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
[ 54, 81, 12, 97 ]
72
[ "97-81=16", "54*16=864", "864/12=72" ]
Current State: 72:[54, 81, 12, 97], Operations: [] Exploring Operation: 97-81=16, Resulting Numbers: [54, 12, 16] Generated Node #2: [54, 12, 16] from Operation: 97-81=16 Current State: 72:[54, 12, 16], Operations: ['97-81=16'] Exploring Operation: 54*16=864, Resulting Numbers: [12, 864] Generated Node #3: [12, 864] from Operation: 54*16=864 Current State: 72:[12, 864], Operations: ['97-81=16', '54*16=864'] Exploring Operation: 864/12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[54, 81, 12, 97], Operations: [] Exploring Operation: 81-54=27, Resulting Numbers: [12, 97, 27] Generated Node #0,0: 72:[12, 97, 27] Operation: 81-54=27 Exploring Operation: 54+12=66, Resulting Numbers: [81, 97, 66] Generated Node #0,1: 72:[81, 97, 66] Operation: 54+12=66 Exploring Operation: 97-81=16, Resulting Numbers: [54, 12, 16] Generated Node #0,2: 72:[54, 12, 16] Operation: 97-81=16 Exploring Operation: 97-54=43, Resulting Numbers: [81, 12, 43] Generated Node #0,3: 72:[81, 12, 43] Operation: 97-54=43 Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[81, 12, 43], Operations: ['97-54=43'] Exploring Operation: 81-12=69, Resulting Numbers: [43, 69] Generated Node #0,3,0: 72:[43, 69] Operation: 81-12=69 Exploring Operation: 12+43=55, Resulting Numbers: [81, 55] Generated Node #0,3,1: 72:[81, 55] Operation: 12+43=55 Exploring Operation: 43-12=31, Resulting Numbers: [81, 31] Generated Node #0,3,2: 72:[81, 31] Operation: 43-12=31 Exploring Operation: 81-43=38, Resulting Numbers: [12, 38] Generated Node #0,3,3: 72:[12, 38] Operation: 81-43=38 Moving to Node #0,3,3 Current State: 72:[12, 38], Operations: ['97-54=43', '81-43=38'] Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,72 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[43, 69], Operations: ['97-54=43', '81-12=69'] Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,72 unequal: No Solution Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,72 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,72 unequal: No Solution Moving to Node #0,3,2 Current State: 72:[81, 31], Operations: ['97-54=43', '43-12=31'] Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,72 unequal: No Solution Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,72 unequal: No Solution Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,72 unequal: No Solution Moving to Node #0,3,1 Current State: 72:[81, 55], Operations: ['97-54=43', '12+43=55'] Exploring Operation: 81+55=136, Resulting Numbers: [136] 136,72 unequal: No Solution Exploring Operation: 81*55=4455, Resulting Numbers: [4455] 4455,72 unequal: No Solution Exploring Operation: 81-55=26, Resulting Numbers: [26] 26,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[54, 12, 16], Operations: ['97-81=16'] Exploring Operation: 54-16=38, Resulting Numbers: [12, 38] Generated Node #0,2,0: 72:[12, 38] Operation: 54-16=38 Exploring Operation: 54+16=70, Resulting Numbers: [12, 70] Generated Node #0,2,1: 72:[12, 70] Operation: 54+16=70 Exploring Operation: 54-12=42, Resulting Numbers: [16, 42] Generated Node #0,2,2: 72:[16, 42] Operation: 54-12=42 Exploring Operation: 54+12=66, Resulting Numbers: [16, 66] Generated Node #0,2,3: 72:[16, 66] Operation: 54+12=66 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[12, 38], Operations: ['97-81=16', '54-16=38'] Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,72 unequal: No Solution Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[12, 70], Operations: ['97-81=16', '54+16=70'] Exploring Operation: 12*70=840, Resulting Numbers: [840] 840,72 unequal: No Solution Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 12+70=82, Resulting Numbers: [82] 82,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[16, 42], Operations: ['97-81=16', '54-12=42'] Exploring Operation: 16*42=672, Resulting Numbers: [672] 672,72 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 72:[16, 66], Operations: ['97-81=16', '54+12=66'] Exploring Operation: 16*66=1056, Resulting Numbers: [1056] 1056,72 unequal: No Solution Exploring Operation: 16+66=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[12, 97, 27], Operations: ['81-54=27'] Exploring Operation: 97-12=85, Resulting Numbers: [27, 85] Generated Node #0,0,0: 72:[27, 85] Operation: 97-12=85 Exploring Operation: 27-12=15, Resulting Numbers: [97, 15] Generated Node #0,0,1: 72:[97, 15] Operation: 27-12=15 Exploring Operation: 97-27=70, Resulting Numbers: [12, 70] Generated Node #0,0,2: 72:[12, 70] Operation: 97-27=70 Exploring Operation: 12+27=39, Resulting Numbers: [97, 39] Generated Node #0,0,3: 72:[97, 39] Operation: 12+27=39 Moving to Node #0,0,2 Current State: 72:[12, 70], Operations: ['81-54=27', '97-27=70'] Exploring Operation: 12+70=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 12*70=840, Resulting Numbers: [840] 840,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[27, 85], Operations: ['81-54=27', '97-12=85'] Exploring Operation: 85-27=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 27*85=2295, Resulting Numbers: [2295] 2295,72 unequal: No Solution Exploring Operation: 27+85=112, Resulting Numbers: [112] 112,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[97, 39], Operations: ['81-54=27', '12+27=39'] Exploring Operation: 97-39=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 97*39=3783, Resulting Numbers: [3783] 3783,72 unequal: No Solution Exploring Operation: 97+39=136, Resulting Numbers: [136] 136,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[97, 15], Operations: ['81-54=27', '27-12=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,72 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[81, 97, 66], Operations: ['54+12=66'] Exploring Operation: 81-66=15, Resulting Numbers: [97, 15] Generated Node #0,1,0: 72:[97, 15] Operation: 81-66=15 Exploring Operation: 81+66=147, Resulting Numbers: [97, 147] Generated Node #0,1,1: 72:[97, 147] Operation: 81+66=147 Exploring Operation: 97-81=16, Resulting Numbers: [66, 16] Generated Node #0,1,2: 72:[66, 16] Operation: 97-81=16 Exploring Operation: 97-66=31, Resulting Numbers: [81, 31] Generated Node #0,1,3: 72:[81, 31] Operation: 97-66=31 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[66, 16], Operations: ['54+12=66', '97-81=16'] Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,72 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 72:[81, 31], Operations: ['54+12=66', '97-66=31'] Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,72 unequal: No Solution Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[97, 15], Operations: ['54+12=66', '81-66=15'] Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,72 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[97, 147], Operations: ['54+12=66', '81+66=147'] Exploring Operation: 97+147=244, Resulting Numbers: [244] 244,72 unequal: No Solution Exploring Operation: 147-97=50, Resulting Numbers: [50] 50,72 unequal: No Solution Exploring Operation: 97*147=14259, Resulting Numbers: [14259] 14259,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 85, 86, 80, 46 ]
34
[ "86-85=1", "80-46=34", "1*34=34" ]
Current State: 34:[85, 86, 80, 46], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [80, 46, 1] Generated Node #2: [80, 46, 1] from Operation: 86-85=1 Current State: 34:[80, 46, 1], Operations: ['86-85=1'] Exploring Operation: 80-46=34, Resulting Numbers: [1, 34] Generated Node #3: [1, 34] from Operation: 80-46=34 Current State: 34:[1, 34], Operations: ['86-85=1', '80-46=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[85, 86, 80, 46], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [85, 46, 6] Generated Node #0,0: 34:[85, 46, 6] Operation: 86-80=6 Exploring Operation: 85-80=5, Resulting Numbers: [86, 46, 5] Generated Node #0,1: 34:[86, 46, 5] Operation: 85-80=5 Exploring Operation: 86-85=1, Resulting Numbers: [80, 46, 1] Generated Node #0,2: 34:[80, 46, 1] Operation: 86-85=1 Exploring Operation: 85-46=39, Resulting Numbers: [86, 80, 39] Generated Node #0,3: 34:[86, 80, 39] Operation: 85-46=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[80, 46, 1], Operations: ['86-85=1'] Exploring Operation: 46-1=45, Resulting Numbers: [80, 45] Generated Node #0,2,0: 34:[80, 45] Operation: 46-1=45 Exploring Operation: 80*1=80, Resulting Numbers: [46, 80] Generated Node #0,2,1: 34:[46, 80] Operation: 80*1=80 Exploring Operation: 80-1=79, Resulting Numbers: [46, 79] Generated Node #0,2,2: 34:[46, 79] Operation: 80-1=79 Exploring Operation: 80-46=34, Resulting Numbers: [1, 34] Generated Node #0,2,3: 34:[1, 34] Operation: 80-46=34 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 34:[1, 34], Operations: ['86-85=1', '80-46=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[85, 86, 80, 46], Operations: [] Exploring Operation: 86-85=1, Resulting Numbers: [80, 46, 1] Generated Node #0,2: 34:[80, 46, 1] Operation: 86-85=1 Moving to Node #0,2 Current State: 34:[80, 46, 1], Operations: ['86-85=1'] Exploring Operation: 80-46=34, Resulting Numbers: [1, 34] Generated Node #0,2,3: 34:[1, 34] Operation: 80-46=34 Moving to Node #0,2,3 Current State: 34:[1, 34], Operations: ['86-85=1', '80-46=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 69, 60, 69, 8 ]
86
[ "69-60=9", "69+8=77", "9+77=86" ]
Current State: 86:[69, 60, 69, 8], Operations: [] Exploring Operation: 69-60=9, Resulting Numbers: [8, 9] Generated Node #2: [8, 9] from Operation: 69-60=9 Current State: 86:[8, 9], Operations: ['69-60=9'] Exploring Operation: 69+8=77, Resulting Numbers: [9, 77] Generated Node #3: [9, 77] from Operation: 69+8=77 Current State: 86:[9, 77], Operations: ['69-60=9', '69+8=77'] Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[69, 60, 69, 8], Operations: [] Exploring Operation: 69-69=0, Resulting Numbers: [60, 8, 0] Generated Node #0,0: 86:[60, 8, 0] Operation: 69-69=0 Exploring Operation: 69/69=1, Resulting Numbers: [60, 8, 1] Generated Node #0,1: 86:[60, 8, 1] Operation: 69/69=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[60, 8, 1], Operations: ['69/69=1'] Exploring Operation: 60-8=52, Resulting Numbers: [1, 52] Generated Node #0,1,0: 86:[1, 52] Operation: 60-8=52 Exploring Operation: 60+8=68, Resulting Numbers: [1, 68] Generated Node #0,1,1: 86:[1, 68] Operation: 60+8=68 Moving to Node #0,1,0 Current State: 86:[1, 52], Operations: ['69/69=1', '60-8=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[1, 68], Operations: ['69/69=1', '60+8=68'] Exploring Operation: 1+68=69, Resulting Numbers: [69] 69,86 unequal: No Solution Exploring Operation: 1*68=68, Resulting Numbers: [68] 68,86 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 Current State: 86:[60, 8, 0], Operations: ['69-69=0'] Exploring Operation: 60*0=0, Resulting Numbers: [8, 0] Generated Node #0,0,0: 86:[8, 0] Operation: 60*0=0 Exploring Operation: 60-8=52, Resulting Numbers: [0, 52] Generated Node #0,0,1: 86:[0, 52] Operation: 60-8=52 Moving to Node #0,0,0 Current State: 86:[8, 0], Operations: ['69-69=0', '60*0=0'] Exploring Operation: 8*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 8+0=8, Resulting Numbers: [8] 8,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[0, 52], Operations: ['69-69=0', '60-8=52'] Exploring Operation: 0*52=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 0+52=52, Resulting Numbers: [52] 52,86 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
[ 28, 32, 48, 40 ]
30
[ "48-28=20", "40/20=2", "32-2=30" ]
Current State: 30:[28, 32, 48, 40], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [32, 40, 20] Generated Node #2: [32, 40, 20] from Operation: 48-28=20 Current State: 30:[32, 40, 20], Operations: ['48-28=20'] Exploring Operation: 40/20=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 40/20=2 Current State: 30:[32, 2], Operations: ['48-28=20', '40/20=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[28, 32, 48, 40], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [32, 40, 20] Generated Node #0,0: 30:[32, 40, 20] Operation: 48-28=20 Exploring Operation: 48-40=8, Resulting Numbers: [28, 32, 8] Generated Node #0,1: 30:[28, 32, 8] Operation: 48-40=8 Exploring Operation: 48-32=16, Resulting Numbers: [28, 40, 16] Generated Node #0,2: 30:[28, 40, 16] Operation: 48-32=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[28, 32, 8], Operations: ['48-40=8'] Exploring Operation: 28-8=20, Resulting Numbers: [32, 20] Generated Node #0,1,0: 30:[32, 20] Operation: 28-8=20 Exploring Operation: 32/8=4, Resulting Numbers: [28, 4] Generated Node #0,1,1: 30:[28, 4] Operation: 32/8=4 Exploring Operation: 32-28=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 30:[8, 4] Operation: 32-28=4 Moving to Node #0,1,1 Current State: 30:[28, 4], Operations: ['48-40=8', '32/8=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,30 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[8, 4], Operations: ['48-40=8', '32-28=4'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[32, 20], Operations: ['48-40=8', '28-8=20'] Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,30 unequal: No Solution Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,30 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[28, 40, 16], Operations: ['48-32=16'] Exploring Operation: 28-16=12, Resulting Numbers: [40, 12] Generated Node #0,2,0: 30:[40, 12] Operation: 28-16=12 Exploring Operation: 40-16=24, Resulting Numbers: [28, 24] Generated Node #0,2,1: 30:[28, 24] Operation: 40-16=24 Exploring Operation: 40-28=12, Resulting Numbers: [16, 12] Generated Node #0,2,2: 30:[16, 12] Operation: 40-28=12 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 30:[16, 12], Operations: ['48-32=16', '40-28=12'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 30:[28, 24], Operations: ['48-32=16', '40-16=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,30 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,30 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[40, 12], Operations: ['48-32=16', '28-16=12'] Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,30 unequal: No Solution Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,30 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[32, 40, 20], Operations: ['48-28=20'] Exploring Operation: 40/20=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 30:[32, 2] Operation: 40/20=2 Exploring Operation: 40-32=8, Resulting Numbers: [20, 8] Generated Node #0,0,1: 30:[20, 8] Operation: 40-32=8 Exploring Operation: 40-20=20, Resulting Numbers: [32, 20] Generated Node #0,0,2: 30:[32, 20] Operation: 40-20=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[32, 2], Operations: ['48-28=20', '40/20=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,30 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[28, 32, 48, 40], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [32, 40, 20] Generated Node #0,0: 30:[32, 40, 20] Operation: 48-28=20 Moving to Node #0,0 Current State: 30:[32, 40, 20], Operations: ['48-28=20'] Exploring Operation: 40/20=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 30:[32, 2] Operation: 40/20=2 Moving to Node #0,0,0 Current State: 30:[32, 2], Operations: ['48-28=20', '40/20=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 42, 36, 40, 48 ]
94
[ "42-36=6", "40+48=88", "6+88=94" ]
Current State: 94:[42, 36, 40, 48], Operations: [] Exploring Operation: 42-36=6, Resulting Numbers: [40, 48, 6] Generated Node #2: [40, 48, 6] from Operation: 42-36=6 Current State: 94:[40, 48, 6], Operations: ['42-36=6'] Exploring Operation: 40+48=88, Resulting Numbers: [6, 88] Generated Node #3: [6, 88] from Operation: 40+48=88 Current State: 94:[6, 88], Operations: ['42-36=6', '40+48=88'] Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[42, 36, 40, 48], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [42, 48, 4] Generated Node #0,0: 94:[42, 48, 4] Operation: 40-36=4 Moving to Node #0,0 Current State: 94:[42, 48, 4], Operations: ['40-36=4'] Exploring Operation: 42+4=46, Resulting Numbers: [48, 46] Generated Node #0,0,0: 94:[48, 46] Operation: 42+4=46 Moving to Node #0,0,0 Current State: 94:[48, 46], Operations: ['40-36=4', '42+4=46'] Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[42, 36, 40, 48], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [42, 48, 4] Generated Node #0,0: 94:[42, 48, 4] Operation: 40-36=4 Moving to Node #0,0 Current State: 94:[42, 48, 4], Operations: ['40-36=4'] Exploring Operation: 42+4=46, Resulting Numbers: [48, 46] Generated Node #0,0,0: 94:[48, 46] Operation: 42+4=46 Moving to Node #0,0,0 Current State: 94:[48, 46], Operations: ['40-36=4', '42+4=46'] Exploring Operation: 48+46=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 78, 48, 6, 68 ]
52
[ "78+48=126", "6+68=74", "126-74=52" ]
Current State: 52:[78, 48, 6, 68], Operations: [] Exploring Operation: 78+48=126, Resulting Numbers: [6, 68, 126] Generated Node #2: [6, 68, 126] from Operation: 78+48=126 Current State: 52:[6, 68, 126], Operations: ['78+48=126'] Exploring Operation: 6+68=74, Resulting Numbers: [126, 74] Generated Node #3: [126, 74] from Operation: 6+68=74 Current State: 52:[126, 74], Operations: ['78+48=126', '6+68=74'] Exploring Operation: 126-74=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[78, 48, 6, 68], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [48, 68, 13] Generated Node #0,0: 52:[48, 68, 13] Operation: 78/6=13 Exploring Operation: 78-68=10, Resulting Numbers: [48, 6, 10] Generated Node #0,1: 52:[48, 6, 10] Operation: 78-68=10 Moving to Node #0,1 Current State: 52:[48, 6, 10], Operations: ['78-68=10'] Exploring Operation: 48+6=54, Resulting Numbers: [10, 54] Generated Node #0,1,0: 52:[10, 54] Operation: 48+6=54 Exploring Operation: 10-6=4, Resulting Numbers: [48, 4] Generated Node #0,1,1: 52:[48, 4] Operation: 10-6=4 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[48, 4], Operations: ['78-68=10', '10-6=4'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[78, 48, 6, 68], Operations: [] Exploring Operation: 78-68=10, Resulting Numbers: [48, 6, 10] Generated Node #0,1: 52:[48, 6, 10] Operation: 78-68=10 Moving to Node #0,1 Current State: 52:[48, 6, 10], Operations: ['78-68=10'] Exploring Operation: 10-6=4, Resulting Numbers: [48, 4] Generated Node #0,1,1: 52:[48, 4] Operation: 10-6=4 Moving to Node #0,1,1 Current State: 52:[48, 4], Operations: ['78-68=10', '10-6=4'] Exploring Operation: 48+4=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 4, 86, 84, 29 ]
78
[ "84/4=21", "86-29=57", "21+57=78" ]
Current State: 78:[4, 86, 84, 29], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [86, 29, 21] Generated Node #2: [86, 29, 21] from Operation: 84/4=21 Current State: 78:[86, 29, 21], Operations: ['84/4=21'] Exploring Operation: 86-29=57, Resulting Numbers: [21, 57] Generated Node #3: [21, 57] from Operation: 86-29=57 Current State: 78:[21, 57], Operations: ['84/4=21', '86-29=57'] Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[4, 86, 84, 29], Operations: [] Exploring Operation: 29-4=25, Resulting Numbers: [86, 84, 25] Generated Node #0,0: 78:[86, 84, 25] Operation: 29-4=25 Exploring Operation: 86-4=82, Resulting Numbers: [84, 29, 82] Generated Node #0,1: 78:[84, 29, 82] Operation: 86-4=82 Exploring Operation: 84-4=80, Resulting Numbers: [86, 29, 80] Generated Node #0,2: 78:[86, 29, 80] Operation: 84-4=80 Exploring Operation: 86-84=2, Resulting Numbers: [4, 29, 2] Generated Node #0,3: 78:[4, 29, 2] Operation: 86-84=2 Moving to Node #0,3 Current State: 78:[4, 29, 2], Operations: ['86-84=2'] Exploring Operation: 4-2=2, Resulting Numbers: [29, 2] Generated Node #0,3,0: 78:[29, 2] Operation: 4-2=2 Exploring Operation: 29-2=27, Resulting Numbers: [4, 27] Generated Node #0,3,1: 78:[4, 27] Operation: 29-2=27 Exploring Operation: 4+2=6, Resulting Numbers: [29, 6] Generated Node #0,3,2: 78:[29, 6] Operation: 4+2=6 Exploring Operation: 29-4=25, Resulting Numbers: [2, 25] Generated Node #0,3,3: 78:[2, 25] Operation: 29-4=25 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[2, 25], Operations: ['86-84=2', '29-4=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[4, 27], Operations: ['86-84=2', '29-2=27'] Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,78 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[29, 2], Operations: ['86-84=2', '4-2=2'] Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,78 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[29, 6], Operations: ['86-84=2', '4+2=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,78 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,78 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: 78:[86, 29, 80], Operations: ['84-4=80'] Exploring Operation: 80-29=51, Resulting Numbers: [86, 51] Generated Node #0,2,0: 78:[86, 51] Operation: 80-29=51 Exploring Operation: 86+29=115, Resulting Numbers: [80, 115] Generated Node #0,2,1: 78:[80, 115] Operation: 86+29=115 Exploring Operation: 86-80=6, Resulting Numbers: [29, 6] Generated Node #0,2,2: 78:[29, 6] Operation: 86-80=6 Exploring Operation: 86-29=57, Resulting Numbers: [80, 57] Generated Node #0,2,3: 78:[80, 57] Operation: 86-29=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[29, 6], Operations: ['84-4=80', '86-80=6'] Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,78 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[86, 51], Operations: ['84-4=80', '80-29=51'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 86+51=137, Resulting Numbers: [137] 137,78 unequal: No Solution Exploring Operation: 86*51=4386, Resulting Numbers: [4386] 4386,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[80, 57], Operations: ['84-4=80', '86-29=57'] Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,78 unequal: No Solution Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[80, 115], Operations: ['84-4=80', '86+29=115'] Exploring Operation: 80*115=9200, Resulting Numbers: [9200] 9200,78 unequal: No Solution Exploring Operation: 80+115=195, Resulting Numbers: [195] 195,78 unequal: No Solution Exploring Operation: 115-80=35, Resulting Numbers: [35] 35,78 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: 78:[84, 29, 82], Operations: ['86-4=82'] Exploring Operation: 84+29=113, Resulting Numbers: [82, 113] Generated Node #0,1,0: 78:[82, 113] Operation: 84+29=113 Exploring Operation: 84-29=55, Resulting Numbers: [82, 55] Generated Node #0,1,1: 78:[82, 55] Operation: 84-29=55 Exploring Operation: 84-82=2, Resulting Numbers: [29, 2] Generated Node #0,1,2: 78:[29, 2] Operation: 84-82=2 Exploring Operation: 82-29=53, Resulting Numbers: [84, 53] Generated Node #0,1,3: 78:[84, 53] Operation: 82-29=53 Moving to Node #0,0 Current State: 78:[86, 84, 25], Operations: ['29-4=25'] Exploring Operation: 84-25=59, Resulting Numbers: [86, 59] Generated Node #0,0,0: 78:[86, 59] Operation: 84-25=59 Exploring Operation: 86-25=61, Resulting Numbers: [84, 61] Generated Node #0,0,1: 78:[84, 61] Operation: 86-25=61 Exploring Operation: 86+25=111, Resulting Numbers: [84, 111] Generated Node #0,0,2: 78:[84, 111] Operation: 86+25=111 Exploring Operation: 86-84=2, Resulting Numbers: [25, 2] Generated Node #0,0,3: 78:[25, 2] Operation: 86-84=2 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[25, 2], Operations: ['29-4=25', '86-84=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[84, 61], Operations: ['29-4=25', '86-25=61'] Exploring Operation: 84-61=23, Resulting Numbers: [23] 23,78 unequal: No Solution Exploring Operation: 84+61=145, Resulting Numbers: [145] 145,78 unequal: No Solution Exploring Operation: 84*61=5124, Resulting Numbers: [5124] 5124,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[86, 59], Operations: ['29-4=25', '84-25=59'] Exploring Operation: 86+59=145, Resulting Numbers: [145] 145,78 unequal: No Solution Exploring Operation: 86*59=5074, Resulting Numbers: [5074] 5074,78 unequal: No Solution Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[84, 111], Operations: ['29-4=25', '86+25=111'] Exploring Operation: 84+111=195, Resulting Numbers: [195] 195,78 unequal: No Solution Exploring Operation: 111-84=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 84*111=9324, Resulting Numbers: [9324] 9324,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 78:[29, 2], Operations: ['86-4=82', '84-82=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,78 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,78 unequal: No Solution Moving to Node #0,1,3 Current State: 78:[84, 53], Operations: ['86-4=82', '82-29=53'] Exploring Operation: 84+53=137, Resulting Numbers: [137] 137,78 unequal: No Solution Exploring Operation: 84-53=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 84*53=4452, Resulting Numbers: [4452] 4452,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[82, 55], Operations: ['86-4=82', '84-29=55'] Exploring Operation: 82-55=27, Resulting Numbers: [27] 27,78 unequal: No Solution Exploring Operation: 82*55=4510, Resulting Numbers: [4510] 4510,78 unequal: No Solution Exploring Operation: 82+55=137, Resulting Numbers: [137] 137,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[82, 113], Operations: ['86-4=82', '84+29=113'] Exploring Operation: 113-82=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 82+113=195, Resulting Numbers: [195] 195,78 unequal: No Solution Exploring Operation: 82*113=9266, Resulting Numbers: [9266] 9266,78 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 45, 4, 25, 45 ]
85
[ "45*45=2025", "2025/25=81", "4+81=85" ]
Current State: 85:[45, 4, 25, 45], Operations: [] Exploring Operation: 45*45=2025, Resulting Numbers: [4, 25, 2025] Generated Node #2: [4, 25, 2025] from Operation: 45*45=2025 Current State: 85:[4, 25, 2025], Operations: ['45*45=2025'] Exploring Operation: 2025/25=81, Resulting Numbers: [4, 81] Generated Node #3: [4, 81] from Operation: 2025/25=81 Current State: 85:[4, 81], Operations: ['45*45=2025', '2025/25=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[45, 4, 25, 45], Operations: [] Exploring Operation: 45+45=90, Resulting Numbers: [4, 25, 90] Generated Node #0,0: 85:[4, 25, 90] Operation: 45+45=90 Exploring Operation: 45/45=1, Resulting Numbers: [4, 25, 1] Generated Node #0,1: 85:[4, 25, 1] Operation: 45/45=1 Exploring Operation: 45-25=20, Resulting Numbers: [45, 4, 20] Generated Node #0,2: 85:[45, 4, 20] Operation: 45-25=20 Exploring Operation: 45-25=20, Resulting Numbers: [4, 45, 20] Generated Node #0,3: 85:[4, 45, 20] Operation: 45-25=20 Exploring Operation: 45-45=0, Resulting Numbers: [4, 25, 0] Generated Node #0,4: 85:[4, 25, 0] Operation: 45-45=0 Moving to Node #0,1 Current State: 85:[4, 25, 1], Operations: ['45/45=1'] Exploring Operation: 25-1=24, Resulting Numbers: [4, 24] Generated Node #0,1,0: 85:[4, 24] Operation: 25-1=24 Exploring Operation: 4/1=4, Resulting Numbers: [25, 4] Generated Node #0,1,1: 85:[25, 4] Operation: 4/1=4 Exploring Operation: 4+1=5, Resulting Numbers: [25, 5] Generated Node #0,1,2: 85:[25, 5] Operation: 4+1=5 Exploring Operation: 25-4=21, Resulting Numbers: [1, 21] Generated Node #0,1,3: 85:[1, 21] Operation: 25-4=21 Exploring Operation: 4*1=4, Resulting Numbers: [25, 4] Generated Node #0,1,4: 85:[25, 4] Operation: 4*1=4 Moving to Node #0,4 Current State: 85:[4, 25, 0], Operations: ['45-45=0'] Exploring Operation: 25-4=21, Resulting Numbers: [0, 21] Generated Node #0,4,0: 85:[0, 21] Operation: 25-4=21 Exploring Operation: 25*0=0, Resulting Numbers: [4, 0] Generated Node #0,4,1: 85:[4, 0] Operation: 25*0=0 Exploring Operation: 4-0=4, Resulting Numbers: [25, 4] Generated Node #0,4,2: 85:[25, 4] Operation: 4-0=4 Exploring Operation: 4+0=4, Resulting Numbers: [25, 4] Generated Node #0,4,3: 85:[25, 4] Operation: 4+0=4 Exploring Operation: 25+0=25, Resulting Numbers: [4, 25] Generated Node #0,4,4: 85:[4, 25] Operation: 25+0=25 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 85:[4, 0], Operations: ['45-45=0', '25*0=0'] Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,85 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 #0,4,0 Current State: 85:[0, 21], Operations: ['45-45=0', '25-4=21'] Exploring Operation: 0*21=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 0+21=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 21-0=21, Resulting Numbers: [21] 21,85 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 #0,4,2 Current State: 85:[25, 4], Operations: ['45-45=0', '4-0=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 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 #0,4,3 Current State: 85:[25, 4], Operations: ['45-45=0', '4+0=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,85 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 #0,4,4 Current State: 85:[4, 25], Operations: ['45-45=0', '25+0=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 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: 85:[4, 25, 90], Operations: ['45+45=90'] Exploring Operation: 4+25=29, Resulting Numbers: [90, 29] Generated Node #0,0,0: 85:[90, 29] Operation: 4+25=29 Exploring Operation: 90-4=86, Resulting Numbers: [25, 86] Generated Node #0,0,1: 85:[25, 86] Operation: 90-4=86 Exploring Operation: 4+90=94, Resulting Numbers: [25, 94] Generated Node #0,0,2: 85:[25, 94] Operation: 4+90=94 Exploring Operation: 25-4=21, Resulting Numbers: [90, 21] Generated Node #0,0,3: 85:[90, 21] Operation: 25-4=21 Exploring Operation: 4*25=100, Resulting Numbers: [90, 100] Generated Node #0,0,4: 85:[90, 100] Operation: 4*25=100 Moving to Node #0,2 Current State: 85:[45, 4, 20], Operations: ['45-25=20'] Exploring Operation: 20/4=5, Resulting Numbers: [45, 5] Generated Node #0,2,0: 85:[45, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [45, 16] Generated Node #0,2,1: 85:[45, 16] Operation: 20-4=16 Exploring Operation: 45-4=41, Resulting Numbers: [20, 41] Generated Node #0,2,2: 85:[20, 41] Operation: 45-4=41 Exploring Operation: 45-20=25, Resulting Numbers: [4, 25] Generated Node #0,2,3: 85:[4, 25] Operation: 45-20=25 Exploring Operation: 45+20=65, Resulting Numbers: [4, 65] Generated Node #0,2,4: 85:[4, 65] Operation: 45+20=65 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 85:[4, 25], Operations: ['45-25=20', '45-20=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,85 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 #0,2,4 Current State: 85:[4, 65], Operations: ['45-25=20', '45+20=65'] Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,85 unequal: No Solution Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,85 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 #0,2,2 Current State: 85:[20, 41], Operations: ['45-25=20', '45-4=41'] Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,85 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,85 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 #0,2,0 Current State: 85:[45, 5], Operations: ['45-25=20', '20/4=5'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,85 unequal: No Solution Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,85 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 #0,2,1 Current State: 85:[45, 16], Operations: ['45-25=20', '20-4=16'] Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 45*16=720, Resulting Numbers: [720] 720,85 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: 85:[4, 45, 20], Operations: ['45-25=20'] Exploring Operation: 45-4=41, Resulting Numbers: [20, 41] Generated Node #0,3,0: 85:[20, 41] Operation: 45-4=41 Exploring Operation: 45+20=65, Resulting Numbers: [4, 65] Generated Node #0,3,1: 85:[4, 65] Operation: 45+20=65 Exploring Operation: 45-20=25, Resulting Numbers: [4, 25] Generated Node #0,3,2: 85:[4, 25] Operation: 45-20=25 Exploring Operation: 20/4=5, Resulting Numbers: [45, 5] Generated Node #0,3,3: 85:[45, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [45, 16] Generated Node #0,3,4: 85:[45, 16] Operation: 20-4=16 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[4, 25], Operations: ['45-25=20', '45-20=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,85 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 #0,3,1 Current State: 85:[4, 65], Operations: ['45-25=20', '45+20=65'] Exploring Operation: 65-4=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 4+65=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 4*65=260, Resulting Numbers: [260] 260,85 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 #0,3,0 Current State: 85:[20, 41], Operations: ['45-25=20', '45-4=41'] Exploring Operation: 20+41=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 20*41=820, Resulting Numbers: [820] 820,85 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 #0,3,3 Current State: 85:[45, 5], Operations: ['45-25=20', '20/4=5'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,85 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,85 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 #0,3,4 Current State: 85:[45, 16], Operations: ['45-25=20', '20-4=16'] Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 45*16=720, Resulting Numbers: [720] 720,85 unequal: No Solution Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 85:[4, 24], Operations: ['45/45=1', '25-1=24'] Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[1, 21], Operations: ['45/45=1', '25-4=21'] Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 21/1=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 1+21=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[25, 5], Operations: ['45/45=1', '4+1=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,85 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,85 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[90, 21], Operations: ['45+45=90', '25-4=21'] Exploring Operation: 90*21=1890, Resulting Numbers: [1890] 1890,85 unequal: No Solution Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 90+21=111, Resulting Numbers: [111] 111,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[25, 86], Operations: ['45+45=90', '90-4=86'] Exploring Operation: 86-25=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 25*86=2150, Resulting Numbers: [2150] 2150,85 unequal: No Solution Exploring Operation: 25+86=111, Resulting Numbers: [111] 111,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[25, 4], Operations: ['45/45=1', '4*1=4'] Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[25, 4], Operations: ['45/45=1', '4/1=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[90, 29], Operations: ['45+45=90', '4+25=29'] Exploring Operation: 90-29=61, Resulting Numbers: [61] 61,85 unequal: No Solution Exploring Operation: 90+29=119, Resulting Numbers: [119] 119,85 unequal: No Solution Exploring Operation: 90*29=2610, Resulting Numbers: [2610] 2610,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[25, 94], Operations: ['45+45=90', '4+90=94'] Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,85 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,85 unequal: No Solution Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,85 unequal: No Solution Moving to Node #0,0,4 Current State: 85:[90, 100], Operations: ['45+45=90', '4*25=100'] Exploring Operation: 90+100=190, Resulting Numbers: [190] 190,85 unequal: No Solution Exploring Operation: 90*100=9000, Resulting Numbers: [9000] 9000,85 unequal: No Solution Exploring Operation: 100-90=10, Resulting Numbers: [10] 10,85 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 20, 9, 67 ]
35
[ "61-20=41", "9+67=76", "76-41=35" ]
Current State: 35:[61, 20, 9, 67], Operations: [] Exploring Operation: 61-20=41, Resulting Numbers: [9, 67, 41] Generated Node #2: [9, 67, 41] from Operation: 61-20=41 Current State: 35:[9, 67, 41], Operations: ['61-20=41'] Exploring Operation: 9+67=76, Resulting Numbers: [41, 76] Generated Node #3: [41, 76] from Operation: 9+67=76 Current State: 35:[41, 76], Operations: ['61-20=41', '9+67=76'] Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[61, 20, 9, 67], Operations: [] Exploring Operation: 61-20=41, Resulting Numbers: [9, 67, 41] Generated Node #0,0: 35:[9, 67, 41] Operation: 61-20=41 Exploring Operation: 67-61=6, Resulting Numbers: [20, 9, 6] Generated Node #0,1: 35:[20, 9, 6] Operation: 67-61=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[20, 9, 6], Operations: ['67-61=6'] Exploring Operation: 20-9=11, Resulting Numbers: [6, 11] Generated Node #0,1,0: 35:[6, 11] Operation: 20-9=11 Exploring Operation: 20+9=29, Resulting Numbers: [6, 29] Generated Node #0,1,1: 35:[6, 29] Operation: 20+9=29 Moving to Node #0,1,0 Current State: 35:[6, 11], Operations: ['67-61=6', '20-9=11'] Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,35 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[6, 29], Operations: ['67-61=6', '20+9=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,35 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[61, 20, 9, 67], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [20, 9, 6] Generated Node #0,1: 35:[20, 9, 6] Operation: 67-61=6 Moving to Node #0,1 Current State: 35:[20, 9, 6], Operations: ['67-61=6'] Exploring Operation: 20+9=29, Resulting Numbers: [6, 29] Generated Node #0,1,1: 35:[6, 29] Operation: 20+9=29 Moving to Node #0,1,1 Current State: 35:[6, 29], Operations: ['67-61=6', '20+9=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 75, 70, 99, 8 ]
33
[ "75-70=5", "8-5=3", "99/3=33" ]
Current State: 33:[75, 70, 99, 8], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [99, 8, 5] Generated Node #2: [99, 8, 5] from Operation: 75-70=5 Current State: 33:[99, 8, 5], Operations: ['75-70=5'] Exploring Operation: 8-5=3, Resulting Numbers: [99, 3] Generated Node #3: [99, 3] from Operation: 8-5=3 Current State: 33:[99, 3], Operations: ['75-70=5', '8-5=3'] Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[75, 70, 99, 8], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [70, 8, 24] Generated Node #0,0: 33:[70, 8, 24] Operation: 99-75=24 Exploring Operation: 99-70=29, Resulting Numbers: [75, 8, 29] Generated Node #0,1: 33:[75, 8, 29] Operation: 99-70=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[70, 8, 24], Operations: ['99-75=24'] Exploring Operation: 70-24=46, Resulting Numbers: [8, 46] Generated Node #0,0,0: 33:[8, 46] Operation: 70-24=46 Exploring Operation: 24/8=3, Resulting Numbers: [70, 3] Generated Node #0,0,1: 33:[70, 3] Operation: 24/8=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[8, 46], Operations: ['99-75=24', '70-24=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,33 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,33 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 #0,0,1 Current State: 33:[70, 3], Operations: ['99-75=24', '24/8=3'] Exploring Operation: 70+3=73, Resulting Numbers: [73] 73,33 unequal: No Solution Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,33 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:[75, 8, 29], Operations: ['99-70=29'] Exploring Operation: 75-29=46, Resulting Numbers: [8, 46] Generated Node #0,1,0: 33:[8, 46] Operation: 75-29=46 Exploring Operation: 75-8=67, Resulting Numbers: [29, 67] Generated Node #0,1,1: 33:[29, 67] Operation: 75-8=67 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[8, 46], Operations: ['99-70=29', '75-29=46'] Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,33 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 #0,1,1 Current State: 33:[29, 67], Operations: ['99-70=29', '75-8=67'] Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,33 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 No solution found.
