulting Numbers: [146] 146,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[72, 135], Operations: ['11*5=55', '80+55=135'] Exploring Operation: 72+135=207, Resulting Numbers: [207] 207,97 unequal: No Solution Exploring Operation: 135-72=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 72*135=9720, Resulting Numbers: [9720] 9720,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[72, 25], Operations: ['11*5=55', '80-55=25'] Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,97 unequal: No Solution Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,97 unequal: No Solution Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[80, 72, 11, 5], Operations: [] Exploring Operation: 11*5=55, Resulting Numbers: [80, 72, 55] Generated Node #0,0: 97:[80, 72, 55] Operation: 11*5=55 Moving to Node #0,0 Current State: 97:[80, 72, 55], Operations: ['11*5=55'] Exploring Operation: 80-55=25, Resulting Numbers: [72, 25] Generated Node #0,0,3: 97:[72, 25] Operation: 80-55=25 Moving to Node #0,0,3 Current State: 97:[72, 25], Operations: ['11*5=55', '80-55=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
0.940104
hs_4
mult_heuristic
[ 49, 34, 11, 99 ]
74
[ "49+34=83", "99/11=9", "83-9=74" ]
Current State: 74:[49, 34, 11, 99], Operations: [] Exploring Operation: 49+34=83, Resulting Numbers: [11, 99, 83] Generated Node #2: [11, 99, 83] from Operation: 49+34=83 Current State: 74:[11, 99, 83], Operations: ['49+34=83'] Exploring Operation: 99/11=9, Resulting Numbers: [83, 9] Generated Node #3: [83, 9] from Operation: 99/11=9 Current State: 74:[83, 9], Operations: ['49+34=83', '99/11=9'] Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[49, 34, 11, 99], Operations: [] Exploring Operation: 99-49=50, Resulting Numbers: [34, 11, 50] Generated Node #0,0: 74:[34, 11, 50] Operation: 99-49=50 Exploring Operation: 49-11=38, Resulting Numbers: [34, 99, 38] Generated Node #0,1: 74:[34, 99, 38] Operation: 49-11=38 Exploring Operation: 99/11=9, Resulting Numbers: [49, 34, 9] Generated Node #0,2: 74:[49, 34, 9] Operation: 99/11=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[49, 34, 9], Operations: ['99/11=9'] Exploring Operation: 34+9=43, Resulting Numbers: [49, 43] Generated Node #0,2,0: 74:[49, 43] Operation: 34+9=43 Exploring Operation: 49+34=83, Resulting Numbers: [9, 83] Generated Node #0,2,1: 74:[9, 83] Operation: 49+34=83 Exploring Operation: 49-9=40, Resulting Numbers: [34, 40] Generated Node #0,2,2: 74:[34, 40] Operation: 49-9=40 Moving to Node #0,2,2 Current State: 74:[34, 40], Operations: ['99/11=9', '49-9=40'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,74 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[49, 34, 11, 99], Operations: [] Exploring Operation: 99/11=9, Resulting Numbers: [49, 34, 9] Generated Node #0,2: 74:[49, 34, 9] Operation: 99/11=9 Moving to Node #0,2 Current State: 74:[49, 34, 9], Operations: ['99/11=9'] Exploring Operation: 49-9=40, Resulting Numbers: [34, 40] Generated Node #0,2,2: 74:[34, 40] Operation: 49-9=40 Moving to Node #0,2,2 Current State: 74:[34, 40], Operations: ['99/11=9', '49-9=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 11, 2, 26, 12 ]
52
[ "12-11=1", "2*26=52", "1*52=52" ]
Current State: 52:[11, 2, 26, 12], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [2, 26, 1] Generated Node #2: [2, 26, 1] from Operation: 12-11=1 Current State: 52:[2, 26, 1], Operations: ['12-11=1'] Exploring Operation: 2*26=52, Resulting Numbers: [1, 52] Generated Node #3: [1, 52] from Operation: 2*26=52 Current State: 52:[1, 52], Operations: ['12-11=1', '2*26=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[11, 2, 26, 12], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [2, 26, 1] Generated Node #0,0: 52:[2, 26, 1] Operation: 12-11=1 Exploring Operation: 11+2=13, Resulting Numbers: [26, 12, 13] Generated Node #0,1: 52:[26, 12, 13] Operation: 11+2=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[2, 26, 1], Operations: ['12-11=1'] Exploring Operation: 2*1=2, Resulting Numbers: [26, 2] Generated Node #0,0,0: 52:[26, 2] Operation: 2*1=2 Exploring Operation: 2/1=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 52:[26, 2] Operation: 2/1=2 Moving to Node #0,0,0 Current State: 52:[26, 2], Operations: ['12-11=1', '2*1=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[11, 2, 26, 12], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [2, 26, 1] Generated Node #0,0: 52:[2, 26, 1] Operation: 12-11=1 Moving to Node #0,0 Current State: 52:[2, 26, 1], Operations: ['12-11=1'] Exploring Operation: 2*1=2, Resulting Numbers: [26, 2] Generated Node #0,0,0: 52:[26, 2] Operation: 2*1=2 Moving to Node #0,0,0 Current State: 52:[26, 2], Operations: ['12-11=1', '2*1=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 20, 24, 50, 65 ]
71
[ "20+24=44", "50+65=115", "115-44=71" ]
Current State: 71:[20, 24, 50, 65], Operations: [] Exploring Operation: 20+24=44, Resulting Numbers: [50, 65, 44] Generated Node #2: [50, 65, 44] from Operation: 20+24=44 Current State: 71:[50, 65, 44], Operations: ['20+24=44'] Exploring Operation: 50+65=115, Resulting Numbers: [44, 115] Generated Node #3: [44, 115] from Operation: 50+65=115 Current State: 71:[44, 115], Operations: ['20+24=44', '50+65=115'] Exploring Operation: 115-44=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[20, 24, 50, 65], Operations: [] Exploring Operation: 24+50=74, Resulting Numbers: [20, 65, 74] Generated Node #0,0: 71:[20, 65, 74] Operation: 24+50=74 Exploring Operation: 20+50=70, Resulting Numbers: [24, 65, 70] Generated Node #0,1: 71:[24, 65, 70] Operation: 20+50=70 Exploring Operation: 24+65=89, Resulting Numbers: [20, 50, 89] Generated Node #0,2: 71:[20, 50, 89] Operation: 24+65=89 Exploring Operation: 20+65=85, Resulting Numbers: [24, 50, 85] Generated Node #0,3: 71:[24, 50, 85] Operation: 20+65=85 Exploring Operation: 20+24=44, Resulting Numbers: [50, 65, 44] Generated Node #0,4: 71:[50, 65, 44] Operation: 20+24=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[24, 65, 70], Operations: ['20+50=70'] Exploring Operation: 65+70=135, Resulting Numbers: [24, 135] Generated Node #0,1,0: 71:[24, 135] Operation: 65+70=135 Exploring Operation: 24+70=94, Resulting Numbers: [65, 94] Generated Node #0,1,1: 71:[65, 94] Operation: 24+70=94 Exploring Operation: 65-24=41, Resulting Numbers: [70, 41] Generated Node #0,1,2: 71:[70, 41] Operation: 65-24=41 Exploring Operation: 24+65=89, Resulting Numbers: [70, 89] Generated Node #0,1,3: 71:[70, 89] Operation: 24+65=89 Exploring Operation: 70-24=46, Resulting Numbers: [65, 46] Generated Node #0,1,4: 71:[65, 46] Operation: 70-24=46 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 71:[70, 89], Operations: ['20+50=70', '24+65=89'] Exploring Operation: 70*89=6230, Resulting Numbers: [6230] 6230,71 unequal: No Solution Exploring Operation: 70+89=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 89-70=19, Resulting Numbers: [19] 19,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 71:[65, 94], Operations: ['20+50=70', '24+70=94'] Exploring Operation: 65+94=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 94-65=29, Resulting Numbers: [29] 29,71 unequal: No Solution Exploring Operation: 65*94=6110, Resulting Numbers: [6110] 6110,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 71:[70, 41], Operations: ['20+50=70', '65-24=41'] Exploring Operation: 70*41=2870, Resulting Numbers: [2870] 2870,71 unequal: No Solution Exploring Operation: 70+41=111, Resulting Numbers: [111] 111,71 unequal: No Solution Exploring Operation: 70-41=29, Resulting Numbers: [29] 29,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 71:[65, 46], Operations: ['20+50=70', '70-24=46'] Exploring Operation: 65-46=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 65*46=2990, Resulting Numbers: [2990] 2990,71 unequal: No Solution Exploring Operation: 65+46=111, Resulting Numbers: [111] 111,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 71:[24, 135], Operations: ['20+50=70', '65+70=135'] Exploring Operation: 135-24=111, Resulting Numbers: [111] 111,71 unequal: No Solution Exploring Operation: 24+135=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 24*135=3240, Resulting Numbers: [3240] 3240,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 71:[50, 65, 44], Operations: ['20+24=44'] Exploring Operation: 65-44=21, Resulting Numbers: [50, 21] Generated Node #0,4,0: 71:[50, 21] Operation: 65-44=21 Exploring Operation: 50-44=6, Resulting Numbers: [65, 6] Generated Node #0,4,1: 71:[65, 6] Operation: 50-44=6 Exploring Operation: 65+44=109, Resulting Numbers: [50, 109] Generated Node #0,4,2: 71:[50, 109] Operation: 65+44=109 Exploring Operation: 50+44=94, Resulting Numbers: [65, 94] Generated Node #0,4,3: 71:[65, 94] Operation: 50+44=94 Exploring Operation: 50+65=115, Resulting Numbers: [44, 115] Generated Node #0,4,4: 71:[44, 115] Operation: 50+65=115 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 71:[65, 94], Operations: ['20+24=44', '50+44=94'] Exploring Operation: 65*94=6110, Resulting Numbers: [6110] 6110,71 unequal: No Solution Exploring Operation: 65+94=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 94-65=29, Resulting Numbers: [29] 29,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 71:[50, 109], Operations: ['20+24=44', '65+44=109'] Exploring Operation: 50*109=5450, Resulting Numbers: [5450] 5450,71 unequal: No Solution Exploring Operation: 50+109=159, Resulting Numbers: [159] 159,71 unequal: No Solution Exploring Operation: 109-50=59, Resulting Numbers: [59] 59,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 71:[50, 21], Operations: ['20+24=44', '65-44=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[20, 24, 50, 65], Operations: [] Exploring Operation: 20+24=44, Resulting Numbers: [50, 65, 44] Generated Node #0,4: 71:[50, 65, 44] Operation: 20+24=44 Moving to Node #0,4 Current State: 71:[50, 65, 44], Operations: ['20+24=44'] Exploring Operation: 65-44=21, Resulting Numbers: [50, 21] Generated Node #0,4,0: 71:[50, 21] Operation: 65-44=21 Moving to Node #0,4,0 Current State: 71:[50, 21], Operations: ['20+24=44', '65-44=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 88, 44, 53, 73 ]
33
[ "88/44=2", "53*2=106", "106-73=33" ]
Current State: 33:[88, 44, 53, 73], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [53, 73, 2] Generated Node #2: [53, 73, 2] from Operation: 88/44=2 Current State: 33:[53, 73, 2], Operations: ['88/44=2'] Exploring Operation: 53*2=106, Resulting Numbers: [73, 106] Generated Node #3: [73, 106] from Operation: 53*2=106 Current State: 33:[73, 106], Operations: ['88/44=2', '53*2=106'] Exploring Operation: 106-73=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[88, 44, 53, 73], Operations: [] Exploring Operation: 88-53=35, Resulting Numbers: [44, 73, 35] Generated Node #0,0: 33:[44, 73, 35] Operation: 88-53=35 Exploring Operation: 88/44=2, Resulting Numbers: [53, 73, 2] Generated Node #0,1: 33:[53, 73, 2] Operation: 88/44=2 Exploring Operation: 88-73=15, Resulting Numbers: [44, 53, 15] Generated Node #0,2: 33:[44, 53, 15] Operation: 88-73=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[44, 53, 15], Operations: ['88-73=15'] Exploring Operation: 53-44=9, Resulting Numbers: [15, 9] Generated Node #0,2,0: 33:[15, 9] Operation: 53-44=9 Exploring Operation: 53-15=38, Resulting Numbers: [44, 38] Generated Node #0,2,1: 33:[44, 38] Operation: 53-15=38 Exploring Operation: 44-15=29, Resulting Numbers: [53, 29] Generated Node #0,2,2: 33:[53, 29] Operation: 44-15=29 Moving to Node #0,2,0 Current State: 33:[15, 9], Operations: ['88-73=15', '53-44=9'] Exploring Operation: 15*9=135, Resulting Numbers: [135] 135,33 unequal: No Solution Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,33 unequal: No Solution Moving to Node #0,2,1 Current State: 33:[44, 38], Operations: ['88-73=15', '53-15=38'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,33 unequal: No Solution Exploring Operation: 44*38=1672, Resulting Numbers: [1672] 1672,33 unequal: No Solution Moving to Node #0,2,2 Current State: 33:[53, 29], Operations: ['88-73=15', '44-15=29'] Exploring Operation: 53*29=1537, Resulting Numbers: [1537] 1537,33 unequal: No Solution Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 53+29=82, Resulting Numbers: [82] 82,33 unequal: No Solution No 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: 33:[44, 73, 35], Operations: ['88-53=35'] Exploring Operation: 44-35=9, Resulting Numbers: [73, 9] Generated Node #0,0,0: 33:[73, 9] Operation: 44-35=9 Exploring Operation: 73-44=29, Resulting Numbers: [35, 29] Generated Node #0,0,1: 33:[35, 29] Operation: 73-44=29 Exploring Operation: 73-35=38, Resulting Numbers: [44, 38] Generated Node #0,0,2: 33:[44, 38] Operation: 73-35=38 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[35, 29], Operations: ['88-53=35', '73-44=29'] Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,33 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,33 unequal: No Solution No 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: 33:[44, 38], Operations: ['88-53=35', '73-35=38'] Exploring Operation: 44-38=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 44+38=82, Resulting Numbers: [82] 82,33 unequal: No Solution Exploring Operation: 44*38=1672, Resulting Numbers: [1672] 1672,33 unequal: No Solution No 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: 33:[73, 9], Operations: ['88-53=35', '44-35=9'] Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,33 unequal: No Solution Exploring Operation: 73*9=657, Resulting Numbers: [657] 657,33 unequal: No Solution Exploring Operation: 73+9=82, Resulting Numbers: [82] 82,33 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: 33:[53, 73, 2], Operations: ['88/44=2'] Exploring Operation: 73-2=71, Resulting Numbers: [53, 71] Generated Node #0,1,0: 33:[53, 71] Operation: 73-2=71 Exploring Operation: 73-53=20, Resulting Numbers: [2, 20] Generated Node #0,1,1: 33:[2, 20] Operation: 73-53=20 Exploring Operation: 53-2=51, Resulting Numbers: [73, 51] Generated Node #0,1,2: 33:[73, 51] Operation: 53-2=51 Moving to Node #0,1,1 Current State: 33:[2, 20], Operations: ['88/44=2', '73-53=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,33 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[53, 71], Operations: ['88/44=2', '73-2=71'] Exploring Operation: 53*71=3763, Resulting Numbers: [3763] 3763,33 unequal: No Solution Exploring Operation: 71-53=18, Resulting Numbers: [18] 18,33 unequal: No Solution Exploring Operation: 53+71=124, Resulting Numbers: [124] 124,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[73, 51], Operations: ['88/44=2', '53-2=51'] Exploring Operation: 73*51=3723, Resulting Numbers: [3723] 3723,33 unequal: No Solution Exploring Operation: 73-51=22, Resulting Numbers: [22] 22,33 unequal: No Solution Exploring Operation: 73+51=124, Resulting Numbers: [124] 124,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 45, 22, 27, 45 ]
22
[ "45-45=0", "27*0=0", "22+0=22" ]
Current State: 22:[45, 22, 27, 45], Operations: [] Exploring Operation: 45-45=0, Resulting Numbers: [22, 27, 0] Generated Node #2: [22, 27, 0] from Operation: 45-45=0 Current State: 22:[22, 27, 0], Operations: ['45-45=0'] Exploring Operation: 27*0=0, Resulting Numbers: [22, 0] Generated Node #3: [22, 0] from Operation: 27*0=0 Current State: 22:[22, 0], Operations: ['45-45=0', '27*0=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[45, 22, 27, 45], Operations: [] Exploring Operation: 45-27=18, Resulting Numbers: [22, 45, 18] Generated Node #0,0: 22:[22, 45, 18] Operation: 45-27=18 Exploring Operation: 45-45=0, Resulting Numbers: [22, 27, 0] Generated Node #0,1: 22:[22, 27, 0] Operation: 45-45=0 Exploring Operation: 45/45=1, Resulting Numbers: [22, 27, 1] Generated Node #0,2: 22:[22, 27, 1] Operation: 45/45=1 Moving to Node #0,2 Current State: 22:[22, 27, 1], Operations: ['45/45=1'] Exploring Operation: 27-22=5, Resulting Numbers: [1, 5] Generated Node #0,2,0: 22:[1, 5] Operation: 27-22=5 Exploring Operation: 22*1=22, Resulting Numbers: [27, 22] Generated Node #0,2,1: 22:[27, 22] Operation: 22*1=22 Exploring Operation: 27-1=26, Resulting Numbers: [22, 26] Generated Node #0,2,2: 22:[22, 26] Operation: 27-1=26 Moving to Node #0,1 Current State: 22:[22, 27, 0], Operations: ['45-45=0'] Exploring Operation: 27-22=5, Resulting Numbers: [0, 5] Generated Node #0,1,0: 22:[0, 5] Operation: 27-22=5 Exploring Operation: 27*0=0, Resulting Numbers: [22, 0] Generated Node #0,1,1: 22:[22, 0] Operation: 27*0=0 Exploring Operation: 22+0=22, Resulting Numbers: [27, 22] Generated Node #0,1,2: 22:[27, 22] Operation: 22+0=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[22, 0], Operations: ['45-45=0', '27*0=0'] Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[45, 22, 27, 45], Operations: [] Exploring Operation: 45-45=0, Resulting Numbers: [22, 27, 0] Generated Node #0,1: 22:[22, 27, 0] Operation: 45-45=0 Moving to Node #0,1 Current State: 22:[22, 27, 0], Operations: ['45-45=0'] Exploring Operation: 27*0=0, Resulting Numbers: [22, 0] Generated Node #0,1,1: 22:[22, 0] Operation: 27*0=0 Moving to Node #0,1,1 Current State: 22:[22, 0], Operations: ['45-45=0', '27*0=0'] Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 3, 55, 26, 14 ]
71
[ "3*14=42", "55-26=29", "42+29=71" ]
Current State: 71:[3, 55, 26, 14], Operations: [] Exploring Operation: 3*14=42, Resulting Numbers: [55, 26, 42] Generated Node #2: [55, 26, 42] from Operation: 3*14=42 Current State: 71:[55, 26, 42], Operations: ['3*14=42'] Exploring Operation: 55-26=29, Resulting Numbers: [42, 29] Generated Node #3: [42, 29] from Operation: 55-26=29 Current State: 71:[42, 29], Operations: ['3*14=42', '55-26=29'] Exploring Operation: 42+29=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[3, 55, 26, 14], Operations: [] Exploring Operation: 3*26=78, Resulting Numbers: [55, 14, 78] Generated Node #0,0: 71:[55, 14, 78] Operation: 3*26=78 Exploring Operation: 3*14=42, Resulting Numbers: [55, 26, 42] Generated Node #0,1: 71:[55, 26, 42] Operation: 3*14=42 Moving to Node #0,0 Current State: 71:[55, 14, 78], Operations: ['3*26=78'] Exploring Operation: 55+14=69, Resulting Numbers: [78, 69] Generated Node #0,0,0: 71:[78, 69] Operation: 55+14=69 Exploring Operation: 78-14=64, Resulting Numbers: [55, 64] Generated Node #0,0,1: 71:[55, 64] Operation: 78-14=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[78, 69], Operations: ['3*26=78', '55+14=69'] Exploring Operation: 78-69=9, Resulting Numbers: [9] 9,71 unequal: No Solution Exploring Operation: 78+69=147, Resulting Numbers: [147] 147,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[55, 64], Operations: ['3*26=78', '78-14=64'] Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,71 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[55, 26, 42], Operations: ['3*14=42'] Exploring Operation: 26+42=68, Resulting Numbers: [55, 68] Generated Node #0,1,0: 71:[55, 68] Operation: 26+42=68 Exploring Operation: 55+26=81, Resulting Numbers: [42, 81] Generated Node #0,1,1: 71:[42, 81] Operation: 55+26=81 Moving to Node #0,1,0 Current State: 71:[55, 68], Operations: ['3*14=42', '26+42=68'] Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,71 unequal: No Solution Exploring Operation: 55+68=123, Resulting Numbers: [123] 123,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[42, 81], Operations: ['3*14=42', '55+26=81'] Exploring Operation: 42+81=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,71 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 40, 44, 76, 50 ]
42
[ "40+44=84", "76+50=126", "126-84=42" ]
Current State: 42:[40, 44, 76, 50], Operations: [] Exploring Operation: 40+44=84, Resulting Numbers: [76, 50, 84] Generated Node #2: [76, 50, 84] from Operation: 40+44=84 Current State: 42:[76, 50, 84], Operations: ['40+44=84'] Exploring Operation: 76+50=126, Resulting Numbers: [84, 126] Generated Node #3: [84, 126] from Operation: 76+50=126 Current State: 42:[84, 126], Operations: ['40+44=84', '76+50=126'] Exploring Operation: 126-84=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[40, 44, 76, 50], Operations: [] Exploring Operation: 76-40=36, Resulting Numbers: [44, 50, 36] Generated Node #0,0: 42:[44, 50, 36] Operation: 76-40=36 Exploring Operation: 76-50=26, Resulting Numbers: [40, 44, 26] Generated Node #0,1: 42:[40, 44, 26] Operation: 76-50=26 Exploring Operation: 76-44=32, Resulting Numbers: [40, 50, 32] Generated Node #0,2: 42:[40, 50, 32] Operation: 76-44=32 Moving to Node #0,1 Current State: 42:[40, 44, 26], Operations: ['76-50=26'] Exploring Operation: 44-26=18, Resulting Numbers: [40, 18] Generated Node #0,1,0: 42:[40, 18] Operation: 44-26=18 Exploring Operation: 40-26=14, Resulting Numbers: [44, 14] Generated Node #0,1,1: 42:[44, 14] Operation: 40-26=14 Exploring Operation: 44-40=4, Resulting Numbers: [26, 4] Generated Node #0,1,2: 42:[26, 4] Operation: 44-40=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[44, 14], Operations: ['76-50=26', '40-26=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,42 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,42 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 #0,1,0 Current State: 42:[40, 18], Operations: ['76-50=26', '44-26=18'] Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,42 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[26, 4], Operations: ['76-50=26', '44-40=4'] Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,42 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 42:[44, 50, 36], Operations: ['76-40=36'] Exploring Operation: 50-44=6, Resulting Numbers: [36, 6] Generated Node #0,0,0: 42:[36, 6] Operation: 50-44=6 Exploring Operation: 50-36=14, Resulting Numbers: [44, 14] Generated Node #0,0,1: 42:[44, 14] Operation: 50-36=14 Exploring Operation: 44-36=8, Resulting Numbers: [50, 8] Generated Node #0,0,2: 42:[50, 8] Operation: 44-36=8 Moving to Node #0,2 Current State: 42:[40, 50, 32], Operations: ['76-44=32'] Exploring Operation: 50-40=10, Resulting Numbers: [32, 10] Generated Node #0,2,0: 42:[32, 10] Operation: 50-40=10 Exploring Operation: 40-32=8, Resulting Numbers: [50, 8] Generated Node #0,2,1: 42:[50, 8] Operation: 40-32=8 Exploring Operation: 50-32=18, Resulting Numbers: [40, 18] Generated Node #0,2,2: 42:[40, 18] Operation: 50-32=18 Moving to Node #0,0,1 Current State: 42:[44, 14], Operations: ['76-40=36', '50-36=14'] Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,42 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,42 unequal: No Solution Moving to Node #0,2,2 Current State: 42:[40, 18], Operations: ['76-44=32', '50-32=18'] Exploring Operation: 40+18=58, Resulting Numbers: [58] 58,42 unequal: No Solution Exploring Operation: 40-18=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 40*18=720, Resulting Numbers: [720] 720,42 unequal: No Solution Moving to Node #0,0,0 Current State: 42:[36, 6], Operations: ['76-40=36', '50-44=6'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[40, 44, 76, 50], Operations: [] Exploring Operation: 76-40=36, Resulting Numbers: [44, 50, 36] Generated Node #0,0: 42:[44, 50, 36] Operation: 76-40=36 Moving to Node #0,0 Current State: 42:[44, 50, 36], Operations: ['76-40=36'] Exploring Operation: 50-44=6, Resulting Numbers: [36, 6] Generated Node #0,0,0: 42:[36, 6] Operation: 50-44=6 Moving to Node #0,0,0 Current State: 42:[36, 6], Operations: ['76-40=36', '50-44=6'] Exploring Operation: 36+6=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.971354
hs_3
sum_heuristic
[ 41, 30, 52, 2 ]
43
[ "41-30=11", "52+2=54", "54-11=43" ]
Current State: 43:[41, 30, 52, 2], Operations: [] Exploring Operation: 41-30=11, Resulting Numbers: [52, 2, 11] Generated Node #2: [52, 2, 11] from Operation: 41-30=11 Current State: 43:[52, 2, 11], Operations: ['41-30=11'] Exploring Operation: 52+2=54, Resulting Numbers: [11, 54] Generated Node #3: [11, 54] from Operation: 52+2=54 Current State: 43:[11, 54], Operations: ['41-30=11', '52+2=54'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[41, 30, 52, 2], Operations: [] Exploring Operation: 41+2=43, Resulting Numbers: [30, 52, 43] Generated Node #0,0: 43:[30, 52, 43] Operation: 41+2=43 Moving to Node #0,0 Current State: 43:[30, 52, 43], Operations: ['41+2=43'] Exploring Operation: 52-30=22, Resulting Numbers: [43, 22] Generated Node #0,0,0: 43:[43, 22] Operation: 52-30=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[43, 22], Operations: ['41+2=43', '52-30=22'] Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,43 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
[ 3, 48, 65, 2 ]
27
[ "65-2=63", "63/3=21", "48-21=27" ]