0
hs_2
sum_heuristic
[ 2, 77, 71, 69 ]
67
[ "77-69=8", "8/2=4", "71-4=67" ]
Current State: 67:[2, 77, 71, 69], Operations: [] Exploring Operation: 77-69=8, Resulting Numbers: [2, 71, 8] Generated Node #2: [2, 71, 8] from Operation: 77-69=8 Current State: 67:[2, 71, 8], Operations: ['77-69=8'] Exploring Operation: 8/2=4, Resulting Numbers: [71, 4] Generated Node #3: [71, 4] from Operation: 8/2=4 Current State: 67:[71, 4], Operations: ['77-69=8', '8/2=4'] Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[2, 77, 71, 69], Operations: [] Exploring Operation: 71-2=69, Resulting Numbers: [77, 69, 69] Generated Node #0,0: 67:[77, 69, 69] Operation: 71-2=69 Exploring Operation: 69-2=67, Resulting Numbers: [77, 71, 67] Generated Node #0,1: 67:[77, 71, 67] Operation: 69-2=67 Exploring Operation: 77-2=75, Resulting Numbers: [71, 69, 75] Generated Node #0,2: 67:[71, 69, 75] Operation: 77-2=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[77, 69, 69], Operations: ['71-2=69'] Exploring Operation: 77-69=8, Resulting Numbers: [69, 8] Generated Node #0,0,0: 67:[69, 8] Operation: 77-69=8 Exploring Operation: 77-69=8, Resulting Numbers: [69, 8] Generated Node #0,0,1: 67:[69, 8] Operation: 77-69=8 Exploring Operation: 69/69=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 67:[77, 1] Operation: 69/69=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[69, 8], Operations: ['71-2=69', '77-69=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,67 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 67:[69, 8], Operations: ['71-2=69', '77-69=8'] Exploring Operation: 69+8=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 69*8=552, Resulting Numbers: [552] 552,67 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 67:[77, 1], Operations: ['71-2=69', '69/69=1'] Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[77, 71, 67], Operations: ['69-2=67'] Exploring Operation: 77-67=10, Resulting Numbers: [71, 10] Generated Node #0,1,0: 67:[71, 10] Operation: 77-67=10 Exploring Operation: 77-71=6, Resulting Numbers: [67, 6] Generated Node #0,1,1: 67:[67, 6] Operation: 77-71=6 Exploring Operation: 71-67=4, Resulting Numbers: [77, 4] Generated Node #0,1,2: 67:[77, 4] Operation: 71-67=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 67:[71, 10], Operations: ['69-2=67', '77-67=10'] Exploring Operation: 71+10=81, Resulting Numbers: [81] 81,67 unequal: No Solution Exploring Operation: 71*10=710, Resulting Numbers: [710] 710,67 unequal: No Solution Exploring Operation: 71-10=61, Resulting Numbers: [61] 61,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 67:[67, 6], Operations: ['69-2=67', '77-71=6'] Exploring Operation: 67+6=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,67 unequal: No Solution Exploring Operation: 67*6=402, Resulting Numbers: [402] 402,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 67:[77, 4], Operations: ['69-2=67', '71-67=4'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,67 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 67:[71, 69, 75], Operations: ['77-2=75'] Exploring Operation: 75-69=6, Resulting Numbers: [71, 6] Generated Node #0,2,0: 67:[71, 6] Operation: 75-69=6 Exploring Operation: 75-71=4, Resulting Numbers: [69, 4] Generated Node #0,2,1: 67:[69, 4] Operation: 75-71=4 Exploring Operation: 71-69=2, Resulting Numbers: [75, 2] Generated Node #0,2,2: 67:[75, 2] Operation: 71-69=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 67:[71, 6], Operations: ['77-2=75', '75-69=6'] Exploring Operation: 71+6=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,67 unequal: No Solution Exploring Operation: 71*6=426, Resulting Numbers: [426] 426,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 67:[69, 4], Operations: ['77-2=75', '75-71=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,67 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,67 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 67:[75, 2], Operations: ['77-2=75', '71-69=2'] Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,67 unequal: No Solution Exploring Operation: 75*2=150, Resulting Numbers: [150] 150,67 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,67 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 36, 28, 14, 8 ]
56
[ "36-8=28", "28/14=2", "28*2=56" ]
Current State: 56:[36, 28, 14, 8], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [28, 14, 28] Generated Node #2: [28, 14, 28] from Operation: 36-8=28 Current State: 56:[28, 14, 28], Operations: ['36-8=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,56 equal: Goal Reached Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[36, 28, 14, 8], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [28, 14, 28] Generated Node #0,0: 56:[28, 14, 28] Operation: 36-8=28 Exploring Operation: 36-28=8, Resulting Numbers: [14, 8, 8] Generated Node #0,1: 56:[14, 8, 8] Operation: 36-28=8 Exploring Operation: 36+14=50, Resulting Numbers: [28, 8, 50] Generated Node #0,2: 56:[28, 8, 50] Operation: 36+14=50 Exploring Operation: 36-14=22, Resulting Numbers: [28, 8, 22] Generated Node #0,3: 56:[28, 8, 22] Operation: 36-14=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[28, 14, 28], Operations: ['36-8=28'] Exploring Operation: 28+28=56, Resulting Numbers: [14, 56] Generated Node #0,0,0: 56:[14, 56] Operation: 28+28=56 Exploring Operation: 28/14=2, Resulting Numbers: [28, 2] Generated Node #0,0,1: 56:[28, 2] Operation: 28/14=2 Exploring Operation: 28-14=14, Resulting Numbers: [28, 14] Generated Node #0,0,2: 56:[28, 14] Operation: 28-14=14 Exploring Operation: 28-14=14, Resulting Numbers: [28, 14] Generated Node #0,0,3: 56:[28, 14] Operation: 28-14=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[14, 56], Operations: ['36-8=28', '28+28=56'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 14+56=70, Resulting Numbers: [70] 70,56 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,56 unequal: No Solution Exploring Operation: 14*56=784, Resulting Numbers: [784] 784,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[28, 2], Operations: ['36-8=28', '28/14=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,56 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,56 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,56 unequal: No Solution Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[36, 28, 14, 8], Operations: [] Exploring Operation: 36-8=28, Resulting Numbers: [28, 14, 28] Generated Node #0,0: 56:[28, 14, 28] Operation: 36-8=28 Moving to Node #0,0 Current State: 56:[28, 14, 28], Operations: ['36-8=28'] Exploring Operation: 28/14=2, Resulting Numbers: [28, 2] Generated Node #0,0,1: 56:[28, 2] Operation: 28/14=2 Moving to Node #0,0,1 Current State: 56:[28, 2], Operations: ['36-8=28', '28/14=2'] Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 42, 6, 41, 18 ]
45
[ "42-18=24", "24/6=4", "41+4=45" ]
Current State: 45:[42, 6, 41, 18], Operations: [] Exploring Operation: 42-18=24, Resulting Numbers: [6, 41, 24] Generated Node #2: [6, 41, 24] from Operation: 42-18=24 Current State: 45:[6, 41, 24], Operations: ['42-18=24'] Exploring Operation: 24/6=4, Resulting Numbers: [41, 4] Generated Node #3: [41, 4] from Operation: 24/6=4 Current State: 45:[41, 4], Operations: ['42-18=24', '24/6=4'] Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[42, 6, 41, 18], Operations: [] Exploring Operation: 42-41=1, Resulting Numbers: [6, 18, 1] Generated Node #0,0: 45:[6, 18, 1] Operation: 42-41=1 Exploring Operation: 6+41=47, Resulting Numbers: [42, 18, 47] Generated Node #0,1: 45:[42, 18, 47] Operation: 6+41=47 Exploring Operation: 18/6=3, Resulting Numbers: [42, 41, 3] Generated Node #0,2: 45:[42, 41, 3] Operation: 18/6=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[6, 18, 1], Operations: ['42-41=1'] Exploring Operation: 6-1=5, Resulting Numbers: [18, 5] Generated Node #0,0,0: 45:[18, 5] Operation: 6-1=5 Exploring Operation: 18-1=17, Resulting Numbers: [6, 17] Generated Node #0,0,1: 45:[6, 17] Operation: 18-1=17 Exploring Operation: 18/6=3, Resulting Numbers: [1, 3] Generated Node #0,0,2: 45:[1, 3] Operation: 18/6=3 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[1, 3], Operations: ['42-41=1', '18/6=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,45 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 #0,0,0 Current State: 45:[18, 5], Operations: ['42-41=1', '6-1=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,45 unequal: No Solution Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,45 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 #0,0,1 Current State: 45:[6, 17], Operations: ['42-41=1', '18-1=17'] Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,45 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,45 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 #0,2 Current State: 45:[42, 41, 3], Operations: ['18/6=3'] Exploring Operation: 42+3=45, Resulting Numbers: [41, 45] Generated Node #0,2,0: 45:[41, 45] Operation: 42+3=45 Exploring Operation: 42-41=1, Resulting Numbers: [3, 1] Generated Node #0,2,1: 45:[3, 1] Operation: 42-41=1 Exploring Operation: 41+3=44, Resulting Numbers: [42, 44] Generated Node #0,2,2: 45:[42, 44] Operation: 41+3=44 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 45:[3, 1], Operations: ['18/6=3', '42-41=1'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,45 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 #0,2,0 Current State: 45:[41, 45], Operations: ['18/6=3', '42+3=45'] Exploring Operation: 45-41=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 41*45=1845, Resulting Numbers: [1845] 1845,45 unequal: No Solution Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,45 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 #0,2,2 Current State: 45:[42, 44], Operations: ['18/6=3', '41+3=44'] Exploring Operation: 42+44=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 42*44=1848, Resulting Numbers: [1848] 1848,45 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 #0,1 Current State: 45:[42, 18, 47], Operations: ['6+41=47'] Exploring Operation: 42+18=60, Resulting Numbers: [47, 60] Generated Node #0,1,0: 45:[47, 60] Operation: 42+18=60 Exploring Operation: 42-18=24, Resulting Numbers: [47, 24] Generated Node #0,1,1: 45:[47, 24] Operation: 42-18=24 Exploring Operation: 47-42=5, Resulting Numbers: [18, 5] Generated Node #0,1,2: 45:[18, 5] Operation: 47-42=5 Moving to Node #0,1,2 Current State: 45:[18, 5], Operations: ['6+41=47', '47-42=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,45 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 18*5=90, Resulting Numbers: [90] 90,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[47, 24], Operations: ['6+41=47', '42-18=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,45 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[47, 60], Operations: ['6+41=47', '42+18=60'] Exploring Operation: 47*60=2820, Resulting Numbers: [2820] 2820,45 unequal: No Solution Exploring Operation: 47+60=107, Resulting Numbers: [107] 107,45 unequal: No Solution Exploring Operation: 60-47=13, Resulting Numbers: [13] 13,45 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
[ 60, 67, 33, 30 ]
56
[ "67-60=7", "33+30=63", "63-7=56" ]
Current State: 56:[60, 67, 33, 30], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [33, 30, 7] Generated Node #2: [33, 30, 7] from Operation: 67-60=7 Current State: 56:[33, 30, 7], Operations: ['67-60=7'] Exploring Operation: 33+30=63, Resulting Numbers: [7, 63] Generated Node #3: [7, 63] from Operation: 33+30=63 Current State: 56:[7, 63], Operations: ['67-60=7', '33+30=63'] Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[60, 67, 33, 30], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [33, 30, 7] Generated Node #0,0: 56:[33, 30, 7] Operation: 67-60=7 Moving to Node #0,0 Current State: 56:[33, 30, 7], Operations: ['67-60=7'] Exploring Operation: 33-30=3, Resulting Numbers: [7, 3] Generated Node #0,0,0: 56:[7, 3] Operation: 33-30=3 Moving to Node #0,0,0 Current State: 56:[7, 3], Operations: ['67-60=7', '33-30=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,56 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 74, 69, 17, 88 ]
21
[ "74-69=5", "17+88=105", "105/5=21" ]
Current State: 21:[74, 69, 17, 88], Operations: [] Exploring Operation: 74-69=5, Resulting Numbers: [17, 88, 5] Generated Node #2: [17, 88, 5] from Operation: 74-69=5 Current State: 21:[17, 88, 5], Operations: ['74-69=5'] Exploring Operation: 17+88=105, Resulting Numbers: [5, 105] Generated Node #3: [5, 105] from Operation: 17+88=105 Current State: 21:[5, 105], Operations: ['74-69=5', '17+88=105'] Exploring Operation: 105/5=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[74, 69, 17, 88], Operations: [] Exploring Operation: 88-74=14, Resulting Numbers: [69, 17, 14] Generated Node #0,0: 21:[69, 17, 14] Operation: 88-74=14 Moving to Node #0,0 Current State: 21:[69, 17, 14], Operations: ['88-74=14'] Exploring Operation: 69-17=52, Resulting Numbers: [14, 52] Generated Node #0,0,0: 21:[14, 52] Operation: 69-17=52 Moving to Node #0,0,0 Current State: 21:[14, 52], Operations: ['88-74=14', '69-17=52'] Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,21 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 16, 38, 94, 81 ]
41
[ "16+38=54", "94-81=13", "54-13=41" ]
Current State: 41:[16, 38, 94, 81], Operations: [] Exploring Operation: 16+38=54, Resulting Numbers: [94, 81, 54] Generated Node #2: [94, 81, 54] from Operation: 16+38=54 Current State: 41:[94, 81, 54], Operations: ['16+38=54'] Exploring Operation: 94-81=13, Resulting Numbers: [54, 13] Generated Node #3: [54, 13] from Operation: 94-81=13 Current State: 41:[54, 13], Operations: ['16+38=54', '94-81=13'] Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[16, 38, 94, 81], Operations: [] Exploring Operation: 81-38=43, Resulting Numbers: [16, 94, 43] Generated Node #0,0: 41:[16, 94, 43] Operation: 81-38=43 Exploring Operation: 94-81=13, Resulting Numbers: [16, 38, 13] Generated Node #0,1: 41:[16, 38, 13] Operation: 94-81=13 Exploring Operation: 94-16=78, Resulting Numbers: [38, 81, 78] Generated Node #0,2: 41:[38, 81, 78] Operation: 94-16=78 Exploring Operation: 94-38=56, Resulting Numbers: [16, 81, 56] Generated Node #0,3: 41:[16, 81, 56] Operation: 94-38=56 Exploring Operation: 81-16=65, Resulting Numbers: [38, 94, 65] Generated Node #0,4: 41:[38, 94, 65] Operation: 81-16=65 Moving to Node #0,1 Current State: 41:[16, 38, 13], Operations: ['94-81=13'] Exploring Operation: 38+13=51, Resulting Numbers: [16, 51] Generated Node #0,1,0: 41:[16, 51] Operation: 38+13=51 Exploring Operation: 16-13=3, Resulting Numbers: [38, 3] Generated Node #0,1,1: 41:[38, 3] Operation: 16-13=3 Exploring Operation: 16+38=54, Resulting Numbers: [13, 54] Generated Node #0,1,2: 41:[13, 54] Operation: 16+38=54 Exploring Operation: 16+13=29, Resulting Numbers: [38, 29] Generated Node #0,1,3: 41:[38, 29] Operation: 16+13=29 Exploring Operation: 38-13=25, Resulting Numbers: [16, 25] Generated Node #0,1,4: 41:[16, 25] Operation: 38-13=25 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[38, 29], Operations: ['94-81=13', '16+13=29'] Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 38*29=1102, Resulting Numbers: [1102] 1102,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[16, 51], Operations: ['94-81=13', '38+13=51'] Exploring Operation: 16*51=816, Resulting Numbers: [816] 816,41 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 16+51=67, Resulting Numbers: [67] 67,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[38, 3], Operations: ['94-81=13', '16-13=3'] Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,41 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[16, 38, 94, 81], Operations: [] Exploring Operation: 94-81=13, Resulting Numbers: [16, 38, 13] Generated Node #0,1: 41:[16, 38, 13] Operation: 94-81=13 Moving to Node #0,1 Current State: 41:[16, 38, 13], Operations: ['94-81=13'] Exploring Operation: 16-13=3, Resulting Numbers: [38, 3] Generated Node #0,1,1: 41:[38, 3] Operation: 16-13=3 Moving to Node #0,1,1 Current State: 41:[38, 3], Operations: ['94-81=13', '16-13=3'] Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 62, 56, 45, 93 ]
23
[ "62-56=6", "45+93=138", "138/6=23" ]
Current State: 23:[62, 56, 45, 93], Operations: [] Exploring Operation: 62-56=6, Resulting Numbers: [45, 93, 6] Generated Node #2: [45, 93, 6] from Operation: 62-56=6 Current State: 23:[45, 93, 6], Operations: ['62-56=6'] Exploring Operation: 45+93=138, Resulting Numbers: [6, 138] Generated Node #3: [6, 138] from Operation: 45+93=138 Current State: 23:[6, 138], Operations: ['62-56=6', '45+93=138'] Exploring Operation: 138/6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[62, 56, 45, 93], Operations: [] Exploring Operation: 93-62=31, Resulting Numbers: [56, 45, 31] Generated Node #0,0: 23:[56, 45, 31] Operation: 93-62=31 Exploring Operation: 93-56=37, Resulting Numbers: [62, 45, 37] Generated Node #0,1: 23:[62, 45, 37] Operation: 93-56=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[56, 45, 31], Operations: ['93-62=31'] Exploring Operation: 56-45=11, Resulting Numbers: [31, 11] Generated Node #0,0,0: 23:[31, 11] Operation: 56-45=11 Exploring Operation: 56-31=25, Resulting Numbers: [45, 25] Generated Node #0,0,1: 23:[45, 25] Operation: 56-31=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[31, 11], Operations: ['93-62=31', '56-45=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,23 unequal: No Solution No 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: 23:[45, 25], Operations: ['93-62=31', '56-31=25'] Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,23 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: 23:[62, 45, 37], Operations: ['93-56=37'] Exploring Operation: 62-37=25, Resulting Numbers: [45, 25] Generated Node #0,1,0: 23:[45, 25] Operation: 62-37=25 Exploring Operation: 62-45=17, Resulting Numbers: [37, 17] Generated Node #0,1,1: 23:[37, 17] Operation: 62-45=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[37, 17], Operations: ['93-56=37', '62-45=17'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 37+17=54, Resulting Numbers: [54] 54,23 unequal: No Solution No 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: 23:[45, 25], Operations: ['93-56=37', '62-37=25'] Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,23 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
[ 62, 48, 33, 77 ]
58
[ "62-48=14", "77-33=44", "14+44=58" ]
Current State: 58:[62, 48, 33, 77], Operations: [] Exploring Operation: 62-48=14, Resulting Numbers: [33, 77, 14] Generated Node #2: [33, 77, 14] from Operation: 62-48=14 Current State: 58:[33, 77, 14], Operations: ['62-48=14'] Exploring Operation: 77-33=44, Resulting Numbers: [14, 44] Generated Node #3: [14, 44] from Operation: 77-33=44 Current State: 58:[14, 44], Operations: ['62-48=14', '77-33=44'] Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[62, 48, 33, 77], Operations: [] Exploring Operation: 77-62=15, Resulting Numbers: [48, 33, 15] Generated Node #0,0: 58:[48, 33, 15] Operation: 77-62=15 Exploring Operation: 77-48=29, Resulting Numbers: [62, 33, 29] Generated Node #0,1: 58:[62, 33, 29] Operation: 77-48=29 Exploring Operation: 62-33=29, Resulting Numbers: [48, 77, 29] Generated Node #0,2: 58:[48, 77, 29] Operation: 62-33=29 Exploring Operation: 77-33=44, Resulting Numbers: [62, 48, 44] Generated Node #0,3: 58:[62, 48, 44] Operation: 77-33=44 Moving to Node #0,1 Current State: 58:[62, 33, 29], Operations: ['77-48=29'] Exploring Operation: 33-29=4, Resulting Numbers: [62, 4] Generated Node #0,1,0: 58:[62, 4] Operation: 33-29=4 Exploring Operation: 62-33=29, Resulting Numbers: [29, 29] Generated Node #0,1,1: 58:[29, 29] Operation: 62-33=29 Exploring Operation: 62-29=33, Resulting Numbers: [33, 33] Generated Node #0,1,2: 58:[33, 33] Operation: 62-29=33 Exploring Operation: 33+29=62, Resulting Numbers: [62, 62] Generated Node #0,1,3: 58:[62, 62] Operation: 33+29=62 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[29, 29], Operations: ['77-48=29', '62-33=29'] Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[62, 48, 33, 77], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [62, 33, 29] Generated Node #0,1: 58:[62, 33, 29] Operation: 77-48=29 Moving to Node #0,1 Current State: 58:[62, 33, 29], Operations: ['77-48=29'] Exploring Operation: 62-33=29, Resulting Numbers: [29, 29] Generated Node #0,1,1: 58:[29, 29] Operation: 62-33=29 Moving to Node #0,1,1 Current State: 58:[29, 29], Operations: ['77-48=29', '62-33=29'] Exploring Operation: 29+29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 40, 33, 15, 28 ]
23
[ "33-28=5", "40/5=8", "15+8=23" ]
Current State: 23:[40, 33, 15, 28], Operations: [] Exploring Operation: 33-28=5, Resulting Numbers: [40, 15, 5] Generated Node #2: [40, 15, 5] from Operation: 33-28=5 Current State: 23:[40, 15, 5], Operations: ['33-28=5'] Exploring Operation: 40/5=8, Resulting Numbers: [15, 8] Generated Node #3: [15, 8] from Operation: 40/5=8 Current State: 23:[15, 8], Operations: ['33-28=5', '40/5=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[40, 33, 15, 28], Operations: [] Exploring Operation: 33-15=18, Resulting Numbers: [40, 28, 18] Generated Node #0,0: 23:[40, 28, 18] Operation: 33-15=18 Exploring Operation: 40-28=12, Resulting Numbers: [33, 15, 12] Generated Node #0,1: 23:[33, 15, 12] Operation: 40-28=12 Exploring Operation: 40-15=25, Resulting Numbers: [33, 28, 25] Generated Node #0,2: 23:[33, 28, 25] Operation: 40-15=25 Exploring Operation: 40-33=7, Resulting Numbers: [15, 28, 7] Generated Node #0,3: 23:[15, 28, 7] Operation: 40-33=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[33, 28, 25], Operations: ['40-15=25'] Exploring Operation: 33+28=61, Resulting Numbers: [25, 61] Generated Node #0,2,0: 23:[25, 61] Operation: 33+28=61 Exploring Operation: 33-28=5, Resulting Numbers: [25, 5] Generated Node #0,2,1: 23:[25, 5] Operation: 33-28=5 Exploring Operation: 28-25=3, Resulting Numbers: [33, 3] Generated Node #0,2,2: 23:[33, 3] Operation: 28-25=3 Exploring Operation: 33-25=8, Resulting Numbers: [28, 8] Generated Node #0,2,3: 23:[28, 8] Operation: 33-25=8 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 23:[25, 5], Operations: ['40-15=25', '33-28=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,23 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,23 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,23 unequal: No Solution No 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: 23:[28, 8], Operations: ['40-15=25', '33-25=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,23 unequal: No Solution No 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: 23:[33, 3], Operations: ['40-15=25', '28-25=3'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,23 unequal: No Solution No 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: 23:[25, 61], Operations: ['40-15=25', '33+28=61'] Exploring Operation: 25*61=1525, Resulting Numbers: [1525] 1525,23 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 25+61=86, Resulting Numbers: [86] 86,23 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: 23:[40, 28, 18], Operations: ['33-15=18'] Exploring Operation: 28-18=10, Resulting Numbers: [40, 10] Generated Node #0,0,0: 23:[40, 10] Operation: 28-18=10 Exploring Operation: 40-28=12, Resulting Numbers: [18, 12] Generated Node #0,0,1: 23:[18, 12] Operation: 40-28=12 Exploring Operation: 40-18=22, Resulting Numbers: [28, 22] Generated Node #0,0,2: 23:[28, 22] Operation: 40-18=22 Exploring Operation: 40+18=58, Resulting Numbers: [28, 58] Generated Node #0,0,3: 23:[28, 58] Operation: 40+18=58 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[28, 22], Operations: ['33-15=18', '40-18=22'] Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,23 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,23 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,23 unequal: No Solution No 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: 23:[18, 12], Operations: ['33-15=18', '40-28=12'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,23 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,23 unequal: No Solution No 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: 23:[40, 10], Operations: ['33-15=18', '28-18=10'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,23 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,23 unequal: No Solution No 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: 23:[28, 58], Operations: ['33-15=18', '40+18=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,23 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,23 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: 23:[33, 15, 12], Operations: ['40-28=12'] Exploring Operation: 33-12=21, Resulting Numbers: [15, 21] Generated Node #0,1,0: 23:[15, 21] Operation: 33-12=21 Exploring Operation: 33+12=45, Resulting Numbers: [15, 45] Generated Node #0,1,1: 23:[15, 45] Operation: 33+12=45 Exploring Operation: 33-15=18, Resulting Numbers: [12, 18] Generated Node #0,1,2: 23:[12, 18] Operation: 33-15=18 Exploring Operation: 15+12=27, Resulting Numbers: [33, 27] Generated Node #0,1,3: 23:[33, 27] Operation: 15+12=27 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[15, 21], Operations: ['40-28=12', '33-12=21'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,23 unequal: No Solution Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,23 unequal: No Solution No 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: 23:[33, 27], Operations: ['40-28=12', '15+12=27'] Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,23 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,23 unequal: No Solution No 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: 23:[12, 18], Operations: ['40-28=12', '33-15=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,23 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,23 unequal: No Solution No 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: 23:[15, 45], Operations: ['40-28=12', '33+12=45'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 15*45=675, Resulting Numbers: [675] 675,23 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,23 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: 23:[15, 28, 7], Operations: ['40-33=7'] Exploring Operation: 15-7=8, Resulting Numbers: [28, 8] Generated Node #0,3,0: 23:[28, 8] Operation: 15-7=8 Exploring Operation: 28+7=35, Resulting Numbers: [15, 35] Generated Node #0,3,1: 23:[15, 35] Operation: 28+7=35 Exploring Operation: 28-7=21, Resulting Numbers: [15, 21] Generated Node #0,3,2: 23:[15, 21] Operation: 28-7=21 Exploring Operation: 15+7=22, Resulting Numbers: [28, 22] Generated Node #0,3,3: 23:[28, 22] Operation: 15+7=22 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 23:[28, 22], Operations: ['40-33=7', '15+7=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,23 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,23 unequal: No Solution No 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: 23:[15, 21], Operations: ['40-33=7', '28-7=21'] Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,23 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,23 unequal: No Solution No 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: 23:[28, 8], Operations: ['40-33=7', '15-7=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,23 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,23 unequal: No Solution No 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: 23:[15, 35], Operations: ['40-33=7', '28+7=35'] Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,23 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,23 unequal: No Solution Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,23 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
[ 85, 62, 30, 83 ]
94
[ "85+62=147", "83-30=53", "147-53=94" ]
Current State: 94:[85, 62, 30, 83], Operations: [] Exploring Operation: 85+62=147, Resulting Numbers: [30, 83, 147] Generated Node #2: [30, 83, 147] from Operation: 85+62=147 Current State: 94:[30, 83, 147], Operations: ['85+62=147'] Exploring Operation: 83-30=53, Resulting Numbers: [147, 53] Generated Node #3: [147, 53] from Operation: 83-30=53 Current State: 94:[147, 53], Operations: ['85+62=147', '83-30=53'] Exploring Operation: 147-53=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[85, 62, 30, 83], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [85, 83, 92] Generated Node #0,0: 94:[85, 83, 92] Operation: 62+30=92 Exploring Operation: 85-30=55, Resulting Numbers: [62, 83, 55] Generated Node #0,1: 94:[62, 83, 55] Operation: 85-30=55 Exploring Operation: 83-30=53, Resulting Numbers: [85, 62, 53] Generated Node #0,2: 94:[85, 62, 53] Operation: 83-30=53 Exploring Operation: 85-83=2, Resulting Numbers: [62, 30, 2] Generated Node #0,3: 94:[62, 30, 2] Operation: 85-83=2 Exploring Operation: 62-30=32, Resulting Numbers: [85, 83, 32] Generated Node #0,4: 94:[85, 83, 32] Operation: 62-30=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[85, 83, 92], Operations: ['62+30=92'] Exploring Operation: 85+83=168, Resulting Numbers: [92, 168] Generated Node #0,0,0: 94:[92, 168] Operation: 85+83=168 Exploring Operation: 85-83=2, Resulting Numbers: [92, 2] Generated Node #0,0,1: 94:[92, 2] Operation: 85-83=2 Exploring Operation: 92-85=7, Resulting Numbers: [83, 7] Generated Node #0,0,2: 94:[83, 7] Operation: 92-85=7 Exploring Operation: 92-83=9, Resulting Numbers: [85, 9] Generated Node #0,0,3: 94:[85, 9] Operation: 92-83=9 Exploring Operation: 83+92=175, Resulting Numbers: [85, 175] Generated Node #0,0,4: 94:[85, 175] Operation: 83+92=175 Moving to Node #0,0,1 Current State: 94:[92, 2], Operations: ['62+30=92', '85-83=2'] Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,94 unequal: No Solution Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[85, 62, 30, 83], Operations: [] Exploring Operation: 62+30=92, Resulting Numbers: [85, 83, 92] Generated Node #0,0: 94:[85, 83, 92] Operation: 62+30=92 Moving to Node #0,0 Current State: 94:[85, 83, 92], Operations: ['62+30=92'] Exploring Operation: 85-83=2, Resulting Numbers: [92, 2] Generated Node #0,0,1: 94:[92, 2] Operation: 85-83=2 Moving to Node #0,0,1 Current State: 94:[92, 2], Operations: ['62+30=92', '85-83=2'] Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 49, 34, 68, 32 ]
87
[ "34-32=2", "68*2=136", "136-49=87" ]
Current State: 87:[49, 34, 68, 32], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [49, 68, 2] Generated Node #2: [49, 68, 2] from Operation: 34-32=2 Current State: 87:[49, 68, 2], Operations: ['34-32=2'] Exploring Operation: 68*2=136, Resulting Numbers: [49, 136] Generated Node #3: [49, 136] from Operation: 68*2=136 Current State: 87:[49, 136], Operations: ['34-32=2', '68*2=136'] Exploring Operation: 136-49=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[49, 34, 68, 32], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [49, 32, 2] Generated Node #0,0: 87:[49, 32, 2] Operation: 68/34=2 Exploring Operation: 68-49=19, Resulting Numbers: [34, 32, 19] Generated Node #0,1: 87:[34, 32, 19] Operation: 68-49=19 Moving to Node #0,1 Current State: 87:[34, 32, 19], Operations: ['68-49=19'] Exploring Operation: 34-19=15, Resulting Numbers: [32, 15] Generated Node #0,1,0: 87:[32, 15] Operation: 34-19=15 Exploring Operation: 34-32=2, Resulting Numbers: [19, 2] Generated Node #0,1,1: 87:[19, 2] Operation: 34-32=2 Moving to Node #0,0 Current State: 87:[49, 32, 2], Operations: ['68/34=2'] Exploring Operation: 49+32=81, Resulting Numbers: [2, 81] Generated Node #0,0,0: 87:[2, 81] Operation: 49+32=81 Exploring Operation: 49-32=17, Resulting Numbers: [2, 17] Generated Node #0,0,1: 87:[2, 17] Operation: 49-32=17 Moving to Node #0,0,0 Current State: 87:[2, 81], Operations: ['68/34=2', '49+32=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,87 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[19, 2], Operations: ['68-49=19', '34-32=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[2, 17], Operations: ['68/34=2', '49-32=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,87 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[32, 15], Operations: ['68-49=19', '34-19=15'] Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,87 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,87 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 72, 18, 28, 46 ]
70
[ "72/18=4", "28+46=74", "74-4=70" ]
Current State: 70:[72, 18, 28, 46], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [28, 46, 4] Generated Node #2: [28, 46, 4] from Operation: 72/18=4 Current State: 70:[28, 46, 4], Operations: ['72/18=4'] Exploring Operation: 28+46=74, Resulting Numbers: [4, 74] Generated Node #3: [4, 74] from Operation: 28+46=74 Current State: 70:[4, 74], Operations: ['72/18=4', '28+46=74'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[72, 18, 28, 46], Operations: [] Exploring Operation: 46-28=18, Resulting Numbers: [72, 18, 18] Generated Node #0,0: 70:[72, 18, 18] Operation: 46-28=18 Exploring Operation: 28+46=74, Resulting Numbers: [72, 18, 74] Generated Node #0,1: 70:[72, 18, 74] Operation: 28+46=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[72, 18, 18], Operations: ['46-28=18'] Exploring Operation: 18+18=36, Resulting Numbers: [72, 36] Generated Node #0,0,0: 70:[72, 36] Operation: 18+18=36 Exploring Operation: 18/18=1, Resulting Numbers: [72, 1] Generated Node #0,0,1: 70:[72, 1] Operation: 18/18=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[72, 36], Operations: ['46-28=18', '18+18=36'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,70 unequal: No Solution No 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: 70:[72, 1], Operations: ['46-28=18', '18/18=1'] Exploring Operation: 72*1=72, Resulting Numbers: [72] 72,70 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,70 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: 70:[72, 18, 74], Operations: ['28+46=74'] Exploring Operation: 72/18=4, Resulting Numbers: [74, 4] Generated Node #0,1,0: 70:[74, 4] Operation: 72/18=4 Exploring Operation: 74-72=2, Resulting Numbers: [18, 2] Generated Node #0,1,1: 70:[18, 2] Operation: 74-72=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[18, 2], Operations: ['28+46=74', '74-72=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,70 unequal: No Solution No 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: 70:[74, 4], Operations: ['28+46=74', '72/18=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,70 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[72, 18, 28, 46], Operations: [] Exploring Operation: 28+46=74, Resulting Numbers: [72, 18, 74] Generated Node #0,1: 70:[72, 18, 74] Operation: 28+46=74 Moving to Node #0,1 Current State: 70:[72, 18, 74], Operations: ['28+46=74'] Exploring Operation: 72/18=4, Resulting Numbers: [74, 4] Generated Node #0,1,0: 70:[74, 4] Operation: 72/18=4 Moving to Node #0,1,0 Current State: 70:[74, 4], Operations: ['28+46=74', '72/18=4'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 38, 88, 17, 68 ]
16
[ "88*17=1496", "1496/68=22", "38-22=16" ]
Current State: 16:[38, 88, 17, 68], Operations: [] Exploring Operation: 88*17=1496, Resulting Numbers: [38, 68, 1496] Generated Node #2: [38, 68, 1496] from Operation: 88*17=1496 Current State: 16:[38, 68, 1496], Operations: ['88*17=1496'] Exploring Operation: 1496/68=22, Resulting Numbers: [38, 22] Generated Node #3: [38, 22] from Operation: 1496/68=22 Current State: 16:[38, 22], Operations: ['88*17=1496', '1496/68=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[38, 88, 17, 68], Operations: [] Exploring Operation: 38-17=21, Resulting Numbers: [88, 68, 21] Generated Node #0,0: 16:[88, 68, 21] Operation: 38-17=21 Exploring Operation: 88-68=20, Resulting Numbers: [38, 17, 20] Generated Node #0,1: 16:[38, 17, 20] Operation: 88-68=20 Exploring Operation: 88-38=50, Resulting Numbers: [17, 68, 50] Generated Node #0,2: 16:[17, 68, 50] Operation: 88-38=50 Exploring Operation: 68-38=30, Resulting Numbers: [88, 17, 30] Generated Node #0,3: 16:[88, 17, 30] Operation: 68-38=30 Exploring Operation: 68/17=4, Resulting Numbers: [38, 88, 4] Generated Node #0,4: 16:[38, 88, 4] Operation: 68/17=4 Moving to Node #0,1 Current State: 16:[38, 17, 20], Operations: ['88-68=20'] Exploring Operation: 38-20=18, Resulting Numbers: [17, 18] Generated Node #0,1,0: 16:[17, 18] Operation: 38-20=18 Exploring Operation: 20-17=3, Resulting Numbers: [38, 3] Generated Node #0,1,1: 16:[38, 3] Operation: 20-17=3 Exploring Operation: 38+20=58, Resulting Numbers: [17, 58] Generated Node #0,1,2: 16:[17, 58] Operation: 38+20=58 Exploring Operation: 38+17=55, Resulting Numbers: [20, 55] Generated Node #0,1,3: 16:[20, 55] Operation: 38+17=55 Exploring Operation: 38-17=21, Resulting Numbers: [20, 21] Generated Node #0,1,4: 16:[20, 21] Operation: 38-17=21 Moving to Node #0,3 Current State: 16:[88, 17, 30], Operations: ['68-38=30'] Exploring Operation: 88-30=58, Resulting Numbers: [17, 58] Generated Node #0,3,0: 16:[17, 58] Operation: 88-30=58 Exploring Operation: 30-17=13, Resulting Numbers: [88, 13] Generated Node #0,3,1: 16:[88, 13] Operation: 30-17=13 Exploring Operation: 88-17=71, Resulting Numbers: [30, 71] Generated Node #0,3,2: 16:[30, 71] Operation: 88-17=71 Exploring Operation: 88+30=118, Resulting Numbers: [17, 118] Generated Node #0,3,3: 16:[17, 118] Operation: 88+30=118 Exploring Operation: 88+17=105, Resulting Numbers: [30, 105] Generated Node #0,3,4: 16:[30, 105] Operation: 88+17=105 Moving to Node #0,2 Current State: 16:[17, 68, 50], Operations: ['88-38=50'] Exploring Operation: 50-17=33, Resulting Numbers: [68, 33] Generated Node #0,2,0: 16:[68, 33] Operation: 50-17=33 Exploring Operation: 68/17=4, Resulting Numbers: [50, 4] Generated Node #0,2,1: 16:[50, 4] Operation: 68/17=4 Exploring Operation: 68-17=51, Resulting Numbers: [50, 51] Generated Node #0,2,2: 16:[50, 51] Operation: 68-17=51 Exploring Operation: 17+68=85, Resulting Numbers: [50, 85] Generated Node #0,2,3: 16:[50, 85] Operation: 17+68=85 Exploring Operation: 68-50=18, Resulting Numbers: [17, 18] Generated Node #0,2,4: 16:[17, 18] Operation: 68-50=18 Moving to Node #0,4 Current State: 16:[38, 88, 4], Operations: ['68/17=4'] Exploring Operation: 38-4=34, Resulting Numbers: [88, 34] Generated Node #0,4,0: 16:[88, 34] Operation: 38-4=34 Exploring Operation: 88-38=50, Resulting Numbers: [4, 50] Generated Node #0,4,1: 16:[4, 50] Operation: 88-38=50 Exploring Operation: 38+4=42, Resulting Numbers: [88, 42] Generated Node #0,4,2: 16:[88, 42] Operation: 38+4=42 Exploring Operation: 88/4=22, Resulting Numbers: [38, 22] Generated Node #0,4,3: 16:[38, 22] Operation: 88/4=22 Exploring Operation: 88-4=84, Resulting Numbers: [38, 84] Generated Node #0,4,4: 16:[38, 84] Operation: 88-4=84 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 16:[38, 22], Operations: ['68/17=4', '88/4=22'] Exploring Operation: 38*22=836, Resulting Numbers: [836] 836,16 unequal: No Solution Exploring Operation: 38+22=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[38, 88, 17, 68], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [38, 88, 4] Generated Node #0,4: 16:[38, 88, 4] Operation: 68/17=4 Moving to Node #0,4 Current State: 16:[38, 88, 4], Operations: ['68/17=4'] Exploring Operation: 88/4=22, Resulting Numbers: [38, 22] Generated Node #0,4,3: 16:[38, 22] Operation: 88/4=22 Moving to Node #0,4,3 Current State: 16:[38, 22], Operations: ['68/17=4', '88/4=22'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_5
sum_heuristic
[ 29, 5, 65, 18 ]
71
[ "29-5=24", "65-18=47", "24+47=71" ]
Current State: 71:[29, 5, 65, 18], Operations: [] Exploring Operation: 29-5=24, Resulting Numbers: [65, 18, 24] Generated Node #2: [65, 18, 24] from Operation: 29-5=24 Current State: 71:[65, 18, 24], Operations: ['29-5=24'] Exploring Operation: 65-18=47, Resulting Numbers: [24, 47] Generated Node #3: [24, 47] from Operation: 65-18=47 Current State: 71:[24, 47], Operations: ['29-5=24', '65-18=47'] Exploring Operation: 24+47=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[29, 5, 65, 18], Operations: [] Exploring Operation: 5+18=23, Resulting Numbers: [29, 65, 23] Generated Node #0,0: 71:[29, 65, 23] Operation: 5+18=23 Exploring Operation: 5*18=90, Resulting Numbers: [29, 65, 90] Generated Node #0,1: 71:[29, 65, 90] Operation: 5*18=90 Exploring Operation: 29+18=47, Resulting Numbers: [5, 65, 47] Generated Node #0,2: 71:[5, 65, 47] Operation: 29+18=47 Exploring Operation: 5+65=70, Resulting Numbers: [29, 18, 70] Generated Node #0,3: 71:[29, 18, 70] Operation: 5+65=70 Exploring Operation: 29+5=34, Resulting Numbers: [65, 18, 34] Generated Node #0,4: 71:[65, 18, 34] Operation: 29+5=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[29, 65, 90], Operations: ['5*18=90'] Exploring Operation: 29+65=94, Resulting Numbers: [90, 94] Generated Node #0,1,0: 71:[90, 94] Operation: 29+65=94 Exploring Operation: 65-29=36, Resulting Numbers: [90, 36] Generated Node #0,1,1: 71:[90, 36] Operation: 65-29=36 Exploring Operation: 90-65=25, Resulting Numbers: [29, 25] Generated Node #0,1,2: 71:[29, 25] Operation: 90-65=25 Exploring Operation: 90-29=61, Resulting Numbers: [65, 61] Generated Node #0,1,3: 71:[65, 61] Operation: 90-29=61 Exploring Operation: 29+90=119, Resulting Numbers: [65, 119] Generated Node #0,1,4: 71:[65, 119] Operation: 29+90=119 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 71:[65, 61], Operations: ['5*18=90', '90-29=61'] Exploring Operation: 65+61=126, Resulting Numbers: [126] 126,71 unequal: No Solution Exploring Operation: 65*61=3965, Resulting Numbers: [3965] 3965,71 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,71 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:[90, 94], Operations: ['5*18=90', '29+65=94'] Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,71 unequal: No Solution Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,71 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:[90, 36], Operations: ['5*18=90', '65-29=36'] Exploring Operation: 90*36=3240, Resulting Numbers: [3240] 3240,71 unequal: No Solution Exploring Operation: 90+36=126, Resulting Numbers: [126] 126,71 unequal: No Solution Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,71 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, 119], Operations: ['5*18=90', '29+90=119'] Exploring Operation: 119-65=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 65*119=7735, Resulting Numbers: [7735] 7735,71 unequal: No Solution Exploring Operation: 65+119=184, Resulting Numbers: [184] 184,71 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:[29, 25], Operations: ['5*18=90', '90-65=25'] Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 29+25=54, Resulting Numbers: [54] 54,71 unequal: No Solution Exploring Operation: 29*25=725, Resulting Numbers: [725] 725,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[29, 65, 23], Operations: ['5+18=23'] Exploring Operation: 65+23=88, Resulting Numbers: [29, 88] Generated Node #0,0,0: 71:[29, 88] Operation: 65+23=88 Exploring Operation: 29+23=52, Resulting Numbers: [65, 52] Generated Node #0,0,1: 71:[65, 52] Operation: 29+23=52 Exploring Operation: 29-23=6, Resulting Numbers: [65, 6] Generated Node #0,0,2: 71:[65, 6] Operation: 29-23=6 Exploring Operation: 29+65=94, Resulting Numbers: [23, 94] Generated Node #0,0,3: 71:[23, 94] Operation: 29+65=94 Exploring Operation: 65-23=42, Resulting Numbers: [29, 42] Generated Node #0,0,4: 71:[29, 42] Operation: 65-23=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 71:[65, 52], Operations: ['5+18=23', '29+23=52'] Exploring Operation: 65-52=13, Resulting Numbers: [13] 13,71 unequal: No Solution Exploring Operation: 65*52=3380, Resulting Numbers: [3380] 3380,71 unequal: No Solution Exploring Operation: 65+52=117, Resulting Numbers: [117] 117,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[29, 88], Operations: ['5+18=23', '65+23=88'] Exploring Operation: 29*88=2552, Resulting Numbers: [2552] 2552,71 unequal: No Solution Exploring Operation: 29+88=117, Resulting Numbers: [117] 117,71 unequal: No Solution Exploring Operation: 88-29=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 #0,0,2 Current State: 71:[65, 6], Operations: ['5+18=23', '29-23=6'] Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[29, 5, 65, 18], Operations: [] Exploring Operation: 5+18=23, Resulting Numbers: [29, 65, 23] Generated Node #0,0: 71:[29, 65, 23] Operation: 5+18=23 Moving to Node #0,0 Current State: 71:[29, 65, 23], Operations: ['5+18=23'] Exploring Operation: 29-23=6, Resulting Numbers: [65, 6] Generated Node #0,0,2: 71:[65, 6] Operation: 29-23=6 Moving to Node #0,0,2 Current State: 71:[65, 6], Operations: ['5+18=23', '29-23=6'] Exploring Operation: 65+6=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
[ 99, 18, 99, 80 ]
91
[ "99+99=198", "198/18=11", "80+11=91" ]
Current State: 91:[99, 18, 99, 80], Operations: [] Exploring Operation: 99+99=198, Resulting Numbers: [18, 80, 198] Generated Node #2: [18, 80, 198] from Operation: 99+99=198 Current State: 91:[18, 80, 198], Operations: ['99+99=198'] Exploring Operation: 198/18=11, Resulting Numbers: [80, 11] Generated Node #3: [80, 11] from Operation: 198/18=11 Current State: 91:[80, 11], Operations: ['99+99=198', '198/18=11'] Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[99, 18, 99, 80], Operations: [] Exploring Operation: 99-80=19, Resulting Numbers: [18, 99, 19] Generated Node #0,0: 91:[18, 99, 19] Operation: 99-80=19 Exploring Operation: 99/99=1, Resulting Numbers: [18, 80, 1] Generated Node #0,1: 91:[18, 80, 1] Operation: 99/99=1 Exploring Operation: 99-80=19, Resulting Numbers: [99, 18, 19] Generated Node #0,2: 91:[99, 18, 19] Operation: 99-80=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[18, 99, 19], Operations: ['99-80=19'] Exploring Operation: 99-18=81, Resulting Numbers: [19, 81] Generated Node #0,0,0: 91:[19, 81] Operation: 99-18=81 Exploring Operation: 19-18=1, Resulting Numbers: [99, 1] Generated Node #0,0,1: 91:[99, 1] Operation: 19-18=1 Exploring Operation: 99-19=80, Resulting Numbers: [18, 80] Generated Node #0,0,2: 91:[18, 80] Operation: 99-19=80 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 91:[99, 1], Operations: ['99-80=19', '19-18=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 91:[19, 81], Operations: ['99-80=19', '99-18=81'] Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,91 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 91:[18, 80], Operations: ['99-80=19', '99-19=80'] Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,91 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[99, 18, 19], Operations: ['99-80=19'] Exploring Operation: 19-18=1, Resulting Numbers: [99, 1] Generated Node #0,2,0: 91:[99, 1] Operation: 19-18=1 Exploring Operation: 99-19=80, Resulting Numbers: [18, 80] Generated Node #0,2,1: 91:[18, 80] Operation: 99-19=80 Exploring Operation: 99-18=81, Resulting Numbers: [19, 81] Generated Node #0,2,2: 91:[19, 81] Operation: 99-18=81 Moving to Node #0,2,0 Current State: 91:[99, 1], Operations: ['99-80=19', '19-18=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,91 unequal: No Solution Exploring Operation: 99-1=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 99/1=99, Resulting Numbers: [99] 99,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[18, 80], Operations: ['99-80=19', '99-19=80'] Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,91 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,91 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[19, 81], Operations: ['99-80=19', '99-18=81'] Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,91 unequal: No Solution Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,91 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[18, 80, 1], Operations: ['99/99=1'] Exploring Operation: 18+80=98, Resulting Numbers: [1, 98] Generated Node #0,1,0: 91:[1, 98] Operation: 18+80=98 Exploring Operation: 80+1=81, Resulting Numbers: [18, 81] Generated Node #0,1,1: 91:[18, 81] Operation: 80+1=81 Exploring Operation: 18-1=17, Resulting Numbers: [80, 17] Generated Node #0,1,2: 91:[80, 17] Operation: 18-1=17 Moving to Node #0,1,0 Current State: 91:[1, 98], Operations: ['99/99=1', '18+80=98'] Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,91 unequal: No Solution Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 1*98=98, Resulting Numbers: [98] 98,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[18, 81], Operations: ['99/99=1', '80+1=81'] Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,91 unequal: No Solution Exploring Operation: 18*81=1458, Resulting Numbers: [1458] 1458,91 unequal: No Solution Exploring Operation: 18+81=99, Resulting Numbers: [99] 99,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[80, 17], Operations: ['99/99=1', '18-1=17'] Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,91 unequal: No Solution Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 80*17=1360, Resulting Numbers: [1360] 1360,91 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
[ 32, 10, 18, 13 ]
25
[ "32+13=45", "10*45=450", "450/18=25" ]
Current State: 25:[32, 10, 18, 13], Operations: [] Exploring Operation: 32+13=45, Resulting Numbers: [10, 18, 45] Generated Node #2: [10, 18, 45] from Operation: 32+13=45 Current State: 25:[10, 18, 45], Operations: ['32+13=45'] Exploring Operation: 10*45=450, Resulting Numbers: [18, 450] Generated Node #3: [18, 450] from Operation: 10*45=450 Current State: 25:[18, 450], Operations: ['32+13=45', '10*45=450'] Exploring Operation: 450/18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[32, 10, 18, 13], Operations: [] Exploring Operation: 10+13=23, Resulting Numbers: [32, 18, 23] Generated Node #0,0: 25:[32, 18, 23] Operation: 10+13=23 Exploring Operation: 32-10=22, Resulting Numbers: [18, 13, 22] Generated Node #0,1: 25:[18, 13, 22] Operation: 32-10=22 Exploring Operation: 13-10=3, Resulting Numbers: [32, 18, 3] Generated Node #0,2: 25:[32, 18, 3] Operation: 13-10=3 Exploring Operation: 18-13=5, Resulting Numbers: [32, 10, 5] Generated Node #0,3: 25:[32, 10, 5] Operation: 18-13=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[32, 10, 5], Operations: ['18-13=5'] Exploring Operation: 10/5=2, Resulting Numbers: [32, 2] Generated Node #0,3,0: 25:[32, 2] Operation: 10/5=2 Exploring Operation: 10-5=5, Resulting Numbers: [32, 5] Generated Node #0,3,1: 25:[32, 5] Operation: 10-5=5 Exploring Operation: 32-10=22, Resulting Numbers: [5, 22] Generated Node #0,3,2: 25:[5, 22] Operation: 32-10=22 Exploring Operation: 32-5=27, Resulting Numbers: [10, 27] Generated Node #0,3,3: 25:[10, 27] Operation: 32-5=27 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 25:[5, 22], Operations: ['18-13=5', '32-10=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 25:[32, 5], Operations: ['18-13=5', '10-5=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,25 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 25:[10, 27], Operations: ['18-13=5', '32-5=27'] Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 25:[32, 2], Operations: ['18-13=5', '10/5=2'] Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,25 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,25 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:[32, 18, 23], Operations: ['10+13=23'] Exploring Operation: 18+23=41, Resulting Numbers: [32, 41] Generated Node #0,0,0: 25:[32, 41] Operation: 18+23=41 Exploring Operation: 32-18=14, Resulting Numbers: [23, 14] Generated Node #0,0,1: 25:[23, 14] Operation: 32-18=14 Exploring Operation: 32-23=9, Resulting Numbers: [18, 9] Generated Node #0,0,2: 25:[18, 9] Operation: 32-23=9 Exploring Operation: 23-18=5, Resulting Numbers: [32, 5] Generated Node #0,0,3: 25:[32, 5] Operation: 23-18=5 Moving to Node #0,0,3 Current State: 25:[32, 5], Operations: ['10+13=23', '23-18=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[18, 9], Operations: ['10+13=23', '32-23=9'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,25 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[23, 14], Operations: ['10+13=23', '32-18=14'] Exploring Operation: 23-14=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 23+14=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 23*14=322, Resulting Numbers: [322] 322,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[32, 41], Operations: ['10+13=23', '18+23=41'] Exploring Operation: 32*41=1312, Resulting Numbers: [1312] 1312,25 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,25 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 #0,2 Current State: 25:[32, 18, 3], Operations: ['13-10=3'] Exploring Operation: 18+3=21, Resulting Numbers: [32, 21] Generated Node #0,2,0: 25:[32, 21] Operation: 18+3=21 Exploring Operation: 18/3=6, Resulting Numbers: [32, 6] Generated Node #0,2,1: 25:[32, 6] Operation: 18/3=6 Exploring Operation: 32-18=14, Resulting Numbers: [3, 14] Generated Node #0,2,2: 25:[3, 14] Operation: 32-18=14 Exploring Operation: 32-3=29, Resulting Numbers: [18, 29] Generated Node #0,2,3: 25:[18, 29] Operation: 32-3=29 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[32, 6], Operations: ['13-10=3', '18/3=6'] Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,25 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 32+6=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 #0,2,0 Current State: 25:[32, 21], Operations: ['13-10=3', '18+3=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,25 unequal: No Solution Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[3, 14], Operations: ['13-10=3', '32-18=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 25:[18, 29], Operations: ['13-10=3', '32-3=29'] Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,25 unequal: No Solution Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[18, 13, 22], Operations: ['32-10=22'] Exploring Operation: 22-18=4, Resulting Numbers: [13, 4] Generated Node #0,1,0: 25:[13, 4] Operation: 22-18=4 Exploring Operation: 18+13=31, Resulting Numbers: [22, 31] Generated Node #0,1,1: 25:[22, 31] Operation: 18+13=31 Exploring Operation: 18-13=5, Resulting Numbers: [22, 5] Generated Node #0,1,2: 25:[22, 5] Operation: 18-13=5 Exploring Operation: 22-13=9, Resulting Numbers: [18, 9] Generated Node #0,1,3: 25:[18, 9] Operation: 22-13=9 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 25:[22, 5], Operations: ['32-10=22', '18-13=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,25 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[13, 4], Operations: ['32-10=22', '22-18=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,25 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:[22, 31], Operations: ['32-10=22', '18+13=31'] Exploring Operation: 31-22=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 22*31=682, Resulting Numbers: [682] 682,25 unequal: No Solution Exploring Operation: 22+31=53, Resulting Numbers: [53] 53,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 25:[18, 9], Operations: ['32-10=22', '22-13=9'] Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,25 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,25 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,25 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_4
mult_heuristic
[ 84, 78, 48, 81 ]
46
[ "84+78=162", "162/81=2", "48-2=46" ]
Current State: 46:[84, 78, 48, 81], Operations: [] Exploring Operation: 84+78=162, Resulting Numbers: [48, 81, 162] Generated Node #2: [48, 81, 162] from Operation: 84+78=162 Current State: 46:[48, 81, 162], Operations: ['84+78=162'] Exploring Operation: 162/81=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 162/81=2 Current State: 46:[48, 2], Operations: ['84+78=162', '162/81=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[84, 78, 48, 81], Operations: [] Exploring Operation: 84-48=36, Resulting Numbers: [78, 81, 36] Generated Node #0,0: 46:[78, 81, 36] Operation: 84-48=36 Exploring Operation: 84-81=3, Resulting Numbers: [78, 48, 3] Generated Node #0,1: 46:[78, 48, 3] Operation: 84-81=3 Exploring Operation: 78-48=30, Resulting Numbers: [84, 81, 30] Generated Node #0,2: 46:[84, 81, 30] Operation: 78-48=30 Exploring Operation: 84-78=6, Resulting Numbers: [48, 81, 6] Generated Node #0,3: 46:[48, 81, 6] Operation: 84-78=6 Exploring Operation: 81-78=3, Resulting Numbers: [84, 48, 3] Generated Node #0,4: 46:[84, 48, 3] Operation: 81-78=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[78, 48, 3], Operations: ['84-81=3'] Exploring Operation: 78-3=75, Resulting Numbers: [48, 75] Generated Node #0,1,0: 46:[48, 75] Operation: 78-3=75 Exploring Operation: 48-3=45, Resulting Numbers: [78, 45] Generated Node #0,1,1: 46:[78, 45] Operation: 48-3=45 Exploring Operation: 78+3=81, Resulting Numbers: [48, 81] Generated Node #0,1,2: 46:[48, 81] Operation: 78+3=81 Exploring Operation: 78-48=30, Resulting Numbers: [3, 30] Generated Node #0,1,3: 46:[3, 30] Operation: 78-48=30 Exploring Operation: 78/3=26, Resulting Numbers: [48, 26] Generated Node #0,1,4: 46:[48, 26] Operation: 78/3=26 Moving to Node #0,1,4 Current State: 46:[48, 26], Operations: ['84-81=3', '78/3=26'] Exploring Operation: 48+26=74, Resulting Numbers: [74] 74,46 unequal: No Solution Exploring Operation: 48*26=1248, Resulting Numbers: [1248] 1248,46 unequal: No Solution Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,46 unequal: No Solution Moving to Node #0,1,3 Current State: 46:[3, 30], Operations: ['84-81=3', '78-48=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,46 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[48, 75], Operations: ['84-81=3', '78-3=75'] Exploring Operation: 48*75=3600, Resulting Numbers: [3600] 3600,46 unequal: No Solution Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 48+75=123, Resulting Numbers: [123] 123,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[78, 45], Operations: ['84-81=3', '48-3=45'] Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,46 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[48, 81], Operations: ['84-81=3', '78+3=81'] Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 48+81=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 48*81=3888, Resulting Numbers: [3888] 3888,46 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 #0,3 Current State: 46:[48, 81, 6], Operations: ['84-78=6'] Exploring Operation: 48-6=42, Resulting Numbers: [81, 42] Generated Node #0,3,0: 46:[81, 42] Operation: 48-6=42 Exploring Operation: 81-48=33, Resulting Numbers: [6, 33] Generated Node #0,3,1: 46:[6, 33] Operation: 81-48=33 Exploring Operation: 81-6=75, Resulting Numbers: [48, 75] Generated Node #0,3,2: 46:[48, 75] Operation: 81-6=75 Exploring Operation: 48/6=8, Resulting Numbers: [81, 8] Generated Node #0,3,3: 46:[81, 8] Operation: 48/6=8 Exploring Operation: 48+6=54, Resulting Numbers: [81, 54] Generated Node #0,3,4: 46:[81, 54] Operation: 48+6=54 Moving to Node #0,3,1 Current State: 46:[6, 33], Operations: ['84-78=6', '81-48=33'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,46 unequal: No Solution Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[48, 75], Operations: ['84-78=6', '81-6=75'] Exploring Operation: 48*75=3600, Resulting Numbers: [3600] 3600,46 unequal: No Solution Exploring Operation: 48+75=123, Resulting Numbers: [123] 123,46 unequal: No Solution Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[81, 42], Operations: ['84-78=6', '48-6=42'] Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,46 unequal: No Solution Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[81, 8], Operations: ['84-78=6', '48/6=8'] Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,46 unequal: No Solution Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,46 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,46 unequal: No Solution Moving to Node #0,3,4 Current State: 46:[81, 54], Operations: ['84-78=6', '48+6=54'] Exploring Operation: 81+54=135, Resulting Numbers: [135] 135,46 unequal: No Solution Exploring Operation: 81*54=4374, Resulting Numbers: [4374] 4374,46 unequal: No Solution Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,46 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 #0,4 Current State: 46:[84, 48, 3], Operations: ['81-78=3'] Exploring Operation: 48-3=45, Resulting Numbers: [84, 45] Generated Node #0,4,0: 46:[84, 45] Operation: 48-3=45 Exploring Operation: 84+3=87, Resulting Numbers: [48, 87] Generated Node #0,4,1: 46:[48, 87] Operation: 84+3=87 Exploring Operation: 84/3=28, Resulting Numbers: [48, 28] Generated Node #0,4,2: 46:[48, 28] Operation: 84/3=28 Exploring Operation: 84-3=81, Resulting Numbers: [48, 81] Generated Node #0,4,3: 46:[48, 81] Operation: 84-3=81 Exploring Operation: 84-48=36, Resulting Numbers: [3, 36] Generated Node #0,4,4: 46:[3, 36] Operation: 84-48=36 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 46:[48, 28], Operations: ['81-78=3', '84/3=28'] Exploring Operation: 48*28=1344, Resulting Numbers: [1344] 1344,46 unequal: No Solution Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,46 unequal: No Solution Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,46 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 #0,4,4 Current State: 46:[3, 36], Operations: ['81-78=3', '84-48=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,46 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 #0,4,3 Current State: 46:[48, 81], Operations: ['81-78=3', '84-3=81'] Exploring Operation: 48+81=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 48*81=3888, Resulting Numbers: [3888] 3888,46 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 #0,4,0 Current State: 46:[84, 45], Operations: ['81-78=3', '48-3=45'] Exploring Operation: 84*45=3780, Resulting Numbers: [3780] 3780,46 unequal: No Solution Exploring Operation: 84+45=129, Resulting Numbers: [129] 129,46 unequal: No Solution Exploring Operation: 84-45=39, Resulting Numbers: [39] 39,46 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 #0,4,1 Current State: 46:[48, 87], Operations: ['81-78=3', '84+3=87'] Exploring Operation: 48*87=4176, Resulting Numbers: [4176] 4176,46 unequal: No Solution Exploring Operation: 87-48=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 48+87=135, Resulting Numbers: [135] 135,46 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 #0,0 Current State: 46:[78, 81, 36], Operations: ['84-48=36'] Exploring Operation: 81+36=117, Resulting Numbers: [78, 117] Generated Node #0,0,0: 46:[78, 117] Operation: 81+36=117 Exploring Operation: 81-78=3, Resulting Numbers: [36, 3] Generated Node #0,0,1: 46:[36, 3] Operation: 81-78=3 Exploring Operation: 81-36=45, Resulting Numbers: [78, 45] Generated Node #0,0,2: 46:[78, 45] Operation: 81-36=45 Exploring Operation: 78+36=114, Resulting Numbers: [81, 114] Generated Node #0,0,3: 46:[81, 114] Operation: 78+36=114 Exploring Operation: 78-36=42, Resulting Numbers: [81, 42] Generated Node #0,0,4: 46:[81, 42] Operation: 78-36=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 46:[36, 3], Operations: ['84-48=36', '81-78=3'] Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,46 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 #0,0,2 Current State: 46:[78, 45], Operations: ['84-48=36', '81-36=45'] Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,46 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,46 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 #0,0,4 Current State: 46:[81, 42], Operations: ['84-48=36', '78-36=42'] Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 81*42=3402, Resulting Numbers: [3402] 3402,46 unequal: No Solution Exploring Operation: 81+42=123, Resulting Numbers: [123] 123,46 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 #0,0,0 Current State: 46:[78, 117], Operations: ['84-48=36', '81+36=117'] Exploring Operation: 117-78=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 78*117=9126, Resulting Numbers: [9126] 9126,46 unequal: No Solution Exploring Operation: 78+117=195, Resulting Numbers: [195] 195,46 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 #0,0,3 Current State: 46:[81, 114], Operations: ['84-48=36', '78+36=114'] Exploring Operation: 114-81=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 81+114=195, Resulting Numbers: [195] 195,46 unequal: No Solution Exploring Operation: 81*114=9234, Resulting Numbers: [9234] 9234,46 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 #0,2 Current State: 46:[84, 81, 30], Operations: ['78-48=30'] Exploring Operation: 81+30=111, Resulting Numbers: [84, 111] Generated Node #0,2,0: 46:[84, 111] Operation: 81+30=111 Exploring Operation: 84+30=114, Resulting Numbers: [81, 114] Generated Node #0,2,1: 46:[81, 114] Operation: 84+30=114 Exploring Operation: 81-30=51, Resulting Numbers: [84, 51] Generated Node #0,2,2: 46:[84, 51] Operation: 81-30=51 Exploring Operation: 84-30=54, Resulting Numbers: [81, 54] Generated Node #0,2,3: 46:[81, 54] Operation: 84-30=54 Exploring Operation: 84-81=3, Resulting Numbers: [30, 3] Generated Node #0,2,4: 46:[30, 3] Operation: 84-81=3 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 46:[30, 3], Operations: ['78-48=30', '84-81=3'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,46 unequal: No Solution Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,46 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[84, 51], Operations: ['78-48=30', '81-30=51'] Exploring Operation: 84*51=4284, Resulting Numbers: [4284] 4284,46 unequal: No Solution Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 84+51=135, Resulting Numbers: [135] 135,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 46:[81, 54], Operations: ['78-48=30', '84-30=54'] Exploring Operation: 81+54=135, Resulting Numbers: [135] 135,46 unequal: No Solution Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 81*54=4374, Resulting Numbers: [4374] 4374,46 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:[84, 111], Operations: ['78-48=30', '81+30=111'] Exploring Operation: 84*111=9324, Resulting Numbers: [9324] 9324,46 unequal: No Solution Exploring Operation: 111-84=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 84+111=195, Resulting Numbers: [195] 195,46 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:[81, 114], Operations: ['78-48=30', '84+30=114'] Exploring Operation: 114-81=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 81+114=195, Resulting Numbers: [195] 195,46 unequal: No Solution Exploring Operation: 81*114=9234, Resulting Numbers: [9234] 9234,46 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 No solution found.