Current State: 27:[3, 48, 65, 2], Operations: [] Exploring Operation: 65-2=63, Resulting Numbers: [3, 48, 63] Generated Node #2: [3, 48, 63] from Operation: 65-2=63 Current State: 27:[3, 48, 63], Operations: ['65-2=63'] Exploring Operation: 63/3=21, Resulting Numbers: [48, 21] Generated Node #3: [48, 21] from Operation: 63/3=21 Current State: 27:[48, 21], Operations: ['65-2=63', '63/3=21'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[3, 48, 65, 2], Operations: [] Exploring Operation: 65-48=17, Resulting Numbers: [3, 2, 17] Generated Node #0,0: 27:[3, 2, 17] Operation: 65-48=17 Exploring Operation: 48/3=16, Resulting Numbers: [65, 2, 16] Generated Node #0,1: 27:[65, 2, 16] Operation: 48/3=16 Exploring Operation: 48/2=24, Resulting Numbers: [3, 65, 24] Generated Node #0,2: 27:[3, 65, 24] Operation: 48/2=24 Exploring Operation: 65-3=62, Resulting Numbers: [48, 2, 62] Generated Node #0,3: 27:[48, 2, 62] Operation: 65-3=62 Exploring Operation: 48-3=45, Resulting Numbers: [65, 2, 45] Generated Node #0,4: 27:[65, 2, 45] Operation: 48-3=45 Moving to Node #0,0 Current State: 27:[3, 2, 17], Operations: ['65-48=17'] Exploring Operation: 2+17=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 27:[3, 19] Operation: 2+17=19 Exploring Operation: 2*17=34, Resulting Numbers: [3, 34] Generated Node #0,0,1: 27:[3, 34] Operation: 2*17=34 Exploring Operation: 3+17=20, Resulting Numbers: [2, 20] Generated Node #0,0,2: 27:[2, 20] Operation: 3+17=20 Exploring Operation: 17-2=15, Resulting Numbers: [3, 15] Generated Node #0,0,3: 27:[3, 15] Operation: 17-2=15 Exploring Operation: 17-3=14, Resulting Numbers: [2, 14] Generated Node #0,0,4: 27:[2, 14] Operation: 17-3=14 Moving to Node #0,2 Current State: 27:[3, 65, 24], Operations: ['48/2=24'] Exploring Operation: 65-24=41, Resulting Numbers: [3, 41] Generated Node #0,2,0: 27:[3, 41] Operation: 65-24=41 Exploring Operation: 3+65=68, Resulting Numbers: [24, 68] Generated Node #0,2,1: 27:[24, 68] Operation: 3+65=68 Exploring Operation: 3+24=27, Resulting Numbers: [65, 27] Generated Node #0,2,2: 27:[65, 27] Operation: 3+24=27 Exploring Operation: 65-3=62, Resulting Numbers: [24, 62] Generated Node #0,2,3: 27:[24, 62] Operation: 65-3=62 Exploring Operation: 24/3=8, Resulting Numbers: [65, 8] Generated Node #0,2,4: 27:[65, 8] Operation: 24/3=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[3, 41], Operations: ['48/2=24', '65-24=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,27 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[65, 27], Operations: ['48/2=24', '3+24=27'] Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 65+27=92, Resulting Numbers: [92] 92,27 unequal: No Solution Exploring Operation: 65*27=1755, Resulting Numbers: [1755] 1755,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[24, 62], Operations: ['48/2=24', '65-3=62'] Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,27 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,27 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 27:[65, 8], Operations: ['48/2=24', '24/3=8'] Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,27 unequal: No Solution Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,27 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[24, 68], Operations: ['48/2=24', '3+65=68'] Exploring Operation: 24*68=1632, Resulting Numbers: [1632] 1632,27 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 24+68=92, Resulting Numbers: [92] 92,27 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: 27:[65, 2, 16], Operations: ['48/3=16'] Exploring Operation: 65-2=63, Resulting Numbers: [16, 63] Generated Node #0,1,0: 27:[16, 63] Operation: 65-2=63 Exploring Operation: 65-16=49, Resulting Numbers: [2, 49] Generated Node #0,1,1: 27:[2, 49] Operation: 65-16=49 Exploring Operation: 16-2=14, Resulting Numbers: [65, 14] Generated Node #0,1,2: 27:[65, 14] Operation: 16-2=14 Exploring Operation: 2*16=32, Resulting Numbers: [65, 32] Generated Node #0,1,3: 27:[65, 32] Operation: 2*16=32 Exploring Operation: 16/2=8, Resulting Numbers: [65, 8] Generated Node #0,1,4: 27:[65, 8] Operation: 16/2=8 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[2, 49], Operations: ['48/3=16', '65-16=49'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,27 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 27:[65, 8], Operations: ['48/3=16', '16/2=8'] Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 65*8=520, Resulting Numbers: [520] 520,27 unequal: No Solution Exploring Operation: 65+8=73, Resulting Numbers: [73] 73,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[16, 63], Operations: ['48/3=16', '65-2=63'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,27 unequal: No Solution Exploring Operation: 16+63=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 16*63=1008, Resulting Numbers: [1008] 1008,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 27:[65, 14], Operations: ['48/3=16', '16-2=14'] Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 27:[65, 32], Operations: ['48/3=16', '2*16=32'] Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,27 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,27 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,27 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: 27:[48, 2, 62], Operations: ['65-3=62'] Exploring Operation: 62-2=60, Resulting Numbers: [48, 60] Generated Node #0,3,0: 27:[48, 60] Operation: 62-2=60 Exploring Operation: 48/2=24, Resulting Numbers: [62, 24] Generated Node #0,3,1: 27:[62, 24] Operation: 48/2=24 Exploring Operation: 62-48=14, Resulting Numbers: [2, 14] Generated Node #0,3,2: 27:[2, 14] Operation: 62-48=14 Exploring Operation: 48-2=46, Resulting Numbers: [62, 46] Generated Node #0,3,3: 27:[62, 46] Operation: 48-2=46 Exploring Operation: 62/2=31, Resulting Numbers: [48, 31] Generated Node #0,3,4: 27:[48, 31] Operation: 62/2=31 Moving to Node #0,4 Current State: 27:[65, 2, 45], Operations: ['48-3=45'] Exploring Operation: 65+2=67, Resulting Numbers: [45, 67] Generated Node #0,4,0: 27:[45, 67] Operation: 65+2=67 Exploring Operation: 65-45=20, Resulting Numbers: [2, 20] Generated Node #0,4,1: 27:[2, 20] Operation: 65-45=20 Exploring Operation: 65-2=63, Resulting Numbers: [45, 63] Generated Node #0,4,2: 27:[45, 63] Operation: 65-2=63 Exploring Operation: 45-2=43, Resulting Numbers: [65, 43] Generated Node #0,4,3: 27:[65, 43] Operation: 45-2=43 Exploring Operation: 2+45=47, Resulting Numbers: [65, 47] Generated Node #0,4,4: 27:[65, 47] Operation: 2+45=47 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 27:[2, 20], Operations: ['48-3=45', '65-45=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,27 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 #0,4,2 Current State: 27:[45, 63], Operations: ['48-3=45', '65-2=63'] Exploring Operation: 45+63=108, Resulting Numbers: [108] 108,27 unequal: No Solution Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 45*63=2835, Resulting Numbers: [2835] 2835,27 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 #0,4,3 Current State: 27:[65, 43], Operations: ['48-3=45', '45-2=43'] Exploring Operation: 65*43=2795, Resulting Numbers: [2795] 2795,27 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 65+43=108, Resulting Numbers: [108] 108,27 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 #0,4,0 Current State: 27:[45, 67], Operations: ['48-3=45', '65+2=67'] Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,27 unequal: No Solution Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,27 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 #0,4,4 Current State: 27:[65, 47], Operations: ['48-3=45', '2+45=47'] Exploring Operation: 65*47=3055, Resulting Numbers: [3055] 3055,27 unequal: No Solution Exploring Operation: 65+47=112, Resulting Numbers: [112] 112,27 unequal: No Solution Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 27:[3, 15], Operations: ['65-48=17', '17-2=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[2, 14], Operations: ['65-3=62', '62-48=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,27 unequal: No Solution Moving to Node #0,0,4 Current State: 27:[2, 14], Operations: ['65-48=17', '17-3=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,27 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[3, 34], Operations: ['65-48=17', '2*17=34'] Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,27 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,27 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[2, 20], Operations: ['65-48=17', '3+17=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[3, 19], Operations: ['65-48=17', '2+17=19'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,27 unequal: No Solution Moving to Node #0,3,4 Current State: 27:[48, 31], Operations: ['65-3=62', '62/2=31'] Exploring Operation: 48+31=79, Resulting Numbers: [79] 79,27 unequal: No Solution Exploring Operation: 48*31=1488, Resulting Numbers: [1488] 1488,27 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[62, 24], Operations: ['65-3=62', '48/2=24'] Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,27 unequal: No Solution Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,27 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[62, 46], Operations: ['65-3=62', '48-2=46'] Exploring Operation: 62*46=2852, Resulting Numbers: [2852] 2852,27 unequal: No Solution Exploring Operation: 62+46=108, Resulting Numbers: [108] 108,27 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[48, 60], Operations: ['65-3=62', '62-2=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,27 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,27 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,27 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 5, 67, 79, 85 ]
25
[ "79-67=12", "5*12=60", "85-60=25" ]
Current State: 25:[5, 67, 79, 85], Operations: [] Exploring Operation: 79-67=12, Resulting Numbers: [5, 85, 12] Generated Node #2: [5, 85, 12] from Operation: 79-67=12 Current State: 25:[5, 85, 12], Operations: ['79-67=12'] Exploring Operation: 5*12=60, Resulting Numbers: [85, 60] Generated Node #3: [85, 60] from Operation: 5*12=60 Current State: 25:[85, 60], Operations: ['79-67=12', '5*12=60'] Exploring Operation: 85-60=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[5, 67, 79, 85], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [5, 67, 6] Generated Node #0,0: 25:[5, 67, 6] Operation: 85-79=6 Exploring Operation: 85-67=18, Resulting Numbers: [5, 79, 18] Generated Node #0,1: 25:[5, 79, 18] Operation: 85-67=18 Exploring Operation: 79-67=12, Resulting Numbers: [5, 85, 12] Generated Node #0,2: 25:[5, 85, 12] Operation: 79-67=12 Moving to Node #0,0 Current State: 25:[5, 67, 6], Operations: ['85-79=6'] Exploring Operation: 6-5=1, Resulting Numbers: [67, 1] Generated Node #0,0,0: 25:[67, 1] Operation: 6-5=1 Exploring Operation: 67-6=61, Resulting Numbers: [5, 61] Generated Node #0,0,1: 25:[5, 61] Operation: 67-6=61 Exploring Operation: 67-5=62, Resulting Numbers: [6, 62] Generated Node #0,0,2: 25:[6, 62] Operation: 67-5=62 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[5, 61], Operations: ['85-79=6', '67-6=61'] Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,25 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,25 unequal: No Solution Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,25 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 #0,0,2 Current State: 25:[6, 62], Operations: ['85-79=6', '67-5=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,25 unequal: No Solution Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,25 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 #0,0,0 Current State: 25:[67, 1], Operations: ['85-79=6', '6-5=1'] Exploring Operation: 67*1=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,25 unequal: No Solution Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,25 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: 25:[5, 79, 18], Operations: ['85-67=18'] Exploring Operation: 5+18=23, Resulting Numbers: [79, 23] Generated Node #0,1,0: 25:[79, 23] Operation: 5+18=23 Exploring Operation: 79-5=74, Resulting Numbers: [18, 74] Generated Node #0,1,1: 25:[18, 74] Operation: 79-5=74 Exploring Operation: 79-18=61, Resulting Numbers: [5, 61] Generated Node #0,1,2: 25:[5, 61] Operation: 79-18=61 Moving to Node #0,2 Current State: 25:[5, 85, 12], Operations: ['79-67=12'] Exploring Operation: 85-12=73, Resulting Numbers: [5, 73] Generated Node #0,2,0: 25:[5, 73] Operation: 85-12=73 Exploring Operation: 85/5=17, Resulting Numbers: [12, 17] Generated Node #0,2,1: 25:[12, 17] Operation: 85/5=17 Exploring Operation: 85-5=80, Resulting Numbers: [12, 80] Generated Node #0,2,2: 25:[12, 80] Operation: 85-5=80 Moving to Node #0,2,1 Current State: 25:[12, 17], Operations: ['79-67=12', '85/5=17'] Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,25 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,25 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[5, 61], Operations: ['85-67=18', '79-18=61'] Exploring Operation: 5+61=66, Resulting Numbers: [66] 66,25 unequal: No Solution Exploring Operation: 5*61=305, Resulting Numbers: [305] 305,25 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[5, 73], Operations: ['79-67=12', '85-12=73'] Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 5+73=78, Resulting Numbers: [78] 78,25 unequal: No Solution Exploring Operation: 5*73=365, Resulting Numbers: [365] 365,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[18, 74], Operations: ['85-67=18', '79-5=74'] Exploring Operation: 74-18=56, Resulting Numbers: [56] 56,25 unequal: No Solution Exploring Operation: 18+74=92, Resulting Numbers: [92] 92,25 unequal: No Solution Exploring Operation: 18*74=1332, Resulting Numbers: [1332] 1332,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[79, 23], Operations: ['85-67=18', '5+18=23'] Exploring Operation: 79*23=1817, Resulting Numbers: [1817] 1817,25 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,25 unequal: No Solution Exploring Operation: 79+23=102, Resulting Numbers: [102] 102,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[12, 80], Operations: ['79-67=12', '85-5=80'] Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,25 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,25 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 71, 2, 92, 45 ]
73
[ "71+92=163", "2*45=90", "163-90=73" ]
Current State: 73:[71, 2, 92, 45], Operations: [] Exploring Operation: 71+92=163, Resulting Numbers: [2, 45, 163] Generated Node #2: [2, 45, 163] from Operation: 71+92=163 Current State: 73:[2, 45, 163], Operations: ['71+92=163'] Exploring Operation: 2*45=90, Resulting Numbers: [163, 90] Generated Node #3: [163, 90] from Operation: 2*45=90 Current State: 73:[163, 90], Operations: ['71+92=163', '2*45=90'] Exploring Operation: 163-90=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[71, 2, 92, 45], Operations: [] Exploring Operation: 2+45=47, Resulting Numbers: [71, 92, 47] Generated Node #0,0: 73:[71, 92, 47] Operation: 2+45=47 Exploring Operation: 71-2=69, Resulting Numbers: [92, 45, 69] Generated Node #0,1: 73:[92, 45, 69] Operation: 71-2=69 Exploring Operation: 71+2=73, Resulting Numbers: [92, 45, 73] Generated Node #0,2: 73:[92, 45, 73] Operation: 71+2=73 Exploring Operation: 2*45=90, Resulting Numbers: [71, 92, 90] Generated Node #0,3: 73:[71, 92, 90] Operation: 2*45=90 Exploring Operation: 92-2=90, Resulting Numbers: [71, 45, 90] Generated Node #0,4: 73:[71, 45, 90] Operation: 92-2=90 Start Sub Search at level 1: Moving to Node #0,3 Current State: 73:[71, 92, 90], Operations: ['2*45=90'] Exploring Operation: 92-71=21, Resulting Numbers: [90, 21] Generated Node #0,3,0: 73:[90, 21] Operation: 92-71=21 Exploring Operation: 90-71=19, Resulting Numbers: [92, 19] Generated Node #0,3,1: 73:[92, 19] Operation: 90-71=19 Exploring Operation: 71+90=161, Resulting Numbers: [92, 161] Generated Node #0,3,2: 73:[92, 161] Operation: 71+90=161 Exploring Operation: 71+92=163, Resulting Numbers: [90, 163] Generated Node #0,3,3: 73:[90, 163] Operation: 71+92=163 Exploring Operation: 92-90=2, Resulting Numbers: [71, 2] Generated Node #0,3,4: 73:[71, 2] Operation: 92-90=2 Moving to Node #0,3,0 Current State: 73:[90, 21], Operations: ['2*45=90', '92-71=21'] Exploring Operation: 90+21=111, Resulting Numbers: [111] 111,73 unequal: No Solution Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 90*21=1890, Resulting Numbers: [1890] 1890,73 unequal: No Solution Moving to Node #0,3,4 Current State: 73:[71, 2], Operations: ['2*45=90', '92-90=2'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,73 unequal: No Solution Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,73 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[71, 2, 92, 45], Operations: [] Exploring Operation: 2*45=90, Resulting Numbers: [71, 92, 90] Generated Node #0,3: 73:[71, 92, 90] Operation: 2*45=90 Moving to Node #0,3 Current State: 73:[71, 92, 90], Operations: ['2*45=90'] Exploring Operation: 92-90=2, Resulting Numbers: [71, 2] Generated Node #0,3,4: 73:[71, 2] Operation: 92-90=2 Moving to Node #0,3,4 Current State: 73:[71, 2], Operations: ['2*45=90', '92-90=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 22, 57, 34, 30 ]
83
[ "22+57=79", "34-30=4", "79+4=83" ]
Current State: 83:[22, 57, 34, 30], Operations: [] Exploring Operation: 22+57=79, Resulting Numbers: [34, 30, 79] Generated Node #2: [34, 30, 79] from Operation: 22+57=79 Current State: 83:[34, 30, 79], Operations: ['22+57=79'] Exploring Operation: 34-30=4, Resulting Numbers: [79, 4] Generated Node #3: [79, 4] from Operation: 34-30=4 Current State: 83:[79, 4], Operations: ['22+57=79', '34-30=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[22, 57, 34, 30], Operations: [] Exploring Operation: 22+30=52, Resulting Numbers: [57, 34, 52] Generated Node #0,0: 83:[57, 34, 52] Operation: 22+30=52 Exploring Operation: 22+34=56, Resulting Numbers: [57, 30, 56] Generated Node #0,1: 83:[57, 30, 56] Operation: 22+34=56 Exploring Operation: 22+57=79, Resulting Numbers: [34, 30, 79] Generated Node #0,2: 83:[34, 30, 79] Operation: 22+57=79 Moving to Node #0,0 Current State: 83:[57, 34, 52], Operations: ['22+30=52'] Exploring Operation: 57+52=109, Resulting Numbers: [34, 109] Generated Node #0,0,0: 83:[34, 109] Operation: 57+52=109 Exploring Operation: 57+34=91, Resulting Numbers: [52, 91] Generated Node #0,0,1: 83:[52, 91] Operation: 57+34=91 Exploring Operation: 34+52=86, Resulting Numbers: [57, 86] Generated Node #0,0,2: 83:[57, 86] Operation: 34+52=86 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[57, 86], Operations: ['22+30=52', '34+52=86'] Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 57*86=4902, Resulting Numbers: [4902] 4902,83 unequal: No Solution Exploring Operation: 57+86=143, Resulting Numbers: [143] 143,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[52, 91], Operations: ['22+30=52', '57+34=91'] Exploring Operation: 91-52=39, Resulting Numbers: [39] 39,83 unequal: No Solution Exploring Operation: 52*91=4732, Resulting Numbers: [4732] 4732,83 unequal: No Solution Exploring Operation: 52+91=143, Resulting Numbers: [143] 143,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[34, 109], Operations: ['22+30=52', '57+52=109'] Exploring Operation: 34*109=3706, Resulting Numbers: [3706] 3706,83 unequal: No Solution Exploring Operation: 34+109=143, Resulting Numbers: [143] 143,83 unequal: No Solution Exploring Operation: 109-34=75, Resulting Numbers: [75] 75,83 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: 83:[57, 30, 56], Operations: ['22+34=56'] Exploring Operation: 30+56=86, Resulting Numbers: [57, 86] Generated Node #0,1,0: 83:[57, 86] Operation: 30+56=86 Exploring Operation: 57+30=87, Resulting Numbers: [56, 87] Generated Node #0,1,1: 83:[56, 87] Operation: 57+30=87 Exploring Operation: 57-30=27, Resulting Numbers: [56, 27] Generated Node #0,1,2: 83:[56, 27] Operation: 57-30=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[57, 86], Operations: ['22+34=56', '30+56=86'] Exploring Operation: 57*86=4902, Resulting Numbers: [4902] 4902,83 unequal: No Solution Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,83 unequal: No Solution Exploring Operation: 57+86=143, Resulting Numbers: [143] 143,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[56, 87], Operations: ['22+34=56', '57+30=87'] Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,83 unequal: No Solution Exploring Operation: 56*87=4872, Resulting Numbers: [4872] 4872,83 unequal: No Solution Exploring Operation: 56+87=143, Resulting Numbers: [143] 143,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[56, 27], Operations: ['22+34=56', '57-30=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[22, 57, 34, 30], Operations: [] Exploring Operation: 22+34=56, Resulting Numbers: [57, 30, 56] Generated Node #0,1: 83:[57, 30, 56] Operation: 22+34=56 Moving to Node #0,1 Current State: 83:[57, 30, 56], Operations: ['22+34=56'] Exploring Operation: 57-30=27, Resulting Numbers: [56, 27] Generated Node #0,1,2: 83:[56, 27] Operation: 57-30=27 Moving to Node #0,1,2 Current State: 83:[56, 27], Operations: ['22+34=56', '57-30=27'] Exploring Operation: 56+27=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
sum_heuristic
[ 94, 28, 27, 56 ]
65
[ "94-27=67", "56/28=2", "67-2=65" ]
Current State: 65:[94, 28, 27, 56], Operations: [] Exploring Operation: 94-27=67, Resulting Numbers: [28, 56, 67] Generated Node #2: [28, 56, 67] from Operation: 94-27=67 Current State: 65:[28, 56, 67], Operations: ['94-27=67'] Exploring Operation: 56/28=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 56/28=2 Current State: 65:[67, 2], Operations: ['94-27=67', '56/28=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[94, 28, 27, 56], Operations: [] Exploring Operation: 94-27=67, Resulting Numbers: [28, 56, 67] Generated Node #0,0: 65:[28, 56, 67] Operation: 94-27=67 Exploring Operation: 28+27=55, Resulting Numbers: [94, 56, 55] Generated Node #0,1: 65:[94, 56, 55] Operation: 28+27=55 Exploring Operation: 94-28=66, Resulting Numbers: [27, 56, 66] Generated Node #0,2: 65:[27, 56, 66] Operation: 94-28=66 Exploring Operation: 56/28=2, Resulting Numbers: [94, 27, 2] Generated Node #0,3: 65:[94, 27, 2] Operation: 56/28=2 Exploring Operation: 28-27=1, Resulting Numbers: [94, 56, 1] Generated Node #0,4: 65:[94, 56, 1] Operation: 28-27=1 Moving to Node #0,2 Current State: 65:[27, 56, 66], Operations: ['94-28=66'] Exploring Operation: 27+66=93, Resulting Numbers: [56, 93] Generated Node #0,2,0: 65:[56, 93] Operation: 27+66=93 Exploring Operation: 66-27=39, Resulting Numbers: [56, 39] Generated Node #0,2,1: 65:[56, 39] Operation: 66-27=39 Exploring Operation: 27+56=83, Resulting Numbers: [66, 83] Generated Node #0,2,2: 65:[66, 83] Operation: 27+56=83 Exploring Operation: 56-27=29, Resulting Numbers: [66, 29] Generated Node #0,2,3: 65:[66, 29] Operation: 56-27=29 Exploring Operation: 66-56=10, Resulting Numbers: [27, 10] Generated Node #0,2,4: 65:[27, 10] Operation: 66-56=10 Moving to Node #0,0 Current State: 65:[28, 56, 67], Operations: ['94-27=67'] Exploring Operation: 67-28=39, Resulting Numbers: [56, 39] Generated Node #0,0,0: 65:[56, 39] Operation: 67-28=39 Exploring Operation: 56-28=28, Resulting Numbers: [67, 28] Generated Node #0,0,1: 65:[67, 28] Operation: 56-28=28 Exploring Operation: 28+56=84, Resulting Numbers: [67, 84] Generated Node #0,0,2: 65:[67, 84] Operation: 28+56=84 Exploring Operation: 67-56=11, Resulting Numbers: [28, 11] Generated Node #0,0,3: 65:[28, 11] Operation: 67-56=11 Exploring Operation: 56/28=2, Resulting Numbers: [67, 2] Generated Node #0,0,4: 65:[67, 2] Operation: 56/28=2 Moving to Node #0,4 Current State: 65:[94, 56, 1], Operations: ['28-27=1'] Exploring Operation: 94-1=93, Resulting Numbers: [56, 93] Generated Node #0,4,0: 65:[56, 93] Operation: 94-1=93 Exploring Operation: 94-56=38, Resulting Numbers: [1, 38] Generated Node #0,4,1: 65:[1, 38] Operation: 94-56=38 Exploring Operation: 94/1=94, Resulting Numbers: [56, 94] Generated Node #0,4,2: 65:[56, 94] Operation: 94/1=94 Exploring Operation: 94*1=94, Resulting Numbers: [56, 94] Generated Node #0,4,3: 65:[56, 94] Operation: 94*1=94 Exploring Operation: 56+1=57, Resulting Numbers: [94, 57] Generated Node #0,4,4: 65:[94, 57] Operation: 56+1=57 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[1, 38], Operations: ['28-27=1', '94-56=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,65 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,65 unequal: No Solution No 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: 65:[56, 93], Operations: ['28-27=1', '94-1=93'] Exploring Operation: 56+93=149, Resulting Numbers: [149] 149,65 unequal: No Solution Exploring Operation: 93-56=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 56*93=5208, Resulting Numbers: [5208] 5208,65 unequal: No Solution No 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: 65:[94, 57], Operations: ['28-27=1', '56+1=57'] Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 94+57=151, Resulting Numbers: [151] 151,65 unequal: No Solution Exploring Operation: 94*57=5358, Resulting Numbers: [5358] 5358,65 unequal: No Solution No 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: 65:[56, 94], Operations: ['28-27=1', '94/1=94'] Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 56*94=5264, Resulting Numbers: [5264] 5264,65 unequal: No Solution Exploring Operation: 56+94=150, Resulting Numbers: [150] 150,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 65:[56, 94], Operations: ['28-27=1', '94*1=94'] Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 56*94=5264, Resulting Numbers: [5264] 5264,65 unequal: No Solution Exploring Operation: 56+94=150, Resulting Numbers: [150] 150,65 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: 65:[94, 27, 2], Operations: ['56/28=2'] Exploring Operation: 27-2=25, Resulting Numbers: [94, 25] Generated Node #0,3,0: 65:[94, 25] Operation: 27-2=25 Exploring Operation: 94-2=92, Resulting Numbers: [27, 92] Generated Node #0,3,1: 65:[27, 92] Operation: 94-2=92 Exploring Operation: 94/2=47, Resulting Numbers: [27, 47] Generated Node #0,3,2: 65:[27, 47] Operation: 94/2=47 Exploring Operation: 27*2=54, Resulting Numbers: [94, 54] Generated Node #0,3,3: 65:[94, 54] Operation: 27*2=54 Exploring Operation: 94-27=67, Resulting Numbers: [2, 67] Generated Node #0,3,4: 65:[2, 67] Operation: 94-27=67 Moving to Node #0,1 Current State: 65:[94, 56, 55], Operations: ['28+27=55'] Exploring Operation: 56-55=1, Resulting Numbers: [94, 1] Generated Node #0,1,0: 65:[94, 1] Operation: 56-55=1 Exploring Operation: 94+55=149, Resulting Numbers: [56, 149] Generated Node #0,1,1: 65:[56, 149] Operation: 94+55=149 Exploring Operation: 94-55=39, Resulting Numbers: [56, 39] Generated Node #0,1,2: 65:[56, 39] Operation: 94-55=39 Exploring Operation: 94-56=38, Resulting Numbers: [55, 38] Generated Node #0,1,3: 65:[55, 38] Operation: 94-56=38 Exploring Operation: 56+55=111, Resulting Numbers: [94, 111] Generated Node #0,1,4: 65:[94, 111] Operation: 56+55=111 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[94, 1], Operations: ['28+27=55', '56-55=1'] Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,65 unequal: No Solution Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,65 unequal: No Solution Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,65 unequal: No Solution Exploring Operation: 94+1=95, Resulting Numbers: [95] 95,65 unequal: No Solution No 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: 65:[56, 39], Operations: ['28+27=55', '94-55=39'] Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,65 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,65 unequal: No Solution No 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: 65:[55, 38], Operations: ['28+27=55', '94-56=38'] Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,65 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,65 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 65:[94, 111], Operations: ['28+27=55', '56+55=111'] Exploring Operation: 94+111=205, Resulting Numbers: [205] 205,65 unequal: No Solution Exploring Operation: 111-94=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 94*111=10434, Resulting Numbers: [10434] 10434,65 unequal: No Solution No 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: 65:[56, 149], Operations: ['28+27=55', '94+55=149'] Exploring Operation: 56*149=8344, Resulting Numbers: [8344] 8344,65 unequal: No Solution Exploring Operation: 149-56=93, Resulting Numbers: [93] 93,65 unequal: No Solution Exploring Operation: 56+149=205, Resulting Numbers: [205] 205,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 65:[67, 2], Operations: ['94-27=67', '56/28=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[94, 28, 27, 56], Operations: [] Exploring Operation: 94-27=67, Resulting Numbers: [28, 56, 67] Generated Node #0,0: 65:[28, 56, 67] Operation: 94-27=67 Moving to Node #0,0 Current State: 65:[28, 56, 67], Operations: ['94-27=67'] Exploring Operation: 56/28=2, Resulting Numbers: [67, 2] Generated Node #0,0,4: 65:[67, 2] Operation: 56/28=2 Moving to Node #0,0,4 Current State: 65:[67, 2], Operations: ['94-27=67', '56/28=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.94184
hs_5
mult_heuristic
[ 42, 95, 65, 80 ]
44
[ "95+65=160", "160/80=2", "42+2=44" ]
Current State: 44:[42, 95, 65, 80], Operations: [] Exploring Operation: 95+65=160, Resulting Numbers: [42, 80, 160] Generated Node #2: [42, 80, 160] from Operation: 95+65=160 Current State: 44:[42, 80, 160], Operations: ['95+65=160'] Exploring Operation: 160/80=2, Resulting Numbers: [42, 2] Generated Node #3: [42, 2] from Operation: 160/80=2 Current State: 44:[42, 2], Operations: ['95+65=160', '160/80=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[42, 95, 65, 80], Operations: [] Exploring Operation: 95-65=30, Resulting Numbers: [42, 80, 30] Generated Node #0,0: 44:[42, 80, 30] Operation: 95-65=30 Exploring Operation: 80-65=15, Resulting Numbers: [42, 95, 15] Generated Node #0,1: 44:[42, 95, 15] Operation: 80-65=15 Exploring Operation: 95-80=15, Resulting Numbers: [42, 65, 15] Generated Node #0,2: 44:[42, 65, 15] Operation: 95-80=15 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[42, 65, 15], Operations: ['95-80=15'] Exploring Operation: 65-15=50, Resulting Numbers: [42, 50] Generated Node #0,2,0: 44:[42, 50] Operation: 65-15=50 Exploring Operation: 42-15=27, Resulting Numbers: [65, 27] Generated Node #0,2,1: 44:[65, 27] Operation: 42-15=27 Exploring Operation: 65-42=23, Resulting Numbers: [15, 23] Generated Node #0,2,2: 44:[15, 23] Operation: 65-42=23 Moving to Node #0,2,2 Current State: 44:[15, 23], Operations: ['95-80=15', '65-42=23'] Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 15*23=345, Resulting Numbers: [345] 345,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[42, 50], Operations: ['95-80=15', '65-15=50'] Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,44 unequal: No Solution Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[65, 27], Operations: ['95-80=15', '42-15=27'] Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 65+27=92, Resulting Numbers: [92] 92,44 unequal: No Solution Exploring Operation: 65*27=1755, Resulting Numbers: [1755] 1755,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[42, 80, 30], Operations: ['95-65=30'] Exploring Operation: 80-30=50, Resulting Numbers: [42, 50] Generated Node #0,0,0: 44:[42, 50] Operation: 80-30=50 Exploring Operation: 80-42=38, Resulting Numbers: [30, 38] Generated Node #0,0,1: 44:[30, 38] Operation: 80-42=38 Exploring Operation: 42-30=12, Resulting Numbers: [80, 12] Generated Node #0,0,2: 44:[80, 12] Operation: 42-30=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[42, 50], Operations: ['95-65=30', '80-30=50'] Exploring Operation: 42+50=92, Resulting Numbers: [92] 92,44 unequal: No Solution Exploring Operation: 50-42=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 42*50=2100, Resulting Numbers: [2100] 2100,44 unequal: No Solution No 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: 44:[30, 38], Operations: ['95-65=30', '80-42=38'] Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 30+38=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 30*38=1140, Resulting Numbers: [1140] 1140,44 unequal: No Solution No 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: 44:[80, 12], Operations: ['95-65=30', '42-30=12'] Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 80+12=92, Resulting Numbers: [92] 92,44 unequal: No Solution Exploring Operation: 80*12=960, Resulting Numbers: [960] 960,44 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: 44:[42, 95, 15], Operations: ['80-65=15'] Exploring Operation: 95-15=80, Resulting Numbers: [42, 80] Generated Node #0,1,0: 44:[42, 80] Operation: 95-15=80 Exploring Operation: 95-42=53, Resulting Numbers: [15, 53] Generated Node #0,1,1: 44:[15, 53] Operation: 95-42=53 Exploring Operation: 42-15=27, Resulting Numbers: [95, 27] Generated Node #0,1,2: 44:[95, 27] Operation: 42-15=27 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 44:[15, 53], Operations: ['80-65=15', '95-42=53'] Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,44 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,44 unequal: No Solution No 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: 44:[42, 80], Operations: ['80-65=15', '95-15=80'] Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,44 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,44 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,44 unequal: No Solution No 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: 44:[95, 27], Operations: ['80-65=15', '42-15=27'] Exploring Operation: 95*27=2565, Resulting Numbers: [2565] 2565,44 unequal: No Solution Exploring Operation: 95-27=68, Resulting Numbers: [68] 68,44 unequal: No Solution Exploring Operation: 95+27=122, Resulting Numbers: [122] 122,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 22, 27, 36, 80 ]
38
[ "27*80=2160", "2160/36=60", "60-22=38" ]
Current State: 38:[22, 27, 36, 80], Operations: [] Exploring Operation: 27*80=2160, Resulting Numbers: [22, 36, 2160] Generated Node #2: [22, 36, 2160] from Operation: 27*80=2160 Current State: 38:[22, 36, 2160], Operations: ['27*80=2160'] Exploring Operation: 2160/36=60, Resulting Numbers: [22, 60] Generated Node #3: [22, 60] from Operation: 2160/36=60 Current State: 38:[22, 60], Operations: ['27*80=2160', '2160/36=60'] Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[22, 27, 36, 80], Operations: [] Exploring Operation: 80-36=44, Resulting Numbers: [22, 27, 44] Generated Node #0,0: 38:[22, 27, 44] Operation: 80-36=44 Exploring Operation: 80-27=53, Resulting Numbers: [22, 36, 53] Generated Node #0,1: 38:[22, 36, 53] Operation: 80-27=53 Exploring Operation: 80-22=58, Resulting Numbers: [27, 36, 58] Generated Node #0,2: 38:[27, 36, 58] Operation: 80-22=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[22, 27, 44], Operations: ['80-36=44'] Exploring Operation: 27-22=5, Resulting Numbers: [44, 5] Generated Node #0,0,0: 38:[44, 5] Operation: 27-22=5 Exploring Operation: 44-27=17, Resulting Numbers: [22, 17] Generated Node #0,0,1: 38:[22, 17] Operation: 44-27=17 Exploring Operation: 44/22=2, Resulting Numbers: [27, 2] Generated Node #0,0,2: 38:[27, 2] Operation: 44/22=2 Moving to Node #0,0,1 Current State: 38:[22, 17], Operations: ['80-36=44', '44-27=17'] Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[27, 2], Operations: ['80-36=44', '44/22=2'] Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,38 unequal: No Solution Exploring Operation: 27*2=54, Resulting Numbers: [54] 54,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[44, 5], Operations: ['80-36=44', '27-22=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,38 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 44*5=220, Resulting Numbers: [220] 220,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 38:[22, 36, 53], Operations: ['80-27=53'] Exploring Operation: 53-22=31, Resulting Numbers: [36, 31] Generated Node #0,1,0: 38:[36, 31] Operation: 53-22=31 Exploring Operation: 53-36=17, Resulting Numbers: [22, 17] Generated Node #0,1,1: 38:[22, 17] Operation: 53-36=17 Exploring Operation: 36-22=14, Resulting Numbers: [53, 14] Generated Node #0,1,2: 38:[53, 14] Operation: 36-22=14 Moving to Node #0,1,1 Current State: 38:[22, 17], Operations: ['80-27=53', '53-36=17'] Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[36, 31], Operations: ['80-27=53', '53-22=31'] Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,38 unequal: No Solution Exploring Operation: 36*31=1116, Resulting Numbers: [1116] 1116,38 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[53, 14], Operations: ['80-27=53', '36-22=14'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 53*14=742, Resulting Numbers: [742] 742,38 unequal: No Solution Exploring Operation: 53+14=67, Resulting Numbers: [67] 67,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[27, 36, 58], Operations: ['80-22=58'] Exploring Operation: 36-27=9, Resulting Numbers: [58, 9] Generated Node #0,2,0: 38:[58, 9] Operation: 36-27=9 Exploring Operation: 58-27=31, Resulting Numbers: [36, 31] Generated Node #0,2,1: 38:[36, 31] Operation: 58-27=31 Exploring Operation: 58-36=22, Resulting Numbers: [27, 22] Generated Node #0,2,2: 38:[27, 22] Operation: 58-36=22 Moving to Node #0,2,1 Current State: 38:[36, 31], Operations: ['80-22=58', '58-27=31'] Exploring Operation: 36*31=1116, Resulting Numbers: [1116] 1116,38 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[27, 22], Operations: ['80-22=58', '58-36=22'] Exploring Operation: 27*22=594, Resulting Numbers: [594] 594,38 unequal: No Solution Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,38 unequal: No Solution Exploring Operation: 27+22=49, Resulting Numbers: [49] 49,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[58, 9], Operations: ['80-22=58', '36-27=9'] Exploring Operation: 58*9=522, Resulting Numbers: [522] 522,38 unequal: No Solution Exploring Operation: 58+9=67, Resulting Numbers: [67] 67,38 unequal: No Solution Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 53, 44, 85, 62 ]
14
[ "53-44=9", "85-62=23", "23-9=14" ]
Current State: 14:[53, 44, 85, 62], Operations: [] Exploring Operation: 53-44=9, Resulting Numbers: [85, 62, 9] Generated Node #2: [85, 62, 9] from Operation: 53-44=9 Current State: 14:[85, 62, 9], Operations: ['53-44=9'] Exploring Operation: 85-62=23, Resulting Numbers: [9, 23] Generated Node #3: [9, 23] from Operation: 85-62=23 Current State: 14:[9, 23], Operations: ['53-44=9', '85-62=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[53, 44, 85, 62], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [53, 44, 23] Generated Node #0,0: 14:[53, 44, 23] Operation: 85-62=23 Exploring Operation: 85-53=32, Resulting Numbers: [44, 62, 32] Generated Node #0,1: 14:[44, 62, 32] Operation: 85-53=32 Moving to Node #0,0 Current State: 14:[53, 44, 23], Operations: ['85-62=23'] Exploring Operation: 53-44=9, Resulting Numbers: [23, 9] Generated Node #0,0,0: 14:[23, 9] Operation: 53-44=9 Exploring Operation: 53-23=30, Resulting Numbers: [44, 30] Generated Node #0,0,1: 14:[44, 30] Operation: 53-23=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[23, 9], Operations: ['85-62=23', '53-44=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[53, 44, 85, 62], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [53, 44, 23] Generated Node #0,0: 14:[53, 44, 23] Operation: 85-62=23 Moving to Node #0,0 Current State: 14:[53, 44, 23], Operations: ['85-62=23'] Exploring Operation: 53-44=9, Resulting Numbers: [23, 9] Generated Node #0,0,0: 14:[23, 9] Operation: 53-44=9 Moving to Node #0,0,0 Current State: 14:[23, 9], Operations: ['85-62=23', '53-44=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 79, 62, 51, 43 ]
40
[ "79-62=17", "51/17=3", "43-3=40" ]
Current State: 40:[79, 62, 51, 43], Operations: [] Exploring Operation: 79-62=17, Resulting Numbers: [51, 43, 17] Generated Node #2: [51, 43, 17] from Operation: 79-62=17 Current State: 40:[51, 43, 17], Operations: ['79-62=17'] Exploring Operation: 51/17=3, Resulting Numbers: [43, 3] Generated Node #3: [43, 3] from Operation: 51/17=3 Current State: 40:[43, 3], Operations: ['79-62=17', '51/17=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[79, 62, 51, 43], Operations: [] Exploring Operation: 79-51=28, Resulting Numbers: [62, 43, 28] Generated Node #0,0: 40:[62, 43, 28] Operation: 79-51=28 Exploring Operation: 62-43=19, Resulting Numbers: [79, 51, 19] Generated Node #0,1: 40:[79, 51, 19] Operation: 62-43=19 Exploring Operation: 79-43=36, Resulting Numbers: [62, 51, 36] Generated Node #0,2: 40:[62, 51, 36] Operation: 79-43=36 Exploring Operation: 79-62=17, Resulting Numbers: [51, 43, 17] Generated Node #0,3: 40:[51, 43, 17] Operation: 79-62=17 Exploring Operation: 62-51=11, Resulting Numbers: [79, 43, 11] Generated Node #0,4: 40:[79, 43, 11] Operation: 62-51=11 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[51, 43, 17], Operations: ['79-62=17'] Exploring Operation: 51-17=34, Resulting Numbers: [43, 34] Generated Node #0,3,0: 40:[43, 34] Operation: 51-17=34 Exploring Operation: 43-17=26, Resulting Numbers: [51, 26] Generated Node #0,3,1: 40:[51, 26] Operation: 43-17=26 Exploring Operation: 51-43=8, Resulting Numbers: [17, 8] Generated Node #0,3,2: 40:[17, 8] Operation: 51-43=8 Exploring Operation: 51+17=68, Resulting Numbers: [43, 68] Generated Node #0,3,3: 40:[43, 68] Operation: 51+17=68 Exploring Operation: 51/17=3, Resulting Numbers: [43, 3] Generated Node #0,3,4: 40:[43, 3] Operation: 51/17=3 Moving to Node #0,3,2 Current State: 40:[17, 8], Operations: ['79-62=17', '51-43=8'] Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,40 unequal: No Solution Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,40 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,40 unequal: No Solution Moving to Node #0,3,4 Current State: 40:[43, 3], Operations: ['79-62=17', '51/17=3'] Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,40 unequal: No Solution Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[79, 62, 51, 43], Operations: [] Exploring Operation: 79-62=17, Resulting Numbers: [51, 43, 17] Generated Node #0,3: 40:[51, 43, 17] Operation: 79-62=17 Moving to Node #0,3 Current State: 40:[51, 43, 17], Operations: ['79-62=17'] Exploring Operation: 51/17=3, Resulting Numbers: [43, 3] Generated Node #0,3,4: 40:[43, 3] Operation: 51/17=3 Moving to Node #0,3,4 Current State: 40:[43, 3], Operations: ['79-62=17', '51/17=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 91, 33, 6, 7 ]
98
[ "33-6=27", "7*27=189", "189-91=98" ]
Current State: 98:[91, 33, 6, 7], Operations: [] Exploring Operation: 33-6=27, Resulting Numbers: [91, 7, 27] Generated Node #2: [91, 7, 27] from Operation: 33-6=27 Current State: 98:[91, 7, 27], Operations: ['33-6=27'] Exploring Operation: 7*27=189, Resulting Numbers: [91, 189] Generated Node #3: [91, 189] from Operation: 7*27=189 Current State: 98:[91, 189], Operations: ['33-6=27', '7*27=189'] Exploring Operation: 189-91=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[91, 33, 6, 7], Operations: [] Exploring Operation: 91-33=58, Resulting Numbers: [6, 7, 58] Generated Node #0,0: 98:[6, 7, 58] Operation: 91-33=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[6, 7, 58], Operations: ['91-33=58'] Exploring Operation: 58-6=52, Resulting Numbers: [7, 52] Generated Node #0,0,0: 98:[7, 52] Operation: 58-6=52 Moving to Node #0,0,0 Current State: 98:[7, 52], Operations: ['91-33=58', '58-6=52'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,98 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
[ 43, 41, 15, 25 ]
20
[ "43-41=2", "15+25=40", "40/2=20" ]
Current State: 20:[43, 41, 15, 25], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [15, 25, 2] Generated Node #2: [15, 25, 2] from Operation: 43-41=2 Current State: 20:[15, 25, 2], Operations: ['43-41=2'] Exploring Operation: 15+25=40, Resulting Numbers: [2, 40] Generated Node #3: [2, 40] from Operation: 15+25=40 Current State: 20:[2, 40], Operations: ['43-41=2', '15+25=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[43, 41, 15, 25], Operations: [] Exploring Operation: 43-15=28, Resulting Numbers: [41, 25, 28] Generated Node #0,0: 20:[41, 25, 28] Operation: 43-15=28 Exploring Operation: 41-15=26, Resulting Numbers: [43, 25, 26] Generated Node #0,1: 20:[43, 25, 26] Operation: 41-15=26 Exploring Operation: 41-25=16, Resulting Numbers: [43, 15, 16] Generated Node #0,2: 20:[43, 15, 16] Operation: 41-25=16 Exploring Operation: 43-41=2, Resulting Numbers: [15, 25, 2] Generated Node #0,3: 20:[15, 25, 2] Operation: 43-41=2 Exploring Operation: 43-25=18, Resulting Numbers: [41, 15, 18] Generated Node #0,4: 20:[41, 15, 18] Operation: 43-25=18 Start Sub Search at level 1: Moving to Node #0,3 Current State: 20:[15, 25, 2], Operations: ['43-41=2'] Exploring Operation: 25+2=27, Resulting Numbers: [15, 27] Generated Node #0,3,0: 20:[15, 27] Operation: 25+2=27 Exploring Operation: 25-15=10, Resulting Numbers: [2, 10] Generated Node #0,3,1: 20:[2, 10] Operation: 25-15=10 Exploring Operation: 15-2=13, Resulting Numbers: [25, 13] Generated Node #0,3,2: 20:[25, 13] Operation: 15-2=13 Exploring Operation: 15+2=17, Resulting Numbers: [25, 17] Generated Node #0,3,3: 20:[25, 17] Operation: 15+2=17 Exploring Operation: 25-2=23, Resulting Numbers: [15, 23] Generated Node #0,3,4: 20:[15, 23] Operation: 25-2=23 Moving to Node #0,3,1 Current State: 20:[2, 10], Operations: ['43-41=2', '25-15=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[43, 41, 15, 25], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [15, 25, 2] Generated Node #0,3: 20:[15, 25, 2] Operation: 43-41=2 Moving to Node #0,3 Current State: 20:[15, 25, 2], Operations: ['43-41=2'] Exploring Operation: 25-15=10, Resulting Numbers: [2, 10] Generated Node #0,3,1: 20:[2, 10] Operation: 25-15=10 Moving to Node #0,3,1 Current State: 20:[2, 10], Operations: ['43-41=2', '25-15=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 52, 65, 37, 40 ]
13
[ "65*40=2600", "2600/52=50", "50-37=13" ]
Current State: 13:[52, 65, 37, 40], Operations: [] Exploring Operation: 65*40=2600, Resulting Numbers: [52, 37, 2600] Generated Node #2: [52, 37, 2600] from Operation: 65*40=2600 Current State: 13:[52, 37, 2600], Operations: ['65*40=2600'] Exploring Operation: 2600/52=50, Resulting Numbers: [37, 50] Generated Node #3: [37, 50] from Operation: 2600/52=50 Current State: 13:[37, 50], Operations: ['65*40=2600', '2600/52=50'] Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[52, 65, 37, 40], Operations: [] Exploring Operation: 52-40=12, Resulting Numbers: [65, 37, 12] Generated Node #0,0: 13:[65, 37, 12] Operation: 52-40=12 Exploring Operation: 65-40=25, Resulting Numbers: [52, 37, 25] Generated Node #0,1: 13:[52, 37, 25] Operation: 65-40=25 Exploring Operation: 52-37=15, Resulting Numbers: [65, 40, 15] Generated Node #0,2: 13:[65, 40, 15] Operation: 52-37=15 Exploring Operation: 65-52=13, Resulting Numbers: [37, 40, 13] Generated Node #0,3: 13:[37, 40, 13] Operation: 65-52=13 Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[37, 40, 13], Operations: ['65-52=13'] Exploring Operation: 40-13=27, Resulting Numbers: [37, 27] Generated Node #0,3,0: 13:[37, 27] Operation: 40-13=27 Exploring Operation: 37-13=24, Resulting Numbers: [40, 24] Generated Node #0,3,1: 13:[40, 24] Operation: 37-13=24 Exploring Operation: 37+40=77, Resulting Numbers: [13, 77] Generated Node #0,3,2: 13:[13, 77] Operation: 37+40=77 Exploring Operation: 40-37=3, Resulting Numbers: [13, 3] Generated Node #0,3,3: 13:[13, 3] Operation: 40-37=3 Moving to Node #0,3,3 Current State: 13:[13, 3], Operations: ['65-52=13', '40-37=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,13 unequal: No Solution Moving to Node #0,3,1 Current State: 13:[40, 24], Operations: ['65-52=13', '37-13=24'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,13 unequal: No Solution Moving to Node #0,3,0 Current State: 13:[37, 27], Operations: ['65-52=13', '40-13=27'] Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,13 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,13 unequal: No Solution Moving to Node #0,3,2 Current State: 13:[13, 77], Operations: ['65-52=13', '37+40=77'] Exploring Operation: 77-13=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 13+77=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 13*77=1001, Resulting Numbers: [1001] 1001,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[52, 37, 25], Operations: ['65-40=25'] Exploring Operation: 52-25=27, Resulting Numbers: [37, 27] Generated Node #0,1,0: 13:[37, 27] Operation: 52-25=27 Exploring Operation: 52-37=15, Resulting Numbers: [25, 15] Generated Node #0,1,1: 13:[25, 15] Operation: 52-37=15 Exploring Operation: 52+37=89, Resulting Numbers: [25, 89] Generated Node #0,1,2: 13:[25, 89] Operation: 52+37=89 Exploring Operation: 37-25=12, Resulting Numbers: [52, 12] Generated Node #0,1,3: 13:[52, 12] Operation: 37-25=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[25, 15], Operations: ['65-40=25', '52-37=15'] Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,13 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[37, 27], Operations: ['65-40=25', '52-25=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,13 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 13:[52, 12], Operations: ['65-40=25', '37-25=12'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[25, 89], Operations: ['65-40=25', '52+37=89'] Exploring Operation: 25*89=2225, Resulting Numbers: [2225] 2225,13 unequal: No Solution Exploring Operation: 89-25=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 25+89=114, Resulting Numbers: [114] 114,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[65, 37, 12], Operations: ['52-40=12'] Exploring Operation: 65-12=53, Resulting Numbers: [37, 53] Generated Node #0,0,0: 13:[37, 53] Operation: 65-12=53 Exploring Operation: 65+12=77, Resulting Numbers: [37, 77] Generated Node #0,0,1: 13:[37, 77] Operation: 65+12=77 Exploring Operation: 65-37=28, Resulting Numbers: [12, 28] Generated Node #0,0,2: 13:[12, 28] Operation: 65-37=28 Exploring Operation: 37-12=25, Resulting Numbers: [65, 25] Generated Node #0,0,3: 13:[65, 25] Operation: 37-12=25 Moving to Node #0,0,2 Current State: 13:[12, 28], Operations: ['52-40=12', '65-37=28'] Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,13 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[65, 25], Operations: ['52-40=12', '37-12=25'] Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,13 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[37, 53], Operations: ['52-40=12', '65-12=53'] Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,13 unequal: No Solution Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[37, 77], Operations: ['52-40=12', '65+12=77'] Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,13 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,13 unequal: No Solution Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[65, 40, 15], Operations: ['52-37=15'] Exploring Operation: 65+40=105, Resulting Numbers: [15, 105] Generated Node #0,2,0: 13:[15, 105] Operation: 65+40=105 Exploring Operation: 65-40=25, Resulting Numbers: [15, 25] Generated Node #0,2,1: 13:[15, 25] Operation: 65-40=25 Exploring Operation: 65-15=50, Resulting Numbers: [40, 50] Generated Node #0,2,2: 13:[40, 50] Operation: 65-15=50 Exploring Operation: 40-15=25, Resulting Numbers: [65, 25] Generated Node #0,2,3: 13:[65, 25] Operation: 40-15=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[15, 25], Operations: ['52-37=15', '65-40=25'] Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,13 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[40, 50], Operations: ['52-37=15', '65-15=50'] Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,13 unequal: No Solution Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 13:[65, 25], Operations: ['52-37=15', '40-15=25'] Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 13:[15, 105], Operations: ['52-37=15', '65+40=105'] Exploring Operation: 105/15=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 105-15=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 15+105=120, Resulting Numbers: [120] 120,13 unequal: No Solution Exploring Operation: 15*105=1575, Resulting Numbers: [1575] 1575,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 53, 74, 47, 74 ]
47
[ "74-74=0", "53*0=0", "47+0=47" ]
Current State: 47:[53, 74, 47, 74], Operations: [] Exploring Operation: 74-74=0, Resulting Numbers: [53, 47, 0] Generated Node #2: [53, 47, 0] from Operation: 74-74=0 Current State: 47:[53, 47, 0], Operations: ['74-74=0'] Exploring Operation: 53*0=0, Resulting Numbers: [47, 0] Generated Node #3: [47, 0] from Operation: 53*0=0 Current State: 47:[47, 0], Operations: ['74-74=0', '53*0=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[53, 74, 47, 74], Operations: [] Exploring Operation: 74/74=1, Resulting Numbers: [53, 47, 1] Generated Node #0,0: 47:[53, 47, 1] Operation: 74/74=1 Exploring Operation: 74-53=21, Resulting Numbers: [47, 74, 21] Generated Node #0,1: 47:[47, 74, 21] Operation: 74-53=21 Moving to Node #0,0 Current State: 47:[53, 47, 1], Operations: ['74/74=1'] Exploring Operation: 53-1=52, Resulting Numbers: [47, 52] Generated Node #0,0,0: 47:[47, 52] Operation: 53-1=52 Exploring Operation: 53*1=53, Resulting Numbers: [47, 53] Generated Node #0,0,1: 47:[47, 53] Operation: 53*1=53 Moving to Node #0,1 Current State: 47:[47, 74, 21], Operations: ['74-53=21'] Exploring Operation: 74-21=53, Resulting Numbers: [47, 53] Generated Node #0,1,0: 47:[47, 53] Operation: 74-21=53 Exploring Operation: 74-47=27, Resulting Numbers: [21, 27] Generated Node #0,1,1: 47:[21, 27] Operation: 74-47=27 Moving to Node #0,0,0 Current State: 47:[47, 52], Operations: ['74/74=1', '53-1=52'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[47, 53], Operations: ['74-53=21', '74-21=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,47 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[47, 53], Operations: ['74/74=1', '53*1=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,47 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[21, 27], Operations: ['74-53=21', '74-47=27'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 79, 59, 9, 42 ]
13
[ "79-59=20", "42-9=33", "33-20=13" ]
Current State: 13:[79, 59, 9, 42], Operations: [] Exploring Operation: 79-59=20, Resulting Numbers: [9, 42, 20] Generated Node #2: [9, 42, 20] from Operation: 79-59=20 Current State: 13:[9, 42, 20], Operations: ['79-59=20'] Exploring Operation: 42-9=33, Resulting Numbers: [20, 33] Generated Node #3: [20, 33] from Operation: 42-9=33 Current State: 13:[20, 33], Operations: ['79-59=20', '42-9=33'] Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[79, 59, 9, 42], Operations: [] Exploring Operation: 79-42=37, Resulting Numbers: [59, 9, 37] Generated Node #0,0: 13:[59, 9, 37] Operation: 79-42=37 Exploring Operation: 59-42=17, Resulting Numbers: [79, 9, 17] Generated Node #0,1: 13:[79, 9, 17] Operation: 59-42=17 Exploring Operation: 79-59=20, Resulting Numbers: [9, 42, 20] Generated Node #0,2: 13:[9, 42, 20] Operation: 79-59=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[9, 42, 20], Operations: ['79-59=20'] Exploring Operation: 20-9=11, Resulting Numbers: [42, 11] Generated Node #0,2,0: 13:[42, 11] Operation: 20-9=11 Exploring Operation: 42-20=22, Resulting Numbers: [9, 22] Generated Node #0,2,1: 13:[9, 22] Operation: 42-20=22 Exploring Operation: 42-9=33, Resulting Numbers: [20, 33] Generated Node #0,2,2: 13:[20, 33] Operation: 42-9=33 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 13:[9, 22], Operations: ['79-59=20', '42-20=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[79, 59, 9, 42], Operations: [] Exploring Operation: 79-59=20, Resulting Numbers: [9, 42, 20] Generated Node #0,2: 13:[9, 42, 20] Operation: 79-59=20 Moving to Node #0,2 Current State: 13:[9, 42, 20], Operations: ['79-59=20'] Exploring Operation: 42-20=22, Resulting Numbers: [9, 22] Generated Node #0,2,1: 13:[9, 22] Operation: 42-20=22 Moving to Node #0,2,1 Current State: 13:[9, 22], Operations: ['79-59=20', '42-20=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 14, 88, 88, 4 ]
80
[ "14+88=102", "88/4=22", "102-22=80" ]
Current State: 80:[14, 88, 88, 4], Operations: [] Exploring Operation: 14+88=102, Resulting Numbers: [4, 102] Generated Node #2: [4, 102] from Operation: 14+88=102 Current State: 80:[4, 102], Operations: ['14+88=102'] Exploring Operation: 88/4=22, Resulting Numbers: [102, 22] Generated Node #3: [102, 22] from Operation: 88/4=22 Current State: 80:[102, 22], Operations: ['14+88=102', '88/4=22'] Exploring Operation: 102-22=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[14, 88, 88, 4], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [14, 88, 22] Generated Node #0,0: 80:[14, 88, 22] Operation: 88/4=22 Exploring Operation: 88-14=74, Resulting Numbers: [88, 4, 74] Generated Node #0,1: 80:[88, 4, 74] Operation: 88-14=74 Exploring Operation: 88-88=0, Resulting Numbers: [14, 4, 0] Generated Node #0,2: 80:[14, 4, 0] Operation: 88-88=0 Exploring Operation: 88/4=22, Resulting Numbers: [14, 88, 22] Generated Node #0,3: 80:[14, 88, 22] Operation: 88/4=22 Exploring Operation: 88/88=1, Resulting Numbers: [14, 4, 1] Generated Node #0,4: 80:[14, 4, 1] Operation: 88/88=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 80:[14, 4, 1], Operations: ['88/88=1'] Exploring Operation: 14*1=14, Resulting Numbers: [4, 14] Generated Node #0,4,0: 80:[4, 14] Operation: 14*1=14 Exploring Operation: 14-4=10, Resulting Numbers: [1, 10] Generated Node #0,4,1: 80:[1, 10] Operation: 14-4=10 Exploring Operation: 4+1=5, Resulting Numbers: [14, 5] Generated Node #0,4,2: 80:[14, 5] Operation: 4+1=5 Exploring Operation: 14+1=15, Resulting Numbers: [4, 15] Generated Node #0,4,3: 80:[4, 15] Operation: 14+1=15 Exploring Operation: 14/1=14, Resulting Numbers: [4, 14] Generated Node #0,4,4: 80:[4, 14] Operation: 14/1=14 Moving to Node #0,4,1 Current State: 80:[1, 10], Operations: ['88/88=1', '14-4=10'] Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,80 unequal: No Solution Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[4, 15], Operations: ['88/88=1', '14+1=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,4,0 Current State: 80:[4, 14], Operations: ['88/88=1', '14*1=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[14, 5], Operations: ['88/88=1', '4+1=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[4, 14], Operations: ['88/88=1', '14/1=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,80 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:[14, 4, 0], Operations: ['88-88=0'] Exploring Operation: 4+0=4, Resulting Numbers: [14, 4] Generated Node #0,2,0: 80:[14, 4] Operation: 4+0=4 Exploring Operation: 14+0=14, Resulting Numbers: [4, 14] Generated Node #0,2,1: 80:[4, 14] Operation: 14+0=14 Exploring Operation: 14-0=14, Resulting Numbers: [4, 14] Generated Node #0,2,2: 80:[4, 14] Operation: 14-0=14 Exploring Operation: 14*0=0, Resulting Numbers: [4, 0] Generated Node #0,2,3: 80:[4, 0] Operation: 14*0=0 Exploring Operation: 14-4=10, Resulting Numbers: [0, 10] Generated Node #0,2,4: 80:[0, 10] Operation: 14-4=10 Moving to Node #0,2,0 Current State: 80:[14, 4], Operations: ['88-88=0', '4+0=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[4, 14], Operations: ['88-88=0', '14-0=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,80 unequal: No Solution Moving to Node #0,2,4 Current State: 80:[0, 10], Operations: ['88-88=0', '14-4=10'] Exploring Operation: 10-0=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 0+10=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 0*10=0, Resulting Numbers: [0] 0,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[4, 14], Operations: ['88-88=0', '14+0=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[4, 0], Operations: ['88-88=0', '14*0=0'] Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[14, 88, 22], Operations: ['88/4=22'] Exploring Operation: 88/22=4, Resulting Numbers: [14, 4] Generated Node #0,0,0: 80:[14, 4] Operation: 88/22=4 Exploring Operation: 88-14=74, Resulting Numbers: [22, 74] Generated Node #0,0,1: 80:[22, 74] Operation: 88-14=74 Exploring Operation: 88-22=66, Resulting Numbers: [14, 66] Generated Node #0,0,2: 80:[14, 66] Operation: 88-22=66 Exploring Operation: 14+22=36, Resulting Numbers: [88, 36] Generated Node #0,0,3: 80:[88, 36] Operation: 14+22=36 Exploring Operation: 22-14=8, Resulting Numbers: [88, 8] Generated Node #0,0,4: 80:[88, 8] Operation: 22-14=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[14, 4], Operations: ['88/4=22', '88/22=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,80 unequal: No Solution No 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: 80:[22, 74], Operations: ['88/4=22', '88-14=74'] Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,80 unequal: No Solution No 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: 80:[88, 8], Operations: ['88/4=22', '22-14=8'] Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 88*8=704, Resulting Numbers: [704] 704,80 unequal: No Solution Exploring Operation: 88+8=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[14, 88, 88, 4], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [14, 88, 22] Generated Node #0,0: 80:[14, 88, 22] Operation: 88/4=22 Moving to Node #0,0 Current State: 80:[14, 88, 22], Operations: ['88/4=22'] Exploring Operation: 22-14=8, Resulting Numbers: [88, 8] Generated Node #0,0,4: 80:[88, 8] Operation: 22-14=8 Moving to Node #0,0,4 Current State: 80:[88, 8], Operations: ['88/4=22', '22-14=8'] Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.943576