0
hs_5
mult_heuristic
[ 36, 90, 29, 17 ]
42
[ "90-36=54", "29-17=12", "54-12=42" ]
Current State: 42:[36, 90, 29, 17], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [29, 17, 54] Generated Node #2: [29, 17, 54] from Operation: 90-36=54 Current State: 42:[29, 17, 54], Operations: ['90-36=54'] Exploring Operation: 29-17=12, Resulting Numbers: [54, 12] Generated Node #3: [54, 12] from Operation: 29-17=12 Current State: 42:[54, 12], Operations: ['90-36=54', '29-17=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[36, 90, 29, 17], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [29, 17, 54] Generated Node #0,0: 42:[29, 17, 54] Operation: 90-36=54 Exploring Operation: 90-29=61, Resulting Numbers: [36, 17, 61] Generated Node #0,1: 42:[36, 17, 61] Operation: 90-29=61 Exploring Operation: 36-29=7, Resulting Numbers: [90, 17, 7] Generated Node #0,2: 42:[90, 17, 7] Operation: 36-29=7 Exploring Operation: 90-17=73, Resulting Numbers: [36, 29, 73] Generated Node #0,3: 42:[36, 29, 73] Operation: 90-17=73 Moving to Node #0,0 Current State: 42:[29, 17, 54], Operations: ['90-36=54'] Exploring Operation: 29+17=46, Resulting Numbers: [54, 46] Generated Node #0,0,0: 42:[54, 46] Operation: 29+17=46 Exploring Operation: 54-29=25, Resulting Numbers: [17, 25] Generated Node #0,0,1: 42:[17, 25] Operation: 54-29=25 Exploring Operation: 29-17=12, Resulting Numbers: [54, 12] Generated Node #0,0,2: 42:[54, 12] Operation: 29-17=12 Exploring Operation: 54-17=37, Resulting Numbers: [29, 37] Generated Node #0,0,3: 42:[29, 37] Operation: 54-17=37 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[17, 25], Operations: ['90-36=54', '54-29=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,42 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[36, 90, 29, 17], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [29, 17, 54] Generated Node #0,0: 42:[29, 17, 54] Operation: 90-36=54 Moving to Node #0,0 Current State: 42:[29, 17, 54], Operations: ['90-36=54'] Exploring Operation: 54-29=25, Resulting Numbers: [17, 25] Generated Node #0,0,1: 42:[17, 25] Operation: 54-29=25 Moving to Node #0,0,1 Current State: 42:[17, 25], Operations: ['90-36=54', '54-29=25'] Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 1, 81, 23, 17 ]
75
[ "1*81=81", "23-17=6", "81-6=75" ]
Current State: 75:[1, 81, 23, 17], Operations: [] Exploring Operation: 1*81=81, Resulting Numbers: [23, 17, 81] Generated Node #2: [23, 17, 81] from Operation: 1*81=81 Current State: 75:[23, 17, 81], Operations: ['1*81=81'] Exploring Operation: 23-17=6, Resulting Numbers: [81, 6] Generated Node #3: [81, 6] from Operation: 23-17=6 Current State: 75:[81, 6], Operations: ['1*81=81', '23-17=6'] Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[1, 81, 23, 17], Operations: [] Exploring Operation: 17-1=16, Resulting Numbers: [81, 23, 16] Generated Node #0,0: 75:[81, 23, 16] Operation: 17-1=16 Exploring Operation: 81-1=80, Resulting Numbers: [23, 17, 80] Generated Node #0,1: 75:[23, 17, 80] Operation: 81-1=80 Exploring Operation: 1+23=24, Resulting Numbers: [81, 17, 24] Generated Node #0,2: 75:[81, 17, 24] Operation: 1+23=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[81, 23, 16], Operations: ['17-1=16'] Exploring Operation: 23-16=7, Resulting Numbers: [81, 7] Generated Node #0,0,0: 75:[81, 7] Operation: 23-16=7 Exploring Operation: 81-16=65, Resulting Numbers: [23, 65] Generated Node #0,0,1: 75:[23, 65] Operation: 81-16=65 Exploring Operation: 81-23=58, Resulting Numbers: [16, 58] Generated Node #0,0,2: 75:[16, 58] Operation: 81-23=58 Moving to Node #0,0,0 Current State: 75:[81, 7], Operations: ['17-1=16', '23-16=7'] Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,75 unequal: No Solution Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,75 unequal: No Solution Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[23, 65], Operations: ['17-1=16', '81-16=65'] Exploring Operation: 65-23=42, Resulting Numbers: [42] 42,75 unequal: No Solution Exploring Operation: 23+65=88, Resulting Numbers: [88] 88,75 unequal: No Solution Exploring Operation: 23*65=1495, Resulting Numbers: [1495] 1495,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[16, 58], Operations: ['17-1=16', '81-23=58'] Exploring Operation: 16*58=928, Resulting Numbers: [928] 928,75 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,75 unequal: No Solution Exploring Operation: 16+58=74, Resulting Numbers: [74] 74,75 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 Current State: 75:[23, 17, 80], Operations: ['81-1=80'] Exploring Operation: 80-17=63, Resulting Numbers: [23, 63] Generated Node #0,1,0: 75:[23, 63] Operation: 80-17=63 Exploring Operation: 23-17=6, Resulting Numbers: [80, 6] Generated Node #0,1,1: 75:[80, 6] Operation: 23-17=6 Exploring Operation: 23+17=40, Resulting Numbers: [80, 40] Generated Node #0,1,2: 75:[80, 40] Operation: 23+17=40 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 75:[80, 6], Operations: ['81-1=80', '23-17=6'] Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,75 unequal: No Solution Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,75 unequal: No Solution Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 75:[23, 63], Operations: ['81-1=80', '80-17=63'] Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 23*63=1449, Resulting Numbers: [1449] 1449,75 unequal: No Solution Exploring Operation: 23+63=86, Resulting Numbers: [86] 86,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 75:[80, 40], Operations: ['81-1=80', '23+17=40'] Exploring Operation: 80-40=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 80/40=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 80+40=120, Resulting Numbers: [120] 120,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[81, 17, 24], Operations: ['1+23=24'] Exploring Operation: 81-17=64, Resulting Numbers: [24, 64] Generated Node #0,2,0: 75:[24, 64] Operation: 81-17=64 Exploring Operation: 24-17=7, Resulting Numbers: [81, 7] Generated Node #0,2,1: 75:[81, 7] Operation: 24-17=7 Exploring Operation: 81-24=57, Resulting Numbers: [17, 57] Generated Node #0,2,2: 75:[17, 57] Operation: 81-24=57 Moving to Node #0,2,1 Current State: 75:[81, 7], Operations: ['1+23=24', '24-17=7'] Exploring Operation: 81+7=88, Resulting Numbers: [88] 88,75 unequal: No Solution Exploring Operation: 81*7=567, Resulting Numbers: [567] 567,75 unequal: No Solution Exploring Operation: 81-7=74, Resulting Numbers: [74] 74,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[24, 64], Operations: ['1+23=24', '81-17=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 Exploring Operation: 24*64=1536, Resulting Numbers: [1536] 1536,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[17, 57], Operations: ['1+23=24', '81-24=57'] Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 17*57=969, Resulting Numbers: [969] 969,75 unequal: No Solution Exploring Operation: 17+57=74, Resulting Numbers: [74] 74,75 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, 69, 87, 31 ]
59
[ "69/23=3", "87-31=56", "3+56=59" ]
Current State: 59:[23, 69, 87, 31], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [87, 31, 3] Generated Node #2: [87, 31, 3] from Operation: 69/23=3 Current State: 59:[87, 31, 3], Operations: ['69/23=3'] Exploring Operation: 87-31=56, Resulting Numbers: [3, 56] Generated Node #3: [3, 56] from Operation: 87-31=56 Current State: 59:[3, 56], Operations: ['69/23=3', '87-31=56'] Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[23, 69, 87, 31], Operations: [] Exploring Operation: 23+31=54, Resulting Numbers: [69, 87, 54] Generated Node #0,0: 59:[69, 87, 54] Operation: 23+31=54 Exploring Operation: 87-31=56, Resulting Numbers: [23, 69, 56] Generated Node #0,1: 59:[23, 69, 56] Operation: 87-31=56 Exploring Operation: 87-23=64, Resulting Numbers: [69, 31, 64] Generated Node #0,2: 59:[69, 31, 64] Operation: 87-23=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[69, 87, 54], Operations: ['23+31=54'] Exploring Operation: 87-69=18, Resulting Numbers: [54, 18] Generated Node #0,0,0: 59:[54, 18] Operation: 87-69=18 Exploring Operation: 87-54=33, Resulting Numbers: [69, 33] Generated Node #0,0,1: 59:[69, 33] Operation: 87-54=33 Exploring Operation: 69-54=15, Resulting Numbers: [87, 15] Generated Node #0,0,2: 59:[87, 15] Operation: 69-54=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 59:[69, 33], Operations: ['23+31=54', '87-54=33'] Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,59 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,59 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,59 unequal: No Solution No 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: 59:[54, 18], Operations: ['23+31=54', '87-69=18'] Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,59 unequal: No Solution No 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: 59:[87, 15], Operations: ['23+31=54', '69-54=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,59 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,59 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,59 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: 59:[69, 31, 64], Operations: ['87-23=64'] Exploring Operation: 69-31=38, Resulting Numbers: [64, 38] Generated Node #0,2,0: 59:[64, 38] Operation: 69-31=38 Exploring Operation: 69+31=100, Resulting Numbers: [64, 100] Generated Node #0,2,1: 59:[64, 100] Operation: 69+31=100 Exploring Operation: 64-31=33, Resulting Numbers: [69, 33] Generated Node #0,2,2: 59:[69, 33] Operation: 64-31=33 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[64, 38], Operations: ['87-23=64', '69-31=38'] Exploring Operation: 64+38=102, Resulting Numbers: [102] 102,59 unequal: No Solution Exploring Operation: 64*38=2432, Resulting Numbers: [2432] 2432,59 unequal: No Solution Exploring Operation: 64-38=26, Resulting Numbers: [26] 26,59 unequal: No Solution No 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: 59:[69, 33], Operations: ['87-23=64', '64-31=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,59 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,59 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,59 unequal: No Solution No 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: 59:[64, 100], Operations: ['87-23=64', '69+31=100'] Exploring Operation: 64*100=6400, Resulting Numbers: [6400] 6400,59 unequal: No Solution Exploring Operation: 100-64=36, Resulting Numbers: [36] 36,59 unequal: No Solution Exploring Operation: 64+100=164, Resulting Numbers: [164] 164,59 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: 59:[23, 69, 56], Operations: ['87-31=56'] Exploring Operation: 69-23=46, Resulting Numbers: [56, 46] Generated Node #0,1,0: 59:[56, 46] Operation: 69-23=46 Exploring Operation: 23+69=92, Resulting Numbers: [56, 92] Generated Node #0,1,1: 59:[56, 92] Operation: 23+69=92 Exploring Operation: 23+56=79, Resulting Numbers: [69, 79] Generated Node #0,1,2: 59:[69, 79] Operation: 23+56=79 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[56, 46], Operations: ['87-31=56', '69-23=46'] Exploring Operation: 56*46=2576, Resulting Numbers: [2576] 2576,59 unequal: No Solution Exploring Operation: 56+46=102, Resulting Numbers: [102] 102,59 unequal: No Solution Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,59 unequal: No Solution No 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: 59:[69, 79], Operations: ['87-31=56', '23+56=79'] Exploring Operation: 69+79=148, Resulting Numbers: [148] 148,59 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,59 unequal: No Solution Exploring Operation: 69*79=5451, Resulting Numbers: [5451] 5451,59 unequal: No Solution No 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: 59:[56, 92], Operations: ['87-31=56', '23+69=92'] Exploring Operation: 56+92=148, Resulting Numbers: [148] 148,59 unequal: No Solution Exploring Operation: 56*92=5152, Resulting Numbers: [5152] 5152,59 unequal: No Solution Exploring Operation: 92-56=36, Resulting Numbers: [36] 36,59 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
[ 54, 32, 2, 18 ]
58
[ "54-32=22", "2*18=36", "22+36=58" ]
Current State: 58:[54, 32, 2, 18], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [2, 18, 22] Generated Node #2: [2, 18, 22] from Operation: 54-32=22 Current State: 58:[2, 18, 22], Operations: ['54-32=22'] Exploring Operation: 2*18=36, Resulting Numbers: [22, 36] Generated Node #3: [22, 36] from Operation: 2*18=36 Current State: 58:[22, 36], Operations: ['54-32=22', '2*18=36'] Exploring Operation: 22+36=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[54, 32, 2, 18], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [54, 32, 36] Generated Node #0,0: 58:[54, 32, 36] Operation: 2*18=36 Exploring Operation: 32+18=50, Resulting Numbers: [54, 2, 50] Generated Node #0,1: 58:[54, 2, 50] Operation: 32+18=50 Exploring Operation: 18/2=9, Resulting Numbers: [54, 32, 9] Generated Node #0,2: 58:[54, 32, 9] Operation: 18/2=9 Exploring Operation: 54/18=3, Resulting Numbers: [32, 2, 3] Generated Node #0,3: 58:[32, 2, 3] Operation: 54/18=3 Exploring Operation: 54-18=36, Resulting Numbers: [32, 2, 36] Generated Node #0,4: 58:[32, 2, 36] Operation: 54-18=36 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[32, 2, 3], Operations: ['54/18=3'] Exploring Operation: 32+2=34, Resulting Numbers: [3, 34] Generated Node #0,3,0: 58:[3, 34] Operation: 32+2=34 Exploring Operation: 32-2=30, Resulting Numbers: [3, 30] Generated Node #0,3,1: 58:[3, 30] Operation: 32-2=30 Exploring Operation: 3-2=1, Resulting Numbers: [32, 1] Generated Node #0,3,2: 58:[32, 1] Operation: 3-2=1 Exploring Operation: 32+3=35, Resulting Numbers: [2, 35] Generated Node #0,3,3: 58:[2, 35] Operation: 32+3=35 Exploring Operation: 32-3=29, Resulting Numbers: [2, 29] Generated Node #0,3,4: 58:[2, 29] Operation: 32-3=29 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 58:[2, 29], Operations: ['54/18=3', '32-3=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,58 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[54, 32, 2, 18], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [32, 2, 3] Generated Node #0,3: 58:[32, 2, 3] Operation: 54/18=3 Moving to Node #0,3 Current State: 58:[32, 2, 3], Operations: ['54/18=3'] Exploring Operation: 32-3=29, Resulting Numbers: [2, 29] Generated Node #0,3,4: 58:[2, 29] Operation: 32-3=29 Moving to Node #0,3,4 Current State: 58:[2, 29], Operations: ['54/18=3', '32-3=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 74, 79, 3, 66 ]
27
[ "79-74=5", "66/3=22", "5+22=27" ]
Current State: 27:[74, 79, 3, 66], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [3, 66, 5] Generated Node #2: [3, 66, 5] from Operation: 79-74=5 Current State: 27:[3, 66, 5], Operations: ['79-74=5'] Exploring Operation: 66/3=22, Resulting Numbers: [5, 22] Generated Node #3: [5, 22] from Operation: 66/3=22 Current State: 27:[5, 22], Operations: ['79-74=5', '66/3=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[74, 79, 3, 66], Operations: [] Exploring Operation: 79-66=13, Resulting Numbers: [74, 3, 13] Generated Node #0,0: 27:[74, 3, 13] Operation: 79-66=13 Exploring Operation: 79-74=5, Resulting Numbers: [3, 66, 5] Generated Node #0,1: 27:[3, 66, 5] Operation: 79-74=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[3, 66, 5], Operations: ['79-74=5'] Exploring Operation: 66/3=22, Resulting Numbers: [5, 22] Generated Node #0,1,0: 27:[5, 22] Operation: 66/3=22 Exploring Operation: 66-5=61, Resulting Numbers: [3, 61] Generated Node #0,1,1: 27:[3, 61] Operation: 66-5=61 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[5, 22], Operations: ['79-74=5', '66/3=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[74, 79, 3, 66], Operations: [] Exploring Operation: 79-74=5, Resulting Numbers: [3, 66, 5] Generated Node #0,1: 27:[3, 66, 5] Operation: 79-74=5 Moving to Node #0,1 Current State: 27:[3, 66, 5], Operations: ['79-74=5'] Exploring Operation: 66/3=22, Resulting Numbers: [5, 22] Generated Node #0,1,0: 27:[5, 22] Operation: 66/3=22 Moving to Node #0,1,0 Current State: 27:[5, 22], Operations: ['79-74=5', '66/3=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 8, 18, 16, 13 ]
32
[ "8+18=26", "16*26=416", "416/13=32" ]
Current State: 32:[8, 18, 16, 13], Operations: [] Exploring Operation: 8+18=26, Resulting Numbers: [16, 13, 26] Generated Node #2: [16, 13, 26] from Operation: 8+18=26 Current State: 32:[16, 13, 26], Operations: ['8+18=26'] Exploring Operation: 16*26=416, Resulting Numbers: [13, 416] Generated Node #3: [13, 416] from Operation: 16*26=416 Current State: 32:[13, 416], Operations: ['8+18=26', '16*26=416'] Exploring Operation: 416/13=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[8, 18, 16, 13], Operations: [] Exploring Operation: 18+13=31, Resulting Numbers: [8, 16, 31] Generated Node #0,0: 32:[8, 16, 31] Operation: 18+13=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[8, 16, 31], Operations: ['18+13=31'] Exploring Operation: 16-8=8, Resulting Numbers: [31, 8] Generated Node #0,0,0: 32:[31, 8] Operation: 16-8=8 Moving to Node #0,0,0 Current State: 32:[31, 8], Operations: ['18+13=31', '16-8=8'] Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 87, 84, 23, 27 ]
47
[ "87-84=3", "23+27=50", "50-3=47" ]
Current State: 47:[87, 84, 23, 27], Operations: [] Exploring Operation: 87-84=3, Resulting Numbers: [23, 27, 3] Generated Node #2: [23, 27, 3] from Operation: 87-84=3 Current State: 47:[23, 27, 3], Operations: ['87-84=3'] Exploring Operation: 23+27=50, Resulting Numbers: [3, 50] Generated Node #3: [3, 50] from Operation: 23+27=50 Current State: 47:[3, 50], Operations: ['87-84=3', '23+27=50'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[87, 84, 23, 27], Operations: [] Exploring Operation: 84-23=61, Resulting Numbers: [87, 27, 61] Generated Node #0,0: 47:[87, 27, 61] Operation: 84-23=61 Exploring Operation: 87-27=60, Resulting Numbers: [84, 23, 60] Generated Node #0,1: 47:[84, 23, 60] Operation: 87-27=60 Exploring Operation: 87-23=64, Resulting Numbers: [84, 27, 64] Generated Node #0,2: 47:[84, 27, 64] Operation: 87-23=64 Exploring Operation: 84-27=57, Resulting Numbers: [87, 23, 57] Generated Node #0,3: 47:[87, 23, 57] Operation: 84-27=57 Moving to Node #0,0 Current State: 47:[87, 27, 61], Operations: ['84-23=61'] Exploring Operation: 87-61=26, Resulting Numbers: [27, 26] Generated Node #0,0,0: 47:[27, 26] Operation: 87-61=26 Exploring Operation: 87-27=60, Resulting Numbers: [61, 60] Generated Node #0,0,1: 47:[61, 60] Operation: 87-27=60 Exploring Operation: 87+27=114, Resulting Numbers: [61, 114] Generated Node #0,0,2: 47:[61, 114] Operation: 87+27=114 Exploring Operation: 61-27=34, Resulting Numbers: [87, 34] Generated Node #0,0,3: 47:[87, 34] Operation: 61-27=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[61, 60], Operations: ['84-23=61', '87-27=60'] Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 61*60=3660, Resulting Numbers: [3660] 3660,47 unequal: No Solution Exploring Operation: 61+60=121, Resulting Numbers: [121] 121,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[27, 26], Operations: ['84-23=61', '87-61=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,47 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[87, 34], Operations: ['84-23=61', '61-27=34'] Exploring Operation: 87*34=2958, Resulting Numbers: [2958] 2958,47 unequal: No Solution Exploring Operation: 87-34=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 87+34=121, Resulting Numbers: [121] 121,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[61, 114], Operations: ['84-23=61', '87+27=114'] Exploring Operation: 61*114=6954, Resulting Numbers: [6954] 6954,47 unequal: No Solution Exploring Operation: 114-61=53, Resulting Numbers: [53] 53,47 unequal: No Solution Exploring Operation: 61+114=175, Resulting Numbers: [175] 175,47 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: 47:[84, 27, 64], Operations: ['87-23=64'] Exploring Operation: 84+27=111, Resulting Numbers: [64, 111] Generated Node #0,2,0: 47:[64, 111] Operation: 84+27=111 Exploring Operation: 64-27=37, Resulting Numbers: [84, 37] Generated Node #0,2,1: 47:[84, 37] Operation: 64-27=37 Exploring Operation: 84-64=20, Resulting Numbers: [27, 20] Generated Node #0,2,2: 47:[27, 20] Operation: 84-64=20 Exploring Operation: 84-27=57, Resulting Numbers: [64, 57] Generated Node #0,2,3: 47:[64, 57] Operation: 84-27=57 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 47:[64, 57], Operations: ['87-23=64', '84-27=57'] Exploring Operation: 64+57=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,47 unequal: No Solution Exploring Operation: 64*57=3648, Resulting Numbers: [3648] 3648,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[84, 37], Operations: ['87-23=64', '64-27=37'] Exploring Operation: 84*37=3108, Resulting Numbers: [3108] 3108,47 unequal: No Solution Exploring Operation: 84+37=121, Resulting Numbers: [121] 121,47 unequal: No Solution Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[87, 84, 23, 27], Operations: [] Exploring Operation: 87-23=64, Resulting Numbers: [84, 27, 64] Generated Node #0,2: 47:[84, 27, 64] Operation: 87-23=64 Moving to Node #0,2 Current State: 47:[84, 27, 64], Operations: ['87-23=64'] Exploring Operation: 64-27=37, Resulting Numbers: [84, 37] Generated Node #0,2,1: 47:[84, 37] Operation: 64-27=37 Moving to Node #0,2,1 Current State: 47:[84, 37], Operations: ['87-23=64', '64-27=37'] Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 28, 18, 99, 14 ]
41
[ "28-18=10", "14*10=140", "140-99=41" ]
Current State: 41:[28, 18, 99, 14], Operations: [] Exploring Operation: 28-18=10, Resulting Numbers: [99, 14, 10] Generated Node #2: [99, 14, 10] from Operation: 28-18=10 Current State: 41:[99, 14, 10], Operations: ['28-18=10'] Exploring Operation: 14*10=140, Resulting Numbers: [99, 140] Generated Node #3: [99, 140] from Operation: 14*10=140 Current State: 41:[99, 140], Operations: ['28-18=10', '14*10=140'] Exploring Operation: 140-99=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[28, 18, 99, 14], Operations: [] Exploring Operation: 99-18=81, Resulting Numbers: [28, 14, 81] Generated Node #0,0: 41:[28, 14, 81] Operation: 99-18=81 Exploring Operation: 99-28=71, Resulting Numbers: [18, 14, 71] Generated Node #0,1: 41:[18, 14, 71] Operation: 99-28=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[28, 14, 81], Operations: ['99-18=81'] Exploring Operation: 81-14=67, Resulting Numbers: [28, 67] Generated Node #0,0,0: 41:[28, 67] Operation: 81-14=67 Exploring Operation: 81-28=53, Resulting Numbers: [14, 53] Generated Node #0,0,1: 41:[14, 53] Operation: 81-28=53 Moving to Node #0,0,0 Current State: 41:[28, 67], Operations: ['99-18=81', '81-14=67'] Exploring Operation: 28+67=95, Resulting Numbers: [95] 95,41 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[14, 53], Operations: ['99-18=81', '81-28=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[18, 14, 71], Operations: ['99-28=71'] Exploring Operation: 18+14=32, Resulting Numbers: [71, 32] Generated Node #0,1,0: 41:[71, 32] Operation: 18+14=32 Exploring Operation: 71-18=53, Resulting Numbers: [14, 53] Generated Node #0,1,1: 41:[14, 53] Operation: 71-18=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[71, 32], Operations: ['99-28=71', '18+14=32'] Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 71+32=103, Resulting Numbers: [103] 103,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[14, 53], Operations: ['99-28=71', '71-18=53'] Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 57, 44, 16, 87 ]
35
[ "57+87=144", "144/16=9", "44-9=35" ]
Current State: 35:[57, 44, 16, 87], Operations: [] Exploring Operation: 57+87=144, Resulting Numbers: [44, 16, 144] Generated Node #2: [44, 16, 144] from Operation: 57+87=144 Current State: 35:[44, 16, 144], Operations: ['57+87=144'] Exploring Operation: 144/16=9, Resulting Numbers: [44, 9] Generated Node #3: [44, 9] from Operation: 144/16=9 Current State: 35:[44, 9], Operations: ['57+87=144', '144/16=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[57, 44, 16, 87], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [57, 16, 43] Generated Node #0,0: 35:[57, 16, 43] Operation: 87-44=43 Exploring Operation: 87-57=30, Resulting Numbers: [44, 16, 30] Generated Node #0,1: 35:[44, 16, 30] Operation: 87-57=30 Moving to Node #0,1 Current State: 35:[44, 16, 30], Operations: ['87-57=30'] Exploring Operation: 44-16=28, Resulting Numbers: [30, 28] Generated Node #0,1,0: 35:[30, 28] Operation: 44-16=28 Exploring Operation: 44-30=14, Resulting Numbers: [16, 14] Generated Node #0,1,1: 35:[16, 14] Operation: 44-30=14 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[30, 28], Operations: ['87-57=30', '44-16=28'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[16, 14], Operations: ['87-57=30', '44-30=14'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,35 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,35 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: 35:[57, 16, 43], Operations: ['87-44=43'] Exploring Operation: 57-43=14, Resulting Numbers: [16, 14] Generated Node #0,0,0: 35:[16, 14] Operation: 57-43=14 Exploring Operation: 57-16=41, Resulting Numbers: [43, 41] Generated Node #0,0,1: 35:[43, 41] Operation: 57-16=41 Moving to Node #0,0,1 Current State: 35:[43, 41], Operations: ['87-44=43', '57-16=41'] Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[16, 14], Operations: ['87-44=43', '57-43=14'] Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,35 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,35 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 56, 58, 4, 46 ]
82
[ "58+46=104", "104/4=26", "56+26=82" ]
Current State: 82:[56, 58, 4, 46], Operations: [] Exploring Operation: 58+46=104, Resulting Numbers: [56, 4, 104] Generated Node #2: [56, 4, 104] from Operation: 58+46=104 Current State: 82:[56, 4, 104], Operations: ['58+46=104'] Exploring Operation: 104/4=26, Resulting Numbers: [56, 26] Generated Node #3: [56, 26] from Operation: 104/4=26 Current State: 82:[56, 26], Operations: ['58+46=104', '104/4=26'] Exploring Operation: 56+26=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[56, 58, 4, 46], Operations: [] Exploring Operation: 56-4=52, Resulting Numbers: [58, 46, 52] Generated Node #0,0: 82:[58, 46, 52] Operation: 56-4=52 Exploring Operation: 58-46=12, Resulting Numbers: [56, 4, 12] Generated Node #0,1: 82:[56, 4, 12] Operation: 58-46=12 Exploring Operation: 58-56=2, Resulting Numbers: [4, 46, 2] Generated Node #0,2: 82:[4, 46, 2] Operation: 58-56=2 Exploring Operation: 56-46=10, Resulting Numbers: [58, 4, 10] Generated Node #0,3: 82:[58, 4, 10] Operation: 56-46=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[4, 46, 2], Operations: ['58-56=2'] Exploring Operation: 4-2=2, Resulting Numbers: [46, 2] Generated Node #0,2,0: 82:[46, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [46, 2] Generated Node #0,2,1: 82:[46, 2] Operation: 4/2=2 Exploring Operation: 46-4=42, Resulting Numbers: [2, 42] Generated Node #0,2,2: 82:[2, 42] Operation: 46-4=42 Exploring Operation: 46-2=44, Resulting Numbers: [4, 44] Generated Node #0,2,3: 82:[4, 44] Operation: 46-2=44 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[2, 42], Operations: ['58-56=2', '46-4=42'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 2+42=44, Resulting Numbers: [44] 44,82 unequal: No Solution Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,82 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[46, 2], Operations: ['58-56=2', '4-2=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,82 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,82 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[46, 2], Operations: ['58-56=2', '4/2=2'] Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,82 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,82 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[4, 44], Operations: ['58-56=2', '46-2=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,82 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[56, 4, 12], Operations: ['58-46=12'] Exploring Operation: 56-12=44, Resulting Numbers: [4, 44] Generated Node #0,1,0: 82:[4, 44] Operation: 56-12=44 Exploring Operation: 56+12=68, Resulting Numbers: [4, 68] Generated Node #0,1,1: 82:[4, 68] Operation: 56+12=68 Exploring Operation: 56-4=52, Resulting Numbers: [12, 52] Generated Node #0,1,2: 82:[12, 52] Operation: 56-4=52 Exploring Operation: 12/4=3, Resulting Numbers: [56, 3] Generated Node #0,1,3: 82:[56, 3] Operation: 12/4=3 Moving to Node #0,1,0 Current State: 82:[4, 44], Operations: ['58-46=12', '56-12=44'] Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,82 unequal: No Solution Exploring Operation: 4*44=176, Resulting Numbers: [176] 176,82 unequal: No Solution Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[56, 3], Operations: ['58-46=12', '12/4=3'] Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,82 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,82 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[4, 68], Operations: ['58-46=12', '56+12=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,82 unequal: No Solution Moving to Node #0,1,2 Current State: 82:[12, 52], Operations: ['58-46=12', '56-4=52'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,82 unequal: No Solution Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[58, 4, 10], Operations: ['56-46=10'] Exploring Operation: 58-4=54, Resulting Numbers: [10, 54] Generated Node #0,3,0: 82:[10, 54] Operation: 58-4=54 Exploring Operation: 58-10=48, Resulting Numbers: [4, 48] Generated Node #0,3,1: 82:[4, 48] Operation: 58-10=48 Exploring Operation: 4*10=40, Resulting Numbers: [58, 40] Generated Node #0,3,2: 82:[58, 40] Operation: 4*10=40 Exploring Operation: 58+10=68, Resulting Numbers: [4, 68] Generated Node #0,3,3: 82:[4, 68] Operation: 58+10=68 Moving to Node #0,3,1 Current State: 82:[4, 48], Operations: ['56-46=10', '58-10=48'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,82 unequal: No Solution Exploring Operation: 4*48=192, Resulting Numbers: [192] 192,82 unequal: No Solution Exploring Operation: 4+48=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[4, 68], Operations: ['56-46=10', '58+10=68'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,82 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[58, 40], Operations: ['56-46=10', '4*10=40'] Exploring Operation: 58*40=2320, Resulting Numbers: [2320] 2320,82 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 58+40=98, Resulting Numbers: [98] 98,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[10, 54], Operations: ['56-46=10', '58-4=54'] Exploring Operation: 10*54=540, Resulting Numbers: [540] 540,82 unequal: No Solution Exploring Operation: 10+54=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 54-10=44, Resulting Numbers: [44] 44,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[58, 46, 52], Operations: ['56-4=52'] Exploring Operation: 52-46=6, Resulting Numbers: [58, 6] Generated Node #0,0,0: 82:[58, 6] Operation: 52-46=6 Exploring Operation: 58+46=104, Resulting Numbers: [52, 104] Generated Node #0,0,1: 82:[52, 104] Operation: 58+46=104 Exploring Operation: 58-52=6, Resulting Numbers: [46, 6] Generated Node #0,0,2: 82:[46, 6] Operation: 58-52=6 Exploring Operation: 58-46=12, Resulting Numbers: [52, 12] Generated Node #0,0,3: 82:[52, 12] Operation: 58-46=12 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[46, 6], Operations: ['56-4=52', '58-52=6'] Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,82 unequal: No Solution Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,82 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[58, 6], Operations: ['56-4=52', '52-46=6'] Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,82 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 82:[52, 12], Operations: ['56-4=52', '58-46=12'] Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,82 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,82 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 82:[52, 104], Operations: ['56-4=52', '58+46=104'] Exploring Operation: 104/52=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 52+104=156, Resulting Numbers: [156] 156,82 unequal: No Solution Exploring Operation: 52*104=5408, Resulting Numbers: [5408] 5408,82 unequal: No Solution Exploring Operation: 104-52=52, Resulting Numbers: [52] 52,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 57, 50, 95, 83 ]
53
[ "57*50=2850", "2850/95=30", "83-30=53" ]
Current State: 53:[57, 50, 95, 83], Operations: [] Exploring Operation: 57*50=2850, Resulting Numbers: [95, 83, 2850] Generated Node #2: [95, 83, 2850] from Operation: 57*50=2850 Current State: 53:[95, 83, 2850], Operations: ['57*50=2850'] Exploring Operation: 2850/95=30, Resulting Numbers: [83, 30] Generated Node #3: [83, 30] from Operation: 2850/95=30 Current State: 53:[83, 30], Operations: ['57*50=2850', '2850/95=30'] Exploring Operation: 83-30=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[57, 50, 95, 83], Operations: [] Exploring Operation: 83-57=26, Resulting Numbers: [50, 95, 26] Generated Node #0,0: 53:[50, 95, 26] Operation: 83-57=26 Exploring Operation: 95-83=12, Resulting Numbers: [57, 50, 12] Generated Node #0,1: 53:[57, 50, 12] Operation: 95-83=12 Exploring Operation: 83-50=33, Resulting Numbers: [57, 95, 33] Generated Node #0,2: 53:[57, 95, 33] Operation: 83-50=33 Exploring Operation: 95-57=38, Resulting Numbers: [50, 83, 38] Generated Node #0,3: 53:[50, 83, 38] Operation: 95-57=38 Exploring Operation: 95-50=45, Resulting Numbers: [57, 83, 45] Generated Node #0,4: 53:[57, 83, 45] Operation: 95-50=45 Start Sub Search at level 1: Moving to Node #0,4 Current State: 53:[57, 83, 45], Operations: ['95-50=45'] Exploring Operation: 57+45=102, Resulting Numbers: [83, 102] Generated Node #0,4,0: 53:[83, 102] Operation: 57+45=102 Exploring Operation: 83+45=128, Resulting Numbers: [57, 128] Generated Node #0,4,1: 53:[57, 128] Operation: 83+45=128 Exploring Operation: 83-57=26, Resulting Numbers: [45, 26] Generated Node #0,4,2: 53:[45, 26] Operation: 83-57=26 Exploring Operation: 57-45=12, Resulting Numbers: [83, 12] Generated Node #0,4,3: 53:[83, 12] Operation: 57-45=12 Exploring Operation: 83-45=38, Resulting Numbers: [57, 38] Generated Node #0,4,4: 53:[57, 38] Operation: 83-45=38 Moving to Node #0,4,4 Current State: 53:[57, 38], Operations: ['95-50=45', '83-45=38'] Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[45, 26], Operations: ['95-50=45', '83-57=26'] Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,53 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[83, 12], Operations: ['95-50=45', '57-45=12'] Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,53 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,53 unequal: No Solution Moving to Node #0,4,0 Current State: 53:[83, 102], Operations: ['95-50=45', '57+45=102'] Exploring Operation: 83*102=8466, Resulting Numbers: [8466] 8466,53 unequal: No Solution Exploring Operation: 83+102=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 102-83=19, Resulting Numbers: [19] 19,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[57, 128], Operations: ['95-50=45', '83+45=128'] Exploring Operation: 57*128=7296, Resulting Numbers: [7296] 7296,53 unequal: No Solution Exploring Operation: 128-57=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 57+128=185, Resulting Numbers: [185] 185,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[57, 50, 12], Operations: ['95-83=12'] Exploring Operation: 57+12=69, Resulting Numbers: [50, 69] Generated Node #0,1,0: 53:[50, 69] Operation: 57+12=69 Exploring Operation: 57-12=45, Resulting Numbers: [50, 45] Generated Node #0,1,1: 53:[50, 45] Operation: 57-12=45 Exploring Operation: 57-50=7, Resulting Numbers: [12, 7] Generated Node #0,1,2: 53:[12, 7] Operation: 57-50=7 Exploring Operation: 50-12=38, Resulting Numbers: [57, 38] Generated Node #0,1,3: 53:[57, 38] Operation: 50-12=38 Exploring Operation: 50+12=62, Resulting Numbers: [57, 62] Generated Node #0,1,4: 53:[57, 62] Operation: 50+12=62 Moving to Node #0,1,1 Current State: 53:[50, 45], Operations: ['95-83=12', '57-12=45'] Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,53 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,53 unequal: No Solution Moving to Node #0,1,4 Current State: 53:[57, 62], Operations: ['95-83=12', '50+12=62'] Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 57*62=3534, Resulting Numbers: [3534] 3534,53 unequal: No Solution Exploring Operation: 57+62=119, Resulting Numbers: [119] 119,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[50, 69], Operations: ['95-83=12', '57+12=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[57, 38], Operations: ['95-83=12', '50-12=38'] Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 57*38=2166, Resulting Numbers: [2166] 2166,53 unequal: No Solution Exploring Operation: 57+38=95, Resulting Numbers: [95] 95,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[12, 7], Operations: ['95-83=12', '57-50=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,53 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 #0,3 Current State: 53:[50, 83, 38], Operations: ['95-57=38'] Exploring Operation: 83-38=45, Resulting Numbers: [50, 45] Generated Node #0,3,0: 53:[50, 45] Operation: 83-38=45 Exploring Operation: 50-38=12, Resulting Numbers: [83, 12] Generated Node #0,3,1: 53:[83, 12] Operation: 50-38=12 Exploring Operation: 83-50=33, Resulting Numbers: [38, 33] Generated Node #0,3,2: 53:[38, 33] Operation: 83-50=33 Exploring Operation: 83+38=121, Resulting Numbers: [50, 121] Generated Node #0,3,3: 53:[50, 121] Operation: 83+38=121 Exploring Operation: 50+38=88, Resulting Numbers: [83, 88] Generated Node #0,3,4: 53:[83, 88] Operation: 50+38=88 Moving to Node #0,3,0 Current State: 53:[50, 45], Operations: ['95-57=38', '83-38=45'] Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,53 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[38, 33], Operations: ['95-57=38', '83-50=33'] Exploring Operation: 38*33=1254, Resulting Numbers: [1254] 1254,53 unequal: No Solution Exploring Operation: 38+33=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,3,4 Current State: 53:[83, 88], Operations: ['95-57=38', '50+38=88'] Exploring Operation: 83+88=171, Resulting Numbers: [171] 171,53 unequal: No Solution Exploring Operation: 83*88=7304, Resulting Numbers: [7304] 7304,53 unequal: No Solution Exploring Operation: 88-83=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[83, 12], Operations: ['95-57=38', '50-38=12'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,53 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[50, 121], Operations: ['95-57=38', '83+38=121'] Exploring Operation: 50+121=171, Resulting Numbers: [171] 171,53 unequal: No Solution Exploring Operation: 50*121=6050, Resulting Numbers: [6050] 6050,53 unequal: No Solution Exploring Operation: 121-50=71, Resulting Numbers: [71] 71,53 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 #0,2 Current State: 53:[57, 95, 33], Operations: ['83-50=33'] Exploring Operation: 57+33=90, Resulting Numbers: [95, 90] Generated Node #0,2,0: 53:[95, 90] Operation: 57+33=90 Exploring Operation: 95+33=128, Resulting Numbers: [57, 128] Generated Node #0,2,1: 53:[57, 128] Operation: 95+33=128 Exploring Operation: 57-33=24, Resulting Numbers: [95, 24] Generated Node #0,2,2: 53:[95, 24] Operation: 57-33=24 Exploring Operation: 95-33=62, Resulting Numbers: [57, 62] Generated Node #0,2,3: 53:[57, 62] Operation: 95-33=62 Exploring Operation: 95-57=38, Resulting Numbers: [33, 38] Generated Node #0,2,4: 53:[33, 38] Operation: 95-57=38 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 53:[57, 62], Operations: ['83-50=33', '95-33=62'] Exploring Operation: 57+62=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 57*62=3534, Resulting Numbers: [3534] 3534,53 unequal: No Solution Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 53:[33, 38], Operations: ['83-50=33', '95-57=38'] Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,53 unequal: No Solution Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 53:[95, 24], Operations: ['83-50=33', '57-33=24'] Exploring Operation: 95-24=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 95*24=2280, Resulting Numbers: [2280] 2280,53 unequal: No Solution Exploring Operation: 95+24=119, Resulting Numbers: [119] 119,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 53:[95, 90], Operations: ['83-50=33', '57+33=90'] Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 53:[57, 128], Operations: ['83-50=33', '95+33=128'] Exploring Operation: 57+128=185, Resulting Numbers: [185] 185,53 unequal: No Solution Exploring Operation: 128-57=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 57*128=7296, Resulting Numbers: [7296] 7296,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[50, 95, 26], Operations: ['83-57=26'] Exploring Operation: 50+26=76, Resulting Numbers: [95, 76] Generated Node #0,0,0: 53:[95, 76] Operation: 50+26=76 Exploring Operation: 95+26=121, Resulting Numbers: [50, 121] Generated Node #0,0,1: 53:[50, 121] Operation: 95+26=121 Exploring Operation: 95-26=69, Resulting Numbers: [50, 69] Generated Node #0,0,2: 53:[50, 69] Operation: 95-26=69 Exploring Operation: 50-26=24, Resulting Numbers: [95, 24] Generated Node #0,0,3: 53:[95, 24] Operation: 50-26=24 Exploring Operation: 95-50=45, Resulting Numbers: [26, 45] Generated Node #0,0,4: 53:[26, 45] Operation: 95-50=45 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[50, 69], Operations: ['83-57=26', '95-26=69'] Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,53 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 53:[26, 45], Operations: ['83-57=26', '95-50=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,53 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[95, 76], Operations: ['83-57=26', '50+26=76'] Exploring Operation: 95*76=7220, Resulting Numbers: [7220] 7220,53 unequal: No Solution Exploring Operation: 95-76=19, Resulting Numbers: [19] 19,53 unequal: No Solution Exploring Operation: 95+76=171, Resulting Numbers: [171] 171,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[50, 121], Operations: ['83-57=26', '95+26=121'] Exploring Operation: 121-50=71, Resulting Numbers: [71] 71,53 unequal: No Solution Exploring Operation: 50*121=6050, Resulting Numbers: [6050] 6050,53 unequal: No Solution Exploring Operation: 50+121=171, Resulting Numbers: [171] 171,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 53:[95, 24], Operations: ['83-57=26', '50-26=24'] Exploring Operation: 95*24=2280, Resulting Numbers: [2280] 2280,53 unequal: No Solution Exploring Operation: 95+24=119, Resulting Numbers: [119] 119,53 unequal: No Solution Exploring Operation: 95-24=71, Resulting Numbers: [71] 71,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 43, 60, 5, 11 ]
42
[ "43+11=54", "60/5=12", "54-12=42" ]
Current State: 42:[43, 60, 5, 11], Operations: [] Exploring Operation: 43+11=54, Resulting Numbers: [60, 5, 54] Generated Node #2: [60, 5, 54] from Operation: 43+11=54 Current State: 42:[60, 5, 54], Operations: ['43+11=54'] Exploring Operation: 60/5=12, Resulting Numbers: [54, 12] Generated Node #3: [54, 12] from Operation: 60/5=12 Current State: 42:[54, 12], Operations: ['43+11=54', '60/5=12'] Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[43, 60, 5, 11], Operations: [] Exploring Operation: 60/5=12, Resulting Numbers: [43, 11, 12] Generated Node #0,0: 42:[43, 11, 12] Operation: 60/5=12 Moving to Node #0,0 Current State: 42:[43, 11, 12], Operations: ['60/5=12'] Exploring Operation: 12-11=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 42:[43, 1] Operation: 12-11=1 Moving to Node #0,0,0 Current State: 42:[43, 1], Operations: ['60/5=12', '12-11=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[43, 60, 5, 11], Operations: [] Exploring Operation: 60/5=12, Resulting Numbers: [43, 11, 12] Generated Node #0,0: 42:[43, 11, 12] Operation: 60/5=12 Moving to Node #0,0 Current State: 42:[43, 11, 12], Operations: ['60/5=12'] Exploring Operation: 12-11=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 42:[43, 1] Operation: 12-11=1 Moving to Node #0,0,0 Current State: 42:[43, 1], Operations: ['60/5=12', '12-11=1'] Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 2, 11, 88, 42 ]
78
[ "42/2=21", "11+88=99", "99-21=78" ]
Current State: 78:[2, 11, 88, 42], Operations: [] Exploring Operation: 42/2=21, Resulting Numbers: [11, 88, 21] Generated Node #2: [11, 88, 21] from Operation: 42/2=21 Current State: 78:[11, 88, 21], Operations: ['42/2=21'] Exploring Operation: 11+88=99, Resulting Numbers: [21, 99] Generated Node #3: [21, 99] from Operation: 11+88=99 Current State: 78:[21, 99], Operations: ['42/2=21', '11+88=99'] Exploring Operation: 99-21=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[2, 11, 88, 42], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [2, 11, 46] Generated Node #0,0: 78:[2, 11, 46] Operation: 88-42=46 Exploring Operation: 88/2=44, Resulting Numbers: [11, 42, 44] Generated Node #0,1: 78:[11, 42, 44] Operation: 88/2=44 Exploring Operation: 88-11=77, Resulting Numbers: [2, 42, 77] Generated Node #0,2: 78:[2, 42, 77] Operation: 88-11=77 Exploring Operation: 88/11=8, Resulting Numbers: [2, 42, 8] Generated Node #0,3: 78:[2, 42, 8] Operation: 88/11=8 Moving to Node #0,2 Current State: 78:[2, 42, 77], Operations: ['88-11=77'] Exploring Operation: 77-42=35, Resulting Numbers: [2, 35] Generated Node #0,2,0: 78:[2, 35] Operation: 77-42=35 Exploring Operation: 42-2=40, Resulting Numbers: [77, 40] Generated Node #0,2,1: 78:[77, 40] Operation: 42-2=40 Exploring Operation: 2+77=79, Resulting Numbers: [42, 79] Generated Node #0,2,2: 78:[42, 79] Operation: 2+77=79 Exploring Operation: 2+42=44, Resulting Numbers: [77, 44] Generated Node #0,2,3: 78:[77, 44] Operation: 2+42=44 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[77, 40], Operations: ['88-11=77', '42-2=40'] Exploring Operation: 77*40=3080, Resulting Numbers: [3080] 3080,78 unequal: No Solution Exploring Operation: 77-40=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 77+40=117, Resulting Numbers: [117] 117,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[2, 35], Operations: ['88-11=77', '77-42=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,78 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[42, 79], Operations: ['88-11=77', '2+77=79'] Exploring Operation: 42*79=3318, Resulting Numbers: [3318] 3318,78 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 42+79=121, Resulting Numbers: [121] 121,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[77, 44], Operations: ['88-11=77', '2+42=44'] Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,78 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,78 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: 78:[2, 42, 8], Operations: ['88/11=8'] Exploring Operation: 8-2=6, Resulting Numbers: [42, 6] Generated Node #0,3,0: 78:[42, 6] Operation: 8-2=6 Exploring Operation: 42-8=34, Resulting Numbers: [2, 34] Generated Node #0,3,1: 78:[2, 34] Operation: 42-8=34 Exploring Operation: 8/2=4, Resulting Numbers: [42, 4] Generated Node #0,3,2: 78:[42, 4] Operation: 8/2=4 Exploring Operation: 42-2=40, Resulting Numbers: [8, 40] Generated Node #0,3,3: 78:[8, 40] Operation: 42-2=40 Moving to Node #0,0 Current State: 78:[2, 11, 46], Operations: ['88-42=46'] Exploring Operation: 46-11=35, Resulting Numbers: [2, 35] Generated Node #0,0,0: 78:[2, 35] Operation: 46-11=35 Exploring Operation: 46-2=44, Resulting Numbers: [11, 44] Generated Node #0,0,1: 78:[11, 44] Operation: 46-2=44 Exploring Operation: 46/2=23, Resulting Numbers: [11, 23] Generated Node #0,0,2: 78:[11, 23] Operation: 46/2=23 Exploring Operation: 2+11=13, Resulting Numbers: [46, 13] Generated Node #0,0,3: 78:[46, 13] Operation: 2+11=13 Moving to Node #0,1 Current State: 78:[11, 42, 44], Operations: ['88/2=44'] Exploring Operation: 44-42=2, Resulting Numbers: [11, 2] Generated Node #0,1,0: 78:[11, 2] Operation: 44-42=2 Exploring Operation: 42-11=31, Resulting Numbers: [44, 31] Generated Node #0,1,1: 78:[44, 31] Operation: 42-11=31 Exploring Operation: 44/11=4, Resulting Numbers: [42, 4] Generated Node #0,1,2: 78:[42, 4] Operation: 44/11=4 Exploring Operation: 44-11=33, Resulting Numbers: [42, 33] Generated Node #0,1,3: 78:[42, 33] Operation: 44-11=33 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[11, 2], Operations: ['88/2=44', '44-42=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,78 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[42, 4], Operations: ['88/2=44', '44/11=4'] Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,78 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[42, 33], Operations: ['88/2=44', '44-11=33'] Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,78 unequal: No Solution Exploring Operation: 42-33=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 42*33=1386, Resulting Numbers: [1386] 1386,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[44, 31], Operations: ['88/2=44', '42-11=31'] Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 44+31=75, Resulting Numbers: [75] 75,78 unequal: No Solution Exploring Operation: 44*31=1364, Resulting Numbers: [1364] 1364,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 78:[42, 6], Operations: ['88/11=8', '8-2=6'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,78 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 42*6=252, Resulting Numbers: [252] 252,78 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[8, 40], Operations: ['88/11=8', '42-2=40'] Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,78 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,78 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[42, 4], Operations: ['88/11=8', '8/2=4'] Exploring Operation: 42*4=168, Resulting Numbers: [168] 168,78 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 42+4=46, Resulting Numbers: [46] 46,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[2, 35], Operations: ['88-42=46', '46-11=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,78 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[11, 23], Operations: ['88-42=46', '46/2=23'] Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[2, 34], Operations: ['88/11=8', '42-8=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[11, 44], Operations: ['88-42=46', '46-2=44'] Exploring Operation: 11+44=55, Resulting Numbers: [55] 55,78 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 11*44=484, Resulting Numbers: [484] 484,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[46, 13], Operations: ['88-42=46', '2+11=13'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 46*13=598, Resulting Numbers: [598] 598,78 unequal: No Solution Exploring Operation: 46+13=59, Resulting Numbers: [59] 59,78 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 49, 99, 98, 12 ]