hs_5
mult_heuristic
[ 61, 92, 94, 74 ]
87
[ "94-92=2", "74*2=148", "148-61=87" ]
Current State: 87:[61, 92, 94, 74], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [61, 74, 2] Generated Node #2: [61, 74, 2] from Operation: 94-92=2 Current State: 87:[61, 74, 2], Operations: ['94-92=2'] Exploring Operation: 74*2=148, Resulting Numbers: [61, 148] Generated Node #3: [61, 148] from Operation: 74*2=148 Current State: 87:[61, 148], Operations: ['94-92=2', '74*2=148'] Exploring Operation: 148-61=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[61, 92, 94, 74], Operations: [] Exploring Operation: 94-61=33, Resulting Numbers: [92, 74, 33] Generated Node #0,0: 87:[92, 74, 33] Operation: 94-61=33 Exploring Operation: 92-61=31, Resulting Numbers: [94, 74, 31] Generated Node #0,1: 87:[94, 74, 31] Operation: 92-61=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[92, 74, 33], Operations: ['94-61=33'] Exploring Operation: 74-33=41, Resulting Numbers: [92, 41] Generated Node #0,0,0: 87:[92, 41] Operation: 74-33=41 Exploring Operation: 92-74=18, Resulting Numbers: [33, 18] Generated Node #0,0,1: 87:[33, 18] Operation: 92-74=18 Moving to Node #0,0,1 Current State: 87:[33, 18], Operations: ['94-61=33', '92-74=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[92, 41], Operations: ['94-61=33', '74-33=41'] Exploring Operation: 92+41=133, Resulting Numbers: [133] 133,87 unequal: No Solution Exploring Operation: 92-41=51, Resulting Numbers: [51] 51,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[94, 74, 31], Operations: ['92-61=31'] Exploring Operation: 94-74=20, Resulting Numbers: [31, 20] Generated Node #0,1,0: 87:[31, 20] Operation: 94-74=20 Exploring Operation: 74-31=43, Resulting Numbers: [94, 43] Generated Node #0,1,1: 87:[94, 43] Operation: 74-31=43 Moving to Node #0,1,0 Current State: 87:[31, 20], Operations: ['92-61=31', '94-74=20'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,87 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[94, 43], Operations: ['92-61=31', '74-31=43'] Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 94+43=137, Resulting Numbers: [137] 137,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 21, 17, 96, 32 ]
60
[ "21-17=4", "96-32=64", "64-4=60" ]
Current State: 60:[21, 17, 96, 32], Operations: [] Exploring Operation: 21-17=4, Resulting Numbers: [96, 32, 4] Generated Node #2: [96, 32, 4] from Operation: 21-17=4 Current State: 60:[96, 32, 4], Operations: ['21-17=4'] Exploring Operation: 96-32=64, Resulting Numbers: [4, 64] Generated Node #3: [4, 64] from Operation: 96-32=64 Current State: 60:[4, 64], Operations: ['21-17=4', '96-32=64'] Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[21, 17, 96, 32], Operations: [] Exploring Operation: 96-17=79, Resulting Numbers: [21, 32, 79] Generated Node #0,0: 60:[21, 32, 79] Operation: 96-17=79 Exploring Operation: 96-32=64, Resulting Numbers: [21, 17, 64] Generated Node #0,1: 60:[21, 17, 64] Operation: 96-32=64 Exploring Operation: 32-17=15, Resulting Numbers: [21, 96, 15] Generated Node #0,2: 60:[21, 96, 15] Operation: 32-17=15 Exploring Operation: 96-21=75, Resulting Numbers: [17, 32, 75] Generated Node #0,3: 60:[17, 32, 75] Operation: 96-21=75 Exploring Operation: 96/32=3, Resulting Numbers: [21, 17, 3] Generated Node #0,4: 60:[21, 17, 3] Operation: 96/32=3 Start Sub Search at level 1: Moving to Node #0,4 Current State: 60:[21, 17, 3], Operations: ['96/32=3'] Exploring Operation: 21-3=18, Resulting Numbers: [17, 18] Generated Node #0,4,0: 60:[17, 18] Operation: 21-3=18 Exploring Operation: 17-3=14, Resulting Numbers: [21, 14] Generated Node #0,4,1: 60:[21, 14] Operation: 17-3=14 Exploring Operation: 21/3=7, Resulting Numbers: [17, 7] Generated Node #0,4,2: 60:[17, 7] Operation: 21/3=7 Exploring Operation: 17+3=20, Resulting Numbers: [21, 20] Generated Node #0,4,3: 60:[21, 20] Operation: 17+3=20 Exploring Operation: 21-17=4, Resulting Numbers: [3, 4] Generated Node #0,4,4: 60:[3, 4] Operation: 21-17=4 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 60:[3, 4], Operations: ['96/32=3', '21-17=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,60 unequal: No Solution No 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: 60:[21, 20], Operations: ['96/32=3', '17+3=20'] Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,60 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,60 unequal: No Solution No 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: 60:[21, 14], Operations: ['96/32=3', '17-3=14'] Exploring Operation: 21*14=294, Resulting Numbers: [294] 294,60 unequal: No Solution Exploring Operation: 21-14=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 21+14=35, Resulting Numbers: [35] 35,60 unequal: No Solution No 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: 60:[17, 7], Operations: ['96/32=3', '21/3=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,60 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,60 unequal: No Solution No 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: 60:[17, 18], Operations: ['96/32=3', '21-3=18'] Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,60 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,60 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: 60:[21, 17, 64], Operations: ['96-32=64'] Exploring Operation: 64-17=47, Resulting Numbers: [21, 47] Generated Node #0,1,0: 60:[21, 47] Operation: 64-17=47 Exploring Operation: 64-21=43, Resulting Numbers: [17, 43] Generated Node #0,1,1: 60:[17, 43] Operation: 64-21=43 Exploring Operation: 21-17=4, Resulting Numbers: [64, 4] Generated Node #0,1,2: 60:[64, 4] Operation: 21-17=4 Exploring Operation: 17+64=81, Resulting Numbers: [21, 81] Generated Node #0,1,3: 60:[21, 81] Operation: 17+64=81 Exploring Operation: 21+17=38, Resulting Numbers: [64, 38] Generated Node #0,1,4: 60:[64, 38] Operation: 21+17=38 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 60:[64, 4], Operations: ['96-32=64', '21-17=4'] Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[21, 17, 96, 32], Operations: [] Exploring Operation: 96-32=64, Resulting Numbers: [21, 17, 64] Generated Node #0,1: 60:[21, 17, 64] Operation: 96-32=64 Moving to Node #0,1 Current State: 60:[21, 17, 64], Operations: ['96-32=64'] Exploring Operation: 21-17=4, Resulting Numbers: [64, 4] Generated Node #0,1,2: 60:[64, 4] Operation: 21-17=4 Moving to Node #0,1,2 Current State: 60:[64, 4], Operations: ['96-32=64', '21-17=4'] Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 15, 54, 80, 97 ]
22
[ "54-15=39", "97-80=17", "39-17=22" ]
Current State: 22:[15, 54, 80, 97], Operations: [] Exploring Operation: 54-15=39, Resulting Numbers: [80, 97, 39] Generated Node #2: [80, 97, 39] from Operation: 54-15=39 Current State: 22:[80, 97, 39], Operations: ['54-15=39'] Exploring Operation: 97-80=17, Resulting Numbers: [39, 17] Generated Node #3: [39, 17] from Operation: 97-80=17 Current State: 22:[39, 17], Operations: ['54-15=39', '97-80=17'] Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[15, 54, 80, 97], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [15, 54, 17] Generated Node #0,0: 22:[15, 54, 17] Operation: 97-80=17 Exploring Operation: 80-54=26, Resulting Numbers: [15, 97, 26] Generated Node #0,1: 22:[15, 97, 26] Operation: 80-54=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[15, 54, 17], Operations: ['97-80=17'] Exploring Operation: 54-17=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 22:[15, 37] Operation: 54-17=37 Exploring Operation: 54-15=39, Resulting Numbers: [17, 39] Generated Node #0,0,1: 22:[17, 39] Operation: 54-15=39 Moving to Node #0,0,0 Current State: 22:[15, 37], Operations: ['97-80=17', '54-17=37'] Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,22 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[15, 54, 80, 97], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [15, 54, 17] Generated Node #0,0: 22:[15, 54, 17] Operation: 97-80=17 Moving to Node #0,0 Current State: 22:[15, 54, 17], Operations: ['97-80=17'] Exploring Operation: 54-17=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 22:[15, 37] Operation: 54-17=37 Moving to Node #0,0,0 Current State: 22:[15, 37], Operations: ['97-80=17', '54-17=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 28, 54, 51, 76 ]
16
[ "76-28=48", "54-51=3", "48/3=16" ]
Current State: 16:[28, 54, 51, 76], Operations: [] Exploring Operation: 76-28=48, Resulting Numbers: [54, 51, 48] Generated Node #2: [54, 51, 48] from Operation: 76-28=48 Current State: 16:[54, 51, 48], Operations: ['76-28=48'] Exploring Operation: 54-51=3, Resulting Numbers: [48, 3] Generated Node #3: [48, 3] from Operation: 54-51=3 Current State: 16:[48, 3], Operations: ['76-28=48', '54-51=3'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[28, 54, 51, 76], Operations: [] Exploring Operation: 76-54=22, Resulting Numbers: [28, 51, 22] Generated Node #0,0: 16:[28, 51, 22] Operation: 76-54=22 Exploring Operation: 76-51=25, Resulting Numbers: [28, 54, 25] Generated Node #0,1: 16:[28, 54, 25] Operation: 76-51=25 Moving to Node #0,0 Current State: 16:[28, 51, 22], Operations: ['76-54=22'] Exploring Operation: 51-28=23, Resulting Numbers: [22, 23] Generated Node #0,0,0: 16:[22, 23] Operation: 51-28=23 Exploring Operation: 51-22=29, Resulting Numbers: [28, 29] Generated Node #0,0,1: 16:[28, 29] Operation: 51-22=29 Moving to Node #0,1 Current State: 16:[28, 54, 25], Operations: ['76-51=25'] Exploring Operation: 54-25=29, Resulting Numbers: [28, 29] Generated Node #0,1,0: 16:[28, 29] Operation: 54-25=29 Exploring Operation: 54-28=26, Resulting Numbers: [25, 26] Generated Node #0,1,1: 16:[25, 26] Operation: 54-28=26 Moving to Node #0,0,0 Current State: 16:[22, 23], Operations: ['76-54=22', '51-28=23'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[25, 26], Operations: ['76-51=25', '54-28=26'] Exploring Operation: 25+26=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[28, 29], Operations: ['76-54=22', '51-22=29'] Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,16 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[28, 29], Operations: ['76-51=25', '54-25=29'] Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,16 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 54, 25, 98, 79 ]
98
[ "54+25=79", "98+79=177", "177-79=98" ]
Current State: 98:[54, 25, 98, 79], Operations: [] Exploring Operation: 54+25=79, Resulting Numbers: [98, 79, 79] Generated Node #2: [98, 79, 79] from Operation: 54+25=79 Current State: 98:[98, 79, 79], Operations: ['54+25=79'] Exploring Operation: 98+79=177, Resulting Numbers: [177] 177,98 equal: Goal Reached Exploring Operation: 177-79=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[54, 25, 98, 79], Operations: [] Exploring Operation: 79-25=54, Resulting Numbers: [54, 98, 54] Generated Node #0,0: 98:[54, 98, 54] Operation: 79-25=54 Exploring Operation: 98-79=19, Resulting Numbers: [54, 25, 19] Generated Node #0,1: 98:[54, 25, 19] Operation: 98-79=19 Exploring Operation: 79-54=25, Resulting Numbers: [25, 98, 25] Generated Node #0,2: 98:[25, 98, 25] Operation: 79-54=25 Exploring Operation: 25+79=104, Resulting Numbers: [54, 98, 104] Generated Node #0,3: 98:[54, 98, 104] Operation: 25+79=104 Moving to Node #0,0 Current State: 98:[54, 98, 54], Operations: ['79-25=54'] Exploring Operation: 54+54=108, Resulting Numbers: [98, 108] Generated Node #0,0,0: 98:[98, 108] Operation: 54+54=108 Exploring Operation: 54-54=0, Resulting Numbers: [98, 0] Generated Node #0,0,1: 98:[98, 0] Operation: 54-54=0 Exploring Operation: 98-54=44, Resulting Numbers: [54, 44] Generated Node #0,0,2: 98:[54, 44] Operation: 98-54=44 Exploring Operation: 54/54=1, Resulting Numbers: [98, 1] Generated Node #0,0,3: 98:[98, 1] Operation: 54/54=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 98:[98, 1], Operations: ['79-25=54', '54/54=1'] Exploring Operation: 98+1=99, Resulting Numbers: [99] 99,98 unequal: No Solution Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[54, 25, 98, 79], Operations: [] Exploring Operation: 79-25=54, Resulting Numbers: [54, 98, 54] Generated Node #0,0: 98:[54, 98, 54] Operation: 79-25=54 Moving to Node #0,0 Current State: 98:[54, 98, 54], Operations: ['79-25=54'] Exploring Operation: 54/54=1, Resulting Numbers: [98, 1] Generated Node #0,0,3: 98:[98, 1] Operation: 54/54=1 Moving to Node #0,0,3 Current State: 98:[98, 1], Operations: ['79-25=54', '54/54=1'] Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 70, 39, 26, 64 ]
70
[ "39+26=65", "65-64=1", "70*1=70" ]
Current State: 70:[70, 39, 26, 64], Operations: [] Exploring Operation: 39+26=65, Resulting Numbers: [70, 64, 65] Generated Node #2: [70, 64, 65] from Operation: 39+26=65 Current State: 70:[70, 64, 65], Operations: ['39+26=65'] Exploring Operation: 65-64=1, Resulting Numbers: [70, 1] Generated Node #3: [70, 1] from Operation: 65-64=1 Current State: 70:[70, 1], Operations: ['39+26=65', '65-64=1'] Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[70, 39, 26, 64], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [70, 39, 38] Generated Node #0,0: 70:[70, 39, 38] Operation: 64-26=38 Exploring Operation: 39-26=13, Resulting Numbers: [70, 64, 13] Generated Node #0,1: 70:[70, 64, 13] Operation: 39-26=13 Exploring Operation: 39+26=65, Resulting Numbers: [70, 64, 65] Generated Node #0,2: 70:[70, 64, 65] Operation: 39+26=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[70, 39, 38], Operations: ['64-26=38'] Exploring Operation: 70-39=31, Resulting Numbers: [38, 31] Generated Node #0,0,0: 70:[38, 31] Operation: 70-39=31 Exploring Operation: 39-38=1, Resulting Numbers: [70, 1] Generated Node #0,0,1: 70:[70, 1] Operation: 39-38=1 Exploring Operation: 70-38=32, Resulting Numbers: [39, 32] Generated Node #0,0,2: 70:[39, 32] Operation: 70-38=32 Moving to Node #0,0,1 Current State: 70:[70, 1], Operations: ['64-26=38', '39-38=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,70 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[70, 39, 26, 64], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [70, 39, 38] Generated Node #0,0: 70:[70, 39, 38] Operation: 64-26=38 Moving to Node #0,0 Current State: 70:[70, 39, 38], Operations: ['64-26=38'] Exploring Operation: 39-38=1, Resulting Numbers: [70, 1] Generated Node #0,0,1: 70:[70, 1] Operation: 39-38=1 Moving to Node #0,0,1 Current State: 70:[70, 1], Operations: ['64-26=38', '39-38=1'] Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 39, 21, 15, 34 ]
11
[ "39+21=60", "15+34=49", "60-49=11" ]
Current State: 11:[39, 21, 15, 34], Operations: [] Exploring Operation: 39+21=60, Resulting Numbers: [15, 34, 60] Generated Node #2: [15, 34, 60] from Operation: 39+21=60 Current State: 11:[15, 34, 60], Operations: ['39+21=60'] Exploring Operation: 15+34=49, Resulting Numbers: [60, 49] Generated Node #3: [60, 49] from Operation: 15+34=49 Current State: 11:[60, 49], Operations: ['39+21=60', '15+34=49'] Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[39, 21, 15, 34], Operations: [] Exploring Operation: 39-21=18, Resulting Numbers: [15, 34, 18] Generated Node #0,0: 11:[15, 34, 18] Operation: 39-21=18 Exploring Operation: 39-34=5, Resulting Numbers: [21, 15, 5] Generated Node #0,1: 11:[21, 15, 5] Operation: 39-34=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[21, 15, 5], Operations: ['39-34=5'] Exploring Operation: 21-5=16, Resulting Numbers: [15, 16] Generated Node #0,1,0: 11:[15, 16] Operation: 21-5=16 Exploring Operation: 21-15=6, Resulting Numbers: [5, 6] Generated Node #0,1,1: 11:[5, 6] Operation: 21-15=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[15, 16], Operations: ['39-34=5', '21-5=16'] Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[5, 6], Operations: ['39-34=5', '21-15=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[39, 21, 15, 34], Operations: [] Exploring Operation: 39-34=5, Resulting Numbers: [21, 15, 5] Generated Node #0,1: 11:[21, 15, 5] Operation: 39-34=5 Moving to Node #0,1 Current State: 11:[21, 15, 5], Operations: ['39-34=5'] Exploring Operation: 21-15=6, Resulting Numbers: [5, 6] Generated Node #0,1,1: 11:[5, 6] Operation: 21-15=6 Moving to Node #0,1,1 Current State: 11:[5, 6], Operations: ['39-34=5', '21-15=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 54, 82, 51, 58 ]
35
[ "82-54=28", "58-51=7", "28+7=35" ]
Current State: 35:[54, 82, 51, 58], Operations: [] Exploring Operation: 82-54=28, Resulting Numbers: [51, 58, 28] Generated Node #2: [51, 58, 28] from Operation: 82-54=28 Current State: 35:[51, 58, 28], Operations: ['82-54=28'] Exploring Operation: 58-51=7, Resulting Numbers: [28, 7] Generated Node #3: [28, 7] from Operation: 58-51=7 Current State: 35:[28, 7], Operations: ['82-54=28', '58-51=7'] Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[54, 82, 51, 58], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [54, 58, 31] Generated Node #0,0: 35:[54, 58, 31] Operation: 82-51=31 Exploring Operation: 82-54=28, Resulting Numbers: [51, 58, 28] Generated Node #0,1: 35:[51, 58, 28] Operation: 82-54=28 Exploring Operation: 58-54=4, Resulting Numbers: [82, 51, 4] Generated Node #0,2: 35:[82, 51, 4] Operation: 58-54=4 Exploring Operation: 82-58=24, Resulting Numbers: [54, 51, 24] Generated Node #0,3: 35:[54, 51, 24] Operation: 82-58=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[54, 58, 31], Operations: ['82-51=31'] Exploring Operation: 54-31=23, Resulting Numbers: [58, 23] Generated Node #0,0,0: 35:[58, 23] Operation: 54-31=23 Exploring Operation: 58-54=4, Resulting Numbers: [31, 4] Generated Node #0,0,1: 35:[31, 4] Operation: 58-54=4 Exploring Operation: 54+31=85, Resulting Numbers: [58, 85] Generated Node #0,0,2: 35:[58, 85] Operation: 54+31=85 Exploring Operation: 58-31=27, Resulting Numbers: [54, 27] Generated Node #0,0,3: 35:[54, 27] Operation: 58-31=27 Moving to Node #0,0,1 Current State: 35:[31, 4], Operations: ['82-51=31', '58-54=4'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,35 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[54, 82, 51, 58], Operations: [] Exploring Operation: 82-51=31, Resulting Numbers: [54, 58, 31] Generated Node #0,0: 35:[54, 58, 31] Operation: 82-51=31 Moving to Node #0,0 Current State: 35:[54, 58, 31], Operations: ['82-51=31'] Exploring Operation: 58-54=4, Resulting Numbers: [31, 4] Generated Node #0,0,1: 35:[31, 4] Operation: 58-54=4 Moving to Node #0,0,1 Current State: 35:[31, 4], Operations: ['82-51=31', '58-54=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 22, 88, 30, 13 ]
92
[ "22+30=52", "52/13=4", "88+4=92" ]
Current State: 92:[22, 88, 30, 13], Operations: [] Exploring Operation: 22+30=52, Resulting Numbers: [88, 13, 52] Generated Node #2: [88, 13, 52] from Operation: 22+30=52 Current State: 92:[88, 13, 52], Operations: ['22+30=52'] Exploring Operation: 52/13=4, Resulting Numbers: [88, 4] Generated Node #3: [88, 4] from Operation: 52/13=4 Current State: 92:[88, 4], Operations: ['22+30=52', '52/13=4'] Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[22, 88, 30, 13], Operations: [] Exploring Operation: 30-13=17, Resulting Numbers: [22, 88, 17] Generated Node #0,0: 92:[22, 88, 17] Operation: 30-13=17 Exploring Operation: 30+13=43, Resulting Numbers: [22, 88, 43] Generated Node #0,1: 92:[22, 88, 43] Operation: 30+13=43 Exploring Operation: 88/22=4, Resulting Numbers: [30, 13, 4] Generated Node #0,2: 92:[30, 13, 4] Operation: 88/22=4 Moving to Node #0,1 Current State: 92:[22, 88, 43], Operations: ['30+13=43'] Exploring Operation: 43-22=21, Resulting Numbers: [88, 21] Generated Node #0,1,0: 92:[88, 21] Operation: 43-22=21 Exploring Operation: 88-43=45, Resulting Numbers: [22, 45] Generated Node #0,1,1: 92:[22, 45] Operation: 88-43=45 Exploring Operation: 88/22=4, Resulting Numbers: [43, 4] Generated Node #0,1,2: 92:[43, 4] Operation: 88/22=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[22, 45], Operations: ['30+13=43', '88-43=45'] Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,92 unequal: No Solution Exploring Operation: 22*45=990, Resulting Numbers: [990] 990,92 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 92:[43, 4], Operations: ['30+13=43', '88/22=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,92 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[88, 21], Operations: ['30+13=43', '43-22=21'] Exploring Operation: 88+21=109, Resulting Numbers: [109] 109,92 unequal: No Solution Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,92 unequal: No Solution Exploring Operation: 88*21=1848, Resulting Numbers: [1848] 1848,92 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: 92:[22, 88, 17], Operations: ['30-13=17'] Exploring Operation: 22+17=39, Resulting Numbers: [88, 39] Generated Node #0,0,0: 92:[88, 39] Operation: 22+17=39 Exploring Operation: 88/22=4, Resulting Numbers: [17, 4] Generated Node #0,0,1: 92:[17, 4] Operation: 88/22=4 Exploring Operation: 22-17=5, Resulting Numbers: [88, 5] Generated Node #0,0,2: 92:[88, 5] Operation: 22-17=5 Moving to Node #0,2 Current State: 92:[30, 13, 4], Operations: ['88/22=4'] Exploring Operation: 30-13=17, Resulting Numbers: [4, 17] Generated Node #0,2,0: 92:[4, 17] Operation: 30-13=17 Exploring Operation: 30+13=43, Resulting Numbers: [4, 43] Generated Node #0,2,1: 92:[4, 43] Operation: 30+13=43 Exploring Operation: 30-4=26, Resulting Numbers: [13, 26] Generated Node #0,2,2: 92:[13, 26] Operation: 30-4=26 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[4, 43], Operations: ['88/22=4', '30+13=43'] Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,92 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[4, 17], Operations: ['88/22=4', '30-13=17'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,92 unequal: No Solution Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,92 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[13, 26], Operations: ['88/22=4', '30-4=26'] Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,92 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,92 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: 92:[88, 5], Operations: ['30-13=17', '22-17=5'] Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,92 unequal: No Solution Exploring Operation: 88*5=440, Resulting Numbers: [440] 440,92 unequal: No Solution Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[17, 4], Operations: ['30-13=17', '88/22=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,92 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,92 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[88, 39], Operations: ['30-13=17', '22+17=39'] Exploring Operation: 88+39=127, Resulting Numbers: [127] 127,92 unequal: No Solution Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 88*39=3432, Resulting Numbers: [3432] 3432,92 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 32, 4, 33, 87 ]
96
[ "32*87=2784", "33-4=29", "2784/29=96" ]
Current State: 96:[32, 4, 33, 87], Operations: [] Exploring Operation: 32*87=2784, Resulting Numbers: [4, 33, 2784] Generated Node #2: [4, 33, 2784] from Operation: 32*87=2784 Current State: 96:[4, 33, 2784], Operations: ['32*87=2784'] Exploring Operation: 33-4=29, Resulting Numbers: [2784, 29] Generated Node #3: [2784, 29] from Operation: 33-4=29 Current State: 96:[2784, 29], Operations: ['32*87=2784', '33-4=29'] Exploring Operation: 2784/29=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[32, 4, 33, 87], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [33, 87, 8] Generated Node #0,0: 96:[33, 87, 8] Operation: 32/4=8 Exploring Operation: 87-32=55, Resulting Numbers: [4, 33, 55] Generated Node #0,1: 96:[4, 33, 55] Operation: 87-32=55 Exploring Operation: 4+87=91, Resulting Numbers: [32, 33, 91] Generated Node #0,2: 96:[32, 33, 91] Operation: 4+87=91 Exploring Operation: 33-32=1, Resulting Numbers: [4, 87, 1] Generated Node #0,3: 96:[4, 87, 1] Operation: 33-32=1 Exploring Operation: 87-33=54, Resulting Numbers: [32, 4, 54] Generated Node #0,4: 96:[32, 4, 54] Operation: 87-33=54 Moving to Node #0,2 Current State: 96:[32, 33, 91], Operations: ['4+87=91'] Exploring Operation: 32+91=123, Resulting Numbers: [33, 123] Generated Node #0,2,0: 96:[33, 123] Operation: 32+91=123 Exploring Operation: 33-32=1, Resulting Numbers: [91, 1] Generated Node #0,2,1: 96:[91, 1] Operation: 33-32=1 Exploring Operation: 32+33=65, Resulting Numbers: [91, 65] Generated Node #0,2,2: 96:[91, 65] Operation: 32+33=65 Exploring Operation: 91-32=59, Resulting Numbers: [33, 59] Generated Node #0,2,3: 96:[33, 59] Operation: 91-32=59 Exploring Operation: 91-33=58, Resulting Numbers: [32, 58] Generated Node #0,2,4: 96:[32, 58] Operation: 91-33=58 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 96:[91, 1], Operations: ['4+87=91', '33-32=1'] Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,96 unequal: No Solution Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,96 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 96:[32, 58], Operations: ['4+87=91', '91-33=58'] Exploring Operation: 32*58=1856, Resulting Numbers: [1856] 1856,96 unequal: No Solution Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 32+58=90, Resulting Numbers: [90] 90,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 96:[33, 59], Operations: ['4+87=91', '91-32=59'] Exploring Operation: 33*59=1947, Resulting Numbers: [1947] 1947,96 unequal: No Solution Exploring Operation: 33+59=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 59-33=26, Resulting Numbers: [26] 26,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 96:[91, 65], Operations: ['4+87=91', '32+33=65'] Exploring Operation: 91*65=5915, Resulting Numbers: [5915] 5915,96 unequal: No Solution Exploring Operation: 91-65=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 91+65=156, Resulting Numbers: [156] 156,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[33, 123], Operations: ['4+87=91', '32+91=123'] Exploring Operation: 33+123=156, Resulting Numbers: [156] 156,96 unequal: No Solution Exploring Operation: 33*123=4059, Resulting Numbers: [4059] 4059,96 unequal: No Solution Exploring Operation: 123-33=90, Resulting Numbers: [90] 90,96 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: 96:[32, 4, 54], Operations: ['87-33=54'] Exploring Operation: 32+4=36, Resulting Numbers: [54, 36] Generated Node #0,4,0: 96:[54, 36] Operation: 32+4=36 Exploring Operation: 54-32=22, Resulting Numbers: [4, 22] Generated Node #0,4,1: 96:[4, 22] Operation: 54-32=22 Exploring Operation: 32-4=28, Resulting Numbers: [54, 28] Generated Node #0,4,2: 96:[54, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [54, 8] Generated Node #0,4,3: 96:[54, 8] Operation: 32/4=8 Exploring Operation: 54-4=50, Resulting Numbers: [32, 50] Generated Node #0,4,4: 96:[32, 50] Operation: 54-4=50 Moving to Node #0,1 Current State: 96:[4, 33, 55], Operations: ['87-32=55'] Exploring Operation: 55-33=22, Resulting Numbers: [4, 22] Generated Node #0,1,0: 96:[4, 22] Operation: 55-33=22 Exploring Operation: 55-4=51, Resulting Numbers: [33, 51] Generated Node #0,1,1: 96:[33, 51] Operation: 55-4=51 Exploring Operation: 33-4=29, Resulting Numbers: [55, 29] Generated Node #0,1,2: 96:[55, 29] Operation: 33-4=29 Exploring Operation: 4+33=37, Resulting Numbers: [55, 37] Generated Node #0,1,3: 96:[55, 37] Operation: 4+33=37 Exploring Operation: 33+55=88, Resulting Numbers: [4, 88] Generated Node #0,1,4: 96:[4, 88] Operation: 33+55=88 Moving to Node #0,0 Current State: 96:[33, 87, 8], Operations: ['32/4=8'] Exploring Operation: 87+8=95, Resulting Numbers: [33, 95] Generated Node #0,0,0: 96:[33, 95] Operation: 87+8=95 Exploring Operation: 33+8=41, Resulting Numbers: [87, 41] Generated Node #0,0,1: 96:[87, 41] Operation: 33+8=41 Exploring Operation: 33-8=25, Resulting Numbers: [87, 25] Generated Node #0,0,2: 96:[87, 25] Operation: 33-8=25 Exploring Operation: 87-8=79, Resulting Numbers: [33, 79] Generated Node #0,0,3: 96:[33, 79] Operation: 87-8=79 Exploring Operation: 87-33=54, Resulting Numbers: [8, 54] Generated Node #0,0,4: 96:[8, 54] Operation: 87-33=54 Moving to Node #0,3 Current State: 96:[4, 87, 1], Operations: ['33-32=1'] Exploring Operation: 87+1=88, Resulting Numbers: [4, 88] Generated Node #0,3,0: 96:[4, 88] Operation: 87+1=88 Exploring Operation: 4/1=4, Resulting Numbers: [87, 4] Generated Node #0,3,1: 96:[87, 4] Operation: 4/1=4 Exploring Operation: 4+87=91, Resulting Numbers: [1, 91] Generated Node #0,3,2: 96:[1, 91] Operation: 4+87=91 Exploring Operation: 4-1=3, Resulting Numbers: [87, 3] Generated Node #0,3,3: 96:[87, 3] Operation: 4-1=3 Exploring Operation: 4*1=4, Resulting Numbers: [87, 4] Generated Node #0,3,4: 96:[87, 4] Operation: 4*1=4 Moving to Node #0,4,1 Current State: 96:[4, 22], Operations: ['87-33=54', '54-32=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,96 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[4, 22], Operations: ['87-32=55', '55-33=22'] Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,96 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,96 unequal: No Solution Moving to Node #0,4,4 Current State: 96:[32, 50], Operations: ['87-33=54', '54-4=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,96 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,96 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[33, 95], Operations: ['32/4=8', '87+8=95'] Exploring Operation: 33+95=128, Resulting Numbers: [128] 128,96 unequal: No Solution Exploring Operation: 33*95=3135, Resulting Numbers: [3135] 3135,96 unequal: No Solution Exploring Operation: 95-33=62, Resulting Numbers: [62] 62,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[33, 51], Operations: ['87-32=55', '55-4=51'] Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 33*51=1683, Resulting Numbers: [1683] 1683,96 unequal: No Solution Exploring Operation: 33+51=84, Resulting Numbers: [84] 84,96 unequal: No Solution Moving to Node #0,4,3 Current State: 96:[54, 8], Operations: ['87-33=54', '32/4=8'] Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,96 unequal: No Solution Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[8, 54], Operations: ['32/4=8', '87-33=54'] Exploring Operation: 8*54=432, Resulting Numbers: [432] 432,96 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 8+54=62, Resulting Numbers: [62] 62,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[1, 91], Operations: ['33-32=1', '4+87=91'] Exploring Operation: 1*91=91, Resulting Numbers: [91] 91,96 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,96 unequal: No Solution Exploring Operation: 1+91=92, Resulting Numbers: [92] 92,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[4, 88], Operations: ['87-32=55', '33+55=88'] Exploring Operation: 4*88=352, Resulting Numbers: [352] 352,96 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[4, 88], Operations: ['33-32=1', '87+1=88'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 4*88=352, Resulting Numbers: [352] 352,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[87, 4], Operations: ['33-32=1', '4*1=4'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,96 unequal: No Solution Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,96 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[87, 3], Operations: ['33-32=1', '4-1=3'] Exploring Operation: 87/3=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 87*3=261, Resulting Numbers: [261] 261,96 unequal: No Solution Exploring Operation: 87-3=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 87+3=90, Resulting Numbers: [90] 90,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[87, 4], Operations: ['33-32=1', '4/1=4'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,96 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,96 unequal: No Solution Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[87, 25], Operations: ['32/4=8', '33-8=25'] Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,96 unequal: No Solution Exploring Operation: 87+25=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 87*25=2175, Resulting Numbers: [2175] 2175,96 unequal: No Solution Moving to Node #0,4,0 Current State: 96:[54, 36], Operations: ['87-33=54', '32+4=36'] Exploring Operation: 54*36=1944, Resulting Numbers: [1944] 1944,96 unequal: No Solution Exploring Operation: 54-36=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 54+36=90, Resulting Numbers: [90] 90,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[55, 29], Operations: ['87-32=55', '33-4=29'] Exploring Operation: 55+29=84, Resulting Numbers: [84] 84,96 unequal: No Solution Exploring Operation: 55*29=1595, Resulting Numbers: [1595] 1595,96 unequal: No Solution Exploring Operation: 55-29=26, Resulting Numbers: [26] 26,96 unequal: No Solution Moving to Node #0,4,2 Current State: 96:[54, 28], Operations: ['87-33=54', '32-4=28'] Exploring Operation: 54*28=1512, Resulting Numbers: [1512] 1512,96 unequal: No Solution Exploring Operation: 54+28=82, Resulting Numbers: [82] 82,96 unequal: No Solution Exploring Operation: 54-28=26, Resulting Numbers: [26] 26,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[55, 37], Operations: ['87-32=55', '4+33=37'] Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 55+37=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 55*37=2035, Resulting Numbers: [2035] 2035,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[87, 41], Operations: ['32/4=8', '33+8=41'] Exploring Operation: 87*41=3567, Resulting Numbers: [3567] 3567,96 unequal: No Solution Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 87+41=128, Resulting Numbers: [128] 128,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[33, 79], Operations: ['32/4=8', '87-8=79'] Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,96 unequal: No Solution Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,96 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,96 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 9, 99, 45, 56 ]
28
[ "99-9=90", "45*56=2520", "2520/90=28" ]
Current State: 28:[9, 99, 45, 56], Operations: [] Exploring Operation: 99-9=90, Resulting Numbers: [45, 56, 90] Generated Node #2: [45, 56, 90] from Operation: 99-9=90 Current State: 28:[45, 56, 90], Operations: ['99-9=90'] Exploring Operation: 45*56=2520, Resulting Numbers: [90, 2520] Generated Node #3: [90, 2520] from Operation: 45*56=2520 Current State: 28:[90, 2520], Operations: ['99-9=90', '45*56=2520'] Exploring Operation: 2520/90=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[9, 99, 45, 56], Operations: [] Exploring Operation: 45/9=5, Resulting Numbers: [99, 56, 5] Generated Node #0,0: 28:[99, 56, 5] Operation: 45/9=5 Exploring Operation: 99-56=43, Resulting Numbers: [9, 45, 43] Generated Node #0,1: 28:[9, 45, 43] Operation: 99-56=43 Exploring Operation: 56-45=11, Resulting Numbers: [9, 99, 11] Generated Node #0,2: 28:[9, 99, 11] Operation: 56-45=11 Exploring Operation: 99/9=11, Resulting Numbers: [45, 56, 11] Generated Node #0,3: 28:[45, 56, 11] Operation: 99/9=11 Exploring Operation: 99-45=54, Resulting Numbers: [9, 56, 54] Generated Node #0,4: 28:[9, 56, 54] Operation: 99-45=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[9, 45, 43], Operations: ['99-56=43'] Exploring Operation: 45/9=5, Resulting Numbers: [43, 5] Generated Node #0,1,0: 28:[43, 5] Operation: 45/9=5 Exploring Operation: 9+45=54, Resulting Numbers: [43, 54] Generated Node #0,1,1: 28:[43, 54] Operation: 9+45=54 Exploring Operation: 45-9=36, Resulting Numbers: [43, 36] Generated Node #0,1,2: 28:[43, 36] Operation: 45-9=36 Exploring Operation: 45-43=2, Resulting Numbers: [9, 2] Generated Node #0,1,3: 28:[9, 2] Operation: 45-43=2 Exploring Operation: 43-9=34, Resulting Numbers: [45, 34] Generated Node #0,1,4: 28:[45, 34] Operation: 43-9=34 Moving to Node #0,1,3 Current State: 28:[9, 2], Operations: ['99-56=43', '45-43=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[43, 5], Operations: ['99-56=43', '45/9=5'] Exploring Operation: 43*5=215, Resulting Numbers: [215] 215,28 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,28 unequal: No Solution Moving to Node #0,1,2 Current State: 28:[43, 36], Operations: ['99-56=43', '45-9=36'] Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,28 unequal: No Solution Exploring Operation: 43*36=1548, Resulting Numbers: [1548] 1548,28 unequal: No Solution Exploring Operation: 43+36=79, Resulting Numbers: [79] 79,28 unequal: No Solution Moving to Node #0,1,4 Current State: 28:[45, 34], Operations: ['99-56=43', '43-9=34'] Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,28 unequal: No Solution Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,28 unequal: No Solution Moving to Node #0,1,1 Current State: 28:[43, 54], Operations: ['99-56=43', '9+45=54'] Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,28 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 28:[45, 56, 11], Operations: ['99/9=11'] Exploring Operation: 56-11=45, Resulting Numbers: [45, 45] Generated Node #0,3,0: 28:[45, 45] Operation: 56-11=45 Exploring Operation: 45-11=34, Resulting Numbers: [56, 34] Generated Node #0,3,1: 28:[56, 34] Operation: 45-11=34 Exploring Operation: 56+11=67, Resulting Numbers: [45, 67] Generated Node #0,3,2: 28:[45, 67] Operation: 56+11=67 Exploring Operation: 56-45=11, Resulting Numbers: [11, 11] Generated Node #0,3,3: 28:[11, 11] Operation: 56-45=11 Exploring Operation: 45+11=56, Resulting Numbers: [56, 56] Generated Node #0,3,4: 28:[56, 56] Operation: 45+11=56 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 28:[11, 11], Operations: ['99/9=11', '56-45=11'] Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,28 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,28 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 #0,3,0 Current State: 28:[45, 45], Operations: ['99/9=11', '56-11=45'] Exploring Operation: 45/45=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 45*45=2025, Resulting Numbers: [2025] 2025,28 unequal: No Solution Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 45-45=0, Resulting Numbers: [0] 0,28 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 #0,3,1 Current State: 28:[56, 34], Operations: ['99/9=11', '45-11=34'] Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,28 unequal: No Solution Exploring Operation: 56*34=1904, Resulting Numbers: [1904] 1904,28 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,28 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 #0,3,2 Current State: 28:[45, 67], Operations: ['99/9=11', '56+11=67'] Exploring Operation: 45+67=112, Resulting Numbers: [112] 112,28 unequal: No Solution Exploring Operation: 67-45=22, Resulting Numbers: [22] 22,28 unequal: No Solution Exploring Operation: 45*67=3015, Resulting Numbers: [3015] 3015,28 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 #0,3,4 Current State: 28:[56, 56], Operations: ['99/9=11', '45+11=56'] Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 56*56=3136, Resulting Numbers: [3136] 3136,28 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 56+56=112, Resulting Numbers: [112] 112,28 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 #0,4 Current State: 28:[9, 56, 54], Operations: ['99-45=54'] Exploring Operation: 54/9=6, Resulting Numbers: [56, 6] Generated Node #0,4,0: 28:[56, 6] Operation: 54/9=6 Exploring Operation: 54-9=45, Resulting Numbers: [56, 45] Generated Node #0,4,1: 28:[56, 45] Operation: 54-9=45 Exploring Operation: 56-9=47, Resulting Numbers: [54, 47] Generated Node #0,4,2: 28:[54, 47] Operation: 56-9=47 Exploring Operation: 9+56=65, Resulting Numbers: [54, 65] Generated Node #0,4,3: 28:[54, 65] Operation: 9+56=65 Exploring Operation: 56-54=2, Resulting Numbers: [9, 2] Generated Node #0,4,4: 28:[9, 2] Operation: 56-54=2 Moving to Node #0,4,4 Current State: 28:[9, 2], Operations: ['99-45=54', '56-54=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[56, 6], Operations: ['99-45=54', '54/9=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,28 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,28 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,28 unequal: No Solution Moving to Node #0,4,1 Current State: 28:[56, 45], Operations: ['99-45=54', '54-9=45'] Exploring Operation: 56+45=101, Resulting Numbers: [101] 101,28 unequal: No Solution Exploring Operation: 56*45=2520, Resulting Numbers: [2520] 2520,28 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,28 unequal: No Solution Moving to Node #0,4,2 Current State: 28:[54, 47], Operations: ['99-45=54', '56-9=47'] Exploring Operation: 54*47=2538, Resulting Numbers: [2538] 2538,28 unequal: No Solution Exploring Operation: 54+47=101, Resulting Numbers: [101] 101,28 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,28 unequal: No Solution Moving to Node #0,4,3 Current State: 28:[54, 65], Operations: ['99-45=54', '9+56=65'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 54*65=3510, Resulting Numbers: [3510] 3510,28 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[9, 99, 11], Operations: ['56-45=11'] Exploring Operation: 99/9=11, Resulting Numbers: [11, 11] Generated Node #0,2,0: 28:[11, 11] Operation: 99/9=11 Exploring Operation: 99/11=9, Resulting Numbers: [9, 9] Generated Node #0,2,1: 28:[9, 9] Operation: 99/11=9 Exploring Operation: 11-9=2, Resulting Numbers: [99, 2] Generated Node #0,2,2: 28:[99, 2] Operation: 11-9=2 Exploring Operation: 99-9=90, Resulting Numbers: [11, 90] Generated Node #0,2,3: 28:[11, 90] Operation: 99-9=90 Exploring Operation: 99-11=88, Resulting Numbers: [9, 88] Generated Node #0,2,4: 28:[9, 88] Operation: 99-11=88 Moving to Node #0,2,1 Current State: 28:[9, 9], Operations: ['56-45=11', '99/11=9'] Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,28 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,28 unequal: No Solution Moving to Node #0,2,0 Current State: 28:[11, 11], Operations: ['56-45=11', '99/9=11'] Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,28 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,28 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,28 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,28 unequal: No Solution Moving to Node #0,2,4 Current State: 28:[9, 88], Operations: ['56-45=11', '99-11=88'] Exploring Operation: 9*88=792, Resulting Numbers: [792] 792,28 unequal: No Solution Exploring Operation: 88-9=79, Resulting Numbers: [79] 79,28 unequal: No Solution Exploring Operation: 9+88=97, Resulting Numbers: [97] 97,28 unequal: No Solution Moving to Node #0,2,3 Current State: 28:[11, 90], Operations: ['56-45=11', '99-9=90'] Exploring Operation: 11*90=990, Resulting Numbers: [990] 990,28 unequal: No Solution Exploring Operation: 90-11=79, Resulting Numbers: [79] 79,28 unequal: No Solution Exploring Operation: 11+90=101, Resulting Numbers: [101] 101,28 unequal: No Solution Moving to Node #0,2,2 Current State: 28:[99, 2], Operations: ['56-45=11', '11-9=2'] Exploring Operation: 99*2=198, Resulting Numbers: [198] 198,28 unequal: No Solution Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,28 unequal: No Solution Exploring Operation: 99+2=101, Resulting Numbers: [101] 101,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[99, 56, 5], Operations: ['45/9=5'] Exploring Operation: 56+5=61, Resulting Numbers: [99, 61] Generated Node #0,0,0: 28:[99, 61] Operation: 56+5=61 Exploring Operation: 99-5=94, Resulting Numbers: [56, 94] Generated Node #0,0,1: 28:[56, 94] Operation: 99-5=94 Exploring Operation: 56-5=51, Resulting Numbers: [99, 51] Generated Node #0,0,2: 28:[99, 51] Operation: 56-5=51 Exploring Operation: 99+5=104, Resulting Numbers: [56, 104] Generated Node #0,0,3: 28:[56, 104] Operation: 99+5=104 Exploring Operation: 99-56=43, Resulting Numbers: [5, 43] Generated Node #0,0,4: 28:[5, 43] Operation: 99-56=43 Moving to Node #0,0,4 Current State: 28:[5, 43], Operations: ['45/9=5', '99-56=43'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,28 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[99, 51], Operations: ['45/9=5', '56-5=51'] Exploring Operation: 99+51=150, Resulting Numbers: [150] 150,28 unequal: No Solution Exploring Operation: 99-51=48, Resulting Numbers: [48] 48,28 unequal: No Solution Exploring Operation: 99*51=5049, Resulting Numbers: [5049] 5049,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[56, 94], Operations: ['45/9=5', '99-5=94'] Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 56+94=150, Resulting Numbers: [150] 150,28 unequal: No Solution Exploring Operation: 56*94=5264, Resulting Numbers: [5264] 5264,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[99, 61], Operations: ['45/9=5', '56+5=61'] Exploring Operation: 99-61=38, Resulting Numbers: [38] 38,28 unequal: No Solution Exploring Operation: 99*61=6039, Resulting Numbers: [6039] 6039,28 unequal: No Solution Exploring Operation: 99+61=160, Resulting Numbers: [160] 160,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[56, 104], Operations: ['45/9=5', '99+5=104'] Exploring Operation: 104-56=48, Resulting Numbers: [48] 48,28 unequal: No Solution Exploring Operation: 56*104=5824, Resulting Numbers: [5824] 5824,28 unequal: No Solution Exploring Operation: 56+104=160, Resulting Numbers: [160] 160,28 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
[ 14, 64, 41, 58 ]
33
[ "64-14=50", "58-41=17", "50-17=33" ]
Current State: 33:[14, 64, 41, 58], Operations: [] Exploring Operation: 64-14=50, Resulting Numbers: [41, 58, 50] Generated Node #2: [41, 58, 50] from Operation: 64-14=50 Current State: 33:[41, 58, 50], Operations: ['64-14=50'] Exploring Operation: 58-41=17, Resulting Numbers: [50, 17] Generated Node #3: [50, 17] from Operation: 58-41=17 Current State: 33:[50, 17], Operations: ['64-14=50', '58-41=17'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[14, 64, 41, 58], Operations: [] Exploring Operation: 58-41=17, Resulting Numbers: [14, 64, 17] Generated Node #0,0: 33:[14, 64, 17] Operation: 58-41=17 Exploring Operation: 64-14=50, Resulting Numbers: [41, 58, 50] Generated Node #0,1: 33:[41, 58, 50] Operation: 64-14=50 Exploring Operation: 64-41=23, Resulting Numbers: [14, 58, 23] Generated Node #0,2: 33:[14, 58, 23] Operation: 64-41=23 Exploring Operation: 64-58=6, Resulting Numbers: [14, 41, 6] Generated Node #0,3: 33:[14, 41, 6] Operation: 64-58=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 33:[14, 41, 6], Operations: ['64-58=6'] Exploring Operation: 14-6=8, Resulting Numbers: [41, 8] Generated Node #0,3,0: 33:[41, 8] Operation: 14-6=8 Exploring Operation: 14+6=20, Resulting Numbers: [41, 20] Generated Node #0,3,1: 33:[41, 20] Operation: 14+6=20 Exploring Operation: 41-6=35, Resulting Numbers: [14, 35] Generated Node #0,3,2: 33:[14, 35] Operation: 41-6=35 Exploring Operation: 41-14=27, Resulting Numbers: [6, 27] Generated Node #0,3,3: 33:[6, 27] Operation: 41-14=27 Moving to Node #0,3,2 Current State: 33:[14, 35], Operations: ['64-58=6', '41-6=35'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,33 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,33 unequal: No Solution Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,33 unequal: No Solution Moving to Node #0,3,3 Current State: 33:[6, 27], Operations: ['64-58=6', '41-14=27'] Exploring Operation: 6*27=162, Resulting Numbers: [162] 162,33 unequal: No Solution Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[14, 64, 41, 58], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [14, 41, 6] Generated Node #0,3: 33:[14, 41, 6] Operation: 64-58=6 Moving to Node #0,3 Current State: 33:[14, 41, 6], Operations: ['64-58=6'] Exploring Operation: 41-14=27, Resulting Numbers: [6, 27] Generated Node #0,3,3: 33:[6, 27] Operation: 41-14=27 Moving to Node #0,3,3 Current State: 33:[6, 27], Operations: ['64-58=6', '41-14=27'] Exploring Operation: 6+27=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 11, 9, 84, 89 ]
79
[ "11-9=2", "84*2=168", "168-89=79" ]
Current State: 79:[11, 9, 84, 89], Operations: [] Exploring Operation: 11-9=2, Resulting Numbers: [84, 89, 2] Generated Node #2: [84, 89, 2] from Operation: 11-9=2 Current State: 79:[84, 89, 2], Operations: ['11-9=2'] Exploring Operation: 84*2=168, Resulting Numbers: [89, 168] Generated Node #3: [89, 168] from Operation: 84*2=168 Current State: 79:[89, 168], Operations: ['11-9=2', '84*2=168'] Exploring Operation: 168-89=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[11, 9, 84, 89], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [84, 89, 99] Generated Node #0,0: 79:[84, 89, 99] Operation: 11*9=99 Exploring Operation: 11+9=20, Resulting Numbers: [84, 89, 20] Generated Node #0,1: 79:[84, 89, 20] Operation: 11+9=20 Exploring Operation: 84-9=75, Resulting Numbers: [11, 89, 75] Generated Node #0,2: 79:[11, 89, 75] Operation: 84-9=75 Exploring Operation: 89-9=80, Resulting Numbers: [11, 84, 80] Generated Node #0,3: 79:[11, 84, 80] Operation: 89-9=80 Exploring Operation: 89-11=78, Resulting Numbers: [9, 84, 78] Generated Node #0,4: 79:[9, 84, 78] Operation: 89-11=78 Moving to Node #0,0 Current State: 79:[84, 89, 99], Operations: ['11*9=99'] Exploring Operation: 99-84=15, Resulting Numbers: [89, 15] Generated Node #0,0,0: 79:[89, 15] Operation: 99-84=15 Exploring Operation: 84+89=173, Resulting Numbers: [99, 173] Generated Node #0,0,1: 79:[99, 173] Operation: 84+89=173 Exploring Operation: 99-89=10, Resulting Numbers: [84, 10] Generated Node #0,0,2: 79:[84, 10] Operation: 99-89=10 Exploring Operation: 84+99=183, Resulting Numbers: [89, 183] Generated Node #0,0,3: 79:[89, 183] Operation: 84+99=183 Exploring Operation: 89-84=5, Resulting Numbers: [99, 5] Generated Node #0,0,4: 79:[99, 5] Operation: 89-84=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[89, 15], Operations: ['11*9=99', '99-84=15'] Exploring Operation: 89*15=1335, Resulting Numbers: [1335] 1335,79 unequal: No Solution Exploring Operation: 89+15=104, Resulting Numbers: [104] 104,79 unequal: No Solution Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,79 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 #0,0,2 Current State: 79:[84, 10], Operations: ['11*9=99', '99-89=10'] Exploring Operation: 84-10=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 84*10=840, Resulting Numbers: [840] 840,79 unequal: No Solution Exploring Operation: 84+10=94, Resulting Numbers: [94] 94,79 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 #0,0,4 Current State: 79:[99, 5], Operations: ['11*9=99', '89-84=5'] Exploring Operation: 99+5=104, Resulting Numbers: [104] 104,79 unequal: No Solution Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,79 unequal: No Solution Exploring Operation: 99*5=495, Resulting Numbers: [495] 495,79 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 #0,0,1 Current State: 79:[99, 173], Operations: ['11*9=99', '84+89=173'] Exploring Operation: 173-99=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 99+173=272, Resulting Numbers: [272] 272,79 unequal: No Solution Exploring Operation: 99*173=17127, Resulting Numbers: [17127] 17127,79 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 #0,0,3 Current State: 79:[89, 183], Operations: ['11*9=99', '84+99=183'] Exploring Operation: 89*183=16287, Resulting Numbers: [16287] 16287,79 unequal: No Solution Exploring Operation: 89+183=272, Resulting Numbers: [272] 272,79 unequal: No Solution Exploring Operation: 183-89=94, Resulting Numbers: [94] 94,79 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: 79:[11, 84, 80], Operations: ['89-9=80'] Exploring Operation: 84-80=4, Resulting Numbers: [11, 4] Generated Node #0,3,0: 79:[11, 4] Operation: 84-80=4 Exploring Operation: 84-11=73, Resulting Numbers: [80, 73] Generated Node #0,3,1: 79:[80, 73] Operation: 84-11=73 Exploring Operation: 11+84=95, Resulting Numbers: [80, 95] Generated Node #0,3,2: 79:[80, 95] Operation: 11+84=95 Exploring Operation: 11+80=91, Resulting Numbers: [84, 91] Generated Node #0,3,3: 79:[84, 91] Operation: 11+80=91 Exploring Operation: 80-11=69, Resulting Numbers: [84, 69] Generated Node #0,3,4: 79:[84, 69] Operation: 80-11=69 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[80, 73], Operations: ['89-9=80', '84-11=73'] Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 80+73=153, Resulting Numbers: [153] 153,79 unequal: No Solution Exploring Operation: 80*73=5840, Resulting Numbers: [5840] 5840,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 79:[84, 69], Operations: ['89-9=80', '80-11=69'] Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,79 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[80, 95], Operations: ['89-9=80', '11+84=95'] Exploring Operation: 95-80=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 80+95=175, Resulting Numbers: [175] 175,79 unequal: No Solution Exploring Operation: 80*95=7600, Resulting Numbers: [7600] 7600,79 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 #0,3,3 Current State: 79:[84, 91], Operations: ['89-9=80', '11+80=91'] Exploring Operation: 91-84=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 84*91=7644, Resulting Numbers: [7644] 7644,79 unequal: No Solution Exploring Operation: 84+91=175, Resulting Numbers: [175] 175,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[11, 4], Operations: ['89-9=80', '84-80=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,79 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: 79:[84, 89, 20], Operations: ['11+9=20'] Exploring Operation: 89-20=69, Resulting Numbers: [84, 69] Generated Node #0,1,0: 79:[84, 69] Operation: 89-20=69 Exploring Operation: 89-84=5, Resulting Numbers: [20, 5] Generated Node #0,1,1: 79:[20, 5] Operation: 89-84=5 Exploring Operation: 89+20=109, Resulting Numbers: [84, 109] Generated Node #0,1,2: 79:[84, 109] Operation: 89+20=109 Exploring Operation: 84+20=104, Resulting Numbers: [89, 104] Generated Node #0,1,3: 79:[89, 104] Operation: 84+20=104 Exploring Operation: 84-20=64, Resulting Numbers: [89, 64] Generated Node #0,1,4: 79:[89, 64] Operation: 84-20=64 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[84, 69], Operations: ['11+9=20', '89-20=69'] Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,79 unequal: No Solution Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 79:[89, 64], Operations: ['11+9=20', '84-20=64'] Exploring Operation: 89-64=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 89+64=153, Resulting Numbers: [153] 153,79 unequal: No Solution Exploring Operation: 89*64=5696, Resulting Numbers: [5696] 5696,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[84, 109], Operations: ['11+9=20', '89+20=109'] Exploring Operation: 84+109=193, Resulting Numbers: [193] 193,79 unequal: No Solution Exploring Operation: 84*109=9156, Resulting Numbers: [9156] 9156,79 unequal: No Solution Exploring Operation: 109-84=25, Resulting Numbers: [25] 25,79 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 #0,1,3 Current State: 79:[89, 104], Operations: ['11+9=20', '84+20=104'] Exploring Operation: 104-89=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 89*104=9256, Resulting Numbers: [9256] 9256,79 unequal: No Solution Exploring Operation: 89+104=193, Resulting Numbers: [193] 193,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[20, 5], Operations: ['11+9=20', '89-84=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 79:[9, 84, 78], Operations: ['89-11=78'] Exploring Operation: 9+84=93, Resulting Numbers: [78, 93] Generated Node #0,4,0: 79:[78, 93] Operation: 9+84=93 Exploring Operation: 9+78=87, Resulting Numbers: [84, 87] Generated Node #0,4,1: 79:[84, 87] Operation: 9+78=87 Exploring Operation: 84-78=6, Resulting Numbers: [9, 6] Generated Node #0,4,2: 79:[9, 6] Operation: 84-78=6 Exploring Operation: 84-9=75, Resulting Numbers: [78, 75] Generated Node #0,4,3: 79:[78, 75] Operation: 84-9=75 Exploring Operation: 78-9=69, Resulting Numbers: [84, 69] Generated Node #0,4,4: 79:[84, 69] Operation: 78-9=69 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 79:[78, 75], Operations: ['89-11=78', '84-9=75'] Exploring Operation: 78-75=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 78*75=5850, Resulting Numbers: [5850] 5850,79 unequal: No Solution Exploring Operation: 78+75=153, Resulting Numbers: [153] 153,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 79:[84, 87], Operations: ['89-11=78', '9+78=87'] Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 84*87=7308, Resulting Numbers: [7308] 7308,79 unequal: No Solution Exploring Operation: 84+87=171, Resulting Numbers: [171] 171,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 79:[78, 93], Operations: ['89-11=78', '9+84=93'] Exploring Operation: 93-78=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 78+93=171, Resulting Numbers: [171] 171,79 unequal: No Solution Exploring Operation: 78*93=7254, Resulting Numbers: [7254] 7254,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 79:[84, 69], Operations: ['89-11=78', '78-9=69'] Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,79 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,79 unequal: No Solution Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 79:[9, 6], Operations: ['89-11=78', '84-78=6'] Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 79:[11, 89, 75], Operations: ['84-9=75'] Exploring Operation: 11+89=100, Resulting Numbers: [75, 100] Generated Node #0,2,0: 79:[75, 100] Operation: 11+89=100 Exploring Operation: 89-11=78, Resulting Numbers: [75, 78] Generated Node #0,2,1: 79:[75, 78] Operation: 89-11=78 Exploring Operation: 75-11=64, Resulting Numbers: [89, 64] Generated Node #0,2,2: 79:[89, 64] Operation: 75-11=64 Exploring Operation: 11+75=86, Resulting Numbers: [89, 86] Generated Node #0,2,3: 79:[89, 86] Operation: 11+75=86 Exploring Operation: 89-75=14, Resulting Numbers: [11, 14] Generated Node #0,2,4: 79:[11, 14] Operation: 89-75=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[75, 78], Operations: ['84-9=75', '89-11=78'] Exploring Operation: 75*78=5850, Resulting Numbers: [5850] 5850,79 unequal: No Solution Exploring Operation: 78-75=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 75+78=153, Resulting Numbers: [153] 153,79 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 #0,2,3 Current State: 79:[89, 86], Operations: ['84-9=75', '11+75=86'] Exploring Operation: 89-86=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 89*86=7654, Resulting Numbers: [7654] 7654,79 unequal: No Solution Exploring Operation: 89+86=175, Resulting Numbers: [175] 175,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[75, 100], Operations: ['84-9=75', '11+89=100'] Exploring Operation: 100-75=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 75+100=175, Resulting Numbers: [175] 175,79 unequal: No Solution Exploring Operation: 75*100=7500, Resulting Numbers: [7500] 7500,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[89, 64], Operations: ['84-9=75', '75-11=64'] Exploring Operation: 89-64=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 89*64=5696, Resulting Numbers: [5696] 5696,79 unequal: No Solution Exploring Operation: 89+64=153, Resulting Numbers: [153] 153,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 79:[11, 14], Operations: ['84-9=75', '89-75=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,79 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