85
[ "98/49=2", "99-12=87", "87-2=85" ]
Current State: 85:[49, 99, 98, 12], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [99, 12, 2] Generated Node #2: [99, 12, 2] from Operation: 98/49=2 Current State: 85:[99, 12, 2], Operations: ['98/49=2'] Exploring Operation: 99-12=87, Resulting Numbers: [2, 87] Generated Node #3: [2, 87] from Operation: 99-12=87 Current State: 85:[2, 87], Operations: ['98/49=2', '99-12=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[49, 99, 98, 12], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [99, 12, 2] Generated Node #0,0: 85:[99, 12, 2] Operation: 98/49=2 Exploring Operation: 99-98=1, Resulting Numbers: [49, 12, 1] Generated Node #0,1: 85:[49, 12, 1] Operation: 99-98=1 Moving to Node #0,0 Current State: 85:[99, 12, 2], Operations: ['98/49=2'] Exploring Operation: 12/2=6, Resulting Numbers: [99, 6] Generated Node #0,0,0: 85:[99, 6] Operation: 12/2=6 Exploring Operation: 99-12=87, Resulting Numbers: [2, 87] Generated Node #0,0,1: 85:[2, 87] Operation: 99-12=87 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[2, 87], Operations: ['98/49=2', '99-12=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[49, 99, 98, 12], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [99, 12, 2] Generated Node #0,0: 85:[99, 12, 2] Operation: 98/49=2 Moving to Node #0,0 Current State: 85:[99, 12, 2], Operations: ['98/49=2'] Exploring Operation: 99-12=87, Resulting Numbers: [2, 87] Generated Node #0,0,1: 85:[2, 87] Operation: 99-12=87 Moving to Node #0,0,1 Current State: 85:[2, 87], Operations: ['98/49=2', '99-12=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 13, 68, 66, 38 ]
64
[ "68-66=2", "13*2=26", "38+26=64" ]
Current State: 64:[13, 68, 66, 38], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [13, 38, 2] Generated Node #2: [13, 38, 2] from Operation: 68-66=2 Current State: 64:[13, 38, 2], Operations: ['68-66=2'] Exploring Operation: 13*2=26, Resulting Numbers: [38, 26] Generated Node #3: [38, 26] from Operation: 13*2=26 Current State: 64:[38, 26], Operations: ['68-66=2', '13*2=26'] Exploring Operation: 38+26=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[13, 68, 66, 38], Operations: [] Exploring Operation: 68-38=30, Resulting Numbers: [13, 66, 30] Generated Node #0,0: 64:[13, 66, 30] Operation: 68-38=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[13, 66, 30], Operations: ['68-38=30'] Exploring Operation: 30-13=17, Resulting Numbers: [66, 17] Generated Node #0,0,0: 64:[66, 17] Operation: 30-13=17 Moving to Node #0,0,0 Current State: 64:[66, 17], Operations: ['68-38=30', '30-13=17'] Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,64 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
[ 73, 2, 73, 72 ]
76
[ "73+2=75", "73-72=1", "75+1=76" ]
Current State: 76:[73, 2, 73, 72], Operations: [] Exploring Operation: 73+2=75, Resulting Numbers: [72, 75] Generated Node #2: [72, 75] from Operation: 73+2=75 Current State: 76:[72, 75], Operations: ['73+2=75'] Exploring Operation: 73-72=1, Resulting Numbers: [75, 1] Generated Node #3: [75, 1] from Operation: 73-72=1 Current State: 76:[75, 1], Operations: ['73+2=75', '73-72=1'] Exploring Operation: 75+1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[73, 2, 73, 72], Operations: [] Exploring Operation: 73-72=1, Resulting Numbers: [2, 73, 1] Generated Node #0,0: 76:[2, 73, 1] Operation: 73-72=1 Exploring Operation: 73-73=0, Resulting Numbers: [2, 72, 0] Generated Node #0,1: 76:[2, 72, 0] Operation: 73-73=0 Exploring Operation: 73+2=75, Resulting Numbers: [73, 72, 75] Generated Node #0,2: 76:[73, 72, 75] Operation: 73+2=75 Exploring Operation: 73-72=1, Resulting Numbers: [73, 2, 1] Generated Node #0,3: 76:[73, 2, 1] Operation: 73-72=1 Exploring Operation: 73/73=1, Resulting Numbers: [2, 72, 1] Generated Node #0,4: 76:[2, 72, 1] Operation: 73/73=1 Moving to Node #0,0 Current State: 76:[2, 73, 1], Operations: ['73-72=1'] Exploring Operation: 2+73=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 76:[1, 75] Operation: 2+73=75 Exploring Operation: 73+1=74, Resulting Numbers: [2, 74] Generated Node #0,0,1: 76:[2, 74] Operation: 73+1=74 Exploring Operation: 2/1=2, Resulting Numbers: [73, 2] Generated Node #0,0,2: 76:[73, 2] Operation: 2/1=2 Exploring Operation: 73*1=73, Resulting Numbers: [2, 73] Generated Node #0,0,3: 76:[2, 73] Operation: 73*1=73 Exploring Operation: 2*1=2, Resulting Numbers: [73, 2] Generated Node #0,0,4: 76:[73, 2] Operation: 2*1=2 Moving to Node #0,3 Current State: 76:[73, 2, 1], Operations: ['73-72=1'] Exploring Operation: 73+2=75, Resulting Numbers: [1, 75] Generated Node #0,3,0: 76:[1, 75] Operation: 73+2=75 Exploring Operation: 73*1=73, Resulting Numbers: [2, 73] Generated Node #0,3,1: 76:[2, 73] Operation: 73*1=73 Exploring Operation: 73/1=73, Resulting Numbers: [2, 73] Generated Node #0,3,2: 76:[2, 73] Operation: 73/1=73 Exploring Operation: 73+1=74, Resulting Numbers: [2, 74] Generated Node #0,3,3: 76:[2, 74] Operation: 73+1=74 Exploring Operation: 2*1=2, Resulting Numbers: [73, 2] Generated Node #0,3,4: 76:[73, 2] Operation: 2*1=2 Moving to Node #0,4 Current State: 76:[2, 72, 1], Operations: ['73/73=1'] Exploring Operation: 2*1=2, Resulting Numbers: [72, 2] Generated Node #0,4,0: 76:[72, 2] Operation: 2*1=2 Exploring Operation: 2/1=2, Resulting Numbers: [72, 2] Generated Node #0,4,1: 76:[72, 2] Operation: 2/1=2 Exploring Operation: 72/2=36, Resulting Numbers: [1, 36] Generated Node #0,4,2: 76:[1, 36] Operation: 72/2=36 Exploring Operation: 2+72=74, Resulting Numbers: [1, 74] Generated Node #0,4,3: 76:[1, 74] Operation: 2+72=74 Exploring Operation: 72+1=73, Resulting Numbers: [2, 73] Generated Node #0,4,4: 76:[2, 73] Operation: 72+1=73 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 76:[1, 36], Operations: ['73/73=1', '72/2=36'] Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,76 unequal: No Solution Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 76:[1, 74], Operations: ['73/73=1', '2+72=74'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 1*74=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 1+74=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 76:[2, 73], Operations: ['73/73=1', '72+1=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,76 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 76:[72, 2], Operations: ['73/73=1', '2*1=2'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 76:[72, 2], Operations: ['73/73=1', '2/1=2'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 76:[2, 72, 0], Operations: ['73-73=0'] Exploring Operation: 2+72=74, Resulting Numbers: [0, 74] Generated Node #0,1,0: 76:[0, 74] Operation: 2+72=74 Exploring Operation: 72*0=0, Resulting Numbers: [2, 0] Generated Node #0,1,1: 76:[2, 0] Operation: 72*0=0 Exploring Operation: 2-0=2, Resulting Numbers: [72, 2] Generated Node #0,1,2: 76:[72, 2] Operation: 2-0=2 Exploring Operation: 72/2=36, Resulting Numbers: [0, 36] Generated Node #0,1,3: 76:[0, 36] Operation: 72/2=36 Exploring Operation: 2+0=2, Resulting Numbers: [72, 2] Generated Node #0,1,4: 76:[72, 2] Operation: 2+0=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[2, 0], Operations: ['73-73=0', '72*0=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[0, 74], Operations: ['73-73=0', '2+72=74'] Exploring Operation: 74-0=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 0+74=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 0*74=0, Resulting Numbers: [0] 0,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 76:[72, 2], Operations: ['73-73=0', '2-0=2'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,76 unequal: No Solution Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 76:[0, 36], Operations: ['73-73=0', '72/2=36'] Exploring Operation: 0*36=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 0+36=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 36-0=36, Resulting Numbers: [36] 36,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 76:[72, 2], Operations: ['73-73=0', '2+0=2'] Exploring Operation: 72+2=74, Resulting Numbers: [74] 74,76 unequal: No Solution Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,76 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 72*2=144, Resulting Numbers: [144] 144,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 76:[73, 72, 75], Operations: ['73+2=75'] Exploring Operation: 73-72=1, Resulting Numbers: [75, 1] Generated Node #0,2,0: 76:[75, 1] Operation: 73-72=1 Exploring Operation: 72+75=147, Resulting Numbers: [73, 147] Generated Node #0,2,1: 76:[73, 147] Operation: 72+75=147 Exploring Operation: 75-72=3, Resulting Numbers: [73, 3] Generated Node #0,2,2: 76:[73, 3] Operation: 75-72=3 Exploring Operation: 73+72=145, Resulting Numbers: [75, 145] Generated Node #0,2,3: 76:[75, 145] Operation: 73+72=145 Exploring Operation: 75-73=2, Resulting Numbers: [72, 2] Generated Node #0,2,4: 76:[72, 2] Operation: 75-73=2 Moving to Node #0,0,0 Current State: 76:[1, 75], Operations: ['73-72=1', '2+73=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 1*75=75, Resulting Numbers: [75] 75,76 unequal: No Solution Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[73, 2, 73, 72], Operations: [] Exploring Operation: 73-72=1, Resulting Numbers: [2, 73, 1] Generated Node #0,0: 76:[2, 73, 1] Operation: 73-72=1 Moving to Node #0,0 Current State: 76:[2, 73, 1], Operations: ['73-72=1'] Exploring Operation: 2+73=75, Resulting Numbers: [1, 75] Generated Node #0,0,0: 76:[1, 75] Operation: 2+73=75 Moving to Node #0,0,0 Current State: 76:[1, 75], Operations: ['73-72=1', '2+73=75'] Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
0.936632
hs_5
sum_heuristic
[ 3, 71, 50, 56 ]
45
[ "71-56=15", "15/3=5", "50-5=45" ]
Current State: 45:[3, 71, 50, 56], Operations: [] Exploring Operation: 71-56=15, Resulting Numbers: [3, 50, 15] Generated Node #2: [3, 50, 15] from Operation: 71-56=15 Current State: 45:[3, 50, 15], Operations: ['71-56=15'] Exploring Operation: 15/3=5, Resulting Numbers: [50, 5] Generated Node #3: [50, 5] from Operation: 15/3=5 Current State: 45:[50, 5], Operations: ['71-56=15', '15/3=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[3, 71, 50, 56], Operations: [] Exploring Operation: 50-3=47, Resulting Numbers: [71, 56, 47] Generated Node #0,0: 45:[71, 56, 47] Operation: 50-3=47 Exploring Operation: 71-3=68, Resulting Numbers: [50, 56, 68] Generated Node #0,1: 45:[50, 56, 68] Operation: 71-3=68 Exploring Operation: 71-50=21, Resulting Numbers: [3, 56, 21] Generated Node #0,2: 45:[3, 56, 21] Operation: 71-50=21 Exploring Operation: 71-56=15, Resulting Numbers: [3, 50, 15] Generated Node #0,3: 45:[3, 50, 15] Operation: 71-56=15 Exploring Operation: 56-50=6, Resulting Numbers: [3, 71, 6] Generated Node #0,4: 45:[3, 71, 6] Operation: 56-50=6 Moving to Node #0,3 Current State: 45:[3, 50, 15], Operations: ['71-56=15'] Exploring Operation: 50-3=47, Resulting Numbers: [15, 47] Generated Node #0,3,0: 45:[15, 47] Operation: 50-3=47 Exploring Operation: 3+50=53, Resulting Numbers: [15, 53] Generated Node #0,3,1: 45:[15, 53] Operation: 3+50=53 Exploring Operation: 15/3=5, Resulting Numbers: [50, 5] Generated Node #0,3,2: 45:[50, 5] Operation: 15/3=5 Exploring Operation: 3+15=18, Resulting Numbers: [50, 18] Generated Node #0,3,3: 45:[50, 18] Operation: 3+15=18 Exploring Operation: 3*15=45, Resulting Numbers: [50, 45] Generated Node #0,3,4: 45:[50, 45] Operation: 3*15=45 Moving to Node #0,2 Current State: 45:[3, 56, 21], Operations: ['71-50=21'] Exploring Operation: 56-3=53, Resulting Numbers: [21, 53] Generated Node #0,2,0: 45:[21, 53] Operation: 56-3=53 Exploring Operation: 21-3=18, Resulting Numbers: [56, 18] Generated Node #0,2,1: 45:[56, 18] Operation: 21-3=18 Exploring Operation: 56-21=35, Resulting Numbers: [3, 35] Generated Node #0,2,2: 45:[3, 35] Operation: 56-21=35 Exploring Operation: 3+56=59, Resulting Numbers: [21, 59] Generated Node #0,2,3: 45:[21, 59] Operation: 3+56=59 Exploring Operation: 21/3=7, Resulting Numbers: [56, 7] Generated Node #0,2,4: 45:[56, 7] Operation: 21/3=7 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[3, 35], Operations: ['71-50=21', '56-21=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,45 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 45:[56, 7], Operations: ['71-50=21', '21/3=7'] Exploring Operation: 56+7=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,45 unequal: No Solution Exploring Operation: 56*7=392, Resulting Numbers: [392] 392,45 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[21, 53], Operations: ['71-50=21', '56-3=53'] Exploring Operation: 21*53=1113, Resulting Numbers: [1113] 1113,45 unequal: No Solution Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 21+53=74, Resulting Numbers: [74] 74,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[56, 18], Operations: ['71-50=21', '21-3=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,45 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[21, 59], Operations: ['71-50=21', '3+56=59'] Exploring Operation: 21*59=1239, Resulting Numbers: [1239] 1239,45 unequal: No Solution Exploring Operation: 21+59=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 45:[3, 71, 6], Operations: ['56-50=6'] Exploring Operation: 71-3=68, Resulting Numbers: [6, 68] Generated Node #0,4,0: 45:[6, 68] Operation: 71-3=68 Exploring Operation: 3+6=9, Resulting Numbers: [71, 9] Generated Node #0,4,1: 45:[71, 9] Operation: 3+6=9 Exploring Operation: 71-6=65, Resulting Numbers: [3, 65] Generated Node #0,4,2: 45:[3, 65] Operation: 71-6=65 Exploring Operation: 6-3=3, Resulting Numbers: [71, 3] Generated Node #0,4,3: 45:[71, 3] Operation: 6-3=3 Exploring Operation: 6/3=2, Resulting Numbers: [71, 2] Generated Node #0,4,4: 45:[71, 2] Operation: 6/3=2 Moving to Node #0,0 Current State: 45:[71, 56, 47], Operations: ['50-3=47'] Exploring Operation: 71+47=118, Resulting Numbers: [56, 118] Generated Node #0,0,0: 45:[56, 118] Operation: 71+47=118 Exploring Operation: 71-47=24, Resulting Numbers: [56, 24] Generated Node #0,0,1: 45:[56, 24] Operation: 71-47=24 Exploring Operation: 71+56=127, Resulting Numbers: [47, 127] Generated Node #0,0,2: 45:[47, 127] Operation: 71+56=127 Exploring Operation: 71-56=15, Resulting Numbers: [47, 15] Generated Node #0,0,3: 45:[47, 15] Operation: 71-56=15 Exploring Operation: 56-47=9, Resulting Numbers: [71, 9] Generated Node #0,0,4: 45:[71, 9] Operation: 56-47=9 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[47, 15], Operations: ['50-3=47', '71-56=15'] Exploring Operation: 47*15=705, Resulting Numbers: [705] 705,45 unequal: No Solution Exploring Operation: 47+15=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[56, 24], Operations: ['50-3=47', '71-47=24'] Exploring Operation: 56*24=1344, Resulting Numbers: [1344] 1344,45 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 56+24=80, Resulting Numbers: [80] 80,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 45:[71, 9], Operations: ['50-3=47', '56-47=9'] Exploring Operation: 71*9=639, Resulting Numbers: [639] 639,45 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[56, 118], Operations: ['50-3=47', '71+47=118'] Exploring Operation: 118-56=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 56*118=6608, Resulting Numbers: [6608] 6608,45 unequal: No Solution Exploring Operation: 56+118=174, Resulting Numbers: [174] 174,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[47, 127], Operations: ['50-3=47', '71+56=127'] Exploring Operation: 127-47=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 47+127=174, Resulting Numbers: [174] 174,45 unequal: No Solution Exploring Operation: 47*127=5969, Resulting Numbers: [5969] 5969,45 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: 45:[50, 56, 68], Operations: ['71-3=68'] Exploring Operation: 68-50=18, Resulting Numbers: [56, 18] Generated Node #0,1,0: 45:[56, 18] Operation: 68-50=18 Exploring Operation: 68-56=12, Resulting Numbers: [50, 12] Generated Node #0,1,1: 45:[50, 12] Operation: 68-56=12 Exploring Operation: 50+68=118, Resulting Numbers: [56, 118] Generated Node #0,1,2: 45:[56, 118] Operation: 50+68=118 Exploring Operation: 56-50=6, Resulting Numbers: [68, 6] Generated Node #0,1,3: 45:[68, 6] Operation: 56-50=6 Exploring Operation: 50+56=106, Resulting Numbers: [68, 106] Generated Node #0,1,4: 45:[68, 106] Operation: 50+56=106 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[50, 12], Operations: ['71-3=68', '68-56=12'] Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,45 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[56, 18], Operations: ['71-3=68', '68-50=18'] Exploring Operation: 56+18=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 56*18=1008, Resulting Numbers: [1008] 1008,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[68, 6], Operations: ['71-3=68', '56-50=6'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[56, 118], Operations: ['71-3=68', '50+68=118'] Exploring Operation: 56+118=174, Resulting Numbers: [174] 174,45 unequal: No Solution Exploring Operation: 56*118=6608, Resulting Numbers: [6608] 6608,45 unequal: No Solution Exploring Operation: 118-56=62, Resulting Numbers: [62] 62,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 45:[68, 106], Operations: ['71-3=68', '50+56=106'] Exploring Operation: 106-68=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 68+106=174, Resulting Numbers: [174] 174,45 unequal: No Solution Exploring Operation: 68*106=7208, Resulting Numbers: [7208] 7208,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 45:[15, 47], Operations: ['71-56=15', '50-3=47'] Exploring Operation: 15+47=62, Resulting Numbers: [62] 62,45 unequal: No Solution Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,45 unequal: No Solution Exploring Operation: 15*47=705, Resulting Numbers: [705] 705,45 unequal: No Solution Moving to Node #0,3,4 Current State: 45:[50, 45], Operations: ['71-56=15', '3*15=45'] Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 50*45=2250, Resulting Numbers: [2250] 2250,45 unequal: No Solution Exploring Operation: 50+45=95, Resulting Numbers: [95] 95,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[50, 5], Operations: ['71-56=15', '15/3=5'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[3, 71, 50, 56], Operations: [] Exploring Operation: 71-56=15, Resulting Numbers: [3, 50, 15] Generated Node #0,3: 45:[3, 50, 15] Operation: 71-56=15 Moving to Node #0,3 Current State: 45:[3, 50, 15], Operations: ['71-56=15'] Exploring Operation: 15/3=5, Resulting Numbers: [50, 5] Generated Node #0,3,2: 45:[50, 5] Operation: 15/3=5 Moving to Node #0,3,2 Current State: 45:[50, 5], Operations: ['71-56=15', '15/3=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.923611
hs_5
sum_heuristic
[ 80, 90, 49, 4 ]
89
[ "90-80=10", "4*10=40", "49+40=89" ]
Current State: 89:[80, 90, 49, 4], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [49, 4, 10] Generated Node #2: [49, 4, 10] from Operation: 90-80=10 Current State: 89:[49, 4, 10], Operations: ['90-80=10'] Exploring Operation: 4*10=40, Resulting Numbers: [49, 40] Generated Node #3: [49, 40] from Operation: 4*10=40 Current State: 89:[49, 40], Operations: ['90-80=10', '4*10=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[80, 90, 49, 4], Operations: [] Exploring Operation: 90+4=94, Resulting Numbers: [80, 49, 94] Generated Node #0,0: 89:[80, 49, 94] Operation: 90+4=94 Exploring Operation: 80+4=84, Resulting Numbers: [90, 49, 84] Generated Node #0,1: 89:[90, 49, 84] Operation: 80+4=84 Exploring Operation: 49+4=53, Resulting Numbers: [80, 90, 53] Generated Node #0,2: 89:[80, 90, 53] Operation: 49+4=53 Exploring Operation: 80-4=76, Resulting Numbers: [90, 49, 76] Generated Node #0,3: 89:[90, 49, 76] Operation: 80-4=76 Exploring Operation: 90-4=86, Resulting Numbers: [80, 49, 86] Generated Node #0,4: 89:[80, 49, 86] Operation: 90-4=86 Moving to Node #0,1 Current State: 89:[90, 49, 84], Operations: ['80+4=84'] Exploring Operation: 90-84=6, Resulting Numbers: [49, 6] Generated Node #0,1,0: 89:[49, 6] Operation: 90-84=6 Exploring Operation: 84-49=35, Resulting Numbers: [90, 35] Generated Node #0,1,1: 89:[90, 35] Operation: 84-49=35 Exploring Operation: 49+84=133, Resulting Numbers: [90, 133] Generated Node #0,1,2: 89:[90, 133] Operation: 49+84=133 Exploring Operation: 90+49=139, Resulting Numbers: [84, 139] Generated Node #0,1,3: 89:[84, 139] Operation: 90+49=139 Exploring Operation: 90-49=41, Resulting Numbers: [84, 41] Generated Node #0,1,4: 89:[84, 41] Operation: 90-49=41 Moving to Node #0,2 Current State: 89:[80, 90, 53], Operations: ['49+4=53'] Exploring Operation: 80-53=27, Resulting Numbers: [90, 27] Generated Node #0,2,0: 89:[90, 27] Operation: 80-53=27 Exploring Operation: 90-80=10, Resulting Numbers: [53, 10] Generated Node #0,2,1: 89:[53, 10] Operation: 90-80=10 Exploring Operation: 80+53=133, Resulting Numbers: [90, 133] Generated Node #0,2,2: 89:[90, 133] Operation: 80+53=133 Exploring Operation: 90-53=37, Resulting Numbers: [80, 37] Generated Node #0,2,3: 89:[80, 37] Operation: 90-53=37 Exploring Operation: 90+53=143, Resulting Numbers: [80, 143] Generated Node #0,2,4: 89:[80, 143] Operation: 90+53=143 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[90, 133], Operations: ['49+4=53', '80+53=133'] Exploring Operation: 90+133=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 90*133=11970, Resulting Numbers: [11970] 11970,89 unequal: No Solution Exploring Operation: 133-90=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[80, 37], Operations: ['49+4=53', '90-53=37'] Exploring Operation: 80*37=2960, Resulting Numbers: [2960] 2960,89 unequal: No Solution Exploring Operation: 80+37=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[90, 27], Operations: ['49+4=53', '80-53=27'] Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 89:[80, 143], Operations: ['49+4=53', '90+53=143'] Exploring Operation: 80*143=11440, Resulting Numbers: [11440] 11440,89 unequal: No Solution Exploring Operation: 80+143=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 143-80=63, Resulting Numbers: [63] 63,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[53, 10], Operations: ['49+4=53', '90-80=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,89 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,89 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: 89:[80, 49, 86], Operations: ['90-4=86'] Exploring Operation: 80-49=31, Resulting Numbers: [86, 31] Generated Node #0,4,0: 89:[86, 31] Operation: 80-49=31 Exploring Operation: 86-49=37, Resulting Numbers: [80, 37] Generated Node #0,4,1: 89:[80, 37] Operation: 86-49=37 Exploring Operation: 80+49=129, Resulting Numbers: [86, 129] Generated Node #0,4,2: 89:[86, 129] Operation: 80+49=129 Exploring Operation: 80+86=166, Resulting Numbers: [49, 166] Generated Node #0,4,3: 89:[49, 166] Operation: 80+86=166 Exploring Operation: 49+86=135, Resulting Numbers: [80, 135] Generated Node #0,4,4: 89:[80, 135] Operation: 49+86=135 Moving to Node #0,0 Current State: 89:[80, 49, 94], Operations: ['90+4=94'] Exploring Operation: 94-80=14, Resulting Numbers: [49, 14] Generated Node #0,0,0: 89:[49, 14] Operation: 94-80=14 Exploring Operation: 80+49=129, Resulting Numbers: [94, 129] Generated Node #0,0,1: 89:[94, 129] Operation: 80+49=129 Exploring Operation: 94-49=45, Resulting Numbers: [80, 45] Generated Node #0,0,2: 89:[80, 45] Operation: 94-49=45 Exploring Operation: 80-49=31, Resulting Numbers: [94, 31] Generated Node #0,0,3: 89:[94, 31] Operation: 80-49=31 Exploring Operation: 49+94=143, Resulting Numbers: [80, 143] Generated Node #0,0,4: 89:[80, 143] Operation: 49+94=143 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[94, 129], Operations: ['90+4=94', '80+49=129'] Exploring Operation: 94*129=12126, Resulting Numbers: [12126] 12126,89 unequal: No Solution Exploring Operation: 94+129=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 129-94=35, Resulting Numbers: [35] 35,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[80, 45], Operations: ['90+4=94', '94-49=45'] Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,89 unequal: No Solution Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,89 unequal: No Solution Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[94, 31], Operations: ['90+4=94', '80-49=31'] Exploring Operation: 94*31=2914, Resulting Numbers: [2914] 2914,89 unequal: No Solution Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 94+31=125, Resulting Numbers: [125] 125,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 89:[80, 143], Operations: ['90+4=94', '49+94=143'] Exploring Operation: 143-80=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 80+143=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 80*143=11440, Resulting Numbers: [11440] 11440,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[49, 14], Operations: ['90+4=94', '94-80=14'] Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,89 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 89:[90, 49, 76], Operations: ['80-4=76'] Exploring Operation: 76-49=27, Resulting Numbers: [90, 27] Generated Node #0,3,0: 89:[90, 27] Operation: 76-49=27 Exploring Operation: 49+76=125, Resulting Numbers: [90, 125] Generated Node #0,3,1: 89:[90, 125] Operation: 49+76=125 Exploring Operation: 90+49=139, Resulting Numbers: [76, 139] Generated Node #0,3,2: 89:[76, 139] Operation: 90+49=139 Exploring Operation: 90-49=41, Resulting Numbers: [76, 41] Generated Node #0,3,3: 89:[76, 41] Operation: 90-49=41 Exploring Operation: 90-76=14, Resulting Numbers: [49, 14] Generated Node #0,3,4: 89:[49, 14] Operation: 90-76=14 Moving to Node #0,3,1 Current State: 89:[90, 125], Operations: ['80-4=76', '49+76=125'] Exploring Operation: 90*125=11250, Resulting Numbers: [11250] 11250,89 unequal: No Solution Exploring Operation: 90+125=215, Resulting Numbers: [215] 215,89 unequal: No Solution Exploring Operation: 125-90=35, Resulting Numbers: [35] 35,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[86, 129], Operations: ['90-4=86', '80+49=129'] Exploring Operation: 86*129=11094, Resulting Numbers: [11094] 11094,89 unequal: No Solution Exploring Operation: 129-86=43, Resulting Numbers: [43] 43,89 unequal: No Solution Exploring Operation: 86+129=215, Resulting Numbers: [215] 215,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[90, 133], Operations: ['80+4=84', '49+84=133'] Exploring Operation: 133-90=43, Resulting Numbers: [43] 43,89 unequal: No Solution Exploring Operation: 90+133=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 90*133=11970, Resulting Numbers: [11970] 11970,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[84, 41], Operations: ['80+4=84', '90-49=41'] Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,89 unequal: No Solution Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,89 unequal: No Solution Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[80, 135], Operations: ['90-4=86', '49+86=135'] Exploring Operation: 80*135=10800, Resulting Numbers: [10800] 10800,89 unequal: No Solution Exploring Operation: 80+135=215, Resulting Numbers: [215] 215,89 unequal: No Solution Exploring Operation: 135-80=55, Resulting Numbers: [55] 55,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[90, 35], Operations: ['80+4=84', '84-49=35'] Exploring Operation: 90+35=125, Resulting Numbers: [125] 125,89 unequal: No Solution Exploring Operation: 90-35=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 90*35=3150, Resulting Numbers: [3150] 3150,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[84, 139], Operations: ['80+4=84', '90+49=139'] Exploring Operation: 84+139=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 84*139=11676, Resulting Numbers: [11676] 11676,89 unequal: No Solution Exploring Operation: 139-84=55, Resulting Numbers: [55] 55,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[76, 41], Operations: ['80-4=76', '90-49=41'] Exploring Operation: 76+41=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 76-41=35, Resulting Numbers: [35] 35,89 unequal: No Solution Exploring Operation: 76*41=3116, Resulting Numbers: [3116] 3116,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[80, 37], Operations: ['90-4=86', '86-49=37'] Exploring Operation: 80+37=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 80*37=2960, Resulting Numbers: [2960] 2960,89 unequal: No Solution Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[86, 31], Operations: ['90-4=86', '80-49=31'] Exploring Operation: 86*31=2666, Resulting Numbers: [2666] 2666,89 unequal: No Solution Exploring Operation: 86+31=117, Resulting Numbers: [117] 117,89 unequal: No Solution Exploring Operation: 86-31=55, Resulting Numbers: [55] 55,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[76, 139], Operations: ['80-4=76', '90+49=139'] Exploring Operation: 139-76=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 76*139=10564, Resulting Numbers: [10564] 10564,89 unequal: No Solution Exploring Operation: 76+139=215, Resulting Numbers: [215] 215,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[90, 27], Operations: ['80-4=76', '76-49=27'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 90*27=2430, Resulting Numbers: [2430] 2430,89 unequal: No Solution Exploring Operation: 90+27=117, Resulting Numbers: [117] 117,89 unequal: No Solution Moving to Node #0,3,4 Current State: 89:[49, 14], Operations: ['80-4=76', '90-76=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,89 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,89 unequal: No Solution Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[49, 166], Operations: ['90-4=86', '80+86=166'] Exploring Operation: 49+166=215, Resulting Numbers: [215] 215,89 unequal: No Solution Exploring Operation: 49*166=8134, Resulting Numbers: [8134] 8134,89 unequal: No Solution Exploring Operation: 166-49=117, Resulting Numbers: [117] 117,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[49, 6], Operations: ['80+4=84', '90-84=6'] Exploring Operation: 49*6=294, Resulting Numbers: [294] 294,89 unequal: No Solution Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,89 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 37, 41, 27, 61 ]
84
[ "41-37=4", "27+61=88", "88-4=84" ]
Current State: 84:[37, 41, 27, 61], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [27, 61, 4] Generated Node #2: [27, 61, 4] from Operation: 41-37=4 Current State: 84:[27, 61, 4], Operations: ['41-37=4'] Exploring Operation: 27+61=88, Resulting Numbers: [4, 88] Generated Node #3: [4, 88] from Operation: 27+61=88 Current State: 84:[4, 88], Operations: ['41-37=4', '27+61=88'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[37, 41, 27, 61], Operations: [] Exploring Operation: 61-37=24, Resulting Numbers: [41, 27, 24] Generated Node #0,0: 84:[41, 27, 24] Operation: 61-37=24 Moving to Node #0,0 Current State: 84:[41, 27, 24], Operations: ['61-37=24'] Exploring Operation: 27-24=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 84:[41, 3] Operation: 27-24=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[41, 3], Operations: ['61-37=24', '27-24=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 62, 33, 45, 27 ]
47
[ "62-33=29", "45-27=18", "29+18=47" ]
Current State: 47:[62, 33, 45, 27], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [45, 27, 29] Generated Node #2: [45, 27, 29] from Operation: 62-33=29 Current State: 47:[45, 27, 29], Operations: ['62-33=29'] Exploring Operation: 45-27=18, Resulting Numbers: [29, 18] Generated Node #3: [29, 18] from Operation: 45-27=18 Current State: 47:[29, 18], Operations: ['62-33=29', '45-27=18'] Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[62, 33, 45, 27], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [45, 27, 29] Generated Node #0,0: 47:[45, 27, 29] Operation: 62-33=29 Exploring Operation: 62-27=35, Resulting Numbers: [33, 45, 35] Generated Node #0,1: 47:[33, 45, 35] Operation: 62-27=35 Exploring Operation: 33+27=60, Resulting Numbers: [62, 45, 60] Generated Node #0,2: 47:[62, 45, 60] Operation: 33+27=60 Moving to Node #0,1 Current State: 47:[33, 45, 35], Operations: ['62-27=35'] Exploring Operation: 45-33=12, Resulting Numbers: [35, 12] Generated Node #0,1,0: 47:[35, 12] Operation: 45-33=12 Exploring Operation: 33+45=78, Resulting Numbers: [35, 78] Generated Node #0,1,1: 47:[35, 78] Operation: 33+45=78 Exploring Operation: 33+35=68, Resulting Numbers: [45, 68] Generated Node #0,1,2: 47:[45, 68] Operation: 33+35=68 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[45, 68], Operations: ['62-27=35', '33+35=68'] Exploring Operation: 45*68=3060, Resulting Numbers: [3060] 3060,47 unequal: No Solution Exploring Operation: 68-45=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 45+68=113, Resulting Numbers: [113] 113,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[35, 78], Operations: ['62-27=35', '33+45=78'] Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 35*78=2730, Resulting Numbers: [2730] 2730,47 unequal: No Solution Exploring Operation: 35+78=113, Resulting Numbers: [113] 113,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[35, 12], Operations: ['62-27=35', '45-33=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[62, 33, 45, 27], Operations: [] Exploring Operation: 62-27=35, Resulting Numbers: [33, 45, 35] Generated Node #0,1: 47:[33, 45, 35] Operation: 62-27=35 Moving to Node #0,1 Current State: 47:[33, 45, 35], Operations: ['62-27=35'] Exploring Operation: 45-33=12, Resulting Numbers: [35, 12] Generated Node #0,1,0: 47:[35, 12] Operation: 45-33=12 Moving to Node #0,1,0 Current State: 47:[35, 12], Operations: ['62-27=35', '45-33=12'] Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 24, 64, 79, 57 ]
66
[ "24+64=88", "79-57=22", "88-22=66" ]
Current State: 66:[24, 64, 79, 57], Operations: [] Exploring Operation: 24+64=88, Resulting Numbers: [79, 57, 88] Generated Node #2: [79, 57, 88] from Operation: 24+64=88 Current State: 66:[79, 57, 88], Operations: ['24+64=88'] Exploring Operation: 79-57=22, Resulting Numbers: [88, 22] Generated Node #3: [88, 22] from Operation: 79-57=22 Current State: 66:[88, 22], Operations: ['24+64=88', '79-57=22'] Exploring Operation: 88-22=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[24, 64, 79, 57], Operations: [] Exploring Operation: 79-57=22, Resulting Numbers: [24, 64, 22] Generated Node #0,0: 66:[24, 64, 22] Operation: 79-57=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[24, 64, 22], Operations: ['79-57=22'] Exploring Operation: 24-22=2, Resulting Numbers: [64, 2] Generated Node #0,0,0: 66:[64, 2] Operation: 24-22=2 Moving to Node #0,0,0 Current State: 66:[64, 2], Operations: ['79-57=22', '24-22=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[24, 64, 79, 57], Operations: [] Exploring Operation: 79-57=22, Resulting Numbers: [24, 64, 22] Generated Node #0,0: 66:[24, 64, 22] Operation: 79-57=22 Moving to Node #0,0 Current State: 66:[24, 64, 22], Operations: ['79-57=22'] Exploring Operation: 24-22=2, Resulting Numbers: [64, 2] Generated Node #0,0,0: 66:[64, 2] Operation: 24-22=2 Moving to Node #0,0,0 Current State: 66:[64, 2], Operations: ['79-57=22', '24-22=2'] Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 99, 23, 36, 4 ]
47
[ "36-23=13", "4*13=52", "99-52=47" ]
Current State: 47:[99, 23, 36, 4], Operations: [] Exploring Operation: 36-23=13, Resulting Numbers: [99, 4, 13] Generated Node #2: [99, 4, 13] from Operation: 36-23=13 Current State: 47:[99, 4, 13], Operations: ['36-23=13'] Exploring Operation: 4*13=52, Resulting Numbers: [99, 52] Generated Node #3: [99, 52] from Operation: 4*13=52 Current State: 47:[99, 52], Operations: ['36-23=13', '4*13=52'] Exploring Operation: 99-52=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[99, 23, 36, 4], Operations: [] Exploring Operation: 99-4=95, Resulting Numbers: [23, 36, 95] Generated Node #0,0: 47:[23, 36, 95] Operation: 99-4=95 Exploring Operation: 99-23=76, Resulting Numbers: [36, 4, 76] Generated Node #0,1: 47:[36, 4, 76] Operation: 99-23=76 Exploring Operation: 99-36=63, Resulting Numbers: [23, 4, 63] Generated Node #0,2: 47:[23, 4, 63] Operation: 99-36=63 Moving to Node #0,0 Current State: 47:[23, 36, 95], Operations: ['99-4=95'] Exploring Operation: 95-36=59, Resulting Numbers: [23, 59] Generated Node #0,0,0: 47:[23, 59] Operation: 95-36=59 Exploring Operation: 95-23=72, Resulting Numbers: [36, 72] Generated Node #0,0,1: 47:[36, 72] Operation: 95-23=72 Exploring Operation: 23+36=59, Resulting Numbers: [95, 59] Generated Node #0,0,2: 47:[95, 59] Operation: 23+36=59 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[23, 59], Operations: ['99-4=95', '95-36=59'] Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 23*59=1357, Resulting Numbers: [1357] 1357,47 unequal: No Solution Exploring Operation: 23+59=82, Resulting Numbers: [82] 82,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[36, 72], Operations: ['99-4=95', '95-23=72'] Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[95, 59], Operations: ['99-4=95', '23+36=59'] Exploring Operation: 95*59=5605, Resulting Numbers: [5605] 5605,47 unequal: No Solution Exploring Operation: 95+59=154, Resulting Numbers: [154] 154,47 unequal: No Solution Exploring Operation: 95-59=36, Resulting Numbers: [36] 36,47 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: 47:[36, 4, 76], Operations: ['99-23=76'] Exploring Operation: 76-4=72, Resulting Numbers: [36, 72] Generated Node #0,1,0: 47:[36, 72] Operation: 76-4=72 Exploring Operation: 76/4=19, Resulting Numbers: [36, 19] Generated Node #0,1,1: 47:[36, 19] Operation: 76/4=19 Exploring Operation: 36+4=40, Resulting Numbers: [76, 40] Generated Node #0,1,2: 47:[76, 40] Operation: 36+4=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[36, 72], Operations: ['99-23=76', '76-4=72'] Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[76, 40], Operations: ['99-23=76', '36+4=40'] Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,47 unequal: No Solution Exploring Operation: 76*40=3040, Resulting Numbers: [3040] 3040,47 unequal: No Solution Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[36, 19], Operations: ['99-23=76', '76/4=19'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,47 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,47 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: 47:[23, 4, 63], Operations: ['99-36=63'] Exploring Operation: 63-4=59, Resulting Numbers: [23, 59] Generated Node #0,2,0: 47:[23, 59] Operation: 63-4=59 Exploring Operation: 23-4=19, Resulting Numbers: [63, 19] Generated Node #0,2,1: 47:[63, 19] Operation: 23-4=19 Exploring Operation: 23+4=27, Resulting Numbers: [63, 27] Generated Node #0,2,2: 47:[63, 27] Operation: 23+4=27 Moving to Node #0,2,0 Current State: 47:[23, 59], Operations: ['99-36=63', '63-4=59'] Exploring Operation: 59-23=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 23+59=82, Resulting Numbers: [82] 82,47 unequal: No Solution Exploring Operation: 23*59=1357, Resulting Numbers: [1357] 1357,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[63, 27], Operations: ['99-36=63', '23+4=27'] Exploring Operation: 63+27=90, Resulting Numbers: [90] 90,47 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 63*27=1701, Resulting Numbers: [1701] 1701,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[63, 19], Operations: ['99-36=63', '23-4=19'] Exploring Operation: 63*19=1197, Resulting Numbers: [1197] 1197,47 unequal: No Solution Exploring Operation: 63+19=82, Resulting Numbers: [82] 82,47 unequal: No Solution Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,47 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 43, 41, 14, 25 ]
78
[ "43-41=2", "14+25=39", "2*39=78" ]
Current State: 78:[43, 41, 14, 25], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [14, 25, 2] Generated Node #2: [14, 25, 2] from Operation: 43-41=2 Current State: 78:[14, 25, 2], Operations: ['43-41=2'] Exploring Operation: 14+25=39, Resulting Numbers: [2, 39] Generated Node #3: [2, 39] from Operation: 14+25=39 Current State: 78:[2, 39], Operations: ['43-41=2', '14+25=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[43, 41, 14, 25], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [14, 25, 2] Generated Node #0,0: 78:[14, 25, 2] Operation: 43-41=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[14, 25, 2], Operations: ['43-41=2'] Exploring Operation: 14+25=39, Resulting Numbers: [2, 39] Generated Node #0,0,0: 78:[2, 39] Operation: 14+25=39 Moving to Node #0,0,0 Current State: 78:[2, 39], Operations: ['43-41=2', '14+25=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[43, 41, 14, 25], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [14, 25, 2] Generated Node #0,0: 78:[14, 25, 2] Operation: 43-41=2 Moving to Node #0,0 Current State: 78:[14, 25, 2], Operations: ['43-41=2'] Exploring Operation: 14+25=39, Resulting Numbers: [2, 39] Generated Node #0,0,0: 78:[2, 39] Operation: 14+25=39 Moving to Node #0,0,0 Current State: 78:[2, 39], Operations: ['43-41=2', '14+25=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 21, 5, 35, 31 ]
70
[ "31-21=10", "35/5=7", "10*7=70" ]
Current State: 70:[21, 5, 35, 31], Operations: [] Exploring Operation: 31-21=10, Resulting Numbers: [5, 35, 10] Generated Node #2: [5, 35, 10] from Operation: 31-21=10 Current State: 70:[5, 35, 10], Operations: ['31-21=10'] Exploring Operation: 35/5=7, Resulting Numbers: [10, 7] Generated Node #3: [10, 7] from Operation: 35/5=7 Current State: 70:[10, 7], Operations: ['31-21=10', '35/5=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[21, 5, 35, 31], Operations: [] Exploring Operation: 5+31=36, Resulting Numbers: [21, 35, 36] Generated Node #0,0: 70:[21, 35, 36] Operation: 5+31=36 Exploring Operation: 35-21=14, Resulting Numbers: [5, 31, 14] Generated Node #0,1: 70:[5, 31, 14] Operation: 35-21=14 Exploring Operation: 31-21=10, Resulting Numbers: [5, 35, 10] Generated Node #0,2: 70:[5, 35, 10] Operation: 31-21=10 Exploring Operation: 21-5=16, Resulting Numbers: [35, 31, 16] Generated Node #0,3: 70:[35, 31, 16] Operation: 21-5=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[5, 35, 10], Operations: ['31-21=10'] Exploring Operation: 10-5=5, Resulting Numbers: [35, 5] Generated Node #0,2,0: 70:[35, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [35, 2] Generated Node #0,2,1: 70:[35, 2] Operation: 10/5=2 Exploring Operation: 5+10=15, Resulting Numbers: [35, 15] Generated Node #0,2,2: 70:[35, 15] Operation: 5+10=15 Exploring Operation: 35/5=7, Resulting Numbers: [10, 7] Generated Node #0,2,3: 70:[10, 7] Operation: 35/5=7 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[35, 5], Operations: ['31-21=10', '10-5=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,70 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,70 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,70 unequal: No Solution No 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: 70:[35, 2], Operations: ['31-21=10', '10/5=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,70 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[21, 5, 35, 31], Operations: [] Exploring Operation: 31-21=10, Resulting Numbers: [5, 35, 10] Generated Node #0,2: 70:[5, 35, 10] Operation: 31-21=10 Moving to Node #0,2 Current State: 70:[5, 35, 10], Operations: ['31-21=10'] Exploring Operation: 10/5=2, Resulting Numbers: [35, 2] Generated Node #0,2,1: 70:[35, 2] Operation: 10/5=2 Moving to Node #0,2,1 Current State: 70:[35, 2], Operations: ['31-21=10', '10/5=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 29, 50, 95, 42 ]
47
[ "50+95=145", "145/29=5", "42+5=47" ]
Current State: 47:[29, 50, 95, 42], Operations: [] Exploring Operation: 50+95=145, Resulting Numbers: [29, 42, 145] Generated Node #2: [29, 42, 145] from Operation: 50+95=145 Current State: 47:[29, 42, 145], Operations: ['50+95=145'] Exploring Operation: 145/29=5, Resulting Numbers: [42, 5] Generated Node #3: [42, 5] from Operation: 145/29=5 Current State: 47:[42, 5], Operations: ['50+95=145', '145/29=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[29, 50, 95, 42], Operations: [] Exploring Operation: 95-29=66, Resulting Numbers: [50, 42, 66] Generated Node #0,0: 47:[50, 42, 66] Operation: 95-29=66 Exploring Operation: 95-50=45, Resulting Numbers: [29, 42, 45] Generated Node #0,1: 47:[29, 42, 45] Operation: 95-50=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[29, 42, 45], Operations: ['95-50=45'] Exploring Operation: 29+42=71, Resulting Numbers: [45, 71] Generated Node #0,1,0: 47:[45, 71] Operation: 29+42=71 Exploring Operation: 29+45=74, Resulting Numbers: [42, 74] Generated Node #0,1,1: 47:[42, 74] Operation: 29+45=74 Moving to Node #0,1,0 Current State: 47:[45, 71], Operations: ['95-50=45', '29+42=71'] Exploring Operation: 71-45=26, Resulting Numbers: [26] 26,47 unequal: No Solution Exploring Operation: 45+71=116, Resulting Numbers: [116] 116,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[42, 74], Operations: ['95-50=45', '29+45=74'] Exploring Operation: 42+74=116, Resulting Numbers: [116] 116,47 unequal: No Solution Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[50, 42, 66], Operations: ['95-29=66'] Exploring Operation: 66-50=16, Resulting Numbers: [42, 16] Generated Node #0,0,0: 47:[42, 16] Operation: 66-50=16 Exploring Operation: 66-42=24, Resulting Numbers: [50, 24] Generated Node #0,0,1: 47:[50, 24] Operation: 66-42=24 Moving to Node #0,0,1 Current State: 47:[50, 24], Operations: ['95-29=66', '66-42=24'] Exploring Operation: 50-24=26, Resulting Numbers: [26] 26,47 unequal: No Solution Exploring Operation: 50+24=74, Resulting Numbers: [74] 74,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[42, 16], Operations: ['95-29=66', '66-50=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,47 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,47 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