[ 84, 91, 51, 24 ]
25
[ "91*24=2184", "2184/84=26", "51-26=25" ]
Current State: 25:[84, 91, 51, 24], Operations: [] Exploring Operation: 91*24=2184, Resulting Numbers: [84, 51, 2184] Generated Node #2: [84, 51, 2184] from Operation: 91*24=2184 Current State: 25:[84, 51, 2184], Operations: ['91*24=2184'] Exploring Operation: 2184/84=26, Resulting Numbers: [51, 26] Generated Node #3: [51, 26] from Operation: 2184/84=26 Current State: 25:[51, 26], Operations: ['91*24=2184', '2184/84=26'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[84, 91, 51, 24], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [51, 24, 7] Generated Node #0,0: 25:[51, 24, 7] Operation: 91-84=7 Exploring Operation: 84-51=33, Resulting Numbers: [91, 24, 33] Generated Node #0,1: 25:[91, 24, 33] Operation: 84-51=33 Moving to Node #0,0 Current State: 25:[51, 24, 7], Operations: ['91-84=7'] Exploring Operation: 51-7=44, Resulting Numbers: [24, 44] Generated Node #0,0,0: 25:[24, 44] Operation: 51-7=44 Exploring Operation: 51-24=27, Resulting Numbers: [7, 27] Generated Node #0,0,1: 25:[7, 27] Operation: 51-24=27 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[7, 27], Operations: ['91-84=7', '51-24=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,25 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 #0,0,0 Current State: 25:[24, 44], Operations: ['91-84=7', '51-7=44'] Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,25 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: 25:[91, 24, 33], Operations: ['84-51=33'] Exploring Operation: 91-24=67, Resulting Numbers: [33, 67] Generated Node #0,1,0: 25:[33, 67] Operation: 91-24=67 Exploring Operation: 91-33=58, Resulting Numbers: [24, 58] Generated Node #0,1,1: 25:[24, 58] Operation: 91-33=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[24, 58], Operations: ['84-51=33', '91-33=58'] Exploring Operation: 24+58=82, Resulting Numbers: [82] 82,25 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,25 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 #0,1,0 Current State: 25:[33, 67], Operations: ['84-51=33', '91-24=67'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,25 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
[ 15, 1, 10, 4 ]
21
[ "15*1=15", "10-4=6", "15+6=21" ]
Current State: 21:[15, 1, 10, 4], Operations: [] Exploring Operation: 15*1=15, Resulting Numbers: [10, 4, 15] Generated Node #2: [10, 4, 15] from Operation: 15*1=15 Current State: 21:[10, 4, 15], Operations: ['15*1=15'] Exploring Operation: 10-4=6, Resulting Numbers: [15, 6] Generated Node #3: [15, 6] from Operation: 10-4=6 Current State: 21:[15, 6], Operations: ['15*1=15', '10-4=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[15, 1, 10, 4], Operations: [] Exploring Operation: 15-10=5, Resulting Numbers: [1, 4, 5] Generated Node #0,0: 21:[1, 4, 5] Operation: 15-10=5 Exploring Operation: 15+10=25, Resulting Numbers: [1, 4, 25] Generated Node #0,1: 21:[1, 4, 25] Operation: 15+10=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[1, 4, 5], Operations: ['15-10=5'] Exploring Operation: 1+5=6, Resulting Numbers: [4, 6] Generated Node #0,0,0: 21:[4, 6] Operation: 1+5=6 Exploring Operation: 4-1=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 21:[5, 3] Operation: 4-1=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[4, 6], Operations: ['15-10=5', '1+5=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[5, 3], Operations: ['15-10=5', '4-1=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[1, 4, 25], Operations: ['15+10=25'] Exploring Operation: 4-1=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 21:[25, 3] Operation: 4-1=3 Exploring Operation: 25-4=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 21:[1, 21] Operation: 25-4=21 Moving to Node #0,1,1 Current State: 21:[1, 21], Operations: ['15+10=25', '25-4=21'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[15, 1, 10, 4], Operations: [] Exploring Operation: 15+10=25, Resulting Numbers: [1, 4, 25] Generated Node #0,1: 21:[1, 4, 25] Operation: 15+10=25 Moving to Node #0,1 Current State: 21:[1, 4, 25], Operations: ['15+10=25'] Exploring Operation: 25-4=21, Resulting Numbers: [1, 21] Generated Node #0,1,1: 21:[1, 21] Operation: 25-4=21 Moving to Node #0,1,1 Current State: 21:[1, 21], Operations: ['15+10=25', '25-4=21'] Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 89, 17, 50, 91 ]
16
[ "91-89=2", "17*2=34", "50-34=16" ]
Current State: 16:[89, 17, 50, 91], Operations: [] Exploring Operation: 91-89=2, Resulting Numbers: [17, 50, 2] Generated Node #2: [17, 50, 2] from Operation: 91-89=2 Current State: 16:[17, 50, 2], Operations: ['91-89=2'] Exploring Operation: 17*2=34, Resulting Numbers: [50, 34] Generated Node #3: [50, 34] from Operation: 17*2=34 Current State: 16:[50, 34], Operations: ['91-89=2', '17*2=34'] Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[89, 17, 50, 91], Operations: [] Exploring Operation: 89-50=39, Resulting Numbers: [17, 91, 39] Generated Node #0,0: 16:[17, 91, 39] Operation: 89-50=39 Exploring Operation: 91-50=41, Resulting Numbers: [89, 17, 41] Generated Node #0,1: 16:[89, 17, 41] Operation: 91-50=41 Exploring Operation: 91-89=2, Resulting Numbers: [17, 50, 2] Generated Node #0,2: 16:[17, 50, 2] Operation: 91-89=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[17, 50, 2], Operations: ['91-89=2'] Exploring Operation: 50/2=25, Resulting Numbers: [17, 25] Generated Node #0,2,0: 16:[17, 25] Operation: 50/2=25 Exploring Operation: 50-17=33, Resulting Numbers: [2, 33] Generated Node #0,2,1: 16:[2, 33] Operation: 50-17=33 Exploring Operation: 50-2=48, Resulting Numbers: [17, 48] Generated Node #0,2,2: 16:[17, 48] Operation: 50-2=48 Moving to Node #0,2,0 Current State: 16:[17, 25], Operations: ['91-89=2', '50/2=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,16 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[2, 33], Operations: ['91-89=2', '50-17=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,16 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[17, 48], Operations: ['91-89=2', '50-2=48'] Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,16 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[17, 91, 39], Operations: ['89-50=39'] Exploring Operation: 39-17=22, Resulting Numbers: [91, 22] Generated Node #0,0,0: 16:[91, 22] Operation: 39-17=22 Exploring Operation: 91-17=74, Resulting Numbers: [39, 74] Generated Node #0,0,1: 16:[39, 74] Operation: 91-17=74 Exploring Operation: 91-39=52, Resulting Numbers: [17, 52] Generated Node #0,0,2: 16:[17, 52] Operation: 91-39=52 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 16:[17, 52], Operations: ['89-50=39', '91-39=52'] Exploring Operation: 17*52=884, Resulting Numbers: [884] 884,16 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,16 unequal: No Solution No 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: 16:[91, 22], Operations: ['89-50=39', '39-17=22'] Exploring Operation: 91*22=2002, Resulting Numbers: [2002] 2002,16 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 91+22=113, Resulting Numbers: [113] 113,16 unequal: No Solution No 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: 16:[39, 74], Operations: ['89-50=39', '91-17=74'] Exploring Operation: 39*74=2886, Resulting Numbers: [2886] 2886,16 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,16 unequal: No Solution Exploring Operation: 39+74=113, Resulting Numbers: [113] 113,16 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: 16:[89, 17, 41], Operations: ['91-50=41'] Exploring Operation: 41-17=24, Resulting Numbers: [89, 24] Generated Node #0,1,0: 16:[89, 24] Operation: 41-17=24 Exploring Operation: 89-17=72, Resulting Numbers: [41, 72] Generated Node #0,1,1: 16:[41, 72] Operation: 89-17=72 Exploring Operation: 89-41=48, Resulting Numbers: [17, 48] Generated Node #0,1,2: 16:[17, 48] Operation: 89-41=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[17, 48], Operations: ['91-50=41', '89-41=48'] Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,16 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,16 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,16 unequal: No Solution No 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: 16:[89, 24], Operations: ['91-50=41', '41-17=24'] Exploring Operation: 89-24=65, Resulting Numbers: [65] 65,16 unequal: No Solution Exploring Operation: 89+24=113, Resulting Numbers: [113] 113,16 unequal: No Solution Exploring Operation: 89*24=2136, Resulting Numbers: [2136] 2136,16 unequal: No Solution No 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: 16:[41, 72], Operations: ['91-50=41', '89-17=72'] Exploring Operation: 41*72=2952, Resulting Numbers: [2952] 2952,16 unequal: No Solution Exploring Operation: 72-41=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 41+72=113, Resulting Numbers: [113] 113,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 5, 88, 72, 61 ]
93
[ "88+72=160", "160/5=32", "61+32=93" ]
Current State: 93:[5, 88, 72, 61], Operations: [] Exploring Operation: 88+72=160, Resulting Numbers: [5, 61, 160] Generated Node #2: [5, 61, 160] from Operation: 88+72=160 Current State: 93:[5, 61, 160], Operations: ['88+72=160'] Exploring Operation: 160/5=32, Resulting Numbers: [61, 32] Generated Node #3: [61, 32] from Operation: 160/5=32 Current State: 93:[61, 32], Operations: ['88+72=160', '160/5=32'] Exploring Operation: 61+32=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[5, 88, 72, 61], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [5, 72, 27] Generated Node #0,0: 93:[5, 72, 27] Operation: 88-61=27 Exploring Operation: 72-61=11, Resulting Numbers: [5, 88, 11] Generated Node #0,1: 93:[5, 88, 11] Operation: 72-61=11 Moving to Node #0,1 Current State: 93:[5, 88, 11], Operations: ['72-61=11'] Exploring Operation: 5+88=93, Resulting Numbers: [11, 93] Generated Node #0,1,0: 93:[11, 93] Operation: 5+88=93 Exploring Operation: 88/11=8, Resulting Numbers: [5, 8] Generated Node #0,1,1: 93:[5, 8] Operation: 88/11=8 Moving to Node #0,0 Current State: 93:[5, 72, 27], Operations: ['88-61=27'] Exploring Operation: 72-27=45, Resulting Numbers: [5, 45] Generated Node #0,0,0: 93:[5, 45] Operation: 72-27=45 Exploring Operation: 72+27=99, Resulting Numbers: [5, 99] Generated Node #0,0,1: 93:[5, 99] Operation: 72+27=99 Moving to Node #0,1,1 Current State: 93:[5, 8], Operations: ['72-61=11', '88/11=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,93 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[5, 99], Operations: ['88-61=27', '72+27=99'] Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,93 unequal: No Solution Exploring Operation: 5+99=104, Resulting Numbers: [104] 104,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[11, 93], Operations: ['72-61=11', '5+88=93'] Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,93 unequal: No Solution Exploring Operation: 11+93=104, Resulting Numbers: [104] 104,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[5, 45], Operations: ['88-61=27', '72-27=45'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,93 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,93 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 64, 30, 67, 3 ]
30
[ "64+30=94", "67-3=64", "94-64=30" ]
Current State: 30:[64, 30, 67, 3], Operations: [] Exploring Operation: 64+30=94, Resulting Numbers: [67, 3, 94] Generated Node #2: [67, 3, 94] from Operation: 64+30=94 Current State: 30:[67, 3, 94], Operations: ['64+30=94'] Exploring Operation: 67-3=64, Resulting Numbers: [94, 64] Generated Node #3: [94, 64] from Operation: 67-3=64 Current State: 30:[94, 64], Operations: ['64+30=94', '67-3=64'] Exploring Operation: 94-64=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[64, 30, 67, 3], Operations: [] Exploring Operation: 67-30=37, Resulting Numbers: [64, 3, 37] Generated Node #0,0: 30:[64, 3, 37] Operation: 67-30=37 Exploring Operation: 64-30=34, Resulting Numbers: [67, 3, 34] Generated Node #0,1: 30:[67, 3, 34] Operation: 64-30=34 Exploring Operation: 67-64=3, Resulting Numbers: [30, 3, 3] Generated Node #0,2: 30:[30, 3, 3] Operation: 67-64=3 Exploring Operation: 64-3=61, Resulting Numbers: [30, 67, 61] Generated Node #0,3: 30:[30, 67, 61] Operation: 64-3=61 Moving to Node #0,2 Current State: 30:[30, 3, 3], Operations: ['67-64=3'] Exploring Operation: 30/3=10, Resulting Numbers: [3, 10] Generated Node #0,2,0: 30:[3, 10] Operation: 30/3=10 Exploring Operation: 3+3=6, Resulting Numbers: [30, 6] Generated Node #0,2,1: 30:[30, 6] Operation: 3+3=6 Exploring Operation: 30/3=10, Resulting Numbers: [3, 10] Generated Node #0,2,2: 30:[3, 10] Operation: 30/3=10 Exploring Operation: 3*3=9, Resulting Numbers: [30, 9] Generated Node #0,2,3: 30:[30, 9] Operation: 3*3=9 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[3, 10], Operations: ['67-64=3', '30/3=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[64, 30, 67, 3], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [30, 3, 3] Generated Node #0,2: 30:[30, 3, 3] Operation: 67-64=3 Moving to Node #0,2 Current State: 30:[30, 3, 3], Operations: ['67-64=3'] Exploring Operation: 30/3=10, Resulting Numbers: [3, 10] Generated Node #0,2,0: 30:[3, 10] Operation: 30/3=10 Moving to Node #0,2,0 Current State: 30:[3, 10], Operations: ['67-64=3', '30/3=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 60, 56, 64, 38 ]
90
[ "60+56=116", "64-38=26", "116-26=90" ]
Current State: 90:[60, 56, 64, 38], Operations: [] Exploring Operation: 60+56=116, Resulting Numbers: [64, 38, 116] Generated Node #2: [64, 38, 116] from Operation: 60+56=116 Current State: 90:[64, 38, 116], Operations: ['60+56=116'] Exploring Operation: 64-38=26, Resulting Numbers: [116, 26] Generated Node #3: [116, 26] from Operation: 64-38=26 Current State: 90:[116, 26], Operations: ['60+56=116', '64-38=26'] Exploring Operation: 116-26=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[60, 56, 64, 38], Operations: [] Exploring Operation: 64-60=4, Resulting Numbers: [56, 38, 4] Generated Node #0,0: 90:[56, 38, 4] Operation: 64-60=4 Moving to Node #0,0 Current State: 90:[56, 38, 4], Operations: ['64-60=4'] Exploring Operation: 56-38=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 90:[4, 18] Operation: 56-38=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[4, 18], Operations: ['64-60=4', '56-38=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,90 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
[ 16, 66, 73, 76 ]
85
[ "16+66=82", "76-73=3", "82+3=85" ]
Current State: 85:[16, 66, 73, 76], Operations: [] Exploring Operation: 16+66=82, Resulting Numbers: [73, 76, 82] Generated Node #2: [73, 76, 82] from Operation: 16+66=82 Current State: 85:[73, 76, 82], Operations: ['16+66=82'] Exploring Operation: 76-73=3, Resulting Numbers: [82, 3] Generated Node #3: [82, 3] from Operation: 76-73=3 Current State: 85:[82, 3], Operations: ['16+66=82', '76-73=3'] Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[16, 66, 73, 76], Operations: [] Exploring Operation: 16+66=82, Resulting Numbers: [73, 76, 82] Generated Node #0,0: 85:[73, 76, 82] Operation: 16+66=82 Exploring Operation: 73-66=7, Resulting Numbers: [16, 76, 7] Generated Node #0,1: 85:[16, 76, 7] Operation: 73-66=7 Exploring Operation: 76-73=3, Resulting Numbers: [16, 66, 3] Generated Node #0,2: 85:[16, 66, 3] Operation: 76-73=3 Exploring Operation: 76-66=10, Resulting Numbers: [16, 73, 10] Generated Node #0,3: 85:[16, 73, 10] Operation: 76-66=10 Moving to Node #0,1 Current State: 85:[16, 76, 7], Operations: ['73-66=7'] Exploring Operation: 16-7=9, Resulting Numbers: [76, 9] Generated Node #0,1,0: 85:[76, 9] Operation: 16-7=9 Exploring Operation: 16+7=23, Resulting Numbers: [76, 23] Generated Node #0,1,1: 85:[76, 23] Operation: 16+7=23 Exploring Operation: 16+76=92, Resulting Numbers: [7, 92] Generated Node #0,1,2: 85:[7, 92] Operation: 16+76=92 Exploring Operation: 76+7=83, Resulting Numbers: [16, 83] Generated Node #0,1,3: 85:[16, 83] Operation: 76+7=83 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 85:[16, 83], Operations: ['73-66=7', '76+7=83'] Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,85 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 85:[7, 92], Operations: ['73-66=7', '16+76=92'] Exploring Operation: 7+92=99, Resulting Numbers: [99] 99,85 unequal: No Solution Exploring Operation: 7*92=644, Resulting Numbers: [644] 644,85 unequal: No Solution Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[16, 66, 73, 76], Operations: [] Exploring Operation: 73-66=7, Resulting Numbers: [16, 76, 7] Generated Node #0,1: 85:[16, 76, 7] Operation: 73-66=7 Moving to Node #0,1 Current State: 85:[16, 76, 7], Operations: ['73-66=7'] Exploring Operation: 16+76=92, Resulting Numbers: [7, 92] Generated Node #0,1,2: 85:[7, 92] Operation: 16+76=92 Moving to Node #0,1,2 Current State: 85:[7, 92], Operations: ['73-66=7', '16+76=92'] Exploring Operation: 92-7=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 36, 15, 97, 53 ]
46
[ "97+53=150", "150/15=10", "36+10=46" ]
Current State: 46:[36, 15, 97, 53], Operations: [] Exploring Operation: 97+53=150, Resulting Numbers: [36, 15, 150] Generated Node #2: [36, 15, 150] from Operation: 97+53=150 Current State: 46:[36, 15, 150], Operations: ['97+53=150'] Exploring Operation: 150/15=10, Resulting Numbers: [36, 10] Generated Node #3: [36, 10] from Operation: 150/15=10 Current State: 46:[36, 10], Operations: ['97+53=150', '150/15=10'] Exploring Operation: 36+10=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[36, 15, 97, 53], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [36, 15, 44] Generated Node #0,0: 46:[36, 15, 44] Operation: 97-53=44 Exploring Operation: 97-15=82, Resulting Numbers: [36, 53, 82] Generated Node #0,1: 46:[36, 53, 82] Operation: 97-15=82 Exploring Operation: 97-36=61, Resulting Numbers: [15, 53, 61] Generated Node #0,2: 46:[15, 53, 61] Operation: 97-36=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[36, 15, 44], Operations: ['97-53=44'] Exploring Operation: 44-36=8, Resulting Numbers: [15, 8] Generated Node #0,0,0: 46:[15, 8] Operation: 44-36=8 Exploring Operation: 36-15=21, Resulting Numbers: [44, 21] Generated Node #0,0,1: 46:[44, 21] Operation: 36-15=21 Exploring Operation: 36+15=51, Resulting Numbers: [44, 51] Generated Node #0,0,2: 46:[44, 51] Operation: 36+15=51 Moving to Node #0,0,1 Current State: 46:[44, 21], Operations: ['97-53=44', '36-15=21'] Exploring Operation: 44+21=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 44*21=924, Resulting Numbers: [924] 924,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[44, 51], Operations: ['97-53=44', '36+15=51'] Exploring Operation: 44+51=95, Resulting Numbers: [95] 95,46 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 44*51=2244, Resulting Numbers: [2244] 2244,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[15, 8], Operations: ['97-53=44', '44-36=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,46 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,46 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 #0,2 Current State: 46:[15, 53, 61], Operations: ['97-36=61'] Exploring Operation: 61-53=8, Resulting Numbers: [15, 8] Generated Node #0,2,0: 46:[15, 8] Operation: 61-53=8 Exploring Operation: 53-15=38, Resulting Numbers: [61, 38] Generated Node #0,2,1: 46:[61, 38] Operation: 53-15=38 Exploring Operation: 61-15=46, Resulting Numbers: [53, 46] Generated Node #0,2,2: 46:[53, 46] Operation: 61-15=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[53, 46], Operations: ['97-36=61', '61-15=46'] Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,46 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,46 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:[15, 8], Operations: ['97-36=61', '61-53=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,46 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,46 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 #0,2,1 Current State: 46:[61, 38], Operations: ['97-36=61', '53-15=38'] Exploring Operation: 61-38=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 61+38=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 61*38=2318, Resulting Numbers: [2318] 2318,46 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 #0,1 Current State: 46:[36, 53, 82], Operations: ['97-15=82'] Exploring Operation: 82-53=29, Resulting Numbers: [36, 29] Generated Node #0,1,0: 46:[36, 29] Operation: 82-53=29 Exploring Operation: 53-36=17, Resulting Numbers: [82, 17] Generated Node #0,1,1: 46:[82, 17] Operation: 53-36=17 Exploring Operation: 82-36=46, Resulting Numbers: [53, 46] Generated Node #0,1,2: 46:[53, 46] Operation: 82-36=46 Moving to Node #0,1,2 Current State: 46:[53, 46], Operations: ['97-15=82', '82-36=46'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,46 unequal: No Solution Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,46 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[36, 29], Operations: ['97-15=82', '82-53=29'] Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,46 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[82, 17], Operations: ['97-15=82', '53-36=17'] Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 82*17=1394, Resulting Numbers: [1394] 1394,46 unequal: No Solution Exploring Operation: 82+17=99, Resulting Numbers: [99] 99,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 17, 5, 83, 36 ]
86
[ "17-5=12", "36/12=3", "83+3=86" ]
Current State: 86:[17, 5, 83, 36], Operations: [] Exploring Operation: 17-5=12, Resulting Numbers: [83, 36, 12] Generated Node #2: [83, 36, 12] from Operation: 17-5=12 Current State: 86:[83, 36, 12], Operations: ['17-5=12'] Exploring Operation: 36/12=3, Resulting Numbers: [83, 3] Generated Node #3: [83, 3] from Operation: 36/12=3 Current State: 86:[83, 3], Operations: ['17-5=12', '36/12=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[17, 5, 83, 36], Operations: [] Exploring Operation: 17*5=85, Resulting Numbers: [83, 36, 85] Generated Node #0,0: 86:[83, 36, 85] Operation: 17*5=85 Exploring Operation: 17+36=53, Resulting Numbers: [5, 83, 53] Generated Node #0,1: 86:[5, 83, 53] Operation: 17+36=53 Moving to Node #0,0 Current State: 86:[83, 36, 85], Operations: ['17*5=85'] Exploring Operation: 85-83=2, Resulting Numbers: [36, 2] Generated Node #0,0,0: 86:[36, 2] Operation: 85-83=2 Exploring Operation: 83-36=47, Resulting Numbers: [85, 47] Generated Node #0,0,1: 86:[85, 47] Operation: 83-36=47 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[85, 47], Operations: ['17*5=85', '83-36=47'] Exploring Operation: 85-47=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 85+47=132, Resulting Numbers: [132] 132,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[36, 2], Operations: ['17*5=85', '85-83=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,86 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: 86:[5, 83, 53], Operations: ['17+36=53'] Exploring Operation: 53-5=48, Resulting Numbers: [83, 48] Generated Node #0,1,0: 86:[83, 48] Operation: 53-5=48 Exploring Operation: 5+83=88, Resulting Numbers: [53, 88] Generated Node #0,1,1: 86:[53, 88] Operation: 5+83=88 Moving to Node #0,1,0 Current State: 86:[83, 48], Operations: ['17+36=53', '53-5=48'] Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 83+48=131, Resulting Numbers: [131] 131,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[53, 88], Operations: ['17+36=53', '5+83=88'] Exploring Operation: 88-53=35, Resulting Numbers: [35] 35,86 unequal: No Solution Exploring Operation: 53+88=141, Resulting Numbers: [141] 141,86 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 21, 62, 75 ]
17
[ "62-21=41", "75-41=34", "34/2=17" ]
Current State: 17:[2, 21, 62, 75], Operations: [] Exploring Operation: 62-21=41, Resulting Numbers: [2, 75, 41] Generated Node #2: [2, 75, 41] from Operation: 62-21=41 Current State: 17:[2, 75, 41], Operations: ['62-21=41'] Exploring Operation: 75-41=34, Resulting Numbers: [2, 34] Generated Node #3: [2, 34] from Operation: 75-41=34 Current State: 17:[2, 34], Operations: ['62-21=41', '75-41=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[2, 21, 62, 75], Operations: [] Exploring Operation: 75-62=13, Resulting Numbers: [2, 21, 13] Generated Node #0,0: 17:[2, 21, 13] Operation: 75-62=13 Exploring Operation: 62/2=31, Resulting Numbers: [21, 75, 31] Generated Node #0,1: 17:[21, 75, 31] Operation: 62/2=31 Moving to Node #0,0 Current State: 17:[2, 21, 13], Operations: ['75-62=13'] Exploring Operation: 21-2=19, Resulting Numbers: [13, 19] Generated Node #0,0,0: 17:[13, 19] Operation: 21-2=19 Exploring Operation: 2+13=15, Resulting Numbers: [21, 15] Generated Node #0,0,1: 17:[21, 15] Operation: 2+13=15 Moving to Node #0,1 Current State: 17:[21, 75, 31], Operations: ['62/2=31'] Exploring Operation: 75-31=44, Resulting Numbers: [21, 44] Generated Node #0,1,0: 17:[21, 44] Operation: 75-31=44 Exploring Operation: 75-21=54, Resulting Numbers: [31, 54] Generated Node #0,1,1: 17:[31, 54] Operation: 75-21=54 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[21, 44], Operations: ['62/2=31', '75-31=44'] Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,17 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,17 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 #0,1,1 Current State: 17:[31, 54], Operations: ['62/2=31', '75-21=54'] Exploring Operation: 31+54=85, Resulting Numbers: [85] 85,17 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,17 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: 17:[13, 19], Operations: ['75-62=13', '21-2=19'] Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[21, 15], Operations: ['75-62=13', '2+13=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,17 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,17 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 18, 17, 37, 86 ]
83
[ "17+37=54", "54/18=3", "86-3=83" ]
Current State: 83:[18, 17, 37, 86], Operations: [] Exploring Operation: 17+37=54, Resulting Numbers: [18, 86, 54] Generated Node #2: [18, 86, 54] from Operation: 17+37=54 Current State: 83:[18, 86, 54], Operations: ['17+37=54'] Exploring Operation: 54/18=3, Resulting Numbers: [86, 3] Generated Node #3: [86, 3] from Operation: 54/18=3 Current State: 83:[86, 3], Operations: ['17+37=54', '54/18=3'] Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[18, 17, 37, 86], Operations: [] Exploring Operation: 18+17=35, Resulting Numbers: [37, 86, 35] Generated Node #0,0: 83:[37, 86, 35] Operation: 18+17=35 Exploring Operation: 18+37=55, Resulting Numbers: [17, 86, 55] Generated Node #0,1: 83:[17, 86, 55] Operation: 18+37=55 Moving to Node #0,0 Current State: 83:[37, 86, 35], Operations: ['18+17=35'] Exploring Operation: 86-35=51, Resulting Numbers: [37, 51] Generated Node #0,0,0: 83:[37, 51] Operation: 86-35=51 Exploring Operation: 37+35=72, Resulting Numbers: [86, 72] Generated Node #0,0,1: 83:[86, 72] Operation: 37+35=72 Moving to Node #0,1 Current State: 83:[17, 86, 55], Operations: ['18+37=55'] Exploring Operation: 17+55=72, Resulting Numbers: [86, 72] Generated Node #0,1,0: 83:[86, 72] Operation: 17+55=72 Exploring Operation: 86-17=69, Resulting Numbers: [55, 69] Generated Node #0,1,1: 83:[55, 69] Operation: 86-17=69 Moving to Node #0,0,1 Current State: 83:[86, 72], Operations: ['18+17=35', '37+35=72'] Exploring Operation: 86+72=158, Resulting Numbers: [158] 158,83 unequal: No Solution Exploring Operation: 86-72=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[86, 72], Operations: ['18+37=55', '17+55=72'] Exploring Operation: 86+72=158, Resulting Numbers: [158] 158,83 unequal: No Solution Exploring Operation: 86-72=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[55, 69], Operations: ['18+37=55', '86-17=69'] Exploring Operation: 55+69=124, Resulting Numbers: [124] 124,83 unequal: No Solution Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[37, 51], Operations: ['18+17=35', '86-35=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,83 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 32, 44, 68, 40 ]