[ 52, 4, 77, 76 ]
56
[ "52+4=56", "77-76=1", "56*1=56" ]
Current State: 56:[52, 4, 77, 76], Operations: [] Exploring Operation: 52+4=56, Resulting Numbers: [77, 76, 56] Generated Node #2: [77, 76, 56] from Operation: 52+4=56 Current State: 56:[77, 76, 56], Operations: ['52+4=56'] Exploring Operation: 77-76=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 77-76=1 Current State: 56:[56, 1], Operations: ['52+4=56', '77-76=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[52, 4, 77, 76], Operations: [] Exploring Operation: 77-52=25, Resulting Numbers: [4, 76, 25] Generated Node #0,0: 56:[4, 76, 25] Operation: 77-52=25 Exploring Operation: 77-76=1, Resulting Numbers: [52, 4, 1] Generated Node #0,1: 56:[52, 4, 1] Operation: 77-76=1 Moving to Node #0,1 Current State: 56:[52, 4, 1], Operations: ['77-76=1'] Exploring Operation: 52+4=56, Resulting Numbers: [1, 56] Generated Node #0,1,0: 56:[1, 56] Operation: 52+4=56 Exploring Operation: 52/4=13, Resulting Numbers: [1, 13] Generated Node #0,1,1: 56:[1, 13] Operation: 52/4=13 Moving to Node #0,0 Current State: 56:[4, 76, 25], Operations: ['77-52=25'] Exploring Operation: 76/4=19, Resulting Numbers: [25, 19] Generated Node #0,0,0: 56:[25, 19] Operation: 76/4=19 Exploring Operation: 76-25=51, Resulting Numbers: [4, 51] Generated Node #0,0,1: 56:[4, 51] Operation: 76-25=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[4, 51], Operations: ['77-52=25', '76-25=51'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,56 unequal: No Solution Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[25, 19], Operations: ['77-52=25', '76/4=19'] Exploring Operation: 25+19=44, Resulting Numbers: [44] 44,56 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 56:[1, 56], Operations: ['77-76=1', '52+4=56'] Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[52, 4, 77, 76], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [52, 4, 1] Generated Node #0,1: 56:[52, 4, 1] Operation: 77-76=1 Moving to Node #0,1 Current State: 56:[52, 4, 1], Operations: ['77-76=1'] Exploring Operation: 52+4=56, Resulting Numbers: [1, 56] Generated Node #0,1,0: 56:[1, 56] Operation: 52+4=56 Moving to Node #0,1,0 Current State: 56:[1, 56], Operations: ['77-76=1', '52+4=56'] Exploring Operation: 1*56=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 4, 96, 70, 84 ]
67
[ "96-84=12", "12/4=3", "70-3=67" ]
Current State: 67:[4, 96, 70, 84], Operations: [] Exploring Operation: 96-84=12, Resulting Numbers: [4, 70, 12] Generated Node #2: [4, 70, 12] from Operation: 96-84=12 Current State: 67:[4, 70, 12], Operations: ['96-84=12'] Exploring Operation: 12/4=3, Resulting Numbers: [70, 3] Generated Node #3: [70, 3] from Operation: 12/4=3 Current State: 67:[70, 3], Operations: ['96-84=12', '12/4=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[4, 96, 70, 84], Operations: [] Exploring Operation: 96-4=92, Resulting Numbers: [70, 84, 92] Generated Node #0,0: 67:[70, 84, 92] Operation: 96-4=92 Exploring Operation: 84-4=80, Resulting Numbers: [96, 70, 80] Generated Node #0,1: 67:[96, 70, 80] Operation: 84-4=80 Exploring Operation: 70-4=66, Resulting Numbers: [96, 84, 66] Generated Node #0,2: 67:[96, 84, 66] Operation: 70-4=66 Exploring Operation: 4+96=100, Resulting Numbers: [70, 84, 100] Generated Node #0,3: 67:[70, 84, 100] Operation: 4+96=100 Moving to Node #0,0 Current State: 67:[70, 84, 92], Operations: ['96-4=92'] Exploring Operation: 70+84=154, Resulting Numbers: [92, 154] Generated Node #0,0,0: 67:[92, 154] Operation: 70+84=154 Exploring Operation: 92-70=22, Resulting Numbers: [84, 22] Generated Node #0,0,1: 67:[84, 22] Operation: 92-70=22 Exploring Operation: 92-84=8, Resulting Numbers: [70, 8] Generated Node #0,0,2: 67:[70, 8] Operation: 92-84=8 Exploring Operation: 84-70=14, Resulting Numbers: [92, 14] Generated Node #0,0,3: 67:[92, 14] Operation: 84-70=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[84, 22], Operations: ['96-4=92', '92-70=22'] Exploring Operation: 84*22=1848, Resulting Numbers: [1848] 1848,67 unequal: No Solution Exploring Operation: 84-22=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 84+22=106, Resulting Numbers: [106] 106,67 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 #0,0,2 Current State: 67:[70, 8], Operations: ['96-4=92', '92-84=8'] Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 70*8=560, Resulting Numbers: [560] 560,67 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,67 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 #0,0,3 Current State: 67:[92, 14], Operations: ['96-4=92', '84-70=14'] Exploring Operation: 92+14=106, Resulting Numbers: [106] 106,67 unequal: No Solution Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 92*14=1288, Resulting Numbers: [1288] 1288,67 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 #0,0,0 Current State: 67:[92, 154], Operations: ['96-4=92', '70+84=154'] Exploring Operation: 92+154=246, Resulting Numbers: [246] 246,67 unequal: No Solution Exploring Operation: 92*154=14168, Resulting Numbers: [14168] 14168,67 unequal: No Solution Exploring Operation: 154-92=62, Resulting Numbers: [62] 62,67 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: 67:[96, 70, 80], Operations: ['84-4=80'] Exploring Operation: 96-80=16, Resulting Numbers: [70, 16] Generated Node #0,1,0: 67:[70, 16] Operation: 96-80=16 Exploring Operation: 96+70=166, Resulting Numbers: [80, 166] Generated Node #0,1,1: 67:[80, 166] Operation: 96+70=166 Exploring Operation: 80-70=10, Resulting Numbers: [96, 10] Generated Node #0,1,2: 67:[96, 10] Operation: 80-70=10 Exploring Operation: 96-70=26, Resulting Numbers: [80, 26] Generated Node #0,1,3: 67:[80, 26] Operation: 96-70=26 Moving to Node #0,2 Current State: 67:[96, 84, 66], Operations: ['70-4=66'] Exploring Operation: 96-84=12, Resulting Numbers: [66, 12] Generated Node #0,2,0: 67:[66, 12] Operation: 96-84=12 Exploring Operation: 84-66=18, Resulting Numbers: [96, 18] Generated Node #0,2,1: 67:[96, 18] Operation: 84-66=18 Exploring Operation: 96+66=162, Resulting Numbers: [84, 162] Generated Node #0,2,2: 67:[84, 162] Operation: 96+66=162 Exploring Operation: 96-66=30, Resulting Numbers: [84, 30] Generated Node #0,2,3: 67:[84, 30] Operation: 96-66=30 Moving to Node #0,3 Current State: 67:[70, 84, 100], Operations: ['4+96=100'] Exploring Operation: 84-70=14, Resulting Numbers: [100, 14] Generated Node #0,3,0: 67:[100, 14] Operation: 84-70=14 Exploring Operation: 100-84=16, Resulting Numbers: [70, 16] Generated Node #0,3,1: 67:[70, 16] Operation: 100-84=16 Exploring Operation: 70+84=154, Resulting Numbers: [100, 154] Generated Node #0,3,2: 67:[100, 154] Operation: 70+84=154 Exploring Operation: 100-70=30, Resulting Numbers: [84, 30] Generated Node #0,3,3: 67:[84, 30] Operation: 100-70=30 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[70, 16], Operations: ['4+96=100', '100-84=16'] Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 70*16=1120, Resulting Numbers: [1120] 1120,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 67:[84, 30], Operations: ['4+96=100', '100-70=30'] Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[100, 14], Operations: ['4+96=100', '84-70=14'] Exploring Operation: 100*14=1400, Resulting Numbers: [1400] 1400,67 unequal: No Solution Exploring Operation: 100-14=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 100+14=114, Resulting Numbers: [114] 114,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 67:[100, 154], Operations: ['4+96=100', '70+84=154'] Exploring Operation: 100*154=15400, Resulting Numbers: [15400] 15400,67 unequal: No Solution Exploring Operation: 100+154=254, Resulting Numbers: [254] 254,67 unequal: No Solution Exploring Operation: 154-100=54, Resulting Numbers: [54] 54,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 67:[70, 16], Operations: ['84-4=80', '96-80=16'] Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 70*16=1120, Resulting Numbers: [1120] 1120,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[80, 26], Operations: ['84-4=80', '96-70=26'] Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 80*26=2080, Resulting Numbers: [2080] 2080,67 unequal: No Solution Exploring Operation: 80+26=106, Resulting Numbers: [106] 106,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[84, 30], Operations: ['70-4=66', '96-66=30'] Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,67 unequal: No Solution Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[66, 12], Operations: ['70-4=66', '96-84=12'] Exploring Operation: 66-12=54, Resulting Numbers: [54] 54,67 unequal: No Solution Exploring Operation: 66*12=792, Resulting Numbers: [792] 792,67 unequal: No Solution Exploring Operation: 66+12=78, Resulting Numbers: [78] 78,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[96, 18], Operations: ['70-4=66', '84-66=18'] Exploring Operation: 96*18=1728, Resulting Numbers: [1728] 1728,67 unequal: No Solution Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 96+18=114, Resulting Numbers: [114] 114,67 unequal: No Solution Moving to Node #0,1,2 Current State: 67:[96, 10], Operations: ['84-4=80', '80-70=10'] Exploring Operation: 96*10=960, Resulting Numbers: [960] 960,67 unequal: No Solution Exploring Operation: 96+10=106, Resulting Numbers: [106] 106,67 unequal: No Solution Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[80, 166], Operations: ['84-4=80', '96+70=166'] Exploring Operation: 80+166=246, Resulting Numbers: [246] 246,67 unequal: No Solution Exploring Operation: 166-80=86, Resulting Numbers: [86] 86,67 unequal: No Solution Exploring Operation: 80*166=13280, Resulting Numbers: [13280] 13280,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[84, 162], Operations: ['70-4=66', '96+66=162'] Exploring Operation: 162-84=78, Resulting Numbers: [78] 78,67 unequal: No Solution Exploring Operation: 84+162=246, Resulting Numbers: [246] 246,67 unequal: No Solution Exploring Operation: 84*162=13608, Resulting Numbers: [13608] 13608,67 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 55, 91, 92, 81 ]
27
[ "55+91=146", "92+81=173", "173-146=27" ]
Current State: 27:[55, 91, 92, 81], Operations: [] Exploring Operation: 55+91=146, Resulting Numbers: [92, 81, 146] Generated Node #2: [92, 81, 146] from Operation: 55+91=146 Current State: 27:[92, 81, 146], Operations: ['55+91=146'] Exploring Operation: 92+81=173, Resulting Numbers: [146, 173] Generated Node #3: [146, 173] from Operation: 92+81=173 Current State: 27:[146, 173], Operations: ['55+91=146', '92+81=173'] Exploring Operation: 173-146=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[55, 91, 92, 81], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [55, 91, 11] Generated Node #0,0: 27:[55, 91, 11] Operation: 92-81=11 Exploring Operation: 92-91=1, Resulting Numbers: [55, 81, 1] Generated Node #0,1: 27:[55, 81, 1] Operation: 92-91=1 Exploring Operation: 91-81=10, Resulting Numbers: [55, 92, 10] Generated Node #0,2: 27:[55, 92, 10] Operation: 91-81=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[55, 81, 1], Operations: ['92-91=1'] Exploring Operation: 81-55=26, Resulting Numbers: [1, 26] Generated Node #0,1,0: 27:[1, 26] Operation: 81-55=26 Exploring Operation: 81-1=80, Resulting Numbers: [55, 80] Generated Node #0,1,1: 27:[55, 80] Operation: 81-1=80 Exploring Operation: 55-1=54, Resulting Numbers: [81, 54] Generated Node #0,1,2: 27:[81, 54] Operation: 55-1=54 Moving to Node #0,1,0 Current State: 27:[1, 26], Operations: ['92-91=1', '81-55=26'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[55, 91, 92, 81], Operations: [] Exploring Operation: 92-91=1, Resulting Numbers: [55, 81, 1] Generated Node #0,1: 27:[55, 81, 1] Operation: 92-91=1 Moving to Node #0,1 Current State: 27:[55, 81, 1], Operations: ['92-91=1'] Exploring Operation: 81-55=26, Resulting Numbers: [1, 26] Generated Node #0,1,0: 27:[1, 26] Operation: 81-55=26 Moving to Node #0,1,0 Current State: 27:[1, 26], Operations: ['92-91=1', '81-55=26'] Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 2, 4, 73, 13 ]
91
[ "13-4=9", "2*9=18", "73+18=91" ]
Current State: 91:[2, 4, 73, 13], Operations: [] Exploring Operation: 13-4=9, Resulting Numbers: [2, 73, 9] Generated Node #2: [2, 73, 9] from Operation: 13-4=9 Current State: 91:[2, 73, 9], Operations: ['13-4=9'] Exploring Operation: 2*9=18, Resulting Numbers: [73, 18] Generated Node #3: [73, 18] from Operation: 2*9=18 Current State: 91:[73, 18], Operations: ['13-4=9', '2*9=18'] Exploring Operation: 73+18=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[2, 4, 73, 13], Operations: [] Exploring Operation: 73+13=86, Resulting Numbers: [2, 4, 86] Generated Node #0,0: 91:[2, 4, 86] Operation: 73+13=86 Exploring Operation: 2*4=8, Resulting Numbers: [73, 13, 8] Generated Node #0,1: 91:[73, 13, 8] Operation: 2*4=8 Exploring Operation: 2+4=6, Resulting Numbers: [73, 13, 6] Generated Node #0,2: 91:[73, 13, 6] Operation: 2+4=6 Moving to Node #0,0 Current State: 91:[2, 4, 86], Operations: ['73+13=86'] Exploring Operation: 2+4=6, Resulting Numbers: [86, 6] Generated Node #0,0,0: 91:[86, 6] Operation: 2+4=6 Exploring Operation: 2*4=8, Resulting Numbers: [86, 8] Generated Node #0,0,1: 91:[86, 8] Operation: 2*4=8 Exploring Operation: 2+86=88, Resulting Numbers: [4, 88] Generated Node #0,0,2: 91:[4, 88] Operation: 2+86=88 Moving to Node #0,1 Current State: 91:[73, 13, 8], Operations: ['2*4=8'] Exploring Operation: 13-8=5, Resulting Numbers: [73, 5] Generated Node #0,1,0: 91:[73, 5] Operation: 13-8=5 Exploring Operation: 73+13=86, Resulting Numbers: [8, 86] Generated Node #0,1,1: 91:[8, 86] Operation: 73+13=86 Exploring Operation: 73+8=81, Resulting Numbers: [13, 81] Generated Node #0,1,2: 91:[13, 81] Operation: 73+8=81 Moving to Node #0,2 Current State: 91:[73, 13, 6], Operations: ['2+4=6'] Exploring Operation: 13-6=7, Resulting Numbers: [73, 7] Generated Node #0,2,0: 91:[73, 7] Operation: 13-6=7 Exploring Operation: 73+6=79, Resulting Numbers: [13, 79] Generated Node #0,2,1: 91:[13, 79] Operation: 73+6=79 Exploring Operation: 73+13=86, Resulting Numbers: [6, 86] Generated Node #0,2,2: 91:[6, 86] Operation: 73+13=86 Moving to Node #0,0,0 Current State: 91:[86, 6], Operations: ['73+13=86', '2+4=6'] Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,91 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[4, 88], Operations: ['73+13=86', '2+86=88'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,91 unequal: No Solution Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[6, 86], Operations: ['2+4=6', '73+13=86'] Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,91 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[86, 8], Operations: ['73+13=86', '2*4=8'] Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,91 unequal: No Solution Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,91 unequal: No Solution Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[8, 86], Operations: ['2*4=8', '73+13=86'] Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,91 unequal: No Solution Exploring Operation: 8*86=688, Resulting Numbers: [688] 688,91 unequal: No Solution Exploring Operation: 8+86=94, Resulting Numbers: [94] 94,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[13, 81], Operations: ['2*4=8', '73+8=81'] Exploring Operation: 13+81=94, Resulting Numbers: [94] 94,91 unequal: No Solution Exploring Operation: 13*81=1053, Resulting Numbers: [1053] 1053,91 unequal: No Solution Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[13, 79], Operations: ['2+4=6', '73+6=79'] Exploring Operation: 13*79=1027, Resulting Numbers: [1027] 1027,91 unequal: No Solution Exploring Operation: 79-13=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 13+79=92, Resulting Numbers: [92] 92,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[73, 7], Operations: ['2+4=6', '13-6=7'] Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,91 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,91 unequal: No Solution Exploring Operation: 73*7=511, Resulting Numbers: [511] 511,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[73, 5], Operations: ['2*4=8', '13-8=5'] Exploring Operation: 73*5=365, Resulting Numbers: [365] 365,91 unequal: No Solution Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,91 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,91 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 7, 50, 17, 4 ]
46
[ "7+17=24", "4*24=96", "96-50=46" ]
Current State: 46:[7, 50, 17, 4], Operations: [] Exploring Operation: 7+17=24, Resulting Numbers: [50, 4, 24] Generated Node #2: [50, 4, 24] from Operation: 7+17=24 Current State: 46:[50, 4, 24], Operations: ['7+17=24'] Exploring Operation: 4*24=96, Resulting Numbers: [50, 96] Generated Node #3: [50, 96] from Operation: 4*24=96 Current State: 46:[50, 96], Operations: ['7+17=24', '4*24=96'] Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[7, 50, 17, 4], Operations: [] Exploring Operation: 17+4=21, Resulting Numbers: [7, 50, 21] Generated Node #0,0: 46:[7, 50, 21] Operation: 17+4=21 Exploring Operation: 50-7=43, Resulting Numbers: [17, 4, 43] Generated Node #0,1: 46:[17, 4, 43] Operation: 50-7=43 Exploring Operation: 7-4=3, Resulting Numbers: [50, 17, 3] Generated Node #0,2: 46:[50, 17, 3] Operation: 7-4=3 Exploring Operation: 50-4=46, Resulting Numbers: [7, 17, 46] Generated Node #0,3: 46:[7, 17, 46] Operation: 50-4=46 Exploring Operation: 7+17=24, Resulting Numbers: [50, 4, 24] Generated Node #0,4: 46:[50, 4, 24] Operation: 7+17=24 Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[50, 4, 24], Operations: ['7+17=24'] Exploring Operation: 24-4=20, Resulting Numbers: [50, 20] Generated Node #0,4,0: 46:[50, 20] Operation: 24-4=20 Exploring Operation: 50-4=46, Resulting Numbers: [24, 46] Generated Node #0,4,1: 46:[24, 46] Operation: 50-4=46 Exploring Operation: 50+4=54, Resulting Numbers: [24, 54] Generated Node #0,4,2: 46:[24, 54] Operation: 50+4=54 Exploring Operation: 50-24=26, Resulting Numbers: [4, 26] Generated Node #0,4,3: 46:[4, 26] Operation: 50-24=26 Exploring Operation: 24/4=6, Resulting Numbers: [50, 6] Generated Node #0,4,4: 46:[50, 6] Operation: 24/4=6 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 46:[24, 46], Operations: ['7+17=24', '50-4=46'] Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 24*46=1104, Resulting Numbers: [1104] 1104,46 unequal: No Solution Exploring Operation: 24+46=70, Resulting Numbers: [70] 70,46 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 #0,4,3 Current State: 46:[4, 26], Operations: ['7+17=24', '50-24=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,46 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,46 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 #0,4,0 Current State: 46:[50, 20], Operations: ['7+17=24', '24-4=20'] Exploring Operation: 50+20=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 50*20=1000, Resulting Numbers: [1000] 1000,46 unequal: No Solution Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,46 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 #0,4,4 Current State: 46:[50, 6], Operations: ['7+17=24', '24/4=6'] Exploring Operation: 50*6=300, Resulting Numbers: [300] 300,46 unequal: No Solution Exploring Operation: 50-6=44, Resulting Numbers: [44] 44,46 unequal: No Solution Exploring Operation: 50+6=56, Resulting Numbers: [56] 56,46 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 #0,4,2 Current State: 46:[24, 54], Operations: ['7+17=24', '50+4=54'] Exploring Operation: 24+54=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 24*54=1296, Resulting Numbers: [1296] 1296,46 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 #0,0 Current State: 46:[7, 50, 21], Operations: ['17+4=21'] Exploring Operation: 50-21=29, Resulting Numbers: [7, 29] Generated Node #0,0,0: 46:[7, 29] Operation: 50-21=29 Exploring Operation: 7+21=28, Resulting Numbers: [50, 28] Generated Node #0,0,1: 46:[50, 28] Operation: 7+21=28 Exploring Operation: 7+50=57, Resulting Numbers: [21, 57] Generated Node #0,0,2: 46:[21, 57] Operation: 7+50=57 Exploring Operation: 50-7=43, Resulting Numbers: [21, 43] Generated Node #0,0,3: 46:[21, 43] Operation: 50-7=43 Exploring Operation: 21/7=3, Resulting Numbers: [50, 3] Generated Node #0,0,4: 46:[50, 3] Operation: 21/7=3 Moving to Node #0,0,3 Current State: 46:[21, 43], Operations: ['17+4=21', '50-7=43'] Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,46 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[50, 3], Operations: ['17+4=21', '21/7=3'] Exploring Operation: 50*3=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[50, 28], Operations: ['17+4=21', '7+21=28'] Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 50+28=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 50*28=1400, Resulting Numbers: [1400] 1400,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[7, 29], Operations: ['17+4=21', '50-21=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[21, 57], Operations: ['17+4=21', '7+50=57'] Exploring Operation: 21+57=78, Resulting Numbers: [78] 78,46 unequal: No Solution Exploring Operation: 57-21=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 21*57=1197, Resulting Numbers: [1197] 1197,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[17, 4, 43], Operations: ['50-7=43'] Exploring Operation: 17+4=21, Resulting Numbers: [43, 21] Generated Node #0,1,0: 46:[43, 21] Operation: 17+4=21 Exploring Operation: 43-17=26, Resulting Numbers: [4, 26] Generated Node #0,1,1: 46:[4, 26] Operation: 43-17=26 Exploring Operation: 4+43=47, Resulting Numbers: [17, 47] Generated Node #0,1,2: 46:[17, 47] Operation: 4+43=47 Exploring Operation: 17-4=13, Resulting Numbers: [43, 13] Generated Node #0,1,3: 46:[43, 13] Operation: 17-4=13 Exploring Operation: 43-4=39, Resulting Numbers: [17, 39] Generated Node #0,1,4: 46:[17, 39] Operation: 43-4=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[43, 21], Operations: ['50-7=43', '17+4=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,46 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 46:[4, 26], Operations: ['50-7=43', '43-17=26'] Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,46 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[17, 47], Operations: ['50-7=43', '4+43=47'] Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,46 unequal: No Solution Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[43, 13], Operations: ['50-7=43', '17-4=13'] Exploring Operation: 43*13=559, Resulting Numbers: [559] 559,46 unequal: No Solution Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,46 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 46:[17, 39], Operations: ['50-7=43', '43-4=39'] Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 17*39=663, Resulting Numbers: [663] 663,46 unequal: No Solution Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[50, 17, 3], Operations: ['7-4=3'] Exploring Operation: 17*3=51, Resulting Numbers: [50, 51] Generated Node #0,2,0: 46:[50, 51] Operation: 17*3=51 Exploring Operation: 50-3=47, Resulting Numbers: [17, 47] Generated Node #0,2,1: 46:[17, 47] Operation: 50-3=47 Exploring Operation: 50-17=33, Resulting Numbers: [3, 33] Generated Node #0,2,2: 46:[3, 33] Operation: 50-17=33 Exploring Operation: 50+3=53, Resulting Numbers: [17, 53] Generated Node #0,2,3: 46:[17, 53] Operation: 50+3=53 Exploring Operation: 17+3=20, Resulting Numbers: [50, 20] Generated Node #0,2,4: 46:[50, 20] Operation: 17+3=20 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[17, 47], Operations: ['7-4=3', '50-3=47'] Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 46:[50, 20], Operations: ['7-4=3', '17+3=20'] Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 50+20=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 50*20=1000, Resulting Numbers: [1000] 1000,46 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:[50, 51], Operations: ['7-4=3', '17*3=51'] Exploring Operation: 50+51=101, Resulting Numbers: [101] 101,46 unequal: No Solution Exploring Operation: 50*51=2550, Resulting Numbers: [2550] 2550,46 unequal: No Solution Exploring Operation: 51-50=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[3, 33], Operations: ['7-4=3', '50-17=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 3+33=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 46:[17, 53], Operations: ['7-4=3', '50+3=53'] Exploring Operation: 17*53=901, Resulting Numbers: [901] 901,46 unequal: No Solution Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 17+53=70, Resulting Numbers: [70] 70,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[7, 17, 46], Operations: ['50-4=46'] Exploring Operation: 17-7=10, Resulting Numbers: [46, 10] Generated Node #0,3,0: 46:[46, 10] Operation: 17-7=10 Exploring Operation: 46-7=39, Resulting Numbers: [17, 39] Generated Node #0,3,1: 46:[17, 39] Operation: 46-7=39 Exploring Operation: 7+46=53, Resulting Numbers: [17, 53] Generated Node #0,3,2: 46:[17, 53] Operation: 7+46=53 Exploring Operation: 46-17=29, Resulting Numbers: [7, 29] Generated Node #0,3,3: 46:[7, 29] Operation: 46-17=29 Exploring Operation: 7+17=24, Resulting Numbers: [46, 24] Generated Node #0,3,4: 46:[46, 24] Operation: 7+17=24 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 46:[46, 24], Operations: ['50-4=46', '7+17=24'] Exploring Operation: 46-24=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 46+24=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 46*24=1104, Resulting Numbers: [1104] 1104,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 46:[46, 10], Operations: ['50-4=46', '17-7=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,46 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 46:[7, 29], Operations: ['50-4=46', '46-17=29'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,46 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 46:[17, 39], Operations: ['50-4=46', '46-7=39'] Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 17*39=663, Resulting Numbers: [663] 663,46 unequal: No Solution Exploring Operation: 17+39=56, Resulting Numbers: [56] 56,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 46:[17, 53], Operations: ['50-4=46', '7+46=53'] Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 17+53=70, Resulting Numbers: [70] 70,46 unequal: No Solution Exploring Operation: 17*53=901, Resulting Numbers: [901] 901,46 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 No solution found.
0
hs_5
mult_heuristic
[ 99, 30, 78, 11 ]
12
[ "99/11=9", "30+78=108", "108/9=12" ]
Current State: 12:[99, 30, 78, 11], Operations: [] Exploring Operation: 99/11=9, Resulting Numbers: [30, 78, 9] Generated Node #2: [30, 78, 9] from Operation: 99/11=9 Current State: 12:[30, 78, 9], Operations: ['99/11=9'] Exploring Operation: 30+78=108, Resulting Numbers: [9, 108] Generated Node #3: [9, 108] from Operation: 30+78=108 Current State: 12:[9, 108], Operations: ['99/11=9', '30+78=108'] Exploring Operation: 108/9=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[99, 30, 78, 11], Operations: [] Exploring Operation: 78-30=48, Resulting Numbers: [99, 11, 48] Generated Node #0,0: 12:[99, 11, 48] Operation: 78-30=48 Exploring Operation: 99-30=69, Resulting Numbers: [78, 11, 69] Generated Node #0,1: 12:[78, 11, 69] Operation: 99-30=69 Exploring Operation: 99-11=88, Resulting Numbers: [30, 78, 88] Generated Node #0,2: 12:[30, 78, 88] Operation: 99-11=88 Exploring Operation: 99/11=9, Resulting Numbers: [30, 78, 9] Generated Node #0,3: 12:[30, 78, 9] Operation: 99/11=9 Exploring Operation: 99-78=21, Resulting Numbers: [30, 11, 21] Generated Node #0,4: 12:[30, 11, 21] Operation: 99-78=21 Moving to Node #0,4 Current State: 12:[30, 11, 21], Operations: ['99-78=21'] Exploring Operation: 11+21=32, Resulting Numbers: [30, 32] Generated Node #0,4,0: 12:[30, 32] Operation: 11+21=32 Exploring Operation: 30-21=9, Resulting Numbers: [11, 9] Generated Node #0,4,1: 12:[11, 9] Operation: 30-21=9 Exploring Operation: 30+11=41, Resulting Numbers: [21, 41] Generated Node #0,4,2: 12:[21, 41] Operation: 30+11=41 Exploring Operation: 21-11=10, Resulting Numbers: [30, 10] Generated Node #0,4,3: 12:[30, 10] Operation: 21-11=10 Exploring Operation: 30-11=19, Resulting Numbers: [21, 19] Generated Node #0,4,4: 12:[21, 19] Operation: 30-11=19 Moving to Node #0,3 Current State: 12:[30, 78, 9], Operations: ['99/11=9'] Exploring Operation: 78-30=48, Resulting Numbers: [9, 48] Generated Node #0,3,0: 12:[9, 48] Operation: 78-30=48 Exploring Operation: 78+9=87, Resulting Numbers: [30, 87] Generated Node #0,3,1: 12:[30, 87] Operation: 78+9=87 Exploring Operation: 30-9=21, Resulting Numbers: [78, 21] Generated Node #0,3,2: 12:[78, 21] Operation: 30-9=21 Exploring Operation: 78-9=69, Resulting Numbers: [30, 69] Generated Node #0,3,3: 12:[30, 69] Operation: 78-9=69 Exploring Operation: 30+9=39, Resulting Numbers: [78, 39] Generated Node #0,3,4: 12:[78, 39] Operation: 30+9=39 Moving to Node #0,0 Current State: 12:[99, 11, 48], Operations: ['78-30=48'] Exploring Operation: 99+11=110, Resulting Numbers: [48, 110] Generated Node #0,0,0: 12:[48, 110] Operation: 99+11=110 Exploring Operation: 99-48=51, Resulting Numbers: [11, 51] Generated Node #0,0,1: 12:[11, 51] Operation: 99-48=51 Exploring Operation: 48-11=37, Resulting Numbers: [99, 37] Generated Node #0,0,2: 12:[99, 37] Operation: 48-11=37 Exploring Operation: 99/11=9, Resulting Numbers: [48, 9] Generated Node #0,0,3: 12:[48, 9] Operation: 99/11=9 Exploring Operation: 99-11=88, Resulting Numbers: [48, 88] Generated Node #0,0,4: 12:[48, 88] Operation: 99-11=88 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 12:[48, 9], Operations: ['78-30=48', '99/11=9'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[11, 51], Operations: ['78-30=48', '99-48=51'] Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,12 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[99, 37], Operations: ['78-30=48', '48-11=37'] Exploring Operation: 99+37=136, Resulting Numbers: [136] 136,12 unequal: No Solution Exploring Operation: 99*37=3663, Resulting Numbers: [3663] 3663,12 unequal: No Solution Exploring Operation: 99-37=62, Resulting Numbers: [62] 62,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 12:[48, 88], Operations: ['78-30=48', '99-11=88'] Exploring Operation: 48*88=4224, Resulting Numbers: [4224] 4224,12 unequal: No Solution Exploring Operation: 48+88=136, Resulting Numbers: [136] 136,12 unequal: No Solution Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[48, 110], Operations: ['78-30=48', '99+11=110'] Exploring Operation: 48+110=158, Resulting Numbers: [158] 158,12 unequal: No Solution Exploring Operation: 48*110=5280, Resulting Numbers: [5280] 5280,12 unequal: No Solution Exploring Operation: 110-48=62, Resulting Numbers: [62] 62,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 12:[78, 11, 69], Operations: ['99-30=69'] Exploring Operation: 78+11=89, Resulting Numbers: [69, 89] Generated Node #0,1,0: 12:[69, 89] Operation: 78+11=89 Exploring Operation: 69-11=58, Resulting Numbers: [78, 58] Generated Node #0,1,1: 12:[78, 58] Operation: 69-11=58 Exploring Operation: 78-11=67, Resulting Numbers: [69, 67] Generated Node #0,1,2: 12:[69, 67] Operation: 78-11=67 Exploring Operation: 11+69=80, Resulting Numbers: [78, 80] Generated Node #0,1,3: 12:[78, 80] Operation: 11+69=80 Exploring Operation: 78-69=9, Resulting Numbers: [11, 9] Generated Node #0,1,4: 12:[11, 9] Operation: 78-69=9 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 12:[11, 9], Operations: ['99-30=69', '78-69=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[78, 58], Operations: ['99-30=69', '69-11=58'] Exploring Operation: 78-58=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 78*58=4524, Resulting Numbers: [4524] 4524,12 unequal: No Solution Exploring Operation: 78+58=136, Resulting Numbers: [136] 136,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[69, 67], Operations: ['99-30=69', '78-11=67'] Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,12 unequal: No Solution Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[69, 89], Operations: ['99-30=69', '78+11=89'] Exploring Operation: 89-69=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 69+89=158, Resulting Numbers: [158] 158,12 unequal: No Solution Exploring Operation: 69*89=6141, Resulting Numbers: [6141] 6141,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 12:[78, 80], Operations: ['99-30=69', '11+69=80'] Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 78*80=6240, Resulting Numbers: [6240] 6240,12 unequal: No Solution Exploring Operation: 78+80=158, Resulting Numbers: [158] 158,12 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: 12:[30, 78, 88], Operations: ['99-11=88'] Exploring Operation: 30+88=118, Resulting Numbers: [78, 118] Generated Node #0,2,0: 12:[78, 118] Operation: 30+88=118 Exploring Operation: 30+78=108, Resulting Numbers: [88, 108] Generated Node #0,2,1: 12:[88, 108] Operation: 30+78=108 Exploring Operation: 78-30=48, Resulting Numbers: [88, 48] Generated Node #0,2,2: 12:[88, 48] Operation: 78-30=48 Exploring Operation: 88-78=10, Resulting Numbers: [30, 10] Generated Node #0,2,3: 12:[30, 10] Operation: 88-78=10 Exploring Operation: 88-30=58, Resulting Numbers: [78, 58] Generated Node #0,2,4: 12:[78, 58] Operation: 88-30=58 Moving to Node #0,4,1 Current State: 12:[11, 9], Operations: ['99-78=21', '30-21=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,12 unequal: No Solution Exploring Operation: 11+9=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,12 unequal: No Solution Moving to Node #0,4,4 Current State: 12:[21, 19], Operations: ['99-78=21', '30-11=19'] Exploring Operation: 21+19=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 21*19=399, Resulting Numbers: [399] 399,12 unequal: No Solution Moving to Node #0,4,3 Current State: 12:[30, 10], Operations: ['99-78=21', '21-11=10'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,12 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[30, 10], Operations: ['99-11=88', '88-78=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 30*10=300, Resulting Numbers: [300] 300,12 unequal: No Solution Moving to Node #0,4,2 Current State: 12:[21, 41], Operations: ['99-78=21', '30+11=41'] Exploring Operation: 21*41=861, Resulting Numbers: [861] 861,12 unequal: No Solution Exploring Operation: 21+41=62, Resulting Numbers: [62] 62,12 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,4,0 Current State: 12:[30, 32], Operations: ['99-78=21', '11+21=32'] Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,12 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,12 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[9, 48], Operations: ['99/11=9', '78-30=48'] Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,12 unequal: No Solution Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[78, 21], Operations: ['99/11=9', '30-9=21'] Exploring Operation: 78*21=1638, Resulting Numbers: [1638] 1638,12 unequal: No Solution Exploring Operation: 78-21=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 78+21=99, Resulting Numbers: [99] 99,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[30, 69], Operations: ['99/11=9', '78-9=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,12 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[78, 39], Operations: ['99/11=9', '30+9=39'] Exploring Operation: 78*39=3042, Resulting Numbers: [3042] 3042,12 unequal: No Solution Exploring Operation: 78+39=117, Resulting Numbers: [117] 117,12 unequal: No Solution Exploring Operation: 78-39=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 78/39=2, Resulting Numbers: [2] 2,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[30, 87], Operations: ['99/11=9', '78+9=87'] Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 30+87=117, Resulting Numbers: [117] 117,12 unequal: No Solution Exploring Operation: 30*87=2610, Resulting Numbers: [2610] 2610,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[78, 58], Operations: ['99-11=88', '88-30=58'] Exploring Operation: 78*58=4524, Resulting Numbers: [4524] 4524,12 unequal: No Solution Exploring Operation: 78+58=136, Resulting Numbers: [136] 136,12 unequal: No Solution Exploring Operation: 78-58=20, Resulting Numbers: [20] 20,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[88, 48], Operations: ['99-11=88', '78-30=48'] Exploring Operation: 88+48=136, Resulting Numbers: [136] 136,12 unequal: No Solution Exploring Operation: 88*48=4224, Resulting Numbers: [4224] 4224,12 unequal: No Solution Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[78, 118], Operations: ['99-11=88', '30+88=118'] Exploring Operation: 78+118=196, Resulting Numbers: [196] 196,12 unequal: No Solution Exploring Operation: 118-78=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 78*118=9204, Resulting Numbers: [9204] 9204,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[88, 108], Operations: ['99-11=88', '30+78=108'] Exploring Operation: 88+108=196, Resulting Numbers: [196] 196,12 unequal: No Solution Exploring Operation: 108-88=20, Resulting Numbers: [20] 20,12 unequal: No Solution Exploring Operation: 88*108=9504, Resulting Numbers: [9504] 9504,12 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 90, 86, 84, 80 ]
69
[ "86-80=6", "90/6=15", "84-15=69" ]
Current State: 69:[90, 86, 84, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [90, 84, 6] Generated Node #2: [90, 84, 6] from Operation: 86-80=6 Current State: 69:[90, 84, 6], Operations: ['86-80=6'] Exploring Operation: 90/6=15, Resulting Numbers: [84, 15] Generated Node #3: [84, 15] from Operation: 90/6=15 Current State: 69:[84, 15], Operations: ['86-80=6', '90/6=15'] Exploring Operation: 84-15=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[90, 86, 84, 80], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [84, 80, 4] Generated Node #0,0: 69:[84, 80, 4] Operation: 90-86=4 Moving to Node #0,0 Current State: 69:[84, 80, 4], Operations: ['90-86=4'] Exploring Operation: 84-80=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 69:[4, 4] Operation: 84-80=4 Moving to Node #0,0,0 Current State: 69:[4, 4], Operations: ['90-86=4', '84-80=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,69 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 57, 77, 43, 86 ]
18
[ "77-57=20", "86/43=2", "20-2=18" ]
Current State: 18:[57, 77, 43, 86], Operations: [] Exploring Operation: 77-57=20, Resulting Numbers: [43, 86, 20] Generated Node #2: [43, 86, 20] from Operation: 77-57=20 Current State: 18:[43, 86, 20], Operations: ['77-57=20'] Exploring Operation: 86/43=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 86/43=2 Current State: 18:[20, 2], Operations: ['77-57=20', '86/43=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[57, 77, 43, 86], Operations: [] Exploring Operation: 86-57=29, Resulting Numbers: [77, 43, 29] Generated Node #0,0: 18:[77, 43, 29] Operation: 86-57=29 Exploring Operation: 77-43=34, Resulting Numbers: [57, 86, 34] Generated Node #0,1: 18:[57, 86, 34] Operation: 77-43=34 Exploring Operation: 77-57=20, Resulting Numbers: [43, 86, 20] Generated Node #0,2: 18:[43, 86, 20] Operation: 77-57=20 Exploring Operation: 86/43=2, Resulting Numbers: [57, 77, 2] Generated Node #0,3: 18:[57, 77, 2] Operation: 86/43=2 Exploring Operation: 86-77=9, Resulting Numbers: [57, 43, 9] Generated Node #0,4: 18:[57, 43, 9] Operation: 86-77=9 Moving to Node #0,4 Current State: 18:[57, 43, 9], Operations: ['86-77=9'] Exploring Operation: 57-9=48, Resulting Numbers: [43, 48] Generated Node #0,4,0: 18:[43, 48] Operation: 57-9=48 Exploring Operation: 57+9=66, Resulting Numbers: [43, 66] Generated Node #0,4,1: 18:[43, 66] Operation: 57+9=66 Exploring Operation: 43+9=52, Resulting Numbers: [57, 52] Generated Node #0,4,2: 18:[57, 52] Operation: 43+9=52 Exploring Operation: 57-43=14, Resulting Numbers: [9, 14] Generated Node #0,4,3: 18:[9, 14] Operation: 57-43=14 Exploring Operation: 43-9=34, Resulting Numbers: [57, 34] Generated Node #0,4,4: 18:[57, 34] Operation: 43-9=34 Moving to Node #0,2 Current State: 18:[43, 86, 20], Operations: ['77-57=20'] Exploring Operation: 86-20=66, Resulting Numbers: [43, 66] Generated Node #0,2,0: 18:[43, 66] Operation: 86-20=66 Exploring Operation: 86-43=43, Resulting Numbers: [20, 43] Generated Node #0,2,1: 18:[20, 43] Operation: 86-43=43 Exploring Operation: 86/43=2, Resulting Numbers: [20, 2] Generated Node #0,2,2: 18:[20, 2] Operation: 86/43=2 Exploring Operation: 43-20=23, Resulting Numbers: [86, 23] Generated Node #0,2,3: 18:[86, 23] Operation: 43-20=23 Exploring Operation: 43+86=129, Resulting Numbers: [20, 129] Generated Node #0,2,4: 18:[20, 129] Operation: 43+86=129 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[20, 2], Operations: ['77-57=20', '86/43=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[57, 77, 43, 86], Operations: [] Exploring Operation: 77-57=20, Resulting Numbers: [43, 86, 20] Generated Node #0,2: 18:[43, 86, 20] Operation: 77-57=20 Moving to Node #0,2 Current State: 18:[43, 86, 20], Operations: ['77-57=20'] Exploring Operation: 86/43=2, Resulting Numbers: [20, 2] Generated Node #0,2,2: 18:[20, 2] Operation: 86/43=2 Moving to Node #0,2,2 Current State: 18:[20, 2], Operations: ['77-57=20', '86/43=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 29, 58, 6, 42 ]
90
[ "58/29=2", "42*2=84", "6+84=90" ]
Current State: 90:[29, 58, 6, 42], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [6, 42, 2] Generated Node #2: [6, 42, 2] from Operation: 58/29=2 Current State: 90:[6, 42, 2], Operations: ['58/29=2'] Exploring Operation: 42*2=84, Resulting Numbers: [6, 84] Generated Node #3: [6, 84] from Operation: 42*2=84 Current State: 90:[6, 84], Operations: ['58/29=2', '42*2=84'] Exploring Operation: 6+84=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[29, 58, 6, 42], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [6, 42, 2] Generated Node #0,0: 90:[6, 42, 2] Operation: 58/29=2 Exploring Operation: 58-42=16, Resulting Numbers: [29, 6, 16] Generated Node #0,1: 90:[29, 6, 16] Operation: 58-42=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[29, 6, 16], Operations: ['58-42=16'] Exploring Operation: 16-6=10, Resulting Numbers: [29, 10] Generated Node #0,1,0: 90:[29, 10] Operation: 16-6=10 Exploring Operation: 29+16=45, Resulting Numbers: [6, 45] Generated Node #0,1,1: 90:[6, 45] Operation: 29+16=45 Moving to Node #0,1,1 Current State: 90:[6, 45], Operations: ['58-42=16', '29+16=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[29, 10], Operations: ['58-42=16', '16-6=10'] Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,90 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[6, 42, 2], Operations: ['58/29=2'] Exploring Operation: 42+2=44, Resulting Numbers: [6, 44] Generated Node #0,0,0: 90:[6, 44] Operation: 42+2=44 Exploring Operation: 42/6=7, Resulting Numbers: [2, 7] Generated Node #0,0,1: 90:[2, 7] Operation: 42/6=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[6, 44], Operations: ['58/29=2', '42+2=44'] Exploring Operation: 6+44=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[2, 7], Operations: ['58/29=2', '42/6=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,90 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 90, 87, 94, 5 ]
78
[ "90+87=177", "94+5=99", "177-99=78" ]
Current State: 78:[90, 87, 94, 5], Operations: [] Exploring Operation: 90+87=177, Resulting Numbers: [94, 5, 177] Generated Node #2: [94, 5, 177] from Operation: 90+87=177 Current State: 78:[94, 5, 177], Operations: ['90+87=177'] Exploring Operation: 94+5=99, Resulting Numbers: [177, 99] Generated Node #3: [177, 99] from Operation: 94+5=99 Current State: 78:[177, 99], Operations: ['90+87=177', '94+5=99'] Exploring Operation: 177-99=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[90, 87, 94, 5], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [94, 5, 3] Generated Node #0,0: 78:[94, 5, 3] Operation: 90-87=3 Exploring Operation: 94-90=4, Resulting Numbers: [87, 5, 4] Generated Node #0,1: 78:[87, 5, 4] Operation: 94-90=4 Exploring Operation: 94-87=7, Resulting Numbers: [90, 5, 7] Generated Node #0,2: 78:[90, 5, 7] Operation: 94-87=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[87, 5, 4], Operations: ['94-90=4'] Exploring Operation: 87-4=83, Resulting Numbers: [5, 83] Generated Node #0,1,0: 78:[5, 83] Operation: 87-4=83 Exploring Operation: 5-4=1, Resulting Numbers: [87, 1] Generated Node #0,1,1: 78:[87, 1] Operation: 5-4=1 Exploring Operation: 87-5=82, Resulting Numbers: [4, 82] Generated Node #0,1,2: 78:[4, 82] Operation: 87-5=82 Moving to Node #0,1,2 Current State: 78:[4, 82], Operations: ['94-90=4', '87-5=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[90, 87, 94, 5], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [87, 5, 4] Generated Node #0,1: 78:[87, 5, 4] Operation: 94-90=4 Moving to Node #0,1 Current State: 78:[87, 5, 4], Operations: ['94-90=4'] Exploring Operation: 87-5=82, Resulting Numbers: [4, 82] Generated Node #0,1,2: 78:[4, 82] Operation: 87-5=82 Moving to Node #0,1,2 Current State: 78:[4, 82], Operations: ['94-90=4', '87-5=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 8, 95, 36, 90 ]
46
[ "95*36=3420", "3420/90=38", "8+38=46" ]
Current State: 46:[8, 95, 36, 90], Operations: [] Exploring Operation: 95*36=3420, Resulting Numbers: [8, 90, 3420] Generated Node #2: [8, 90, 3420] from Operation: 95*36=3420 Current State: 46:[8, 90, 3420], Operations: ['95*36=3420'] Exploring Operation: 3420/90=38, Resulting Numbers: [8, 38] Generated Node #3: [8, 38] from Operation: 3420/90=38 Current State: 46:[8, 38], Operations: ['95*36=3420', '3420/90=38'] Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[8, 95, 36, 90], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [8, 95, 54] Generated Node #0,0: 46:[8, 95, 54] Operation: 90-36=54 Exploring Operation: 95-36=59, Resulting Numbers: [8, 90, 59] Generated Node #0,1: 46:[8, 90, 59] Operation: 95-36=59 Exploring Operation: 8+36=44, Resulting Numbers: [95, 90, 44] Generated Node #0,2: 46:[95, 90, 44] Operation: 8+36=44 Exploring Operation: 95-8=87, Resulting Numbers: [36, 90, 87] Generated Node #0,3: 46:[36, 90, 87] Operation: 95-8=87 Exploring Operation: 95-90=5, Resulting Numbers: [8, 36, 5] Generated Node #0,4: 46:[8, 36, 5] Operation: 95-90=5 Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[8, 36, 5], Operations: ['95-90=5'] Exploring Operation: 36+5=41, Resulting Numbers: [8, 41] Generated Node #0,4,0: 46:[8, 41] Operation: 36+5=41 Exploring Operation: 36-5=31, Resulting Numbers: [8, 31] Generated Node #0,4,1: 46:[8, 31] Operation: 36-5=31 Exploring Operation: 8+36=44, Resulting Numbers: [5, 44] Generated Node #0,4,2: 46:[5, 44] Operation: 8+36=44 Exploring Operation: 8-5=3, Resulting Numbers: [36, 3] Generated Node #0,4,3: 46:[36, 3] Operation: 8-5=3 Exploring Operation: 36-8=28, Resulting Numbers: [5, 28] Generated Node #0,4,4: 46:[5, 28] Operation: 36-8=28 Moving to Node #0,4,2 Current State: 46:[5, 44], Operations: ['95-90=5', '8+36=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 5+44=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 5*44=220, Resulting Numbers: [220] 220,46 unequal: No Solution Moving to Node #0,4,4 Current State: 46:[5, 28], Operations: ['95-90=5', '36-8=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,46 unequal: No Solution Moving to Node #0,4,0 Current State: 46:[8, 41], Operations: ['95-90=5', '36+5=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,46 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,46 unequal: No Solution Moving to Node #0,4,3 Current State: 46:[36, 3], Operations: ['95-90=5', '8-5=3'] Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,46 unequal: No Solution Moving to Node #0,4,1 Current State: 46:[8, 31], Operations: ['95-90=5', '36-5=31'] Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,46 unequal: No Solution Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[8, 95, 54], Operations: ['90-36=54'] Exploring Operation: 54-8=46, Resulting Numbers: [95, 46] Generated Node #0,0,0: 46:[95, 46] Operation: 54-8=46 Exploring Operation: 95-8=87, Resulting Numbers: [54, 87] Generated Node #0,0,1: 46:[54, 87] Operation: 95-8=87 Exploring Operation: 8+54=62, Resulting Numbers: [95, 62] Generated Node #0,0,2: 46:[95, 62] Operation: 8+54=62 Exploring Operation: 95-54=41, Resulting Numbers: [8, 41] Generated Node #0,0,3: 46:[8, 41] Operation: 95-54=41 Exploring Operation: 8+95=103, Resulting Numbers: [54, 103] Generated Node #0,0,4: 46:[54, 103] Operation: 8+95=103 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 46:[8, 41], Operations: ['90-36=54', '95-54=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,46 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 #0,0,0 Current State: 46:[95, 46], Operations: ['90-36=54', '54-8=46'] Exploring Operation: 95*46=4370, Resulting Numbers: [4370] 4370,46 unequal: No Solution Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 95+46=141, Resulting Numbers: [141] 141,46 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 #0,0,1 Current State: 46:[54, 87], Operations: ['90-36=54', '95-8=87'] Exploring Operation: 54*87=4698, Resulting Numbers: [4698] 4698,46 unequal: No Solution Exploring Operation: 87-54=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 54+87=141, Resulting Numbers: [141] 141,46 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 #0,0,2 Current State: 46:[95, 62], Operations: ['90-36=54', '8+54=62'] Exploring Operation: 95+62=157, Resulting Numbers: [157] 157,46 unequal: No Solution Exploring Operation: 95-62=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 95*62=5890, Resulting Numbers: [5890] 5890,46 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 #0,0,4 Current State: 46:[54, 103], Operations: ['90-36=54', '8+95=103'] Exploring Operation: 54*103=5562, Resulting Numbers: [5562] 5562,46 unequal: No Solution Exploring Operation: 103-54=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 54+103=157, Resulting Numbers: [157] 157,46 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:[8, 90, 59], Operations: ['95-36=59'] Exploring Operation: 59-8=51, Resulting Numbers: [90, 51] Generated Node #0,1,0: 46:[90, 51] Operation: 59-8=51 Exploring Operation: 8+59=67, Resulting Numbers: [90, 67] Generated Node #0,1,1: 46:[90, 67] Operation: 8+59=67 Exploring Operation: 90-8=82, Resulting Numbers: [59, 82] Generated Node #0,1,2: 46:[59, 82] Operation: 90-8=82 Exploring Operation: 90-59=31, Resulting Numbers: [8, 31] Generated Node #0,1,3: 46:[8, 31] Operation: 90-59=31 Exploring Operation: 8+90=98, Resulting Numbers: [59, 98] Generated Node #0,1,4: 46:[59, 98] Operation: 8+90=98 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 46:[8, 31], Operations: ['95-36=59', '90-59=31'] Exploring Operation: 8+31=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 8*31=248, Resulting Numbers: [248] 248,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 46:[90, 51], Operations: ['95-36=59', '59-8=51'] Exploring Operation: 90+51=141, Resulting Numbers: [141] 141,46 unequal: No Solution Exploring Operation: 90-51=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 90*51=4590, Resulting Numbers: [4590] 4590,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[59, 82], Operations: ['95-36=59', '90-8=82'] Exploring Operation: 59+82=141, Resulting Numbers: [141] 141,46 unequal: No Solution Exploring Operation: 59*82=4838, Resulting Numbers: [4838] 4838,46 unequal: No Solution Exploring Operation: 82-59=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 #0,1,1 Current State: 46:[90, 67], Operations: ['95-36=59', '8+59=67'] Exploring Operation: 90-67=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 90+67=157, Resulting Numbers: [157] 157,46 unequal: No Solution Exploring Operation: 90*67=6030, Resulting Numbers: [6030] 6030,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 46:[59, 98], Operations: ['95-36=59', '8+90=98'] Exploring Operation: 98-59=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 59+98=157, Resulting Numbers: [157] 157,46 unequal: No Solution Exploring Operation: 59*98=5782, Resulting Numbers: [5782] 5782,46 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 #0,2 Current State: 46:[95, 90, 44], Operations: ['8+36=44'] Exploring Operation: 95-44=51, Resulting Numbers: [90, 51] Generated Node #0,2,0: 46:[90, 51] Operation: 95-44=51 Exploring Operation: 90-44=46, Resulting Numbers: [95, 46] Generated Node #0,2,1: 46:[95, 46] Operation: 90-44=46 Exploring Operation: 90+44=134, Resulting Numbers: [95, 134] Generated Node #0,2,2: 46:[95, 134] Operation: 90+44=134 Exploring Operation: 95+44=139, Resulting Numbers: [90, 139] Generated Node #0,2,3: 46:[90, 139] Operation: 95+44=139 Exploring Operation: 95-90=5, Resulting Numbers: [44, 5] Generated Node #0,2,4: 46:[44, 5] Operation: 95-90=5 Moving to Node #0,2,4 Current State: 46:[44, 5], Operations: ['8+36=44', '95-90=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 44*5=220, Resulting Numbers: [220] 220,46 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[95, 46], Operations: ['8+36=44', '90-44=46'] Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 95*46=4370, Resulting Numbers: [4370] 4370,46 unequal: No Solution Exploring Operation: 95+46=141, Resulting Numbers: [141] 141,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[90, 51], Operations: ['8+36=44', '95-44=51'] Exploring Operation: 90-51=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 90*51=4590, Resulting Numbers: [4590] 4590,46 unequal: No Solution Exploring Operation: 90+51=141, Resulting Numbers: [141] 141,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[95, 134], Operations: ['8+36=44', '90+44=134'] Exploring Operation: 134-95=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 95*134=12730, Resulting Numbers: [12730] 12730,46 unequal: No Solution Exploring Operation: 95+134=229, Resulting Numbers: [229] 229,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[90, 139], Operations: ['8+36=44', '95+44=139'] Exploring Operation: 90+139=229, Resulting Numbers: [229] 229,46 unequal: No Solution Exploring Operation: 139-90=49, Resulting Numbers: [49] 49,46 unequal: No Solution Exploring Operation: 90*139=12510, Resulting Numbers: [12510] 12510,46 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 #0,3 Current State: 46:[36, 90, 87], Operations: ['95-8=87'] Exploring Operation: 90-36=54, Resulting Numbers: [87, 54] Generated Node #0,3,0: 46:[87, 54] Operation: 90-36=54 Exploring Operation: 87-36=51, Resulting Numbers: [90, 51] Generated Node #0,3,1: 46:[90, 51] Operation: 87-36=51 Exploring Operation: 90-87=3, Resulting Numbers: [36, 3] Generated Node #0,3,2: 46:[36, 3] Operation: 90-87=3 Exploring Operation: 36+90=126, Resulting Numbers: [87, 126] Generated Node #0,3,3: 46:[87, 126] Operation: 36+90=126 Exploring Operation: 36+87=123, Resulting Numbers: [90, 123] Generated Node #0,3,4: 46:[90, 123] Operation: 36+87=123 Moving to Node #0,3,2 Current State: 46:[36, 3], Operations: ['95-8=87', '90-87=3'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,46 unequal: No Solution Exploring Operation: 36+3=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 36*3=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[90, 51], Operations: ['95-8=87', '87-36=51'] Exploring Operation: 90-51=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 90*51=4590, Resulting Numbers: [4590] 4590,46 unequal: No Solution Exploring Operation: 90+51=141, Resulting Numbers: [141] 141,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[87, 54], Operations: ['95-8=87', '90-36=54'] Exploring Operation: 87*54=4698, Resulting Numbers: [4698] 4698,46 unequal: No Solution Exploring Operation: 87+54=141, Resulting Numbers: [141] 141,46 unequal: No Solution Exploring Operation: 87-54=33, Resulting Numbers: [33] 33,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[87, 126], Operations: ['95-8=87', '36+90=126'] Exploring Operation: 126-87=39, Resulting Numbers: [39] 39,46 unequal: No Solution Exploring Operation: 87+126=213, Resulting Numbers: [213] 213,46 unequal: No Solution Exploring Operation: 87*126=10962, Resulting Numbers: [10962] 10962,46 unequal: No Solution Moving to Node #0,3,4 Current State: 46:[90, 123], Operations: ['95-8=87', '36+87=123'] Exploring Operation: 123-90=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 90*123=11070, Resulting Numbers: [11070] 11070,46 unequal: No Solution Exploring Operation: 90+123=213, Resulting Numbers: [213] 213,46 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
[ 97, 91, 39, 59 ]
90
[ "97+91=188", "39+59=98", "188-98=90" ]
Current State: 90:[97, 91, 39, 59], Operations: [] Exploring Operation: 97+91=188, Resulting Numbers: [39, 59, 188] Generated Node #2: [39, 59, 188] from Operation: 97+91=188 Current State: 90:[39, 59, 188], Operations: ['97+91=188'] Exploring Operation: 39+59=98, Resulting Numbers: [188, 98] Generated Node #3: [188, 98] from Operation: 39+59=98 Current State: 90:[188, 98], Operations: ['97+91=188', '39+59=98'] Exploring Operation: 188-98=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[97, 91, 39, 59], Operations: [] Exploring Operation: 59-39=20, Resulting Numbers: [97, 91, 20] Generated Node #0,0: 90:[97, 91, 20] Operation: 59-39=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[97, 91, 20], Operations: ['59-39=20'] Exploring Operation: 97-91=6, Resulting Numbers: [20, 6] Generated Node #0,0,0: 90:[20, 6] Operation: 97-91=6 Moving to Node #0,0,0 Current State: 90:[20, 6], Operations: ['59-39=20', '97-91=6'] Exploring Operation: 20-6=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
mult_heuristic
[ 59, 99, 29, 95 ]
34
[ "59+99=158", "29+95=124", "158-124=34" ]
Current State: 34:[59, 99, 29, 95], Operations: [] Exploring Operation: 59+99=158, Resulting Numbers: [29, 95, 158] Generated Node #2: [29, 95, 158] from Operation: 59+99=158 Current State: 34:[29, 95, 158], Operations: ['59+99=158'] Exploring Operation: 29+95=124, Resulting Numbers: [158, 124] Generated Node #3: [158, 124] from Operation: 29+95=124 Current State: 34:[158, 124], Operations: ['59+99=158', '29+95=124'] Exploring Operation: 158-124=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[59, 99, 29, 95], Operations: [] Exploring Operation: 95-29=66, Resulting Numbers: [59, 99, 66] Generated Node #0,0: 34:[59, 99, 66] Operation: 95-29=66 Exploring Operation: 99-59=40, Resulting Numbers: [29, 95, 40] Generated Node #0,1: 34:[29, 95, 40] Operation: 99-59=40 Exploring Operation: 99-95=4, Resulting Numbers: [59, 29, 4] Generated Node #0,2: 34:[59, 29, 4] Operation: 99-95=4 Exploring Operation: 95-59=36, Resulting Numbers: [99, 29, 36] Generated Node #0,3: 34:[99, 29, 36] Operation: 95-59=36 Exploring Operation: 99-29=70, Resulting Numbers: [59, 95, 70] Generated Node #0,4: 34:[59, 95, 70] Operation: 99-29=70 Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[59, 29, 4], Operations: ['99-95=4'] Exploring Operation: 29-4=25, Resulting Numbers: [59, 25] Generated Node #0,2,0: 34:[59, 25] Operation: 29-4=25 Exploring Operation: 59-29=30, Resulting Numbers: [4, 30] Generated Node #0,2,1: 34:[4, 30] Operation: 59-29=30 Exploring Operation: 59-4=55, Resulting Numbers: [29, 55] Generated Node #0,2,2: 34:[29, 55] Operation: 59-4=55 Exploring Operation: 29+4=33, Resulting Numbers: [59, 33] Generated Node #0,2,3: 34:[59, 33] Operation: 29+4=33 Exploring Operation: 59+4=63, Resulting Numbers: [29, 63] Generated Node #0,2,4: 34:[29, 63] Operation: 59+4=63 Moving to Node #0,2,1 Current State: 34:[4, 30], Operations: ['99-95=4', '59-29=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[59, 99, 29, 95], Operations: [] Exploring Operation: 99-95=4, Resulting Numbers: [59, 29, 4] Generated Node #0,2: 34:[59, 29, 4] Operation: 99-95=4 Moving to Node #0,2 Current State: 34:[59, 29, 4], Operations: ['99-95=4'] Exploring Operation: 59-29=30, Resulting Numbers: [4, 30] Generated Node #0,2,1: 34:[4, 30] Operation: 59-29=30 Moving to Node #0,2,1 Current State: 34:[4, 30], Operations: ['99-95=4', '59-29=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 94, 94, 8, 14 ]
23
[ "94/94=1", "8+14=22", "1+22=23" ]
Current State: 23:[94, 94, 8, 14], Operations: [] Exploring Operation: 94/94=1, Resulting Numbers: [8, 14, 1] Generated Node #2: [8, 14, 1] from Operation: 94/94=1 Current State: 23:[8, 14, 1], Operations: ['94/94=1'] Exploring Operation: 8+14=22, Resulting Numbers: [1, 22] Generated Node #3: [1, 22] from Operation: 8+14=22 Current State: 23:[1, 22], Operations: ['94/94=1', '8+14=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[94, 94, 8, 14], Operations: [] Exploring Operation: 94-94=0, Resulting Numbers: [8, 14, 0] Generated Node #0,0: 23:[8, 14, 0] Operation: 94-94=0 Exploring Operation: 94/94=1, Resulting Numbers: [8, 14, 1] Generated Node #0,1: 23:[8, 14, 1] Operation: 94/94=1 Moving to Node #0,1 Current State: 23:[8, 14, 1], Operations: ['94/94=1'] Exploring Operation: 8+14=22, Resulting Numbers: [1, 22] Generated Node #0,1,0: 23:[1, 22] Operation: 8+14=22 Exploring Operation: 8+1=9, Resulting Numbers: [14, 9] Generated Node #0,1,1: 23:[14, 9] Operation: 8+1=9 Moving to Node #0,0 Current State: 23:[8, 14, 0], Operations: ['94-94=0'] Exploring Operation: 8+14=22, Resulting Numbers: [0, 22] Generated Node #0,0,0: 23:[0, 22] Operation: 8+14=22 Exploring Operation: 8+0=8, Resulting Numbers: [14, 8] Generated Node #0,0,1: 23:[14, 8] Operation: 8+0=8 Moving to Node #0,1,0 Current State: 23:[1, 22], Operations: ['94/94=1', '8+14=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[94, 94, 8, 14], Operations: [] Exploring Operation: 94/94=1, Resulting Numbers: [8, 14, 1] Generated Node #0,1: 23:[8, 14, 1] Operation: 94/94=1 Moving to Node #0,1 Current State: 23:[8, 14, 1], Operations: ['94/94=1'] Exploring Operation: 8+14=22, Resulting Numbers: [1, 22] Generated Node #0,1,0: 23:[1, 22] Operation: 8+14=22 Moving to Node #0,1,0 Current State: 23:[1, 22], Operations: ['94/94=1', '8+14=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 69, 94, 52, 51 ]
97
[ "69-52=17", "51/17=3", "94+3=97" ]
Current State: 97:[69, 94, 52, 51], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [94, 51, 17] Generated Node #2: [94, 51, 17] from Operation: 69-52=17 Current State: 97:[94, 51, 17], Operations: ['69-52=17'] Exploring Operation: 51/17=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 51/17=3 Current State: 97:[94, 3], Operations: ['69-52=17', '51/17=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[69, 94, 52, 51], Operations: [] Exploring Operation: 52+51=103, Resulting Numbers: [69, 94, 103] Generated Node #0,0: 97:[69, 94, 103] Operation: 52+51=103 Exploring Operation: 94+52=146, Resulting Numbers: [69, 51, 146] Generated Node #0,1: 97:[69, 51, 146] Operation: 94+52=146 Exploring Operation: 94+51=145, Resulting Numbers: [69, 52, 145] Generated Node #0,2: 97:[69, 52, 145] Operation: 94+51=145 Exploring Operation: 69+51=120, Resulting Numbers: [94, 52, 120] Generated Node #0,3: 97:[94, 52, 120] Operation: 69+51=120 Exploring Operation: 69+52=121, Resulting Numbers: [94, 51, 121] Generated Node #0,4: 97:[94, 51, 121] Operation: 69+52=121 Moving to Node #0,0 Current State: 97:[69, 94, 103], Operations: ['52+51=103'] Exploring Operation: 69+103=172, Resulting Numbers: [94, 172] Generated Node #0,0,0: 97:[94, 172] Operation: 69+103=172 Exploring Operation: 103-69=34, Resulting Numbers: [94, 34] Generated Node #0,0,1: 97:[94, 34] Operation: 103-69=34 Exploring Operation: 94-69=25, Resulting Numbers: [103, 25] Generated Node #0,0,2: 97:[103, 25] Operation: 94-69=25 Exploring Operation: 103-94=9, Resulting Numbers: [69, 9] Generated Node #0,0,3: 97:[69, 9] Operation: 103-94=9 Exploring Operation: 69+94=163, Resulting Numbers: [103, 163] Generated Node #0,0,4: 97:[103, 163] Operation: 69+94=163 Moving to Node #0,3 Current State: 97:[94, 52, 120], Operations: ['69+51=120'] Exploring Operation: 120-52=68, Resulting Numbers: [94, 68] Generated Node #0,3,0: 97:[94, 68] Operation: 120-52=68 Exploring Operation: 52+120=172, Resulting Numbers: [94, 172] Generated Node #0,3,1: 97:[94, 172] Operation: 52+120=172 Exploring Operation: 94-52=42, Resulting Numbers: [120, 42] Generated Node #0,3,2: 97:[120, 42] Operation: 94-52=42 Exploring Operation: 94+52=146, Resulting Numbers: [120, 146] Generated Node #0,3,3: 97:[120, 146] Operation: 94+52=146 Exploring Operation: 120-94=26, Resulting Numbers: [52, 26] Generated Node #0,3,4: 97:[52, 26] Operation: 120-94=26 Moving to Node #0,4 Current State: 97:[94, 51, 121], Operations: ['69+52=121'] Exploring Operation: 94+51=145, Resulting Numbers: [121, 145] Generated Node #0,4,0: 97:[121, 145] Operation: 94+51=145 Exploring Operation: 51+121=172, Resulting Numbers: [94, 172] Generated Node #0,4,1: 97:[94, 172] Operation: 51+121=172 Exploring Operation: 121-94=27, Resulting Numbers: [51, 27] Generated Node #0,4,2: 97:[51, 27] Operation: 121-94=27 Exploring Operation: 94-51=43, Resulting Numbers: [121, 43] Generated Node #0,4,3: 97:[121, 43] Operation: 94-51=43 Exploring Operation: 121-51=70, Resulting Numbers: [94, 70] Generated Node #0,4,4: 97:[94, 70] Operation: 121-51=70 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 97:[94, 70], Operations: ['69+52=121', '121-51=70'] Exploring Operation: 94+70=164, Resulting Numbers: [164] 164,97 unequal: No Solution Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 94*70=6580, Resulting Numbers: [6580] 6580,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 97:[121, 145], Operations: ['69+52=121', '94+51=145'] Exploring Operation: 121*145=17545, Resulting Numbers: [17545] 17545,97 unequal: No Solution Exploring Operation: 121+145=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 145-121=24, Resulting Numbers: [24] 24,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 97:[94, 172], Operations: ['69+52=121', '51+121=172'] Exploring Operation: 94+172=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 94*172=16168, Resulting Numbers: [16168] 16168,97 unequal: No Solution Exploring Operation: 172-94=78, Resulting Numbers: [78] 78,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 97:[121, 43], Operations: ['69+52=121', '94-51=43'] Exploring Operation: 121+43=164, Resulting Numbers: [164] 164,97 unequal: No Solution Exploring Operation: 121-43=78, Resulting Numbers: [78] 78,97 unequal: No Solution Exploring Operation: 121*43=5203, Resulting Numbers: [5203] 5203,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 97:[51, 27], Operations: ['69+52=121', '121-94=27'] Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,97 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 97:[69, 52, 145], Operations: ['94+51=145'] Exploring Operation: 69+52=121, Resulting Numbers: [145, 121] Generated Node #0,2,0: 97:[145, 121] Operation: 69+52=121 Exploring Operation: 145-69=76, Resulting Numbers: [52, 76] Generated Node #0,2,1: 97:[52, 76] Operation: 145-69=76 Exploring Operation: 145-52=93, Resulting Numbers: [69, 93] Generated Node #0,2,2: 97:[69, 93] Operation: 145-52=93 Exploring Operation: 52+145=197, Resulting Numbers: [69, 197] Generated Node #0,2,3: 97:[69, 197] Operation: 52+145=197 Exploring Operation: 69-52=17, Resulting Numbers: [145, 17] Generated Node #0,2,4: 97:[145, 17] Operation: 69-52=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[69, 93], Operations: ['94+51=145', '145-52=93'] Exploring Operation: 69*93=6417, Resulting Numbers: [6417] 6417,97 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 69+93=162, Resulting Numbers: [162] 162,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[52, 76], Operations: ['94+51=145', '145-69=76'] Exploring Operation: 52+76=128, Resulting Numbers: [128] 128,97 unequal: No Solution Exploring Operation: 52*76=3952, Resulting Numbers: [3952] 3952,97 unequal: No Solution Exploring Operation: 76-52=24, Resulting Numbers: [24] 24,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[145, 121], Operations: ['94+51=145', '69+52=121'] Exploring Operation: 145-121=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 145+121=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 145*121=17545, Resulting Numbers: [17545] 17545,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[69, 197], Operations: ['94+51=145', '52+145=197'] Exploring Operation: 69*197=13593, Resulting Numbers: [13593] 13593,97 unequal: No Solution Exploring Operation: 69+197=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 197-69=128, Resulting Numbers: [128] 128,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 97:[145, 17], Operations: ['94+51=145', '69-52=17'] Exploring Operation: 145+17=162, Resulting Numbers: [162] 162,97 unequal: No Solution Exploring Operation: 145*17=2465, Resulting Numbers: [2465] 2465,97 unequal: No Solution Exploring Operation: 145-17=128, Resulting Numbers: [128] 128,97 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: 97:[69, 51, 146], Operations: ['94+52=146'] Exploring Operation: 51+146=197, Resulting Numbers: [69, 197] Generated Node #0,1,0: 97:[69, 197] Operation: 51+146=197 Exploring Operation: 69+51=120, Resulting Numbers: [146, 120] Generated Node #0,1,1: 97:[146, 120] Operation: 69+51=120 Exploring Operation: 146-51=95, Resulting Numbers: [69, 95] Generated Node #0,1,2: 97:[69, 95] Operation: 146-51=95 Exploring Operation: 146-69=77, Resulting Numbers: [51, 77] Generated Node #0,1,3: 97:[51, 77] Operation: 146-69=77 Exploring Operation: 69-51=18, Resulting Numbers: [146, 18] Generated Node #0,1,4: 97:[146, 18] Operation: 69-51=18 Moving to Node #0,1,2 Current State: 97:[69, 95], Operations: ['94+52=146', '146-51=95'] Exploring Operation: 69+95=164, Resulting Numbers: [164] 164,97 unequal: No Solution Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 69*95=6555, Resulting Numbers: [6555] 6555,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[94, 68], Operations: ['69+51=120', '120-52=68'] Exploring Operation: 94+68=162, Resulting Numbers: [162] 162,97 unequal: No Solution Exploring Operation: 94*68=6392, Resulting Numbers: [6392] 6392,97 unequal: No Solution Exploring Operation: 94-68=26, Resulting Numbers: [26] 26,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[94, 34], Operations: ['52+51=103', '103-69=34'] Exploring Operation: 94*34=3196, Resulting Numbers: [3196] 3196,97 unequal: No Solution Exploring Operation: 94-34=60, Resulting Numbers: [60] 60,97 unequal: No Solution Exploring Operation: 94+34=128, Resulting Numbers: [128] 128,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[51, 77], Operations: ['94+52=146', '146-69=77'] Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,97 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 51*77=3927, Resulting Numbers: [3927] 3927,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[120, 146], Operations: ['69+51=120', '94+52=146'] Exploring Operation: 146-120=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 120*146=17520, Resulting Numbers: [17520] 17520,97 unequal: No Solution Exploring Operation: 120+146=266, Resulting Numbers: [266] 266,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[146, 120], Operations: ['94+52=146', '69+51=120'] Exploring Operation: 146+120=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 146-120=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 146*120=17520, Resulting Numbers: [17520] 17520,97 unequal: No Solution Moving to Node #0,0,4 Current State: 97:[103, 163], Operations: ['52+51=103', '69+94=163'] Exploring Operation: 103*163=16789, Resulting Numbers: [16789] 16789,97 unequal: No Solution Exploring Operation: 103+163=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 163-103=60, Resulting Numbers: [60] 60,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[94, 172], Operations: ['52+51=103', '69+103=172'] Exploring Operation: 94+172=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 172-94=78, Resulting Numbers: [78] 78,97 unequal: No Solution Exploring Operation: 94*172=16168, Resulting Numbers: [16168] 16168,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[103, 25], Operations: ['52+51=103', '94-69=25'] Exploring Operation: 103-25=78, Resulting Numbers: [78] 78,97 unequal: No Solution Exploring Operation: 103*25=2575, Resulting Numbers: [2575] 2575,97 unequal: No Solution Exploring Operation: 103+25=128, Resulting Numbers: [128] 128,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[120, 42], Operations: ['69+51=120', '94-52=42'] Exploring Operation: 120+42=162, Resulting Numbers: [162] 162,97 unequal: No Solution Exploring Operation: 120*42=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution Exploring Operation: 120-42=78, Resulting Numbers: [78] 78,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[94, 172], Operations: ['69+51=120', '52+120=172'] Exploring Operation: 94*172=16168, Resulting Numbers: [16168] 16168,97 unequal: No Solution Exploring Operation: 94+172=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 172-94=78, Resulting Numbers: [78] 78,97 unequal: No Solution Moving to Node #0,3,4 Current State: 97:[52, 26], Operations: ['69+51=120', '120-94=26'] Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,97 unequal: No Solution Exploring Operation: 52*26=1352, Resulting Numbers: [1352] 1352,97 unequal: No Solution Exploring Operation: 52+26=78, Resulting Numbers: [78] 78,97 unequal: No Solution Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[69, 9], Operations: ['52+51=103', '103-94=9'] Exploring Operation: 69+9=78, Resulting Numbers: [78] 78,97 unequal: No Solution Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,97 unequal: No Solution Exploring Operation: 69*9=621, Resulting Numbers: [621] 621,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[69, 197], Operations: ['94+52=146', '51+146=197'] Exploring Operation: 69+197=266, Resulting Numbers: [266] 266,97 unequal: No Solution Exploring Operation: 69*197=13593, Resulting Numbers: [13593] 13593,97 unequal: No Solution Exploring Operation: 197-69=128, Resulting Numbers: [128] 128,97 unequal: No Solution Moving to Node #0,1,4 Current State: 97:[146, 18], Operations: ['94+52=146', '69-51=18'] Exploring Operation: 146-18=128, Resulting Numbers: [128] 128,97 unequal: No Solution Exploring Operation: 146*18=2628, Resulting Numbers: [2628] 2628,97 unequal: No Solution Exploring Operation: 146+18=164, Resulting Numbers: [164] 164,97 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 82, 9, 37, 93 ]
98
[ "82-37=45", "45/9=5", "93+5=98" ]
Current State: 98:[82, 9, 37, 93], Operations: [] Exploring Operation: 82-37=45, Resulting Numbers: [9, 93, 45] Generated Node #2: [9, 93, 45] from Operation: 82-37=45 Current State: 98:[9, 93, 45], Operations: ['82-37=45'] Exploring Operation: 45/9=5, Resulting Numbers: [93, 5] Generated Node #3: [93, 5] from Operation: 45/9=5 Current State: 98:[93, 5], Operations: ['82-37=45', '45/9=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[82, 9, 37, 93], Operations: [] Exploring Operation: 82-37=45, Resulting Numbers: [9, 93, 45] Generated Node #0,0: 98:[9, 93, 45] Operation: 82-37=45 Exploring Operation: 82+9=91, Resulting Numbers: [37, 93, 91] Generated Node #0,1: 98:[37, 93, 91] Operation: 82+9=91 Exploring Operation: 93-82=11, Resulting Numbers: [9, 37, 11] Generated Node #0,2: 98:[9, 37, 11] Operation: 93-82=11 Exploring Operation: 9+37=46, Resulting Numbers: [82, 93, 46] Generated Node #0,3: 98:[82, 93, 46] Operation: 9+37=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[9, 93, 45], Operations: ['82-37=45'] Exploring Operation: 9+93=102, Resulting Numbers: [45, 102] Generated Node #0,0,0: 98:[45, 102] Operation: 9+93=102 Exploring Operation: 45/9=5, Resulting Numbers: [93, 5] Generated Node #0,0,1: 98:[93, 5] Operation: 45/9=5 Exploring Operation: 93-45=48, Resulting Numbers: [9, 48] Generated Node #0,0,2: 98:[9, 48] Operation: 93-45=48 Exploring Operation: 9+45=54, Resulting Numbers: [93, 54] Generated Node #0,0,3: 98:[93, 54] Operation: 9+45=54 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 98:[9, 48], Operations: ['82-37=45', '93-45=48'] Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,98 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,98 unequal: No Solution Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 98:[93, 5], Operations: ['82-37=45', '45/9=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[82, 9, 37, 93], Operations: [] Exploring Operation: 82-37=45, Resulting Numbers: [9, 93, 45] Generated Node #0,0: 98:[9, 93, 45] Operation: 82-37=45 Moving to Node #0,0 Current State: 98:[9, 93, 45], Operations: ['82-37=45'] Exploring Operation: 45/9=5, Resulting Numbers: [93, 5] Generated Node #0,0,1: 98:[93, 5] Operation: 45/9=5 Moving to Node #0,0,1 Current State: 98:[93, 5], Operations: ['82-37=45', '45/9=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 50, 81, 59, 8 ]
80
[ "50+81=131", "59-8=51", "131-51=80" ]
Current State: 80:[50, 81, 59, 8], Operations: [] Exploring Operation: 50+81=131, Resulting Numbers: [59, 8, 131] Generated Node #2: [59, 8, 131] from Operation: 50+81=131 Current State: 80:[59, 8, 131], Operations: ['50+81=131'] Exploring Operation: 59-8=51, Resulting Numbers: [131, 51] Generated Node #3: [131, 51] from Operation: 59-8=51 Current State: 80:[131, 51], Operations: ['50+81=131', '59-8=51'] Exploring Operation: 131-51=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[50, 81, 59, 8], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [81, 8, 9] Generated Node #0,0: 80:[81, 8, 9] Operation: 59-50=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[81, 8, 9], Operations: ['59-50=9'] Exploring Operation: 81/9=9, Resulting Numbers: [8, 9] Generated Node #0,0,0: 80:[8, 9] Operation: 81/9=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[8, 9], Operations: ['59-50=9', '81/9=9'] Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 48, 9, 57, 44 ]
45
[ "48+9=57", "57/57=1", "44+1=45" ]
Current State: 45:[48, 9, 57, 44], Operations: [] Exploring Operation: 48+9=57, Resulting Numbers: [57, 44, 57] Generated Node #2: [57, 44, 57] from Operation: 48+9=57 Current State: 45:[57, 44, 57], Operations: ['48+9=57'] Exploring Operation: 57/57=1, Resulting Numbers: [44, 1] Generated Node #3: [44, 1] from Operation: 57/57=1 Current State: 45:[44, 1], Operations: ['48+9=57', '57/57=1'] Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[48, 9, 57, 44], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [48, 9, 13] Generated Node #0,0: 45:[48, 9, 13] Operation: 57-44=13 Exploring Operation: 57-48=9, Resulting Numbers: [9, 44, 9] Generated Node #0,1: 45:[9, 44, 9] Operation: 57-48=9 Moving to Node #0,1 Current State: 45:[9, 44, 9], Operations: ['57-48=9'] Exploring Operation: 9+9=18, Resulting Numbers: [44, 18] Generated Node #0,1,0: 45:[44, 18] Operation: 9+9=18 Exploring Operation: 9/9=1, Resulting Numbers: [44, 1] Generated Node #0,1,1: 45:[44, 1] Operation: 9/9=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[44, 1], Operations: ['57-48=9', '9/9=1'] Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[48, 9, 57, 44], Operations: [] Exploring Operation: 57-48=9, Resulting Numbers: [9, 44, 9] Generated Node #0,1: 45:[9, 44, 9] Operation: 57-48=9 Moving to Node #0,1 Current State: 45:[9, 44, 9], Operations: ['57-48=9'] Exploring Operation: 9/9=1, Resulting Numbers: [44, 1] Generated Node #0,1,1: 45:[44, 1] Operation: 9/9=1 Moving to Node #0,1,1 Current State: 45:[44, 1], Operations: ['57-48=9', '9/9=1'] Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 26, 2, 2, 17 ]
14
[ "26-2=24", "24-17=7", "2*7=14" ]
Current State: 14:[26, 2, 2, 17], Operations: [] Exploring Operation: 26-2=24, Resulting Numbers: [17, 24] Generated Node #2: [17, 24] from Operation: 26-2=24 Current State: 14:[17, 24], Operations: ['26-2=24'] Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,14 equal: Goal Reached Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[26, 2, 2, 17], Operations: [] Exploring Operation: 26-17=9, Resulting Numbers: [2, 2, 9] Generated Node #0,0: 14:[2, 2, 9] Operation: 26-17=9 Exploring Operation: 26/2=13, Resulting Numbers: [2, 17, 13] Generated Node #0,1: 14:[2, 17, 13] Operation: 26/2=13 Exploring Operation: 26/2=13, Resulting Numbers: [2, 17, 13] Generated Node #0,2: 14:[2, 17, 13] Operation: 26/2=13 Exploring Operation: 26-2=24, Resulting Numbers: [2, 17, 24] Generated Node #0,3: 14:[2, 17, 24] Operation: 26-2=24 Moving to Node #0,0 Current State: 14:[2, 2, 9], Operations: ['26-17=9'] Exploring Operation: 9-2=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 9-2=7 Exploring Operation: 2/2=1, Resulting Numbers: [9, 1] Generated Node #0,0,1: 14:[9, 1] Operation: 2/2=1 Exploring Operation: 2+9=11, Resulting Numbers: [2, 11] Generated Node #0,0,2: 14:[2, 11] Operation: 2+9=11 Exploring Operation: 9-2=7, Resulting Numbers: [2, 7] Generated Node #0,0,3: 14:[2, 7] Operation: 9-2=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[2, 7], Operations: ['26-17=9', '9-2=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,14 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[26, 2, 2, 17], Operations: [] Exploring Operation: 26-17=9, Resulting Numbers: [2, 2, 9] Generated Node #0,0: 14:[2, 2, 9] Operation: 26-17=9 Moving to Node #0,0 Current State: 14:[2, 2, 9], Operations: ['26-17=9'] Exploring Operation: 9-2=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 14:[2, 7] Operation: 9-2=7 Moving to Node #0,0,0 Current State: 14:[2, 7], Operations: ['26-17=9', '9-2=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 84, 13, 48, 3 ]
63
[ "84/3=28", "48-13=35", "28+35=63" ]
Current State: 63:[84, 13, 48, 3], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [13, 48, 28] Generated Node #2: [13, 48, 28] from Operation: 84/3=28 Current State: 63:[13, 48, 28], Operations: ['84/3=28'] Exploring Operation: 48-13=35, Resulting Numbers: [28, 35] Generated Node #3: [28, 35] from Operation: 48-13=35 Current State: 63:[28, 35], Operations: ['84/3=28', '48-13=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[84, 13, 48, 3], Operations: [] Exploring Operation: 84-13=71, Resulting Numbers: [48, 3, 71] Generated Node #0,0: 63:[48, 3, 71] Operation: 84-13=71 Exploring Operation: 13+48=61, Resulting Numbers: [84, 3, 61] Generated Node #0,1: 63:[84, 3, 61] Operation: 13+48=61 Exploring Operation: 84-48=36, Resulting Numbers: [13, 3, 36] Generated Node #0,2: 63:[13, 3, 36] Operation: 84-48=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[13, 3, 36], Operations: ['84-48=36'] Exploring Operation: 36-13=23, Resulting Numbers: [3, 23] Generated Node #0,2,0: 63:[3, 23] Operation: 36-13=23 Exploring Operation: 36/3=12, Resulting Numbers: [13, 12] Generated Node #0,2,1: 63:[13, 12] Operation: 36/3=12 Exploring Operation: 13+36=49, Resulting Numbers: [3, 49] Generated Node #0,2,2: 63:[3, 49] Operation: 13+36=49 Moving to Node #0,2,0 Current State: 63:[3, 23], Operations: ['84-48=36', '36-13=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,63 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[13, 12], Operations: ['84-48=36', '36/3=12'] Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,63 unequal: No Solution Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[3, 49], Operations: ['84-48=36', '13+36=49'] Exploring Operation: 3*49=147, Resulting Numbers: [147] 147,63 unequal: No Solution Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,63 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[48, 3, 71], Operations: ['84-13=71'] Exploring Operation: 71-48=23, Resulting Numbers: [3, 23] Generated Node #0,0,0: 63:[3, 23] Operation: 71-48=23 Exploring Operation: 48+3=51, Resulting Numbers: [71, 51] Generated Node #0,0,1: 63:[71, 51] Operation: 48+3=51 Exploring Operation: 48/3=16, Resulting Numbers: [71, 16] Generated Node #0,0,2: 63:[71, 16] Operation: 48/3=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[3, 23], Operations: ['84-13=71', '71-48=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,63 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,63 unequal: No Solution No 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: 63:[71, 16], Operations: ['84-13=71', '48/3=16'] Exploring Operation: 71-16=55, Resulting Numbers: [55] 55,63 unequal: No Solution Exploring Operation: 71*16=1136, Resulting Numbers: [1136] 1136,63 unequal: No Solution Exploring Operation: 71+16=87, Resulting Numbers: [87] 87,63 unequal: No Solution No 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: 63:[71, 51], Operations: ['84-13=71', '48+3=51'] Exploring Operation: 71+51=122, Resulting Numbers: [122] 122,63 unequal: No Solution Exploring Operation: 71*51=3621, Resulting Numbers: [3621] 3621,63 unequal: No Solution Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,63 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: 63:[84, 3, 61], Operations: ['13+48=61'] Exploring Operation: 84/3=28, Resulting Numbers: [61, 28] Generated Node #0,1,0: 63:[61, 28] Operation: 84/3=28 Exploring Operation: 84-61=23, Resulting Numbers: [3, 23] Generated Node #0,1,1: 63:[3, 23] Operation: 84-61=23 Exploring Operation: 84-3=81, Resulting Numbers: [61, 81] Generated Node #0,1,2: 63:[61, 81] Operation: 84-3=81 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[3, 23], Operations: ['13+48=61', '84-61=23'] Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,63 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,63 unequal: No Solution No 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: 63:[61, 28], Operations: ['13+48=61', '84/3=28'] Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,63 unequal: No Solution Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,63 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,63 unequal: No Solution No 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: 63:[61, 81], Operations: ['13+48=61', '84-3=81'] Exploring Operation: 61+81=142, Resulting Numbers: [142] 142,63 unequal: No Solution Exploring Operation: 81-61=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 61*81=4941, Resulting Numbers: [4941] 4941,63 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
[ 53, 30, 59, 54 ]
88
[ "53+30=83", "59-54=5", "83+5=88" ]
Current State: 88:[53, 30, 59, 54], Operations: [] Exploring Operation: 53+30=83, Resulting Numbers: [59, 54, 83] Generated Node #2: [59, 54, 83] from Operation: 53+30=83 Current State: 88:[59, 54, 83], Operations: ['53+30=83'] Exploring Operation: 59-54=5, Resulting Numbers: [83, 5] Generated Node #3: [83, 5] from Operation: 59-54=5 Current State: 88:[83, 5], Operations: ['53+30=83', '59-54=5'] Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[53, 30, 59, 54], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [53, 30, 5] Generated Node #0,0: 88:[53, 30, 5] Operation: 59-54=5 Exploring Operation: 59-53=6, Resulting Numbers: [30, 54, 6] Generated Node #0,1: 88:[30, 54, 6] Operation: 59-53=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[53, 30, 5], Operations: ['59-54=5'] Exploring Operation: 53-30=23, Resulting Numbers: [5, 23] Generated Node #0,0,0: 88:[5, 23] Operation: 53-30=23 Exploring Operation: 53+30=83, Resulting Numbers: [5, 83] Generated Node #0,0,1: 88:[5, 83] Operation: 53+30=83 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[5, 23], Operations: ['59-54=5', '53-30=23'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[5, 83], Operations: ['59-54=5', '53+30=83'] Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,88 unequal: No Solution Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[53, 30, 59, 54], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [53, 30, 5] Generated Node #0,0: 88:[53, 30, 5] Operation: 59-54=5 Moving to Node #0,0 Current State: 88:[53, 30, 5], Operations: ['59-54=5'] Exploring Operation: 53+30=83, Resulting Numbers: [5, 83] Generated Node #0,0,1: 88:[5, 83] Operation: 53+30=83 Moving to Node #0,0,1 Current State: 88:[5, 83], Operations: ['59-54=5', '53+30=83'] Exploring Operation: 5+83=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 48, 6, 56, 70 ]
77
[ "48/6=8", "56/8=7", "70+7=77" ]
Current State: 77:[48, 6, 56, 70], Operations: [] Exploring Operation: 48/6=8, Resulting Numbers: [56, 70, 8] Generated Node #2: [56, 70, 8] from Operation: 48/6=8 Current State: 77:[56, 70, 8], Operations: ['48/6=8'] Exploring Operation: 56/8=7, Resulting Numbers: [70, 7] Generated Node #3: [70, 7] from Operation: 56/8=7 Current State: 77:[70, 7], Operations: ['48/6=8', '56/8=7'] Exploring Operation: 70+7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[48, 6, 56, 70], Operations: [] Exploring Operation: 56-48=8, Resulting Numbers: [6, 70, 8] Generated Node #0,0: 77:[6, 70, 8] Operation: 56-48=8 Exploring Operation: 48/6=8, Resulting Numbers: [56, 70, 8] Generated Node #0,1: 77:[56, 70, 8] Operation: 48/6=8 Exploring Operation: 70-48=22, Resulting Numbers: [6, 56, 22] Generated Node #0,2: 77:[6, 56, 22] Operation: 70-48=22 Exploring Operation: 48+56=104, Resulting Numbers: [6, 70, 104] Generated Node #0,3: 77:[6, 70, 104] Operation: 48+56=104 Exploring Operation: 70-56=14, Resulting Numbers: [48, 6, 14] Generated Node #0,4: 77:[48, 6, 14] Operation: 70-56=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[6, 70, 8], Operations: ['56-48=8'] Exploring Operation: 8-6=2, Resulting Numbers: [70, 2] Generated Node #0,0,0: 77:[70, 2] Operation: 8-6=2 Exploring Operation: 70+8=78, Resulting Numbers: [6, 78] Generated Node #0,0,1: 77:[6, 78] Operation: 70+8=78 Exploring Operation: 6+70=76, Resulting Numbers: [8, 76] Generated Node #0,0,2: 77:[8, 76] Operation: 6+70=76 Exploring Operation: 70-6=64, Resulting Numbers: [8, 64] Generated Node #0,0,3: 77:[8, 64] Operation: 70-6=64 Exploring Operation: 6+8=14, Resulting Numbers: [70, 14] Generated Node #0,0,4: 77:[70, 14] Operation: 6+8=14 Moving to Node #0,0,1 Current State: 77:[6, 78], Operations: ['56-48=8', '70+8=78'] Exploring Operation: 78/6=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 78-6=72, Resulting Numbers: [72] 72,77 unequal: No Solution Exploring Operation: 6+78=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 6*78=468, Resulting Numbers: [468] 468,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[8, 76], Operations: ['56-48=8', '6+70=76'] Exploring Operation: 8+76=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 8*76=608, Resulting Numbers: [608] 608,77 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,77 unequal: No Solution Moving to Node #0,0,4 Current State: 77:[70, 14], Operations: ['56-48=8', '6+8=14'] Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,77 unequal: No Solution Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,77 unequal: No Solution Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 70*14=980, Resulting Numbers: [980] 980,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[70, 2], Operations: ['56-48=8', '8-6=2'] Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,77 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,77 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[8, 64], Operations: ['56-48=8', '70-6=64'] Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,77 unequal: No Solution Exploring Operation: 8+64=72, Resulting Numbers: [72] 72,77 unequal: No Solution Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 8*64=512, Resulting Numbers: [512] 512,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[56, 70, 8], Operations: ['48/6=8'] Exploring Operation: 70-56=14, Resulting Numbers: [8, 14] Generated Node #0,1,0: 77:[8, 14] Operation: 70-56=14 Exploring Operation: 56+8=64, Resulting Numbers: [70, 64] Generated Node #0,1,1: 77:[70, 64] Operation: 56+8=64 Exploring Operation: 70+8=78, Resulting Numbers: [56, 78] Generated Node #0,1,2: 77:[56, 78] Operation: 70+8=78 Exploring Operation: 56-8=48, Resulting Numbers: [70, 48] Generated Node #0,1,3: 77:[70, 48] Operation: 56-8=48 Exploring Operation: 56/8=7, Resulting Numbers: [70, 7] Generated Node #0,1,4: 77:[70, 7] Operation: 56/8=7 Moving to Node #0,1,0 Current State: 77:[8, 14], Operations: ['48/6=8', '70-56=14'] Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,77 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,77 unequal: No Solution Moving to Node #0,1,4 Current State: 77:[70, 7], Operations: ['48/6=8', '56/8=7'] Exploring Operation: 70+7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[48, 6, 56, 70], Operations: [] Exploring Operation: 48/6=8, Resulting Numbers: [56, 70, 8] Generated Node #0,1: 77:[56, 70, 8] Operation: 48/6=8 Moving to Node #0,1 Current State: 77:[56, 70, 8], Operations: ['48/6=8'] Exploring Operation: 56/8=7, Resulting Numbers: [70, 7] Generated Node #0,1,4: 77:[70, 7] Operation: 56/8=7 Moving to Node #0,1,4 Current State: 77:[70, 7], Operations: ['48/6=8', '56/8=7'] Exploring Operation: 70+7=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
mult_heuristic
[ 6, 12, 20, 68 ]
14
[ "12/6=2", "68/2=34", "34-20=14" ]
Current State: 14:[6, 12, 20, 68], Operations: [] Exploring Operation: 12/6=2, Resulting Numbers: [20, 68, 2] Generated Node #2: [20, 68, 2] from Operation: 12/6=2 Current State: 14:[20, 68, 2], Operations: ['12/6=2'] Exploring Operation: 68/2=34, Resulting Numbers: [20, 34] Generated Node #3: [20, 34] from Operation: 68/2=34 Current State: 14:[20, 34], Operations: ['12/6=2', '68/2=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[6, 12, 20, 68], Operations: [] Exploring Operation: 68-12=56, Resulting Numbers: [6, 20, 56] Generated Node #0,0: 14:[6, 20, 56] Operation: 68-12=56 Exploring Operation: 68-20=48, Resulting Numbers: [6, 12, 48] Generated Node #0,1: 14:[6, 12, 48] Operation: 68-20=48 Moving to Node #0,1 Current State: 14:[6, 12, 48], Operations: ['68-20=48'] Exploring Operation: 48/12=4, Resulting Numbers: [6, 4] Generated Node #0,1,0: 14:[6, 4] Operation: 48/12=4 Exploring Operation: 48/6=8, Resulting Numbers: [12, 8] Generated Node #0,1,1: 14:[12, 8] Operation: 48/6=8 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[6, 4], Operations: ['68-20=48', '48/12=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[12, 8], Operations: ['68-20=48', '48/6=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 14:[6, 20, 56], Operations: ['68-12=56'] Exploring Operation: 20-6=14, Resulting Numbers: [56, 14] Generated Node #0,0,0: 14:[56, 14] Operation: 20-6=14 Exploring Operation: 56-20=36, Resulting Numbers: [6, 36] Generated Node #0,0,1: 14:[6, 36] Operation: 56-20=36 Moving to Node #0,0,1 Current State: 14:[6, 36], Operations: ['68-12=56', '56-20=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[56, 14], Operations: ['68-12=56', '20-6=14'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,14 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 2, 11, 57, 75 ]
89
[ "75-11=64", "64/2=32", "57+32=89" ]