96
[ "44-32=12", "68+40=108", "108-12=96" ]
Current State: 96:[32, 44, 68, 40], Operations: [] Exploring Operation: 44-32=12, Resulting Numbers: [68, 40, 12] Generated Node #2: [68, 40, 12] from Operation: 44-32=12 Current State: 96:[68, 40, 12], Operations: ['44-32=12'] Exploring Operation: 68+40=108, Resulting Numbers: [12, 108] Generated Node #3: [12, 108] from Operation: 68+40=108 Current State: 96:[12, 108], Operations: ['44-32=12', '68+40=108'] Exploring Operation: 108-12=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[32, 44, 68, 40], Operations: [] Exploring Operation: 32+68=100, Resulting Numbers: [44, 40, 100] Generated Node #0,0: 96:[44, 40, 100] Operation: 32+68=100 Exploring Operation: 68-44=24, Resulting Numbers: [32, 40, 24] Generated Node #0,1: 96:[32, 40, 24] Operation: 68-44=24 Exploring Operation: 68-40=28, Resulting Numbers: [32, 44, 28] Generated Node #0,2: 96:[32, 44, 28] Operation: 68-40=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[32, 40, 24], Operations: ['68-44=24'] Exploring Operation: 32-24=8, Resulting Numbers: [40, 8] Generated Node #0,1,0: 96:[40, 8] Operation: 32-24=8 Exploring Operation: 40-32=8, Resulting Numbers: [24, 8] Generated Node #0,1,1: 96:[24, 8] Operation: 40-32=8 Exploring Operation: 40-24=16, Resulting Numbers: [32, 16] Generated Node #0,1,2: 96:[32, 16] Operation: 40-24=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[24, 8], Operations: ['68-44=24', '40-32=8'] Exploring Operation: 24+8=32, Resulting Numbers: [32] 32,96 unequal: No Solution Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 24/8=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 #0,1,2 Current State: 96:[32, 16], Operations: ['68-44=24', '40-24=16'] Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,96 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:[40, 8], Operations: ['68-44=24', '32-24=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,96 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:[32, 44, 28], Operations: ['68-40=28'] Exploring Operation: 32-28=4, Resulting Numbers: [44, 4] Generated Node #0,2,0: 96:[44, 4] Operation: 32-28=4 Exploring Operation: 44-32=12, Resulting Numbers: [28, 12] Generated Node #0,2,1: 96:[28, 12] Operation: 44-32=12 Exploring Operation: 44-28=16, Resulting Numbers: [32, 16] Generated Node #0,2,2: 96:[32, 16] Operation: 44-28=16 Moving to Node #0,2,2 Current State: 96:[32, 16], Operations: ['68-40=28', '44-28=16'] Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[44, 4], Operations: ['68-40=28', '32-28=4'] Exploring Operation: 44+4=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,96 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[28, 12], Operations: ['68-40=28', '44-32=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,96 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,96 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,96 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 #0,0 Current State: 96:[44, 40, 100], Operations: ['32+68=100'] Exploring Operation: 44-40=4, Resulting Numbers: [100, 4] Generated Node #0,0,0: 96:[100, 4] Operation: 44-40=4 Exploring Operation: 100-44=56, Resulting Numbers: [40, 56] Generated Node #0,0,1: 96:[40, 56] Operation: 100-44=56 Exploring Operation: 44+40=84, Resulting Numbers: [100, 84] Generated Node #0,0,2: 96:[100, 84] Operation: 44+40=84 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[100, 4], Operations: ['32+68=100', '44-40=4'] Exploring Operation: 100/4=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[32, 44, 68, 40], Operations: [] Exploring Operation: 32+68=100, Resulting Numbers: [44, 40, 100] Generated Node #0,0: 96:[44, 40, 100] Operation: 32+68=100 Moving to Node #0,0 Current State: 96:[44, 40, 100], Operations: ['32+68=100'] Exploring Operation: 44-40=4, Resulting Numbers: [100, 4] Generated Node #0,0,0: 96:[100, 4] Operation: 44-40=4 Moving to Node #0,0,0 Current State: 96:[100, 4], Operations: ['32+68=100', '44-40=4'] Exploring Operation: 100-4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 98, 3, 69, 11 ]
64
[ "98-11=87", "69/3=23", "87-23=64" ]
Current State: 64:[98, 3, 69, 11], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [3, 69, 87] Generated Node #2: [3, 69, 87] from Operation: 98-11=87 Current State: 64:[3, 69, 87], Operations: ['98-11=87'] Exploring Operation: 69/3=23, Resulting Numbers: [87, 23] Generated Node #3: [87, 23] from Operation: 69/3=23 Current State: 64:[87, 23], Operations: ['98-11=87', '69/3=23'] Exploring Operation: 87-23=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[98, 3, 69, 11], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [3, 69, 87] Generated Node #0,0: 64:[3, 69, 87] Operation: 98-11=87 Exploring Operation: 69-3=66, Resulting Numbers: [98, 11, 66] Generated Node #0,1: 64:[98, 11, 66] Operation: 69-3=66 Exploring Operation: 98-3=95, Resulting Numbers: [69, 11, 95] Generated Node #0,2: 64:[69, 11, 95] Operation: 98-3=95 Exploring Operation: 98-69=29, Resulting Numbers: [3, 11, 29] Generated Node #0,3: 64:[3, 11, 29] Operation: 98-69=29 Start Sub Search at level 1: Moving to Node #0,3 Current State: 64:[3, 11, 29], Operations: ['98-69=29'] Exploring Operation: 29-11=18, Resulting Numbers: [3, 18] Generated Node #0,3,0: 64:[3, 18] Operation: 29-11=18 Exploring Operation: 3+29=32, Resulting Numbers: [11, 32] Generated Node #0,3,1: 64:[11, 32] Operation: 3+29=32 Exploring Operation: 3*11=33, Resulting Numbers: [29, 33] Generated Node #0,3,2: 64:[29, 33] Operation: 3*11=33 Exploring Operation: 11-3=8, Resulting Numbers: [29, 8] Generated Node #0,3,3: 64:[29, 8] Operation: 11-3=8 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 64:[3, 18], Operations: ['98-69=29', '29-11=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 64:[11, 32], Operations: ['98-69=29', '3+29=32'] Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,64 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 64:[29, 8], Operations: ['98-69=29', '11-3=8'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,64 unequal: No Solution Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 64:[29, 33], Operations: ['98-69=29', '3*11=33'] Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 29*33=957, Resulting Numbers: [957] 957,64 unequal: No Solution Exploring Operation: 29+33=62, Resulting Numbers: [62] 62,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[3, 69, 87], Operations: ['98-11=87'] Exploring Operation: 87-3=84, Resulting Numbers: [69, 84] Generated Node #0,0,0: 64:[69, 84] Operation: 87-3=84 Exploring Operation: 87/3=29, Resulting Numbers: [69, 29] Generated Node #0,0,1: 64:[69, 29] Operation: 87/3=29 Exploring Operation: 69-3=66, Resulting Numbers: [87, 66] Generated Node #0,0,2: 64:[87, 66] Operation: 69-3=66 Exploring Operation: 87-69=18, Resulting Numbers: [3, 18] Generated Node #0,0,3: 64:[3, 18] Operation: 87-69=18 Moving to Node #0,0,3 Current State: 64:[3, 18], Operations: ['98-11=87', '87-69=18'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,64 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[69, 29], Operations: ['98-11=87', '87/3=29'] Exploring Operation: 69+29=98, Resulting Numbers: [98] 98,64 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 69*29=2001, Resulting Numbers: [2001] 2001,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[87, 66], Operations: ['98-11=87', '69-3=66'] Exploring Operation: 87-66=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 87*66=5742, Resulting Numbers: [5742] 5742,64 unequal: No Solution Exploring Operation: 87+66=153, Resulting Numbers: [153] 153,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[69, 84], Operations: ['98-11=87', '87-3=84'] Exploring Operation: 69*84=5796, Resulting Numbers: [5796] 5796,64 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 69+84=153, Resulting Numbers: [153] 153,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[98, 11, 66], Operations: ['69-3=66'] Exploring Operation: 98-11=87, Resulting Numbers: [66, 87] Generated Node #0,1,0: 64:[66, 87] Operation: 98-11=87 Exploring Operation: 98-66=32, Resulting Numbers: [11, 32] Generated Node #0,1,1: 64:[11, 32] Operation: 98-66=32 Exploring Operation: 66/11=6, Resulting Numbers: [98, 6] Generated Node #0,1,2: 64:[98, 6] Operation: 66/11=6 Exploring Operation: 66-11=55, Resulting Numbers: [98, 55] Generated Node #0,1,3: 64:[98, 55] Operation: 66-11=55 Moving to Node #0,1,1 Current State: 64:[11, 32], Operations: ['69-3=66', '98-66=32'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 11*32=352, Resulting Numbers: [352] 352,64 unequal: No Solution Exploring Operation: 11+32=43, Resulting Numbers: [43] 43,64 unequal: No Solution Moving to Node #0,1,0 Current State: 64:[66, 87], Operations: ['69-3=66', '98-11=87'] Exploring Operation: 66+87=153, Resulting Numbers: [153] 153,64 unequal: No Solution Exploring Operation: 87-66=21, Resulting Numbers: [21] 21,64 unequal: No Solution Exploring Operation: 66*87=5742, Resulting Numbers: [5742] 5742,64 unequal: No Solution Moving to Node #0,1,2 Current State: 64:[98, 6], Operations: ['69-3=66', '66/11=6'] Exploring Operation: 98*6=588, Resulting Numbers: [588] 588,64 unequal: No Solution Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,64 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,64 unequal: No Solution Moving to Node #0,1,3 Current State: 64:[98, 55], Operations: ['69-3=66', '66-11=55'] Exploring Operation: 98-55=43, Resulting Numbers: [43] 43,64 unequal: No Solution Exploring Operation: 98*55=5390, Resulting Numbers: [5390] 5390,64 unequal: No Solution Exploring Operation: 98+55=153, Resulting Numbers: [153] 153,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[69, 11, 95], Operations: ['98-3=95'] Exploring Operation: 95-69=26, Resulting Numbers: [11, 26] Generated Node #0,2,0: 64:[11, 26] Operation: 95-69=26 Exploring Operation: 95-11=84, Resulting Numbers: [69, 84] Generated Node #0,2,1: 64:[69, 84] Operation: 95-11=84 Exploring Operation: 69+11=80, Resulting Numbers: [95, 80] Generated Node #0,2,2: 64:[95, 80] Operation: 69+11=80 Exploring Operation: 69-11=58, Resulting Numbers: [95, 58] Generated Node #0,2,3: 64:[95, 58] Operation: 69-11=58 Moving to Node #0,2,0 Current State: 64:[11, 26], Operations: ['98-3=95', '95-69=26'] Exploring Operation: 11*26=286, Resulting Numbers: [286] 286,64 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 11+26=37, Resulting Numbers: [37] 37,64 unequal: No Solution Moving to Node #0,2,1 Current State: 64:[69, 84], Operations: ['98-3=95', '95-11=84'] Exploring Operation: 69+84=153, Resulting Numbers: [153] 153,64 unequal: No Solution Exploring Operation: 69*84=5796, Resulting Numbers: [5796] 5796,64 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,64 unequal: No Solution Moving to Node #0,2,3 Current State: 64:[95, 58], Operations: ['98-3=95', '69-11=58'] Exploring Operation: 95-58=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 95*58=5510, Resulting Numbers: [5510] 5510,64 unequal: No Solution Exploring Operation: 95+58=153, Resulting Numbers: [153] 153,64 unequal: No Solution Moving to Node #0,2,2 Current State: 64:[95, 80], Operations: ['98-3=95', '69+11=80'] Exploring Operation: 95*80=7600, Resulting Numbers: [7600] 7600,64 unequal: No Solution Exploring Operation: 95+80=175, Resulting Numbers: [175] 175,64 unequal: No Solution Exploring Operation: 95-80=15, Resulting Numbers: [15] 15,64 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
[ 24, 81, 3, 14 ]
75
[ "24/3=8", "81-14=67", "8+67=75" ]
Current State: 75:[24, 81, 3, 14], Operations: [] Exploring Operation: 24/3=8, Resulting Numbers: [81, 14, 8] Generated Node #2: [81, 14, 8] from Operation: 24/3=8 Current State: 75:[81, 14, 8], Operations: ['24/3=8'] Exploring Operation: 81-14=67, Resulting Numbers: [8, 67] Generated Node #3: [8, 67] from Operation: 81-14=67 Current State: 75:[8, 67], Operations: ['24/3=8', '81-14=67'] Exploring Operation: 8+67=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[24, 81, 3, 14], Operations: [] Exploring Operation: 81-3=78, Resulting Numbers: [24, 14, 78] Generated Node #0,0: 75:[24, 14, 78] Operation: 81-3=78 Exploring Operation: 81/3=27, Resulting Numbers: [24, 14, 27] Generated Node #0,1: 75:[24, 14, 27] Operation: 81/3=27 Moving to Node #0,1 Current State: 75:[24, 14, 27], Operations: ['81/3=27'] Exploring Operation: 27-24=3, Resulting Numbers: [14, 3] Generated Node #0,1,0: 75:[14, 3] Operation: 27-24=3 Exploring Operation: 27-14=13, Resulting Numbers: [24, 13] Generated Node #0,1,1: 75:[24, 13] Operation: 27-14=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[14, 3], Operations: ['81/3=27', '27-24=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,75 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[24, 13], Operations: ['81/3=27', '27-14=13'] Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,75 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: 75:[24, 14, 78], Operations: ['81-3=78'] Exploring Operation: 78-14=64, Resulting Numbers: [24, 64] Generated Node #0,0,0: 75:[24, 64] Operation: 78-14=64 Exploring Operation: 24-14=10, Resulting Numbers: [78, 10] Generated Node #0,0,1: 75:[78, 10] Operation: 24-14=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[78, 10], Operations: ['81-3=78', '24-14=10'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,75 unequal: No Solution Exploring Operation: 78+10=88, Resulting Numbers: [88] 88,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[24, 64], Operations: ['81-3=78', '78-14=64'] Exploring Operation: 64-24=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 24+64=88, Resulting Numbers: [88] 88,75 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
[ 29, 28, 67, 52 ]
62
[ "29+28=57", "67+52=119", "119-57=62" ]
Current State: 62:[29, 28, 67, 52], Operations: [] Exploring Operation: 29+28=57, Resulting Numbers: [67, 52, 57] Generated Node #2: [67, 52, 57] from Operation: 29+28=57 Current State: 62:[67, 52, 57], Operations: ['29+28=57'] Exploring Operation: 67+52=119, Resulting Numbers: [57, 119] Generated Node #3: [57, 119] from Operation: 67+52=119 Current State: 62:[57, 119], Operations: ['29+28=57', '67+52=119'] Exploring Operation: 119-57=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[29, 28, 67, 52], Operations: [] Exploring Operation: 52-28=24, Resulting Numbers: [29, 67, 24] Generated Node #0,0: 62:[29, 67, 24] Operation: 52-28=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[29, 67, 24], Operations: ['52-28=24'] Exploring Operation: 29-24=5, Resulting Numbers: [67, 5] Generated Node #0,0,0: 62:[67, 5] Operation: 29-24=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[67, 5], Operations: ['52-28=24', '29-24=5'] Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[29, 28, 67, 52], Operations: [] Exploring Operation: 52-28=24, Resulting Numbers: [29, 67, 24] Generated Node #0,0: 62:[29, 67, 24] Operation: 52-28=24 Moving to Node #0,0 Current State: 62:[29, 67, 24], Operations: ['52-28=24'] Exploring Operation: 29-24=5, Resulting Numbers: [67, 5] Generated Node #0,0,0: 62:[67, 5] Operation: 29-24=5 Moving to Node #0,0,0 Current State: 62:[67, 5], Operations: ['52-28=24', '29-24=5'] Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 66, 90, 31, 6 ]
70
[ "66/6=11", "90-31=59", "11+59=70" ]
Current State: 70:[66, 90, 31, 6], Operations: [] Exploring Operation: 66/6=11, Resulting Numbers: [90, 31, 11] Generated Node #2: [90, 31, 11] from Operation: 66/6=11 Current State: 70:[90, 31, 11], Operations: ['66/6=11'] Exploring Operation: 90-31=59, Resulting Numbers: [11, 59] Generated Node #3: [11, 59] from Operation: 90-31=59 Current State: 70:[11, 59], Operations: ['66/6=11', '90-31=59'] Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[66, 90, 31, 6], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [66, 31, 15] Generated Node #0,0: 70:[66, 31, 15] Operation: 90/6=15 Moving to Node #0,0 Current State: 70:[66, 31, 15], Operations: ['90/6=15'] Exploring Operation: 66-31=35, Resulting Numbers: [15, 35] Generated Node #0,0,0: 70:[15, 35] Operation: 66-31=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[15, 35], Operations: ['90/6=15', '66-31=35'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,70 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
[ 9, 8, 28, 9 ]
53
[ "9*8=72", "28-9=19", "72-19=53" ]
Current State: 53:[9, 8, 28, 9], Operations: [] Exploring Operation: 9*8=72, Resulting Numbers: [28, 72] Generated Node #2: [28, 72] from Operation: 9*8=72 Current State: 53:[28, 72], Operations: ['9*8=72'] Exploring Operation: 28-9=19, Resulting Numbers: [72, 19] Generated Node #3: [72, 19] from Operation: 28-9=19 Current State: 53:[72, 19], Operations: ['9*8=72', '28-9=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[9, 8, 28, 9], Operations: [] Exploring Operation: 9+28=37, Resulting Numbers: [8, 9, 37] Generated Node #0,0: 53:[8, 9, 37] Operation: 9+28=37 Exploring Operation: 8*9=72, Resulting Numbers: [9, 28, 72] Generated Node #0,1: 53:[9, 28, 72] Operation: 8*9=72 Exploring Operation: 9*9=81, Resulting Numbers: [8, 28, 81] Generated Node #0,2: 53:[8, 28, 81] Operation: 9*9=81 Exploring Operation: 9+8=17, Resulting Numbers: [28, 9, 17] Generated Node #0,3: 53:[28, 9, 17] Operation: 9+8=17 Exploring Operation: 9*8=72, Resulting Numbers: [28, 9, 72] Generated Node #0,4: 53:[28, 9, 72] Operation: 9*8=72 Moving to Node #0,1 Current State: 53:[9, 28, 72], Operations: ['8*9=72'] Exploring Operation: 9+28=37, Resulting Numbers: [72, 37] Generated Node #0,1,0: 53:[72, 37] Operation: 9+28=37 Exploring Operation: 28-9=19, Resulting Numbers: [72, 19] Generated Node #0,1,1: 53:[72, 19] Operation: 28-9=19 Exploring Operation: 9+72=81, Resulting Numbers: [28, 81] Generated Node #0,1,2: 53:[28, 81] Operation: 9+72=81 Exploring Operation: 72-9=63, Resulting Numbers: [28, 63] Generated Node #0,1,3: 53:[28, 63] Operation: 72-9=63 Exploring Operation: 72-28=44, Resulting Numbers: [9, 44] Generated Node #0,1,4: 53:[9, 44] Operation: 72-28=44 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[72, 37], Operations: ['8*9=72', '9+28=37'] Exploring Operation: 72-37=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 72*37=2664, Resulting Numbers: [2664] 2664,53 unequal: No Solution Exploring Operation: 72+37=109, Resulting Numbers: [109] 109,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[28, 63], Operations: ['8*9=72', '72-9=63'] Exploring Operation: 63-28=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 28+63=91, Resulting Numbers: [91] 91,53 unequal: No Solution Exploring Operation: 28*63=1764, Resulting Numbers: [1764] 1764,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[72, 19], Operations: ['8*9=72', '28-9=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[9, 8, 28, 9], Operations: [] Exploring Operation: 8*9=72, Resulting Numbers: [9, 28, 72] Generated Node #0,1: 53:[9, 28, 72] Operation: 8*9=72 Moving to Node #0,1 Current State: 53:[9, 28, 72], Operations: ['8*9=72'] Exploring Operation: 28-9=19, Resulting Numbers: [72, 19] Generated Node #0,1,1: 53:[72, 19] Operation: 28-9=19 Moving to Node #0,1,1 Current State: 53:[72, 19], Operations: ['8*9=72', '28-9=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 35, 55, 2, 76 ]
86
[ "55-35=20", "20/2=10", "76+10=86" ]
Current State: 86:[35, 55, 2, 76], Operations: [] Exploring Operation: 55-35=20, Resulting Numbers: [2, 76, 20] Generated Node #2: [2, 76, 20] from Operation: 55-35=20 Current State: 86:[2, 76, 20], Operations: ['55-35=20'] Exploring Operation: 20/2=10, Resulting Numbers: [76, 10] Generated Node #3: [76, 10] from Operation: 20/2=10 Current State: 86:[76, 10], Operations: ['55-35=20', '20/2=10'] Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[35, 55, 2, 76], Operations: [] Exploring Operation: 35+55=90, Resulting Numbers: [2, 76, 90] Generated Node #0,0: 86:[2, 76, 90] Operation: 35+55=90 Exploring Operation: 76-35=41, Resulting Numbers: [55, 2, 41] Generated Node #0,1: 86:[55, 2, 41] Operation: 76-35=41 Moving to Node #0,0 Current State: 86:[2, 76, 90], Operations: ['35+55=90'] Exploring Operation: 76/2=38, Resulting Numbers: [90, 38] Generated Node #0,0,0: 86:[90, 38] Operation: 76/2=38 Exploring Operation: 2+76=78, Resulting Numbers: [90, 78] Generated Node #0,0,1: 86:[90, 78] Operation: 2+76=78 Moving to Node #0,1 Current State: 86:[55, 2, 41], Operations: ['76-35=41'] Exploring Operation: 55+41=96, Resulting Numbers: [2, 96] Generated Node #0,1,0: 86:[2, 96] Operation: 55+41=96 Exploring Operation: 55-2=53, Resulting Numbers: [41, 53] Generated Node #0,1,1: 86:[41, 53] Operation: 55-2=53 Moving to Node #0,0,0 Current State: 86:[90, 38], Operations: ['35+55=90', '76/2=38'] Exploring Operation: 90-38=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 90+38=128, Resulting Numbers: [128] 128,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[2, 96], Operations: ['76-35=41', '55+41=96'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[90, 78], Operations: ['35+55=90', '2+76=78'] Exploring Operation: 90+78=168, Resulting Numbers: [168] 168,86 unequal: No Solution Exploring Operation: 90-78=12, Resulting Numbers: [12] 12,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[41, 53], Operations: ['76-35=41', '55-2=53'] Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,86 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 5, 51, 35, 31 ]
75
[ "35/5=7", "51+31=82", "82-7=75" ]
Current State: 75:[5, 51, 35, 31], Operations: [] Exploring Operation: 35/5=7, Resulting Numbers: [51, 31, 7] Generated Node #2: [51, 31, 7] from Operation: 35/5=7 Current State: 75:[51, 31, 7], Operations: ['35/5=7'] Exploring Operation: 51+31=82, Resulting Numbers: [7, 82] Generated Node #3: [7, 82] from Operation: 51+31=82 Current State: 75:[7, 82], Operations: ['35/5=7', '51+31=82'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[5, 51, 35, 31], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [5, 31, 16] Generated Node #0,0: 75:[5, 31, 16] Operation: 51-35=16 Exploring Operation: 51+31=82, Resulting Numbers: [5, 35, 82] Generated Node #0,1: 75:[5, 35, 82] Operation: 51+31=82 Exploring Operation: 51+35=86, Resulting Numbers: [5, 31, 86] Generated Node #0,2: 75:[5, 31, 86] Operation: 51+35=86 Exploring Operation: 51-31=20, Resulting Numbers: [5, 35, 20] Generated Node #0,3: 75:[5, 35, 20] Operation: 51-31=20 Exploring Operation: 35-31=4, Resulting Numbers: [5, 51, 4] Generated Node #0,4: 75:[5, 51, 4] Operation: 35-31=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[5, 31, 16], Operations: ['51-35=16'] Exploring Operation: 5+16=21, Resulting Numbers: [31, 21] Generated Node #0,0,0: 75:[31, 21] Operation: 5+16=21 Exploring Operation: 31-5=26, Resulting Numbers: [16, 26] Generated Node #0,0,1: 75:[16, 26] Operation: 31-5=26 Exploring Operation: 31-16=15, Resulting Numbers: [5, 15] Generated Node #0,0,2: 75:[5, 15] Operation: 31-16=15 Exploring Operation: 16-5=11, Resulting Numbers: [31, 11] Generated Node #0,0,3: 75:[31, 11] Operation: 16-5=11 Exploring Operation: 5*16=80, Resulting Numbers: [31, 80] Generated Node #0,0,4: 75:[31, 80] Operation: 5*16=80 Moving to Node #0,0,2 Current State: 75:[5, 15], Operations: ['51-35=16', '31-16=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[5, 51, 35, 31], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [5, 31, 16] Generated Node #0,0: 75:[5, 31, 16] Operation: 51-35=16 Moving to Node #0,0 Current State: 75:[5, 31, 16], Operations: ['51-35=16'] Exploring Operation: 31-16=15, Resulting Numbers: [5, 15] Generated Node #0,0,2: 75:[5, 15] Operation: 31-16=15 Moving to Node #0,0,2 Current State: 75:[5, 15], Operations: ['51-35=16', '31-16=15'] Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 24, 99, 30, 32 ]
87
[ "32-30=2", "24/2=12", "99-12=87" ]
Current State: 87:[24, 99, 30, 32], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [24, 99, 2] Generated Node #2: [24, 99, 2] from Operation: 32-30=2 Current State: 87:[24, 99, 2], Operations: ['32-30=2'] Exploring Operation: 24/2=12, Resulting Numbers: [99, 12] Generated Node #3: [99, 12] from Operation: 24/2=12 Current State: 87:[99, 12], Operations: ['32-30=2', '24/2=12'] Exploring Operation: 99-12=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[24, 99, 30, 32], Operations: [] Exploring Operation: 30-24=6, Resulting Numbers: [99, 32, 6] Generated Node #0,0: 87:[99, 32, 6] Operation: 30-24=6 Exploring Operation: 99-24=75, Resulting Numbers: [30, 32, 75] Generated Node #0,1: 87:[30, 32, 75] Operation: 99-24=75 Exploring Operation: 32-24=8, Resulting Numbers: [99, 30, 8] Generated Node #0,2: 87:[99, 30, 8] Operation: 32-24=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[30, 32, 75], Operations: ['99-24=75'] Exploring Operation: 75-30=45, Resulting Numbers: [32, 45] Generated Node #0,1,0: 87:[32, 45] Operation: 75-30=45 Exploring Operation: 75-32=43, Resulting Numbers: [30, 43] Generated Node #0,1,1: 87:[30, 43] Operation: 75-32=43 Exploring Operation: 32-30=2, Resulting Numbers: [75, 2] Generated Node #0,1,2: 87:[75, 2] Operation: 32-30=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[75, 2], Operations: ['99-24=75', '32-30=2'] Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,87 unequal: No Solution Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[30, 43], Operations: ['99-24=75', '75-32=43'] Exploring Operation: 30*43=1290, Resulting Numbers: [1290] 1290,87 unequal: No Solution Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 30+43=73, Resulting Numbers: [73] 73,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[32, 45], Operations: ['99-24=75', '75-30=45'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,87 unequal: No Solution Exploring Operation: 32+45=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 32*45=1440, Resulting Numbers: [1440] 1440,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[99, 32, 6], Operations: ['30-24=6'] Exploring Operation: 32-6=26, Resulting Numbers: [99, 26] Generated Node #0,0,0: 87:[99, 26] Operation: 32-6=26 Exploring Operation: 99-6=93, Resulting Numbers: [32, 93] Generated Node #0,0,1: 87:[32, 93] Operation: 99-6=93 Exploring Operation: 99+6=105, Resulting Numbers: [32, 105] Generated Node #0,0,2: 87:[32, 105] Operation: 99+6=105 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[32, 93], Operations: ['30-24=6', '99-6=93'] Exploring Operation: 32*93=2976, Resulting Numbers: [2976] 2976,87 unequal: No Solution Exploring Operation: 32+93=125, Resulting Numbers: [125] 125,87 unequal: No Solution Exploring Operation: 93-32=61, Resulting Numbers: [61] 61,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[99, 26], Operations: ['30-24=6', '32-6=26'] Exploring Operation: 99-26=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 99+26=125, Resulting Numbers: [125] 125,87 unequal: No Solution Exploring Operation: 99*26=2574, Resulting Numbers: [2574] 2574,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[32, 105], Operations: ['30-24=6', '99+6=105'] Exploring Operation: 32*105=3360, Resulting Numbers: [3360] 3360,87 unequal: No Solution Exploring Operation: 105-32=73, Resulting Numbers: [73] 73,87 unequal: No Solution Exploring Operation: 32+105=137, Resulting Numbers: [137] 137,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[99, 30, 8], Operations: ['32-24=8'] Exploring Operation: 99-8=91, Resulting Numbers: [30, 91] Generated Node #0,2,0: 87:[30, 91] Operation: 99-8=91 Exploring Operation: 30-8=22, Resulting Numbers: [99, 22] Generated Node #0,2,1: 87:[99, 22] Operation: 30-8=22 Exploring Operation: 99+8=107, Resulting Numbers: [30, 107] Generated Node #0,2,2: 87:[30, 107] Operation: 99+8=107 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[30, 91], Operations: ['32-24=8', '99-8=91'] Exploring Operation: 30*91=2730, Resulting Numbers: [2730] 2730,87 unequal: No Solution Exploring Operation: 91-30=61, Resulting Numbers: [61] 61,87 unequal: No Solution Exploring Operation: 30+91=121, Resulting Numbers: [121] 121,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[99, 22], Operations: ['32-24=8', '30-8=22'] Exploring Operation: 99+22=121, Resulting Numbers: [121] 121,87 unequal: No Solution Exploring Operation: 99*22=2178, Resulting Numbers: [2178] 2178,87 unequal: No Solution Exploring Operation: 99-22=77, Resulting Numbers: [77] 77,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[30, 107], Operations: ['32-24=8', '99+8=107'] Exploring Operation: 107-30=77, Resulting Numbers: [77] 77,87 unequal: No Solution Exploring Operation: 30*107=3210, Resulting Numbers: [3210] 3210,87 unequal: No Solution Exploring Operation: 30+107=137, Resulting Numbers: [137] 137,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 63, 32, 72, 50 ]