Current State: 89:[2, 11, 57, 75], Operations: [] Exploring Operation: 75-11=64, Resulting Numbers: [2, 57, 64] Generated Node #2: [2, 57, 64] from Operation: 75-11=64 Current State: 89:[2, 57, 64], Operations: ['75-11=64'] Exploring Operation: 64/2=32, Resulting Numbers: [57, 32] Generated Node #3: [57, 32] from Operation: 64/2=32 Current State: 89:[57, 32], Operations: ['75-11=64', '64/2=32'] Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[2, 11, 57, 75], Operations: [] Exploring Operation: 2+57=59, Resulting Numbers: [11, 75, 59] Generated Node #0,0: 89:[11, 75, 59] Operation: 2+57=59 Exploring Operation: 2*57=114, Resulting Numbers: [11, 75, 114] Generated Node #0,1: 89:[11, 75, 114] Operation: 2*57=114 Exploring Operation: 2*11=22, Resulting Numbers: [57, 75, 22] Generated Node #0,2: 89:[57, 75, 22] Operation: 2*11=22 Exploring Operation: 2+11=13, Resulting Numbers: [57, 75, 13] Generated Node #0,3: 89:[57, 75, 13] Operation: 2+11=13 Exploring Operation: 2+75=77, Resulting Numbers: [11, 57, 77] Generated Node #0,4: 89:[11, 57, 77] Operation: 2+75=77 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[57, 75, 22], Operations: ['2*11=22'] Exploring Operation: 57-22=35, Resulting Numbers: [75, 35] Generated Node #0,2,0: 89:[75, 35] Operation: 57-22=35 Exploring Operation: 57+22=79, Resulting Numbers: [75, 79] Generated Node #0,2,1: 89:[75, 79] Operation: 57+22=79 Exploring Operation: 75-22=53, Resulting Numbers: [57, 53] Generated Node #0,2,2: 89:[57, 53] Operation: 75-22=53 Exploring Operation: 75+22=97, Resulting Numbers: [57, 97] Generated Node #0,2,3: 89:[57, 97] Operation: 75+22=97 Exploring Operation: 57+75=132, Resulting Numbers: [22, 132] Generated Node #0,2,4: 89:[22, 132] Operation: 57+75=132 Moving to Node #0,2,1 Current State: 89:[75, 79], Operations: ['2*11=22', '57+22=79'] Exploring Operation: 75*79=5925, Resulting Numbers: [5925] 5925,89 unequal: No Solution Exploring Operation: 75+79=154, Resulting Numbers: [154] 154,89 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[57, 97], Operations: ['2*11=22', '75+22=97'] Exploring Operation: 57+97=154, Resulting Numbers: [154] 154,89 unequal: No Solution Exploring Operation: 97-57=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 57*97=5529, Resulting Numbers: [5529] 5529,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[75, 35], Operations: ['2*11=22', '57-22=35'] Exploring Operation: 75-35=40, Resulting Numbers: [40] 40,89 unequal: No Solution Exploring Operation: 75+35=110, Resulting Numbers: [110] 110,89 unequal: No Solution Exploring Operation: 75*35=2625, Resulting Numbers: [2625] 2625,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[57, 53], Operations: ['2*11=22', '75-22=53'] Exploring Operation: 57*53=3021, Resulting Numbers: [3021] 3021,89 unequal: No Solution Exploring Operation: 57+53=110, Resulting Numbers: [110] 110,89 unequal: No Solution Exploring Operation: 57-53=4, Resulting Numbers: [4] 4,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[22, 132], Operations: ['2*11=22', '57+75=132'] Exploring Operation: 22*132=2904, Resulting Numbers: [2904] 2904,89 unequal: No Solution Exploring Operation: 22+132=154, Resulting Numbers: [154] 154,89 unequal: No Solution Exploring Operation: 132/22=6, Resulting Numbers: [6] 6,89 unequal: No Solution Exploring Operation: 132-22=110, Resulting Numbers: [110] 110,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[11, 75, 114], Operations: ['2*57=114'] Exploring Operation: 114-75=39, Resulting Numbers: [11, 39] Generated Node #0,1,0: 89:[11, 39] Operation: 114-75=39 Exploring Operation: 11+114=125, Resulting Numbers: [75, 125] Generated Node #0,1,1: 89:[75, 125] Operation: 11+114=125 Exploring Operation: 114-11=103, Resulting Numbers: [75, 103] Generated Node #0,1,2: 89:[75, 103] Operation: 114-11=103 Exploring Operation: 11+75=86, Resulting Numbers: [114, 86] Generated Node #0,1,3: 89:[114, 86] Operation: 11+75=86 Exploring Operation: 75-11=64, Resulting Numbers: [114, 64] Generated Node #0,1,4: 89:[114, 64] Operation: 75-11=64 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[75, 103], Operations: ['2*57=114', '114-11=103'] Exploring Operation: 75+103=178, Resulting Numbers: [178] 178,89 unequal: No Solution Exploring Operation: 103-75=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 75*103=7725, Resulting Numbers: [7725] 7725,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 89:[114, 86], Operations: ['2*57=114', '11+75=86'] Exploring Operation: 114*86=9804, Resulting Numbers: [9804] 9804,89 unequal: No Solution Exploring Operation: 114+86=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 114-86=28, Resulting Numbers: [28] 28,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[75, 125], Operations: ['2*57=114', '11+114=125'] Exploring Operation: 75+125=200, Resulting Numbers: [200] 200,89 unequal: No Solution Exploring Operation: 75*125=9375, Resulting Numbers: [9375] 9375,89 unequal: No Solution Exploring Operation: 125-75=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 89:[114, 64], Operations: ['2*57=114', '75-11=64'] Exploring Operation: 114-64=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 114+64=178, Resulting Numbers: [178] 178,89 unequal: No Solution Exploring Operation: 114*64=7296, Resulting Numbers: [7296] 7296,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[11, 39], Operations: ['2*57=114', '114-75=39'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,89 unequal: No Solution Exploring Operation: 11*39=429, Resulting Numbers: [429] 429,89 unequal: No Solution Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[11, 75, 59], Operations: ['2+57=59'] Exploring Operation: 75-11=64, Resulting Numbers: [59, 64] Generated Node #0,0,0: 89:[59, 64] Operation: 75-11=64 Exploring Operation: 75+59=134, Resulting Numbers: [11, 134] Generated Node #0,0,1: 89:[11, 134] Operation: 75+59=134 Exploring Operation: 11+59=70, Resulting Numbers: [75, 70] Generated Node #0,0,2: 89:[75, 70] Operation: 11+59=70 Exploring Operation: 59-11=48, Resulting Numbers: [75, 48] Generated Node #0,0,3: 89:[75, 48] Operation: 59-11=48 Exploring Operation: 11+75=86, Resulting Numbers: [59, 86] Generated Node #0,0,4: 89:[59, 86] Operation: 11+75=86 Moving to Node #0,0,2 Current State: 89:[75, 70], Operations: ['2+57=59', '11+59=70'] Exploring Operation: 75+70=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 75-70=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 75*70=5250, Resulting Numbers: [5250] 5250,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[59, 86], Operations: ['2+57=59', '11+75=86'] Exploring Operation: 59*86=5074, Resulting Numbers: [5074] 5074,89 unequal: No Solution Exploring Operation: 59+86=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 86-59=27, Resulting Numbers: [27] 27,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[59, 64], Operations: ['2+57=59', '75-11=64'] Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,89 unequal: No Solution Exploring Operation: 59+64=123, Resulting Numbers: [123] 123,89 unequal: No Solution Exploring Operation: 59*64=3776, Resulting Numbers: [3776] 3776,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[75, 48], Operations: ['2+57=59', '59-11=48'] Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,89 unequal: No Solution Exploring Operation: 75+48=123, Resulting Numbers: [123] 123,89 unequal: No Solution Exploring Operation: 75*48=3600, Resulting Numbers: [3600] 3600,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[11, 134], Operations: ['2+57=59', '75+59=134'] Exploring Operation: 11+134=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 134-11=123, Resulting Numbers: [123] 123,89 unequal: No Solution Exploring Operation: 11*134=1474, Resulting Numbers: [1474] 1474,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[57, 75, 13], Operations: ['2+11=13'] Exploring Operation: 57-13=44, Resulting Numbers: [75, 44] Generated Node #0,3,0: 89:[75, 44] Operation: 57-13=44 Exploring Operation: 75+13=88, Resulting Numbers: [57, 88] Generated Node #0,3,1: 89:[57, 88] Operation: 75+13=88 Exploring Operation: 57+13=70, Resulting Numbers: [75, 70] Generated Node #0,3,2: 89:[75, 70] Operation: 57+13=70 Exploring Operation: 75-13=62, Resulting Numbers: [57, 62] Generated Node #0,3,3: 89:[57, 62] Operation: 75-13=62 Exploring Operation: 57+75=132, Resulting Numbers: [13, 132] Generated Node #0,3,4: 89:[13, 132] Operation: 57+75=132 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 89:[57, 88], Operations: ['2+11=13', '75+13=88'] Exploring Operation: 57+88=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 88-57=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 57*88=5016, Resulting Numbers: [5016] 5016,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 89:[75, 70], Operations: ['2+11=13', '57+13=70'] Exploring Operation: 75+70=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 75*70=5250, Resulting Numbers: [5250] 5250,89 unequal: No Solution Exploring Operation: 75-70=5, Resulting Numbers: [5] 5,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 89:[75, 44], Operations: ['2+11=13', '57-13=44'] Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,89 unequal: No Solution Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 89:[57, 62], Operations: ['2+11=13', '75-13=62'] Exploring Operation: 57+62=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 57*62=3534, Resulting Numbers: [3534] 3534,89 unequal: No Solution Exploring Operation: 62-57=5, Resulting Numbers: [5] 5,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 89:[13, 132], Operations: ['2+11=13', '57+75=132'] Exploring Operation: 13+132=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 132-13=119, Resulting Numbers: [119] 119,89 unequal: No Solution Exploring Operation: 13*132=1716, Resulting Numbers: [1716] 1716,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 89:[11, 57, 77], Operations: ['2+75=77'] Exploring Operation: 77-11=66, Resulting Numbers: [57, 66] Generated Node #0,4,0: 89:[57, 66] Operation: 77-11=66 Exploring Operation: 77/11=7, Resulting Numbers: [57, 7] Generated Node #0,4,1: 89:[57, 7] Operation: 77/11=7 Exploring Operation: 11+77=88, Resulting Numbers: [57, 88] Generated Node #0,4,2: 89:[57, 88] Operation: 11+77=88 Exploring Operation: 57-11=46, Resulting Numbers: [77, 46] Generated Node #0,4,3: 89:[77, 46] Operation: 57-11=46 Exploring Operation: 11+57=68, Resulting Numbers: [77, 68] Generated Node #0,4,4: 89:[77, 68] Operation: 11+57=68 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 89:[57, 88], Operations: ['2+75=77', '11+77=88'] Exploring Operation: 57+88=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 57*88=5016, Resulting Numbers: [5016] 5016,89 unequal: No Solution Exploring Operation: 88-57=31, Resulting Numbers: [31] 31,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 89:[77, 68], Operations: ['2+75=77', '11+57=68'] Exploring Operation: 77+68=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 77*68=5236, Resulting Numbers: [5236] 5236,89 unequal: No Solution Exploring Operation: 77-68=9, Resulting Numbers: [9] 9,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 89:[57, 66], Operations: ['2+75=77', '77-11=66'] Exploring Operation: 57*66=3762, Resulting Numbers: [3762] 3762,89 unequal: No Solution Exploring Operation: 66-57=9, Resulting Numbers: [9] 9,89 unequal: No Solution Exploring Operation: 57+66=123, Resulting Numbers: [123] 123,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 89:[77, 46], Operations: ['2+75=77', '57-11=46'] Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,89 unequal: No Solution Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,89 unequal: No Solution Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 89:[57, 7], Operations: ['2+75=77', '77/11=7'] Exploring Operation: 57+7=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 57*7=399, Resulting Numbers: [399] 399,89 unequal: No Solution Exploring Operation: 57-7=50, Resulting Numbers: [50] 50,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 66, 13, 68, 91 ]
14
[ "68-66=2", "91/13=7", "2*7=14" ]
Current State: 14:[66, 13, 68, 91], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [13, 91, 2] Generated Node #2: [13, 91, 2] from Operation: 68-66=2 Current State: 14:[13, 91, 2], Operations: ['68-66=2'] Exploring Operation: 91/13=7, Resulting Numbers: [2, 7] Generated Node #3: [2, 7] from Operation: 91/13=7 Current State: 14:[2, 7], Operations: ['68-66=2', '91/13=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[66, 13, 68, 91], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [13, 91, 2] Generated Node #0,0: 14:[13, 91, 2] Operation: 68-66=2 Exploring Operation: 91-68=23, Resulting Numbers: [66, 13, 23] Generated Node #0,1: 14:[66, 13, 23] Operation: 91-68=23 Exploring Operation: 91-66=25, Resulting Numbers: [13, 68, 25] Generated Node #0,2: 14:[13, 68, 25] Operation: 91-66=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[66, 13, 23], Operations: ['91-68=23'] Exploring Operation: 66-23=43, Resulting Numbers: [13, 43] Generated Node #0,1,0: 14:[13, 43] Operation: 66-23=43 Exploring Operation: 23-13=10, Resulting Numbers: [66, 10] Generated Node #0,1,1: 14:[66, 10] Operation: 23-13=10 Exploring Operation: 66-13=53, Resulting Numbers: [23, 53] Generated Node #0,1,2: 14:[23, 53] Operation: 66-13=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[13, 43], Operations: ['91-68=23', '66-23=43'] Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,14 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 14:[23, 53], Operations: ['91-68=23', '66-13=53'] Exploring Operation: 23*53=1219, Resulting Numbers: [1219] 1219,14 unequal: No Solution Exploring Operation: 23+53=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[66, 10], Operations: ['91-68=23', '23-13=10'] Exploring Operation: 66+10=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 66*10=660, Resulting Numbers: [660] 660,14 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[13, 68, 25], Operations: ['91-66=25'] Exploring Operation: 68-13=55, Resulting Numbers: [25, 55] Generated Node #0,2,0: 14:[25, 55] Operation: 68-13=55 Exploring Operation: 25-13=12, Resulting Numbers: [68, 12] Generated Node #0,2,1: 14:[68, 12] Operation: 25-13=12 Exploring Operation: 68-25=43, Resulting Numbers: [13, 43] Generated Node #0,2,2: 14:[13, 43] Operation: 68-25=43 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 14:[13, 43], Operations: ['91-66=25', '68-25=43'] Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,14 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 14:[25, 55], Operations: ['91-66=25', '68-13=55'] Exploring Operation: 25+55=80, Resulting Numbers: [80] 80,14 unequal: No Solution Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,14 unequal: No Solution Exploring Operation: 25*55=1375, Resulting Numbers: [1375] 1375,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 14:[68, 12], Operations: ['91-66=25', '25-13=12'] Exploring Operation: 68*12=816, Resulting Numbers: [816] 816,14 unequal: No Solution Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,14 unequal: No Solution Exploring Operation: 68+12=80, Resulting Numbers: [80] 80,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[13, 91, 2], Operations: ['68-66=2'] Exploring Operation: 91-2=89, Resulting Numbers: [13, 89] Generated Node #0,0,0: 14:[13, 89] Operation: 91-2=89 Exploring Operation: 91-13=78, Resulting Numbers: [2, 78] Generated Node #0,0,1: 14:[2, 78] Operation: 91-13=78 Exploring Operation: 91/13=7, Resulting Numbers: [2, 7] Generated Node #0,0,2: 14:[2, 7] Operation: 91/13=7 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 14:[2, 7], Operations: ['68-66=2', '91/13=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,14 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[66, 13, 68, 91], Operations: [] Exploring Operation: 68-66=2, Resulting Numbers: [13, 91, 2] Generated Node #0,0: 14:[13, 91, 2] Operation: 68-66=2 Moving to Node #0,0 Current State: 14:[13, 91, 2], Operations: ['68-66=2'] Exploring Operation: 91/13=7, Resulting Numbers: [2, 7] Generated Node #0,0,2: 14:[2, 7] Operation: 91/13=7 Moving to Node #0,0,2 Current State: 14:[2, 7], Operations: ['68-66=2', '91/13=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 22, 63, 62, 23 ]
40
[ "22*63=1386", "62*23=1426", "1426-1386=40" ]
Current State: 40:[22, 63, 62, 23], Operations: [] Exploring Operation: 22*63=1386, Resulting Numbers: [62, 23, 1386] Generated Node #2: [62, 23, 1386] from Operation: 22*63=1386 Current State: 40:[62, 23, 1386], Operations: ['22*63=1386'] Exploring Operation: 62*23=1426, Resulting Numbers: [1386, 1426] Generated Node #3: [1386, 1426] from Operation: 62*23=1426 Current State: 40:[1386, 1426], Operations: ['22*63=1386', '62*23=1426'] Exploring Operation: 1426-1386=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[22, 63, 62, 23], Operations: [] Exploring Operation: 63-62=1, Resulting Numbers: [22, 23, 1] Generated Node #0,0: 40:[22, 23, 1] Operation: 63-62=1 Exploring Operation: 62-22=40, Resulting Numbers: [63, 23, 40] Generated Node #0,1: 40:[63, 23, 40] Operation: 62-22=40 Exploring Operation: 63-22=41, Resulting Numbers: [62, 23, 41] Generated Node #0,2: 40:[62, 23, 41] Operation: 63-22=41 Exploring Operation: 63-23=40, Resulting Numbers: [22, 62, 40] Generated Node #0,3: 40:[22, 62, 40] Operation: 63-23=40 Moving to Node #0,0 Current State: 40:[22, 23, 1], Operations: ['63-62=1'] Exploring Operation: 22-1=21, Resulting Numbers: [23, 21] Generated Node #0,0,0: 40:[23, 21] Operation: 22-1=21 Exploring Operation: 22*1=22, Resulting Numbers: [23, 22] Generated Node #0,0,1: 40:[23, 22] Operation: 22*1=22 Exploring Operation: 23-1=22, Resulting Numbers: [22, 22] Generated Node #0,0,2: 40:[22, 22] Operation: 23-1=22 Exploring Operation: 23-22=1, Resulting Numbers: [1, 1] Generated Node #0,0,3: 40:[1, 1] Operation: 23-22=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 40:[1, 1], Operations: ['63-62=1', '23-22=1'] Exploring Operation: 1*1=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 1/1=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 1-1=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 1+1=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[23, 21], Operations: ['63-62=1', '22-1=21'] Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,40 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[22, 22], Operations: ['63-62=1', '23-1=22'] Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,40 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[23, 22], Operations: ['63-62=1', '22*1=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,40 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: 40:[22, 62, 40], Operations: ['63-23=40'] Exploring Operation: 22+62=84, Resulting Numbers: [40, 84] Generated Node #0,3,0: 40:[40, 84] Operation: 22+62=84 Exploring Operation: 62-40=22, Resulting Numbers: [22, 22] Generated Node #0,3,1: 40:[22, 22] Operation: 62-40=22 Exploring Operation: 40-22=18, Resulting Numbers: [62, 18] Generated Node #0,3,2: 40:[62, 18] Operation: 40-22=18 Exploring Operation: 62-22=40, Resulting Numbers: [40, 40] Generated Node #0,3,3: 40:[40, 40] Operation: 62-22=40 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 40:[40, 40], Operations: ['63-23=40', '62-22=40'] Exploring Operation: 40*40=1600, Resulting Numbers: [1600] 1600,40 unequal: No Solution Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,40 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 #0,3,1 Current State: 40:[22, 22], Operations: ['63-23=40', '62-40=22'] Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,40 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,40 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 #0,3,2 Current State: 40:[62, 18], Operations: ['63-23=40', '40-22=18'] Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,40 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 #0,3,0 Current State: 40:[40, 84], Operations: ['63-23=40', '22+62=84'] Exploring Operation: 40*84=3360, Resulting Numbers: [3360] 3360,40 unequal: No Solution Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,40 unequal: No Solution Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,40 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: 40:[62, 23, 41], Operations: ['63-22=41'] Exploring Operation: 62-23=39, Resulting Numbers: [41, 39] Generated Node #0,2,0: 40:[41, 39] Operation: 62-23=39 Exploring Operation: 41-23=18, Resulting Numbers: [62, 18] Generated Node #0,2,1: 40:[62, 18] Operation: 41-23=18 Exploring Operation: 62-41=21, Resulting Numbers: [23, 21] Generated Node #0,2,2: 40:[23, 21] Operation: 62-41=21 Exploring Operation: 62+23=85, Resulting Numbers: [41, 85] Generated Node #0,2,3: 40:[41, 85] Operation: 62+23=85 Moving to Node #0,1 Current State: 40:[63, 23, 40], Operations: ['62-22=40'] Exploring Operation: 40-23=17, Resulting Numbers: [63, 17] Generated Node #0,1,0: 40:[63, 17] Operation: 40-23=17 Exploring Operation: 63-40=23, Resulting Numbers: [23, 23] Generated Node #0,1,1: 40:[23, 23] Operation: 63-40=23 Exploring Operation: 63-23=40, Resulting Numbers: [40, 40] Generated Node #0,1,2: 40:[40, 40] Operation: 63-23=40 Exploring Operation: 63+23=86, Resulting Numbers: [40, 86] Generated Node #0,1,3: 40:[40, 86] Operation: 63+23=86 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[40, 40], Operations: ['62-22=40', '63-23=40'] Exploring Operation: 40*40=1600, Resulting Numbers: [1600] 1600,40 unequal: No Solution Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,40 unequal: No Solution Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,40 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 #0,1,1 Current State: 40:[23, 23], Operations: ['62-22=40', '63-40=23'] Exploring Operation: 23-23=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 23*23=529, Resulting Numbers: [529] 529,40 unequal: No Solution Exploring Operation: 23+23=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 23/23=1, Resulting Numbers: [1] 1,40 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 #0,1,0 Current State: 40:[63, 17], Operations: ['62-22=40', '40-23=17'] Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 63+17=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 63*17=1071, Resulting Numbers: [1071] 1071,40 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 #0,1,3 Current State: 40:[40, 86], Operations: ['62-22=40', '63+23=86'] Exploring Operation: 40+86=126, Resulting Numbers: [126] 126,40 unequal: No Solution Exploring Operation: 86-40=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 40*86=3440, Resulting Numbers: [3440] 3440,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 40:[41, 39], Operations: ['63-22=41', '62-23=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,40 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[23, 21], Operations: ['63-22=41', '62-41=21'] Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,40 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,40 unequal: No Solution Moving to Node #0,2,1 Current State: 40:[62, 18], Operations: ['63-22=41', '41-23=18'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,40 unequal: No Solution Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,40 unequal: No Solution Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,40 unequal: No Solution Moving to Node #0,2,3 Current State: 40:[41, 85], Operations: ['63-22=41', '62+23=85'] Exploring Operation: 41*85=3485, Resulting Numbers: [3485] 3485,40 unequal: No Solution Exploring Operation: 41+85=126, Resulting Numbers: [126] 126,40 unequal: No Solution Exploring Operation: 85-41=44, Resulting Numbers: [44] 44,40 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 61, 16, 35, 2 ]
55
[ "61-16=45", "2*45=90", "90-35=55" ]
Current State: 55:[61, 16, 35, 2], Operations: [] Exploring Operation: 61-16=45, Resulting Numbers: [35, 2, 45] Generated Node #2: [35, 2, 45] from Operation: 61-16=45 Current State: 55:[35, 2, 45], Operations: ['61-16=45'] Exploring Operation: 2*45=90, Resulting Numbers: [35, 90] Generated Node #3: [35, 90] from Operation: 2*45=90 Current State: 55:[35, 90], Operations: ['61-16=45', '2*45=90'] Exploring Operation: 90-35=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[61, 16, 35, 2], Operations: [] Exploring Operation: 16+35=51, Resulting Numbers: [61, 2, 51] Generated Node #0,0: 55:[61, 2, 51] Operation: 16+35=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[61, 2, 51], Operations: ['16+35=51'] Exploring Operation: 61-51=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 55:[2, 10] Operation: 61-51=10 Moving to Node #0,0,0 Current State: 55:[2, 10], Operations: ['16+35=51', '61-51=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,55 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
[ 82, 44, 74, 60 ]
72
[ "82-60=22", "44/22=2", "74-2=72" ]
Current State: 72:[82, 44, 74, 60], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [44, 74, 22] Generated Node #2: [44, 74, 22] from Operation: 82-60=22 Current State: 72:[44, 74, 22], Operations: ['82-60=22'] Exploring Operation: 44/22=2, Resulting Numbers: [74, 2] Generated Node #3: [74, 2] from Operation: 44/22=2 Current State: 72:[74, 2], Operations: ['82-60=22', '44/22=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[82, 44, 74, 60], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [44, 74, 22] Generated Node #0,0: 72:[44, 74, 22] Operation: 82-60=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[44, 74, 22], Operations: ['82-60=22'] Exploring Operation: 44/22=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 72:[74, 2] Operation: 44/22=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[74, 2], Operations: ['82-60=22', '44/22=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[82, 44, 74, 60], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [44, 74, 22] Generated Node #0,0: 72:[44, 74, 22] Operation: 82-60=22 Moving to Node #0,0 Current State: 72:[44, 74, 22], Operations: ['82-60=22'] Exploring Operation: 44/22=2, Resulting Numbers: [74, 2] Generated Node #0,0,0: 72:[74, 2] Operation: 44/22=2 Moving to Node #0,0,0 Current State: 72:[74, 2], Operations: ['82-60=22', '44/22=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 35, 71, 14, 60 ]
60
[ "35+71=106", "60-14=46", "106-46=60" ]
Current State: 60:[35, 71, 14, 60], Operations: [] Exploring Operation: 35+71=106, Resulting Numbers: [14, 60, 106] Generated Node #2: [14, 60, 106] from Operation: 35+71=106 Current State: 60:[14, 60, 106], Operations: ['35+71=106'] Exploring Operation: 60-14=46, Resulting Numbers: [106, 46] Generated Node #3: [106, 46] from Operation: 60-14=46 Current State: 60:[106, 46], Operations: ['35+71=106', '60-14=46'] Exploring Operation: 106-46=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[35, 71, 14, 60], Operations: [] Exploring Operation: 71-35=36, Resulting Numbers: [14, 60, 36] Generated Node #0,0: 60:[14, 60, 36] Operation: 71-35=36 Exploring Operation: 71-14=57, Resulting Numbers: [35, 60, 57] Generated Node #0,1: 60:[35, 60, 57] Operation: 71-14=57 Exploring Operation: 71-60=11, Resulting Numbers: [35, 14, 11] Generated Node #0,2: 60:[35, 14, 11] Operation: 71-60=11 Moving to Node #0,0 Current State: 60:[14, 60, 36], Operations: ['71-35=36'] Exploring Operation: 14+36=50, Resulting Numbers: [60, 50] Generated Node #0,0,0: 60:[60, 50] Operation: 14+36=50 Exploring Operation: 60-36=24, Resulting Numbers: [14, 24] Generated Node #0,0,1: 60:[14, 24] Operation: 60-36=24 Exploring Operation: 36-14=22, Resulting Numbers: [60, 22] Generated Node #0,0,2: 60:[60, 22] Operation: 36-14=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 60:[60, 22], Operations: ['71-35=36', '36-14=22'] Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,60 unequal: No Solution Exploring Operation: 60*22=1320, Resulting Numbers: [1320] 1320,60 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,60 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:[14, 24], Operations: ['71-35=36', '60-36=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 14*24=336, Resulting Numbers: [336] 336,60 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,60 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 #0,0,0 Current State: 60:[60, 50], Operations: ['71-35=36', '14+36=50'] Exploring Operation: 60-50=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 60+50=110, Resulting Numbers: [110] 110,60 unequal: No Solution Exploring Operation: 60*50=3000, Resulting Numbers: [3000] 3000,60 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:[35, 14, 11], Operations: ['71-60=11'] Exploring Operation: 35-14=21, Resulting Numbers: [11, 21] Generated Node #0,2,0: 60:[11, 21] Operation: 35-14=21 Exploring Operation: 14-11=3, Resulting Numbers: [35, 3] Generated Node #0,2,1: 60:[35, 3] Operation: 14-11=3 Exploring Operation: 35-11=24, Resulting Numbers: [14, 24] Generated Node #0,2,2: 60:[14, 24] Operation: 35-11=24 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 60:[11, 21], Operations: ['71-60=11', '35-14=21'] Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 60:[35, 3], Operations: ['71-60=11', '14-11=3'] Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,60 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,60 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 60:[14, 24], Operations: ['71-60=11', '35-11=24'] Exploring Operation: 14*24=336, Resulting Numbers: [336] 336,60 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 60:[35, 60, 57], Operations: ['71-14=57'] Exploring Operation: 57-35=22, Resulting Numbers: [60, 22] Generated Node #0,1,0: 60:[60, 22] Operation: 57-35=22 Exploring Operation: 60-57=3, Resulting Numbers: [35, 3] Generated Node #0,1,1: 60:[35, 3] Operation: 60-57=3 Exploring Operation: 60-35=25, Resulting Numbers: [57, 25] Generated Node #0,1,2: 60:[57, 25] Operation: 60-35=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[60, 22], Operations: ['71-14=57', '57-35=22'] Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,60 unequal: No Solution Exploring Operation: 60*22=1320, Resulting Numbers: [1320] 1320,60 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[35, 3], Operations: ['71-14=57', '60-57=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,60 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[57, 25], Operations: ['71-14=57', '60-35=25'] Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,60 unequal: No Solution Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,60 unequal: No Solution Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,60 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
[ 18, 38, 52, 7 ]
80
[ "52-38=14", "7*14=98", "98-18=80" ]
Current State: 80:[18, 38, 52, 7], Operations: [] Exploring Operation: 52-38=14, Resulting Numbers: [18, 7, 14] Generated Node #2: [18, 7, 14] from Operation: 52-38=14 Current State: 80:[18, 7, 14], Operations: ['52-38=14'] Exploring Operation: 7*14=98, Resulting Numbers: [18, 98] Generated Node #3: [18, 98] from Operation: 7*14=98 Current State: 80:[18, 98], Operations: ['52-38=14', '7*14=98'] Exploring Operation: 98-18=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[18, 38, 52, 7], Operations: [] Exploring Operation: 52-38=14, Resulting Numbers: [18, 7, 14] Generated Node #0,0: 80:[18, 7, 14] Operation: 52-38=14 Moving to Node #0,0 Current State: 80:[18, 7, 14], Operations: ['52-38=14'] Exploring Operation: 18-14=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 80:[7, 4] Operation: 18-14=4 Moving to Node #0,0,0 Current State: 80:[7, 4], Operations: ['52-38=14', '18-14=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,80 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 6, 74, 8, 76 ]
50
[ "6*8=48", "76-74=2", "48+2=50" ]
Current State: 50:[6, 74, 8, 76], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [74, 76, 48] Generated Node #2: [74, 76, 48] from Operation: 6*8=48 Current State: 50:[74, 76, 48], Operations: ['6*8=48'] Exploring Operation: 76-74=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 76-74=2 Current State: 50:[48, 2], Operations: ['6*8=48', '76-74=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[6, 74, 8, 76], Operations: [] Exploring Operation: 74-8=66, Resulting Numbers: [6, 76, 66] Generated Node #0,0: 50:[6, 76, 66] Operation: 74-8=66 Exploring Operation: 74-6=68, Resulting Numbers: [8, 76, 68] Generated Node #0,1: 50:[8, 76, 68] Operation: 74-6=68 Exploring Operation: 76-74=2, Resulting Numbers: [6, 8, 2] Generated Node #0,2: 50:[6, 8, 2] Operation: 76-74=2 Exploring Operation: 76-6=70, Resulting Numbers: [74, 8, 70] Generated Node #0,3: 50:[74, 8, 70] Operation: 76-6=70 Exploring Operation: 76-8=68, Resulting Numbers: [6, 74, 68] Generated Node #0,4: 50:[6, 74, 68] Operation: 76-8=68 Moving to Node #0,2 Current State: 50:[6, 8, 2], Operations: ['76-74=2'] Exploring Operation: 8-6=2, Resulting Numbers: [2, 2] Generated Node #0,2,0: 50:[2, 2] Operation: 8-6=2 Exploring Operation: 8/2=4, Resulting Numbers: [6, 4] Generated Node #0,2,1: 50:[6, 4] Operation: 8/2=4 Exploring Operation: 8-2=6, Resulting Numbers: [6, 6] Generated Node #0,2,2: 50:[6, 6] Operation: 8-2=6 Exploring Operation: 6*8=48, Resulting Numbers: [2, 48] Generated Node #0,2,3: 50:[2, 48] Operation: 6*8=48 Exploring Operation: 8+2=10, Resulting Numbers: [6, 10] Generated Node #0,2,4: 50:[6, 10] Operation: 8+2=10 Moving to Node #0,4 Current State: 50:[6, 74, 68], Operations: ['76-8=68'] Exploring Operation: 6+74=80, Resulting Numbers: [68, 80] Generated Node #0,4,0: 50:[68, 80] Operation: 6+74=80 Exploring Operation: 74-6=68, Resulting Numbers: [68, 68] Generated Node #0,4,1: 50:[68, 68] Operation: 74-6=68 Exploring Operation: 6+68=74, Resulting Numbers: [74, 74] Generated Node #0,4,2: 50:[74, 74] Operation: 6+68=74 Exploring Operation: 74-68=6, Resulting Numbers: [6, 6] Generated Node #0,4,3: 50:[6, 6] Operation: 74-68=6 Exploring Operation: 68-6=62, Resulting Numbers: [74, 62] Generated Node #0,4,4: 50:[74, 62] Operation: 68-6=62 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 50:[6, 6], Operations: ['76-8=68', '74-68=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,50 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 50:[68, 68], Operations: ['76-8=68', '74-6=68'] Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,50 unequal: No Solution Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 50:[74, 62], Operations: ['76-8=68', '68-6=62'] Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,50 unequal: No Solution Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,50 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 50:[68, 80], Operations: ['76-8=68', '6+74=80'] Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,50 unequal: No Solution Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,50 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 50:[74, 74], Operations: ['76-8=68', '6+68=74'] Exploring Operation: 74/74=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 74-74=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 74*74=5476, Resulting Numbers: [5476] 5476,50 unequal: No Solution Exploring Operation: 74+74=148, Resulting Numbers: [148] 148,50 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: 50:[6, 76, 66], Operations: ['74-8=66'] Exploring Operation: 6+76=82, Resulting Numbers: [66, 82] Generated Node #0,0,0: 50:[66, 82] Operation: 6+76=82 Exploring Operation: 76-66=10, Resulting Numbers: [6, 10] Generated Node #0,0,1: 50:[6, 10] Operation: 76-66=10 Exploring Operation: 76-6=70, Resulting Numbers: [66, 70] Generated Node #0,0,2: 50:[66, 70] Operation: 76-6=70 Exploring Operation: 66-6=60, Resulting Numbers: [76, 60] Generated Node #0,0,3: 50:[76, 60] Operation: 66-6=60 Exploring Operation: 66/6=11, Resulting Numbers: [76, 11] Generated Node #0,0,4: 50:[76, 11] Operation: 66/6=11 Moving to Node #0,1 Current State: 50:[8, 76, 68], Operations: ['74-6=68'] Exploring Operation: 68-8=60, Resulting Numbers: [76, 60] Generated Node #0,1,0: 50:[76, 60] Operation: 68-8=60 Exploring Operation: 76-68=8, Resulting Numbers: [8, 8] Generated Node #0,1,1: 50:[8, 8] Operation: 76-68=8 Exploring Operation: 8+76=84, Resulting Numbers: [68, 84] Generated Node #0,1,2: 50:[68, 84] Operation: 8+76=84 Exploring Operation: 76-8=68, Resulting Numbers: [68, 68] Generated Node #0,1,3: 50:[68, 68] Operation: 76-8=68 Exploring Operation: 8+68=76, Resulting Numbers: [76, 76] Generated Node #0,1,4: 50:[76, 76] Operation: 8+68=76 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[8, 8], Operations: ['74-6=68', '76-68=8'] Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,50 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[76, 60], Operations: ['74-6=68', '68-8=60'] Exploring Operation: 76+60=136, Resulting Numbers: [136] 136,50 unequal: No Solution Exploring Operation: 76-60=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 76*60=4560, Resulting Numbers: [4560] 4560,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 50:[68, 68], Operations: ['74-6=68', '76-8=68'] Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,50 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,50 unequal: No Solution Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[68, 84], Operations: ['74-6=68', '8+76=84'] Exploring Operation: 68+84=152, Resulting Numbers: [152] 152,50 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 68*84=5712, Resulting Numbers: [5712] 5712,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 50:[76, 76], Operations: ['74-6=68', '8+68=76'] Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,50 unequal: No Solution Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,50 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,50 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,50 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: 50:[74, 8, 70], Operations: ['76-6=70'] Exploring Operation: 70-8=62, Resulting Numbers: [74, 62] Generated Node #0,3,0: 50:[74, 62] Operation: 70-8=62 Exploring Operation: 8+70=78, Resulting Numbers: [74, 78] Generated Node #0,3,1: 50:[74, 78] Operation: 8+70=78 Exploring Operation: 74-8=66, Resulting Numbers: [70, 66] Generated Node #0,3,2: 50:[70, 66] Operation: 74-8=66 Exploring Operation: 74-70=4, Resulting Numbers: [8, 4] Generated Node #0,3,3: 50:[8, 4] Operation: 74-70=4 Exploring Operation: 74+8=82, Resulting Numbers: [70, 82] Generated Node #0,3,4: 50:[70, 82] Operation: 74+8=82 Moving to Node #0,2,0 Current State: 50:[2, 2], Operations: ['76-74=2', '8-6=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[6, 10], Operations: ['74-8=66', '76-66=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,50 unequal: No Solution Moving to Node #0,2,4 Current State: 50:[6, 10], Operations: ['76-74=2', '8+2=10'] Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,50 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[6, 4], Operations: ['76-74=2', '8/2=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,50 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[2, 48], Operations: ['76-74=2', '6*8=48'] Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,50 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,50 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[6, 74, 8, 76], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [6, 8, 2] Generated Node #0,2: 50:[6, 8, 2] Operation: 76-74=2 Moving to Node #0,2 Current State: 50:[6, 8, 2], Operations: ['76-74=2'] Exploring Operation: 6*8=48, Resulting Numbers: [2, 48] Generated Node #0,2,3: 50:[2, 48] Operation: 6*8=48 Moving to Node #0,2,3 Current State: 50:[2, 48], Operations: ['76-74=2', '6*8=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.925347
hs_5
mult_heuristic
[ 43, 32, 66, 96 ]
63
[ "43*96=4128", "4128/32=129", "129-66=63" ]
Current State: 63:[43, 32, 66, 96], Operations: [] Exploring Operation: 43*96=4128, Resulting Numbers: [32, 66, 4128] Generated Node #2: [32, 66, 4128] from Operation: 43*96=4128 Current State: 63:[32, 66, 4128], Operations: ['43*96=4128'] Exploring Operation: 4128/32=129, Resulting Numbers: [66, 129] Generated Node #3: [66, 129] from Operation: 4128/32=129 Current State: 63:[66, 129], Operations: ['43*96=4128', '4128/32=129'] Exploring Operation: 129-66=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[43, 32, 66, 96], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [43, 66, 3] Generated Node #0,0: 63:[43, 66, 3] Operation: 96/32=3 Exploring Operation: 96-43=53, Resulting Numbers: [32, 66, 53] Generated Node #0,1: 63:[32, 66, 53] Operation: 96-43=53 Exploring Operation: 96-32=64, Resulting Numbers: [43, 66, 64] Generated Node #0,2: 63:[43, 66, 64] Operation: 96-32=64 Moving to Node #0,0 Current State: 63:[43, 66, 3], Operations: ['96/32=3'] Exploring Operation: 66-3=63, Resulting Numbers: [43, 63] Generated Node #0,0,0: 63:[43, 63] Operation: 66-3=63 Exploring Operation: 43+3=46, Resulting Numbers: [66, 46] Generated Node #0,0,1: 63:[66, 46] Operation: 43+3=46 Exploring Operation: 66-43=23, Resulting Numbers: [3, 23] Generated Node #0,0,2: 63:[3, 23] Operation: 66-43=23 Moving to Node #0,1 Current State: 63:[32, 66, 53], Operations: ['96-43=53'] Exploring Operation: 66-53=13, Resulting Numbers: [32, 13] Generated Node #0,1,0: 63:[32, 13] Operation: 66-53=13 Exploring Operation: 53-32=21, Resulting Numbers: [66, 21] Generated Node #0,1,1: 63:[66, 21] Operation: 53-32=21 Exploring Operation: 66-32=34, Resulting Numbers: [53, 34] Generated Node #0,1,2: 63:[53, 34] Operation: 66-32=34 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[66, 21], Operations: ['96-43=53', '53-32=21'] Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,63 unequal: No Solution Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 66*21=1386, Resulting Numbers: [1386] 1386,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[32, 13], Operations: ['96-43=53', '66-53=13'] Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,63 unequal: No Solution Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[53, 34], Operations: ['96-43=53', '66-32=34'] Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,63 unequal: No Solution Exploring Operation: 53+34=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 53*34=1802, Resulting Numbers: [1802] 1802,63 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: 63:[43, 66, 64], Operations: ['96-32=64'] Exploring Operation: 66-43=23, Resulting Numbers: [64, 23] Generated Node #0,2,0: 63:[64, 23] Operation: 66-43=23 Exploring Operation: 64-43=21, Resulting Numbers: [66, 21] Generated Node #0,2,1: 63:[66, 21] Operation: 64-43=21 Exploring Operation: 66-64=2, Resulting Numbers: [43, 2] Generated Node #0,2,2: 63:[43, 2] Operation: 66-64=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[64, 23], Operations: ['96-32=64', '66-43=23'] Exploring Operation: 64-23=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 64+23=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 64*23=1472, Resulting Numbers: [1472] 1472,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[66, 21], Operations: ['96-32=64', '64-43=21'] Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,63 unequal: No Solution Exploring Operation: 66*21=1386, Resulting Numbers: [1386] 1386,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[43, 2], Operations: ['96-32=64', '66-64=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,63 unequal: No Solution Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,63 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: 63:[3, 23], Operations: ['96/32=3', '66-43=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,63 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[43, 63], Operations: ['96/32=3', '66-3=63'] Exploring Operation: 43+63=106, Resulting Numbers: [106] 106,63 unequal: No Solution Exploring Operation: 43*63=2709, Resulting Numbers: [2709] 2709,63 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[66, 46], Operations: ['96/32=3', '43+3=46'] Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,63 unequal: No Solution Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,63 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 83, 61, 44, 28 ]
94
[ "83-61=22", "44+28=72", "22+72=94" ]
Current State: 94:[83, 61, 44, 28], Operations: [] Exploring Operation: 83-61=22, Resulting Numbers: [44, 28, 22] Generated Node #2: [44, 28, 22] from Operation: 83-61=22 Current State: 94:[44, 28, 22], Operations: ['83-61=22'] Exploring Operation: 44+28=72, Resulting Numbers: [22, 72] Generated Node #3: [22, 72] from Operation: 44+28=72 Current State: 94:[22, 72], Operations: ['83-61=22', '44+28=72'] Exploring Operation: 22+72=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[83, 61, 44, 28], Operations: [] Exploring Operation: 61+28=89, Resulting Numbers: [83, 44, 89] Generated Node #0,0: 94:[83, 44, 89] Operation: 61+28=89 Exploring Operation: 61-28=33, Resulting Numbers: [83, 44, 33] Generated Node #0,1: 94:[83, 44, 33] Operation: 61-28=33 Exploring Operation: 83-28=55, Resulting Numbers: [61, 44, 55] Generated Node #0,2: 94:[61, 44, 55] Operation: 83-28=55 Moving to Node #0,0 Current State: 94:[83, 44, 89], Operations: ['61+28=89'] Exploring Operation: 89-44=45, Resulting Numbers: [83, 45] Generated Node #0,0,0: 94:[83, 45] Operation: 89-44=45 Exploring Operation: 83-44=39, Resulting Numbers: [89, 39] Generated Node #0,0,1: 94:[89, 39] Operation: 83-44=39 Exploring Operation: 89-83=6, Resulting Numbers: [44, 6] Generated Node #0,0,2: 94:[44, 6] Operation: 89-83=6 Moving to Node #0,2 Current State: 94:[61, 44, 55], Operations: ['83-28=55'] Exploring Operation: 44+55=99, Resulting Numbers: [61, 99] Generated Node #0,2,0: 94:[61, 99] Operation: 44+55=99 Exploring Operation: 61-55=6, Resulting Numbers: [44, 6] Generated Node #0,2,1: 94:[44, 6] Operation: 61-55=6 Exploring Operation: 61+44=105, Resulting Numbers: [55, 105] Generated Node #0,2,2: 94:[55, 105] Operation: 61+44=105 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 94:[44, 6], Operations: ['83-28=55', '61-55=6'] Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,94 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 94:[61, 99], Operations: ['83-28=55', '44+55=99'] Exploring Operation: 99-61=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 61*99=6039, Resulting Numbers: [6039] 6039,94 unequal: No Solution Exploring Operation: 61+99=160, Resulting Numbers: [160] 160,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 94:[55, 105], Operations: ['83-28=55', '61+44=105'] Exploring Operation: 105-55=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 55*105=5775, Resulting Numbers: [5775] 5775,94 unequal: No Solution Exploring Operation: 55+105=160, Resulting Numbers: [160] 160,94 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: 94:[83, 44, 33], Operations: ['61-28=33'] Exploring Operation: 83-44=39, Resulting Numbers: [33, 39] Generated Node #0,1,0: 94:[33, 39] Operation: 83-44=39 Exploring Operation: 83-33=50, Resulting Numbers: [44, 50] Generated Node #0,1,1: 94:[44, 50] Operation: 83-33=50 Exploring Operation: 44-33=11, Resulting Numbers: [83, 11] Generated Node #0,1,2: 94:[83, 11] Operation: 44-33=11 Moving to Node #0,1,1 Current State: 94:[44, 50], Operations: ['61-28=33', '83-33=50'] Exploring Operation: 44*50=2200, Resulting Numbers: [2200] 2200,94 unequal: No Solution Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[83, 61, 44, 28], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [83, 44, 33] Generated Node #0,1: 94:[83, 44, 33] Operation: 61-28=33 Moving to Node #0,1 Current State: 94:[83, 44, 33], Operations: ['61-28=33'] Exploring Operation: 83-33=50, Resulting Numbers: [44, 50] Generated Node #0,1,1: 94:[44, 50] Operation: 83-33=50 Moving to Node #0,1,1 Current State: 94:[44, 50], Operations: ['61-28=33', '83-33=50'] Exploring Operation: 44+50=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 40, 1, 20, 16 ]
43
[ "40-1=39", "20-16=4", "39+4=43" ]
Current State: 43:[40, 1, 20, 16], Operations: [] Exploring Operation: 40-1=39, Resulting Numbers: [20, 16, 39] Generated Node #2: [20, 16, 39] from Operation: 40-1=39 Current State: 43:[20, 16, 39], Operations: ['40-1=39'] Exploring Operation: 20-16=4, Resulting Numbers: [39, 4] Generated Node #3: [39, 4] from Operation: 20-16=4 Current State: 43:[39, 4], Operations: ['40-1=39', '20-16=4'] Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[40, 1, 20, 16], Operations: [] Exploring Operation: 1+20=21, Resulting Numbers: [40, 16, 21] Generated Node #0,0: 43:[40, 16, 21] Operation: 1+20=21 Exploring Operation: 40+1=41, Resulting Numbers: [20, 16, 41] Generated Node #0,1: 43:[20, 16, 41] Operation: 40+1=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[40, 16, 21], Operations: ['1+20=21'] Exploring Operation: 40+16=56, Resulting Numbers: [21, 56] Generated Node #0,0,0: 43:[21, 56] Operation: 40+16=56 Exploring Operation: 16+21=37, Resulting Numbers: [40, 37] Generated Node #0,0,1: 43:[40, 37] Operation: 16+21=37 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[40, 37], Operations: ['1+20=21', '16+21=37'] Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,43 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[21, 56], Operations: ['1+20=21', '40+16=56'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,43 unequal: No Solution Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,43 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: 43:[20, 16, 41], Operations: ['40+1=41'] Exploring Operation: 20+16=36, Resulting Numbers: [41, 36] Generated Node #0,1,0: 43:[41, 36] Operation: 20+16=36 Exploring Operation: 16+41=57, Resulting Numbers: [20, 57] Generated Node #0,1,1: 43:[20, 57] Operation: 16+41=57 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[41, 36], Operations: ['40+1=41', '20+16=36'] Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,43 unequal: No Solution Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[20, 57], Operations: ['40+1=41', '16+41=57'] Exploring Operation: 20+57=77, Resulting Numbers: [77] 77,43 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 24, 98, 51, 2 ]
96
[ "51*2=102", "102-98=4", "24*4=96" ]
Current State: 96:[24, 98, 51, 2], Operations: [] Exploring Operation: 51*2=102, Resulting Numbers: [24, 98, 102] Generated Node #2: [24, 98, 102] from Operation: 51*2=102 Current State: 96:[24, 98, 102], Operations: ['51*2=102'] Exploring Operation: 102-98=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 102-98=4 Current State: 96:[24, 4], Operations: ['51*2=102', '102-98=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[24, 98, 51, 2], Operations: [] Exploring Operation: 51-24=27, Resulting Numbers: [98, 2, 27] Generated Node #0,0: 96:[98, 2, 27] Operation: 51-24=27 Exploring Operation: 98-51=47, Resulting Numbers: [24, 2, 47] Generated Node #0,1: 96:[24, 2, 47] Operation: 98-51=47 Exploring Operation: 98-2=96, Resulting Numbers: [24, 51, 96] Generated Node #0,2: 96:[24, 51, 96] Operation: 98-2=96 Exploring Operation: 51-2=49, Resulting Numbers: [24, 98, 49] Generated Node #0,3: 96:[24, 98, 49] Operation: 51-2=49 Exploring Operation: 98/2=49, Resulting Numbers: [24, 51, 49] Generated Node #0,4: 96:[24, 51, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[24, 2, 47], Operations: ['98-51=47'] Exploring Operation: 2*47=94, Resulting Numbers: [24, 94] Generated Node #0,1,0: 96:[24, 94] Operation: 2*47=94 Exploring Operation: 24*2=48, Resulting Numbers: [47, 48] Generated Node #0,1,1: 96:[47, 48] Operation: 24*2=48 Exploring Operation: 24/2=12, Resulting Numbers: [47, 12] Generated Node #0,1,2: 96:[47, 12] Operation: 24/2=12 Exploring Operation: 2+47=49, Resulting Numbers: [24, 49] Generated Node #0,1,3: 96:[24, 49] Operation: 2+47=49 Exploring Operation: 47-24=23, Resulting Numbers: [2, 23] Generated Node #0,1,4: 96:[2, 23] Operation: 47-24=23 Moving to Node #0,1,1 Current State: 96:[47, 48], Operations: ['98-51=47', '24*2=48'] Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[24, 49], Operations: ['98-51=47', '2+47=49'] Exploring Operation: 24+49=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 24*49=1176, Resulting Numbers: [1176] 1176,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[47, 12], Operations: ['98-51=47', '24/2=12'] Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,96 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[2, 23], Operations: ['98-51=47', '47-24=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[24, 94], Operations: ['98-51=47', '2*47=94'] Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,96 unequal: No Solution Exploring Operation: 24*94=2256, Resulting Numbers: [2256] 2256,96 unequal: No Solution Exploring Operation: 24+94=118, Resulting Numbers: [118] 118,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[24, 51, 96], Operations: ['98-2=96'] Exploring Operation: 24+51=75, Resulting Numbers: [96, 75] Generated Node #0,2,0: 96:[96, 75] Operation: 24+51=75 Exploring Operation: 96-51=45, Resulting Numbers: [24, 45] Generated Node #0,2,1: 96:[24, 45] Operation: 96-51=45 Exploring Operation: 24+96=120, Resulting Numbers: [51, 120] Generated Node #0,2,2: 96:[51, 120] Operation: 24+96=120 Exploring Operation: 51-24=27, Resulting Numbers: [96, 27] Generated Node #0,2,3: 96:[96, 27] Operation: 51-24=27 Exploring Operation: 96/24=4, Resulting Numbers: [51, 4] Generated Node #0,2,4: 96:[51, 4] Operation: 96/24=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[24, 45], Operations: ['98-2=96', '96-51=45'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,96 unequal: No Solution Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 96:[96, 27], Operations: ['98-2=96', '51-24=27'] Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,96 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 96:[51, 4], Operations: ['98-2=96', '96/24=4'] Exploring Operation: 51+4=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 51*4=204, Resulting Numbers: [204] 204,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[96, 75], Operations: ['98-2=96', '24+51=75'] Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,96 unequal: No Solution Exploring Operation: 96*75=7200, Resulting Numbers: [7200] 7200,96 unequal: No Solution Exploring Operation: 96+75=171, Resulting Numbers: [171] 171,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 96:[51, 120], Operations: ['98-2=96', '24+96=120'] Exploring Operation: 51+120=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 51*120=6120, Resulting Numbers: [6120] 6120,96 unequal: No Solution Exploring Operation: 120-51=69, Resulting Numbers: [69] 69,96 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 #0,3 Current State: 96:[24, 98, 49], Operations: ['51-2=49'] Exploring Operation: 24+49=73, Resulting Numbers: [98, 73] Generated Node #0,3,0: 96:[98, 73] Operation: 24+49=73 Exploring Operation: 49-24=25, Resulting Numbers: [98, 25] Generated Node #0,3,1: 96:[98, 25] Operation: 49-24=25 Exploring Operation: 98-49=49, Resulting Numbers: [24, 49] Generated Node #0,3,2: 96:[24, 49] Operation: 98-49=49 Exploring Operation: 98-24=74, Resulting Numbers: [49, 74] Generated Node #0,3,3: 96:[49, 74] Operation: 98-24=74 Exploring Operation: 98/49=2, Resulting Numbers: [24, 2] Generated Node #0,3,4: 96:[24, 2] Operation: 98/49=2 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 96:[24, 2], Operations: ['51-2=49', '98/49=2'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 96:[24, 49], Operations: ['51-2=49', '98-49=49'] Exploring Operation: 24*49=1176, Resulting Numbers: [1176] 1176,96 unequal: No Solution Exploring Operation: 24+49=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 96:[98, 25], Operations: ['51-2=49', '49-24=25'] Exploring Operation: 98+25=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 98*25=2450, Resulting Numbers: [2450] 2450,96 unequal: No Solution Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 96:[49, 74], Operations: ['51-2=49', '98-24=74'] Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 49*74=3626, Resulting Numbers: [3626] 3626,96 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 96:[98, 73], Operations: ['51-2=49', '24+49=73'] Exploring Operation: 98+73=171, Resulting Numbers: [171] 171,96 unequal: No Solution Exploring Operation: 98-73=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 98*73=7154, Resulting Numbers: [7154] 7154,96 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 #0,4 Current State: 96:[24, 51, 49], Operations: ['98/2=49'] Exploring Operation: 51-49=2, Resulting Numbers: [24, 2] Generated Node #0,4,0: 96:[24, 2] Operation: 51-49=2 Exploring Operation: 51-24=27, Resulting Numbers: [49, 27] Generated Node #0,4,1: 96:[49, 27] Operation: 51-24=27 Exploring Operation: 24+51=75, Resulting Numbers: [49, 75] Generated Node #0,4,2: 96:[49, 75] Operation: 24+51=75 Exploring Operation: 51+49=100, Resulting Numbers: [24, 100] Generated Node #0,4,3: 96:[24, 100] Operation: 51+49=100 Exploring Operation: 49-24=25, Resulting Numbers: [51, 25] Generated Node #0,4,4: 96:[51, 25] Operation: 49-24=25 Moving to Node #0,4,0 Current State: 96:[24, 2], Operations: ['98/2=49', '51-49=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,4,3 Current State: 96:[24, 100], Operations: ['98/2=49', '51+49=100'] Exploring Operation: 24*100=2400, Resulting Numbers: [2400] 2400,96 unequal: No Solution Exploring Operation: 24+100=124, Resulting Numbers: [124] 124,96 unequal: No Solution Exploring Operation: 100-24=76, Resulting Numbers: [76] 76,96 unequal: No Solution Moving to Node #0,4,1 Current State: 96:[49, 27], Operations: ['98/2=49', '51-24=27'] Exploring Operation: 49+27=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 49*27=1323, Resulting Numbers: [1323] 1323,96 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,4,4 Current State: 96:[51, 25], Operations: ['98/2=49', '49-24=25'] Exploring Operation: 51-25=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 51+25=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 51*25=1275, Resulting Numbers: [1275] 1275,96 unequal: No Solution Moving to Node #0,4,2 Current State: 96:[49, 75], Operations: ['98/2=49', '24+51=75'] Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,96 unequal: No Solution Exploring Operation: 49*75=3675, Resulting Numbers: [3675] 3675,96 unequal: No Solution Exploring Operation: 49+75=124, Resulting Numbers: [124] 124,96 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:[98, 2, 27], Operations: ['51-24=27'] Exploring Operation: 98+2=100, Resulting Numbers: [27, 100] Generated Node #0,0,0: 96:[27, 100] Operation: 98+2=100 Exploring Operation: 2+27=29, Resulting Numbers: [98, 29] Generated Node #0,0,1: 96:[98, 29] Operation: 2+27=29 Exploring Operation: 27-2=25, Resulting Numbers: [98, 25] Generated Node #0,0,2: 96:[98, 25] Operation: 27-2=25 Exploring Operation: 98-2=96, Resulting Numbers: [27, 96] Generated Node #0,0,3: 96:[27, 96] Operation: 98-2=96 Exploring Operation: 98/2=49, Resulting Numbers: [27, 49] Generated Node #0,0,4: 96:[27, 49] Operation: 98/2=49 Moving to Node #0,0,2 Current State: 96:[98, 25], Operations: ['51-24=27', '27-2=25'] Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 98*25=2450, Resulting Numbers: [2450] 2450,96 unequal: No Solution Exploring Operation: 98+25=123, Resulting Numbers: [123] 123,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[27, 96], Operations: ['51-24=27', '98-2=96'] Exploring Operation: 27+96=123, Resulting Numbers: [123] 123,96 unequal: No Solution Exploring Operation: 27*96=2592, Resulting Numbers: [2592] 2592,96 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[27, 49], Operations: ['51-24=27', '98/2=49'] Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,96 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[98, 29], Operations: ['51-24=27', '2+27=29'] Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,96 unequal: No Solution Exploring Operation: 98*29=2842, Resulting Numbers: [2842] 2842,96 unequal: No Solution Exploring Operation: 98+29=127, Resulting Numbers: [127] 127,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[27, 100], Operations: ['51-24=27', '98+2=100'] Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,96 unequal: No Solution Exploring Operation: 27*100=2700, Resulting Numbers: [2700] 2700,96 unequal: No Solution Exploring Operation: 27+100=127, Resulting Numbers: [127] 127,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 2, 14, 98, 14 ]
95
[ "98-2=96", "14/14=1", "96-1=95" ]
Current State: 95:[2, 14, 98, 14], Operations: [] Exploring Operation: 98-2=96, Resulting Numbers: [14, 14, 96] Generated Node #2: [14, 14, 96] from Operation: 98-2=96 Current State: 95:[14, 14, 96], Operations: ['98-2=96'] Exploring Operation: 14/14=1, Resulting Numbers: [96, 1] Generated Node #3: [96, 1] from Operation: 14/14=1 Current State: 95:[96, 1], Operations: ['98-2=96', '14/14=1'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[2, 14, 98, 14], Operations: [] Exploring Operation: 14/14=1, Resulting Numbers: [2, 98, 1] Generated Node #0,0: 95:[2, 98, 1] Operation: 14/14=1 Exploring Operation: 14/2=7, Resulting Numbers: [14, 98, 7] Generated Node #0,1: 95:[14, 98, 7] Operation: 14/2=7 Exploring Operation: 14/2=7, Resulting Numbers: [98, 14, 7] Generated Node #0,2: 95:[98, 14, 7] Operation: 14/2=7 Exploring Operation: 98/14=7, Resulting Numbers: [2, 14, 7] Generated Node #0,3: 95:[2, 14, 7] Operation: 98/14=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[2, 98, 1], Operations: ['14/14=1'] Exploring Operation: 98-2=96, Resulting Numbers: [1, 96] Generated Node #0,0,0: 95:[1, 96] Operation: 98-2=96 Exploring Operation: 2+1=3, Resulting Numbers: [98, 3] Generated Node #0,0,1: 95:[98, 3] Operation: 2+1=3 Exploring Operation: 2*1=2, Resulting Numbers: [98, 2] Generated Node #0,0,2: 95:[98, 2] Operation: 2*1=2 Exploring Operation: 98-1=97, Resulting Numbers: [2, 97] Generated Node #0,0,3: 95:[2, 97] Operation: 98-1=97 Moving to Node #0,0,0 Current State: 95:[1, 96], Operations: ['14/14=1', '98-2=96'] Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 1+96=97, Resulting Numbers: [97] 97,95 unequal: No Solution Exploring Operation: 1*96=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[2, 14, 98, 14], Operations: [] Exploring Operation: 14/14=1, Resulting Numbers: [2, 98, 1] Generated Node #0,0: 95:[2, 98, 1] Operation: 14/14=1 Moving to Node #0,0 Current State: 95:[2, 98, 1], Operations: ['14/14=1'] Exploring Operation: 98-2=96, Resulting Numbers: [1, 96] Generated Node #0,0,0: 95:[1, 96] Operation: 98-2=96 Moving to Node #0,0,0 Current State: 95:[1, 96], Operations: ['14/14=1', '98-2=96'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 84, 61, 49, 23 ]
30
[ "61-49=12", "84/12=7", "23+7=30" ]
Current State: 30:[84, 61, 49, 23], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [84, 23, 12] Generated Node #2: [84, 23, 12] from Operation: 61-49=12 Current State: 30:[84, 23, 12], Operations: ['61-49=12'] Exploring Operation: 84/12=7, Resulting Numbers: [23, 7] Generated Node #3: [23, 7] from Operation: 84/12=7 Current State: 30:[23, 7], Operations: ['61-49=12', '84/12=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[84, 61, 49, 23], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [61, 23, 35] Generated Node #0,0: 30:[61, 23, 35] Operation: 84-49=35 Exploring Operation: 84-61=23, Resulting Numbers: [49, 23, 23] Generated Node #0,1: 30:[49, 23, 23] Operation: 84-61=23 Moving to Node #0,1 Current State: 30:[49, 23, 23], Operations: ['84-61=23'] Exploring Operation: 49-23=26, Resulting Numbers: [23, 26] Generated Node #0,1,0: 30:[23, 26] Operation: 49-23=26 Exploring Operation: 49-23=26, Resulting Numbers: [23, 26] Generated Node #0,1,1: 30:[23, 26] Operation: 49-23=26 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[23, 26], Operations: ['84-61=23', '49-23=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,30 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[23, 26], Operations: ['84-61=23', '49-23=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,30 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: 30:[61, 23, 35], Operations: ['84-49=35'] Exploring Operation: 61-35=26, Resulting Numbers: [23, 26] Generated Node #0,0,0: 30:[23, 26] Operation: 61-35=26 Exploring Operation: 61-23=38, Resulting Numbers: [35, 38] Generated Node #0,0,1: 30:[35, 38] Operation: 61-23=38 Moving to Node #0,0,0 Current State: 30:[23, 26], Operations: ['84-49=35', '61-35=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,30 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[35, 38], Operations: ['84-49=35', '61-23=38'] Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,30 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 1, 98, 56, 87 ]
67
[ "1*98=98", "87-56=31", "98-31=67" ]
Current State: 67:[1, 98, 56, 87], Operations: [] Exploring Operation: 1*98=98, Resulting Numbers: [56, 87, 98] Generated Node #2: [56, 87, 98] from Operation: 1*98=98 Current State: 67:[56, 87, 98], Operations: ['1*98=98'] Exploring Operation: 87-56=31, Resulting Numbers: [98, 31] Generated Node #3: [98, 31] from Operation: 87-56=31 Current State: 67:[98, 31], Operations: ['1*98=98', '87-56=31'] Exploring Operation: 98-31=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[1, 98, 56, 87], Operations: [] Exploring Operation: 98-1=97, Resulting Numbers: [56, 87, 97] Generated Node #0,0: 67:[56, 87, 97] Operation: 98-1=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[56, 87, 97], Operations: ['98-1=97'] Exploring Operation: 97-56=41, Resulting Numbers: [87, 41] Generated Node #0,0,0: 67:[87, 41] Operation: 97-56=41 Moving to Node #0,0,0 Current State: 67:[87, 41], Operations: ['98-1=97', '97-56=41'] Exploring Operation: 87-41=46, Resulting Numbers: [46] 46,67 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
[ 33, 53, 7, 28 ]
41
[ "53-33=20", "28-7=21", "20+21=41" ]
Current State: 41:[33, 53, 7, 28], Operations: [] Exploring Operation: 53-33=20, Resulting Numbers: [7, 28, 20] Generated Node #2: [7, 28, 20] from Operation: 53-33=20 Current State: 41:[7, 28, 20], Operations: ['53-33=20'] Exploring Operation: 28-7=21, Resulting Numbers: [20, 21] Generated Node #3: [20, 21] from Operation: 28-7=21 Current State: 41:[20, 21], Operations: ['53-33=20', '28-7=21'] Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[33, 53, 7, 28], Operations: [] Exploring Operation: 33+7=40, Resulting Numbers: [53, 28, 40] Generated Node #0,0: 41:[53, 28, 40] Operation: 33+7=40 Exploring Operation: 53-7=46, Resulting Numbers: [33, 28, 46] Generated Node #0,1: 41:[33, 28, 46] Operation: 53-7=46 Exploring Operation: 7+28=35, Resulting Numbers: [33, 53, 35] Generated Node #0,2: 41:[33, 53, 35] Operation: 7+28=35 Moving to Node #0,0 Current State: 41:[53, 28, 40], Operations: ['33+7=40'] Exploring Operation: 28+40=68, Resulting Numbers: [53, 68] Generated Node #0,0,0: 41:[53, 68] Operation: 28+40=68 Exploring Operation: 53+28=81, Resulting Numbers: [40, 81] Generated Node #0,0,1: 41:[40, 81] Operation: 53+28=81 Exploring Operation: 53-28=25, Resulting Numbers: [40, 25] Generated Node #0,0,2: 41:[40, 25] Operation: 53-28=25 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[40, 25], Operations: ['33+7=40', '53-28=25'] Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 40*25=1000, Resulting Numbers: [1000] 1000,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[53, 68], Operations: ['33+7=40', '28+40=68'] Exploring Operation: 53*68=3604, Resulting Numbers: [3604] 3604,41 unequal: No Solution Exploring Operation: 53+68=121, Resulting Numbers: [121] 121,41 unequal: No Solution Exploring Operation: 68-53=15, Resulting Numbers: [15] 15,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[40, 81], Operations: ['33+7=40', '53+28=81'] Exploring Operation: 40*81=3240, Resulting Numbers: [3240] 3240,41 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[33, 53, 7, 28], Operations: [] Exploring Operation: 33+7=40, Resulting Numbers: [53, 28, 40] Generated Node #0,0: 41:[53, 28, 40] Operation: 33+7=40 Moving to Node #0,0 Current State: 41:[53, 28, 40], Operations: ['33+7=40'] Exploring Operation: 53+28=81, Resulting Numbers: [40, 81] Generated Node #0,0,1: 41:[40, 81] Operation: 53+28=81 Moving to Node #0,0,1 Current State: 41:[40, 81], Operations: ['33+7=40', '53+28=81'] Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 38, 4, 18, 26 ]
70
[ "26-18=8", "4*8=32", "38+32=70" ]
Current State: 70:[38, 4, 18, 26], Operations: [] Exploring Operation: 26-18=8, Resulting Numbers: [38, 4, 8] Generated Node #2: [38, 4, 8] from Operation: 26-18=8 Current State: 70:[38, 4, 8], Operations: ['26-18=8'] Exploring Operation: 4*8=32, Resulting Numbers: [38, 32] Generated Node #3: [38, 32] from Operation: 4*8=32 Current State: 70:[38, 32], Operations: ['26-18=8', '4*8=32'] Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[38, 4, 18, 26], Operations: [] Exploring Operation: 26-18=8, Resulting Numbers: [38, 4, 8] Generated Node #0,0: 70:[38, 4, 8] Operation: 26-18=8 Exploring Operation: 38-26=12, Resulting Numbers: [4, 18, 12] Generated Node #0,1: 70:[4, 18, 12] Operation: 38-26=12 Exploring Operation: 38+26=64, Resulting Numbers: [4, 18, 64] Generated Node #0,2: 70:[4, 18, 64] Operation: 38+26=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[38, 4, 8], Operations: ['26-18=8'] Exploring Operation: 8/4=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 70:[38, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [38, 4] Generated Node #0,0,1: 70:[38, 4] Operation: 8-4=4 Exploring Operation: 38-4=34, Resulting Numbers: [8, 34] Generated Node #0,0,2: 70:[8, 34] Operation: 38-4=34 Moving to Node #0,0,2 Current State: 70:[8, 34], Operations: ['26-18=8', '38-4=34'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,70 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[38, 2], Operations: ['26-18=8', '8/4=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,70 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[38, 4], Operations: ['26-18=8', '8-4=4'] Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,70 unequal: No Solution Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[4, 18, 12], Operations: ['38-26=12'] Exploring Operation: 4*18=72, Resulting Numbers: [12, 72] Generated Node #0,1,0: 70:[12, 72] Operation: 4*18=72 Exploring Operation: 18-4=14, Resulting Numbers: [12, 14] Generated Node #0,1,1: 70:[12, 14] Operation: 18-4=14 Exploring Operation: 18-12=6, Resulting Numbers: [4, 6] Generated Node #0,1,2: 70:[4, 6] Operation: 18-12=6 Moving to Node #0,1,1 Current State: 70:[12, 14], Operations: ['38-26=12', '18-4=14'] Exploring Operation: 12*14=168, Resulting Numbers: [168] 168,70 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[4, 6], Operations: ['38-26=12', '18-12=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[12, 72], Operations: ['38-26=12', '4*18=72'] Exploring Operation: 72/12=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 12+72=84, Resulting Numbers: [84] 84,70 unequal: No Solution Exploring Operation: 72-12=60, Resulting Numbers: [60] 60,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[4, 18, 64], Operations: ['38+26=64'] Exploring Operation: 64/4=16, Resulting Numbers: [18, 16] Generated Node #0,2,0: 70:[18, 16] Operation: 64/4=16 Exploring Operation: 4+64=68, Resulting Numbers: [18, 68] Generated Node #0,2,1: 70:[18, 68] Operation: 4+64=68 Exploring Operation: 18-4=14, Resulting Numbers: [64, 14] Generated Node #0,2,2: 70:[64, 14] Operation: 18-4=14 Moving to Node #0,2,0 Current State: 70:[18, 16], Operations: ['38+26=64', '64/4=16'] Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,70 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[18, 68], Operations: ['38+26=64', '4+64=68'] Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,70 unequal: No Solution Exploring Operation: 18*68=1224, Resulting Numbers: [1224] 1224,70 unequal: No Solution Exploring Operation: 18+68=86, Resulting Numbers: [86] 86,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[64, 14], Operations: ['38+26=64', '18-4=14'] Exploring Operation: 64*14=896, Resulting Numbers: [896] 896,70 unequal: No Solution Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,70 unequal: No Solution Exploring Operation: 64+14=78, Resulting Numbers: [78] 78,70 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
[ 40, 76, 57, 77 ]
96
[ "40+76=116", "77-57=20", "116-20=96" ]
Current State: 96:[40, 76, 57, 77], Operations: [] Exploring Operation: 40+76=116, Resulting Numbers: [57, 77, 116] Generated Node #2: [57, 77, 116] from Operation: 40+76=116 Current State: 96:[57, 77, 116], Operations: ['40+76=116'] Exploring Operation: 77-57=20, Resulting Numbers: [116, 20] Generated Node #3: [116, 20] from Operation: 77-57=20 Current State: 96:[116, 20], Operations: ['40+76=116', '77-57=20'] Exploring Operation: 116-20=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[40, 76, 57, 77], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [40, 57, 1] Generated Node #0,0: 96:[40, 57, 1] Operation: 77-76=1 Exploring Operation: 76-57=19, Resulting Numbers: [40, 77, 19] Generated Node #0,1: 96:[40, 77, 19] Operation: 76-57=19 Exploring Operation: 76-40=36, Resulting Numbers: [57, 77, 36] Generated Node #0,2: 96:[57, 77, 36] Operation: 76-40=36 Exploring Operation: 77-40=37, Resulting Numbers: [76, 57, 37] Generated Node #0,3: 96:[76, 57, 37] Operation: 77-40=37 Exploring Operation: 77-57=20, Resulting Numbers: [40, 76, 20] Generated Node #0,4: 96:[40, 76, 20] Operation: 77-57=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[40, 57, 1], Operations: ['77-76=1'] Exploring Operation: 40+1=41, Resulting Numbers: [57, 41] Generated Node #0,0,0: 96:[57, 41] Operation: 40+1=41 Exploring Operation: 40-1=39, Resulting Numbers: [57, 39] Generated Node #0,0,1: 96:[57, 39] Operation: 40-1=39 Exploring Operation: 57-40=17, Resulting Numbers: [1, 17] Generated Node #0,0,2: 96:[1, 17] Operation: 57-40=17 Exploring Operation: 57-1=56, Resulting Numbers: [40, 56] Generated Node #0,0,3: 96:[40, 56] Operation: 57-1=56 Exploring Operation: 40+57=97, Resulting Numbers: [1, 97] Generated Node #0,0,4: 96:[1, 97] Operation: 40+57=97 Moving to Node #0,0,2 Current State: 96:[1, 17], Operations: ['77-76=1', '57-40=17'] Exploring Operation: 1+17=18, Resulting Numbers: [18] 18,96 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,96 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[1, 97], Operations: ['77-76=1', '40+57=97'] Exploring Operation: 1*97=97, Resulting Numbers: [97] 97,96 unequal: No Solution Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[40, 76, 57, 77], Operations: [] Exploring Operation: 77-76=1, Resulting Numbers: [40, 57, 1] Generated Node #0,0: 96:[40, 57, 1] Operation: 77-76=1 Moving to Node #0,0 Current State: 96:[40, 57, 1], Operations: ['77-76=1'] Exploring Operation: 40+57=97, Resulting Numbers: [1, 97] Generated Node #0,0,4: 96:[1, 97] Operation: 40+57=97 Moving to Node #0,0,4 Current State: 96:[1, 97], Operations: ['77-76=1', '40+57=97'] Exploring Operation: 97-1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 8, 73, 45, 93 ]
17
[ "73-8=65", "93-45=48", "65-48=17" ]
Current State: 17:[8, 73, 45, 93], Operations: [] Exploring Operation: 73-8=65, Resulting Numbers: [45, 93, 65] Generated Node #2: [45, 93, 65] from Operation: 73-8=65 Current State: 17:[45, 93, 65], Operations: ['73-8=65'] Exploring Operation: 93-45=48, Resulting Numbers: [65, 48] Generated Node #3: [65, 48] from Operation: 93-45=48 Current State: 17:[65, 48], Operations: ['73-8=65', '93-45=48'] Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[8, 73, 45, 93], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [8, 73, 48] Generated Node #0,0: 17:[8, 73, 48] Operation: 93-45=48 Exploring Operation: 93-73=20, Resulting Numbers: [8, 45, 20] Generated Node #0,1: 17:[8, 45, 20] Operation: 93-73=20 Exploring Operation: 73-45=28, Resulting Numbers: [8, 93, 28] Generated Node #0,2: 17:[8, 93, 28] Operation: 73-45=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[8, 45, 20], Operations: ['93-73=20'] Exploring Operation: 45-8=37, Resulting Numbers: [20, 37] Generated Node #0,1,0: 17:[20, 37] Operation: 45-8=37 Exploring Operation: 45-20=25, Resulting Numbers: [8, 25] Generated Node #0,1,1: 17:[8, 25] Operation: 45-20=25 Exploring Operation: 20-8=12, Resulting Numbers: [45, 12] Generated Node #0,1,2: 17:[45, 12] Operation: 20-8=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 17:[8, 25], Operations: ['93-73=20', '45-20=25'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[8, 73, 45, 93], Operations: [] Exploring Operation: 93-73=20, Resulting Numbers: [8, 45, 20] Generated Node #0,1: 17:[8, 45, 20] Operation: 93-73=20 Moving to Node #0,1 Current State: 17:[8, 45, 20], Operations: ['93-73=20'] Exploring Operation: 45-20=25, Resulting Numbers: [8, 25] Generated Node #0,1,1: 17:[8, 25] Operation: 45-20=25 Moving to Node #0,1,1 Current State: 17:[8, 25], Operations: ['93-73=20', '45-20=25'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 69, 92, 25, 45 ]
93
[ "92-69=23", "25+45=70", "23+70=93" ]
Current State: 93:[69, 92, 25, 45], Operations: [] Exploring Operation: 92-69=23, Resulting Numbers: [25, 45, 23] Generated Node #2: [25, 45, 23] from Operation: 92-69=23 Current State: 93:[25, 45, 23], Operations: ['92-69=23'] Exploring Operation: 25+45=70, Resulting Numbers: [23, 70] Generated Node #3: [23, 70] from Operation: 25+45=70 Current State: 93:[23, 70], Operations: ['92-69=23', '25+45=70'] Exploring Operation: 23+70=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[69, 92, 25, 45], Operations: [] Exploring Operation: 69+25=94, Resulting Numbers: [92, 45, 94] Generated Node #0,0: 93:[92, 45, 94] Operation: 69+25=94 Exploring Operation: 69-45=24, Resulting Numbers: [92, 25, 24] Generated Node #0,1: 93:[92, 25, 24] Operation: 69-45=24 Exploring Operation: 69-25=44, Resulting Numbers: [92, 45, 44] Generated Node #0,2: 93:[92, 45, 44] Operation: 69-25=44 Exploring Operation: 92-69=23, Resulting Numbers: [25, 45, 23] Generated Node #0,3: 93:[25, 45, 23] Operation: 92-69=23 Moving to Node #0,1 Current State: 93:[92, 25, 24], Operations: ['69-45=24'] Exploring Operation: 25+24=49, Resulting Numbers: [92, 49] Generated Node #0,1,0: 93:[92, 49] Operation: 25+24=49 Exploring Operation: 25-24=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 93:[92, 1] Operation: 25-24=1 Exploring Operation: 92+24=116, Resulting Numbers: [25, 116] Generated Node #0,1,2: 93:[25, 116] Operation: 92+24=116 Exploring Operation: 92+25=117, Resulting Numbers: [24, 117] Generated Node #0,1,3: 93:[24, 117] Operation: 92+25=117 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[92, 1], Operations: ['69-45=24', '25-24=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[69, 92, 25, 45], Operations: [] Exploring Operation: 69-45=24, Resulting Numbers: [92, 25, 24] Generated Node #0,1: 93:[92, 25, 24] Operation: 69-45=24 Moving to Node #0,1 Current State: 93:[92, 25, 24], Operations: ['69-45=24'] Exploring Operation: 25-24=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 93:[92, 1] Operation: 25-24=1 Moving to Node #0,1,1 Current State: 93:[92, 1], Operations: ['69-45=24', '25-24=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 16, 82, 83, 44 ]
28
[ "44-16=28", "83-82=1", "28*1=28" ]
Current State: 28:[16, 82, 83, 44], Operations: [] Exploring Operation: 44-16=28, Resulting Numbers: [82, 83, 28] Generated Node #2: [82, 83, 28] from Operation: 44-16=28 Current State: 28:[82, 83, 28], Operations: ['44-16=28'] Exploring Operation: 83-82=1, Resulting Numbers: [28, 1] Generated Node #3: [28, 1] from Operation: 83-82=1 Current State: 28:[28, 1], Operations: ['44-16=28', '83-82=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[16, 82, 83, 44], Operations: [] Exploring Operation: 83-44=39, Resulting Numbers: [16, 82, 39] Generated Node #0,0: 28:[16, 82, 39] Operation: 83-44=39 Exploring Operation: 83-82=1, Resulting Numbers: [16, 44, 1] Generated Node #0,1: 28:[16, 44, 1] Operation: 83-82=1 Exploring Operation: 82-44=38, Resulting Numbers: [16, 83, 38] Generated Node #0,2: 28:[16, 83, 38] Operation: 82-44=38 Exploring Operation: 82-16=66, Resulting Numbers: [83, 44, 66] Generated Node #0,3: 28:[83, 44, 66] Operation: 82-16=66 Moving to Node #0,1 Current State: 28:[16, 44, 1], Operations: ['83-82=1'] Exploring Operation: 16*1=16, Resulting Numbers: [44, 16] Generated Node #0,1,0: 28:[44, 16] Operation: 16*1=16 Exploring Operation: 44-1=43, Resulting Numbers: [16, 43] Generated Node #0,1,1: 28:[16, 43] Operation: 44-1=43 Exploring Operation: 44-16=28, Resulting Numbers: [1, 28] Generated Node #0,1,2: 28:[1, 28] Operation: 44-16=28 Exploring Operation: 16-1=15, Resulting Numbers: [44, 15] Generated Node #0,1,3: 28:[44, 15] Operation: 16-1=15 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[1, 28], Operations: ['83-82=1', '44-16=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,28 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[16, 82, 83, 44], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [16, 44, 1] Generated Node #0,1: 28:[16, 44, 1] Operation: 83-82=1 Moving to Node #0,1 Current State: 28:[16, 44, 1], Operations: ['83-82=1'] Exploring Operation: 44-16=28, Resulting Numbers: [1, 28] Generated Node #0,1,2: 28:[1, 28] Operation: 44-16=28 Moving to Node #0,1,2 Current State: 28:[1, 28], Operations: ['83-82=1', '44-16=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 46, 16, 42, 25 ]
37
[ "46-16=30", "42+25=67", "67-30=37" ]
Current State: 37:[46, 16, 42, 25], Operations: [] Exploring Operation: 46-16=30, Resulting Numbers: [42, 25, 30] Generated Node #2: [42, 25, 30] from Operation: 46-16=30 Current State: 37:[42, 25, 30], Operations: ['46-16=30'] Exploring Operation: 42+25=67, Resulting Numbers: [30, 67] Generated Node #3: [30, 67] from Operation: 42+25=67 Current State: 37:[30, 67], Operations: ['46-16=30', '42+25=67'] Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[46, 16, 42, 25], Operations: [] Exploring Operation: 42-16=26, Resulting Numbers: [46, 25, 26] Generated Node #0,0: 37:[46, 25, 26] Operation: 42-16=26 Exploring Operation: 46+16=62, Resulting Numbers: [42, 25, 62] Generated Node #0,1: 37:[42, 25, 62] Operation: 46+16=62 Exploring Operation: 16+25=41, Resulting Numbers: [46, 42, 41] Generated Node #0,2: 37:[46, 42, 41] Operation: 16+25=41 Exploring Operation: 46-16=30, Resulting Numbers: [42, 25, 30] Generated Node #0,3: 37:[42, 25, 30] Operation: 46-16=30 Moving to Node #0,2 Current State: 37:[46, 42, 41], Operations: ['16+25=41'] Exploring Operation: 42-41=1, Resulting Numbers: [46, 1] Generated Node #0,2,0: 37:[46, 1] Operation: 42-41=1 Exploring Operation: 46+42=88, Resulting Numbers: [41, 88] Generated Node #0,2,1: 37:[41, 88] Operation: 46+42=88 Exploring Operation: 46-42=4, Resulting Numbers: [41, 4] Generated Node #0,2,2: 37:[41, 4] Operation: 46-42=4 Exploring Operation: 46-41=5, Resulting Numbers: [42, 5] Generated Node #0,2,3: 37:[42, 5] Operation: 46-41=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 37:[41, 4], Operations: ['16+25=41', '46-42=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[46, 16, 42, 25], Operations: [] Exploring Operation: 16+25=41, Resulting Numbers: [46, 42, 41] Generated Node #0,2: 37:[46, 42, 41] Operation: 16+25=41 Moving to Node #0,2 Current State: 37:[46, 42, 41], Operations: ['16+25=41'] Exploring Operation: 46-42=4, Resulting Numbers: [41, 4] Generated Node #0,2,2: 37:[41, 4] Operation: 46-42=4 Moving to Node #0,2,2 Current State: 37:[41, 4], Operations: ['16+25=41', '46-42=4'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 55, 99, 91, 35 ]
28
[ "55+99=154", "91+35=126", "154-126=28" ]
Current State: 28:[55, 99, 91, 35], Operations: [] Exploring Operation: 55+99=154, Resulting Numbers: [91, 35, 154] Generated Node #2: [91, 35, 154] from Operation: 55+99=154 Current State: 28:[91, 35, 154], Operations: ['55+99=154'] Exploring Operation: 91+35=126, Resulting Numbers: [154, 126] Generated Node #3: [154, 126] from Operation: 91+35=126 Current State: 28:[154, 126], Operations: ['55+99=154', '91+35=126'] Exploring Operation: 154-126=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[55, 99, 91, 35], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [91, 35, 44] Generated Node #0,0: 28:[91, 35, 44] Operation: 99-55=44 Exploring Operation: 91-55=36, Resulting Numbers: [99, 35, 36] Generated Node #0,1: 28:[99, 35, 36] Operation: 91-55=36 Exploring Operation: 99-91=8, Resulting Numbers: [55, 35, 8] Generated Node #0,2: 28:[55, 35, 8] Operation: 99-91=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[55, 35, 8], Operations: ['99-91=8'] Exploring Operation: 55-8=47, Resulting Numbers: [35, 47] Generated Node #0,2,0: 28:[35, 47] Operation: 55-8=47 Exploring Operation: 55-35=20, Resulting Numbers: [8, 20] Generated Node #0,2,1: 28:[8, 20] Operation: 55-35=20 Exploring Operation: 35-8=27, Resulting Numbers: [55, 27] Generated Node #0,2,2: 28:[55, 27] Operation: 35-8=27 Moving to Node #0,2,1 Current State: 28:[8, 20], Operations: ['99-91=8', '55-35=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[55, 99, 91, 35], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [55, 35, 8] Generated Node #0,2: 28:[55, 35, 8] Operation: 99-91=8 Moving to Node #0,2 Current State: 28:[55, 35, 8], Operations: ['99-91=8'] Exploring Operation: 55-35=20, Resulting Numbers: [8, 20] Generated Node #0,2,1: 28:[8, 20] Operation: 55-35=20 Moving to Node #0,2,1 Current State: 28:[8, 20], Operations: ['99-91=8', '55-35=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 77, 6, 29, 27 ]
70
[ "77+27=104", "6*29=174", "174-104=70" ]
Current State: 70:[77, 6, 29, 27], Operations: [] Exploring Operation: 77+27=104, Resulting Numbers: [6, 29, 104] Generated Node #2: [6, 29, 104] from Operation: 77+27=104 Current State: 70:[6, 29, 104], Operations: ['77+27=104'] Exploring Operation: 6*29=174, Resulting Numbers: [104, 174] Generated Node #3: [104, 174] from Operation: 6*29=174 Current State: 70:[104, 174], Operations: ['77+27=104', '6*29=174'] Exploring Operation: 174-104=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[77, 6, 29, 27], Operations: [] Exploring Operation: 77-6=71, Resulting Numbers: [29, 27, 71] Generated Node #0,0: 70:[29, 27, 71] Operation: 77-6=71 Exploring Operation: 27-6=21, Resulting Numbers: [77, 29, 21] Generated Node #0,1: 70:[77, 29, 21] Operation: 27-6=21 Exploring Operation: 6+29=35, Resulting Numbers: [77, 27, 35] Generated Node #0,2: 70:[77, 27, 35] Operation: 6+29=35 Exploring Operation: 6+27=33, Resulting Numbers: [77, 29, 33] Generated Node #0,3: 70:[77, 29, 33] Operation: 6+27=33 Exploring Operation: 29-27=2, Resulting Numbers: [77, 6, 2] Generated Node #0,4: 70:[77, 6, 2] Operation: 29-27=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 70:[77, 6, 2], Operations: ['29-27=2'] Exploring Operation: 77-6=71, Resulting Numbers: [2, 71] Generated Node #0,4,0: 70:[2, 71] Operation: 77-6=71 Exploring Operation: 77-2=75, Resulting Numbers: [6, 75] Generated Node #0,4,1: 70:[6, 75] Operation: 77-2=75 Exploring Operation: 6+2=8, Resulting Numbers: [77, 8] Generated Node #0,4,2: 70:[77, 8] Operation: 6+2=8 Exploring Operation: 6-2=4, Resulting Numbers: [77, 4] Generated Node #0,4,3: 70:[77, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [77, 3] Generated Node #0,4,4: 70:[77, 3] Operation: 6/2=3 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 70:[2, 71], Operations: ['29-27=2', '77-6=71'] Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,70 unequal: No Solution Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,70 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,70 unequal: No Solution No 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: 70:[6, 75], Operations: ['29-27=2', '77-2=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,70 unequal: No Solution Exploring Operation: 6*75=450, Resulting Numbers: [450] 450,70 unequal: No Solution Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,70 unequal: No Solution No 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: 70:[77, 8], Operations: ['29-27=2', '6+2=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,70 unequal: No Solution No 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: 70:[77, 4], Operations: ['29-27=2', '6-2=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,70 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,70 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,70 unequal: No Solution No 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: 70:[77, 3], Operations: ['29-27=2', '6/2=3'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,70 unequal: No Solution Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,70 unequal: No Solution Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,70 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: 70:[29, 27, 71], Operations: ['77-6=71'] Exploring Operation: 71-27=44, Resulting Numbers: [29, 44] Generated Node #0,0,0: 70:[29, 44] Operation: 71-27=44 Exploring Operation: 29+27=56, Resulting Numbers: [71, 56] Generated Node #0,0,1: 70:[71, 56] Operation: 29+27=56 Exploring Operation: 71-29=42, Resulting Numbers: [27, 42] Generated Node #0,0,2: 70:[27, 42] Operation: 71-29=42 Exploring Operation: 29-27=2, Resulting Numbers: [71, 2] Generated Node #0,0,3: 70:[71, 2] Operation: 29-27=2 Exploring Operation: 27+71=98, Resulting Numbers: [29, 98] Generated Node #0,0,4: 70:[29, 98] Operation: 27+71=98 Moving to Node #0,0,3 Current State: 70:[71, 2], Operations: ['77-6=71', '29-27=2'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,70 unequal: No Solution Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[71, 56], Operations: ['77-6=71', '29+27=56'] Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,70 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[29, 44], Operations: ['77-6=71', '71-27=44'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 29*44=1276, Resulting Numbers: [1276] 1276,70 unequal: No Solution Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[27, 42], Operations: ['77-6=71', '71-29=42'] Exploring Operation: 27*42=1134, Resulting Numbers: [1134] 1134,70 unequal: No Solution Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,70 unequal: No Solution Moving to Node #0,0,4 Current State: 70:[29, 98], Operations: ['77-6=71', '27+71=98'] Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 29*98=2842, Resulting Numbers: [2842] 2842,70 unequal: No Solution Exploring Operation: 29+98=127, Resulting Numbers: [127] 127,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[77, 27, 35], Operations: ['6+29=35'] Exploring Operation: 77+27=104, Resulting Numbers: [35, 104] Generated Node #0,2,0: 70:[35, 104] Operation: 77+27=104 Exploring Operation: 77-27=50, Resulting Numbers: [35, 50] Generated Node #0,2,1: 70:[35, 50] Operation: 77-27=50 Exploring Operation: 27+35=62, Resulting Numbers: [77, 62] Generated Node #0,2,2: 70:[77, 62] Operation: 27+35=62 Exploring Operation: 35-27=8, Resulting Numbers: [77, 8] Generated Node #0,2,3: 70:[77, 8] Operation: 35-27=8 Exploring Operation: 77-35=42, Resulting Numbers: [27, 42] Generated Node #0,2,4: 70:[27, 42] Operation: 77-35=42 Moving to Node #0,2,3 Current State: 70:[77, 8], Operations: ['6+29=35', '35-27=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[77, 62], Operations: ['6+29=35', '27+35=62'] Exploring Operation: 77+62=139, Resulting Numbers: [139] 139,70 unequal: No Solution Exploring Operation: 77*62=4774, Resulting Numbers: [4774] 4774,70 unequal: No Solution Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[35, 50], Operations: ['6+29=35', '77-27=50'] Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,70 unequal: No Solution Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,70 unequal: No Solution Moving to Node #0,2,4 Current State: 70:[27, 42], Operations: ['6+29=35', '77-35=42'] Exploring Operation: 27*42=1134, Resulting Numbers: [1134] 1134,70 unequal: No Solution Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[35, 104], Operations: ['6+29=35', '77+27=104'] Exploring Operation: 35+104=139, Resulting Numbers: [139] 139,70 unequal: No Solution Exploring Operation: 35*104=3640, Resulting Numbers: [3640] 3640,70 unequal: No Solution Exploring Operation: 104-35=69, Resulting Numbers: [69] 69,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[77, 29, 33], Operations: ['6+27=33'] Exploring Operation: 29+33=62, Resulting Numbers: [77, 62] Generated Node #0,3,0: 70:[77, 62] Operation: 29+33=62 Exploring Operation: 77-29=48, Resulting Numbers: [33, 48] Generated Node #0,3,1: 70:[33, 48] Operation: 77-29=48 Exploring Operation: 77-33=44, Resulting Numbers: [29, 44] Generated Node #0,3,2: 70:[29, 44] Operation: 77-33=44 Exploring Operation: 77+29=106, Resulting Numbers: [33, 106] Generated Node #0,3,3: 70:[33, 106] Operation: 77+29=106 Exploring Operation: 33-29=4, Resulting Numbers: [77, 4] Generated Node #0,3,4: 70:[77, 4] Operation: 33-29=4 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 70:[77, 4], Operations: ['6+27=33', '33-29=4'] Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,70 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,70 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,70 unequal: No Solution No 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: 70:[77, 62], Operations: ['6+27=33', '29+33=62'] Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 77+62=139, Resulting Numbers: [139] 139,70 unequal: No Solution Exploring Operation: 77*62=4774, Resulting Numbers: [4774] 4774,70 unequal: No Solution No 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: 70:[33, 48], Operations: ['6+27=33', '77-29=48'] Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,70 unequal: No Solution Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,70 unequal: No Solution No 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: 70:[29, 44], Operations: ['6+27=33', '77-33=44'] Exploring Operation: 29*44=1276, Resulting Numbers: [1276] 1276,70 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,70 unequal: No Solution No 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: 70:[33, 106], Operations: ['6+27=33', '77+29=106'] Exploring Operation: 106-33=73, Resulting Numbers: [73] 73,70 unequal: No Solution Exploring Operation: 33+106=139, Resulting Numbers: [139] 139,70 unequal: No Solution Exploring Operation: 33*106=3498, Resulting Numbers: [3498] 3498,70 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: 70:[77, 29, 21], Operations: ['27-6=21'] Exploring Operation: 77-29=48, Resulting Numbers: [21, 48] Generated Node #0,1,0: 70:[21, 48] Operation: 77-29=48 Exploring Operation: 29-21=8, Resulting Numbers: [77, 8] Generated Node #0,1,1: 70:[77, 8] Operation: 29-21=8 Exploring Operation: 29+21=50, Resulting Numbers: [77, 50] Generated Node #0,1,2: 70:[77, 50] Operation: 29+21=50 Exploring Operation: 77+21=98, Resulting Numbers: [29, 98] Generated Node #0,1,3: 70:[29, 98] Operation: 77+21=98 Exploring Operation: 77-21=56, Resulting Numbers: [29, 56] Generated Node #0,1,4: 70:[29, 56] Operation: 77-21=56 Moving to Node #0,1,1 Current State: 70:[77, 8], Operations: ['27-6=21', '29-21=8'] Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,70 unequal: No Solution Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,70 unequal: No Solution Moving to Node #0,1,4 Current State: 70:[29, 56], Operations: ['27-6=21', '77-21=56'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 29*56=1624, Resulting Numbers: [1624] 1624,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[21, 48], Operations: ['27-6=21', '77-29=48'] Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[77, 50], Operations: ['27-6=21', '29+21=50'] Exploring Operation: 77+50=127, Resulting Numbers: [127] 127,70 unequal: No Solution Exploring Operation: 77*50=3850, Resulting Numbers: [3850] 3850,70 unequal: No Solution Exploring Operation: 77-50=27, Resulting Numbers: [27] 27,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[29, 98], Operations: ['27-6=21', '77+21=98'] Exploring Operation: 29*98=2842, Resulting Numbers: [2842] 2842,70 unequal: No Solution Exploring Operation: 29+98=127, Resulting Numbers: [127] 127,70 unequal: No Solution Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 11, 86, 35, 8 ]
19
[ "11-8=3", "35*3=105", "105-86=19" ]
Current State: 19:[11, 86, 35, 8], Operations: [] Exploring Operation: 11-8=3, Resulting Numbers: [86, 35, 3] Generated Node #2: [86, 35, 3] from Operation: 11-8=3 Current State: 19:[86, 35, 3], Operations: ['11-8=3'] Exploring Operation: 35*3=105, Resulting Numbers: [86, 105] Generated Node #3: [86, 105] from Operation: 35*3=105 Current State: 19:[86, 105], Operations: ['11-8=3', '35*3=105'] Exploring Operation: 105-86=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[11, 86, 35, 8], Operations: [] Exploring Operation: 86-35=51, Resulting Numbers: [11, 8, 51] Generated Node #0,0: 19:[11, 8, 51] Operation: 86-35=51 Moving to Node #0,0 Current State: 19:[11, 8, 51], Operations: ['86-35=51'] Exploring Operation: 11+8=19, Resulting Numbers: [51, 19] Generated Node #0,0,0: 19:[51, 19] Operation: 11+8=19 Moving to Node #0,0,0 Current State: 19:[51, 19], Operations: ['86-35=51', '11+8=19'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,19 unequal: No Solution No solution found.
0
hs_1
sum_heuristic