67
[ "50-32=18", "72/18=4", "63+4=67" ]
Current State: 67:[63, 32, 72, 50], Operations: [] Exploring Operation: 50-32=18, Resulting Numbers: [63, 72, 18] Generated Node #2: [63, 72, 18] from Operation: 50-32=18 Current State: 67:[63, 72, 18], Operations: ['50-32=18'] Exploring Operation: 72/18=4, Resulting Numbers: [63, 4] Generated Node #3: [63, 4] from Operation: 72/18=4 Current State: 67:[63, 4], Operations: ['50-32=18', '72/18=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[63, 32, 72, 50], Operations: [] Exploring Operation: 32+50=82, Resulting Numbers: [63, 72, 82] Generated Node #0,0: 67:[63, 72, 82] Operation: 32+50=82 Moving to Node #0,0 Current State: 67:[63, 72, 82], Operations: ['32+50=82'] Exploring Operation: 82-63=19, Resulting Numbers: [72, 19] Generated Node #0,0,0: 67:[72, 19] Operation: 82-63=19 Moving to Node #0,0,0 Current State: 67:[72, 19], Operations: ['32+50=82', '82-63=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,67 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 37, 40, 64, 75 ]
83
[ "64*75=4800", "4800/40=120", "120-37=83" ]
Current State: 83:[37, 40, 64, 75], Operations: [] Exploring Operation: 64*75=4800, Resulting Numbers: [37, 40, 4800] Generated Node #2: [37, 40, 4800] from Operation: 64*75=4800 Current State: 83:[37, 40, 4800], Operations: ['64*75=4800'] Exploring Operation: 4800/40=120, Resulting Numbers: [37, 120] Generated Node #3: [37, 120] from Operation: 4800/40=120 Current State: 83:[37, 120], Operations: ['64*75=4800', '4800/40=120'] Exploring Operation: 120-37=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[37, 40, 64, 75], Operations: [] Exploring Operation: 40+64=104, Resulting Numbers: [37, 75, 104] Generated Node #0,0: 83:[37, 75, 104] Operation: 40+64=104 Exploring Operation: 37+40=77, Resulting Numbers: [64, 75, 77] Generated Node #0,1: 83:[64, 75, 77] Operation: 37+40=77 Exploring Operation: 37+75=112, Resulting Numbers: [40, 64, 112] Generated Node #0,2: 83:[40, 64, 112] Operation: 37+75=112 Exploring Operation: 37+64=101, Resulting Numbers: [40, 75, 101] Generated Node #0,3: 83:[40, 75, 101] Operation: 37+64=101 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[64, 75, 77], Operations: ['37+40=77'] Exploring Operation: 75-64=11, Resulting Numbers: [77, 11] Generated Node #0,1,0: 83:[77, 11] Operation: 75-64=11 Exploring Operation: 64+75=139, Resulting Numbers: [77, 139] Generated Node #0,1,1: 83:[77, 139] Operation: 64+75=139 Exploring Operation: 64+77=141, Resulting Numbers: [75, 141] Generated Node #0,1,2: 83:[75, 141] Operation: 64+77=141 Exploring Operation: 77-64=13, Resulting Numbers: [75, 13] Generated Node #0,1,3: 83:[75, 13] Operation: 77-64=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[77, 139], Operations: ['37+40=77', '64+75=139'] Exploring Operation: 77+139=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 77*139=10703, Resulting Numbers: [10703] 10703,83 unequal: No Solution Exploring Operation: 139-77=62, Resulting Numbers: [62] 62,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[75, 141], Operations: ['37+40=77', '64+77=141'] Exploring Operation: 75*141=10575, Resulting Numbers: [10575] 10575,83 unequal: No Solution Exploring Operation: 141-75=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 75+141=216, Resulting Numbers: [216] 216,83 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:[77, 11], Operations: ['37+40=77', '75-64=11'] Exploring Operation: 77-11=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 77*11=847, Resulting Numbers: [847] 847,83 unequal: No Solution Exploring Operation: 77+11=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 77/11=7, Resulting Numbers: [7] 7,83 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 #0,1,3 Current State: 83:[75, 13], Operations: ['37+40=77', '77-64=13'] Exploring Operation: 75-13=62, Resulting Numbers: [62] 62,83 unequal: No Solution Exploring Operation: 75+13=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 75*13=975, Resulting Numbers: [975] 975,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 83:[40, 75, 101], Operations: ['37+64=101'] Exploring Operation: 40+101=141, Resulting Numbers: [75, 141] Generated Node #0,3,0: 83:[75, 141] Operation: 40+101=141 Exploring Operation: 40+75=115, Resulting Numbers: [101, 115] Generated Node #0,3,1: 83:[101, 115] Operation: 40+75=115 Exploring Operation: 75-40=35, Resulting Numbers: [101, 35] Generated Node #0,3,2: 83:[101, 35] Operation: 75-40=35 Exploring Operation: 101-40=61, Resulting Numbers: [75, 61] Generated Node #0,3,3: 83:[75, 61] Operation: 101-40=61 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 83:[75, 61], Operations: ['37+64=101', '101-40=61'] Exploring Operation: 75+61=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 75-61=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 75*61=4575, Resulting Numbers: [4575] 4575,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 83:[101, 115], Operations: ['37+64=101', '40+75=115'] Exploring Operation: 101+115=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 115-101=14, Resulting Numbers: [14] 14,83 unequal: No Solution Exploring Operation: 101*115=11615, Resulting Numbers: [11615] 11615,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 83:[75, 141], Operations: ['37+64=101', '40+101=141'] Exploring Operation: 141-75=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 75*141=10575, Resulting Numbers: [10575] 10575,83 unequal: No Solution Exploring Operation: 75+141=216, Resulting Numbers: [216] 216,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 83:[101, 35], Operations: ['37+64=101', '75-40=35'] Exploring Operation: 101-35=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 101*35=3535, Resulting Numbers: [3535] 3535,83 unequal: No Solution Exploring Operation: 101+35=136, Resulting Numbers: [136] 136,83 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 #0,0 Current State: 83:[37, 75, 104], Operations: ['40+64=104'] Exploring Operation: 104-37=67, Resulting Numbers: [75, 67] Generated Node #0,0,0: 83:[75, 67] Operation: 104-37=67 Exploring Operation: 37+104=141, Resulting Numbers: [75, 141] Generated Node #0,0,1: 83:[75, 141] Operation: 37+104=141 Exploring Operation: 75-37=38, Resulting Numbers: [104, 38] Generated Node #0,0,2: 83:[104, 38] Operation: 75-37=38 Exploring Operation: 37+75=112, Resulting Numbers: [104, 112] Generated Node #0,0,3: 83:[104, 112] Operation: 37+75=112 Moving to Node #0,0,0 Current State: 83:[75, 67], Operations: ['40+64=104', '104-37=67'] Exploring Operation: 75*67=5025, Resulting Numbers: [5025] 5025,83 unequal: No Solution Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 75+67=142, Resulting Numbers: [142] 142,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[104, 112], Operations: ['40+64=104', '37+75=112'] Exploring Operation: 104+112=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 104*112=11648, Resulting Numbers: [11648] 11648,83 unequal: No Solution Exploring Operation: 112-104=8, Resulting Numbers: [8] 8,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[104, 38], Operations: ['40+64=104', '75-37=38'] Exploring Operation: 104*38=3952, Resulting Numbers: [3952] 3952,83 unequal: No Solution Exploring Operation: 104+38=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 104-38=66, Resulting Numbers: [66] 66,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[75, 141], Operations: ['40+64=104', '37+104=141'] Exploring Operation: 75+141=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 141-75=66, Resulting Numbers: [66] 66,83 unequal: No Solution Exploring Operation: 75*141=10575, Resulting Numbers: [10575] 10575,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[40, 64, 112], Operations: ['37+75=112'] Exploring Operation: 112-64=48, Resulting Numbers: [40, 48] Generated Node #0,2,0: 83:[40, 48] Operation: 112-64=48 Exploring Operation: 112-40=72, Resulting Numbers: [64, 72] Generated Node #0,2,1: 83:[64, 72] Operation: 112-40=72 Exploring Operation: 64-40=24, Resulting Numbers: [112, 24] Generated Node #0,2,2: 83:[112, 24] Operation: 64-40=24 Exploring Operation: 40+64=104, Resulting Numbers: [112, 104] Generated Node #0,2,3: 83:[112, 104] Operation: 40+64=104 Moving to Node #0,2,1 Current State: 83:[64, 72], Operations: ['37+75=112', '112-40=72'] Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,83 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[112, 104], Operations: ['37+75=112', '40+64=104'] Exploring Operation: 112+104=216, Resulting Numbers: [216] 216,83 unequal: No Solution Exploring Operation: 112-104=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 112*104=11648, Resulting Numbers: [11648] 11648,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[40, 48], Operations: ['37+75=112', '112-64=48'] Exploring Operation: 40+48=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,83 unequal: No Solution Exploring Operation: 40*48=1920, Resulting Numbers: [1920] 1920,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[112, 24], Operations: ['37+75=112', '64-40=24'] Exploring Operation: 112-24=88, Resulting Numbers: [88] 88,83 unequal: No Solution Exploring Operation: 112+24=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 112*24=2688, Resulting Numbers: [2688] 2688,83 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
[ 40, 48, 61, 15 ]
67
[ "40*48=1920", "1920/15=128", "128-61=67" ]
Current State: 67:[40, 48, 61, 15], Operations: [] Exploring Operation: 40*48=1920, Resulting Numbers: [61, 15, 1920] Generated Node #2: [61, 15, 1920] from Operation: 40*48=1920 Current State: 67:[61, 15, 1920], Operations: ['40*48=1920'] Exploring Operation: 1920/15=128, Resulting Numbers: [61, 128] Generated Node #3: [61, 128] from Operation: 1920/15=128 Current State: 67:[61, 128], Operations: ['40*48=1920', '1920/15=128'] Exploring Operation: 128-61=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[40, 48, 61, 15], Operations: [] Exploring Operation: 48+15=63, Resulting Numbers: [40, 61, 63] Generated Node #0,0: 67:[40, 61, 63] Operation: 48+15=63 Exploring Operation: 40+15=55, Resulting Numbers: [48, 61, 55] Generated Node #0,1: 67:[48, 61, 55] Operation: 40+15=55 Exploring Operation: 61+15=76, Resulting Numbers: [40, 48, 76] Generated Node #0,2: 67:[40, 48, 76] Operation: 61+15=76 Moving to Node #0,0 Current State: 67:[40, 61, 63], Operations: ['48+15=63'] Exploring Operation: 40+61=101, Resulting Numbers: [63, 101] Generated Node #0,0,0: 67:[63, 101] Operation: 40+61=101 Exploring Operation: 40+63=103, Resulting Numbers: [61, 103] Generated Node #0,0,1: 67:[61, 103] Operation: 40+63=103 Exploring Operation: 61-40=21, Resulting Numbers: [63, 21] Generated Node #0,0,2: 67:[63, 21] Operation: 61-40=21 Moving to Node #0,1 Current State: 67:[48, 61, 55], Operations: ['40+15=55'] Exploring Operation: 48+61=109, Resulting Numbers: [55, 109] Generated Node #0,1,0: 67:[55, 109] Operation: 48+61=109 Exploring Operation: 61-48=13, Resulting Numbers: [55, 13] Generated Node #0,1,1: 67:[55, 13] Operation: 61-48=13 Exploring Operation: 48+55=103, Resulting Numbers: [61, 103] Generated Node #0,1,2: 67:[61, 103] Operation: 48+55=103 Moving to Node #0,2 Current State: 67:[40, 48, 76], Operations: ['61+15=76'] Exploring Operation: 76-40=36, Resulting Numbers: [48, 36] Generated Node #0,2,0: 67:[48, 36] Operation: 76-40=36 Exploring Operation: 40+48=88, Resulting Numbers: [76, 88] Generated Node #0,2,1: 67:[76, 88] Operation: 40+48=88 Exploring Operation: 76-48=28, Resulting Numbers: [40, 28] Generated Node #0,2,2: 67:[40, 28] Operation: 76-48=28 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[76, 88], Operations: ['61+15=76', '40+48=88'] Exploring Operation: 88-76=12, Resulting Numbers: [12] 12,67 unequal: No Solution Exploring Operation: 76*88=6688, Resulting Numbers: [6688] 6688,67 unequal: No Solution Exploring Operation: 76+88=164, Resulting Numbers: [164] 164,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[48, 36], Operations: ['61+15=76', '76-40=36'] Exploring Operation: 48+36=84, Resulting Numbers: [84] 84,67 unequal: No Solution Exploring Operation: 48*36=1728, Resulting Numbers: [1728] 1728,67 unequal: No Solution Exploring Operation: 48-36=12, Resulting Numbers: [12] 12,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[40, 28], Operations: ['61+15=76', '76-48=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,67 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,67 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: 67:[63, 101], Operations: ['48+15=63', '40+61=101'] Exploring Operation: 63+101=164, Resulting Numbers: [164] 164,67 unequal: No Solution Exploring Operation: 101-63=38, Resulting Numbers: [38] 38,67 unequal: No Solution Exploring Operation: 63*101=6363, Resulting Numbers: [6363] 6363,67 unequal: No Solution Moving to Node #0,0,1 Current State: 67:[61, 103], Operations: ['48+15=63', '40+63=103'] Exploring Operation: 61+103=164, Resulting Numbers: [164] 164,67 unequal: No Solution Exploring Operation: 61*103=6283, Resulting Numbers: [6283] 6283,67 unequal: No Solution Exploring Operation: 103-61=42, Resulting Numbers: [42] 42,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[61, 103], Operations: ['40+15=55', '48+55=103'] Exploring Operation: 103-61=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 61+103=164, Resulting Numbers: [164] 164,67 unequal: No Solution Exploring Operation: 61*103=6283, Resulting Numbers: [6283] 6283,67 unequal: No Solution Moving to Node #0,0,2 Current State: 67:[63, 21], Operations: ['48+15=63', '61-40=21'] Exploring Operation: 63-21=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 63/21=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 63+21=84, Resulting Numbers: [84] 84,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[55, 109], Operations: ['40+15=55', '48+61=109'] Exploring Operation: 109-55=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 55*109=5995, Resulting Numbers: [5995] 5995,67 unequal: No Solution Exploring Operation: 55+109=164, Resulting Numbers: [164] 164,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[55, 13], Operations: ['40+15=55', '61-48=13'] Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,67 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,67 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 19, 53, 39, 89 ]
94
[ "53-19=34", "39+89=128", "128-34=94" ]
Current State: 94:[19, 53, 39, 89], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [39, 89, 34] Generated Node #2: [39, 89, 34] from Operation: 53-19=34 Current State: 94:[39, 89, 34], Operations: ['53-19=34'] Exploring Operation: 39+89=128, Resulting Numbers: [34, 128] Generated Node #3: [34, 128] from Operation: 39+89=128 Current State: 94:[34, 128], Operations: ['53-19=34', '39+89=128'] Exploring Operation: 128-34=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[19, 53, 39, 89], Operations: [] Exploring Operation: 19+39=58, Resulting Numbers: [53, 89, 58] Generated Node #0,0: 94:[53, 89, 58] Operation: 19+39=58 Exploring Operation: 53+39=92, Resulting Numbers: [19, 89, 92] Generated Node #0,1: 94:[19, 89, 92] Operation: 53+39=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[53, 89, 58], Operations: ['19+39=58'] Exploring Operation: 89-53=36, Resulting Numbers: [58, 36] Generated Node #0,0,0: 94:[58, 36] Operation: 89-53=36 Exploring Operation: 58-53=5, Resulting Numbers: [89, 5] Generated Node #0,0,1: 94:[89, 5] Operation: 58-53=5 Moving to Node #0,0,1 Current State: 94:[89, 5], Operations: ['19+39=58', '58-53=5'] Exploring Operation: 89+5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[19, 53, 39, 89], Operations: [] Exploring Operation: 19+39=58, Resulting Numbers: [53, 89, 58] Generated Node #0,0: 94:[53, 89, 58] Operation: 19+39=58 Moving to Node #0,0 Current State: 94:[53, 89, 58], Operations: ['19+39=58'] Exploring Operation: 58-53=5, Resulting Numbers: [89, 5] Generated Node #0,0,1: 94:[89, 5] Operation: 58-53=5 Moving to Node #0,0,1 Current State: 94:[89, 5], Operations: ['19+39=58', '58-53=5'] Exploring Operation: 89+5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 23, 13, 59, 88 ]
54
[ "88-23=65", "65/13=5", "59-5=54" ]
Current State: 54:[23, 13, 59, 88], Operations: [] Exploring Operation: 88-23=65, Resulting Numbers: [13, 59, 65] Generated Node #2: [13, 59, 65] from Operation: 88-23=65 Current State: 54:[13, 59, 65], Operations: ['88-23=65'] Exploring Operation: 65/13=5, Resulting Numbers: [59, 5] Generated Node #3: [59, 5] from Operation: 65/13=5 Current State: 54:[59, 5], Operations: ['88-23=65', '65/13=5'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[23, 13, 59, 88], Operations: [] Exploring Operation: 88-23=65, Resulting Numbers: [13, 59, 65] Generated Node #0,0: 54:[13, 59, 65] Operation: 88-23=65 Exploring Operation: 88-59=29, Resulting Numbers: [23, 13, 29] Generated Node #0,1: 54:[23, 13, 29] Operation: 88-59=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[23, 13, 29], Operations: ['88-59=29'] Exploring Operation: 29-23=6, Resulting Numbers: [13, 6] Generated Node #0,1,0: 54:[13, 6] Operation: 29-23=6 Exploring Operation: 23-13=10, Resulting Numbers: [29, 10] Generated Node #0,1,1: 54:[29, 10] Operation: 23-13=10 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[29, 10], Operations: ['88-59=29', '23-13=10'] Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[13, 6], Operations: ['88-59=29', '29-23=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[13, 59, 65], Operations: ['88-23=65'] Exploring Operation: 65/13=5, Resulting Numbers: [59, 5] Generated Node #0,0,0: 54:[59, 5] Operation: 65/13=5 Exploring Operation: 65-59=6, Resulting Numbers: [13, 6] Generated Node #0,0,1: 54:[13, 6] Operation: 65-59=6 Moving to Node #0,0,1 Current State: 54:[13, 6], Operations: ['88-23=65', '65-59=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[59, 5], Operations: ['88-23=65', '65/13=5'] Exploring Operation: 59+5=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[23, 13, 59, 88], Operations: [] Exploring Operation: 88-23=65, Resulting Numbers: [13, 59, 65] Generated Node #0,0: 54:[13, 59, 65] Operation: 88-23=65 Moving to Node #0,0 Current State: 54:[13, 59, 65], Operations: ['88-23=65'] Exploring Operation: 65/13=5, Resulting Numbers: [59, 5] Generated Node #0,0,0: 54:[59, 5] Operation: 65/13=5 Moving to Node #0,0,0 Current State: 54:[59, 5], Operations: ['88-23=65', '65/13=5'] Exploring Operation: 59-5=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 8, 22, 11, 29 ]
42
[ "29-8=21", "22/11=2", "21*2=42" ]
Current State: 42:[8, 22, 11, 29], Operations: [] Exploring Operation: 29-8=21, Resulting Numbers: [22, 11, 21] Generated Node #2: [22, 11, 21] from Operation: 29-8=21 Current State: 42:[22, 11, 21], Operations: ['29-8=21'] Exploring Operation: 22/11=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 22/11=2 Current State: 42:[21, 2], Operations: ['29-8=21', '22/11=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[8, 22, 11, 29], Operations: [] Exploring Operation: 11+29=40, Resulting Numbers: [8, 22, 40] Generated Node #0,0: 42:[8, 22, 40] Operation: 11+29=40 Exploring Operation: 29-8=21, Resulting Numbers: [22, 11, 21] Generated Node #0,1: 42:[22, 11, 21] Operation: 29-8=21 Exploring Operation: 29-22=7, Resulting Numbers: [8, 11, 7] Generated Node #0,2: 42:[8, 11, 7] Operation: 29-22=7 Moving to Node #0,0 Current State: 42:[8, 22, 40], Operations: ['11+29=40'] Exploring Operation: 40-22=18, Resulting Numbers: [8, 18] Generated Node #0,0,0: 42:[8, 18] Operation: 40-22=18 Exploring Operation: 22-8=14, Resulting Numbers: [40, 14] Generated Node #0,0,1: 42:[40, 14] Operation: 22-8=14 Exploring Operation: 40/8=5, Resulting Numbers: [22, 5] Generated Node #0,0,2: 42:[22, 5] Operation: 40/8=5 Moving to Node #0,1 Current State: 42:[22, 11, 21], Operations: ['29-8=21'] Exploring Operation: 22-11=11, Resulting Numbers: [21, 11] Generated Node #0,1,0: 42:[21, 11] Operation: 22-11=11 Exploring Operation: 22+21=43, Resulting Numbers: [11, 43] Generated Node #0,1,1: 42:[11, 43] Operation: 22+21=43 Exploring Operation: 22/11=2, Resulting Numbers: [21, 2] Generated Node #0,1,2: 42:[21, 2] Operation: 22/11=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[21, 2], Operations: ['29-8=21', '22/11=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[8, 22, 11, 29], Operations: [] Exploring Operation: 29-8=21, Resulting Numbers: [22, 11, 21] Generated Node #0,1: 42:[22, 11, 21] Operation: 29-8=21 Moving to Node #0,1 Current State: 42:[22, 11, 21], Operations: ['29-8=21'] Exploring Operation: 22/11=2, Resulting Numbers: [21, 2] Generated Node #0,1,2: 42:[21, 2] Operation: 22/11=2 Moving to Node #0,1,2 Current State: 42:[21, 2], Operations: ['29-8=21', '22/11=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 57, 77, 42, 55 ]
70
[ "57-55=2", "77-42=35", "2*35=70" ]
Current State: 70:[57, 77, 42, 55], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [77, 42, 2] Generated Node #2: [77, 42, 2] from Operation: 57-55=2 Current State: 70:[77, 42, 2], Operations: ['57-55=2'] Exploring Operation: 77-42=35, Resulting Numbers: [2, 35] Generated Node #3: [2, 35] from Operation: 77-42=35 Current State: 70:[2, 35], Operations: ['57-55=2', '77-42=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[57, 77, 42, 55], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [77, 42, 2] Generated Node #0,0: 70:[77, 42, 2] Operation: 57-55=2 Exploring Operation: 55-42=13, Resulting Numbers: [57, 77, 13] Generated Node #0,1: 70:[57, 77, 13] Operation: 55-42=13 Exploring Operation: 57-42=15, Resulting Numbers: [77, 55, 15] Generated Node #0,2: 70:[77, 55, 15] Operation: 57-42=15 Moving to Node #0,0 Current State: 70:[77, 42, 2], Operations: ['57-55=2'] Exploring Operation: 42-2=40, Resulting Numbers: [77, 40] Generated Node #0,0,0: 70:[77, 40] Operation: 42-2=40 Exploring Operation: 77-42=35, Resulting Numbers: [2, 35] Generated Node #0,0,1: 70:[2, 35] Operation: 77-42=35 Exploring Operation: 77-2=75, Resulting Numbers: [42, 75] Generated Node #0,0,2: 70:[42, 75] Operation: 77-2=75 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[2, 35], Operations: ['57-55=2', '77-42=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,70 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,70 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[57, 77, 42, 55], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [77, 42, 2] Generated Node #0,0: 70:[77, 42, 2] Operation: 57-55=2 Moving to Node #0,0 Current State: 70:[77, 42, 2], Operations: ['57-55=2'] Exploring Operation: 77-42=35, Resulting Numbers: [2, 35] Generated Node #0,0,1: 70:[2, 35] Operation: 77-42=35 Moving to Node #0,0,1 Current State: 70:[2, 35], Operations: ['57-55=2', '77-42=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 52, 73, 66, 58 ]
62
[ "58-52=6", "66/6=11", "73-11=62" ]
Current State: 62:[52, 73, 66, 58], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [73, 66, 6] Generated Node #2: [73, 66, 6] from Operation: 58-52=6 Current State: 62:[73, 66, 6], Operations: ['58-52=6'] Exploring Operation: 66/6=11, Resulting Numbers: [73, 11] Generated Node #3: [73, 11] from Operation: 66/6=11 Current State: 62:[73, 11], Operations: ['58-52=6', '66/6=11'] Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[52, 73, 66, 58], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [73, 66, 6] Generated Node #0,0: 62:[73, 66, 6] Operation: 58-52=6 Exploring Operation: 73-52=21, Resulting Numbers: [66, 58, 21] Generated Node #0,1: 62:[66, 58, 21] Operation: 73-52=21 Moving to Node #0,1 Current State: 62:[66, 58, 21], Operations: ['73-52=21'] Exploring Operation: 66-58=8, Resulting Numbers: [21, 8] Generated Node #0,1,0: 62:[21, 8] Operation: 66-58=8 Exploring Operation: 58-21=37, Resulting Numbers: [66, 37] Generated Node #0,1,1: 62:[66, 37] Operation: 58-21=37 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[66, 37], Operations: ['73-52=21', '58-21=37'] Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 66+37=103, Resulting Numbers: [103] 103,62 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:[21, 8], Operations: ['73-52=21', '66-58=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,62 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,62 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:[73, 66, 6], Operations: ['58-52=6'] Exploring Operation: 73-6=67, Resulting Numbers: [66, 67] Generated Node #0,0,0: 62:[66, 67] Operation: 73-6=67 Exploring Operation: 73-66=7, Resulting Numbers: [6, 7] Generated Node #0,0,1: 62:[6, 7] Operation: 73-66=7 Moving to Node #0,0,0 Current State: 62:[66, 67], Operations: ['58-52=6', '73-6=67'] Exploring Operation: 67-66=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 66+67=133, Resulting Numbers: [133] 133,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[6, 7], Operations: ['58-52=6', '73-66=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,62 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 52, 22, 68, 1 ]
97
[ "52-22=30", "68-1=67", "30+67=97" ]
Current State: 97:[52, 22, 68, 1], Operations: [] Exploring Operation: 52-22=30, Resulting Numbers: [68, 1, 30] Generated Node #2: [68, 1, 30] from Operation: 52-22=30 Current State: 97:[68, 1, 30], Operations: ['52-22=30'] Exploring Operation: 68-1=67, Resulting Numbers: [30, 67] Generated Node #3: [30, 67] from Operation: 68-1=67 Current State: 97:[30, 67], Operations: ['52-22=30', '68-1=67'] Exploring Operation: 30+67=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[52, 22, 68, 1], Operations: [] Exploring Operation: 52+22=74, Resulting Numbers: [68, 1, 74] Generated Node #0,0: 97:[68, 1, 74] Operation: 52+22=74 Moving to Node #0,0 Current State: 97:[68, 1, 74], Operations: ['52+22=74'] Exploring Operation: 68+1=69, Resulting Numbers: [74, 69] Generated Node #0,0,0: 97:[74, 69] Operation: 68+1=69 Moving to Node #0,0,0 Current State: 97:[74, 69], Operations: ['52+22=74', '68+1=69'] Exploring Operation: 74+69=143, Resulting Numbers: [143] 143,97 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 78, 56, 3, 8 ]
11
[ "78-56=22", "3+8=11", "22-11=11" ]
Current State: 11:[78, 56, 3, 8], Operations: [] Exploring Operation: 78-56=22, Resulting Numbers: [3, 8, 22] Generated Node #2: [3, 8, 22] from Operation: 78-56=22 Current State: 11:[3, 8, 22], Operations: ['78-56=22'] Exploring Operation: 3+8=11, Resulting Numbers: [22, 11] Generated Node #3: [22, 11] from Operation: 3+8=11 Current State: 11:[22, 11], Operations: ['78-56=22', '3+8=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[78, 56, 3, 8], Operations: [] Exploring Operation: 78-56=22, Resulting Numbers: [3, 8, 22] Generated Node #0,0: 11:[3, 8, 22] Operation: 78-56=22 Exploring Operation: 78/3=26, Resulting Numbers: [56, 8, 26] Generated Node #0,1: 11:[56, 8, 26] Operation: 78/3=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[3, 8, 22], Operations: ['78-56=22'] Exploring Operation: 3+8=11, Resulting Numbers: [22, 11] Generated Node #0,0,0: 11:[22, 11] Operation: 3+8=11 Exploring Operation: 22-3=19, Resulting Numbers: [8, 19] Generated Node #0,0,1: 11:[8, 19] Operation: 22-3=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[22, 11], Operations: ['78-56=22', '3+8=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[78, 56, 3, 8], Operations: [] Exploring Operation: 78-56=22, Resulting Numbers: [3, 8, 22] Generated Node #0,0: 11:[3, 8, 22] Operation: 78-56=22 Moving to Node #0,0 Current State: 11:[3, 8, 22], Operations: ['78-56=22'] Exploring Operation: 3+8=11, Resulting Numbers: [22, 11] Generated Node #0,0,0: 11:[22, 11] Operation: 3+8=11 Moving to Node #0,0,0 Current State: 11:[22, 11], Operations: ['78-56=22', '3+8=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic