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
[ 72, 3, 71, 39 ]
60
[ "72-39=33", "33/3=11", "71-11=60" ]
Current State: 60:[72, 3, 71, 39], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [3, 71, 33] Generated Node #2: [3, 71, 33] from Operation: 72-39=33 Current State: 60:[3, 71, 33], Operations: ['72-39=33'] Exploring Operation: 33/3=11, Resulting Numbers: [71, 11] Generated Node #3: [71, 11] from Operation: 33/3=11 Current State: 60:[71, 11], Operations: ['72-39=33', '33/3=11'] Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[72, 3, 71, 39], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [3, 39, 1] Generated Node #0,0: 60:[3, 39, 1] Operation: 72-71=1 Exploring Operation: 71-39=32, Resulting Numbers: [72, 3, 32] Generated Node #0,1: 60:[72, 3, 32] Operation: 71-39=32 Exploring Operation: 72-39=33, Resulting Numbers: [3, 71, 33] Generated Node #0,2: 60:[3, 71, 33] Operation: 72-39=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[3, 39, 1], Operations: ['72-71=1'] Exploring Operation: 39-3=36, Resulting Numbers: [1, 36] Generated Node #0,0,0: 60:[1, 36] Operation: 39-3=36 Exploring Operation: 39-1=38, Resulting Numbers: [3, 38] Generated Node #0,0,1: 60:[3, 38] Operation: 39-1=38 Exploring Operation: 39/3=13, Resulting Numbers: [1, 13] Generated Node #0,0,2: 60:[1, 13] Operation: 39/3=13 Moving to Node #0,0,2 Current State: 60:[1, 13], Operations: ['72-71=1', '39/3=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,60 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[1, 36], Operations: ['72-71=1', '39-3=36'] Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[3, 38], Operations: ['72-71=1', '39-1=38'] Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,60 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 Current State: 60:[72, 3, 32], Operations: ['71-39=32'] Exploring Operation: 72-3=69, Resulting Numbers: [32, 69] Generated Node #0,1,0: 60:[32, 69] Operation: 72-3=69 Exploring Operation: 72-32=40, Resulting Numbers: [3, 40] Generated Node #0,1,1: 60:[3, 40] Operation: 72-32=40 Exploring Operation: 72/3=24, Resulting Numbers: [32, 24] Generated Node #0,1,2: 60:[32, 24] Operation: 72/3=24 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 60:[32, 24], Operations: ['71-39=32', '72/3=24'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,60 unequal: No Solution Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,60 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 60:[3, 40], Operations: ['71-39=32', '72-32=40'] Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,60 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,60 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 60:[32, 69], Operations: ['71-39=32', '72-3=69'] Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,60 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,60 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[3, 71, 33], Operations: ['72-39=33'] Exploring Operation: 33-3=30, Resulting Numbers: [71, 30] Generated Node #0,2,0: 60:[71, 30] Operation: 33-3=30 Exploring Operation: 71-33=38, Resulting Numbers: [3, 38] Generated Node #0,2,1: 60:[3, 38] Operation: 71-33=38 Exploring Operation: 71-3=68, Resulting Numbers: [33, 68] Generated Node #0,2,2: 60:[33, 68] Operation: 71-3=68 Moving to Node #0,2,1 Current State: 60:[3, 38], Operations: ['72-39=33', '71-33=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 3*38=114, Resulting Numbers: [114] 114,60 unequal: No Solution Exploring Operation: 3+38=41, Resulting Numbers: [41] 41,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[71, 30], Operations: ['72-39=33', '33-3=30'] Exploring Operation: 71*30=2130, Resulting Numbers: [2130] 2130,60 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,60 unequal: No Solution Exploring Operation: 71+30=101, Resulting Numbers: [101] 101,60 unequal: No Solution Moving to Node #0,2,2 Current State: 60:[33, 68], Operations: ['72-39=33', '71-3=68'] Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,60 unequal: No Solution Exploring Operation: 33*68=2244, Resulting Numbers: [2244] 2244,60 unequal: No Solution Exploring Operation: 33+68=101, Resulting Numbers: [101] 101,60 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
[ 84, 81, 90, 63 ]
79
[ "81-63=18", "90/18=5", "84-5=79" ]
Current State: 79:[84, 81, 90, 63], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [84, 90, 18] Generated Node #2: [84, 90, 18] from Operation: 81-63=18 Current State: 79:[84, 90, 18], Operations: ['81-63=18'] Exploring Operation: 90/18=5, Resulting Numbers: [84, 5] Generated Node #3: [84, 5] from Operation: 90/18=5 Current State: 79:[84, 5], Operations: ['81-63=18', '90/18=5'] Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[84, 81, 90, 63], Operations: [] Exploring Operation: 84-63=21, Resulting Numbers: [81, 90, 21] Generated Node #0,0: 79:[81, 90, 21] Operation: 84-63=21 Exploring Operation: 84+63=147, Resulting Numbers: [81, 90, 147] Generated Node #0,1: 79:[81, 90, 147] Operation: 84+63=147 Exploring Operation: 81-63=18, Resulting Numbers: [84, 90, 18] Generated Node #0,2: 79:[84, 90, 18] Operation: 81-63=18 Exploring Operation: 90-63=27, Resulting Numbers: [84, 81, 27] Generated Node #0,3: 79:[84, 81, 27] Operation: 90-63=27 Moving to Node #0,3 Current State: 79:[84, 81, 27], Operations: ['90-63=27'] Exploring Operation: 81+27=108, Resulting Numbers: [84, 108] Generated Node #0,3,0: 79:[84, 108] Operation: 81+27=108 Exploring Operation: 84-27=57, Resulting Numbers: [81, 57] Generated Node #0,3,1: 79:[81, 57] Operation: 84-27=57 Exploring Operation: 81-27=54, Resulting Numbers: [84, 54] Generated Node #0,3,2: 79:[84, 54] Operation: 81-27=54 Exploring Operation: 84+27=111, Resulting Numbers: [81, 111] Generated Node #0,3,3: 79:[81, 111] Operation: 84+27=111 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[81, 57], Operations: ['90-63=27', '84-27=57'] Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 81+57=138, Resulting Numbers: [138] 138,79 unequal: No Solution Exploring Operation: 81*57=4617, Resulting Numbers: [4617] 4617,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[84, 54], Operations: ['90-63=27', '81-27=54'] Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,79 unequal: No Solution Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[84, 108], Operations: ['90-63=27', '81+27=108'] Exploring Operation: 108-84=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 84+108=192, Resulting Numbers: [192] 192,79 unequal: No Solution Exploring Operation: 84*108=9072, Resulting Numbers: [9072] 9072,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[81, 111], Operations: ['90-63=27', '84+27=111'] Exploring Operation: 111-81=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 81*111=8991, Resulting Numbers: [8991] 8991,79 unequal: No Solution Exploring Operation: 81+111=192, Resulting Numbers: [192] 192,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 79:[81, 90, 21], Operations: ['84-63=21'] Exploring Operation: 90-21=69, Resulting Numbers: [81, 69] Generated Node #0,0,0: 79:[81, 69] Operation: 90-21=69 Exploring Operation: 81+21=102, Resulting Numbers: [90, 102] Generated Node #0,0,1: 79:[90, 102] Operation: 81+21=102 Exploring Operation: 90+21=111, Resulting Numbers: [81, 111] Generated Node #0,0,2: 79:[81, 111] Operation: 90+21=111 Exploring Operation: 81-21=60, Resulting Numbers: [90, 60] Generated Node #0,0,3: 79:[90, 60] Operation: 81-21=60 Moving to Node #0,2 Current State: 79:[84, 90, 18], Operations: ['81-63=18'] Exploring Operation: 84+18=102, Resulting Numbers: [90, 102] Generated Node #0,2,0: 79:[90, 102] Operation: 84+18=102 Exploring Operation: 90+18=108, Resulting Numbers: [84, 108] Generated Node #0,2,1: 79:[84, 108] Operation: 90+18=108 Exploring Operation: 90-18=72, Resulting Numbers: [84, 72] Generated Node #0,2,2: 79:[84, 72] Operation: 90-18=72 Exploring Operation: 84-18=66, Resulting Numbers: [90, 66] Generated Node #0,2,3: 79:[90, 66] Operation: 84-18=66 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[84, 72], Operations: ['81-63=18', '90-18=72'] Exploring Operation: 84-72=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 84*72=6048, Resulting Numbers: [6048] 6048,79 unequal: No Solution Exploring Operation: 84+72=156, Resulting Numbers: [156] 156,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[90, 66], Operations: ['81-63=18', '84-18=66'] Exploring Operation: 90+66=156, Resulting Numbers: [156] 156,79 unequal: No Solution Exploring Operation: 90-66=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 90*66=5940, Resulting Numbers: [5940] 5940,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[90, 102], Operations: ['81-63=18', '84+18=102'] Exploring Operation: 102-90=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 90+102=192, Resulting Numbers: [192] 192,79 unequal: No Solution Exploring Operation: 90*102=9180, Resulting Numbers: [9180] 9180,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[84, 108], Operations: ['81-63=18', '90+18=108'] Exploring Operation: 84*108=9072, Resulting Numbers: [9072] 9072,79 unequal: No Solution Exploring Operation: 108-84=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 84+108=192, Resulting Numbers: [192] 192,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 79:[81, 90, 147], Operations: ['84+63=147'] Exploring Operation: 90-81=9, Resulting Numbers: [147, 9] Generated Node #0,1,0: 79:[147, 9] Operation: 90-81=9 Exploring Operation: 147-81=66, Resulting Numbers: [90, 66] Generated Node #0,1,1: 79:[90, 66] Operation: 147-81=66 Exploring Operation: 81+90=171, Resulting Numbers: [147, 171] Generated Node #0,1,2: 79:[147, 171] Operation: 81+90=171 Exploring Operation: 147-90=57, Resulting Numbers: [81, 57] Generated Node #0,1,3: 79:[81, 57] Operation: 147-90=57 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[90, 66], Operations: ['84+63=147', '147-81=66'] Exploring Operation: 90-66=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 90+66=156, Resulting Numbers: [156] 156,79 unequal: No Solution Exploring Operation: 90*66=5940, Resulting Numbers: [5940] 5940,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[81, 57], Operations: ['84+63=147', '147-90=57'] Exploring Operation: 81-57=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 81+57=138, Resulting Numbers: [138] 138,79 unequal: No Solution Exploring Operation: 81*57=4617, Resulting Numbers: [4617] 4617,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[147, 9], Operations: ['84+63=147', '90-81=9'] Exploring Operation: 147-9=138, Resulting Numbers: [138] 138,79 unequal: No Solution Exploring Operation: 147+9=156, Resulting Numbers: [156] 156,79 unequal: No Solution Exploring Operation: 147*9=1323, Resulting Numbers: [1323] 1323,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[147, 171], Operations: ['84+63=147', '81+90=171'] Exploring Operation: 147+171=318, Resulting Numbers: [318] 318,79 unequal: No Solution Exploring Operation: 171-147=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 147*171=25137, Resulting Numbers: [25137] 25137,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 79:[81, 69], Operations: ['84-63=21', '90-21=69'] Exploring Operation: 81*69=5589, Resulting Numbers: [5589] 5589,79 unequal: No Solution Exploring Operation: 81-69=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 81+69=150, Resulting Numbers: [150] 150,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[90, 60], Operations: ['84-63=21', '81-21=60'] Exploring Operation: 90+60=150, Resulting Numbers: [150] 150,79 unequal: No Solution Exploring Operation: 90*60=5400, Resulting Numbers: [5400] 5400,79 unequal: No Solution Exploring Operation: 90-60=30, Resulting Numbers: [30] 30,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[81, 111], Operations: ['84-63=21', '90+21=111'] Exploring Operation: 111-81=30, Resulting Numbers: [30] 30,79 unequal: No Solution Exploring Operation: 81*111=8991, Resulting Numbers: [8991] 8991,79 unequal: No Solution Exploring Operation: 81+111=192, Resulting Numbers: [192] 192,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[90, 102], Operations: ['84-63=21', '81+21=102'] Exploring Operation: 102-90=12, Resulting Numbers: [12] 12,79 unequal: No Solution Exploring Operation: 90+102=192, Resulting Numbers: [192] 192,79 unequal: No Solution Exploring Operation: 90*102=9180, Resulting Numbers: [9180] 9180,79 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 30, 50, 2, 42 ]
68
[ "30*2=60", "50-42=8", "60+8=68" ]
Current State: 68:[30, 50, 2, 42], Operations: [] Exploring Operation: 30*2=60, Resulting Numbers: [50, 42, 60] Generated Node #2: [50, 42, 60] from Operation: 30*2=60 Current State: 68:[50, 42, 60], Operations: ['30*2=60'] Exploring Operation: 50-42=8, Resulting Numbers: [60, 8] Generated Node #3: [60, 8] from Operation: 50-42=8 Current State: 68:[60, 8], Operations: ['30*2=60', '50-42=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[30, 50, 2, 42], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [30, 2, 8] Generated Node #0,0: 68:[30, 2, 8] Operation: 50-42=8 Exploring Operation: 50-30=20, Resulting Numbers: [2, 42, 20] Generated Node #0,1: 68:[2, 42, 20] Operation: 50-30=20 Exploring Operation: 30+50=80, Resulting Numbers: [2, 42, 80] Generated Node #0,2: 68:[2, 42, 80] Operation: 30+50=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[30, 2, 8], Operations: ['50-42=8'] Exploring Operation: 8/2=4, Resulting Numbers: [30, 4] Generated Node #0,0,0: 68:[30, 4] Operation: 8/2=4 Exploring Operation: 30+8=38, Resulting Numbers: [2, 38] Generated Node #0,0,1: 68:[2, 38] Operation: 30+8=38 Exploring Operation: 30-8=22, Resulting Numbers: [2, 22] Generated Node #0,0,2: 68:[2, 22] Operation: 30-8=22 Moving to Node #0,0,0 Current State: 68:[30, 4], Operations: ['50-42=8', '8/2=4'] Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,68 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[2, 38], Operations: ['50-42=8', '30+8=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[2, 22], Operations: ['50-42=8', '30-8=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[2, 42, 20], Operations: ['50-30=20'] Exploring Operation: 42/2=21, Resulting Numbers: [20, 21] Generated Node #0,1,0: 68:[20, 21] Operation: 42/2=21 Exploring Operation: 42+20=62, Resulting Numbers: [2, 62] Generated Node #0,1,1: 68:[2, 62] Operation: 42+20=62 Exploring Operation: 42-20=22, Resulting Numbers: [2, 22] Generated Node #0,1,2: 68:[2, 22] Operation: 42-20=22 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[2, 22], Operations: ['50-30=20', '42-20=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[2, 62], Operations: ['50-30=20', '42+20=62'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,68 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[20, 21], Operations: ['50-30=20', '42/2=21'] Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[2, 42, 80], Operations: ['30+50=80'] Exploring Operation: 80/2=40, Resulting Numbers: [42, 40] Generated Node #0,2,0: 68:[42, 40] Operation: 80/2=40 Exploring Operation: 42/2=21, Resulting Numbers: [80, 21] Generated Node #0,2,1: 68:[80, 21] Operation: 42/2=21 Exploring Operation: 80-42=38, Resulting Numbers: [2, 38] Generated Node #0,2,2: 68:[2, 38] Operation: 80-42=38 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[2, 38], Operations: ['30+50=80', '80-42=38'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,68 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[42, 40], Operations: ['30+50=80', '80/2=40'] Exploring Operation: 42*40=1680, Resulting Numbers: [1680] 1680,68 unequal: No Solution Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,68 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 68:[80, 21], Operations: ['30+50=80', '42/2=21'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,68 unequal: No Solution Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 56, 21, 60, 53 ]
91
[ "60-53=7", "21*7=147", "147-56=91" ]
Current State: 91:[56, 21, 60, 53], Operations: [] Exploring Operation: 60-53=7, Resulting Numbers: [56, 21, 7] Generated Node #2: [56, 21, 7] from Operation: 60-53=7 Current State: 91:[56, 21, 7], Operations: ['60-53=7'] Exploring Operation: 21*7=147, Resulting Numbers: [56, 147] Generated Node #3: [56, 147] from Operation: 21*7=147 Current State: 91:[56, 147], Operations: ['60-53=7', '21*7=147'] Exploring Operation: 147-56=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[56, 21, 60, 53], Operations: [] Exploring Operation: 56-53=3, Resulting Numbers: [21, 60, 3] Generated Node #0,0: 91:[21, 60, 3] Operation: 56-53=3 Exploring Operation: 60-53=7, Resulting Numbers: [56, 21, 7] Generated Node #0,1: 91:[56, 21, 7] Operation: 60-53=7 Moving to Node #0,0 Current State: 91:[21, 60, 3], Operations: ['56-53=3'] Exploring Operation: 21+60=81, Resulting Numbers: [3, 81] Generated Node #0,0,0: 91:[3, 81] Operation: 21+60=81 Exploring Operation: 60/3=20, Resulting Numbers: [21, 20] Generated Node #0,0,1: 91:[21, 20] Operation: 60/3=20 Moving to Node #0,1 Current State: 91:[56, 21, 7], Operations: ['60-53=7'] Exploring Operation: 56/7=8, Resulting Numbers: [21, 8] Generated Node #0,1,0: 91:[21, 8] Operation: 56/7=8 Exploring Operation: 56+21=77, Resulting Numbers: [7, 77] Generated Node #0,1,1: 91:[7, 77] Operation: 56+21=77 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[21, 8], Operations: ['60-53=7', '56/7=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,91 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,91 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 #0,1,1 Current State: 91:[7, 77], Operations: ['60-53=7', '56+21=77'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 7+77=84, Resulting Numbers: [84] 84,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 91:[3, 81], Operations: ['56-53=3', '21+60=81'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,91 unequal: No Solution Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[21, 20], Operations: ['56-53=3', '60/3=20'] Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,91 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,91 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 11, 14, 63, 6 ]
10
[ "14-11=3", "63-3=60", "60/6=10" ]
Current State: 10:[11, 14, 63, 6], Operations: [] Exploring Operation: 14-11=3, Resulting Numbers: [63, 6, 3] Generated Node #2: [63, 6, 3] from Operation: 14-11=3 Current State: 10:[63, 6, 3], Operations: ['14-11=3'] Exploring Operation: 63-3=60, Resulting Numbers: [6, 60] Generated Node #3: [6, 60] from Operation: 63-3=60 Current State: 10:[6, 60], Operations: ['14-11=3', '63-3=60'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[11, 14, 63, 6], Operations: [] Exploring Operation: 14-6=8, Resulting Numbers: [11, 63, 8] Generated Node #0,0: 10:[11, 63, 8] Operation: 14-6=8 Exploring Operation: 63-11=52, Resulting Numbers: [14, 6, 52] Generated Node #0,1: 10:[14, 6, 52] Operation: 63-11=52 Exploring Operation: 63-14=49, Resulting Numbers: [11, 6, 49] Generated Node #0,2: 10:[11, 6, 49] Operation: 63-14=49 Exploring Operation: 63-6=57, Resulting Numbers: [11, 14, 57] Generated Node #0,3: 10:[11, 14, 57] Operation: 63-6=57 Exploring Operation: 14-11=3, Resulting Numbers: [63, 6, 3] Generated Node #0,4: 10:[63, 6, 3] Operation: 14-11=3 Moving to Node #0,2 Current State: 10:[11, 6, 49], Operations: ['63-14=49'] Exploring Operation: 49-6=43, Resulting Numbers: [11, 43] Generated Node #0,2,0: 10:[11, 43] Operation: 49-6=43 Exploring Operation: 6+49=55, Resulting Numbers: [11, 55] Generated Node #0,2,1: 10:[11, 55] Operation: 6+49=55 Exploring Operation: 11-6=5, Resulting Numbers: [49, 5] Generated Node #0,2,2: 10:[49, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [49, 17] Generated Node #0,2,3: 10:[49, 17] Operation: 11+6=17 Exploring Operation: 49-11=38, Resulting Numbers: [6, 38] Generated Node #0,2,4: 10:[6, 38] Operation: 49-11=38 Moving to Node #0,1 Current State: 10:[14, 6, 52], Operations: ['63-11=52'] Exploring Operation: 52-14=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 10:[6, 38] Operation: 52-14=38 Exploring Operation: 52-6=46, Resulting Numbers: [14, 46] Generated Node #0,1,1: 10:[14, 46] Operation: 52-6=46 Exploring Operation: 14-6=8, Resulting Numbers: [52, 8] Generated Node #0,1,2: 10:[52, 8] Operation: 14-6=8 Exploring Operation: 14+6=20, Resulting Numbers: [52, 20] Generated Node #0,1,3: 10:[52, 20] Operation: 14+6=20 Exploring Operation: 6+52=58, Resulting Numbers: [14, 58] Generated Node #0,1,4: 10:[14, 58] Operation: 6+52=58 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[6, 38], Operations: ['63-11=52', '52-14=38'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,10 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[14, 46], Operations: ['63-11=52', '52-6=46'] Exploring Operation: 14+46=60, Resulting Numbers: [60] 60,10 unequal: No Solution Exploring Operation: 14*46=644, Resulting Numbers: [644] 644,10 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[52, 8], Operations: ['63-11=52', '14-6=8'] Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,10 unequal: No Solution Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,10 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 10:[52, 20], Operations: ['63-11=52', '14+6=20'] Exploring Operation: 52*20=1040, Resulting Numbers: [1040] 1040,10 unequal: No Solution Exploring Operation: 52-20=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 52+20=72, Resulting Numbers: [72] 72,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 10:[14, 58], Operations: ['63-11=52', '6+52=58'] Exploring Operation: 14+58=72, Resulting Numbers: [72] 72,10 unequal: No Solution Exploring Operation: 14*58=812, Resulting Numbers: [812] 812,10 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,10 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: 10:[11, 14, 57], Operations: ['63-6=57'] Exploring Operation: 14-11=3, Resulting Numbers: [57, 3] Generated Node #0,3,0: 10:[57, 3] Operation: 14-11=3 Exploring Operation: 57-11=46, Resulting Numbers: [14, 46] Generated Node #0,3,1: 10:[14, 46] Operation: 57-11=46 Exploring Operation: 11+14=25, Resulting Numbers: [57, 25] Generated Node #0,3,2: 10:[57, 25] Operation: 11+14=25 Exploring Operation: 11+57=68, Resulting Numbers: [14, 68] Generated Node #0,3,3: 10:[14, 68] Operation: 11+57=68 Exploring Operation: 57-14=43, Resulting Numbers: [11, 43] Generated Node #0,3,4: 10:[11, 43] Operation: 57-14=43 Moving to Node #0,4 Current State: 10:[63, 6, 3], Operations: ['14-11=3'] Exploring Operation: 63/3=21, Resulting Numbers: [6, 21] Generated Node #0,4,0: 10:[6, 21] Operation: 63/3=21 Exploring Operation: 6+3=9, Resulting Numbers: [63, 9] Generated Node #0,4,1: 10:[63, 9] Operation: 6+3=9 Exploring Operation: 63-6=57, Resulting Numbers: [3, 57] Generated Node #0,4,2: 10:[3, 57] Operation: 63-6=57 Exploring Operation: 63-3=60, Resulting Numbers: [6, 60] Generated Node #0,4,3: 10:[6, 60] Operation: 63-3=60 Exploring Operation: 6/3=2, Resulting Numbers: [63, 2] Generated Node #0,4,4: 10:[63, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 10:[6, 21], Operations: ['14-11=3', '63/3=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,10 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,10 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 10:[3, 57], Operations: ['14-11=3', '63-6=57'] Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,10 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,10 unequal: No Solution Exploring Operation: 3*57=171, Resulting Numbers: [171] 171,10 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 10:[6, 60], Operations: ['14-11=3', '63-3=60'] Exploring Operation: 6+60=66, Resulting Numbers: [66] 66,10 unequal: No Solution Exploring Operation: 6*60=360, Resulting Numbers: [360] 360,10 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,10 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[11, 14, 63, 6], Operations: [] Exploring Operation: 14-11=3, Resulting Numbers: [63, 6, 3] Generated Node #0,4: 10:[63, 6, 3] Operation: 14-11=3 Moving to Node #0,4 Current State: 10:[63, 6, 3], Operations: ['14-11=3'] Exploring Operation: 63-3=60, Resulting Numbers: [6, 60] Generated Node #0,4,3: 10:[6, 60] Operation: 63-3=60 Moving to Node #0,4,3 Current State: 10:[6, 60], Operations: ['14-11=3', '63-3=60'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.952257
hs_5
sum_heuristic
[ 9, 49, 1, 36 ]
21
[ "9+49=58", "1+36=37", "58-37=21" ]
Current State: 21:[9, 49, 1, 36], Operations: [] Exploring Operation: 9+49=58, Resulting Numbers: [1, 36, 58] Generated Node #2: [1, 36, 58] from Operation: 9+49=58 Current State: 21:[1, 36, 58], Operations: ['9+49=58'] Exploring Operation: 1+36=37, Resulting Numbers: [58, 37] Generated Node #3: [58, 37] from Operation: 1+36=37 Current State: 21:[58, 37], Operations: ['9+49=58', '1+36=37'] Exploring Operation: 58-37=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[9, 49, 1, 36], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [9, 1, 13] Generated Node #0,0: 21:[9, 1, 13] Operation: 49-36=13 Exploring Operation: 49-9=40, Resulting Numbers: [1, 36, 40] Generated Node #0,1: 21:[1, 36, 40] Operation: 49-9=40 Exploring Operation: 36/9=4, Resulting Numbers: [49, 1, 4] Generated Node #0,2: 21:[49, 1, 4] Operation: 36/9=4 Exploring Operation: 36-9=27, Resulting Numbers: [49, 1, 27] Generated Node #0,3: 21:[49, 1, 27] Operation: 36-9=27 Moving to Node #0,0 Current State: 21:[9, 1, 13], Operations: ['49-36=13'] Exploring Operation: 13-9=4, Resulting Numbers: [1, 4] Generated Node #0,0,0: 21:[1, 4] Operation: 13-9=4 Exploring Operation: 9+13=22, Resulting Numbers: [1, 22] Generated Node #0,0,1: 21:[1, 22] Operation: 9+13=22 Exploring Operation: 9-1=8, Resulting Numbers: [13, 8] Generated Node #0,0,2: 21:[13, 8] Operation: 9-1=8 Exploring Operation: 13-1=12, Resulting Numbers: [9, 12] Generated Node #0,0,3: 21:[9, 12] Operation: 13-1=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[1, 4], Operations: ['49-36=13', '13-9=4'] Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,21 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[1, 22], Operations: ['49-36=13', '9+13=22'] Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,21 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[9, 49, 1, 36], Operations: [] Exploring Operation: 49-36=13, Resulting Numbers: [9, 1, 13] Generated Node #0,0: 21:[9, 1, 13] Operation: 49-36=13 Moving to Node #0,0 Current State: 21:[9, 1, 13], Operations: ['49-36=13'] Exploring Operation: 9+13=22, Resulting Numbers: [1, 22] Generated Node #0,0,1: 21:[1, 22] Operation: 9+13=22 Moving to Node #0,0,1 Current State: 21:[1, 22], Operations: ['49-36=13', '9+13=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 4, 80, 4, 44 ]
24
[ "4*44=176", "176-80=96", "96/4=24" ]
Current State: 24:[4, 80, 4, 44], Operations: [] Exploring Operation: 4*44=176, Resulting Numbers: [80, 176] Generated Node #2: [80, 176] from Operation: 4*44=176 Current State: 24:[80, 176], Operations: ['4*44=176'] Exploring Operation: 176-80=96, Resulting Numbers: [96] 96,24 equal: Goal Reached Exploring Operation: 96/4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[4, 80, 4, 44], Operations: [] Exploring Operation: 80/4=20, Resulting Numbers: [4, 44, 20] Generated Node #0,0: 24:[4, 44, 20] Operation: 80/4=20 Exploring Operation: 80-44=36, Resulting Numbers: [4, 4, 36] Generated Node #0,1: 24:[4, 4, 36] Operation: 80-44=36 Exploring Operation: 80/4=20, Resulting Numbers: [4, 44, 20] Generated Node #0,2: 24:[4, 44, 20] Operation: 80/4=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[4, 4, 36], Operations: ['80-44=36'] Exploring Operation: 36/4=9, Resulting Numbers: [4, 9] Generated Node #0,1,0: 24:[4, 9] Operation: 36/4=9 Exploring Operation: 36/4=9, Resulting Numbers: [4, 9] Generated Node #0,1,1: 24:[4, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [4, 32] Generated Node #0,1,2: 24:[4, 32] Operation: 36-4=32 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[4, 9], Operations: ['80-44=36', '36/4=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,24 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[4, 9], Operations: ['80-44=36', '36/4=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,24 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[4, 32], Operations: ['80-44=36', '36-4=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[4, 44, 20], Operations: ['80/4=20'] Exploring Operation: 44-20=24, Resulting Numbers: [4, 24] Generated Node #0,0,0: 24:[4, 24] Operation: 44-20=24 Exploring Operation: 44/4=11, Resulting Numbers: [20, 11] Generated Node #0,0,1: 24:[20, 11] Operation: 44/4=11 Exploring Operation: 44-4=40, Resulting Numbers: [20, 40] Generated Node #0,0,2: 24:[20, 40] Operation: 44-4=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[4, 24], Operations: ['80/4=20', '44-20=24'] Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[20, 11], Operations: ['80/4=20', '44/4=11'] Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,24 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[20, 40], Operations: ['80/4=20', '44-4=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[4, 44, 20], Operations: ['80/4=20'] Exploring Operation: 44/4=11, Resulting Numbers: [20, 11] Generated Node #0,2,0: 24:[20, 11] Operation: 44/4=11 Exploring Operation: 44-4=40, Resulting Numbers: [20, 40] Generated Node #0,2,1: 24:[20, 40] Operation: 44-4=40 Exploring Operation: 44-20=24, Resulting Numbers: [4, 24] Generated Node #0,2,2: 24:[4, 24] Operation: 44-20=24 Moving to Node #0,2,2 Current State: 24:[4, 24], Operations: ['80/4=20', '44-20=24'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[20, 11], Operations: ['80/4=20', '44/4=11'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,24 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,24 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[20, 40], Operations: ['80/4=20', '44-4=40'] Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,24 unequal: No Solution Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,24 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
[ 61, 91, 82, 25 ]
68
[ "61*91=5551", "25+5551=5576", "5576/82=68" ]
Current State: 68:[61, 91, 82, 25], Operations: [] Exploring Operation: 61*91=5551, Resulting Numbers: [82, 25, 5551] Generated Node #2: [82, 25, 5551] from Operation: 61*91=5551 Current State: 68:[82, 25, 5551], Operations: ['61*91=5551'] Exploring Operation: 25+5551=5576, Resulting Numbers: [82, 5576] Generated Node #3: [82, 5576] from Operation: 25+5551=5576 Current State: 68:[82, 5576], Operations: ['61*91=5551', '25+5551=5576'] Exploring Operation: 5576/82=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[61, 91, 82, 25], Operations: [] Exploring Operation: 91-25=66, Resulting Numbers: [61, 82, 66] Generated Node #0,0: 68:[61, 82, 66] Operation: 91-25=66 Exploring Operation: 91-82=9, Resulting Numbers: [61, 25, 9] Generated Node #0,1: 68:[61, 25, 9] Operation: 91-82=9 Moving to Node #0,1 Current State: 68:[61, 25, 9], Operations: ['91-82=9'] Exploring Operation: 61-25=36, Resulting Numbers: [9, 36] Generated Node #0,1,0: 68:[9, 36] Operation: 61-25=36 Exploring Operation: 25+9=34, Resulting Numbers: [61, 34] Generated Node #0,1,1: 68:[61, 34] Operation: 25+9=34 Moving to Node #0,0 Current State: 68:[61, 82, 66], Operations: ['91-25=66'] Exploring Operation: 82-61=21, Resulting Numbers: [66, 21] Generated Node #0,0,0: 68:[66, 21] Operation: 82-61=21 Exploring Operation: 82-66=16, Resulting Numbers: [61, 16] Generated Node #0,0,1: 68:[61, 16] Operation: 82-66=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[66, 21], Operations: ['91-25=66', '82-61=21'] Exploring Operation: 66+21=87, Resulting Numbers: [87] 87,68 unequal: No Solution Exploring Operation: 66-21=45, Resulting Numbers: [45] 45,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[61, 16], Operations: ['91-25=66', '82-66=16'] Exploring Operation: 61+16=77, Resulting Numbers: [77] 77,68 unequal: No Solution Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,68 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: 68:[9, 36], Operations: ['91-82=9', '61-25=36'] Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[61, 34], Operations: ['91-82=9', '25+9=34'] Exploring Operation: 61-34=27, Resulting Numbers: [27] 27,68 unequal: No Solution Exploring Operation: 61+34=95, Resulting Numbers: [95] 95,68 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 77, 92, 95, 22 ]
12
[ "77+92=169", "95+169=264", "264/22=12" ]
Current State: 12:[77, 92, 95, 22], Operations: [] Exploring Operation: 77+92=169, Resulting Numbers: [95, 22, 169] Generated Node #2: [95, 22, 169] from Operation: 77+92=169 Current State: 12:[95, 22, 169], Operations: ['77+92=169'] Exploring Operation: 95+169=264, Resulting Numbers: [22, 264] Generated Node #3: [22, 264] from Operation: 95+169=264 Current State: 12:[22, 264], Operations: ['77+92=169', '95+169=264'] Exploring Operation: 264/22=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[77, 92, 95, 22], Operations: [] Exploring Operation: 92-77=15, Resulting Numbers: [95, 22, 15] Generated Node #0,0: 12:[95, 22, 15] Operation: 92-77=15 Exploring Operation: 95-92=3, Resulting Numbers: [77, 22, 3] Generated Node #0,1: 12:[77, 22, 3] Operation: 95-92=3 Moving to Node #0,1 Current State: 12:[77, 22, 3], Operations: ['95-92=3'] Exploring Operation: 77-22=55, Resulting Numbers: [3, 55] Generated Node #0,1,0: 12:[3, 55] Operation: 77-22=55 Exploring Operation: 77-3=74, Resulting Numbers: [22, 74] Generated Node #0,1,1: 12:[22, 74] Operation: 77-3=74 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[3, 55], Operations: ['95-92=3', '77-22=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,12 unequal: No Solution Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,12 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:[22, 74], Operations: ['95-92=3', '77-3=74'] Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,12 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 12:[95, 22, 15], Operations: ['92-77=15'] Exploring Operation: 95-22=73, Resulting Numbers: [15, 73] Generated Node #0,0,0: 12:[15, 73] Operation: 95-22=73 Exploring Operation: 95-15=80, Resulting Numbers: [22, 80] Generated Node #0,0,1: 12:[22, 80] Operation: 95-15=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[15, 73], Operations: ['92-77=15', '95-22=73'] Exploring Operation: 15+73=88, Resulting Numbers: [88] 88,12 unequal: No Solution Exploring Operation: 73-15=58, Resulting Numbers: [58] 58,12 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:[22, 80], Operations: ['92-77=15', '95-15=80'] Exploring Operation: 22+80=102, Resulting Numbers: [102] 102,12 unequal: No Solution Exploring Operation: 80-22=58, Resulting Numbers: [58] 58,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 45, 60, 64, 25 ]
44
[ "45*60=2700", "2700/25=108", "108-64=44" ]
Current State: 44:[45, 60, 64, 25], Operations: [] Exploring Operation: 45*60=2700, Resulting Numbers: [64, 25, 2700] Generated Node #2: [64, 25, 2700] from Operation: 45*60=2700 Current State: 44:[64, 25, 2700], Operations: ['45*60=2700'] Exploring Operation: 2700/25=108, Resulting Numbers: [64, 108] Generated Node #3: [64, 108] from Operation: 2700/25=108 Current State: 44:[64, 108], Operations: ['45*60=2700', '2700/25=108'] Exploring Operation: 108-64=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[45, 60, 64, 25], Operations: [] Exploring Operation: 64-45=19, Resulting Numbers: [60, 25, 19] Generated Node #0,0: 44:[60, 25, 19] Operation: 64-45=19 Exploring Operation: 64-25=39, Resulting Numbers: [45, 60, 39] Generated Node #0,1: 44:[45, 60, 39] Operation: 64-25=39 Exploring Operation: 64-60=4, Resulting Numbers: [45, 25, 4] Generated Node #0,2: 44:[45, 25, 4] Operation: 64-60=4 Moving to Node #0,2 Current State: 44:[45, 25, 4], Operations: ['64-60=4'] Exploring Operation: 25-4=21, Resulting Numbers: [45, 21] Generated Node #0,2,0: 44:[45, 21] Operation: 25-4=21 Exploring Operation: 45-4=41, Resulting Numbers: [25, 41] Generated Node #0,2,1: 44:[25, 41] Operation: 45-4=41 Exploring Operation: 45-25=20, Resulting Numbers: [4, 20] Generated Node #0,2,2: 44:[4, 20] Operation: 45-25=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[45, 21], Operations: ['64-60=4', '25-4=21'] Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,44 unequal: No Solution Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,44 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[4, 20], Operations: ['64-60=4', '45-25=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[25, 41], Operations: ['64-60=4', '45-4=41'] Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,44 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,44 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 44:[60, 25, 19], Operations: ['64-45=19'] Exploring Operation: 60-25=35, Resulting Numbers: [19, 35] Generated Node #0,0,0: 44:[19, 35] Operation: 60-25=35 Exploring Operation: 60-19=41, Resulting Numbers: [25, 41] Generated Node #0,0,1: 44:[25, 41] Operation: 60-19=41 Exploring Operation: 25+19=44, Resulting Numbers: [60, 44] Generated Node #0,0,2: 44:[60, 44] Operation: 25+19=44 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 44:[25, 41], Operations: ['64-45=19', '60-19=41'] Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,44 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[19, 35], Operations: ['64-45=19', '60-25=35'] Exploring Operation: 19*35=665, Resulting Numbers: [665] 665,44 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 44:[60, 44], Operations: ['64-45=19', '25+19=44'] Exploring Operation: 60+44=104, Resulting Numbers: [104] 104,44 unequal: No Solution Exploring Operation: 60*44=2640, Resulting Numbers: [2640] 2640,44 unequal: No Solution Exploring Operation: 60-44=16, Resulting Numbers: [16] 16,44 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: 44:[45, 60, 39], Operations: ['64-25=39'] Exploring Operation: 60-45=15, Resulting Numbers: [39, 15] Generated Node #0,1,0: 44:[39, 15] Operation: 60-45=15 Exploring Operation: 45-39=6, Resulting Numbers: [60, 6] Generated Node #0,1,1: 44:[60, 6] Operation: 45-39=6 Exploring Operation: 60-39=21, Resulting Numbers: [45, 21] Generated Node #0,1,2: 44:[45, 21] Operation: 60-39=21 Moving to Node #0,1,2 Current State: 44:[45, 21], Operations: ['64-25=39', '60-39=21'] Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,44 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,44 unequal: No Solution Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[39, 15], Operations: ['64-25=39', '60-45=15'] Exploring Operation: 39*15=585, Resulting Numbers: [585] 585,44 unequal: No Solution Exploring Operation: 39+15=54, Resulting Numbers: [54] 54,44 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[60, 6], Operations: ['64-25=39', '45-39=6'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,44 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,44 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 18, 64, 54, 68 ]
96
[ "18+64=82", "68-54=14", "82+14=96" ]
Current State: 96:[18, 64, 54, 68], Operations: [] Exploring Operation: 18+64=82, Resulting Numbers: [54, 68, 82] Generated Node #2: [54, 68, 82] from Operation: 18+64=82 Current State: 96:[54, 68, 82], Operations: ['18+64=82'] Exploring Operation: 68-54=14, Resulting Numbers: [82, 14] Generated Node #3: [82, 14] from Operation: 68-54=14 Current State: 96:[82, 14], Operations: ['18+64=82', '68-54=14'] Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[18, 64, 54, 68], Operations: [] Exploring Operation: 68-64=4, Resulting Numbers: [18, 54, 4] Generated Node #0,0: 96:[18, 54, 4] Operation: 68-64=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[18, 54, 4], Operations: ['68-64=4'] Exploring Operation: 54/18=3, Resulting Numbers: [4, 3] Generated Node #0,0,0: 96:[4, 3] Operation: 54/18=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[4, 3], Operations: ['68-64=4', '54/18=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 40, 91, 90, 90 ]
49
[ "40+91=131", "90+90=180", "180-131=49" ]
Current State: 49:[40, 91, 90, 90], Operations: [] Exploring Operation: 40+91=131, Resulting Numbers: [90, 90, 131] Generated Node #2: [90, 90, 131] from Operation: 40+91=131 Current State: 49:[90, 90, 131], Operations: ['40+91=131'] Exploring Operation: 90+90=180, Resulting Numbers: [131, 180] Generated Node #3: [131, 180] from Operation: 90+90=180 Current State: 49:[131, 180], Operations: ['40+91=131', '90+90=180'] Exploring Operation: 180-131=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[40, 91, 90, 90], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [40, 90, 1] Generated Node #0,0: 49:[40, 90, 1] Operation: 91-90=1 Moving to Node #0,0 Current State: 49:[40, 90, 1], Operations: ['91-90=1'] Exploring Operation: 90-40=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 49:[1, 50] Operation: 90-40=50 Moving to Node #0,0,0 Current State: 49:[1, 50], Operations: ['91-90=1', '90-40=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[40, 91, 90, 90], Operations: [] Exploring Operation: 91-90=1, Resulting Numbers: [40, 90, 1] Generated Node #0,0: 49:[40, 90, 1] Operation: 91-90=1 Moving to Node #0,0 Current State: 49:[40, 90, 1], Operations: ['91-90=1'] Exploring Operation: 90-40=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 49:[1, 50] Operation: 90-40=50 Moving to Node #0,0,0 Current State: 49:[1, 50], Operations: ['91-90=1', '90-40=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 4, 59, 20, 41 ]
34
[ "59-4=55", "41-20=21", "55-21=34" ]
Current State: 34:[4, 59, 20, 41], Operations: [] Exploring Operation: 59-4=55, Resulting Numbers: [20, 41, 55] Generated Node #2: [20, 41, 55] from Operation: 59-4=55 Current State: 34:[20, 41, 55], Operations: ['59-4=55'] Exploring Operation: 41-20=21, Resulting Numbers: [55, 21] Generated Node #3: [55, 21] from Operation: 41-20=21 Current State: 34:[55, 21], Operations: ['59-4=55', '41-20=21'] Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[4, 59, 20, 41], Operations: [] Exploring Operation: 59-4=55, Resulting Numbers: [20, 41, 55] Generated Node #0,0: 34:[20, 41, 55] Operation: 59-4=55 Exploring Operation: 59-41=18, Resulting Numbers: [4, 20, 18] Generated Node #0,1: 34:[4, 20, 18] Operation: 59-41=18 Exploring Operation: 59-20=39, Resulting Numbers: [4, 41, 39] Generated Node #0,2: 34:[4, 41, 39] Operation: 59-20=39 Moving to Node #0,1 Current State: 34:[4, 20, 18], Operations: ['59-41=18'] Exploring Operation: 20/4=5, Resulting Numbers: [18, 5] Generated Node #0,1,0: 34:[18, 5] Operation: 20/4=5 Exploring Operation: 20-4=16, Resulting Numbers: [18, 16] Generated Node #0,1,1: 34:[18, 16] Operation: 20-4=16 Exploring Operation: 20-18=2, Resulting Numbers: [4, 2] Generated Node #0,1,2: 34:[4, 2] Operation: 20-18=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[18, 16], Operations: ['59-41=18', '20-4=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[4, 59, 20, 41], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [4, 20, 18] Generated Node #0,1: 34:[4, 20, 18] Operation: 59-41=18 Moving to Node #0,1 Current State: 34:[4, 20, 18], Operations: ['59-41=18'] Exploring Operation: 20-4=16, Resulting Numbers: [18, 16] Generated Node #0,1,1: 34:[18, 16] Operation: 20-4=16 Moving to Node #0,1,1 Current State: 34:[18, 16], Operations: ['59-41=18', '20-4=16'] Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 11, 49, 59, 77 ]
98
[ "49-11=38", "59+77=136", "136-38=98" ]
Current State: 98:[11, 49, 59, 77], Operations: [] Exploring Operation: 49-11=38, Resulting Numbers: [59, 77, 38] Generated Node #2: [59, 77, 38] from Operation: 49-11=38 Current State: 98:[59, 77, 38], Operations: ['49-11=38'] Exploring Operation: 59+77=136, Resulting Numbers: [38, 136] Generated Node #3: [38, 136] from Operation: 59+77=136 Current State: 98:[38, 136], Operations: ['49-11=38', '59+77=136'] Exploring Operation: 136-38=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[11, 49, 59, 77], Operations: [] Exploring Operation: 11+77=88, Resulting Numbers: [49, 59, 88] Generated Node #0,0: 98:[49, 59, 88] Operation: 11+77=88 Exploring Operation: 77-59=18, Resulting Numbers: [11, 49, 18] Generated Node #0,1: 98:[11, 49, 18] Operation: 77-59=18 Exploring Operation: 77/11=7, Resulting Numbers: [49, 59, 7] Generated Node #0,2: 98:[49, 59, 7] Operation: 77/11=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[11, 49, 18], Operations: ['77-59=18'] Exploring Operation: 11+49=60, Resulting Numbers: [18, 60] Generated Node #0,1,0: 98:[18, 60] Operation: 11+49=60 Exploring Operation: 49-11=38, Resulting Numbers: [18, 38] Generated Node #0,1,1: 98:[18, 38] Operation: 49-11=38 Exploring Operation: 18-11=7, Resulting Numbers: [49, 7] Generated Node #0,1,2: 98:[49, 7] Operation: 18-11=7 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[49, 7], Operations: ['77-59=18', '18-11=7'] Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,98 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[18, 60], Operations: ['77-59=18', '11+49=60'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,98 unequal: No Solution Exploring Operation: 18+60=78, Resulting Numbers: [78] 78,98 unequal: No Solution Exploring Operation: 18*60=1080, Resulting Numbers: [1080] 1080,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[18, 38], Operations: ['77-59=18', '49-11=38'] Exploring Operation: 18*38=684, Resulting Numbers: [684] 684,98 unequal: No Solution Exploring Operation: 38-18=20, Resulting Numbers: [20] 20,98 unequal: No Solution Exploring Operation: 18+38=56, Resulting Numbers: [56] 56,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[49, 59, 7], Operations: ['77/11=7'] Exploring Operation: 59-7=52, Resulting Numbers: [49, 52] Generated Node #0,2,0: 98:[49, 52] Operation: 59-7=52 Exploring Operation: 49+59=108, Resulting Numbers: [7, 108] Generated Node #0,2,1: 98:[7, 108] Operation: 49+59=108 Exploring Operation: 59-49=10, Resulting Numbers: [7, 10] Generated Node #0,2,2: 98:[7, 10] Operation: 59-49=10 Moving to Node #0,2,0 Current State: 98:[49, 52], Operations: ['77/11=7', '59-7=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,98 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[7, 10], Operations: ['77/11=7', '59-49=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,98 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,98 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[7, 108], Operations: ['77/11=7', '49+59=108'] Exploring Operation: 7+108=115, Resulting Numbers: [115] 115,98 unequal: No Solution Exploring Operation: 108-7=101, Resulting Numbers: [101] 101,98 unequal: No Solution Exploring Operation: 7*108=756, Resulting Numbers: [756] 756,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[49, 59, 88], Operations: ['11+77=88'] Exploring Operation: 49+59=108, Resulting Numbers: [88, 108] Generated Node #0,0,0: 98:[88, 108] Operation: 49+59=108 Exploring Operation: 88-59=29, Resulting Numbers: [49, 29] Generated Node #0,0,1: 98:[49, 29] Operation: 88-59=29 Exploring Operation: 59-49=10, Resulting Numbers: [88, 10] Generated Node #0,0,2: 98:[88, 10] Operation: 59-49=10 Moving to Node #0,0,2 Current State: 98:[88, 10], Operations: ['11+77=88', '59-49=10'] Exploring Operation: 88*10=880, Resulting Numbers: [880] 880,98 unequal: No Solution Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,98 unequal: No Solution Exploring Operation: 88+10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[11, 49, 59, 77], Operations: [] Exploring Operation: 11+77=88, Resulting Numbers: [49, 59, 88] Generated Node #0,0: 98:[49, 59, 88] Operation: 11+77=88 Moving to Node #0,0 Current State: 98:[49, 59, 88], Operations: ['11+77=88'] Exploring Operation: 59-49=10, Resulting Numbers: [88, 10] Generated Node #0,0,2: 98:[88, 10] Operation: 59-49=10 Moving to Node #0,0,2 Current State: 98:[88, 10], Operations: ['11+77=88', '59-49=10'] Exploring Operation: 88+10=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_3
mult_heuristic
[ 41, 7, 81, 23 ]
24
[ "41-7=34", "81-23=58", "58-34=24" ]
Current State: 24:[41, 7, 81, 23], Operations: [] Exploring Operation: 41-7=34, Resulting Numbers: [81, 23, 34] Generated Node #2: [81, 23, 34] from Operation: 41-7=34 Current State: 24:[81, 23, 34], Operations: ['41-7=34'] Exploring Operation: 81-23=58, Resulting Numbers: [34, 58] Generated Node #3: [34, 58] from Operation: 81-23=58 Current State: 24:[34, 58], Operations: ['41-7=34', '81-23=58'] Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[41, 7, 81, 23], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [7, 23, 40] Generated Node #0,0: 24:[7, 23, 40] Operation: 81-41=40 Exploring Operation: 81-23=58, Resulting Numbers: [41, 7, 58] Generated Node #0,1: 24:[41, 7, 58] Operation: 81-23=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[7, 23, 40], Operations: ['81-41=40'] Exploring Operation: 40-23=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 24:[7, 17] Operation: 40-23=17 Exploring Operation: 40-7=33, Resulting Numbers: [23, 33] Generated Node #0,0,1: 24:[23, 33] Operation: 40-7=33 Moving to Node #0,0,0 Current State: 24:[7, 17], Operations: ['81-41=40', '40-23=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[41, 7, 81, 23], Operations: [] Exploring Operation: 81-41=40, Resulting Numbers: [7, 23, 40] Generated Node #0,0: 24:[7, 23, 40] Operation: 81-41=40 Moving to Node #0,0 Current State: 24:[7, 23, 40], Operations: ['81-41=40'] Exploring Operation: 40-23=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 24:[7, 17] Operation: 40-23=17 Moving to Node #0,0,0 Current State: 24:[7, 17], Operations: ['81-41=40', '40-23=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 15, 32, 12, 15 ]
80
[ "15+15=30", "32*30=960", "960/12=80" ]
Current State: 80:[15, 32, 12, 15], Operations: [] Exploring Operation: 15+15=30, Resulting Numbers: [32, 12, 30] Generated Node #2: [32, 12, 30] from Operation: 15+15=30 Current State: 80:[32, 12, 30], Operations: ['15+15=30'] Exploring Operation: 32*30=960, Resulting Numbers: [12, 960] Generated Node #3: [12, 960] from Operation: 32*30=960 Current State: 80:[12, 960], Operations: ['15+15=30', '32*30=960'] Exploring Operation: 960/12=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[15, 32, 12, 15], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [15, 15, 20] Generated Node #0,0: 80:[15, 15, 20] Operation: 32-12=20 Exploring Operation: 32-15=17, Resulting Numbers: [12, 15, 17] Generated Node #0,1: 80:[12, 15, 17] Operation: 32-15=17 Exploring Operation: 32+12=44, Resulting Numbers: [15, 15, 44] Generated Node #0,2: 80:[15, 15, 44] Operation: 32+12=44 Exploring Operation: 32-15=17, Resulting Numbers: [15, 12, 17] Generated Node #0,3: 80:[15, 12, 17] Operation: 32-15=17 Moving to Node #0,0 Current State: 80:[15, 15, 20], Operations: ['32-12=20'] Exploring Operation: 15-15=0, Resulting Numbers: [20, 0] Generated Node #0,0,0: 80:[20, 0] Operation: 15-15=0 Exploring Operation: 20-15=5, Resulting Numbers: [15, 5] Generated Node #0,0,1: 80:[15, 5] Operation: 20-15=5 Exploring Operation: 15/15=1, Resulting Numbers: [20, 1] Generated Node #0,0,2: 80:[20, 1] Operation: 15/15=1 Exploring Operation: 20-15=5, Resulting Numbers: [15, 5] Generated Node #0,0,3: 80:[15, 5] Operation: 20-15=5 Moving to Node #0,3 Current State: 80:[15, 12, 17], Operations: ['32-15=17'] Exploring Operation: 17-12=5, Resulting Numbers: [15, 5] Generated Node #0,3,0: 80:[15, 5] Operation: 17-12=5 Exploring Operation: 17-15=2, Resulting Numbers: [12, 2] Generated Node #0,3,1: 80:[12, 2] Operation: 17-15=2 Exploring Operation: 15-12=3, Resulting Numbers: [17, 3] Generated Node #0,3,2: 80:[17, 3] Operation: 15-12=3 Exploring Operation: 15+12=27, Resulting Numbers: [17, 27] Generated Node #0,3,3: 80:[17, 27] Operation: 15+12=27 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[15, 5], Operations: ['32-15=17', '17-12=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[12, 2], Operations: ['32-15=17', '17-15=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 80:[17, 3], Operations: ['32-15=17', '15-12=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 80:[17, 27], Operations: ['32-15=17', '15+12=27'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,80 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,80 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: 80:[12, 15, 17], Operations: ['32-15=17'] Exploring Operation: 12+15=27, Resulting Numbers: [17, 27] Generated Node #0,1,0: 80:[17, 27] Operation: 12+15=27 Exploring Operation: 17-15=2, Resulting Numbers: [12, 2] Generated Node #0,1,1: 80:[12, 2] Operation: 17-15=2 Exploring Operation: 17-12=5, Resulting Numbers: [15, 5] Generated Node #0,1,2: 80:[15, 5] Operation: 17-12=5 Exploring Operation: 15-12=3, Resulting Numbers: [17, 3] Generated Node #0,1,3: 80:[17, 3] Operation: 15-12=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[15, 5], Operations: ['32-15=17', '17-12=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[12, 2], Operations: ['32-15=17', '17-15=2'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[17, 3], Operations: ['32-15=17', '15-12=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[17, 27], Operations: ['32-15=17', '12+15=27'] Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 17*27=459, Resulting Numbers: [459] 459,80 unequal: No Solution Exploring Operation: 17+27=44, Resulting Numbers: [44] 44,80 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: 80:[15, 15, 44], Operations: ['32+12=44'] Exploring Operation: 44-15=29, Resulting Numbers: [15, 29] Generated Node #0,2,0: 80:[15, 29] Operation: 44-15=29 Exploring Operation: 44-15=29, Resulting Numbers: [15, 29] Generated Node #0,2,1: 80:[15, 29] Operation: 44-15=29 Exploring Operation: 15-15=0, Resulting Numbers: [44, 0] Generated Node #0,2,2: 80:[44, 0] Operation: 15-15=0 Exploring Operation: 15/15=1, Resulting Numbers: [44, 1] Generated Node #0,2,3: 80:[44, 1] Operation: 15/15=1 Moving to Node #0,0,1 Current State: 80:[15, 5], Operations: ['32-12=20', '20-15=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,80 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[15, 5], Operations: ['32-12=20', '20-15=5'] Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[20, 1], Operations: ['32-12=20', '15/15=1'] Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[20, 0], Operations: ['32-12=20', '15-15=0'] Exploring Operation: 20*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 20-0=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 20+0=20, Resulting Numbers: [20] 20,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[44, 1], Operations: ['32+12=44', '15/15=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,80 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[44, 0], Operations: ['32+12=44', '15-15=0'] Exploring Operation: 44+0=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 44-0=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 44*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[15, 29], Operations: ['32+12=44', '44-15=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[15, 29], Operations: ['32+12=44', '44-15=29'] Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,80 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,80 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,80 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 64, 54, 2, 29 ]
15
[ "64+29=93", "54*2=108", "108-93=15" ]
Current State: 15:[64, 54, 2, 29], Operations: [] Exploring Operation: 64+29=93, Resulting Numbers: [54, 2, 93] Generated Node #2: [54, 2, 93] from Operation: 64+29=93 Current State: 15:[54, 2, 93], Operations: ['64+29=93'] Exploring Operation: 54*2=108, Resulting Numbers: [93, 108] Generated Node #3: [93, 108] from Operation: 54*2=108 Current State: 15:[93, 108], Operations: ['64+29=93', '54*2=108'] Exploring Operation: 108-93=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[64, 54, 2, 29], Operations: [] Exploring Operation: 64-54=10, Resulting Numbers: [2, 29, 10] Generated Node #0,0: 15:[2, 29, 10] Operation: 64-54=10 Moving to Node #0,0 Current State: 15:[2, 29, 10], Operations: ['64-54=10'] Exploring Operation: 29-10=19, Resulting Numbers: [2, 19] Generated Node #0,0,0: 15:[2, 19] Operation: 29-10=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[2, 19], Operations: ['64-54=10', '29-10=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,15 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
[ 5, 75, 34, 40 ]
57
[ "75+40=115", "115/5=23", "34+23=57" ]
Current State: 57:[5, 75, 34, 40], Operations: [] Exploring Operation: 75+40=115, Resulting Numbers: [5, 34, 115] Generated Node #2: [5, 34, 115] from Operation: 75+40=115 Current State: 57:[5, 34, 115], Operations: ['75+40=115'] Exploring Operation: 115/5=23, Resulting Numbers: [34, 23] Generated Node #3: [34, 23] from Operation: 115/5=23 Current State: 57:[34, 23], Operations: ['75+40=115', '115/5=23'] Exploring Operation: 34+23=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[5, 75, 34, 40], Operations: [] Exploring Operation: 40-34=6, Resulting Numbers: [5, 75, 6] Generated Node #0,0: 57:[5, 75, 6] Operation: 40-34=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[5, 75, 6], Operations: ['40-34=6'] Exploring Operation: 75/5=15, Resulting Numbers: [6, 15] Generated Node #0,0,0: 57:[6, 15] Operation: 75/5=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[6, 15], Operations: ['40-34=6', '75/5=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,57 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, 84, 72, 84 ]
80
[ "84-72=12", "48/12=4", "84-4=80" ]
Current State: 80:[48, 84, 72, 84], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [48, 12] Generated Node #2: [48, 12] from Operation: 84-72=12 Current State: 80:[48, 12], Operations: ['84-72=12'] Exploring Operation: 48/12=4, Resulting Numbers: [4] 4,80 equal: Goal Reached Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[48, 84, 72, 84], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [84, 84, 24] Generated Node #0,0: 80:[84, 84, 24] Operation: 72-48=24 Exploring Operation: 84-72=12, Resulting Numbers: [48, 84, 12] Generated Node #0,1: 80:[48, 84, 12] Operation: 84-72=12 Exploring Operation: 84-72=12, Resulting Numbers: [48, 84, 12] Generated Node #0,2: 80:[48, 84, 12] Operation: 84-72=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[84, 84, 24], Operations: ['72-48=24'] Exploring Operation: 84-84=0, Resulting Numbers: [24, 0] Generated Node #0,0,0: 80:[24, 0] Operation: 84-84=0 Exploring Operation: 84/84=1, Resulting Numbers: [24, 1] Generated Node #0,0,1: 80:[24, 1] Operation: 84/84=1 Exploring Operation: 84-24=60, Resulting Numbers: [84, 60] Generated Node #0,0,2: 80:[84, 60] Operation: 84-24=60 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[24, 1], Operations: ['72-48=24', '84/84=1'] Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[24, 0], Operations: ['72-48=24', '84-84=0'] Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 80:[84, 60], Operations: ['72-48=24', '84-24=60'] Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,80 unequal: No Solution Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,80 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[48, 84, 12], Operations: ['84-72=12'] Exploring Operation: 48-12=36, Resulting Numbers: [84, 36] Generated Node #0,1,0: 80:[84, 36] Operation: 48-12=36 Exploring Operation: 48/12=4, Resulting Numbers: [84, 4] Generated Node #0,1,1: 80:[84, 4] Operation: 48/12=4 Exploring Operation: 84-48=36, Resulting Numbers: [12, 36] Generated Node #0,1,2: 80:[12, 36] Operation: 84-48=36 Moving to Node #0,1,1 Current State: 80:[84, 4], Operations: ['84-72=12', '48/12=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[48, 84, 72, 84], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [48, 84, 12] Generated Node #0,1: 80:[48, 84, 12] Operation: 84-72=12 Moving to Node #0,1 Current State: 80:[48, 84, 12], Operations: ['84-72=12'] Exploring Operation: 48/12=4, Resulting Numbers: [84, 4] Generated Node #0,1,1: 80:[84, 4] Operation: 48/12=4 Moving to Node #0,1,1 Current State: 80:[84, 4], Operations: ['84-72=12', '48/12=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 36, 86, 81, 28 ]
40
[ "36-28=8", "86-81=5", "8*5=40" ]
Current State: 40:[36, 86, 81, 28], Operations: [] Exploring Operation: 36-28=8, Resulting Numbers: [86, 81, 8] Generated Node #2: [86, 81, 8] from Operation: 36-28=8 Current State: 40:[86, 81, 8], Operations: ['36-28=8'] Exploring Operation: 86-81=5, Resulting Numbers: [8, 5] Generated Node #3: [8, 5] from Operation: 86-81=5 Current State: 40:[8, 5], Operations: ['36-28=8', '86-81=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[36, 86, 81, 28], Operations: [] Exploring Operation: 81-36=45, Resulting Numbers: [86, 28, 45] Generated Node #0,0: 40:[86, 28, 45] Operation: 81-36=45 Exploring Operation: 86-81=5, Resulting Numbers: [36, 28, 5] Generated Node #0,1: 40:[36, 28, 5] Operation: 86-81=5 Exploring Operation: 86-28=58, Resulting Numbers: [36, 81, 58] Generated Node #0,2: 40:[36, 81, 58] Operation: 86-28=58 Exploring Operation: 86-36=50, Resulting Numbers: [81, 28, 50] Generated Node #0,3: 40:[81, 28, 50] Operation: 86-36=50 Moving to Node #0,1 Current State: 40:[36, 28, 5], Operations: ['86-81=5'] Exploring Operation: 36-28=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 40:[5, 8] Operation: 36-28=8 Exploring Operation: 28-5=23, Resulting Numbers: [36, 23] Generated Node #0,1,1: 40:[36, 23] Operation: 28-5=23 Exploring Operation: 28+5=33, Resulting Numbers: [36, 33] Generated Node #0,1,2: 40:[36, 33] Operation: 28+5=33 Exploring Operation: 36+5=41, Resulting Numbers: [28, 41] Generated Node #0,1,3: 40:[28, 41] Operation: 36+5=41 Moving to Node #0,3 Current State: 40:[81, 28, 50], Operations: ['86-36=50'] Exploring Operation: 81-50=31, Resulting Numbers: [28, 31] Generated Node #0,3,0: 40:[28, 31] Operation: 81-50=31 Exploring Operation: 81-28=53, Resulting Numbers: [50, 53] Generated Node #0,3,1: 40:[50, 53] Operation: 81-28=53 Exploring Operation: 50-28=22, Resulting Numbers: [81, 22] Generated Node #0,3,2: 40:[81, 22] Operation: 50-28=22 Exploring Operation: 81+28=109, Resulting Numbers: [50, 109] Generated Node #0,3,3: 40:[50, 109] Operation: 81+28=109 Moving to Node #0,0 Current State: 40:[86, 28, 45], Operations: ['81-36=45'] Exploring Operation: 86+28=114, Resulting Numbers: [45, 114] Generated Node #0,0,0: 40:[45, 114] Operation: 86+28=114 Exploring Operation: 86-45=41, Resulting Numbers: [28, 41] Generated Node #0,0,1: 40:[28, 41] Operation: 86-45=41 Exploring Operation: 45-28=17, Resulting Numbers: [86, 17] Generated Node #0,0,2: 40:[86, 17] Operation: 45-28=17 Exploring Operation: 86-28=58, Resulting Numbers: [45, 58] Generated Node #0,0,3: 40:[45, 58] Operation: 86-28=58 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[28, 41], Operations: ['81-36=45', '86-45=41'] Exploring Operation: 28*41=1148, Resulting Numbers: [1148] 1148,40 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,40 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 #0,0,3 Current State: 40:[45, 58], Operations: ['81-36=45', '86-28=58'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 45*58=2610, Resulting Numbers: [2610] 2610,40 unequal: No Solution Exploring Operation: 45+58=103, Resulting Numbers: [103] 103,40 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:[86, 17], Operations: ['81-36=45', '45-28=17'] Exploring Operation: 86+17=103, Resulting Numbers: [103] 103,40 unequal: No Solution Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,40 unequal: No Solution Exploring Operation: 86*17=1462, Resulting Numbers: [1462] 1462,40 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:[45, 114], Operations: ['81-36=45', '86+28=114'] Exploring Operation: 114-45=69, Resulting Numbers: [69] 69,40 unequal: No Solution Exploring Operation: 45*114=5130, Resulting Numbers: [5130] 5130,40 unequal: No Solution Exploring Operation: 45+114=159, Resulting Numbers: [159] 159,40 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:[36, 81, 58], Operations: ['86-28=58'] Exploring Operation: 36+81=117, Resulting Numbers: [58, 117] Generated Node #0,2,0: 40:[58, 117] Operation: 36+81=117 Exploring Operation: 58-36=22, Resulting Numbers: [81, 22] Generated Node #0,2,1: 40:[81, 22] Operation: 58-36=22 Exploring Operation: 81-36=45, Resulting Numbers: [58, 45] Generated Node #0,2,2: 40:[58, 45] Operation: 81-36=45 Exploring Operation: 81-58=23, Resulting Numbers: [36, 23] Generated Node #0,2,3: 40:[36, 23] Operation: 81-58=23 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 40:[36, 23], Operations: ['86-28=58', '81-58=23'] Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 36+23=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 36*23=828, Resulting Numbers: [828] 828,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[58, 45], Operations: ['86-28=58', '81-36=45'] Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 58*45=2610, Resulting Numbers: [2610] 2610,40 unequal: No Solution Exploring Operation: 58+45=103, Resulting Numbers: [103] 103,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 40:[81, 22], Operations: ['86-28=58', '58-36=22'] Exploring Operation: 81-22=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 81+22=103, Resulting Numbers: [103] 103,40 unequal: No Solution Exploring Operation: 81*22=1782, Resulting Numbers: [1782] 1782,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 40:[58, 117], Operations: ['86-28=58', '36+81=117'] Exploring Operation: 58*117=6786, Resulting Numbers: [6786] 6786,40 unequal: No Solution Exploring Operation: 58+117=175, Resulting Numbers: [175] 175,40 unequal: No Solution Exploring Operation: 117-58=59, Resulting Numbers: [59] 59,40 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: 40:[5, 8], Operations: ['86-81=5', '36-28=8'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,40 unequal: No Solution Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[36, 86, 81, 28], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [36, 28, 5] Generated Node #0,1: 40:[36, 28, 5] Operation: 86-81=5 Moving to Node #0,1 Current State: 40:[36, 28, 5], Operations: ['86-81=5'] Exploring Operation: 36-28=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 40:[5, 8] Operation: 36-28=8 Moving to Node #0,1,0 Current State: 40:[5, 8], Operations: ['86-81=5', '36-28=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 22, 45, 80, 86 ]
61
[ "22+45=67", "86-80=6", "67-6=61" ]
Current State: 61:[22, 45, 80, 86], Operations: [] Exploring Operation: 22+45=67, Resulting Numbers: [80, 86, 67] Generated Node #2: [80, 86, 67] from Operation: 22+45=67 Current State: 61:[80, 86, 67], Operations: ['22+45=67'] Exploring Operation: 86-80=6, Resulting Numbers: [67, 6] Generated Node #3: [67, 6] from Operation: 86-80=6 Current State: 61:[67, 6], Operations: ['22+45=67', '86-80=6'] Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[22, 45, 80, 86], Operations: [] Exploring Operation: 80-22=58, Resulting Numbers: [45, 86, 58] Generated Node #0,0: 61:[45, 86, 58] Operation: 80-22=58 Exploring Operation: 86-22=64, Resulting Numbers: [45, 80, 64] Generated Node #0,1: 61:[45, 80, 64] Operation: 86-22=64 Exploring Operation: 86-45=41, Resulting Numbers: [22, 80, 41] Generated Node #0,2: 61:[22, 80, 41] Operation: 86-45=41 Exploring Operation: 22+45=67, Resulting Numbers: [80, 86, 67] Generated Node #0,3: 61:[80, 86, 67] Operation: 22+45=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[45, 80, 64], Operations: ['86-22=64'] Exploring Operation: 80-45=35, Resulting Numbers: [64, 35] Generated Node #0,1,0: 61:[64, 35] Operation: 80-45=35 Exploring Operation: 45+80=125, Resulting Numbers: [64, 125] Generated Node #0,1,1: 61:[64, 125] Operation: 45+80=125 Exploring Operation: 80-64=16, Resulting Numbers: [45, 16] Generated Node #0,1,2: 61:[45, 16] Operation: 80-64=16 Exploring Operation: 64-45=19, Resulting Numbers: [80, 19] Generated Node #0,1,3: 61:[80, 19] Operation: 64-45=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[64, 35], Operations: ['86-22=64', '80-45=35'] Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 64+35=99, Resulting Numbers: [99] 99,61 unequal: No Solution Exploring Operation: 64*35=2240, Resulting Numbers: [2240] 2240,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[45, 16], Operations: ['86-22=64', '80-64=16'] Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[22, 45, 80, 86], Operations: [] Exploring Operation: 86-22=64, Resulting Numbers: [45, 80, 64] Generated Node #0,1: 61:[45, 80, 64] Operation: 86-22=64 Moving to Node #0,1 Current State: 61:[45, 80, 64], Operations: ['86-22=64'] Exploring Operation: 80-64=16, Resulting Numbers: [45, 16] Generated Node #0,1,2: 61:[45, 16] Operation: 80-64=16 Moving to Node #0,1,2 Current State: 61:[45, 16], Operations: ['86-22=64', '80-64=16'] Exploring Operation: 45+16=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 60, 51, 11, 19 ]
80
[ "60-51=9", "11*9=99", "99-19=80" ]
Current State: 80:[60, 51, 11, 19], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [11, 19, 9] Generated Node #2: [11, 19, 9] from Operation: 60-51=9 Current State: 80:[11, 19, 9], Operations: ['60-51=9'] Exploring Operation: 11*9=99, Resulting Numbers: [19, 99] Generated Node #3: [19, 99] from Operation: 11*9=99 Current State: 80:[19, 99], Operations: ['60-51=9', '11*9=99'] Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[60, 51, 11, 19], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [11, 19, 9] Generated Node #0,0: 80:[11, 19, 9] Operation: 60-51=9 Exploring Operation: 60+19=79, Resulting Numbers: [51, 11, 79] Generated Node #0,1: 80:[51, 11, 79] Operation: 60+19=79 Moving to Node #0,0 Current State: 80:[11, 19, 9], Operations: ['60-51=9'] Exploring Operation: 11+9=20, Resulting Numbers: [19, 20] Generated Node #0,0,0: 80:[19, 20] Operation: 11+9=20 Exploring Operation: 19-11=8, Resulting Numbers: [9, 8] Generated Node #0,0,1: 80:[9, 8] Operation: 19-11=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[19, 20], Operations: ['60-51=9', '11+9=20'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[9, 8], Operations: ['60-51=9', '19-11=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,80 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: 80:[51, 11, 79], Operations: ['60+19=79'] Exploring Operation: 79-51=28, Resulting Numbers: [11, 28] Generated Node #0,1,0: 80:[11, 28] Operation: 79-51=28 Exploring Operation: 51-11=40, Resulting Numbers: [79, 40] Generated Node #0,1,1: 80:[79, 40] Operation: 51-11=40 Moving to Node #0,1,1 Current State: 80:[79, 40], Operations: ['60+19=79', '51-11=40'] Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,80 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[11, 28], Operations: ['60+19=79', '79-51=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 11+28=39, Resulting Numbers: [39] 39,80 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 14, 39, 5, 6 ]
86
[ "14*39=546", "546/6=91", "91-5=86" ]
Current State: 86:[14, 39, 5, 6], Operations: [] Exploring Operation: 14*39=546, Resulting Numbers: [5, 6, 546] Generated Node #2: [5, 6, 546] from Operation: 14*39=546 Current State: 86:[5, 6, 546], Operations: ['14*39=546'] Exploring Operation: 546/6=91, Resulting Numbers: [5, 91] Generated Node #3: [5, 91] from Operation: 546/6=91 Current State: 86:[5, 91], Operations: ['14*39=546', '546/6=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[14, 39, 5, 6], Operations: [] Exploring Operation: 14-6=8, Resulting Numbers: [39, 5, 8] Generated Node #0,0: 86:[39, 5, 8] Operation: 14-6=8 Exploring Operation: 14*6=84, Resulting Numbers: [39, 5, 84] Generated Node #0,1: 86:[39, 5, 84] Operation: 14*6=84 Exploring Operation: 14-5=9, Resulting Numbers: [39, 6, 9] Generated Node #0,2: 86:[39, 6, 9] Operation: 14-5=9 Moving to Node #0,1 Current State: 86:[39, 5, 84], Operations: ['14*6=84'] Exploring Operation: 84-39=45, Resulting Numbers: [5, 45] Generated Node #0,1,0: 86:[5, 45] Operation: 84-39=45 Exploring Operation: 39+5=44, Resulting Numbers: [84, 44] Generated Node #0,1,1: 86:[84, 44] Operation: 39+5=44 Exploring Operation: 5+84=89, Resulting Numbers: [39, 89] Generated Node #0,1,2: 86:[39, 89] Operation: 5+84=89 Moving to Node #0,0 Current State: 86:[39, 5, 8], Operations: ['14-6=8'] Exploring Operation: 39+5=44, Resulting Numbers: [8, 44] Generated Node #0,0,0: 86:[8, 44] Operation: 39+5=44 Exploring Operation: 39+8=47, Resulting Numbers: [5, 47] Generated Node #0,0,1: 86:[5, 47] Operation: 39+8=47 Exploring Operation: 8-5=3, Resulting Numbers: [39, 3] Generated Node #0,0,2: 86:[39, 3] Operation: 8-5=3 Moving to Node #0,2 Current State: 86:[39, 6, 9], Operations: ['14-5=9'] Exploring Operation: 9-6=3, Resulting Numbers: [39, 3] Generated Node #0,2,0: 86:[39, 3] Operation: 9-6=3 Exploring Operation: 39+9=48, Resulting Numbers: [6, 48] Generated Node #0,2,1: 86:[6, 48] Operation: 39+9=48 Exploring Operation: 39+6=45, Resulting Numbers: [9, 45] Generated Node #0,2,2: 86:[9, 45] Operation: 39+6=45 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[39, 3], Operations: ['14-5=9', '9-6=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[6, 48], Operations: ['14-5=9', '39+9=48'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,86 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[9, 45], Operations: ['14-5=9', '39+6=45'] Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,86 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 86:[84, 44], Operations: ['14*6=84', '39+5=44'] Exploring Operation: 84-44=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 84+44=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 84*44=3696, Resulting Numbers: [3696] 3696,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[5, 45], Operations: ['14*6=84', '84-39=45'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,86 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[39, 3], Operations: ['14-6=8', '8-5=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,86 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[39, 89], Operations: ['14*6=84', '5+84=89'] Exploring Operation: 39+89=128, Resulting Numbers: [128] 128,86 unequal: No Solution Exploring Operation: 39*89=3471, Resulting Numbers: [3471] 3471,86 unequal: No Solution Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[5, 47], Operations: ['14-6=8', '39+8=47'] Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,86 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[8, 44], Operations: ['14-6=8', '39+5=44'] Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,86 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,86 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 56, 28, 16, 37 ]
23
[ "56/28=2", "37-16=21", "2+21=23" ]
Current State: 23:[56, 28, 16, 37], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [16, 37, 2] Generated Node #2: [16, 37, 2] from Operation: 56/28=2 Current State: 23:[16, 37, 2], Operations: ['56/28=2'] Exploring Operation: 37-16=21, Resulting Numbers: [2, 21] Generated Node #3: [2, 21] from Operation: 37-16=21 Current State: 23:[2, 21], Operations: ['56/28=2', '37-16=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[56, 28, 16, 37], Operations: [] Exploring Operation: 56-37=19, Resulting Numbers: [28, 16, 19] Generated Node #0,0: 23:[28, 16, 19] Operation: 56-37=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[28, 16, 19], Operations: ['56-37=19'] Exploring Operation: 28-16=12, Resulting Numbers: [19, 12] Generated Node #0,0,0: 23:[19, 12] Operation: 28-16=12 Moving to Node #0,0,0 Current State: 23:[19, 12], Operations: ['56-37=19', '28-16=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 28, 9, 42, 10 ]
76
[ "42-28=14", "9*10=90", "90-14=76" ]
Current State: 76:[28, 9, 42, 10], Operations: [] Exploring Operation: 42-28=14, Resulting Numbers: [9, 10, 14] Generated Node #2: [9, 10, 14] from Operation: 42-28=14 Current State: 76:[9, 10, 14], Operations: ['42-28=14'] Exploring Operation: 9*10=90, Resulting Numbers: [14, 90] Generated Node #3: [14, 90] from Operation: 9*10=90 Current State: 76:[14, 90], Operations: ['42-28=14', '9*10=90'] Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[28, 9, 42, 10], Operations: [] Exploring Operation: 28+10=38, Resulting Numbers: [9, 42, 38] Generated Node #0,0: 76:[9, 42, 38] Operation: 28+10=38 Exploring Operation: 28-9=19, Resulting Numbers: [42, 10, 19] Generated Node #0,1: 76:[42, 10, 19] Operation: 28-9=19 Moving to Node #0,0 Current State: 76:[9, 42, 38], Operations: ['28+10=38'] Exploring Operation: 42-38=4, Resulting Numbers: [9, 4] Generated Node #0,0,0: 76:[9, 4] Operation: 42-38=4 Exploring Operation: 42-9=33, Resulting Numbers: [38, 33] Generated Node #0,0,1: 76:[38, 33] Operation: 42-9=33 Moving to Node #0,1 Current State: 76:[42, 10, 19], Operations: ['28-9=19'] Exploring Operation: 19-10=9, Resulting Numbers: [42, 9] Generated Node #0,1,0: 76:[42, 9] Operation: 19-10=9 Exploring Operation: 42-10=32, Resulting Numbers: [19, 32] Generated Node #0,1,1: 76:[19, 32] Operation: 42-10=32 Moving to Node #0,0,0 Current State: 76:[9, 4], Operations: ['28+10=38', '42-38=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[38, 33], Operations: ['28+10=38', '42-9=33'] Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 38+33=71, Resulting Numbers: [71] 71,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[19, 32], Operations: ['28-9=19', '42-10=32'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[42, 9], Operations: ['28-9=19', '19-10=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 42+9=51, Resulting Numbers: [51] 51,76 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 3, 77, 4, 57 ]
82
[ "57-4=53", "3*53=159", "159-77=82" ]
Current State: 82:[3, 77, 4, 57], Operations: [] Exploring Operation: 57-4=53, Resulting Numbers: [3, 77, 53] Generated Node #2: [3, 77, 53] from Operation: 57-4=53 Current State: 82:[3, 77, 53], Operations: ['57-4=53'] Exploring Operation: 3*53=159, Resulting Numbers: [77, 159] Generated Node #3: [77, 159] from Operation: 3*53=159 Current State: 82:[77, 159], Operations: ['57-4=53', '3*53=159'] Exploring Operation: 159-77=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[3, 77, 4, 57], Operations: [] Exploring Operation: 77+4=81, Resulting Numbers: [3, 57, 81] Generated Node #0,0: 82:[3, 57, 81] Operation: 77+4=81 Exploring Operation: 57-4=53, Resulting Numbers: [3, 77, 53] Generated Node #0,1: 82:[3, 77, 53] Operation: 57-4=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[3, 57, 81], Operations: ['77+4=81'] Exploring Operation: 57-3=54, Resulting Numbers: [81, 54] Generated Node #0,0,0: 82:[81, 54] Operation: 57-3=54 Exploring Operation: 57/3=19, Resulting Numbers: [81, 19] Generated Node #0,0,1: 82:[81, 19] Operation: 57/3=19 Moving to Node #0,0,0 Current State: 82:[81, 54], Operations: ['77+4=81', '57-3=54'] Exploring Operation: 81-54=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 81+54=135, Resulting Numbers: [135] 135,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[81, 19], Operations: ['77+4=81', '57/3=19'] Exploring Operation: 81+19=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[3, 77, 53], Operations: ['57-4=53'] Exploring Operation: 3+77=80, Resulting Numbers: [53, 80] Generated Node #0,1,0: 82:[53, 80] Operation: 3+77=80 Exploring Operation: 53-3=50, Resulting Numbers: [77, 50] Generated Node #0,1,1: 82:[77, 50] Operation: 53-3=50 Moving to Node #0,1,0 Current State: 82:[53, 80], Operations: ['57-4=53', '3+77=80'] Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,82 unequal: No Solution Exploring Operation: 53+80=133, Resulting Numbers: [133] 133,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[77, 50], Operations: ['57-4=53', '53-3=50'] Exploring Operation: 77+50=127, Resulting Numbers: [127] 127,82 unequal: No Solution Exploring Operation: 77-50=27, Resulting Numbers: [27] 27,82 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
[ 32, 42, 40, 4 ]
72
[ "32+4=36", "42-40=2", "36*2=72" ]
Current State: 72:[32, 42, 40, 4], Operations: [] Exploring Operation: 32+4=36, Resulting Numbers: [42, 40, 36] Generated Node #2: [42, 40, 36] from Operation: 32+4=36 Current State: 72:[42, 40, 36], Operations: ['32+4=36'] Exploring Operation: 42-40=2, Resulting Numbers: [36, 2] Generated Node #3: [36, 2] from Operation: 42-40=2 Current State: 72:[36, 2], Operations: ['32+4=36', '42-40=2'] Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[32, 42, 40, 4], Operations: [] Exploring Operation: 32+40=72, Resulting Numbers: [42, 4, 72] Generated Node #0,0: 72:[42, 4, 72] Operation: 32+40=72 Exploring Operation: 42-32=10, Resulting Numbers: [40, 4, 10] Generated Node #0,1: 72:[40, 4, 10] Operation: 42-32=10 Exploring Operation: 32+42=74, Resulting Numbers: [40, 4, 74] Generated Node #0,2: 72:[40, 4, 74] Operation: 32+42=74 Exploring Operation: 40-32=8, Resulting Numbers: [42, 4, 8] Generated Node #0,3: 72:[42, 4, 8] Operation: 40-32=8 Exploring Operation: 42-40=2, Resulting Numbers: [32, 4, 2] Generated Node #0,4: 72:[32, 4, 2] Operation: 42-40=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[32, 4, 2], Operations: ['42-40=2'] Exploring Operation: 32/2=16, Resulting Numbers: [4, 16] Generated Node #0,4,0: 72:[4, 16] Operation: 32/2=16 Exploring Operation: 32+2=34, Resulting Numbers: [4, 34] Generated Node #0,4,1: 72:[4, 34] Operation: 32+2=34 Exploring Operation: 32/4=8, Resulting Numbers: [2, 8] Generated Node #0,4,2: 72:[2, 8] Operation: 32/4=8 Exploring Operation: 32-4=28, Resulting Numbers: [2, 28] Generated Node #0,4,3: 72:[2, 28] Operation: 32-4=28 Exploring Operation: 32+4=36, Resulting Numbers: [2, 36] Generated Node #0,4,4: 72:[2, 36] Operation: 32+4=36 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 72:[2, 8], Operations: ['42-40=2', '32/4=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,72 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,72 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 #0,4,4 Current State: 72:[2, 36], Operations: ['42-40=2', '32+4=36'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[32, 42, 40, 4], Operations: [] Exploring Operation: 42-40=2, Resulting Numbers: [32, 4, 2] Generated Node #0,4: 72:[32, 4, 2] Operation: 42-40=2 Moving to Node #0,4 Current State: 72:[32, 4, 2], Operations: ['42-40=2'] Exploring Operation: 32+4=36, Resulting Numbers: [2, 36] Generated Node #0,4,4: 72:[2, 36] Operation: 32+4=36 Moving to Node #0,4,4 Current State: 72:[2, 36], Operations: ['42-40=2', '32+4=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 92, 68, 20, 12 ]
16
[ "92-68=24", "20-12=8", "24-8=16" ]
Current State: 16:[92, 68, 20, 12], Operations: [] Exploring Operation: 92-68=24, Resulting Numbers: [20, 12, 24] Generated Node #2: [20, 12, 24] from Operation: 92-68=24 Current State: 16:[20, 12, 24], Operations: ['92-68=24'] Exploring Operation: 20-12=8, Resulting Numbers: [24, 8] Generated Node #3: [24, 8] from Operation: 20-12=8 Current State: 16:[24, 8], Operations: ['92-68=24', '20-12=8'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[92, 68, 20, 12], Operations: [] Exploring Operation: 68-20=48, Resulting Numbers: [92, 12, 48] Generated Node #0,0: 16:[92, 12, 48] Operation: 68-20=48 Exploring Operation: 92-12=80, Resulting Numbers: [68, 20, 80] Generated Node #0,1: 16:[68, 20, 80] Operation: 92-12=80 Exploring Operation: 92-20=72, Resulting Numbers: [68, 12, 72] Generated Node #0,2: 16:[68, 12, 72] Operation: 92-20=72 Exploring Operation: 92-68=24, Resulting Numbers: [20, 12, 24] Generated Node #0,3: 16:[20, 12, 24] Operation: 92-68=24 Moving to Node #0,3 Current State: 16:[20, 12, 24], Operations: ['92-68=24'] Exploring Operation: 24/12=2, Resulting Numbers: [20, 2] Generated Node #0,3,0: 16:[20, 2] Operation: 24/12=2 Exploring Operation: 24-20=4, Resulting Numbers: [12, 4] Generated Node #0,3,1: 16:[12, 4] Operation: 24-20=4 Exploring Operation: 24-12=12, Resulting Numbers: [20, 12] Generated Node #0,3,2: 16:[20, 12] Operation: 24-12=12 Exploring Operation: 20-12=8, Resulting Numbers: [24, 8] Generated Node #0,3,3: 16:[24, 8] Operation: 20-12=8 Moving to Node #0,2 Current State: 16:[68, 12, 72], Operations: ['92-20=72'] Exploring Operation: 72/12=6, Resulting Numbers: [68, 6] Generated Node #0,2,0: 16:[68, 6] Operation: 72/12=6 Exploring Operation: 72-12=60, Resulting Numbers: [68, 60] Generated Node #0,2,1: 16:[68, 60] Operation: 72-12=60 Exploring Operation: 72-68=4, Resulting Numbers: [12, 4] Generated Node #0,2,2: 16:[12, 4] Operation: 72-68=4 Exploring Operation: 68-12=56, Resulting Numbers: [72, 56] Generated Node #0,2,3: 16:[72, 56] Operation: 68-12=56 Moving to Node #0,0 Current State: 16:[92, 12, 48], Operations: ['68-20=48'] Exploring Operation: 48/12=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 16:[92, 4] Operation: 48/12=4 Exploring Operation: 92-48=44, Resulting Numbers: [12, 44] Generated Node #0,0,1: 16:[12, 44] Operation: 92-48=44 Exploring Operation: 92-12=80, Resulting Numbers: [48, 80] Generated Node #0,0,2: 16:[48, 80] Operation: 92-12=80 Exploring Operation: 48-12=36, Resulting Numbers: [92, 36] Generated Node #0,0,3: 16:[92, 36] Operation: 48-12=36 Moving to Node #0,1 Current State: 16:[68, 20, 80], Operations: ['92-12=80'] Exploring Operation: 80-68=12, Resulting Numbers: [20, 12] Generated Node #0,1,0: 16:[20, 12] Operation: 80-68=12 Exploring Operation: 68-20=48, Resulting Numbers: [80, 48] Generated Node #0,1,1: 16:[80, 48] Operation: 68-20=48 Exploring Operation: 80/20=4, Resulting Numbers: [68, 4] Generated Node #0,1,2: 16:[68, 4] Operation: 80/20=4 Exploring Operation: 80-20=60, Resulting Numbers: [68, 60] Generated Node #0,1,3: 16:[68, 60] Operation: 80-20=60 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[20, 12], Operations: ['92-12=80', '80-68=12'] Exploring Operation: 20*12=240, Resulting Numbers: [240] 240,16 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 16:[68, 4], Operations: ['92-12=80', '80/20=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,16 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,16 unequal: No Solution Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,16 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[80, 48], Operations: ['92-12=80', '68-20=48'] Exploring Operation: 80+48=128, Resulting Numbers: [128] 128,16 unequal: No Solution Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,16 unequal: No Solution Exploring Operation: 80*48=3840, Resulting Numbers: [3840] 3840,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 16:[68, 60], Operations: ['92-12=80', '80-20=60'] Exploring Operation: 68+60=128, Resulting Numbers: [128] 128,16 unequal: No Solution Exploring Operation: 68-60=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 68*60=4080, Resulting Numbers: [4080] 4080,16 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: 16:[20, 2], Operations: ['92-68=24', '24/12=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,16 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,16 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,16 unequal: No Solution Moving to Node #0,3,1 Current State: 16:[12, 4], Operations: ['92-68=24', '24-20=4'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,16 unequal: No Solution Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[92, 68, 20, 12], Operations: [] Exploring Operation: 92-68=24, Resulting Numbers: [20, 12, 24] Generated Node #0,3: 16:[20, 12, 24] Operation: 92-68=24 Moving to Node #0,3 Current State: 16:[20, 12, 24], Operations: ['92-68=24'] Exploring Operation: 24-20=4, Resulting Numbers: [12, 4] Generated Node #0,3,1: 16:[12, 4] Operation: 24-20=4 Moving to Node #0,3,1 Current State: 16:[12, 4], Operations: ['92-68=24', '24-20=4'] Exploring Operation: 12+4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.961806
hs_4
mult_heuristic
[ 3, 30, 98, 5 ]
96
[ "30/3=10", "10/5=2", "98-2=96" ]
Current State: 96:[3, 30, 98, 5], Operations: [] Exploring Operation: 30/3=10, Resulting Numbers: [98, 5, 10] Generated Node #2: [98, 5, 10] from Operation: 30/3=10 Current State: 96:[98, 5, 10], Operations: ['30/3=10'] Exploring Operation: 10/5=2, Resulting Numbers: [98, 2] Generated Node #3: [98, 2] from Operation: 10/5=2 Current State: 96:[98, 2], Operations: ['30/3=10', '10/5=2'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[3, 30, 98, 5], Operations: [] Exploring Operation: 3+5=8, Resulting Numbers: [30, 98, 8] Generated Node #0,0: 96:[30, 98, 8] Operation: 3+5=8 Exploring Operation: 3+30=33, Resulting Numbers: [98, 5, 33] Generated Node #0,1: 96:[98, 5, 33] Operation: 3+30=33 Exploring Operation: 30-5=25, Resulting Numbers: [3, 98, 25] Generated Node #0,2: 96:[3, 98, 25] Operation: 30-5=25 Exploring Operation: 98-3=95, Resulting Numbers: [30, 5, 95] Generated Node #0,3: 96:[30, 5, 95] Operation: 98-3=95 Exploring Operation: 30/5=6, Resulting Numbers: [3, 98, 6] Generated Node #0,4: 96:[3, 98, 6] Operation: 30/5=6 Moving to Node #0,4 Current State: 96:[3, 98, 6], Operations: ['30/5=6'] Exploring Operation: 6/3=2, Resulting Numbers: [98, 2] Generated Node #0,4,0: 96:[98, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [98, 3] Generated Node #0,4,1: 96:[98, 3] Operation: 6-3=3 Exploring Operation: 3+6=9, Resulting Numbers: [98, 9] Generated Node #0,4,2: 96:[98, 9] Operation: 3+6=9 Exploring Operation: 98-3=95, Resulting Numbers: [6, 95] Generated Node #0,4,3: 96:[6, 95] Operation: 98-3=95 Exploring Operation: 3*6=18, Resulting Numbers: [98, 18] Generated Node #0,4,4: 96:[98, 18] Operation: 3*6=18 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 96:[6, 95], Operations: ['30/5=6', '98-3=95'] Exploring Operation: 6+95=101, Resulting Numbers: [101] 101,96 unequal: No Solution Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,96 unequal: No Solution Exploring Operation: 6*95=570, Resulting Numbers: [570] 570,96 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 #0,4,0 Current State: 96:[98, 2], Operations: ['30/5=6', '6/3=2'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[3, 30, 98, 5], Operations: [] Exploring Operation: 30/5=6, Resulting Numbers: [3, 98, 6] Generated Node #0,4: 96:[3, 98, 6] Operation: 30/5=6 Moving to Node #0,4 Current State: 96:[3, 98, 6], Operations: ['30/5=6'] Exploring Operation: 6/3=2, Resulting Numbers: [98, 2] Generated Node #0,4,0: 96:[98, 2] Operation: 6/3=2 Moving to Node #0,4,0 Current State: 96:[98, 2], Operations: ['30/5=6', '6/3=2'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 14, 13, 8, 2 ]
15
[ "14-13=1", "8*2=16", "16-1=15" ]
Current State: 15:[14, 13, 8, 2], Operations: [] Exploring Operation: 14-13=1, Resulting Numbers: [8, 2, 1] Generated Node #2: [8, 2, 1] from Operation: 14-13=1 Current State: 15:[8, 2, 1], Operations: ['14-13=1'] Exploring Operation: 8*2=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 8*2=16 Current State: 15:[1, 16], Operations: ['14-13=1', '8*2=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[14, 13, 8, 2], Operations: [] Exploring Operation: 13-8=5, Resulting Numbers: [14, 2, 5] Generated Node #0,0: 15:[14, 2, 5] Operation: 13-8=5 Exploring Operation: 13+2=15, Resulting Numbers: [14, 8, 15] Generated Node #0,1: 15:[14, 8, 15] Operation: 13+2=15 Exploring Operation: 8*2=16, Resulting Numbers: [14, 13, 16] Generated Node #0,2: 15:[14, 13, 16] Operation: 8*2=16 Exploring Operation: 14-8=6, Resulting Numbers: [13, 2, 6] Generated Node #0,3: 15:[13, 2, 6] Operation: 14-8=6 Moving to Node #0,0 Current State: 15:[14, 2, 5], Operations: ['13-8=5'] Exploring Operation: 14/2=7, Resulting Numbers: [5, 7] Generated Node #0,0,0: 15:[5, 7] Operation: 14/2=7 Exploring Operation: 5-2=3, Resulting Numbers: [14, 3] Generated Node #0,0,1: 15:[14, 3] Operation: 5-2=3 Exploring Operation: 14+2=16, Resulting Numbers: [5, 16] Generated Node #0,0,2: 15:[5, 16] Operation: 14+2=16 Exploring Operation: 14-2=12, Resulting Numbers: [5, 12] Generated Node #0,0,3: 15:[5, 12] Operation: 14-2=12 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[14, 3], Operations: ['13-8=5', '5-2=3'] Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,15 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[5, 16], Operations: ['13-8=5', '14+2=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[5, 7], Operations: ['13-8=5', '14/2=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,15 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 15:[5, 12], Operations: ['13-8=5', '14-2=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,15 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,15 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: 15:[14, 13, 16], Operations: ['8*2=16'] Exploring Operation: 14-13=1, Resulting Numbers: [16, 1] Generated Node #0,2,0: 15:[16, 1] Operation: 14-13=1 Exploring Operation: 16-14=2, Resulting Numbers: [13, 2] Generated Node #0,2,1: 15:[13, 2] Operation: 16-14=2 Exploring Operation: 14+13=27, Resulting Numbers: [16, 27] Generated Node #0,2,2: 15:[16, 27] Operation: 14+13=27 Exploring Operation: 16-13=3, Resulting Numbers: [14, 3] Generated Node #0,2,3: 15:[14, 3] Operation: 16-13=3 Moving to Node #0,1 Current State: 15:[14, 8, 15], Operations: ['13+2=15'] Exploring Operation: 15-8=7, Resulting Numbers: [14, 7] Generated Node #0,1,0: 15:[14, 7] Operation: 15-8=7 Exploring Operation: 14+8=22, Resulting Numbers: [15, 22] Generated Node #0,1,1: 15:[15, 22] Operation: 14+8=22 Exploring Operation: 15-14=1, Resulting Numbers: [8, 1] Generated Node #0,1,2: 15:[8, 1] Operation: 15-14=1 Exploring Operation: 14-8=6, Resulting Numbers: [15, 6] Generated Node #0,1,3: 15:[15, 6] Operation: 14-8=6 Moving to Node #0,3 Current State: 15:[13, 2, 6], Operations: ['14-8=6'] Exploring Operation: 6-2=4, Resulting Numbers: [13, 4] Generated Node #0,3,0: 15:[13, 4] Operation: 6-2=4 Exploring Operation: 13+2=15, Resulting Numbers: [6, 15] Generated Node #0,3,1: 15:[6, 15] Operation: 13+2=15 Exploring Operation: 6/2=3, Resulting Numbers: [13, 3] Generated Node #0,3,2: 15:[13, 3] Operation: 6/2=3 Exploring Operation: 13-6=7, Resulting Numbers: [2, 7] Generated Node #0,3,3: 15:[2, 7] Operation: 13-6=7 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 15:[6, 15], Operations: ['14-8=6', '13+2=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 15:[13, 3], Operations: ['14-8=6', '6/2=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,15 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 15:[13, 4], Operations: ['14-8=6', '6-2=4'] Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 15:[2, 7], Operations: ['14-8=6', '13-6=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 15:[14, 3], Operations: ['8*2=16', '16-13=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,15 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[15, 6], Operations: ['13+2=15', '14-8=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,15 unequal: No Solution Moving to Node #0,2,1 Current State: 15:[13, 2], Operations: ['8*2=16', '16-14=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,15 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[14, 13, 8, 2], Operations: [] Exploring Operation: 8*2=16, Resulting Numbers: [14, 13, 16] Generated Node #0,2: 15:[14, 13, 16] Operation: 8*2=16 Moving to Node #0,2 Current State: 15:[14, 13, 16], Operations: ['8*2=16'] Exploring Operation: 16-14=2, Resulting Numbers: [13, 2] Generated Node #0,2,1: 15:[13, 2] Operation: 16-14=2 Moving to Node #0,2,1 Current State: 15:[13, 2], Operations: ['8*2=16', '16-14=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.951389
hs_4
mult_heuristic
[ 78, 52, 36, 45 ]
99
[ "78*36=2808", "2808/52=54", "45+54=99" ]
Current State: 99:[78, 52, 36, 45], Operations: [] Exploring Operation: 78*36=2808, Resulting Numbers: [52, 45, 2808] Generated Node #2: [52, 45, 2808] from Operation: 78*36=2808 Current State: 99:[52, 45, 2808], Operations: ['78*36=2808'] Exploring Operation: 2808/52=54, Resulting Numbers: [45, 54] Generated Node #3: [45, 54] from Operation: 2808/52=54 Current State: 99:[45, 54], Operations: ['78*36=2808', '2808/52=54'] Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[78, 52, 36, 45], Operations: [] Exploring Operation: 52+45=97, Resulting Numbers: [78, 36, 97] Generated Node #0,0: 99:[78, 36, 97] Operation: 52+45=97 Exploring Operation: 78-45=33, Resulting Numbers: [52, 36, 33] Generated Node #0,1: 99:[52, 36, 33] Operation: 78-45=33 Exploring Operation: 78-52=26, Resulting Numbers: [36, 45, 26] Generated Node #0,2: 99:[36, 45, 26] Operation: 78-52=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[52, 36, 33], Operations: ['78-45=33'] Exploring Operation: 52-36=16, Resulting Numbers: [33, 16] Generated Node #0,1,0: 99:[33, 16] Operation: 52-36=16 Exploring Operation: 52+36=88, Resulting Numbers: [33, 88] Generated Node #0,1,1: 99:[33, 88] Operation: 52+36=88 Exploring Operation: 52-33=19, Resulting Numbers: [36, 19] Generated Node #0,1,2: 99:[36, 19] Operation: 52-33=19 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[33, 16], Operations: ['78-45=33', '52-36=16'] Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,99 unequal: No Solution Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,99 unequal: No Solution No 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: 99:[33, 88], Operations: ['78-45=33', '52+36=88'] Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 33+88=121, Resulting Numbers: [121] 121,99 unequal: No Solution Exploring Operation: 33*88=2904, Resulting Numbers: [2904] 2904,99 unequal: No Solution No 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: 99:[36, 19], Operations: ['78-45=33', '52-33=19'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,99 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: 99:[36, 45, 26], Operations: ['78-52=26'] Exploring Operation: 36-26=10, Resulting Numbers: [45, 10] Generated Node #0,2,0: 99:[45, 10] Operation: 36-26=10 Exploring Operation: 45-26=19, Resulting Numbers: [36, 19] Generated Node #0,2,1: 99:[36, 19] Operation: 45-26=19 Exploring Operation: 45-36=9, Resulting Numbers: [26, 9] Generated Node #0,2,2: 99:[26, 9] Operation: 45-36=9 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[26, 9], Operations: ['78-52=26', '45-36=9'] Exploring Operation: 26+9=35, Resulting Numbers: [35] 35,99 unequal: No Solution Exploring Operation: 26*9=234, Resulting Numbers: [234] 234,99 unequal: No Solution Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,99 unequal: No Solution No 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: 99:[36, 19], Operations: ['78-52=26', '45-26=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,99 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,99 unequal: No Solution No 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: 99:[45, 10], Operations: ['78-52=26', '36-26=10'] Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 45*10=450, Resulting Numbers: [450] 450,99 unequal: No Solution Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,99 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: 99:[78, 36, 97], Operations: ['52+45=97'] Exploring Operation: 78-36=42, Resulting Numbers: [97, 42] Generated Node #0,0,0: 99:[97, 42] Operation: 78-36=42 Exploring Operation: 78+36=114, Resulting Numbers: [97, 114] Generated Node #0,0,1: 99:[97, 114] Operation: 78+36=114 Exploring Operation: 97-78=19, Resulting Numbers: [36, 19] Generated Node #0,0,2: 99:[36, 19] Operation: 97-78=19 Moving to Node #0,0,0 Current State: 99:[97, 42], Operations: ['52+45=97', '78-36=42'] Exploring Operation: 97-42=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 97+42=139, Resulting Numbers: [139] 139,99 unequal: No Solution Exploring Operation: 97*42=4074, Resulting Numbers: [4074] 4074,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[36, 19], Operations: ['52+45=97', '97-78=19'] Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[97, 114], Operations: ['52+45=97', '78+36=114'] Exploring Operation: 97*114=11058, Resulting Numbers: [11058] 11058,99 unequal: No Solution Exploring Operation: 114-97=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 97+114=211, Resulting Numbers: [211] 211,99 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
[ 39, 54, 53, 50 ]
57
[ "53-50=3", "54/3=18", "39+18=57" ]
Current State: 57:[39, 54, 53, 50], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [39, 54, 3] Generated Node #2: [39, 54, 3] from Operation: 53-50=3 Current State: 57:[39, 54, 3], Operations: ['53-50=3'] Exploring Operation: 54/3=18, Resulting Numbers: [39, 18] Generated Node #3: [39, 18] from Operation: 54/3=18 Current State: 57:[39, 18], Operations: ['53-50=3', '54/3=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[39, 54, 53, 50], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [39, 54, 3] Generated Node #0,0: 57:[39, 54, 3] Operation: 53-50=3 Exploring Operation: 54-50=4, Resulting Numbers: [39, 53, 4] Generated Node #0,1: 57:[39, 53, 4] Operation: 54-50=4 Exploring Operation: 50-39=11, Resulting Numbers: [54, 53, 11] Generated Node #0,2: 57:[54, 53, 11] Operation: 50-39=11 Exploring Operation: 54-39=15, Resulting Numbers: [53, 50, 15] Generated Node #0,3: 57:[53, 50, 15] Operation: 54-39=15 Exploring Operation: 53-39=14, Resulting Numbers: [54, 50, 14] Generated Node #0,4: 57:[54, 50, 14] Operation: 53-39=14 Moving to Node #0,2 Current State: 57:[54, 53, 11], Operations: ['50-39=11'] Exploring Operation: 54+11=65, Resulting Numbers: [53, 65] Generated Node #0,2,0: 57:[53, 65] Operation: 54+11=65 Exploring Operation: 53-11=42, Resulting Numbers: [54, 42] Generated Node #0,2,1: 57:[54, 42] Operation: 53-11=42 Exploring Operation: 53+11=64, Resulting Numbers: [54, 64] Generated Node #0,2,2: 57:[54, 64] Operation: 53+11=64 Exploring Operation: 54-53=1, Resulting Numbers: [11, 1] Generated Node #0,2,3: 57:[11, 1] Operation: 54-53=1 Exploring Operation: 54-11=43, Resulting Numbers: [53, 43] Generated Node #0,2,4: 57:[53, 43] Operation: 54-11=43 Moving to Node #0,4 Current State: 57:[54, 50, 14], Operations: ['53-39=14'] Exploring Operation: 54-14=40, Resulting Numbers: [50, 40] Generated Node #0,4,0: 57:[50, 40] Operation: 54-14=40 Exploring Operation: 54-50=4, Resulting Numbers: [14, 4] Generated Node #0,4,1: 57:[14, 4] Operation: 54-50=4 Exploring Operation: 54+14=68, Resulting Numbers: [50, 68] Generated Node #0,4,2: 57:[50, 68] Operation: 54+14=68 Exploring Operation: 50-14=36, Resulting Numbers: [54, 36] Generated Node #0,4,3: 57:[54, 36] Operation: 50-14=36 Exploring Operation: 50+14=64, Resulting Numbers: [54, 64] Generated Node #0,4,4: 57:[54, 64] Operation: 50+14=64 Moving to Node #0,3 Current State: 57:[53, 50, 15], Operations: ['54-39=15'] Exploring Operation: 53-15=38, Resulting Numbers: [50, 38] Generated Node #0,3,0: 57:[50, 38] Operation: 53-15=38 Exploring Operation: 50-15=35, Resulting Numbers: [53, 35] Generated Node #0,3,1: 57:[53, 35] Operation: 50-15=35 Exploring Operation: 50+15=65, Resulting Numbers: [53, 65] Generated Node #0,3,2: 57:[53, 65] Operation: 50+15=65 Exploring Operation: 53+15=68, Resulting Numbers: [50, 68] Generated Node #0,3,3: 57:[50, 68] Operation: 53+15=68 Exploring Operation: 53-50=3, Resulting Numbers: [15, 3] Generated Node #0,3,4: 57:[15, 3] Operation: 53-50=3 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 57:[15, 3], Operations: ['54-39=15', '53-50=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 57:[53, 65], Operations: ['54-39=15', '50+15=65'] Exploring Operation: 53*65=3445, Resulting Numbers: [3445] 3445,57 unequal: No Solution Exploring Operation: 65-53=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 53+65=118, Resulting Numbers: [118] 118,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 57:[50, 68], Operations: ['54-39=15', '53+15=68'] Exploring Operation: 50*68=3400, Resulting Numbers: [3400] 3400,57 unequal: No Solution Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 50+68=118, Resulting Numbers: [118] 118,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 57:[53, 35], Operations: ['54-39=15', '50-15=35'] Exploring Operation: 53+35=88, Resulting Numbers: [88] 88,57 unequal: No Solution Exploring Operation: 53*35=1855, Resulting Numbers: [1855] 1855,57 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 57:[50, 38], Operations: ['54-39=15', '53-15=38'] Exploring Operation: 50+38=88, Resulting Numbers: [88] 88,57 unequal: No Solution Exploring Operation: 50*38=1900, Resulting Numbers: [1900] 1900,57 unequal: No Solution Exploring Operation: 50-38=12, Resulting Numbers: [12] 12,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 57:[39, 54, 3], Operations: ['53-50=3'] Exploring Operation: 54/3=18, Resulting Numbers: [39, 18] Generated Node #0,0,0: 57:[39, 18] Operation: 54/3=18 Exploring Operation: 54+3=57, Resulting Numbers: [39, 57] Generated Node #0,0,1: 57:[39, 57] Operation: 54+3=57 Exploring Operation: 39/3=13, Resulting Numbers: [54, 13] Generated Node #0,0,2: 57:[54, 13] Operation: 39/3=13 Exploring Operation: 39+3=42, Resulting Numbers: [54, 42] Generated Node #0,0,3: 57:[54, 42] Operation: 39+3=42 Exploring Operation: 54-39=15, Resulting Numbers: [3, 15] Generated Node #0,0,4: 57:[3, 15] Operation: 54-39=15 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 57:[3, 15], Operations: ['53-50=3', '54-39=15'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[54, 13], Operations: ['53-50=3', '39/3=13'] Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,57 unequal: No Solution Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,57 unequal: No Solution Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[39, 57], Operations: ['53-50=3', '54+3=57'] Exploring Operation: 39+57=96, Resulting Numbers: [96] 96,57 unequal: No Solution Exploring Operation: 57-39=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 39*57=2223, Resulting Numbers: [2223] 2223,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[54, 42], Operations: ['53-50=3', '39+3=42'] Exploring Operation: 54-42=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 54+42=96, Resulting Numbers: [96] 96,57 unequal: No Solution Exploring Operation: 54*42=2268, Resulting Numbers: [2268] 2268,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[39, 18], Operations: ['53-50=3', '54/3=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[39, 54, 53, 50], Operations: [] Exploring Operation: 53-50=3, Resulting Numbers: [39, 54, 3] Generated Node #0,0: 57:[39, 54, 3] Operation: 53-50=3 Moving to Node #0,0 Current State: 57:[39, 54, 3], Operations: ['53-50=3'] Exploring Operation: 54/3=18, Resulting Numbers: [39, 18] Generated Node #0,0,0: 57:[39, 18] Operation: 54/3=18 Moving to Node #0,0,0 Current State: 57:[39, 18], Operations: ['53-50=3', '54/3=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.948785
hs_5
sum_heuristic
[ 45, 51, 54, 3 ]
63
[ "51-45=6", "54+3=57", "6+57=63" ]
Current State: 63:[45, 51, 54, 3], Operations: [] Exploring Operation: 51-45=6, Resulting Numbers: [54, 3, 6] Generated Node #2: [54, 3, 6] from Operation: 51-45=6 Current State: 63:[54, 3, 6], Operations: ['51-45=6'] Exploring Operation: 54+3=57, Resulting Numbers: [6, 57] Generated Node #3: [6, 57] from Operation: 54+3=57 Current State: 63:[6, 57], Operations: ['51-45=6', '54+3=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[45, 51, 54, 3], Operations: [] Exploring Operation: 54-45=9, Resulting Numbers: [51, 3, 9] Generated Node #0,0: 63:[51, 3, 9] Operation: 54-45=9 Exploring Operation: 51-45=6, Resulting Numbers: [54, 3, 6] Generated Node #0,1: 63:[54, 3, 6] Operation: 51-45=6 Exploring Operation: 54-51=3, Resulting Numbers: [45, 3, 3] Generated Node #0,2: 63:[45, 3, 3] Operation: 54-51=3 Exploring Operation: 45/3=15, Resulting Numbers: [51, 54, 15] Generated Node #0,3: 63:[51, 54, 15] Operation: 45/3=15 Moving to Node #0,1 Current State: 63:[54, 3, 6], Operations: ['51-45=6'] Exploring Operation: 54+3=57, Resulting Numbers: [6, 57] Generated Node #0,1,0: 63:[6, 57] Operation: 54+3=57 Exploring Operation: 54+6=60, Resulting Numbers: [3, 60] Generated Node #0,1,1: 63:[3, 60] Operation: 54+6=60 Exploring Operation: 54/6=9, Resulting Numbers: [3, 9] Generated Node #0,1,2: 63:[3, 9] Operation: 54/6=9 Exploring Operation: 54/3=18, Resulting Numbers: [6, 18] Generated Node #0,1,3: 63:[6, 18] Operation: 54/3=18 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[3, 9], Operations: ['51-45=6', '54/6=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,63 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,63 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 #0,1,1 Current State: 63:[3, 60], Operations: ['51-45=6', '54+6=60'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,63 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[45, 51, 54, 3], Operations: [] Exploring Operation: 51-45=6, Resulting Numbers: [54, 3, 6] Generated Node #0,1: 63:[54, 3, 6] Operation: 51-45=6 Moving to Node #0,1 Current State: 63:[54, 3, 6], Operations: ['51-45=6'] Exploring Operation: 54+6=60, Resulting Numbers: [3, 60] Generated Node #0,1,1: 63:[3, 60] Operation: 54+6=60 Moving to Node #0,1,1 Current State: 63:[3, 60], Operations: ['51-45=6', '54+6=60'] Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 52, 67, 57, 28 ]
73
[ "57-52=5", "28*5=140", "140-67=73" ]
Current State: 73:[52, 67, 57, 28], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [67, 28, 5] Generated Node #2: [67, 28, 5] from Operation: 57-52=5 Current State: 73:[67, 28, 5], Operations: ['57-52=5'] Exploring Operation: 28*5=140, Resulting Numbers: [67, 140] Generated Node #3: [67, 140] from Operation: 28*5=140 Current State: 73:[67, 140], Operations: ['57-52=5', '28*5=140'] Exploring Operation: 140-67=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[52, 67, 57, 28], Operations: [] Exploring Operation: 52+28=80, Resulting Numbers: [67, 57, 80] Generated Node #0,0: 73:[67, 57, 80] Operation: 52+28=80 Exploring Operation: 67+28=95, Resulting Numbers: [52, 57, 95] Generated Node #0,1: 73:[52, 57, 95] Operation: 67+28=95 Exploring Operation: 57+28=85, Resulting Numbers: [52, 67, 85] Generated Node #0,2: 73:[52, 67, 85] Operation: 57+28=85 Moving to Node #0,0 Current State: 73:[67, 57, 80], Operations: ['52+28=80'] Exploring Operation: 67-57=10, Resulting Numbers: [80, 10] Generated Node #0,0,0: 73:[80, 10] Operation: 67-57=10 Exploring Operation: 67+57=124, Resulting Numbers: [80, 124] Generated Node #0,0,1: 73:[80, 124] Operation: 67+57=124 Exploring Operation: 80-57=23, Resulting Numbers: [67, 23] Generated Node #0,0,2: 73:[67, 23] Operation: 80-57=23 Moving to Node #0,2 Current State: 73:[52, 67, 85], Operations: ['57+28=85'] Exploring Operation: 52+67=119, Resulting Numbers: [85, 119] Generated Node #0,2,0: 73:[85, 119] Operation: 52+67=119 Exploring Operation: 67-52=15, Resulting Numbers: [85, 15] Generated Node #0,2,1: 73:[85, 15] Operation: 67-52=15 Exploring Operation: 85-52=33, Resulting Numbers: [67, 33] Generated Node #0,2,2: 73:[67, 33] Operation: 85-52=33 Moving to Node #0,1 Current State: 73:[52, 57, 95], Operations: ['67+28=95'] Exploring Operation: 52+57=109, Resulting Numbers: [95, 109] Generated Node #0,1,0: 73:[95, 109] Operation: 52+57=109 Exploring Operation: 95-52=43, Resulting Numbers: [57, 43] Generated Node #0,1,1: 73:[57, 43] Operation: 95-52=43 Exploring Operation: 95-57=38, Resulting Numbers: [52, 38] Generated Node #0,1,2: 73:[52, 38] Operation: 95-57=38 Moving to Node #0,2,2 Current State: 73:[67, 33], Operations: ['57+28=85', '85-52=33'] Exploring Operation: 67+33=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 67*33=2211, Resulting Numbers: [2211] 2211,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[57, 43], Operations: ['67+28=95', '95-52=43'] Exploring Operation: 57+43=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 57-43=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 57*43=2451, Resulting Numbers: [2451] 2451,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[67, 23], Operations: ['52+28=80', '80-57=23'] Exploring Operation: 67+23=90, Resulting Numbers: [90] 90,73 unequal: No Solution Exploring Operation: 67-23=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 67*23=1541, Resulting Numbers: [1541] 1541,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[52, 38], Operations: ['67+28=95', '95-57=38'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 52*38=1976, Resulting Numbers: [1976] 1976,73 unequal: No Solution Exploring Operation: 52+38=90, Resulting Numbers: [90] 90,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[95, 109], Operations: ['67+28=95', '52+57=109'] Exploring Operation: 109-95=14, Resulting Numbers: [14] 14,73 unequal: No Solution Exploring Operation: 95+109=204, Resulting Numbers: [204] 204,73 unequal: No Solution Exploring Operation: 95*109=10355, Resulting Numbers: [10355] 10355,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[85, 119], Operations: ['57+28=85', '52+67=119'] Exploring Operation: 85*119=10115, Resulting Numbers: [10115] 10115,73 unequal: No Solution Exploring Operation: 119-85=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 85+119=204, Resulting Numbers: [204] 204,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[80, 124], Operations: ['52+28=80', '67+57=124'] Exploring Operation: 80*124=9920, Resulting Numbers: [9920] 9920,73 unequal: No Solution Exploring Operation: 124-80=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 80+124=204, Resulting Numbers: [204] 204,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[80, 10], Operations: ['52+28=80', '67-57=10'] Exploring Operation: 80/10=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 80-10=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 80+10=90, Resulting Numbers: [90] 90,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[85, 15], Operations: ['57+28=85', '67-52=15'] Exploring Operation: 85*15=1275, Resulting Numbers: [1275] 1275,73 unequal: No Solution Exploring Operation: 85-15=70, Resulting Numbers: [70] 70,73 unequal: No Solution Exploring Operation: 85+15=100, Resulting Numbers: [100] 100,73 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 79, 57, 72, 71 ]
48
[ "79-71=8", "72/8=9", "57-9=48" ]
Current State: 48:[79, 57, 72, 71], Operations: [] Exploring Operation: 79-71=8, Resulting Numbers: [57, 72, 8] Generated Node #2: [57, 72, 8] from Operation: 79-71=8 Current State: 48:[57, 72, 8], Operations: ['79-71=8'] Exploring Operation: 72/8=9, Resulting Numbers: [57, 9] Generated Node #3: [57, 9] from Operation: 72/8=9 Current State: 48:[57, 9], Operations: ['79-71=8', '72/8=9'] Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[79, 57, 72, 71], Operations: [] Exploring Operation: 79-72=7, Resulting Numbers: [57, 71, 7] Generated Node #0,0: 48:[57, 71, 7] Operation: 79-72=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[57, 71, 7], Operations: ['79-72=7'] Exploring Operation: 71-57=14, Resulting Numbers: [7, 14] Generated Node #0,0,0: 48:[7, 14] Operation: 71-57=14 Moving to Node #0,0,0 Current State: 48:[7, 14], Operations: ['79-72=7', '71-57=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,48 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
[ 58, 65, 92, 95 ]
41
[ "58+65=123", "95-92=3", "123/3=41" ]
Current State: 41:[58, 65, 92, 95], Operations: [] Exploring Operation: 58+65=123, Resulting Numbers: [92, 95, 123] Generated Node #2: [92, 95, 123] from Operation: 58+65=123 Current State: 41:[92, 95, 123], Operations: ['58+65=123'] Exploring Operation: 95-92=3, Resulting Numbers: [123, 3] Generated Node #3: [123, 3] from Operation: 95-92=3 Current State: 41:[123, 3], Operations: ['58+65=123', '95-92=3'] Exploring Operation: 123/3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[58, 65, 92, 95], Operations: [] Exploring Operation: 95-58=37, Resulting Numbers: [65, 92, 37] Generated Node #0,0: 41:[65, 92, 37] Operation: 95-58=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[65, 92, 37], Operations: ['95-58=37'] Exploring Operation: 92-65=27, Resulting Numbers: [37, 27] Generated Node #0,0,0: 41:[37, 27] Operation: 92-65=27 Moving to Node #0,0,0 Current State: 41:[37, 27], Operations: ['95-58=37', '92-65=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,41 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
[ 74, 62, 6, 95 ]
89
[ "74-62=12", "6+95=101", "101-12=89" ]
Current State: 89:[74, 62, 6, 95], Operations: [] Exploring Operation: 74-62=12, Resulting Numbers: [6, 95, 12] Generated Node #2: [6, 95, 12] from Operation: 74-62=12 Current State: 89:[6, 95, 12], Operations: ['74-62=12'] Exploring Operation: 6+95=101, Resulting Numbers: [12, 101] Generated Node #3: [12, 101] from Operation: 6+95=101 Current State: 89:[12, 101], Operations: ['74-62=12', '6+95=101'] Exploring Operation: 101-12=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[74, 62, 6, 95], Operations: [] Exploring Operation: 95-6=89, Resulting Numbers: [74, 62, 89] Generated Node #0,0: 89:[74, 62, 89] Operation: 95-6=89 Exploring Operation: 62+6=68, Resulting Numbers: [74, 95, 68] Generated Node #0,1: 89:[74, 95, 68] Operation: 62+6=68 Exploring Operation: 74+6=80, Resulting Numbers: [62, 95, 80] Generated Node #0,2: 89:[62, 95, 80] Operation: 74+6=80 Moving to Node #0,0 Current State: 89:[74, 62, 89], Operations: ['95-6=89'] Exploring Operation: 74+62=136, Resulting Numbers: [89, 136] Generated Node #0,0,0: 89:[89, 136] Operation: 74+62=136 Exploring Operation: 62+89=151, Resulting Numbers: [74, 151] Generated Node #0,0,1: 89:[74, 151] Operation: 62+89=151 Exploring Operation: 74-62=12, Resulting Numbers: [89, 12] Generated Node #0,0,2: 89:[89, 12] Operation: 74-62=12 Moving to Node #0,1 Current State: 89:[74, 95, 68], Operations: ['62+6=68'] Exploring Operation: 74+68=142, Resulting Numbers: [95, 142] Generated Node #0,1,0: 89:[95, 142] Operation: 74+68=142 Exploring Operation: 95-74=21, Resulting Numbers: [68, 21] Generated Node #0,1,1: 89:[68, 21] Operation: 95-74=21 Exploring Operation: 95-68=27, Resulting Numbers: [74, 27] Generated Node #0,1,2: 89:[74, 27] Operation: 95-68=27 Moving to Node #0,2 Current State: 89:[62, 95, 80], Operations: ['74+6=80'] Exploring Operation: 62+95=157, Resulting Numbers: [80, 157] Generated Node #0,2,0: 89:[80, 157] Operation: 62+95=157 Exploring Operation: 62+80=142, Resulting Numbers: [95, 142] Generated Node #0,2,1: 89:[95, 142] Operation: 62+80=142 Exploring Operation: 95-62=33, Resulting Numbers: [80, 33] Generated Node #0,2,2: 89:[80, 33] Operation: 95-62=33 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[95, 142], Operations: ['74+6=80', '62+80=142'] Exploring Operation: 95*142=13490, Resulting Numbers: [13490] 13490,89 unequal: No Solution Exploring Operation: 95+142=237, Resulting Numbers: [237] 237,89 unequal: No Solution Exploring Operation: 142-95=47, Resulting Numbers: [47] 47,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[80, 33], Operations: ['74+6=80', '95-62=33'] Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 80*33=2640, Resulting Numbers: [2640] 2640,89 unequal: No Solution Exploring Operation: 80+33=113, Resulting Numbers: [113] 113,89 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:[80, 157], Operations: ['74+6=80', '62+95=157'] Exploring Operation: 157-80=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 80*157=12560, Resulting Numbers: [12560] 12560,89 unequal: No Solution Exploring Operation: 80+157=237, Resulting Numbers: [237] 237,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 89:[89, 136], Operations: ['95-6=89', '74+62=136'] Exploring Operation: 136-89=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 89*136=12104, Resulting Numbers: [12104] 12104,89 unequal: No Solution Exploring Operation: 89+136=225, Resulting Numbers: [225] 225,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[95, 142], Operations: ['62+6=68', '74+68=142'] Exploring Operation: 95*142=13490, Resulting Numbers: [13490] 13490,89 unequal: No Solution Exploring Operation: 142-95=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 95+142=237, Resulting Numbers: [237] 237,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[89, 12], Operations: ['95-6=89', '74-62=12'] Exploring Operation: 89+12=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 89*12=1068, Resulting Numbers: [1068] 1068,89 unequal: No Solution Exploring Operation: 89-12=77, Resulting Numbers: [77] 77,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[74, 27], Operations: ['62+6=68', '95-68=27'] Exploring Operation: 74-27=47, Resulting Numbers: [47] 47,89 unequal: No Solution Exploring Operation: 74+27=101, Resulting Numbers: [101] 101,89 unequal: No Solution Exploring Operation: 74*27=1998, Resulting Numbers: [1998] 1998,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[74, 151], Operations: ['95-6=89', '62+89=151'] Exploring Operation: 151-74=77, Resulting Numbers: [77] 77,89 unequal: No Solution Exploring Operation: 74*151=11174, Resulting Numbers: [11174] 11174,89 unequal: No Solution Exploring Operation: 74+151=225, Resulting Numbers: [225] 225,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[68, 21], Operations: ['62+6=68', '95-74=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[74, 62, 6, 95], Operations: [] Exploring Operation: 62+6=68, Resulting Numbers: [74, 95, 68] Generated Node #0,1: 89:[74, 95, 68] Operation: 62+6=68 Moving to Node #0,1 Current State: 89:[74, 95, 68], Operations: ['62+6=68'] Exploring Operation: 95-74=21, Resulting Numbers: [68, 21] Generated Node #0,1,1: 89:[68, 21] Operation: 95-74=21 Moving to Node #0,1,1 Current State: 89:[68, 21], Operations: ['62+6=68', '95-74=21'] Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.96441
hs_3
mult_heuristic
[ 16, 23, 50, 25 ]
36
[ "16+23=39", "50+25=75", "75-39=36" ]
Current State: 36:[16, 23, 50, 25], Operations: [] Exploring Operation: 16+23=39, Resulting Numbers: [50, 25, 39] Generated Node #2: [50, 25, 39] from Operation: 16+23=39 Current State: 36:[50, 25, 39], Operations: ['16+23=39'] Exploring Operation: 50+25=75, Resulting Numbers: [39, 75] Generated Node #3: [39, 75] from Operation: 50+25=75 Current State: 36:[39, 75], Operations: ['16+23=39', '50+25=75'] Exploring Operation: 75-39=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[16, 23, 50, 25], Operations: [] Exploring Operation: 50/25=2, Resulting Numbers: [16, 23, 2] Generated Node #0,0: 36:[16, 23, 2] Operation: 50/25=2 Exploring Operation: 50-16=34, Resulting Numbers: [23, 25, 34] Generated Node #0,1: 36:[23, 25, 34] Operation: 50-16=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[16, 23, 2], Operations: ['50/25=2'] Exploring Operation: 23-16=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 36:[2, 7] Operation: 23-16=7 Exploring Operation: 16+23=39, Resulting Numbers: [2, 39] Generated Node #0,0,1: 36:[2, 39] Operation: 16+23=39 Moving to Node #0,0,0 Current State: 36:[2, 7], Operations: ['50/25=2', '23-16=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[2, 39], Operations: ['50/25=2', '16+23=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,36 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,36 unequal: No Solution No 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: 36:[23, 25, 34], Operations: ['50-16=34'] Exploring Operation: 34-25=9, Resulting Numbers: [23, 9] Generated Node #0,1,0: 36:[23, 9] Operation: 34-25=9 Exploring Operation: 25-23=2, Resulting Numbers: [34, 2] Generated Node #0,1,1: 36:[34, 2] Operation: 25-23=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 36:[34, 2], Operations: ['50-16=34', '25-23=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[16, 23, 50, 25], Operations: [] Exploring Operation: 50-16=34, Resulting Numbers: [23, 25, 34] Generated Node #0,1: 36:[23, 25, 34] Operation: 50-16=34 Moving to Node #0,1 Current State: 36:[23, 25, 34], Operations: ['50-16=34'] Exploring Operation: 25-23=2, Resulting Numbers: [34, 2] Generated Node #0,1,1: 36:[34, 2] Operation: 25-23=2 Moving to Node #0,1,1 Current State: 36:[34, 2], Operations: ['50-16=34', '25-23=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 44, 12, 6, 59 ]
57
[ "59-44=15", "12*6=72", "72-15=57" ]
Current State: 57:[44, 12, 6, 59], Operations: [] Exploring Operation: 59-44=15, Resulting Numbers: [12, 6, 15] Generated Node #2: [12, 6, 15] from Operation: 59-44=15 Current State: 57:[12, 6, 15], Operations: ['59-44=15'] Exploring Operation: 12*6=72, Resulting Numbers: [15, 72] Generated Node #3: [15, 72] from Operation: 12*6=72 Current State: 57:[15, 72], Operations: ['59-44=15', '12*6=72'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[44, 12, 6, 59], Operations: [] Exploring Operation: 12/6=2, Resulting Numbers: [44, 59, 2] Generated Node #0,0: 57:[44, 59, 2] Operation: 12/6=2 Exploring Operation: 12+6=18, Resulting Numbers: [44, 59, 18] Generated Node #0,1: 57:[44, 59, 18] Operation: 12+6=18 Exploring Operation: 44+12=56, Resulting Numbers: [6, 59, 56] Generated Node #0,2: 57:[6, 59, 56] Operation: 44+12=56 Exploring Operation: 44+6=50, Resulting Numbers: [12, 59, 50] Generated Node #0,3: 57:[12, 59, 50] Operation: 44+6=50 Exploring Operation: 59-44=15, Resulting Numbers: [12, 6, 15] Generated Node #0,4: 57:[12, 6, 15] Operation: 59-44=15 Moving to Node #0,2 Current State: 57:[6, 59, 56], Operations: ['44+12=56'] Exploring Operation: 6+59=65, Resulting Numbers: [56, 65] Generated Node #0,2,0: 57:[56, 65] Operation: 6+59=65 Exploring Operation: 59-6=53, Resulting Numbers: [56, 53] Generated Node #0,2,1: 57:[56, 53] Operation: 59-6=53 Exploring Operation: 6+56=62, Resulting Numbers: [59, 62] Generated Node #0,2,2: 57:[59, 62] Operation: 6+56=62 Exploring Operation: 56-6=50, Resulting Numbers: [59, 50] Generated Node #0,2,3: 57:[59, 50] Operation: 56-6=50 Exploring Operation: 59-56=3, Resulting Numbers: [6, 3] Generated Node #0,2,4: 57:[6, 3] Operation: 59-56=3 Moving to Node #0,4 Current State: 57:[12, 6, 15], Operations: ['59-44=15'] Exploring Operation: 12-6=6, Resulting Numbers: [15, 6] Generated Node #0,4,0: 57:[15, 6] Operation: 12-6=6 Exploring Operation: 12+6=18, Resulting Numbers: [15, 18] Generated Node #0,4,1: 57:[15, 18] Operation: 12+6=18 Exploring Operation: 15-12=3, Resulting Numbers: [6, 3] Generated Node #0,4,2: 57:[6, 3] Operation: 15-12=3 Exploring Operation: 12/6=2, Resulting Numbers: [15, 2] Generated Node #0,4,3: 57:[15, 2] Operation: 12/6=2 Exploring Operation: 6+15=21, Resulting Numbers: [12, 21] Generated Node #0,4,4: 57:[12, 21] Operation: 6+15=21 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 57:[6, 3], Operations: ['59-44=15', '15-12=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 57:[15, 18], Operations: ['59-44=15', '12+6=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,57 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 57:[15, 2], Operations: ['59-44=15', '12/6=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,57 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 57:[15, 6], Operations: ['59-44=15', '12-6=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,57 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[12, 21], Operations: ['59-44=15', '6+15=21'] Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 57:[44, 59, 2], Operations: ['12/6=2'] Exploring Operation: 44-2=42, Resulting Numbers: [59, 42] Generated Node #0,0,0: 57:[59, 42] Operation: 44-2=42 Exploring Operation: 44/2=22, Resulting Numbers: [59, 22] Generated Node #0,0,1: 57:[59, 22] Operation: 44/2=22 Exploring Operation: 59-2=57, Resulting Numbers: [44, 57] Generated Node #0,0,2: 57:[44, 57] Operation: 59-2=57 Exploring Operation: 59-44=15, Resulting Numbers: [2, 15] Generated Node #0,0,3: 57:[2, 15] Operation: 59-44=15 Exploring Operation: 44+2=46, Resulting Numbers: [59, 46] Generated Node #0,0,4: 57:[59, 46] Operation: 44+2=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[59, 22], Operations: ['12/6=2', '44/2=22'] Exploring Operation: 59+22=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 59*22=1298, Resulting Numbers: [1298] 1298,57 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[2, 15], Operations: ['12/6=2', '59-44=15'] Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,57 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,57 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[44, 57], Operations: ['12/6=2', '59-2=57'] Exploring Operation: 44*57=2508, Resulting Numbers: [2508] 2508,57 unequal: No Solution Exploring Operation: 44+57=101, Resulting Numbers: [101] 101,57 unequal: No Solution Exploring Operation: 57-44=13, Resulting Numbers: [13] 13,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 57:[59, 46], Operations: ['12/6=2', '44+2=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,57 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[59, 42], Operations: ['12/6=2', '44-2=42'] Exploring Operation: 59*42=2478, Resulting Numbers: [2478] 2478,57 unequal: No Solution Exploring Operation: 59+42=101, Resulting Numbers: [101] 101,57 unequal: No Solution Exploring Operation: 59-42=17, Resulting Numbers: [17] 17,57 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: 57:[44, 59, 18], Operations: ['12+6=18'] Exploring Operation: 59+18=77, Resulting Numbers: [44, 77] Generated Node #0,1,0: 57:[44, 77] Operation: 59+18=77 Exploring Operation: 44+18=62, Resulting Numbers: [59, 62] Generated Node #0,1,1: 57:[59, 62] Operation: 44+18=62 Exploring Operation: 44-18=26, Resulting Numbers: [59, 26] Generated Node #0,1,2: 57:[59, 26] Operation: 44-18=26 Exploring Operation: 59-18=41, Resulting Numbers: [44, 41] Generated Node #0,1,3: 57:[44, 41] Operation: 59-18=41 Exploring Operation: 59-44=15, Resulting Numbers: [18, 15] Generated Node #0,1,4: 57:[18, 15] Operation: 59-44=15 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 57:[18, 15], Operations: ['12+6=18', '59-44=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,57 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[59, 62], Operations: ['12+6=18', '44+18=62'] Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,57 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[59, 26], Operations: ['12+6=18', '44-18=26'] Exploring Operation: 59*26=1534, Resulting Numbers: [1534] 1534,57 unequal: No Solution Exploring Operation: 59-26=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 59+26=85, Resulting Numbers: [85] 85,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[44, 41], Operations: ['12+6=18', '59-18=41'] Exploring Operation: 44+41=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 44*41=1804, Resulting Numbers: [1804] 1804,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[44, 77], Operations: ['12+6=18', '59+18=77'] Exploring Operation: 44+77=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 44*77=3388, Resulting Numbers: [3388] 3388,57 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,57 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: 57:[12, 59, 50], Operations: ['44+6=50'] Exploring Operation: 59-50=9, Resulting Numbers: [12, 9] Generated Node #0,3,0: 57:[12, 9] Operation: 59-50=9 Exploring Operation: 50-12=38, Resulting Numbers: [59, 38] Generated Node #0,3,1: 57:[59, 38] Operation: 50-12=38 Exploring Operation: 12+59=71, Resulting Numbers: [50, 71] Generated Node #0,3,2: 57:[50, 71] Operation: 12+59=71 Exploring Operation: 12+50=62, Resulting Numbers: [59, 62] Generated Node #0,3,3: 57:[59, 62] Operation: 12+50=62 Exploring Operation: 59-12=47, Resulting Numbers: [50, 47] Generated Node #0,3,4: 57:[50, 47] Operation: 59-12=47 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 57:[59, 62], Operations: ['44+6=50', '12+50=62'] Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 57:[12, 9], Operations: ['44+6=50', '59-50=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,57 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 57:[50, 47], Operations: ['44+6=50', '59-12=47'] Exploring Operation: 50-47=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 50+47=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 50*47=2350, Resulting Numbers: [2350] 2350,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 57:[59, 38], Operations: ['44+6=50', '50-12=38'] Exploring Operation: 59*38=2242, Resulting Numbers: [2242] 2242,57 unequal: No Solution Exploring Operation: 59+38=97, Resulting Numbers: [97] 97,57 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 57:[50, 71], Operations: ['44+6=50', '12+59=71'] Exploring Operation: 71-50=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 50+71=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 50*71=3550, Resulting Numbers: [3550] 3550,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,4 Current State: 57:[6, 3], Operations: ['44+12=56', '59-56=3'] Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,57 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[56, 53], Operations: ['44+12=56', '59-6=53'] Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 56*53=2968, Resulting Numbers: [2968] 2968,57 unequal: No Solution Exploring Operation: 56+53=109, Resulting Numbers: [109] 109,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[59, 62], Operations: ['44+12=56', '6+56=62'] Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,57 unequal: No Solution Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[56, 65], Operations: ['44+12=56', '6+59=65'] Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,57 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,57 unequal: No Solution Moving to Node #0,2,3 Current State: 57:[59, 50], Operations: ['44+12=56', '56-6=50'] Exploring Operation: 59+50=109, Resulting Numbers: [109] 109,57 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 59*50=2950, Resulting Numbers: [2950] 2950,57 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 20, 37, 10, 62 ]
69
[ "37-20=17", "62-10=52", "17+52=69" ]
Current State: 69:[20, 37, 10, 62], Operations: [] Exploring Operation: 37-20=17, Resulting Numbers: [10, 62, 17] Generated Node #2: [10, 62, 17] from Operation: 37-20=17 Current State: 69:[10, 62, 17], Operations: ['37-20=17'] Exploring Operation: 62-10=52, Resulting Numbers: [17, 52] Generated Node #3: [17, 52] from Operation: 62-10=52 Current State: 69:[17, 52], Operations: ['37-20=17', '62-10=52'] Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[20, 37, 10, 62], Operations: [] Exploring Operation: 62-37=25, Resulting Numbers: [20, 10, 25] Generated Node #0,0: 69:[20, 10, 25] Operation: 62-37=25 Moving to Node #0,0 Current State: 69:[20, 10, 25], Operations: ['62-37=25'] Exploring Operation: 20/10=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 69:[25, 2] Operation: 20/10=2 Moving to Node #0,0,0 Current State: 69:[25, 2], Operations: ['62-37=25', '20/10=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,69 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 72, 59, 50, 26 ]
37
[ "72-59=13", "50-26=24", "13+24=37" ]
Current State: 37:[72, 59, 50, 26], Operations: [] Exploring Operation: 72-59=13, Resulting Numbers: [50, 26, 13] Generated Node #2: [50, 26, 13] from Operation: 72-59=13 Current State: 37:[50, 26, 13], Operations: ['72-59=13'] Exploring Operation: 50-26=24, Resulting Numbers: [13, 24] Generated Node #3: [13, 24] from Operation: 50-26=24 Current State: 37:[13, 24], Operations: ['72-59=13', '50-26=24'] Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[72, 59, 50, 26], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [59, 26, 22] Generated Node #0,0: 37:[59, 26, 22] Operation: 72-50=22 Exploring Operation: 72-59=13, Resulting Numbers: [50, 26, 13] Generated Node #0,1: 37:[50, 26, 13] Operation: 72-59=13 Exploring Operation: 72-26=46, Resulting Numbers: [59, 50, 46] Generated Node #0,2: 37:[59, 50, 46] Operation: 72-26=46 Exploring Operation: 59-26=33, Resulting Numbers: [72, 50, 33] Generated Node #0,3: 37:[72, 50, 33] Operation: 59-26=33 Exploring Operation: 50-26=24, Resulting Numbers: [72, 59, 24] Generated Node #0,4: 37:[72, 59, 24] Operation: 50-26=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[59, 50, 46], Operations: ['72-26=46'] Exploring Operation: 59-50=9, Resulting Numbers: [46, 9] Generated Node #0,2,0: 37:[46, 9] Operation: 59-50=9 Exploring Operation: 59+46=105, Resulting Numbers: [50, 105] Generated Node #0,2,1: 37:[50, 105] Operation: 59+46=105 Exploring Operation: 50-46=4, Resulting Numbers: [59, 4] Generated Node #0,2,2: 37:[59, 4] Operation: 50-46=4 Exploring Operation: 59+50=109, Resulting Numbers: [46, 109] Generated Node #0,2,3: 37:[46, 109] Operation: 59+50=109 Exploring Operation: 59-46=13, Resulting Numbers: [50, 13] Generated Node #0,2,4: 37:[50, 13] Operation: 59-46=13 Moving to Node #0,2,0 Current State: 37:[46, 9], Operations: ['72-26=46', '59-50=9'] Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,37 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[72, 59, 50, 26], Operations: [] Exploring Operation: 72-26=46, Resulting Numbers: [59, 50, 46] Generated Node #0,2: 37:[59, 50, 46] Operation: 72-26=46 Moving to Node #0,2 Current State: 37:[59, 50, 46], Operations: ['72-26=46'] Exploring Operation: 59-50=9, Resulting Numbers: [46, 9] Generated Node #0,2,0: 37:[46, 9] Operation: 59-50=9 Moving to Node #0,2,0 Current State: 37:[46, 9], Operations: ['72-26=46', '59-50=9'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 33, 33, 30, 76 ]
40
[ "33+33=66", "30+76=106", "106-66=40" ]
Current State: 40:[33, 33, 30, 76], Operations: [] Exploring Operation: 33+33=66, Resulting Numbers: [30, 76, 66] Generated Node #2: [30, 76, 66] from Operation: 33+33=66 Current State: 40:[30, 76, 66], Operations: ['33+33=66'] Exploring Operation: 30+76=106, Resulting Numbers: [66, 106] Generated Node #3: [66, 106] from Operation: 30+76=106 Current State: 40:[66, 106], Operations: ['33+33=66', '30+76=106'] Exploring Operation: 106-66=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[33, 33, 30, 76], Operations: [] Exploring Operation: 76-33=43, Resulting Numbers: [33, 30, 43] Generated Node #0,0: 40:[33, 30, 43] Operation: 76-33=43 Exploring Operation: 76-33=43, Resulting Numbers: [33, 30, 43] Generated Node #0,1: 40:[33, 30, 43] Operation: 76-33=43 Exploring Operation: 76-30=46, Resulting Numbers: [33, 33, 46] Generated Node #0,2: 40:[33, 33, 46] Operation: 76-30=46 Moving to Node #0,0 Current State: 40:[33, 30, 43], Operations: ['76-33=43'] Exploring Operation: 43-33=10, Resulting Numbers: [30, 10] Generated Node #0,0,0: 40:[30, 10] Operation: 43-33=10 Exploring Operation: 33-30=3, Resulting Numbers: [43, 3] Generated Node #0,0,1: 40:[43, 3] Operation: 33-30=3 Exploring Operation: 43-30=13, Resulting Numbers: [33, 13] Generated Node #0,0,2: 40:[33, 13] Operation: 43-30=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[43, 3], Operations: ['76-33=43', '33-30=3'] Exploring Operation: 43+3=46, Resulting Numbers: [46] 46,40 unequal: No Solution Exploring Operation: 43*3=129, Resulting Numbers: [129] 129,40 unequal: No Solution Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[33, 33, 30, 76], Operations: [] Exploring Operation: 76-33=43, Resulting Numbers: [33, 30, 43] Generated Node #0,0: 40:[33, 30, 43] Operation: 76-33=43 Moving to Node #0,0 Current State: 40:[33, 30, 43], Operations: ['76-33=43'] Exploring Operation: 33-30=3, Resulting Numbers: [43, 3] Generated Node #0,0,1: 40:[43, 3] Operation: 33-30=3 Moving to Node #0,0,1 Current State: 40:[43, 3], Operations: ['76-33=43', '33-30=3'] Exploring Operation: 43-3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 87, 24, 25, 41 ]
58
[ "41-25=16", "87*16=1392", "1392/24=58" ]
Current State: 58:[87, 24, 25, 41], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [87, 24, 16] Generated Node #2: [87, 24, 16] from Operation: 41-25=16 Current State: 58:[87, 24, 16], Operations: ['41-25=16'] Exploring Operation: 87*16=1392, Resulting Numbers: [24, 1392] Generated Node #3: [24, 1392] from Operation: 87*16=1392 Current State: 58:[24, 1392], Operations: ['41-25=16', '87*16=1392'] Exploring Operation: 1392/24=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[87, 24, 25, 41], Operations: [] Exploring Operation: 87-24=63, Resulting Numbers: [25, 41, 63] Generated Node #0,0: 58:[25, 41, 63] Operation: 87-24=63 Exploring Operation: 87-41=46, Resulting Numbers: [24, 25, 46] Generated Node #0,1: 58:[24, 25, 46] Operation: 87-41=46 Exploring Operation: 87-25=62, Resulting Numbers: [24, 41, 62] Generated Node #0,2: 58:[24, 41, 62] Operation: 87-25=62 Exploring Operation: 24+41=65, Resulting Numbers: [87, 25, 65] Generated Node #0,3: 58:[87, 25, 65] Operation: 24+41=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[25, 41, 63], Operations: ['87-24=63'] Exploring Operation: 63-41=22, Resulting Numbers: [25, 22] Generated Node #0,0,0: 58:[25, 22] Operation: 63-41=22 Exploring Operation: 41-25=16, Resulting Numbers: [63, 16] Generated Node #0,0,1: 58:[63, 16] Operation: 41-25=16 Exploring Operation: 25+41=66, Resulting Numbers: [63, 66] Generated Node #0,0,2: 58:[63, 66] Operation: 25+41=66 Exploring Operation: 63-25=38, Resulting Numbers: [41, 38] Generated Node #0,0,3: 58:[41, 38] Operation: 63-25=38 Moving to Node #0,0,0 Current State: 58:[25, 22], Operations: ['87-24=63', '63-41=22'] Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,58 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[63, 66], Operations: ['87-24=63', '25+41=66'] Exploring Operation: 63+66=129, Resulting Numbers: [129] 129,58 unequal: No Solution Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 63*66=4158, Resulting Numbers: [4158] 4158,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[63, 16], Operations: ['87-24=63', '41-25=16'] Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,58 unequal: No Solution Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,58 unequal: No Solution Moving to Node #0,0,3 Current State: 58:[41, 38], Operations: ['87-24=63', '63-25=38'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,58 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[24, 25, 46], Operations: ['87-41=46'] Exploring Operation: 46-24=22, Resulting Numbers: [25, 22] Generated Node #0,1,0: 58:[25, 22] Operation: 46-24=22 Exploring Operation: 24+46=70, Resulting Numbers: [25, 70] Generated Node #0,1,1: 58:[25, 70] Operation: 24+46=70 Exploring Operation: 46-25=21, Resulting Numbers: [24, 21] Generated Node #0,1,2: 58:[24, 21] Operation: 46-25=21 Exploring Operation: 25-24=1, Resulting Numbers: [46, 1] Generated Node #0,1,3: 58:[46, 1] Operation: 25-24=1 Moving to Node #0,1,0 Current State: 58:[25, 22], Operations: ['87-41=46', '46-24=22'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,58 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,58 unequal: No Solution Moving to Node #0,1,3 Current State: 58:[46, 1], Operations: ['87-41=46', '25-24=1'] Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,58 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[24, 21], Operations: ['87-41=46', '46-25=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,58 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[25, 70], Operations: ['87-41=46', '24+46=70'] Exploring Operation: 70-25=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 25+70=95, Resulting Numbers: [95] 95,58 unequal: No Solution Exploring Operation: 25*70=1750, Resulting Numbers: [1750] 1750,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[24, 41, 62], Operations: ['87-25=62'] Exploring Operation: 24+41=65, Resulting Numbers: [62, 65] Generated Node #0,2,0: 58:[62, 65] Operation: 24+41=65 Exploring Operation: 41-24=17, Resulting Numbers: [62, 17] Generated Node #0,2,1: 58:[62, 17] Operation: 41-24=17 Exploring Operation: 62-41=21, Resulting Numbers: [24, 21] Generated Node #0,2,2: 58:[24, 21] Operation: 62-41=21 Exploring Operation: 62-24=38, Resulting Numbers: [41, 38] Generated Node #0,2,3: 58:[41, 38] Operation: 62-24=38 Moving to Node #0,2,0 Current State: 58:[62, 65], Operations: ['87-25=62', '24+41=65'] Exploring Operation: 62*65=4030, Resulting Numbers: [4030] 4030,58 unequal: No Solution Exploring Operation: 62+65=127, Resulting Numbers: [127] 127,58 unequal: No Solution Exploring Operation: 65-62=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,2,2 Current State: 58:[24, 21], Operations: ['87-25=62', '62-41=21'] Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,58 unequal: No Solution Moving to Node #0,2,1 Current State: 58:[62, 17], Operations: ['87-25=62', '41-24=17'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 62*17=1054, Resulting Numbers: [1054] 1054,58 unequal: No Solution Exploring Operation: 62+17=79, Resulting Numbers: [79] 79,58 unequal: No Solution Moving to Node #0,2,3 Current State: 58:[41, 38], Operations: ['87-25=62', '62-24=38'] Exploring Operation: 41*38=1558, Resulting Numbers: [1558] 1558,58 unequal: No Solution Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[87, 25, 65], Operations: ['24+41=65'] Exploring Operation: 87-25=62, Resulting Numbers: [65, 62] Generated Node #0,3,0: 58:[65, 62] Operation: 87-25=62 Exploring Operation: 65-25=40, Resulting Numbers: [87, 40] Generated Node #0,3,1: 58:[87, 40] Operation: 65-25=40 Exploring Operation: 87+25=112, Resulting Numbers: [65, 112] Generated Node #0,3,2: 58:[65, 112] Operation: 87+25=112 Exploring Operation: 87-65=22, Resulting Numbers: [25, 22] Generated Node #0,3,3: 58:[25, 22] Operation: 87-65=22 Moving to Node #0,3,0 Current State: 58:[65, 62], Operations: ['24+41=65', '87-25=62'] Exploring Operation: 65*62=4030, Resulting Numbers: [4030] 4030,58 unequal: No Solution Exploring Operation: 65+62=127, Resulting Numbers: [127] 127,58 unequal: No Solution Exploring Operation: 65-62=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[25, 22], Operations: ['24+41=65', '87-65=22'] Exploring Operation: 25*22=550, Resulting Numbers: [550] 550,58 unequal: No Solution Exploring Operation: 25+22=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,3,1 Current State: 58:[87, 40], Operations: ['24+41=65', '65-25=40'] Exploring Operation: 87+40=127, Resulting Numbers: [127] 127,58 unequal: No Solution Exploring Operation: 87*40=3480, Resulting Numbers: [3480] 3480,58 unequal: No Solution Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,58 unequal: No Solution Moving to Node #0,3,2 Current State: 58:[65, 112], Operations: ['24+41=65', '87+25=112'] Exploring Operation: 112-65=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 65*112=7280, Resulting Numbers: [7280] 7280,58 unequal: No Solution Exploring Operation: 65+112=177, Resulting Numbers: [177] 177,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 58, 26, 46, 8 ]
42
[ "58-26=32", "32/8=4", "46-4=42" ]
Current State: 42:[58, 26, 46, 8], Operations: [] Exploring Operation: 58-26=32, Resulting Numbers: [46, 8, 32] Generated Node #2: [46, 8, 32] from Operation: 58-26=32 Current State: 42:[46, 8, 32], Operations: ['58-26=32'] Exploring Operation: 32/8=4, Resulting Numbers: [46, 4] Generated Node #3: [46, 4] from Operation: 32/8=4 Current State: 42:[46, 4], Operations: ['58-26=32', '32/8=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[58, 26, 46, 8], Operations: [] Exploring Operation: 58-26=32, Resulting Numbers: [46, 8, 32] Generated Node #0,0: 42:[46, 8, 32] Operation: 58-26=32 Exploring Operation: 58-46=12, Resulting Numbers: [26, 8, 12] Generated Node #0,1: 42:[26, 8, 12] Operation: 58-46=12 Exploring Operation: 58-8=50, Resulting Numbers: [26, 46, 50] Generated Node #0,2: 42:[26, 46, 50] Operation: 58-8=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[26, 8, 12], Operations: ['58-46=12'] Exploring Operation: 26-12=14, Resulting Numbers: [8, 14] Generated Node #0,1,0: 42:[8, 14] Operation: 26-12=14 Exploring Operation: 26-8=18, Resulting Numbers: [12, 18] Generated Node #0,1,1: 42:[12, 18] Operation: 26-8=18 Exploring Operation: 26+12=38, Resulting Numbers: [8, 38] Generated Node #0,1,2: 42:[8, 38] Operation: 26+12=38 Moving to Node #0,1,0 Current State: 42:[8, 14], Operations: ['58-46=12', '26-12=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,42 unequal: No Solution Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,42 unequal: No Solution Moving to Node #0,1,1 Current State: 42:[12, 18], Operations: ['58-46=12', '26-8=18'] Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,42 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[8, 38], Operations: ['58-46=12', '26+12=38'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,42 unequal: No Solution Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,42 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[46, 8, 32], Operations: ['58-26=32'] Exploring Operation: 8+32=40, Resulting Numbers: [46, 40] Generated Node #0,0,0: 42:[46, 40] Operation: 8+32=40 Exploring Operation: 32/8=4, Resulting Numbers: [46, 4] Generated Node #0,0,1: 42:[46, 4] Operation: 32/8=4 Exploring Operation: 46-32=14, Resulting Numbers: [8, 14] Generated Node #0,0,2: 42:[8, 14] Operation: 46-32=14 Moving to Node #0,0,2 Current State: 42:[8, 14], Operations: ['58-26=32', '46-32=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,42 unequal: No Solution Exploring Operation: 8*14=112, Resulting Numbers: [112] 112,42 unequal: No Solution Exploring Operation: 8+14=22, Resulting Numbers: [22] 22,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[46, 4], Operations: ['58-26=32', '32/8=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,42 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[58, 26, 46, 8], Operations: [] Exploring Operation: 58-26=32, Resulting Numbers: [46, 8, 32] Generated Node #0,0: 42:[46, 8, 32] Operation: 58-26=32 Moving to Node #0,0 Current State: 42:[46, 8, 32], Operations: ['58-26=32'] Exploring Operation: 32/8=4, Resulting Numbers: [46, 4] Generated Node #0,0,1: 42:[46, 4] Operation: 32/8=4 Moving to Node #0,0,1 Current State: 42:[46, 4], Operations: ['58-26=32', '32/8=4'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 31, 80, 48, 93 ]
94
[ "80-31=49", "93-48=45", "49+45=94" ]
Current State: 94:[31, 80, 48, 93], Operations: [] Exploring Operation: 80-31=49, Resulting Numbers: [48, 93, 49] Generated Node #2: [48, 93, 49] from Operation: 80-31=49 Current State: 94:[48, 93, 49], Operations: ['80-31=49'] Exploring Operation: 93-48=45, Resulting Numbers: [49, 45] Generated Node #3: [49, 45] from Operation: 93-48=45 Current State: 94:[49, 45], Operations: ['80-31=49', '93-48=45'] Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[31, 80, 48, 93], Operations: [] Exploring Operation: 80-31=49, Resulting Numbers: [48, 93, 49] Generated Node #0,0: 94:[48, 93, 49] Operation: 80-31=49 Exploring Operation: 93/31=3, Resulting Numbers: [80, 48, 3] Generated Node #0,1: 94:[80, 48, 3] Operation: 93/31=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[48, 93, 49], Operations: ['80-31=49'] Exploring Operation: 49-48=1, Resulting Numbers: [93, 1] Generated Node #0,0,0: 94:[93, 1] Operation: 49-48=1 Exploring Operation: 93-48=45, Resulting Numbers: [49, 45] Generated Node #0,0,1: 94:[49, 45] Operation: 93-48=45 Moving to Node #0,0,0 Current State: 94:[93, 1], Operations: ['80-31=49', '49-48=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[31, 80, 48, 93], Operations: [] Exploring Operation: 80-31=49, Resulting Numbers: [48, 93, 49] Generated Node #0,0: 94:[48, 93, 49] Operation: 80-31=49 Moving to Node #0,0 Current State: 94:[48, 93, 49], Operations: ['80-31=49'] Exploring Operation: 49-48=1, Resulting Numbers: [93, 1] Generated Node #0,0,0: 94:[93, 1] Operation: 49-48=1 Moving to Node #0,0,0 Current State: 94:[93, 1], Operations: ['80-31=49', '49-48=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 3, 16, 63, 7 ]
22
[ "3*16=48", "63+7=70", "70-48=22" ]
Current State: 22:[3, 16, 63, 7], Operations: [] Exploring Operation: 3*16=48, Resulting Numbers: [63, 7, 48] Generated Node #2: [63, 7, 48] from Operation: 3*16=48 Current State: 22:[63, 7, 48], Operations: ['3*16=48'] Exploring Operation: 63+7=70, Resulting Numbers: [48, 70] Generated Node #3: [48, 70] from Operation: 63+7=70 Current State: 22:[48, 70], Operations: ['3*16=48', '63+7=70'] Exploring Operation: 70-48=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[3, 16, 63, 7], Operations: [] Exploring Operation: 63/7=9, Resulting Numbers: [3, 16, 9] Generated Node #0,0: 22:[3, 16, 9] Operation: 63/7=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[3, 16, 9], Operations: ['63/7=9'] Exploring Operation: 16-3=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 22:[9, 13] Operation: 16-3=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[9, 13], Operations: ['63/7=9', '16-3=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[3, 16, 63, 7], Operations: [] Exploring Operation: 63/7=9, Resulting Numbers: [3, 16, 9] Generated Node #0,0: 22:[3, 16, 9] Operation: 63/7=9 Moving to Node #0,0 Current State: 22:[3, 16, 9], Operations: ['63/7=9'] Exploring Operation: 16-3=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 22:[9, 13] Operation: 16-3=13 Moving to Node #0,0,0 Current State: 22:[9, 13], Operations: ['63/7=9', '16-3=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 4, 84, 27, 15 ]
36
[ "27-15=12", "4*12=48", "84-48=36" ]
Current State: 36:[4, 84, 27, 15], Operations: [] Exploring Operation: 27-15=12, Resulting Numbers: [4, 84, 12] Generated Node #2: [4, 84, 12] from Operation: 27-15=12 Current State: 36:[4, 84, 12], Operations: ['27-15=12'] Exploring Operation: 4*12=48, Resulting Numbers: [84, 48] Generated Node #3: [84, 48] from Operation: 4*12=48 Current State: 36:[84, 48], Operations: ['27-15=12', '4*12=48'] Exploring Operation: 84-48=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[4, 84, 27, 15], Operations: [] Exploring Operation: 27-15=12, Resulting Numbers: [4, 84, 12] Generated Node #0,0: 36:[4, 84, 12] Operation: 27-15=12 Exploring Operation: 84/4=21, Resulting Numbers: [27, 15, 21] Generated Node #0,1: 36:[27, 15, 21] Operation: 84/4=21 Exploring Operation: 84-27=57, Resulting Numbers: [4, 15, 57] Generated Node #0,2: 36:[4, 15, 57] Operation: 84-27=57 Exploring Operation: 84-15=69, Resulting Numbers: [4, 27, 69] Generated Node #0,3: 36:[4, 27, 69] Operation: 84-15=69 Exploring Operation: 27+15=42, Resulting Numbers: [4, 84, 42] Generated Node #0,4: 36:[4, 84, 42] Operation: 27+15=42 Moving to Node #0,1 Current State: 36:[27, 15, 21], Operations: ['84/4=21'] Exploring Operation: 27-21=6, Resulting Numbers: [15, 6] Generated Node #0,1,0: 36:[15, 6] Operation: 27-21=6 Exploring Operation: 21-15=6, Resulting Numbers: [27, 6] Generated Node #0,1,1: 36:[27, 6] Operation: 21-15=6 Exploring Operation: 15+21=36, Resulting Numbers: [27, 36] Generated Node #0,1,2: 36:[27, 36] Operation: 15+21=36 Exploring Operation: 27-15=12, Resulting Numbers: [21, 12] Generated Node #0,1,3: 36:[21, 12] Operation: 27-15=12 Exploring Operation: 27+15=42, Resulting Numbers: [21, 42] Generated Node #0,1,4: 36:[21, 42] Operation: 27+15=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[15, 6], Operations: ['84/4=21', '27-21=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,36 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,36 unequal: No Solution No 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: 36:[21, 12], Operations: ['84/4=21', '27-15=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,36 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,36 unequal: No Solution No 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: 36:[27, 6], Operations: ['84/4=21', '21-15=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,36 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,36 unequal: No Solution No 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: 36:[27, 36], Operations: ['84/4=21', '15+21=36'] Exploring Operation: 27*36=972, Resulting Numbers: [972] 972,36 unequal: No Solution Exploring Operation: 27+36=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,36 unequal: No Solution No 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: 36:[21, 42], Operations: ['84/4=21', '27+15=42'] Exploring Operation: 21*42=882, Resulting Numbers: [882] 882,36 unequal: No Solution Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 21+42=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,36 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: 36:[4, 15, 57], Operations: ['84-27=57'] Exploring Operation: 4+57=61, Resulting Numbers: [15, 61] Generated Node #0,2,0: 36:[15, 61] Operation: 4+57=61 Exploring Operation: 57-4=53, Resulting Numbers: [15, 53] Generated Node #0,2,1: 36:[15, 53] Operation: 57-4=53 Exploring Operation: 4+15=19, Resulting Numbers: [57, 19] Generated Node #0,2,2: 36:[57, 19] Operation: 4+15=19 Exploring Operation: 15-4=11, Resulting Numbers: [57, 11] Generated Node #0,2,3: 36:[57, 11] Operation: 15-4=11 Exploring Operation: 57-15=42, Resulting Numbers: [4, 42] Generated Node #0,2,4: 36:[4, 42] Operation: 57-15=42 Moving to Node #0,3 Current State: 36:[4, 27, 69], Operations: ['84-15=69'] Exploring Operation: 4+69=73, Resulting Numbers: [27, 73] Generated Node #0,3,0: 36:[27, 73] Operation: 4+69=73 Exploring Operation: 69-27=42, Resulting Numbers: [4, 42] Generated Node #0,3,1: 36:[4, 42] Operation: 69-27=42 Exploring Operation: 69-4=65, Resulting Numbers: [27, 65] Generated Node #0,3,2: 36:[27, 65] Operation: 69-4=65 Exploring Operation: 4+27=31, Resulting Numbers: [69, 31] Generated Node #0,3,3: 36:[69, 31] Operation: 4+27=31 Exploring Operation: 27-4=23, Resulting Numbers: [69, 23] Generated Node #0,3,4: 36:[69, 23] Operation: 27-4=23 Moving to Node #0,0 Current State: 36:[4, 84, 12], Operations: ['27-15=12'] Exploring Operation: 84/4=21, Resulting Numbers: [12, 21] Generated Node #0,0,0: 36:[12, 21] Operation: 84/4=21 Exploring Operation: 12/4=3, Resulting Numbers: [84, 3] Generated Node #0,0,1: 36:[84, 3] Operation: 12/4=3 Exploring Operation: 84/12=7, Resulting Numbers: [4, 7] Generated Node #0,0,2: 36:[4, 7] Operation: 84/12=7 Exploring Operation: 84-4=80, Resulting Numbers: [12, 80] Generated Node #0,0,3: 36:[12, 80] Operation: 84-4=80 Exploring Operation: 84-12=72, Resulting Numbers: [4, 72] Generated Node #0,0,4: 36:[4, 72] Operation: 84-12=72 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[4, 7], Operations: ['27-15=12', '84/12=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,36 unequal: No Solution No 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: 36:[12, 21], Operations: ['27-15=12', '84/4=21'] Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,36 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,36 unequal: No Solution No 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: 36:[4, 72], Operations: ['27-15=12', '84-12=72'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,36 unequal: No Solution Exploring Operation: 4*72=288, Resulting Numbers: [288] 288,36 unequal: No Solution Exploring Operation: 4+72=76, Resulting Numbers: [76] 76,36 unequal: No Solution No 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: 36:[12, 80], Operations: ['27-15=12', '84-4=80'] Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,36 unequal: No Solution Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,36 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,36 unequal: No Solution No 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: 36:[84, 3], Operations: ['27-15=12', '12/4=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,36 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,36 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,36 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: 36:[4, 84, 42], Operations: ['27+15=42'] Exploring Operation: 84/42=2, Resulting Numbers: [4, 2] Generated Node #0,4,0: 36:[4, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [4, 42] Generated Node #0,4,1: 36:[4, 42] Operation: 84-42=42 Exploring Operation: 84/4=21, Resulting Numbers: [42, 21] Generated Node #0,4,2: 36:[42, 21] Operation: 84/4=21 Exploring Operation: 84-4=80, Resulting Numbers: [42, 80] Generated Node #0,4,3: 36:[42, 80] Operation: 84-4=80 Exploring Operation: 42-4=38, Resulting Numbers: [84, 38] Generated Node #0,4,4: 36:[84, 38] Operation: 42-4=38 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 36:[4, 2], Operations: ['27+15=42', '84/42=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,36 unequal: No Solution No 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: 36:[4, 42], Operations: ['27+15=42', '84-42=42'] Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,36 unequal: No Solution No 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: 36:[42, 21], Operations: ['27+15=42', '84/4=21'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,36 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,36 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,36 unequal: No Solution No 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: 36:[42, 80], Operations: ['27+15=42', '84-4=80'] Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,36 unequal: No Solution Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,36 unequal: No Solution No 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: 36:[84, 38], Operations: ['27+15=42', '42-4=38'] Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 84*38=3192, Resulting Numbers: [3192] 3192,36 unequal: No Solution Exploring Operation: 84+38=122, Resulting Numbers: [122] 122,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,4 Current State: 36:[4, 42], Operations: ['84-27=57', '57-15=42'] Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,36 unequal: No Solution Moving to Node #0,3,1 Current State: 36:[4, 42], Operations: ['84-15=69', '69-27=42'] Exploring Operation: 4*42=168, Resulting Numbers: [168] 168,36 unequal: No Solution Exploring Operation: 42-4=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 4+42=46, Resulting Numbers: [46] 46,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[15, 53], Operations: ['84-27=57', '57-4=53'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,36 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[57, 19], Operations: ['84-27=57', '4+15=19'] Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 57+19=76, Resulting Numbers: [76] 76,36 unequal: No Solution Exploring Operation: 57*19=1083, Resulting Numbers: [1083] 1083,36 unequal: No Solution Moving to Node #0,2,3 Current State: 36:[57, 11], Operations: ['84-27=57', '15-4=11'] Exploring Operation: 57*11=627, Resulting Numbers: [627] 627,36 unequal: No Solution Exploring Operation: 57+11=68, Resulting Numbers: [68] 68,36 unequal: No Solution Exploring Operation: 57-11=46, Resulting Numbers: [46] 46,36 unequal: No Solution Moving to Node #0,2,0 Current State: 36:[15, 61], Operations: ['84-27=57', '4+57=61'] Exploring Operation: 15*61=915, Resulting Numbers: [915] 915,36 unequal: No Solution Exploring Operation: 15+61=76, Resulting Numbers: [76] 76,36 unequal: No Solution Exploring Operation: 61-15=46, Resulting Numbers: [46] 46,36 unequal: No Solution Moving to Node #0,3,2 Current State: 36:[27, 65], Operations: ['84-15=69', '69-4=65'] Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 27*65=1755, Resulting Numbers: [1755] 1755,36 unequal: No Solution Exploring Operation: 27+65=92, Resulting Numbers: [92] 92,36 unequal: No Solution Moving to Node #0,3,4 Current State: 36:[69, 23], Operations: ['84-15=69', '27-4=23'] Exploring Operation: 69*23=1587, Resulting Numbers: [1587] 1587,36 unequal: No Solution Exploring Operation: 69-23=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 69+23=92, Resulting Numbers: [92] 92,36 unequal: No Solution Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,36 unequal: No Solution Moving to Node #0,3,3 Current State: 36:[69, 31], Operations: ['84-15=69', '4+27=31'] Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,36 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,36 unequal: No Solution Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,36 unequal: No Solution Moving to Node #0,3,0 Current State: 36:[27, 73], Operations: ['84-15=69', '4+69=73'] Exploring Operation: 27+73=100, Resulting Numbers: [100] 100,36 unequal: No Solution Exploring Operation: 27*73=1971, Resulting Numbers: [1971] 1971,36 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,36 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 92, 46, 64, 79 ]
61
[ "92-46=46", "79-64=15", "46+15=61" ]
Current State: 61:[92, 46, 64, 79], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [64, 79, 46] Generated Node #2: [64, 79, 46] from Operation: 92-46=46 Current State: 61:[64, 79, 46], Operations: ['92-46=46'] Exploring Operation: 79-64=15, Resulting Numbers: [46, 15] Generated Node #3: [46, 15] from Operation: 79-64=15 Current State: 61:[46, 15], Operations: ['92-46=46', '79-64=15'] Exploring Operation: 46+15=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[92, 46, 64, 79], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [64, 79, 46] Generated Node #0,0: 61:[64, 79, 46] Operation: 92-46=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[64, 79, 46], Operations: ['92-46=46'] Exploring Operation: 79-46=33, Resulting Numbers: [64, 33] Generated Node #0,0,0: 61:[64, 33] Operation: 79-46=33 Moving to Node #0,0,0 Current State: 61:[64, 33], Operations: ['92-46=46', '79-46=33'] Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,61 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
[ 98, 38, 31, 48 ]
77
[ "98-38=60", "48-31=17", "60+17=77" ]
Current State: 77:[98, 38, 31, 48], Operations: [] Exploring Operation: 98-38=60, Resulting Numbers: [31, 48, 60] Generated Node #2: [31, 48, 60] from Operation: 98-38=60 Current State: 77:[31, 48, 60], Operations: ['98-38=60'] Exploring Operation: 48-31=17, Resulting Numbers: [60, 17] Generated Node #3: [60, 17] from Operation: 48-31=17 Current State: 77:[60, 17], Operations: ['98-38=60', '48-31=17'] Exploring Operation: 60+17=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[98, 38, 31, 48], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [98, 31, 10] Generated Node #0,0: 77:[98, 31, 10] Operation: 48-38=10 Exploring Operation: 38-31=7, Resulting Numbers: [98, 48, 7] Generated Node #0,1: 77:[98, 48, 7] Operation: 38-31=7 Exploring Operation: 38+48=86, Resulting Numbers: [98, 31, 86] Generated Node #0,2: 77:[98, 31, 86] Operation: 38+48=86 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[98, 31, 10], Operations: ['48-38=10'] Exploring Operation: 98-10=88, Resulting Numbers: [31, 88] Generated Node #0,0,0: 77:[31, 88] Operation: 98-10=88 Exploring Operation: 31-10=21, Resulting Numbers: [98, 21] Generated Node #0,0,1: 77:[98, 21] Operation: 31-10=21 Exploring Operation: 98-31=67, Resulting Numbers: [10, 67] Generated Node #0,0,2: 77:[10, 67] Operation: 98-31=67 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[10, 67], Operations: ['48-38=10', '98-31=67'] Exploring Operation: 10+67=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[98, 38, 31, 48], Operations: [] Exploring Operation: 48-38=10, Resulting Numbers: [98, 31, 10] Generated Node #0,0: 77:[98, 31, 10] Operation: 48-38=10 Moving to Node #0,0 Current State: 77:[98, 31, 10], Operations: ['48-38=10'] Exploring Operation: 98-31=67, Resulting Numbers: [10, 67] Generated Node #0,0,2: 77:[10, 67] Operation: 98-31=67 Moving to Node #0,0,2 Current State: 77:[10, 67], Operations: ['48-38=10', '98-31=67'] Exploring Operation: 10+67=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 4, 35, 52, 24 ]
76
[ "35*52=1820", "4+1820=1824", "1824/24=76" ]
Current State: 76:[4, 35, 52, 24], Operations: [] Exploring Operation: 35*52=1820, Resulting Numbers: [4, 24, 1820] Generated Node #2: [4, 24, 1820] from Operation: 35*52=1820 Current State: 76:[4, 24, 1820], Operations: ['35*52=1820'] Exploring Operation: 4+1820=1824, Resulting Numbers: [24, 1824] Generated Node #3: [24, 1824] from Operation: 4+1820=1824 Current State: 76:[24, 1824], Operations: ['35*52=1820', '4+1820=1824'] Exploring Operation: 1824/24=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[4, 35, 52, 24], Operations: [] Exploring Operation: 52-35=17, Resulting Numbers: [4, 24, 17] Generated Node #0,0: 76:[4, 24, 17] Operation: 52-35=17 Exploring Operation: 52+24=76, Resulting Numbers: [4, 35, 76] Generated Node #0,1: 76:[4, 35, 76] Operation: 52+24=76 Exploring Operation: 52-24=28, Resulting Numbers: [4, 35, 28] Generated Node #0,2: 76:[4, 35, 28] Operation: 52-24=28 Exploring Operation: 52/4=13, Resulting Numbers: [35, 24, 13] Generated Node #0,3: 76:[35, 24, 13] Operation: 52/4=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[4, 35, 76], Operations: ['52+24=76'] Exploring Operation: 76/4=19, Resulting Numbers: [35, 19] Generated Node #0,1,0: 76:[35, 19] Operation: 76/4=19 Exploring Operation: 4+35=39, Resulting Numbers: [76, 39] Generated Node #0,1,1: 76:[76, 39] Operation: 4+35=39 Exploring Operation: 76-35=41, Resulting Numbers: [4, 41] Generated Node #0,1,2: 76:[4, 41] Operation: 76-35=41 Exploring Operation: 35-4=31, Resulting Numbers: [76, 31] Generated Node #0,1,3: 76:[76, 31] Operation: 35-4=31 Moving to Node #0,1,1 Current State: 76:[76, 39], Operations: ['52+24=76', '4+35=39'] Exploring Operation: 76+39=115, Resulting Numbers: [115] 115,76 unequal: No Solution Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 76*39=2964, Resulting Numbers: [2964] 2964,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[4, 41], Operations: ['52+24=76', '76-35=41'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,76 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[35, 19], Operations: ['52+24=76', '76/4=19'] Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,76 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[76, 31], Operations: ['52+24=76', '35-4=31'] Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 76*31=2356, Resulting Numbers: [2356] 2356,76 unequal: No Solution Exploring Operation: 76+31=107, Resulting Numbers: [107] 107,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[4, 24, 17], Operations: ['52-35=17'] Exploring Operation: 24/4=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 76:[17, 6] Operation: 24/4=6 Exploring Operation: 24-4=20, Resulting Numbers: [17, 20] Generated Node #0,0,1: 76:[17, 20] Operation: 24-4=20 Exploring Operation: 24-17=7, Resulting Numbers: [4, 7] Generated Node #0,0,2: 76:[4, 7] Operation: 24-17=7 Exploring Operation: 24+17=41, Resulting Numbers: [4, 41] Generated Node #0,0,3: 76:[4, 41] Operation: 24+17=41 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[17, 20], Operations: ['52-35=17', '24-4=20'] Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,76 unequal: No Solution No 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: 76:[4, 7], Operations: ['52-35=17', '24-17=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,76 unequal: No Solution No 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: 76:[4, 41], Operations: ['52-35=17', '24+17=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,76 unequal: No Solution No 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: 76:[17, 6], Operations: ['52-35=17', '24/4=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,76 unequal: No Solution Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,76 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: 76:[4, 35, 28], Operations: ['52-24=28'] Exploring Operation: 4+28=32, Resulting Numbers: [35, 32] Generated Node #0,2,0: 76:[35, 32] Operation: 4+28=32 Exploring Operation: 28/4=7, Resulting Numbers: [35, 7] Generated Node #0,2,1: 76:[35, 7] Operation: 28/4=7 Exploring Operation: 35-28=7, Resulting Numbers: [4, 7] Generated Node #0,2,2: 76:[4, 7] Operation: 35-28=7 Exploring Operation: 28-4=24, Resulting Numbers: [35, 24] Generated Node #0,2,3: 76:[35, 24] Operation: 28-4=24 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[4, 7], Operations: ['52-24=28', '35-28=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,76 unequal: No Solution No 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: 76:[35, 7], Operations: ['52-24=28', '28/4=7'] Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 35*7=245, Resulting Numbers: [245] 245,76 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,76 unequal: No Solution No 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: 76:[35, 24], Operations: ['52-24=28', '28-4=24'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 35*24=840, Resulting Numbers: [840] 840,76 unequal: No Solution Exploring Operation: 35+24=59, Resulting Numbers: [59] 59,76 unequal: No Solution No 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: 76:[35, 32], Operations: ['52-24=28', '4+28=32'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,76 unequal: No Solution Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,76 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,76 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: 76:[35, 24, 13], Operations: ['52/4=13'] Exploring Operation: 24+13=37, Resulting Numbers: [35, 37] Generated Node #0,3,0: 76:[35, 37] Operation: 24+13=37 Exploring Operation: 35-13=22, Resulting Numbers: [24, 22] Generated Node #0,3,1: 76:[24, 22] Operation: 35-13=22 Exploring Operation: 24-13=11, Resulting Numbers: [35, 11] Generated Node #0,3,2: 76:[35, 11] Operation: 24-13=11 Exploring Operation: 35-24=11, Resulting Numbers: [13, 11] Generated Node #0,3,3: 76:[13, 11] Operation: 35-24=11 Moving to Node #0,3,0 Current State: 76:[35, 37], Operations: ['52/4=13', '24+13=37'] Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,76 unequal: No Solution Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,76 unequal: No Solution Moving to Node #0,3,1 Current State: 76:[24, 22], Operations: ['52/4=13', '35-13=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,76 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,76 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[35, 11], Operations: ['52/4=13', '24-13=11'] Exploring Operation: 35+11=46, Resulting Numbers: [46] 46,76 unequal: No Solution Exploring Operation: 35*11=385, Resulting Numbers: [385] 385,76 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[13, 11], Operations: ['52/4=13', '35-24=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,76 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 6, 14, 55, 18 ]
29
[ "14-6=8", "55-18=37", "37-8=29" ]
Current State: 29:[6, 14, 55, 18], Operations: [] Exploring Operation: 14-6=8, Resulting Numbers: [55, 18, 8] Generated Node #2: [55, 18, 8] from Operation: 14-6=8 Current State: 29:[55, 18, 8], Operations: ['14-6=8'] Exploring Operation: 55-18=37, Resulting Numbers: [8, 37] Generated Node #3: [8, 37] from Operation: 55-18=37 Current State: 29:[8, 37], Operations: ['14-6=8', '55-18=37'] Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[6, 14, 55, 18], Operations: [] Exploring Operation: 6+14=20, Resulting Numbers: [55, 18, 20] Generated Node #0,0: 29:[55, 18, 20] Operation: 6+14=20 Exploring Operation: 55-14=41, Resulting Numbers: [6, 18, 41] Generated Node #0,1: 29:[6, 18, 41] Operation: 55-14=41 Exploring Operation: 6+18=24, Resulting Numbers: [14, 55, 24] Generated Node #0,2: 29:[14, 55, 24] Operation: 6+18=24 Exploring Operation: 55-6=49, Resulting Numbers: [14, 18, 49] Generated Node #0,3: 29:[14, 18, 49] Operation: 55-6=49 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[55, 18, 20], Operations: ['6+14=20'] Exploring Operation: 55+18=73, Resulting Numbers: [20, 73] Generated Node #0,0,0: 29:[20, 73] Operation: 55+18=73 Exploring Operation: 18+20=38, Resulting Numbers: [55, 38] Generated Node #0,0,1: 29:[55, 38] Operation: 18+20=38 Exploring Operation: 55-18=37, Resulting Numbers: [20, 37] Generated Node #0,0,2: 29:[20, 37] Operation: 55-18=37 Exploring Operation: 55-20=35, Resulting Numbers: [18, 35] Generated Node #0,0,3: 29:[18, 35] Operation: 55-20=35 Moving to Node #0,0,2 Current State: 29:[20, 37], Operations: ['6+14=20', '55-18=37'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,29 unequal: No Solution Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[18, 35], Operations: ['6+14=20', '55-20=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[55, 38], Operations: ['6+14=20', '18+20=38'] Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[20, 73], Operations: ['6+14=20', '55+18=73'] Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 20*73=1460, Resulting Numbers: [1460] 1460,29 unequal: No Solution Exploring Operation: 20+73=93, Resulting Numbers: [93] 93,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[6, 18, 41], Operations: ['55-14=41'] Exploring Operation: 6+41=47, Resulting Numbers: [18, 47] Generated Node #0,1,0: 29:[18, 47] Operation: 6+41=47 Exploring Operation: 18-6=12, Resulting Numbers: [41, 12] Generated Node #0,1,1: 29:[41, 12] Operation: 18-6=12 Exploring Operation: 6+18=24, Resulting Numbers: [41, 24] Generated Node #0,1,2: 29:[41, 24] Operation: 6+18=24 Exploring Operation: 41-6=35, Resulting Numbers: [18, 35] Generated Node #0,1,3: 29:[18, 35] Operation: 41-6=35 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 29:[41, 24], Operations: ['55-14=41', '6+18=24'] Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,29 unequal: No Solution Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 29:[18, 35], Operations: ['55-14=41', '41-6=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,29 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[18, 47], Operations: ['55-14=41', '6+41=47'] Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[6, 14, 55, 18], Operations: [] Exploring Operation: 55-14=41, Resulting Numbers: [6, 18, 41] Generated Node #0,1: 29:[6, 18, 41] Operation: 55-14=41 Moving to Node #0,1 Current State: 29:[6, 18, 41], Operations: ['55-14=41'] Exploring Operation: 6+41=47, Resulting Numbers: [18, 47] Generated Node #0,1,0: 29:[18, 47] Operation: 6+41=47 Moving to Node #0,1,0 Current State: 29:[18, 47], Operations: ['55-14=41', '6+41=47'] Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_4
sum_heuristic
[ 78, 94, 1, 51 ]
66
[ "94-78=16", "51-1=50", "16+50=66" ]
Current State: 66:[78, 94, 1, 51], Operations: [] Exploring Operation: 94-78=16, Resulting Numbers: [1, 51, 16] Generated Node #2: [1, 51, 16] from Operation: 94-78=16 Current State: 66:[1, 51, 16], Operations: ['94-78=16'] Exploring Operation: 51-1=50, Resulting Numbers: [16, 50] Generated Node #3: [16, 50] from Operation: 51-1=50 Current State: 66:[16, 50], Operations: ['94-78=16', '51-1=50'] Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[78, 94, 1, 51], Operations: [] Exploring Operation: 94-78=16, Resulting Numbers: [1, 51, 16] Generated Node #0,0: 66:[1, 51, 16] Operation: 94-78=16 Exploring Operation: 94-51=43, Resulting Numbers: [78, 1, 43] Generated Node #0,1: 66:[78, 1, 43] Operation: 94-51=43 Exploring Operation: 78-51=27, Resulting Numbers: [94, 1, 27] Generated Node #0,2: 66:[94, 1, 27] Operation: 78-51=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[1, 51, 16], Operations: ['94-78=16'] Exploring Operation: 51-16=35, Resulting Numbers: [1, 35] Generated Node #0,0,0: 66:[1, 35] Operation: 51-16=35 Exploring Operation: 51+16=67, Resulting Numbers: [1, 67] Generated Node #0,0,1: 66:[1, 67] Operation: 51+16=67 Exploring Operation: 1+51=52, Resulting Numbers: [16, 52] Generated Node #0,0,2: 66:[16, 52] Operation: 1+51=52 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[1, 67], Operations: ['94-78=16', '51+16=67'] Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[78, 94, 1, 51], Operations: [] Exploring Operation: 94-78=16, Resulting Numbers: [1, 51, 16] Generated Node #0,0: 66:[1, 51, 16] Operation: 94-78=16 Moving to Node #0,0 Current State: 66:[1, 51, 16], Operations: ['94-78=16'] Exploring Operation: 51+16=67, Resulting Numbers: [1, 67] Generated Node #0,0,1: 66:[1, 67] Operation: 51+16=67 Moving to Node #0,0,1 Current State: 66:[1, 67], Operations: ['94-78=16', '51+16=67'] Exploring Operation: 67-1=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 24, 52, 73, 75 ]
26
[ "52-24=28", "75-73=2", "28-2=26" ]
Current State: 26:[24, 52, 73, 75], Operations: [] Exploring Operation: 52-24=28, Resulting Numbers: [73, 75, 28] Generated Node #2: [73, 75, 28] from Operation: 52-24=28 Current State: 26:[73, 75, 28], Operations: ['52-24=28'] Exploring Operation: 75-73=2, Resulting Numbers: [28, 2] Generated Node #3: [28, 2] from Operation: 75-73=2 Current State: 26:[28, 2], Operations: ['52-24=28', '75-73=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[24, 52, 73, 75], Operations: [] Exploring Operation: 73-52=21, Resulting Numbers: [24, 75, 21] Generated Node #0,0: 26:[24, 75, 21] Operation: 73-52=21 Exploring Operation: 75-52=23, Resulting Numbers: [24, 73, 23] Generated Node #0,1: 26:[24, 73, 23] Operation: 75-52=23 Exploring Operation: 52-24=28, Resulting Numbers: [73, 75, 28] Generated Node #0,2: 26:[73, 75, 28] Operation: 52-24=28 Exploring Operation: 75-73=2, Resulting Numbers: [24, 52, 2] Generated Node #0,3: 26:[24, 52, 2] Operation: 75-73=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 26:[24, 52, 2], Operations: ['75-73=2'] Exploring Operation: 52-2=50, Resulting Numbers: [24, 50] Generated Node #0,3,0: 26:[24, 50] Operation: 52-2=50 Exploring Operation: 52-24=28, Resulting Numbers: [2, 28] Generated Node #0,3,1: 26:[2, 28] Operation: 52-24=28 Exploring Operation: 24+2=26, Resulting Numbers: [52, 26] Generated Node #0,3,2: 26:[52, 26] Operation: 24+2=26 Exploring Operation: 52/2=26, Resulting Numbers: [24, 26] Generated Node #0,3,3: 26:[24, 26] Operation: 52/2=26 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 26:[2, 28], Operations: ['75-73=2', '52-24=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,26 unequal: No Solution Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,26 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,26 unequal: No Solution Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[24, 52, 73, 75], Operations: [] Exploring Operation: 75-73=2, Resulting Numbers: [24, 52, 2] Generated Node #0,3: 26:[24, 52, 2] Operation: 75-73=2 Moving to Node #0,3 Current State: 26:[24, 52, 2], Operations: ['75-73=2'] Exploring Operation: 52-24=28, Resulting Numbers: [2, 28] Generated Node #0,3,1: 26:[2, 28] Operation: 52-24=28 Moving to Node #0,3,1 Current State: 26:[2, 28], Operations: ['75-73=2', '52-24=28'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 40, 44, 40, 75 ]
75
[ "40-40=0", "44*0=0", "75+0=75" ]
Current State: 75:[40, 44, 40, 75], Operations: [] Exploring Operation: 40-40=0, Resulting Numbers: [44, 75, 0] Generated Node #2: [44, 75, 0] from Operation: 40-40=0 Current State: 75:[44, 75, 0], Operations: ['40-40=0'] Exploring Operation: 44*0=0, Resulting Numbers: [75, 0] Generated Node #3: [75, 0] from Operation: 44*0=0 Current State: 75:[75, 0], Operations: ['40-40=0', '44*0=0'] Exploring Operation: 75+0=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[40, 44, 40, 75], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [40, 75, 4] Generated Node #0,0: 75:[40, 75, 4] Operation: 44-40=4 Exploring Operation: 40/40=1, Resulting Numbers: [44, 75, 1] Generated Node #0,1: 75:[44, 75, 1] Operation: 40/40=1 Exploring Operation: 44-40=4, Resulting Numbers: [40, 75, 4] Generated Node #0,2: 75:[40, 75, 4] Operation: 44-40=4 Moving to Node #0,0 Current State: 75:[40, 75, 4], Operations: ['44-40=4'] Exploring Operation: 40/4=10, Resulting Numbers: [75, 10] Generated Node #0,0,0: 75:[75, 10] Operation: 40/4=10 Exploring Operation: 40-4=36, Resulting Numbers: [75, 36] Generated Node #0,0,1: 75:[75, 36] Operation: 40-4=36 Exploring Operation: 75-40=35, Resulting Numbers: [4, 35] Generated Node #0,0,2: 75:[4, 35] Operation: 75-40=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[75, 10], Operations: ['44-40=4', '40/4=10'] Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,75 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,75 unequal: No Solution Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[75, 36], Operations: ['44-40=4', '40-4=36'] Exploring Operation: 75-36=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 75*36=2700, Resulting Numbers: [2700] 2700,75 unequal: No Solution Exploring Operation: 75+36=111, Resulting Numbers: [111] 111,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[4, 35], Operations: ['44-40=4', '75-40=35'] Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,75 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,75 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: 75:[40, 75, 4], Operations: ['44-40=4'] Exploring Operation: 40/4=10, Resulting Numbers: [75, 10] Generated Node #0,2,0: 75:[75, 10] Operation: 40/4=10 Exploring Operation: 40-4=36, Resulting Numbers: [75, 36] Generated Node #0,2,1: 75:[75, 36] Operation: 40-4=36 Exploring Operation: 75-40=35, Resulting Numbers: [4, 35] Generated Node #0,2,2: 75:[4, 35] Operation: 75-40=35 Moving to Node #0,1 Current State: 75:[44, 75, 1], Operations: ['40/40=1'] Exploring Operation: 44-1=43, Resulting Numbers: [75, 43] Generated Node #0,1,0: 75:[75, 43] Operation: 44-1=43 Exploring Operation: 75-44=31, Resulting Numbers: [1, 31] Generated Node #0,1,1: 75:[1, 31] Operation: 75-44=31 Exploring Operation: 44*1=44, Resulting Numbers: [75, 44] Generated Node #0,1,2: 75:[75, 44] Operation: 44*1=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[1, 31], Operations: ['40/40=1', '75-44=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,75 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 #0,1,0 Current State: 75:[75, 43], Operations: ['40/40=1', '44-1=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,75 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,75 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,75 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 #0,1,2 Current State: 75:[75, 44], Operations: ['40/40=1', '44*1=44'] Exploring Operation: 75+44=119, Resulting Numbers: [119] 119,75 unequal: No Solution Exploring Operation: 75*44=3300, Resulting Numbers: [3300] 3300,75 unequal: No Solution Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,75 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: 75:[75, 10], Operations: ['44-40=4', '40/4=10'] Exploring Operation: 75*10=750, Resulting Numbers: [750] 750,75 unequal: No Solution Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,75 unequal: No Solution Exploring Operation: 75-10=65, Resulting Numbers: [65] 65,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[75, 36], Operations: ['44-40=4', '40-4=36'] Exploring Operation: 75*36=2700, Resulting Numbers: [2700] 2700,75 unequal: No Solution Exploring Operation: 75-36=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 75+36=111, Resulting Numbers: [111] 111,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[4, 35], Operations: ['44-40=4', '75-40=35'] Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,75 unequal: No Solution Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,75 unequal: No Solution Exploring Operation: 4*35=140, Resulting Numbers: [140] 140,75 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 32, 70, 11, 34 ]
57
[ "32+70=102", "11+34=45", "102-45=57" ]
Current State: 57:[32, 70, 11, 34], Operations: [] Exploring Operation: 32+70=102, Resulting Numbers: [11, 34, 102] Generated Node #2: [11, 34, 102] from Operation: 32+70=102 Current State: 57:[11, 34, 102], Operations: ['32+70=102'] Exploring Operation: 11+34=45, Resulting Numbers: [102, 45] Generated Node #3: [102, 45] from Operation: 11+34=45 Current State: 57:[102, 45], Operations: ['32+70=102', '11+34=45'] Exploring Operation: 102-45=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[32, 70, 11, 34], Operations: [] Exploring Operation: 32+34=66, Resulting Numbers: [70, 11, 66] Generated Node #0,0: 57:[70, 11, 66] Operation: 32+34=66 Exploring Operation: 32-11=21, Resulting Numbers: [70, 34, 21] Generated Node #0,1: 57:[70, 34, 21] Operation: 32-11=21 Exploring Operation: 34-32=2, Resulting Numbers: [70, 11, 2] Generated Node #0,2: 57:[70, 11, 2] Operation: 34-32=2 Moving to Node #0,2 Current State: 57:[70, 11, 2], Operations: ['34-32=2'] Exploring Operation: 11*2=22, Resulting Numbers: [70, 22] Generated Node #0,2,0: 57:[70, 22] Operation: 11*2=22 Exploring Operation: 70-11=59, Resulting Numbers: [2, 59] Generated Node #0,2,1: 57:[2, 59] Operation: 70-11=59 Exploring Operation: 70-2=68, Resulting Numbers: [11, 68] Generated Node #0,2,2: 57:[11, 68] Operation: 70-2=68 Moving to Node #0,0 Current State: 57:[70, 11, 66], Operations: ['32+34=66'] Exploring Operation: 70-11=59, Resulting Numbers: [66, 59] Generated Node #0,0,0: 57:[66, 59] Operation: 70-11=59 Exploring Operation: 66-11=55, Resulting Numbers: [70, 55] Generated Node #0,0,1: 57:[70, 55] Operation: 66-11=55 Exploring Operation: 70-66=4, Resulting Numbers: [11, 4] Generated Node #0,0,2: 57:[11, 4] Operation: 70-66=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[11, 4], Operations: ['32+34=66', '70-66=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,57 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[66, 59], Operations: ['32+34=66', '70-11=59'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,57 unequal: No Solution Exploring Operation: 66*59=3894, Resulting Numbers: [3894] 3894,57 unequal: No Solution Exploring Operation: 66+59=125, Resulting Numbers: [125] 125,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[70, 55], Operations: ['32+34=66', '66-11=55'] Exploring Operation: 70-55=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 70*55=3850, Resulting Numbers: [3850] 3850,57 unequal: No Solution Exploring Operation: 70+55=125, Resulting Numbers: [125] 125,57 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: 57:[70, 34, 21], Operations: ['32-11=21'] Exploring Operation: 70-34=36, Resulting Numbers: [21, 36] Generated Node #0,1,0: 57:[21, 36] Operation: 70-34=36 Exploring Operation: 34+21=55, Resulting Numbers: [70, 55] Generated Node #0,1,1: 57:[70, 55] Operation: 34+21=55 Exploring Operation: 34-21=13, Resulting Numbers: [70, 13] Generated Node #0,1,2: 57:[70, 13] Operation: 34-21=13 Moving to Node #0,2,1 Current State: 57:[2, 59], Operations: ['34-32=2', '70-11=59'] Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,57 unequal: No Solution Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[32, 70, 11, 34], Operations: [] Exploring Operation: 34-32=2, Resulting Numbers: [70, 11, 2] Generated Node #0,2: 57:[70, 11, 2] Operation: 34-32=2 Moving to Node #0,2 Current State: 57:[70, 11, 2], Operations: ['34-32=2'] Exploring Operation: 70-11=59, Resulting Numbers: [2, 59] Generated Node #0,2,1: 57:[2, 59] Operation: 70-11=59 Moving to Node #0,2,1 Current State: 57:[2, 59], Operations: ['34-32=2', '70-11=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 89, 2, 86, 63 ]
30
[ "89-86=3", "63-3=60", "60/2=30" ]
Current State: 30:[89, 2, 86, 63], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [2, 63, 3] Generated Node #2: [2, 63, 3] from Operation: 89-86=3 Current State: 30:[2, 63, 3], Operations: ['89-86=3'] Exploring Operation: 63-3=60, Resulting Numbers: [2, 60] Generated Node #3: [2, 60] from Operation: 63-3=60 Current State: 30:[2, 60], Operations: ['89-86=3', '63-3=60'] Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[89, 2, 86, 63], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [2, 63, 3] Generated Node #0,0: 30:[2, 63, 3] Operation: 89-86=3 Moving to Node #0,0 Current State: 30:[2, 63, 3], Operations: ['89-86=3'] Exploring Operation: 63/3=21, Resulting Numbers: [2, 21] Generated Node #0,0,0: 30:[2, 21] Operation: 63/3=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[2, 21], Operations: ['89-86=3', '63/3=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 39, 94, 51 ]
79
[ "39+51=90", "90/6=15", "94-15=79" ]
Current State: 79:[6, 39, 94, 51], Operations: [] Exploring Operation: 39+51=90, Resulting Numbers: [6, 94, 90] Generated Node #2: [6, 94, 90] from Operation: 39+51=90 Current State: 79:[6, 94, 90], Operations: ['39+51=90'] Exploring Operation: 90/6=15, Resulting Numbers: [94, 15] Generated Node #3: [94, 15] from Operation: 90/6=15 Current State: 79:[94, 15], Operations: ['39+51=90', '90/6=15'] Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[6, 39, 94, 51], Operations: [] Exploring Operation: 6+51=57, Resulting Numbers: [39, 94, 57] Generated Node #0,0: 79:[39, 94, 57] Operation: 6+51=57 Exploring Operation: 6+39=45, Resulting Numbers: [94, 51, 45] Generated Node #0,1: 79:[94, 51, 45] Operation: 6+39=45 Exploring Operation: 94-6=88, Resulting Numbers: [39, 51, 88] Generated Node #0,2: 79:[39, 51, 88] Operation: 94-6=88 Moving to Node #0,0 Current State: 79:[39, 94, 57], Operations: ['6+51=57'] Exploring Operation: 39+94=133, Resulting Numbers: [57, 133] Generated Node #0,0,0: 79:[57, 133] Operation: 39+94=133 Exploring Operation: 94-39=55, Resulting Numbers: [57, 55] Generated Node #0,0,1: 79:[57, 55] Operation: 94-39=55 Exploring Operation: 39+57=96, Resulting Numbers: [94, 96] Generated Node #0,0,2: 79:[94, 96] Operation: 39+57=96 Moving to Node #0,1 Current State: 79:[94, 51, 45], Operations: ['6+39=45'] Exploring Operation: 94-51=43, Resulting Numbers: [45, 43] Generated Node #0,1,0: 79:[45, 43] Operation: 94-51=43 Exploring Operation: 51+45=96, Resulting Numbers: [94, 96] Generated Node #0,1,1: 79:[94, 96] Operation: 51+45=96 Exploring Operation: 94-45=49, Resulting Numbers: [51, 49] Generated Node #0,1,2: 79:[51, 49] Operation: 94-45=49 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[94, 96], Operations: ['6+39=45', '51+45=96'] Exploring Operation: 96-94=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 94*96=9024, Resulting Numbers: [9024] 9024,79 unequal: No Solution Exploring Operation: 94+96=190, Resulting Numbers: [190] 190,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[51, 49], Operations: ['6+39=45', '94-45=49'] Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 51*49=2499, Resulting Numbers: [2499] 2499,79 unequal: No Solution Exploring Operation: 51+49=100, Resulting Numbers: [100] 100,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[45, 43], Operations: ['6+39=45', '94-51=43'] Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 45*43=1935, Resulting Numbers: [1935] 1935,79 unequal: No Solution Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 79:[39, 51, 88], Operations: ['94-6=88'] Exploring Operation: 51-39=12, Resulting Numbers: [88, 12] Generated Node #0,2,0: 79:[88, 12] Operation: 51-39=12 Exploring Operation: 39+51=90, Resulting Numbers: [88, 90] Generated Node #0,2,1: 79:[88, 90] Operation: 39+51=90 Exploring Operation: 88-39=49, Resulting Numbers: [51, 49] Generated Node #0,2,2: 79:[51, 49] Operation: 88-39=49 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[88, 90], Operations: ['94-6=88', '39+51=90'] Exploring Operation: 88*90=7920, Resulting Numbers: [7920] 7920,79 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 88+90=178, Resulting Numbers: [178] 178,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[51, 49], Operations: ['94-6=88', '88-39=49'] Exploring Operation: 51*49=2499, Resulting Numbers: [2499] 2499,79 unequal: No Solution Exploring Operation: 51+49=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[88, 12], Operations: ['94-6=88', '51-39=12'] Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,79 unequal: No Solution Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,79 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,79 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: 79:[94, 96], Operations: ['6+51=57', '39+57=96'] Exploring Operation: 94+96=190, Resulting Numbers: [190] 190,79 unequal: No Solution Exploring Operation: 94*96=9024, Resulting Numbers: [9024] 9024,79 unequal: No Solution Exploring Operation: 96-94=2, Resulting Numbers: [2] 2,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[57, 55], Operations: ['6+51=57', '94-39=55'] Exploring Operation: 57*55=3135, Resulting Numbers: [3135] 3135,79 unequal: No Solution Exploring Operation: 57-55=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 57+55=112, Resulting Numbers: [112] 112,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[57, 133], Operations: ['6+51=57', '39+94=133'] Exploring Operation: 57*133=7581, Resulting Numbers: [7581] 7581,79 unequal: No Solution Exploring Operation: 133-57=76, Resulting Numbers: [76] 76,79 unequal: No Solution Exploring Operation: 57+133=190, Resulting Numbers: [190] 190,79 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 3, 24, 18, 9 ]
46
[ "18*9=162", "162-24=138", "138/3=46" ]
Current State: 46:[3, 24, 18, 9], Operations: [] Exploring Operation: 18*9=162, Resulting Numbers: [3, 24, 162] Generated Node #2: [3, 24, 162] from Operation: 18*9=162 Current State: 46:[3, 24, 162], Operations: ['18*9=162'] Exploring Operation: 162-24=138, Resulting Numbers: [3, 138] Generated Node #3: [3, 138] from Operation: 162-24=138 Current State: 46:[3, 138], Operations: ['18*9=162', '162-24=138'] Exploring Operation: 138/3=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[3, 24, 18, 9], Operations: [] Exploring Operation: 18/9=2, Resulting Numbers: [3, 24, 2] Generated Node #0,0: 46:[3, 24, 2] Operation: 18/9=2 Moving to Node #0,0 Current State: 46:[3, 24, 2], Operations: ['18/9=2'] Exploring Operation: 24-3=21, Resulting Numbers: [2, 21] Generated Node #0,0,0: 46:[2, 21] Operation: 24-3=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[2, 21], Operations: ['18/9=2', '24-3=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 93, 23, 74, 40 ]
44
[ "93-23=70", "74+40=114", "114-70=44" ]
Current State: 44:[93, 23, 74, 40], Operations: [] Exploring Operation: 93-23=70, Resulting Numbers: [74, 40, 70] Generated Node #2: [74, 40, 70] from Operation: 93-23=70 Current State: 44:[74, 40, 70], Operations: ['93-23=70'] Exploring Operation: 74+40=114, Resulting Numbers: [70, 114] Generated Node #3: [70, 114] from Operation: 74+40=114 Current State: 44:[70, 114], Operations: ['93-23=70', '74+40=114'] Exploring Operation: 114-70=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[93, 23, 74, 40], Operations: [] Exploring Operation: 93-40=53, Resulting Numbers: [23, 74, 53] Generated Node #0,0: 44:[23, 74, 53] Operation: 93-40=53 Exploring Operation: 93-74=19, Resulting Numbers: [23, 40, 19] Generated Node #0,1: 44:[23, 40, 19] Operation: 93-74=19 Exploring Operation: 93-23=70, Resulting Numbers: [74, 40, 70] Generated Node #0,2: 44:[74, 40, 70] Operation: 93-23=70 Moving to Node #0,1 Current State: 44:[23, 40, 19], Operations: ['93-74=19'] Exploring Operation: 40-19=21, Resulting Numbers: [23, 21] Generated Node #0,1,0: 44:[23, 21] Operation: 40-19=21 Exploring Operation: 23+19=42, Resulting Numbers: [40, 42] Generated Node #0,1,1: 44:[40, 42] Operation: 23+19=42 Exploring Operation: 23-19=4, Resulting Numbers: [40, 4] Generated Node #0,1,2: 44:[40, 4] Operation: 23-19=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 44:[23, 21], Operations: ['93-74=19', '40-19=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[93, 23, 74, 40], Operations: [] Exploring Operation: 93-74=19, Resulting Numbers: [23, 40, 19] Generated Node #0,1: 44:[23, 40, 19] Operation: 93-74=19 Moving to Node #0,1 Current State: 44:[23, 40, 19], Operations: ['93-74=19'] Exploring Operation: 40-19=21, Resulting Numbers: [23, 21] Generated Node #0,1,0: 44:[23, 21] Operation: 40-19=21 Moving to Node #0,1,0 Current State: 44:[23, 21], Operations: ['93-74=19', '40-19=21'] Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 5, 86, 22, 84 ]
55
[ "5*22=110", "86-84=2", "110/2=55" ]
Current State: 55:[5, 86, 22, 84], Operations: [] Exploring Operation: 5*22=110, Resulting Numbers: [86, 84, 110] Generated Node #2: [86, 84, 110] from Operation: 5*22=110 Current State: 55:[86, 84, 110], Operations: ['5*22=110'] Exploring Operation: 86-84=2, Resulting Numbers: [110, 2] Generated Node #3: [110, 2] from Operation: 86-84=2 Current State: 55:[110, 2], Operations: ['5*22=110', '86-84=2'] Exploring Operation: 110/2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[5, 86, 22, 84], Operations: [] Exploring Operation: 86-22=64, Resulting Numbers: [5, 84, 64] Generated Node #0,0: 55:[5, 84, 64] Operation: 86-22=64 Exploring Operation: 84-22=62, Resulting Numbers: [5, 86, 62] Generated Node #0,1: 55:[5, 86, 62] Operation: 84-22=62 Exploring Operation: 86-5=81, Resulting Numbers: [22, 84, 81] Generated Node #0,2: 55:[22, 84, 81] Operation: 86-5=81 Exploring Operation: 86-84=2, Resulting Numbers: [5, 22, 2] Generated Node #0,3: 55:[5, 22, 2] Operation: 86-84=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[5, 22, 2], Operations: ['86-84=2'] Exploring Operation: 22*2=44, Resulting Numbers: [5, 44] Generated Node #0,3,0: 55:[5, 44] Operation: 22*2=44 Exploring Operation: 22-2=20, Resulting Numbers: [5, 20] Generated Node #0,3,1: 55:[5, 20] Operation: 22-2=20 Exploring Operation: 22/2=11, Resulting Numbers: [5, 11] Generated Node #0,3,2: 55:[5, 11] Operation: 22/2=11 Exploring Operation: 22-5=17, Resulting Numbers: [2, 17] Generated Node #0,3,3: 55:[2, 17] Operation: 22-5=17 Moving to Node #0,3,2 Current State: 55:[5, 11], Operations: ['86-84=2', '22/2=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[5, 86, 22, 84], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [5, 22, 2] Generated Node #0,3: 55:[5, 22, 2] Operation: 86-84=2 Moving to Node #0,3 Current State: 55:[5, 22, 2], Operations: ['86-84=2'] Exploring Operation: 22/2=11, Resulting Numbers: [5, 11] Generated Node #0,3,2: 55:[5, 11] Operation: 22/2=11 Moving to Node #0,3,2 Current State: 55:[5, 11], Operations: ['86-84=2', '22/2=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 41, 37, 3, 11 ]
32
[ "41-37=4", "11-3=8", "4*8=32" ]
Current State: 32:[41, 37, 3, 11], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [3, 11, 4] Generated Node #2: [3, 11, 4] from Operation: 41-37=4 Current State: 32:[3, 11, 4], Operations: ['41-37=4'] Exploring Operation: 11-3=8, Resulting Numbers: [4, 8] Generated Node #3: [4, 8] from Operation: 11-3=8 Current State: 32:[4, 8], Operations: ['41-37=4', '11-3=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[41, 37, 3, 11], Operations: [] Exploring Operation: 41-11=30, Resulting Numbers: [37, 3, 30] Generated Node #0,0: 32:[37, 3, 30] Operation: 41-11=30 Exploring Operation: 41-37=4, Resulting Numbers: [3, 11, 4] Generated Node #0,1: 32:[3, 11, 4] Operation: 41-37=4 Exploring Operation: 41-3=38, Resulting Numbers: [37, 11, 38] Generated Node #0,2: 32:[37, 11, 38] Operation: 41-3=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[3, 11, 4], Operations: ['41-37=4'] Exploring Operation: 11-3=8, Resulting Numbers: [4, 8] Generated Node #0,1,0: 32:[4, 8] Operation: 11-3=8 Exploring Operation: 3+11=14, Resulting Numbers: [4, 14] Generated Node #0,1,1: 32:[4, 14] Operation: 3+11=14 Exploring Operation: 3*11=33, Resulting Numbers: [4, 33] Generated Node #0,1,2: 32:[4, 33] Operation: 3*11=33 Moving to Node #0,1,0 Current State: 32:[4, 8], Operations: ['41-37=4', '11-3=8'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[41, 37, 3, 11], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [3, 11, 4] Generated Node #0,1: 32:[3, 11, 4] Operation: 41-37=4 Moving to Node #0,1 Current State: 32:[3, 11, 4], Operations: ['41-37=4'] Exploring Operation: 11-3=8, Resulting Numbers: [4, 8] Generated Node #0,1,0: 32:[4, 8] Operation: 11-3=8 Moving to Node #0,1,0 Current State: 32:[4, 8], Operations: ['41-37=4', '11-3=8'] Exploring Operation: 4*8=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 16, 20, 22, 67 ]
59
[ "22-20=2", "16/2=8", "67-8=59" ]
Current State: 59:[16, 20, 22, 67], Operations: [] Exploring Operation: 22-20=2, Resulting Numbers: [16, 67, 2] Generated Node #2: [16, 67, 2] from Operation: 22-20=2 Current State: 59:[16, 67, 2], Operations: ['22-20=2'] Exploring Operation: 16/2=8, Resulting Numbers: [67, 8] Generated Node #3: [67, 8] from Operation: 16/2=8 Current State: 59:[67, 8], Operations: ['22-20=2', '16/2=8'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[16, 20, 22, 67], Operations: [] Exploring Operation: 16+20=36, Resulting Numbers: [22, 67, 36] Generated Node #0,0: 59:[22, 67, 36] Operation: 16+20=36 Exploring Operation: 20+22=42, Resulting Numbers: [16, 67, 42] Generated Node #0,1: 59:[16, 67, 42] Operation: 20+22=42 Exploring Operation: 16+22=38, Resulting Numbers: [20, 67, 38] Generated Node #0,2: 59:[20, 67, 38] Operation: 16+22=38 Moving to Node #0,0 Current State: 59:[22, 67, 36], Operations: ['16+20=36'] Exploring Operation: 22+67=89, Resulting Numbers: [36, 89] Generated Node #0,0,0: 59:[36, 89] Operation: 22+67=89 Exploring Operation: 22+36=58, Resulting Numbers: [67, 58] Generated Node #0,0,1: 59:[67, 58] Operation: 22+36=58 Exploring Operation: 67-22=45, Resulting Numbers: [36, 45] Generated Node #0,0,2: 59:[36, 45] Operation: 67-22=45 Moving to Node #0,1 Current State: 59:[16, 67, 42], Operations: ['20+22=42'] Exploring Operation: 16+42=58, Resulting Numbers: [67, 58] Generated Node #0,1,0: 59:[67, 58] Operation: 16+42=58 Exploring Operation: 67-16=51, Resulting Numbers: [42, 51] Generated Node #0,1,1: 59:[42, 51] Operation: 67-16=51 Exploring Operation: 16+67=83, Resulting Numbers: [42, 83] Generated Node #0,1,2: 59:[42, 83] Operation: 16+67=83 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[67, 58], Operations: ['20+22=42', '16+42=58'] Exploring Operation: 67*58=3886, Resulting Numbers: [3886] 3886,59 unequal: No Solution Exploring Operation: 67+58=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[42, 51], Operations: ['20+22=42', '67-16=51'] Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[42, 83], Operations: ['20+22=42', '16+67=83'] Exploring Operation: 42+83=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 83-42=41, Resulting Numbers: [41] 41,59 unequal: No Solution Exploring Operation: 42*83=3486, Resulting Numbers: [3486] 3486,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 59:[20, 67, 38], Operations: ['16+22=38'] Exploring Operation: 20+67=87, Resulting Numbers: [38, 87] Generated Node #0,2,0: 59:[38, 87] Operation: 20+67=87 Exploring Operation: 67-20=47, Resulting Numbers: [38, 47] Generated Node #0,2,1: 59:[38, 47] Operation: 67-20=47 Exploring Operation: 20+38=58, Resulting Numbers: [67, 58] Generated Node #0,2,2: 59:[67, 58] Operation: 20+38=58 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 59:[67, 58], Operations: ['16+22=38', '20+38=58'] Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 67+58=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 67*58=3886, Resulting Numbers: [3886] 3886,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 59:[38, 47], Operations: ['16+22=38', '67-20=47'] Exploring Operation: 38+47=85, Resulting Numbers: [85] 85,59 unequal: No Solution Exploring Operation: 38*47=1786, Resulting Numbers: [1786] 1786,59 unequal: No Solution Exploring Operation: 47-38=9, Resulting Numbers: [9] 9,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 59:[38, 87], Operations: ['16+22=38', '20+67=87'] Exploring Operation: 38+87=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 38*87=3306, Resulting Numbers: [3306] 3306,59 unequal: No Solution Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 59:[67, 58], Operations: ['16+20=36', '22+36=58'] Exploring Operation: 67*58=3886, Resulting Numbers: [3886] 3886,59 unequal: No Solution Exploring Operation: 67-58=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 67+58=125, Resulting Numbers: [125] 125,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[36, 45], Operations: ['16+20=36', '67-22=45'] Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 36+45=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 36*45=1620, Resulting Numbers: [1620] 1620,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[36, 89], Operations: ['16+20=36', '22+67=89'] Exploring Operation: 36*89=3204, Resulting Numbers: [3204] 3204,59 unequal: No Solution Exploring Operation: 36+89=125, Resulting Numbers: [125] 125,59 unequal: No Solution Exploring Operation: 89-36=53, Resulting Numbers: [53] 53,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 24, 10, 63, 22 ]
43
[ "24-22=2", "10*2=20", "63-20=43" ]
Current State: 43:[24, 10, 63, 22], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [10, 63, 2] Generated Node #2: [10, 63, 2] from Operation: 24-22=2 Current State: 43:[10, 63, 2], Operations: ['24-22=2'] Exploring Operation: 10*2=20, Resulting Numbers: [63, 20] Generated Node #3: [63, 20] from Operation: 10*2=20 Current State: 43:[63, 20], Operations: ['24-22=2', '10*2=20'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[24, 10, 63, 22], Operations: [] Exploring Operation: 63-10=53, Resulting Numbers: [24, 22, 53] Generated Node #0,0: 43:[24, 22, 53] Operation: 63-10=53 Exploring Operation: 24+22=46, Resulting Numbers: [10, 63, 46] Generated Node #0,1: 43:[10, 63, 46] Operation: 24+22=46 Exploring Operation: 24+10=34, Resulting Numbers: [63, 22, 34] Generated Node #0,2: 43:[63, 22, 34] Operation: 24+10=34 Exploring Operation: 10+22=32, Resulting Numbers: [24, 63, 32] Generated Node #0,3: 43:[24, 63, 32] Operation: 10+22=32 Exploring Operation: 63-22=41, Resulting Numbers: [24, 10, 41] Generated Node #0,4: 43:[24, 10, 41] Operation: 63-22=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[24, 22, 53], Operations: ['63-10=53'] Exploring Operation: 53-22=31, Resulting Numbers: [24, 31] Generated Node #0,0,0: 43:[24, 31] Operation: 53-22=31 Exploring Operation: 53-24=29, Resulting Numbers: [22, 29] Generated Node #0,0,1: 43:[22, 29] Operation: 53-24=29 Exploring Operation: 24+22=46, Resulting Numbers: [53, 46] Generated Node #0,0,2: 43:[53, 46] Operation: 24+22=46 Exploring Operation: 24-22=2, Resulting Numbers: [53, 2] Generated Node #0,0,3: 43:[53, 2] Operation: 24-22=2 Exploring Operation: 22+53=75, Resulting Numbers: [24, 75] Generated Node #0,0,4: 43:[24, 75] Operation: 22+53=75 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[53, 46], Operations: ['63-10=53', '24+22=46'] Exploring Operation: 53+46=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 53*46=2438, Resulting Numbers: [2438] 2438,43 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[24, 31], Operations: ['63-10=53', '53-22=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,43 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 #0,0,1 Current State: 43:[22, 29], Operations: ['63-10=53', '53-24=29'] Exploring Operation: 22*29=638, Resulting Numbers: [638] 638,43 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 22+29=51, Resulting Numbers: [51] 51,43 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 #0,0,3 Current State: 43:[53, 2], Operations: ['63-10=53', '24-22=2'] Exploring Operation: 53*2=106, Resulting Numbers: [106] 106,43 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,43 unequal: No Solution Exploring Operation: 53+2=55, Resulting Numbers: [55] 55,43 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 #0,0,4 Current State: 43:[24, 75], Operations: ['63-10=53', '22+53=75'] Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,43 unequal: No Solution Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,43 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 #0,2 Current State: 43:[63, 22, 34], Operations: ['24+10=34'] Exploring Operation: 63-22=41, Resulting Numbers: [34, 41] Generated Node #0,2,0: 43:[34, 41] Operation: 63-22=41 Exploring Operation: 34-22=12, Resulting Numbers: [63, 12] Generated Node #0,2,1: 43:[63, 12] Operation: 34-22=12 Exploring Operation: 63+22=85, Resulting Numbers: [34, 85] Generated Node #0,2,2: 43:[34, 85] Operation: 63+22=85 Exploring Operation: 63-34=29, Resulting Numbers: [22, 29] Generated Node #0,2,3: 43:[22, 29] Operation: 63-34=29 Exploring Operation: 22+34=56, Resulting Numbers: [63, 56] Generated Node #0,2,4: 43:[63, 56] Operation: 22+34=56 Moving to Node #0,2,0 Current State: 43:[34, 41], Operations: ['24+10=34', '63-22=41'] Exploring Operation: 34+41=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 34*41=1394, Resulting Numbers: [1394] 1394,43 unequal: No Solution Moving to Node #0,2,4 Current State: 43:[63, 56], Operations: ['24+10=34', '22+34=56'] Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,43 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[22, 29], Operations: ['24+10=34', '63-34=29'] Exploring Operation: 22*29=638, Resulting Numbers: [638] 638,43 unequal: No Solution Exploring Operation: 22+29=51, Resulting Numbers: [51] 51,43 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[63, 12], Operations: ['24+10=34', '34-22=12'] Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 63*12=756, Resulting Numbers: [756] 756,43 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[34, 85], Operations: ['24+10=34', '63+22=85'] Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,43 unequal: No Solution Exploring Operation: 34*85=2890, Resulting Numbers: [2890] 2890,43 unequal: No Solution Exploring Operation: 34+85=119, Resulting Numbers: [119] 119,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[24, 63, 32], Operations: ['10+22=32'] Exploring Operation: 32-24=8, Resulting Numbers: [63, 8] Generated Node #0,3,0: 43:[63, 8] Operation: 32-24=8 Exploring Operation: 63-24=39, Resulting Numbers: [32, 39] Generated Node #0,3,1: 43:[32, 39] Operation: 63-24=39 Exploring Operation: 63-32=31, Resulting Numbers: [24, 31] Generated Node #0,3,2: 43:[24, 31] Operation: 63-32=31 Exploring Operation: 24+32=56, Resulting Numbers: [63, 56] Generated Node #0,3,3: 43:[63, 56] Operation: 24+32=56 Exploring Operation: 24+63=87, Resulting Numbers: [32, 87] Generated Node #0,3,4: 43:[32, 87] Operation: 24+63=87 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[32, 39], Operations: ['10+22=32', '63-24=39'] Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,43 unequal: No Solution Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,43 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,43 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 #0,3,2 Current State: 43:[24, 31], Operations: ['10+22=32', '63-32=31'] Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,43 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 #0,3,3 Current State: 43:[63, 56], Operations: ['10+22=32', '24+32=56'] Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,43 unequal: No Solution Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,43 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 #0,3,0 Current State: 43:[63, 8], Operations: ['10+22=32', '32-24=8'] Exploring Operation: 63-8=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 63+8=71, Resulting Numbers: [71] 71,43 unequal: No Solution Exploring Operation: 63*8=504, Resulting Numbers: [504] 504,43 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 #0,3,4 Current State: 43:[32, 87], Operations: ['10+22=32', '24+63=87'] Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 32+87=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 32*87=2784, Resulting Numbers: [2784] 2784,43 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 #0,4 Current State: 43:[24, 10, 41], Operations: ['63-22=41'] Exploring Operation: 24-10=14, Resulting Numbers: [41, 14] Generated Node #0,4,0: 43:[41, 14] Operation: 24-10=14 Exploring Operation: 24+41=65, Resulting Numbers: [10, 65] Generated Node #0,4,1: 43:[10, 65] Operation: 24+41=65 Exploring Operation: 41-10=31, Resulting Numbers: [24, 31] Generated Node #0,4,2: 43:[24, 31] Operation: 41-10=31 Exploring Operation: 24+10=34, Resulting Numbers: [41, 34] Generated Node #0,4,3: 43:[41, 34] Operation: 24+10=34 Exploring Operation: 10+41=51, Resulting Numbers: [24, 51] Generated Node #0,4,4: 43:[24, 51] Operation: 10+41=51 Moving to Node #0,4,3 Current State: 43:[41, 34], Operations: ['63-22=41', '24+10=34'] Exploring Operation: 41+34=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 41-34=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 41*34=1394, Resulting Numbers: [1394] 1394,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[24, 51], Operations: ['63-22=41', '10+41=51'] Exploring Operation: 24+51=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 24*51=1224, Resulting Numbers: [1224] 1224,43 unequal: No Solution Moving to Node #0,4,0 Current State: 43:[41, 14], Operations: ['63-22=41', '24-10=14'] Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[24, 31], Operations: ['63-22=41', '41-10=31'] Exploring Operation: 24*31=744, Resulting Numbers: [744] 744,43 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 24+31=55, Resulting Numbers: [55] 55,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[10, 65], Operations: ['63-22=41', '24+41=65'] Exploring Operation: 10*65=650, Resulting Numbers: [650] 650,43 unequal: No Solution Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,43 unequal: No Solution Exploring Operation: 10+65=75, Resulting Numbers: [75] 75,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[10, 63, 46], Operations: ['24+22=46'] Exploring Operation: 10+63=73, Resulting Numbers: [46, 73] Generated Node #0,1,0: 43:[46, 73] Operation: 10+63=73 Exploring Operation: 63-10=53, Resulting Numbers: [46, 53] Generated Node #0,1,1: 43:[46, 53] Operation: 63-10=53 Exploring Operation: 63-46=17, Resulting Numbers: [10, 17] Generated Node #0,1,2: 43:[10, 17] Operation: 63-46=17 Exploring Operation: 46-10=36, Resulting Numbers: [63, 36] Generated Node #0,1,3: 43:[63, 36] Operation: 46-10=36 Exploring Operation: 10+46=56, Resulting Numbers: [63, 56] Generated Node #0,1,4: 43:[63, 56] Operation: 10+46=56 Moving to Node #0,1,1 Current State: 43:[46, 53], Operations: ['24+22=46', '63-10=53'] Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[63, 36], Operations: ['24+22=46', '46-10=36'] Exploring Operation: 63+36=99, Resulting Numbers: [99] 99,43 unequal: No Solution Exploring Operation: 63*36=2268, Resulting Numbers: [2268] 2268,43 unequal: No Solution Exploring Operation: 63-36=27, Resulting Numbers: [27] 27,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[46, 73], Operations: ['24+22=46', '10+63=73'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 46*73=3358, Resulting Numbers: [3358] 3358,43 unequal: No Solution Exploring Operation: 46+73=119, Resulting Numbers: [119] 119,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[63, 56], Operations: ['24+22=46', '10+46=56'] Exploring Operation: 63+56=119, Resulting Numbers: [119] 119,43 unequal: No Solution Exploring Operation: 63-56=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 63*56=3528, Resulting Numbers: [3528] 3528,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[10, 17], Operations: ['24+22=46', '63-46=17'] Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,43 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 1, 18, 51, 98 ]
29
[ "1*18=18", "98-51=47", "47-18=29" ]
Current State: 29:[1, 18, 51, 98], Operations: [] Exploring Operation: 1*18=18, Resulting Numbers: [51, 98, 18] Generated Node #2: [51, 98, 18] from Operation: 1*18=18 Current State: 29:[51, 98, 18], Operations: ['1*18=18'] Exploring Operation: 98-51=47, Resulting Numbers: [18, 47] Generated Node #3: [18, 47] from Operation: 98-51=47 Current State: 29:[18, 47], Operations: ['1*18=18', '98-51=47'] Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[1, 18, 51, 98], Operations: [] Exploring Operation: 98-51=47, Resulting Numbers: [1, 18, 47] Generated Node #0,0: 29:[1, 18, 47] Operation: 98-51=47 Moving to Node #0,0 Current State: 29:[1, 18, 47], Operations: ['98-51=47'] Exploring Operation: 1+18=19, Resulting Numbers: [47, 19] Generated Node #0,0,0: 29:[47, 19] Operation: 1+18=19 Moving to Node #0,0,0 Current State: 29:[47, 19], Operations: ['98-51=47', '1+18=19'] Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 99, 30, 75, 42 ]
27
[ "75-42=33", "99/33=3", "30-3=27" ]
Current State: 27:[99, 30, 75, 42], Operations: [] Exploring Operation: 75-42=33, Resulting Numbers: [99, 30, 33] Generated Node #2: [99, 30, 33] from Operation: 75-42=33 Current State: 27:[99, 30, 33], Operations: ['75-42=33'] Exploring Operation: 99/33=3, Resulting Numbers: [30, 3] Generated Node #3: [30, 3] from Operation: 99/33=3 Current State: 27:[30, 3], Operations: ['75-42=33', '99/33=3'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[99, 30, 75, 42], Operations: [] Exploring Operation: 99-75=24, Resulting Numbers: [30, 42, 24] Generated Node #0,0: 27:[30, 42, 24] Operation: 99-75=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[30, 42, 24], Operations: ['99-75=24'] Exploring Operation: 42-30=12, Resulting Numbers: [24, 12] Generated Node #0,0,0: 27:[24, 12] Operation: 42-30=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[24, 12], Operations: ['99-75=24', '42-30=12'] Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 75, 15, 78, 8 ]
40
[ "78-75=3", "15*8=120", "120/3=40" ]
Current State: 40:[75, 15, 78, 8], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [15, 8, 3] Generated Node #2: [15, 8, 3] from Operation: 78-75=3 Current State: 40:[15, 8, 3], Operations: ['78-75=3'] Exploring Operation: 15*8=120, Resulting Numbers: [3, 120] Generated Node #3: [3, 120] from Operation: 15*8=120 Current State: 40:[3, 120], Operations: ['78-75=3', '15*8=120'] Exploring Operation: 120/3=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[75, 15, 78, 8], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [15, 8, 3] Generated Node #0,0: 40:[15, 8, 3] Operation: 78-75=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[15, 8, 3], Operations: ['78-75=3'] Exploring Operation: 15/3=5, Resulting Numbers: [8, 5] Generated Node #0,0,0: 40:[8, 5] Operation: 15/3=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[8, 5], Operations: ['78-75=3', '15/3=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[75, 15, 78, 8], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [15, 8, 3] Generated Node #0,0: 40:[15, 8, 3] Operation: 78-75=3 Moving to Node #0,0 Current State: 40:[15, 8, 3], Operations: ['78-75=3'] Exploring Operation: 15/3=5, Resulting Numbers: [8, 5] Generated Node #0,0,0: 40:[8, 5] Operation: 15/3=5 Moving to Node #0,0,0 Current State: 40:[8, 5], Operations: ['78-75=3', '15/3=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 74, 58, 80, 34 ]
42
[ "74*34=2516", "2516-80=2436", "2436/58=42" ]
Current State: 42:[74, 58, 80, 34], Operations: [] Exploring Operation: 74*34=2516, Resulting Numbers: [58, 80, 2516] Generated Node #2: [58, 80, 2516] from Operation: 74*34=2516 Current State: 42:[58, 80, 2516], Operations: ['74*34=2516'] Exploring Operation: 2516-80=2436, Resulting Numbers: [58, 2436] Generated Node #3: [58, 2436] from Operation: 2516-80=2436 Current State: 42:[58, 2436], Operations: ['74*34=2516', '2516-80=2436'] Exploring Operation: 2436/58=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[74, 58, 80, 34], Operations: [] Exploring Operation: 80-58=22, Resulting Numbers: [74, 34, 22] Generated Node #0,0: 42:[74, 34, 22] Operation: 80-58=22 Exploring Operation: 80-74=6, Resulting Numbers: [58, 34, 6] Generated Node #0,1: 42:[58, 34, 6] Operation: 80-74=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[58, 34, 6], Operations: ['80-74=6'] Exploring Operation: 58-34=24, Resulting Numbers: [6, 24] Generated Node #0,1,0: 42:[6, 24] Operation: 58-34=24 Exploring Operation: 58-6=52, Resulting Numbers: [34, 52] Generated Node #0,1,1: 42:[34, 52] Operation: 58-6=52 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[6, 24], Operations: ['80-74=6', '58-34=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[34, 52], Operations: ['80-74=6', '58-6=52'] Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,42 unequal: No Solution Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[74, 34, 22], Operations: ['80-58=22'] Exploring Operation: 74-34=40, Resulting Numbers: [22, 40] Generated Node #0,0,0: 42:[22, 40] Operation: 74-34=40 Exploring Operation: 74-22=52, Resulting Numbers: [34, 52] Generated Node #0,0,1: 42:[34, 52] Operation: 74-22=52 Moving to Node #0,0,0 Current State: 42:[22, 40], Operations: ['80-58=22', '74-34=40'] Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,42 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,42 unequal: No Solution Moving to Node #0,0,1 Current State: 42:[34, 52], Operations: ['80-58=22', '74-22=52'] Exploring Operation: 52-34=18, Resulting Numbers: [18] 18,42 unequal: No Solution Exploring Operation: 34+52=86, Resulting Numbers: [86] 86,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 73, 6, 78, 74 ]
44
[ "78-73=5", "6*5=30", "74-30=44" ]
Current State: 44:[73, 6, 78, 74], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [6, 74, 5] Generated Node #2: [6, 74, 5] from Operation: 78-73=5 Current State: 44:[6, 74, 5], Operations: ['78-73=5'] Exploring Operation: 6*5=30, Resulting Numbers: [74, 30] Generated Node #3: [74, 30] from Operation: 6*5=30 Current State: 44:[74, 30], Operations: ['78-73=5', '6*5=30'] Exploring Operation: 74-30=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[73, 6, 78, 74], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [73, 74, 13] Generated Node #0,0: 44:[73, 74, 13] Operation: 78/6=13 Exploring Operation: 78-73=5, Resulting Numbers: [6, 74, 5] Generated Node #0,1: 44:[6, 74, 5] Operation: 78-73=5 Exploring Operation: 74-73=1, Resulting Numbers: [6, 78, 1] Generated Node #0,2: 44:[6, 78, 1] Operation: 74-73=1 Exploring Operation: 78-74=4, Resulting Numbers: [73, 6, 4] Generated Node #0,3: 44:[73, 6, 4] Operation: 78-74=4 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[73, 6, 4], Operations: ['78-74=4'] Exploring Operation: 73-6=67, Resulting Numbers: [4, 67] Generated Node #0,3,0: 44:[4, 67] Operation: 73-6=67 Exploring Operation: 6+4=10, Resulting Numbers: [73, 10] Generated Node #0,3,1: 44:[73, 10] Operation: 6+4=10 Exploring Operation: 73-4=69, Resulting Numbers: [6, 69] Generated Node #0,3,2: 44:[6, 69] Operation: 73-4=69 Exploring Operation: 6-4=2, Resulting Numbers: [73, 2] Generated Node #0,3,3: 44:[73, 2] Operation: 6-4=2 Moving to Node #0,3,0 Current State: 44:[4, 67], Operations: ['78-74=4', '73-6=67'] Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,44 unequal: No Solution Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,44 unequal: No Solution Moving to Node #0,3,2 Current State: 44:[6, 69], Operations: ['78-74=4', '73-4=69'] Exploring Operation: 6+69=75, Resulting Numbers: [75] 75,44 unequal: No Solution Exploring Operation: 6*69=414, Resulting Numbers: [414] 414,44 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[73, 2], Operations: ['78-74=4', '6-4=2'] Exploring Operation: 73+2=75, Resulting Numbers: [75] 75,44 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,44 unequal: No Solution Exploring Operation: 73*2=146, Resulting Numbers: [146] 146,44 unequal: No Solution Moving to Node #0,3,1 Current State: 44:[73, 10], Operations: ['78-74=4', '6+4=10'] Exploring Operation: 73*10=730, Resulting Numbers: [730] 730,44 unequal: No Solution Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 73+10=83, Resulting Numbers: [83] 83,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[6, 74, 5], Operations: ['78-73=5'] Exploring Operation: 74-6=68, Resulting Numbers: [5, 68] Generated Node #0,1,0: 44:[5, 68] Operation: 74-6=68 Exploring Operation: 6+5=11, Resulting Numbers: [74, 11] Generated Node #0,1,1: 44:[74, 11] Operation: 6+5=11 Exploring Operation: 74-5=69, Resulting Numbers: [6, 69] Generated Node #0,1,2: 44:[6, 69] Operation: 74-5=69 Exploring Operation: 6-5=1, Resulting Numbers: [74, 1] Generated Node #0,1,3: 44:[74, 1] Operation: 6-5=1 Moving to Node #0,1,0 Current State: 44:[5, 68], Operations: ['78-73=5', '74-6=68'] Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 5*68=340, Resulting Numbers: [340] 340,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[6, 69], Operations: ['78-73=5', '74-5=69'] Exploring Operation: 6*69=414, Resulting Numbers: [414] 414,44 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 6+69=75, Resulting Numbers: [75] 75,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[74, 11], Operations: ['78-73=5', '6+5=11'] Exploring Operation: 74*11=814, Resulting Numbers: [814] 814,44 unequal: No Solution Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,44 unequal: No Solution Exploring Operation: 74+11=85, Resulting Numbers: [85] 85,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[74, 1], Operations: ['78-73=5', '6-5=1'] Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,44 unequal: No Solution Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 74+1=75, Resulting Numbers: [75] 75,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[6, 78, 1], Operations: ['74-73=1'] Exploring Operation: 6-1=5, Resulting Numbers: [78, 5] Generated Node #0,2,0: 44:[78, 5] Operation: 6-1=5 Exploring Operation: 78/6=13, Resulting Numbers: [1, 13] Generated Node #0,2,1: 44:[1, 13] Operation: 78/6=13 Exploring Operation: 78-1=77, Resulting Numbers: [6, 77] Generated Node #0,2,2: 44:[6, 77] Operation: 78-1=77 Exploring Operation: 78-6=72, Resulting Numbers: [1, 72] Generated Node #0,2,3: 44:[1, 72] Operation: 78-6=72 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[1, 13], Operations: ['74-73=1', '78/6=13'] Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 1*13=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[1, 72], Operations: ['74-73=1', '78-6=72'] Exploring Operation: 1+72=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 1*72=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,44 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[78, 5], Operations: ['74-73=1', '6-1=5'] Exploring Operation: 78*5=390, Resulting Numbers: [390] 390,44 unequal: No Solution Exploring Operation: 78+5=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 78-5=73, Resulting Numbers: [73] 73,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[6, 77], Operations: ['74-73=1', '78-1=77'] Exploring Operation: 6+77=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 6*77=462, Resulting Numbers: [462] 462,44 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[73, 74, 13], Operations: ['78/6=13'] Exploring Operation: 73+13=86, Resulting Numbers: [74, 86] Generated Node #0,0,0: 44:[74, 86] Operation: 73+13=86 Exploring Operation: 74-73=1, Resulting Numbers: [13, 1] Generated Node #0,0,1: 44:[13, 1] Operation: 74-73=1 Exploring Operation: 73-13=60, Resulting Numbers: [74, 60] Generated Node #0,0,2: 44:[74, 60] Operation: 73-13=60 Exploring Operation: 74-13=61, Resulting Numbers: [73, 61] Generated Node #0,0,3: 44:[73, 61] Operation: 74-13=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[13, 1], Operations: ['78/6=13', '74-73=1'] Exploring Operation: 13*1=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,44 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 13+1=14, Resulting Numbers: [14] 14,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 44:[74, 60], Operations: ['78/6=13', '73-13=60'] Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,44 unequal: No Solution Exploring Operation: 74*60=4440, Resulting Numbers: [4440] 4440,44 unequal: No Solution Exploring Operation: 74+60=134, Resulting Numbers: [134] 134,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 44:[73, 61], Operations: ['78/6=13', '74-13=61'] Exploring Operation: 73-61=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 73+61=134, Resulting Numbers: [134] 134,44 unequal: No Solution Exploring Operation: 73*61=4453, Resulting Numbers: [4453] 4453,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[74, 86], Operations: ['78/6=13', '73+13=86'] Exploring Operation: 74*86=6364, Resulting Numbers: [6364] 6364,44 unequal: No Solution Exploring Operation: 74+86=160, Resulting Numbers: [160] 160,44 unequal: No Solution Exploring Operation: 86-74=12, Resulting Numbers: [12] 12,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 13, 5, 72, 34 ]
75
[ "5+34=39", "39/13=3", "72+3=75" ]
Current State: 75:[13, 5, 72, 34], Operations: [] Exploring Operation: 5+34=39, Resulting Numbers: [13, 72, 39] Generated Node #2: [13, 72, 39] from Operation: 5+34=39 Current State: 75:[13, 72, 39], Operations: ['5+34=39'] Exploring Operation: 39/13=3, Resulting Numbers: [72, 3] Generated Node #3: [72, 3] from Operation: 39/13=3 Current State: 75:[72, 3], Operations: ['5+34=39', '39/13=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[13, 5, 72, 34], Operations: [] Exploring Operation: 34-13=21, Resulting Numbers: [5, 72, 21] Generated Node #0,0: 75:[5, 72, 21] Operation: 34-13=21 Moving to Node #0,0 Current State: 75:[5, 72, 21], Operations: ['34-13=21'] Exploring Operation: 5+21=26, Resulting Numbers: [72, 26] Generated Node #0,0,0: 75:[72, 26] Operation: 5+21=26 Moving to Node #0,0,0 Current State: 75:[72, 26], Operations: ['34-13=21', '5+21=26'] Exploring Operation: 72-26=46, Resulting Numbers: [46] 46,75 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 84, 44, 48, 10 ]
14
[ "48-44=4", "10-4=6", "84/6=14" ]
Current State: 14:[84, 44, 48, 10], Operations: [] Exploring Operation: 48-44=4, Resulting Numbers: [84, 10, 4] Generated Node #2: [84, 10, 4] from Operation: 48-44=4 Current State: 14:[84, 10, 4], Operations: ['48-44=4'] Exploring Operation: 10-4=6, Resulting Numbers: [84, 6] Generated Node #3: [84, 6] from Operation: 10-4=6 Current State: 14:[84, 6], Operations: ['48-44=4', '10-4=6'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[84, 44, 48, 10], Operations: [] Exploring Operation: 84-44=40, Resulting Numbers: [48, 10, 40] Generated Node #0,0: 14:[48, 10, 40] Operation: 84-44=40 Exploring Operation: 84-48=36, Resulting Numbers: [44, 10, 36] Generated Node #0,1: 14:[44, 10, 36] Operation: 84-48=36 Moving to Node #0,1 Current State: 14:[44, 10, 36], Operations: ['84-48=36'] Exploring Operation: 44-10=34, Resulting Numbers: [36, 34] Generated Node #0,1,0: 14:[36, 34] Operation: 44-10=34 Exploring Operation: 44-36=8, Resulting Numbers: [10, 8] Generated Node #0,1,1: 14:[10, 8] Operation: 44-36=8 Moving to Node #0,0 Current State: 14:[48, 10, 40], Operations: ['84-44=40'] Exploring Operation: 48-40=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 14:[10, 8] Operation: 48-40=8 Exploring Operation: 40/10=4, Resulting Numbers: [48, 4] Generated Node #0,0,1: 14:[48, 4] Operation: 40/10=4 Moving to Node #0,1,1 Current State: 14:[10, 8], Operations: ['84-48=36', '44-36=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[10, 8], Operations: ['84-44=40', '48-40=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[48, 4], Operations: ['84-44=40', '40/10=4'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,14 unequal: No Solution Exploring Operation: 48-4=44, Resulting Numbers: [44] 44,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[36, 34], Operations: ['84-48=36', '44-10=34'] Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,14 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 65, 2, 52, 7 ]
17
[ "65+2=67", "52+67=119", "119/7=17" ]
Current State: 17:[65, 2, 52, 7], Operations: [] Exploring Operation: 65+2=67, Resulting Numbers: [52, 7, 67] Generated Node #2: [52, 7, 67] from Operation: 65+2=67 Current State: 17:[52, 7, 67], Operations: ['65+2=67'] Exploring Operation: 52+67=119, Resulting Numbers: [7, 119] Generated Node #3: [7, 119] from Operation: 52+67=119 Current State: 17:[7, 119], Operations: ['65+2=67', '52+67=119'] Exploring Operation: 119/7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[65, 2, 52, 7], Operations: [] Exploring Operation: 65-52=13, Resulting Numbers: [2, 7, 13] Generated Node #0,0: 17:[2, 7, 13] Operation: 65-52=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[2, 7, 13], Operations: ['65-52=13'] Exploring Operation: 2*7=14, Resulting Numbers: [13, 14] Generated Node #0,0,0: 17:[13, 14] Operation: 2*7=14 Moving to Node #0,0,0 Current State: 17:[13, 14], Operations: ['65-52=13', '2*7=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 95, 84, 19 ]
34
[ "10*95=950", "950/19=50", "84-50=34" ]
Current State: 34:[10, 95, 84, 19], Operations: [] Exploring Operation: 10*95=950, Resulting Numbers: [84, 19, 950] Generated Node #2: [84, 19, 950] from Operation: 10*95=950 Current State: 34:[84, 19, 950], Operations: ['10*95=950'] Exploring Operation: 950/19=50, Resulting Numbers: [84, 50] Generated Node #3: [84, 50] from Operation: 950/19=50 Current State: 34:[84, 50], Operations: ['10*95=950', '950/19=50'] Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[10, 95, 84, 19], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [10, 84, 5] Generated Node #0,0: 34:[10, 84, 5] Operation: 95/19=5 Exploring Operation: 95-84=11, Resulting Numbers: [10, 19, 11] Generated Node #0,1: 34:[10, 19, 11] Operation: 95-84=11 Exploring Operation: 95-19=76, Resulting Numbers: [10, 84, 76] Generated Node #0,2: 34:[10, 84, 76] Operation: 95-19=76 Exploring Operation: 84-19=65, Resulting Numbers: [10, 95, 65] Generated Node #0,3: 34:[10, 95, 65] Operation: 84-19=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[10, 19, 11], Operations: ['95-84=11'] Exploring Operation: 10+19=29, Resulting Numbers: [11, 29] Generated Node #0,1,0: 34:[11, 29] Operation: 10+19=29 Exploring Operation: 10+11=21, Resulting Numbers: [19, 21] Generated Node #0,1,1: 34:[19, 21] Operation: 10+11=21 Exploring Operation: 19+11=30, Resulting Numbers: [10, 30] Generated Node #0,1,2: 34:[10, 30] Operation: 19+11=30 Exploring Operation: 11-10=1, Resulting Numbers: [19, 1] Generated Node #0,1,3: 34:[19, 1] Operation: 11-10=1 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 34:[19, 1], Operations: ['95-84=11', '11-10=1'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,34 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,34 unequal: No Solution No 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: 34:[19, 21], Operations: ['95-84=11', '10+11=21'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 19*21=399, Resulting Numbers: [399] 399,34 unequal: No Solution No 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: 34:[11, 29], Operations: ['95-84=11', '10+19=29'] Exploring Operation: 11*29=319, Resulting Numbers: [319] 319,34 unequal: No Solution Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,34 unequal: No Solution No 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: 34:[10, 30], Operations: ['95-84=11', '19+11=30'] Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,34 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,34 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: 34:[10, 84, 5], Operations: ['95/19=5'] Exploring Operation: 10/5=2, Resulting Numbers: [84, 2] Generated Node #0,0,0: 34:[84, 2] Operation: 10/5=2 Exploring Operation: 84-10=74, Resulting Numbers: [5, 74] Generated Node #0,0,1: 34:[5, 74] Operation: 84-10=74 Exploring Operation: 10+5=15, Resulting Numbers: [84, 15] Generated Node #0,0,2: 34:[84, 15] Operation: 10+5=15 Exploring Operation: 84-5=79, Resulting Numbers: [10, 79] Generated Node #0,0,3: 34:[10, 79] Operation: 84-5=79 Moving to Node #0,0,1 Current State: 34:[5, 74], Operations: ['95/19=5', '84-10=74'] Exploring Operation: 5+74=79, Resulting Numbers: [79] 79,34 unequal: No Solution Exploring Operation: 5*74=370, Resulting Numbers: [370] 370,34 unequal: No Solution Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[84, 2], Operations: ['95/19=5', '10/5=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,34 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,34 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,34 unequal: No Solution Moving to Node #0,0,3 Current State: 34:[10, 79], Operations: ['95/19=5', '84-5=79'] Exploring Operation: 10+79=89, Resulting Numbers: [89] 89,34 unequal: No Solution Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,34 unequal: No Solution Exploring Operation: 10*79=790, Resulting Numbers: [790] 790,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[84, 15], Operations: ['95/19=5', '10+5=15'] Exploring Operation: 84-15=69, Resulting Numbers: [69] 69,34 unequal: No Solution Exploring Operation: 84+15=99, Resulting Numbers: [99] 99,34 unequal: No Solution Exploring Operation: 84*15=1260, Resulting Numbers: [1260] 1260,34 unequal: No Solution No 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: 34:[10, 84, 76], Operations: ['95-19=76'] Exploring Operation: 84-10=74, Resulting Numbers: [76, 74] Generated Node #0,2,0: 34:[76, 74] Operation: 84-10=74 Exploring Operation: 10+84=94, Resulting Numbers: [76, 94] Generated Node #0,2,1: 34:[76, 94] Operation: 10+84=94 Exploring Operation: 84-76=8, Resulting Numbers: [10, 8] Generated Node #0,2,2: 34:[10, 8] Operation: 84-76=8 Exploring Operation: 76-10=66, Resulting Numbers: [84, 66] Generated Node #0,2,3: 34:[84, 66] Operation: 76-10=66 Moving to Node #0,2,2 Current State: 34:[10, 8], Operations: ['95-19=76', '84-76=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,34 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,34 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[84, 66], Operations: ['95-19=76', '76-10=66'] Exploring Operation: 84+66=150, Resulting Numbers: [150] 150,34 unequal: No Solution Exploring Operation: 84*66=5544, Resulting Numbers: [5544] 5544,34 unequal: No Solution Exploring Operation: 84-66=18, Resulting Numbers: [18] 18,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[76, 74], Operations: ['95-19=76', '84-10=74'] Exploring Operation: 76-74=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 76+74=150, Resulting Numbers: [150] 150,34 unequal: No Solution Exploring Operation: 76*74=5624, Resulting Numbers: [5624] 5624,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[76, 94], Operations: ['95-19=76', '10+84=94'] Exploring Operation: 76+94=170, Resulting Numbers: [170] 170,34 unequal: No Solution Exploring Operation: 76*94=7144, Resulting Numbers: [7144] 7144,34 unequal: No Solution Exploring Operation: 94-76=18, Resulting Numbers: [18] 18,34 unequal: No Solution No 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: 34:[10, 95, 65], Operations: ['84-19=65'] Exploring Operation: 65-10=55, Resulting Numbers: [95, 55] Generated Node #0,3,0: 34:[95, 55] Operation: 65-10=55 Exploring Operation: 10+95=105, Resulting Numbers: [65, 105] Generated Node #0,3,1: 34:[65, 105] Operation: 10+95=105 Exploring Operation: 95-65=30, Resulting Numbers: [10, 30] Generated Node #0,3,2: 34:[10, 30] Operation: 95-65=30 Exploring Operation: 95-10=85, Resulting Numbers: [65, 85] Generated Node #0,3,3: 34:[65, 85] Operation: 95-10=85 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 34:[10, 30], Operations: ['84-19=65', '95-65=30'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,34 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,34 unequal: No Solution No 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: 34:[95, 55], Operations: ['84-19=65', '65-10=55'] Exploring Operation: 95*55=5225, Resulting Numbers: [5225] 5225,34 unequal: No Solution Exploring Operation: 95-55=40, Resulting Numbers: [40] 40,34 unequal: No Solution Exploring Operation: 95+55=150, Resulting Numbers: [150] 150,34 unequal: No Solution No 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: 34:[65, 85], Operations: ['84-19=65', '95-10=85'] Exploring Operation: 65*85=5525, Resulting Numbers: [5525] 5525,34 unequal: No Solution Exploring Operation: 85-65=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 65+85=150, Resulting Numbers: [150] 150,34 unequal: No Solution No 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: 34:[65, 105], Operations: ['84-19=65', '10+95=105'] Exploring Operation: 65*105=6825, Resulting Numbers: [6825] 6825,34 unequal: No Solution Exploring Operation: 65+105=170, Resulting Numbers: [170] 170,34 unequal: No Solution Exploring Operation: 105-65=40, Resulting Numbers: [40] 40,34 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
[ 55, 30, 3, 28 ]
93
[ "55+28=83", "30/3=10", "83+10=93" ]
Current State: 93:[55, 30, 3, 28], Operations: [] Exploring Operation: 55+28=83, Resulting Numbers: [30, 3, 83] Generated Node #2: [30, 3, 83] from Operation: 55+28=83 Current State: 93:[30, 3, 83], Operations: ['55+28=83'] Exploring Operation: 30/3=10, Resulting Numbers: [83, 10] Generated Node #3: [83, 10] from Operation: 30/3=10 Current State: 93:[83, 10], Operations: ['55+28=83', '30/3=10'] Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[55, 30, 3, 28], Operations: [] Exploring Operation: 55-28=27, Resulting Numbers: [30, 3, 27] Generated Node #0,0: 93:[30, 3, 27] Operation: 55-28=27 Exploring Operation: 55-3=52, Resulting Numbers: [30, 28, 52] Generated Node #0,1: 93:[30, 28, 52] Operation: 55-3=52 Exploring Operation: 55-30=25, Resulting Numbers: [3, 28, 25] Generated Node #0,2: 93:[3, 28, 25] Operation: 55-30=25 Exploring Operation: 55+28=83, Resulting Numbers: [30, 3, 83] Generated Node #0,3: 93:[30, 3, 83] Operation: 55+28=83 Exploring Operation: 55+30=85, Resulting Numbers: [3, 28, 85] Generated Node #0,4: 93:[3, 28, 85] Operation: 55+30=85 Moving to Node #0,0 Current State: 93:[30, 3, 27], Operations: ['55-28=27'] Exploring Operation: 27/3=9, Resulting Numbers: [30, 9] Generated Node #0,0,0: 93:[30, 9] Operation: 27/3=9 Exploring Operation: 30+3=33, Resulting Numbers: [27, 33] Generated Node #0,0,1: 93:[27, 33] Operation: 30+3=33 Exploring Operation: 30*3=90, Resulting Numbers: [27, 90] Generated Node #0,0,2: 93:[27, 90] Operation: 30*3=90 Exploring Operation: 3+27=30, Resulting Numbers: [30, 30] Generated Node #0,0,3: 93:[30, 30] Operation: 3+27=30 Exploring Operation: 30-27=3, Resulting Numbers: [3, 3] Generated Node #0,0,4: 93:[3, 3] Operation: 30-27=3 Moving to Node #0,2 Current State: 93:[3, 28, 25], Operations: ['55-30=25'] Exploring Operation: 3+28=31, Resulting Numbers: [25, 31] Generated Node #0,2,0: 93:[25, 31] Operation: 3+28=31 Exploring Operation: 28-25=3, Resulting Numbers: [3, 3] Generated Node #0,2,1: 93:[3, 3] Operation: 28-25=3 Exploring Operation: 3+25=28, Resulting Numbers: [28, 28] Generated Node #0,2,2: 93:[28, 28] Operation: 3+25=28 Exploring Operation: 25-3=22, Resulting Numbers: [28, 22] Generated Node #0,2,3: 93:[28, 22] Operation: 25-3=22 Exploring Operation: 28-3=25, Resulting Numbers: [25, 25] Generated Node #0,2,4: 93:[25, 25] Operation: 28-3=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[3, 3], Operations: ['55-30=25', '28-25=3'] Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,93 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[25, 31], Operations: ['55-30=25', '3+28=31'] Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[28, 28], Operations: ['55-30=25', '3+25=28'] Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,93 unequal: No Solution Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,93 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[28, 22], Operations: ['55-30=25', '25-3=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 93:[25, 25], Operations: ['55-30=25', '28-3=25'] Exploring Operation: 25/25=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,93 unequal: No Solution Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,93 unequal: No Solution Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,93 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: 93:[30, 3, 83], Operations: ['55+28=83'] Exploring Operation: 30*3=90, Resulting Numbers: [83, 90] Generated Node #0,3,0: 93:[83, 90] Operation: 30*3=90 Exploring Operation: 30-3=27, Resulting Numbers: [83, 27] Generated Node #0,3,1: 93:[83, 27] Operation: 30-3=27 Exploring Operation: 30+3=33, Resulting Numbers: [83, 33] Generated Node #0,3,2: 93:[83, 33] Operation: 30+3=33 Exploring Operation: 3+83=86, Resulting Numbers: [30, 86] Generated Node #0,3,3: 93:[30, 86] Operation: 3+83=86 Exploring Operation: 83-3=80, Resulting Numbers: [30, 80] Generated Node #0,3,4: 93:[30, 80] Operation: 83-3=80 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 93:[30, 86], Operations: ['55+28=83', '3+83=86'] Exploring Operation: 30*86=2580, Resulting Numbers: [2580] 2580,93 unequal: No Solution Exploring Operation: 30+86=116, Resulting Numbers: [116] 116,93 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 93:[83, 33], Operations: ['55+28=83', '30+3=33'] Exploring Operation: 83+33=116, Resulting Numbers: [116] 116,93 unequal: No Solution Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 83*33=2739, Resulting Numbers: [2739] 2739,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 93:[83, 90], Operations: ['55+28=83', '30*3=90'] Exploring Operation: 83+90=173, Resulting Numbers: [173] 173,93 unequal: No Solution Exploring Operation: 83*90=7470, Resulting Numbers: [7470] 7470,93 unequal: No Solution Exploring Operation: 90-83=7, Resulting Numbers: [7] 7,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 93:[83, 27], Operations: ['55+28=83', '30-3=27'] Exploring Operation: 83*27=2241, Resulting Numbers: [2241] 2241,93 unequal: No Solution Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,93 unequal: No Solution Exploring Operation: 83+27=110, Resulting Numbers: [110] 110,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 93:[30, 80], Operations: ['55+28=83', '83-3=80'] Exploring Operation: 30*80=2400, Resulting Numbers: [2400] 2400,93 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 30+80=110, Resulting Numbers: [110] 110,93 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: 93:[3, 28, 85], Operations: ['55+30=85'] Exploring Operation: 3+85=88, Resulting Numbers: [28, 88] Generated Node #0,4,0: 93:[28, 88] Operation: 3+85=88 Exploring Operation: 3*28=84, Resulting Numbers: [85, 84] Generated Node #0,4,1: 93:[85, 84] Operation: 3*28=84 Exploring Operation: 3+28=31, Resulting Numbers: [85, 31] Generated Node #0,4,2: 93:[85, 31] Operation: 3+28=31 Exploring Operation: 28-3=25, Resulting Numbers: [85, 25] Generated Node #0,4,3: 93:[85, 25] Operation: 28-3=25 Exploring Operation: 85-3=82, Resulting Numbers: [28, 82] Generated Node #0,4,4: 93:[28, 82] Operation: 85-3=82 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 93:[28, 88], Operations: ['55+30=85', '3+85=88'] Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 28*88=2464, Resulting Numbers: [2464] 2464,93 unequal: No Solution Exploring Operation: 28+88=116, Resulting Numbers: [116] 116,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 93:[85, 31], Operations: ['55+30=85', '3+28=31'] Exploring Operation: 85+31=116, Resulting Numbers: [116] 116,93 unequal: No Solution Exploring Operation: 85-31=54, Resulting Numbers: [54] 54,93 unequal: No Solution Exploring Operation: 85*31=2635, Resulting Numbers: [2635] 2635,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 93:[85, 25], Operations: ['55+30=85', '28-3=25'] Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 85*25=2125, Resulting Numbers: [2125] 2125,93 unequal: No Solution Exploring Operation: 85+25=110, Resulting Numbers: [110] 110,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 93:[28, 82], Operations: ['55+30=85', '85-3=82'] Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,93 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 93:[85, 84], Operations: ['55+30=85', '3*28=84'] Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 85+84=169, Resulting Numbers: [169] 169,93 unequal: No Solution Exploring Operation: 85*84=7140, Resulting Numbers: [7140] 7140,93 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: 93:[30, 28, 52], Operations: ['55-3=52'] Exploring Operation: 30-28=2, Resulting Numbers: [52, 2] Generated Node #0,1,0: 93:[52, 2] Operation: 30-28=2 Exploring Operation: 52-30=22, Resulting Numbers: [28, 22] Generated Node #0,1,1: 93:[28, 22] Operation: 52-30=22 Exploring Operation: 28+52=80, Resulting Numbers: [30, 80] Generated Node #0,1,2: 93:[30, 80] Operation: 28+52=80 Exploring Operation: 30+52=82, Resulting Numbers: [28, 82] Generated Node #0,1,3: 93:[28, 82] Operation: 30+52=82 Exploring Operation: 52-28=24, Resulting Numbers: [30, 24] Generated Node #0,1,4: 93:[30, 24] Operation: 52-28=24 Moving to Node #0,0,4 Current State: 93:[3, 3], Operations: ['55-28=27', '30-27=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,93 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[30, 30], Operations: ['55-28=27', '3+27=30'] Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,93 unequal: No Solution Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[27, 33], Operations: ['55-28=27', '30+3=33'] Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,93 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,93 unequal: No Solution Exploring Operation: 27*33=891, Resulting Numbers: [891] 891,93 unequal: No Solution Moving to Node #0,0,2 Current State: 93:[27, 90], Operations: ['55-28=27', '30*3=90'] Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 27*90=2430, Resulting Numbers: [2430] 2430,93 unequal: No Solution Exploring Operation: 27+90=117, Resulting Numbers: [117] 117,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[30, 9], Operations: ['55-28=27', '27/3=9'] Exploring Operation: 30*9=270, Resulting Numbers: [270] 270,93 unequal: No Solution Exploring Operation: 30+9=39, Resulting Numbers: [39] 39,93 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,93 unequal: No Solution Moving to Node #0,1,4 Current State: 93:[30, 24], Operations: ['55-3=52', '52-28=24'] Exploring Operation: 30*24=720, Resulting Numbers: [720] 720,93 unequal: No Solution Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,93 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[28, 22], Operations: ['55-3=52', '52-30=22'] Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,93 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,93 unequal: No Solution Moving to Node #0,1,3 Current State: 93:[28, 82], Operations: ['55-3=52', '30+52=82'] Exploring Operation: 28+82=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 28*82=2296, Resulting Numbers: [2296] 2296,93 unequal: No Solution Exploring Operation: 82-28=54, Resulting Numbers: [54] 54,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[30, 80], Operations: ['55-3=52', '28+52=80'] Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,93 unequal: No Solution Exploring Operation: 30+80=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 30*80=2400, Resulting Numbers: [2400] 2400,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[52, 2], Operations: ['55-3=52', '30-28=2'] Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,93 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,93 unequal: No Solution Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,93 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,93 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 55, 78, 19, 60 ]
56
[ "78-55=23", "19+60=79", "79-23=56" ]
Current State: 56:[55, 78, 19, 60], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [19, 60, 23] Generated Node #2: [19, 60, 23] from Operation: 78-55=23 Current State: 56:[19, 60, 23], Operations: ['78-55=23'] Exploring Operation: 19+60=79, Resulting Numbers: [23, 79] Generated Node #3: [23, 79] from Operation: 19+60=79 Current State: 56:[23, 79], Operations: ['78-55=23', '19+60=79'] Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[55, 78, 19, 60], Operations: [] Exploring Operation: 78-19=59, Resulting Numbers: [55, 60, 59] Generated Node #0,0: 56:[55, 60, 59] Operation: 78-19=59 Exploring Operation: 78-60=18, Resulting Numbers: [55, 19, 18] Generated Node #0,1: 56:[55, 19, 18] Operation: 78-60=18 Moving to Node #0,0 Current State: 56:[55, 60, 59], Operations: ['78-19=59'] Exploring Operation: 60-59=1, Resulting Numbers: [55, 1] Generated Node #0,0,0: 56:[55, 1] Operation: 60-59=1 Exploring Operation: 60-55=5, Resulting Numbers: [59, 5] Generated Node #0,0,1: 56:[59, 5] Operation: 60-55=5 Moving to Node #0,1 Current State: 56:[55, 19, 18], Operations: ['78-60=18'] Exploring Operation: 19+18=37, Resulting Numbers: [55, 37] Generated Node #0,1,0: 56:[55, 37] Operation: 19+18=37 Exploring Operation: 19-18=1, Resulting Numbers: [55, 1] Generated Node #0,1,1: 56:[55, 1] Operation: 19-18=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[55, 1], Operations: ['78-60=18', '19-18=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,56 unequal: No Solution Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[55, 78, 19, 60], Operations: [] Exploring Operation: 78-60=18, Resulting Numbers: [55, 19, 18] Generated Node #0,1: 56:[55, 19, 18] Operation: 78-60=18 Moving to Node #0,1 Current State: 56:[55, 19, 18], Operations: ['78-60=18'] Exploring Operation: 19-18=1, Resulting Numbers: [55, 1] Generated Node #0,1,1: 56:[55, 1] Operation: 19-18=1 Moving to Node #0,1,1 Current State: 56:[55, 1], Operations: ['78-60=18', '19-18=1'] Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 50, 78, 29, 84 ]
32
[ "78-50=28", "84/28=3", "29+3=32" ]
Current State: 32:[50, 78, 29, 84], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [29, 84, 28] Generated Node #2: [29, 84, 28] from Operation: 78-50=28 Current State: 32:[29, 84, 28], Operations: ['78-50=28'] Exploring Operation: 84/28=3, Resulting Numbers: [29, 3] Generated Node #3: [29, 3] from Operation: 84/28=3 Current State: 32:[29, 3], Operations: ['78-50=28', '84/28=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[50, 78, 29, 84], Operations: [] Exploring Operation: 84-50=34, Resulting Numbers: [78, 29, 34] Generated Node #0,0: 32:[78, 29, 34] Operation: 84-50=34 Exploring Operation: 78-50=28, Resulting Numbers: [29, 84, 28] Generated Node #0,1: 32:[29, 84, 28] Operation: 78-50=28 Exploring Operation: 84-78=6, Resulting Numbers: [50, 29, 6] Generated Node #0,2: 32:[50, 29, 6] Operation: 84-78=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[50, 29, 6], Operations: ['84-78=6'] Exploring Operation: 50-6=44, Resulting Numbers: [29, 44] Generated Node #0,2,0: 32:[29, 44] Operation: 50-6=44 Exploring Operation: 29+6=35, Resulting Numbers: [50, 35] Generated Node #0,2,1: 32:[50, 35] Operation: 29+6=35 Exploring Operation: 50-29=21, Resulting Numbers: [6, 21] Generated Node #0,2,2: 32:[6, 21] Operation: 50-29=21 Moving to Node #0,2,2 Current State: 32:[6, 21], Operations: ['84-78=6', '50-29=21'] Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,32 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[29, 44], Operations: ['84-78=6', '50-6=44'] Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 29*44=1276, Resulting Numbers: [1276] 1276,32 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[50, 35], Operations: ['84-78=6', '29+6=35'] Exploring Operation: 50+35=85, Resulting Numbers: [85] 85,32 unequal: No Solution Exploring Operation: 50*35=1750, Resulting Numbers: [1750] 1750,32 unequal: No Solution Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[78, 29, 34], Operations: ['84-50=34'] Exploring Operation: 78-34=44, Resulting Numbers: [29, 44] Generated Node #0,0,0: 32:[29, 44] Operation: 78-34=44 Exploring Operation: 78-29=49, Resulting Numbers: [34, 49] Generated Node #0,0,1: 32:[34, 49] Operation: 78-29=49 Exploring Operation: 34-29=5, Resulting Numbers: [78, 5] Generated Node #0,0,2: 32:[78, 5] Operation: 34-29=5 Moving to Node #0,0,0 Current State: 32:[29, 44], Operations: ['84-50=34', '78-34=44'] Exploring Operation: 29+44=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 29*44=1276, Resulting Numbers: [1276] 1276,32 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[34, 49], Operations: ['84-50=34', '78-29=49'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,32 unequal: No Solution Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[78, 5], Operations: ['84-50=34', '34-29=5'] Exploring Operation: 78+5=83, Resulting Numbers: [83] 83,32 unequal: No Solution Exploring Operation: 78-5=73, Resulting Numbers: [73] 73,32 unequal: No Solution Exploring Operation: 78*5=390, Resulting Numbers: [390] 390,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[29, 84, 28], Operations: ['78-50=28'] Exploring Operation: 84/28=3, Resulting Numbers: [29, 3] Generated Node #0,1,0: 32:[29, 3] Operation: 84/28=3 Exploring Operation: 84-28=56, Resulting Numbers: [29, 56] Generated Node #0,1,1: 32:[29, 56] Operation: 84-28=56 Exploring Operation: 84-29=55, Resulting Numbers: [28, 55] Generated Node #0,1,2: 32:[28, 55] Operation: 84-29=55 Moving to Node #0,1,0 Current State: 32:[29, 3], Operations: ['78-50=28', '84/28=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[50, 78, 29, 84], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [29, 84, 28] Generated Node #0,1: 32:[29, 84, 28] Operation: 78-50=28 Moving to Node #0,1 Current State: 32:[29, 84, 28], Operations: ['78-50=28'] Exploring Operation: 84/28=3, Resulting Numbers: [29, 3] Generated Node #0,1,0: 32:[29, 3] Operation: 84/28=3 Moving to Node #0,1,0 Current State: 32:[29, 3], Operations: ['78-50=28', '84/28=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 47, 4, 12, 2 ]
94
[ "47*12=564", "4+2=6", "564/6=94" ]
Current State: 94:[47, 4, 12, 2], Operations: [] Exploring Operation: 47*12=564, Resulting Numbers: [4, 2, 564] Generated Node #2: [4, 2, 564] from Operation: 47*12=564 Current State: 94:[4, 2, 564], Operations: ['47*12=564'] Exploring Operation: 4+2=6, Resulting Numbers: [564, 6] Generated Node #3: [564, 6] from Operation: 4+2=6 Current State: 94:[564, 6], Operations: ['47*12=564', '4+2=6'] Exploring Operation: 564/6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[47, 4, 12, 2], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [47, 2, 3] Generated Node #0,0: 94:[47, 2, 3] Operation: 12/4=3 Exploring Operation: 12/2=6, Resulting Numbers: [47, 4, 6] Generated Node #0,1: 94:[47, 4, 6] Operation: 12/2=6 Exploring Operation: 12-4=8, Resulting Numbers: [47, 2, 8] Generated Node #0,2: 94:[47, 2, 8] Operation: 12-4=8 Exploring Operation: 4*12=48, Resulting Numbers: [47, 2, 48] Generated Node #0,3: 94:[47, 2, 48] Operation: 4*12=48 Moving to Node #0,0 Current State: 94:[47, 2, 3], Operations: ['12/4=3'] Exploring Operation: 47-2=45, Resulting Numbers: [3, 45] Generated Node #0,0,0: 94:[3, 45] Operation: 47-2=45 Exploring Operation: 3-2=1, Resulting Numbers: [47, 1] Generated Node #0,0,1: 94:[47, 1] Operation: 3-2=1 Exploring Operation: 47+2=49, Resulting Numbers: [3, 49] Generated Node #0,0,2: 94:[3, 49] Operation: 47+2=49 Exploring Operation: 47*2=94, Resulting Numbers: [3, 94] Generated Node #0,0,3: 94:[3, 94] Operation: 47*2=94 Moving to Node #0,3 Current State: 94:[47, 2, 48], Operations: ['4*12=48'] Exploring Operation: 47*2=94, Resulting Numbers: [48, 94] Generated Node #0,3,0: 94:[48, 94] Operation: 47*2=94 Exploring Operation: 48-47=1, Resulting Numbers: [2, 1] Generated Node #0,3,1: 94:[2, 1] Operation: 48-47=1 Exploring Operation: 47+48=95, Resulting Numbers: [2, 95] Generated Node #0,3,2: 94:[2, 95] Operation: 47+48=95 Exploring Operation: 48-2=46, Resulting Numbers: [47, 46] Generated Node #0,3,3: 94:[47, 46] Operation: 48-2=46 Moving to Node #0,2 Current State: 94:[47, 2, 8], Operations: ['12-4=8'] Exploring Operation: 47+2=49, Resulting Numbers: [8, 49] Generated Node #0,2,0: 94:[8, 49] Operation: 47+2=49 Exploring Operation: 47*2=94, Resulting Numbers: [8, 94] Generated Node #0,2,1: 94:[8, 94] Operation: 47*2=94 Exploring Operation: 8/2=4, Resulting Numbers: [47, 4] Generated Node #0,2,2: 94:[47, 4] Operation: 8/2=4 Exploring Operation: 8-2=6, Resulting Numbers: [47, 6] Generated Node #0,2,3: 94:[47, 6] Operation: 8-2=6 Moving to Node #0,1 Current State: 94:[47, 4, 6], Operations: ['12/2=6'] Exploring Operation: 47+6=53, Resulting Numbers: [4, 53] Generated Node #0,1,0: 94:[4, 53] Operation: 47+6=53 Exploring Operation: 6-4=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 94:[47, 2] Operation: 6-4=2 Exploring Operation: 47+4=51, Resulting Numbers: [6, 51] Generated Node #0,1,2: 94:[6, 51] Operation: 47+4=51 Exploring Operation: 47-4=43, Resulting Numbers: [6, 43] Generated Node #0,1,3: 94:[6, 43] Operation: 47-4=43 Moving to Node #0,1,1 Current State: 94:[47, 2], Operations: ['12/2=6', '6-4=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[47, 4, 12, 2], Operations: [] Exploring Operation: 12/2=6, Resulting Numbers: [47, 4, 6] Generated Node #0,1: 94:[47, 4, 6] Operation: 12/2=6 Moving to Node #0,1 Current State: 94:[47, 4, 6], Operations: ['12/2=6'] Exploring Operation: 6-4=2, Resulting Numbers: [47, 2] Generated Node #0,1,1: 94:[47, 2] Operation: 6-4=2 Moving to Node #0,1,1 Current State: 94:[47, 2], Operations: ['12/2=6', '6-4=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.978299
hs_4
sum_heuristic
[ 38, 70, 19, 42 ]
85
[ "38+70=108", "42-19=23", "108-23=85" ]
Current State: 85:[38, 70, 19, 42], Operations: [] Exploring Operation: 38+70=108, Resulting Numbers: [19, 42, 108] Generated Node #2: [19, 42, 108] from Operation: 38+70=108 Current State: 85:[19, 42, 108], Operations: ['38+70=108'] Exploring Operation: 42-19=23, Resulting Numbers: [108, 23] Generated Node #3: [108, 23] from Operation: 42-19=23 Current State: 85:[108, 23], Operations: ['38+70=108', '42-19=23'] Exploring Operation: 108-23=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[38, 70, 19, 42], Operations: [] Exploring Operation: 38-19=19, Resulting Numbers: [70, 42, 19] Generated Node #0,0: 85:[70, 42, 19] Operation: 38-19=19 Exploring Operation: 70-42=28, Resulting Numbers: [38, 19, 28] Generated Node #0,1: 85:[38, 19, 28] Operation: 70-42=28 Exploring Operation: 38+42=80, Resulting Numbers: [70, 19, 80] Generated Node #0,2: 85:[70, 19, 80] Operation: 38+42=80 Exploring Operation: 42-38=4, Resulting Numbers: [70, 19, 4] Generated Node #0,3: 85:[70, 19, 4] Operation: 42-38=4 Exploring Operation: 70-38=32, Resulting Numbers: [19, 42, 32] Generated Node #0,4: 85:[19, 42, 32] Operation: 70-38=32 Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[70, 19, 4], Operations: ['42-38=4'] Exploring Operation: 70+19=89, Resulting Numbers: [4, 89] Generated Node #0,3,0: 85:[4, 89] Operation: 70+19=89 Exploring Operation: 19+4=23, Resulting Numbers: [70, 23] Generated Node #0,3,1: 85:[70, 23] Operation: 19+4=23 Exploring Operation: 70-4=66, Resulting Numbers: [19, 66] Generated Node #0,3,2: 85:[19, 66] Operation: 70-4=66 Exploring Operation: 19-4=15, Resulting Numbers: [70, 15] Generated Node #0,3,3: 85:[70, 15] Operation: 19-4=15 Exploring Operation: 70+4=74, Resulting Numbers: [19, 74] Generated Node #0,3,4: 85:[19, 74] Operation: 70+4=74 Moving to Node #0,3,0 Current State: 85:[4, 89], Operations: ['42-38=4', '70+19=89'] Exploring Operation: 4+89=93, Resulting Numbers: [93] 93,85 unequal: No Solution Exploring Operation: 4*89=356, Resulting Numbers: [356] 356,85 unequal: No Solution Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[38, 70, 19, 42], Operations: [] Exploring Operation: 42-38=4, Resulting Numbers: [70, 19, 4] Generated Node #0,3: 85:[70, 19, 4] Operation: 42-38=4 Moving to Node #0,3 Current State: 85:[70, 19, 4], Operations: ['42-38=4'] Exploring Operation: 70+19=89, Resulting Numbers: [4, 89] Generated Node #0,3,0: 85:[4, 89] Operation: 70+19=89 Moving to Node #0,3,0 Current State: 85:[4, 89], Operations: ['42-38=4', '70+19=89'] Exploring Operation: 89-4=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 1, 99, 39, 36 ]
24
[ "1*99=99", "39+36=75", "99-75=24" ]
Current State: 24:[1, 99, 39, 36], Operations: [] Exploring Operation: 1*99=99, Resulting Numbers: [39, 36, 99] Generated Node #2: [39, 36, 99] from Operation: 1*99=99 Current State: 24:[39, 36, 99], Operations: ['1*99=99'] Exploring Operation: 39+36=75, Resulting Numbers: [99, 75] Generated Node #3: [99, 75] from Operation: 39+36=75 Current State: 24:[99, 75], Operations: ['1*99=99', '39+36=75'] Exploring Operation: 99-75=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[1, 99, 39, 36], Operations: [] Exploring Operation: 39-36=3, Resulting Numbers: [1, 99, 3] Generated Node #0,0: 24:[1, 99, 3] Operation: 39-36=3 Exploring Operation: 99-39=60, Resulting Numbers: [1, 36, 60] Generated Node #0,1: 24:[1, 36, 60] Operation: 99-39=60 Exploring Operation: 99-1=98, Resulting Numbers: [39, 36, 98] Generated Node #0,2: 24:[39, 36, 98] Operation: 99-1=98 Exploring Operation: 99-36=63, Resulting Numbers: [1, 39, 63] Generated Node #0,3: 24:[1, 39, 63] Operation: 99-36=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[1, 36, 60], Operations: ['99-39=60'] Exploring Operation: 1*36=36, Resulting Numbers: [60, 36] Generated Node #0,1,0: 24:[60, 36] Operation: 1*36=36 Exploring Operation: 60-36=24, Resulting Numbers: [1, 24] Generated Node #0,1,1: 24:[1, 24] Operation: 60-36=24 Exploring Operation: 60-1=59, Resulting Numbers: [36, 59] Generated Node #0,1,2: 24:[36, 59] Operation: 60-1=59 Exploring Operation: 36-1=35, Resulting Numbers: [60, 35] Generated Node #0,1,3: 24:[60, 35] Operation: 36-1=35 Moving to Node #0,1,1 Current State: 24:[1, 24], Operations: ['99-39=60', '60-36=24'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[1, 99, 39, 36], Operations: [] Exploring Operation: 99-39=60, Resulting Numbers: [1, 36, 60] Generated Node #0,1: 24:[1, 36, 60] Operation: 99-39=60 Moving to Node #0,1 Current State: 24:[1, 36, 60], Operations: ['99-39=60'] Exploring Operation: 60-36=24, Resulting Numbers: [1, 24] Generated Node #0,1,1: 24:[1, 24] Operation: 60-36=24 Moving to Node #0,1,1 Current State: 24:[1, 24], Operations: ['99-39=60', '60-36=24'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 27, 8, 29, 80 ]
20
[ "29-27=2", "80/8=10", "2*10=20" ]
Current State: 20:[27, 8, 29, 80], Operations: [] Exploring Operation: 29-27=2, Resulting Numbers: [8, 80, 2] Generated Node #2: [8, 80, 2] from Operation: 29-27=2 Current State: 20:[8, 80, 2], Operations: ['29-27=2'] Exploring Operation: 80/8=10, Resulting Numbers: [2, 10] Generated Node #3: [2, 10] from Operation: 80/8=10 Current State: 20:[2, 10], Operations: ['29-27=2', '80/8=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[27, 8, 29, 80], Operations: [] Exploring Operation: 80-27=53, Resulting Numbers: [8, 29, 53] Generated Node #0,0: 20:[8, 29, 53] Operation: 80-27=53 Exploring Operation: 80/8=10, Resulting Numbers: [27, 29, 10] Generated Node #0,1: 20:[27, 29, 10] Operation: 80/8=10 Exploring Operation: 80-29=51, Resulting Numbers: [27, 8, 51] Generated Node #0,2: 20:[27, 8, 51] Operation: 80-29=51 Moving to Node #0,1 Current State: 20:[27, 29, 10], Operations: ['80/8=10'] Exploring Operation: 27-10=17, Resulting Numbers: [29, 17] Generated Node #0,1,0: 20:[29, 17] Operation: 27-10=17 Exploring Operation: 29-10=19, Resulting Numbers: [27, 19] Generated Node #0,1,1: 20:[27, 19] Operation: 29-10=19 Exploring Operation: 29-27=2, Resulting Numbers: [10, 2] Generated Node #0,1,2: 20:[10, 2] Operation: 29-27=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[10, 2], Operations: ['80/8=10', '29-27=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[27, 8, 29, 80], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [27, 29, 10] Generated Node #0,1: 20:[27, 29, 10] Operation: 80/8=10 Moving to Node #0,1 Current State: 20:[27, 29, 10], Operations: ['80/8=10'] Exploring Operation: 29-27=2, Resulting Numbers: [10, 2] Generated Node #0,1,2: 20:[10, 2] Operation: 29-27=2 Moving to Node #0,1,2 Current State: 20:[10, 2], Operations: ['80/8=10', '29-27=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 2, 20, 68, 87 ]
63
[ "68-20=48", "48/2=24", "87-24=63" ]
Current State: 63:[2, 20, 68, 87], Operations: [] Exploring Operation: 68-20=48, Resulting Numbers: [2, 87, 48] Generated Node #2: [2, 87, 48] from Operation: 68-20=48 Current State: 63:[2, 87, 48], Operations: ['68-20=48'] Exploring Operation: 48/2=24, Resulting Numbers: [87, 24] Generated Node #3: [87, 24] from Operation: 48/2=24 Current State: 63:[87, 24], Operations: ['68-20=48', '48/2=24'] Exploring Operation: 87-24=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[2, 20, 68, 87], Operations: [] Exploring Operation: 87-20=67, Resulting Numbers: [2, 68, 67] Generated Node #0,0: 63:[2, 68, 67] Operation: 87-20=67 Exploring Operation: 87-68=19, Resulting Numbers: [2, 20, 19] Generated Node #0,1: 63:[2, 20, 19] Operation: 87-68=19 Moving to Node #0,1 Current State: 63:[2, 20, 19], Operations: ['87-68=19'] Exploring Operation: 2+19=21, Resulting Numbers: [20, 21] Generated Node #0,1,0: 63:[20, 21] Operation: 2+19=21 Exploring Operation: 2+20=22, Resulting Numbers: [19, 22] Generated Node #0,1,1: 63:[19, 22] Operation: 2+20=22 Moving to Node #0,0 Current State: 63:[2, 68, 67], Operations: ['87-20=67'] Exploring Operation: 68-2=66, Resulting Numbers: [67, 66] Generated Node #0,0,0: 63:[67, 66] Operation: 68-2=66 Exploring Operation: 68-67=1, Resulting Numbers: [2, 1] Generated Node #0,0,1: 63:[2, 1] Operation: 68-67=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[2, 1], Operations: ['87-20=67', '68-67=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[67, 66], Operations: ['87-20=67', '68-2=66'] Exploring Operation: 67+66=133, Resulting Numbers: [133] 133,63 unequal: No Solution Exploring Operation: 67-66=1, Resulting Numbers: [1] 1,63 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: 63:[20, 21], Operations: ['87-68=19', '2+19=21'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[19, 22], Operations: ['87-68=19', '2+20=22'] Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,63 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 21, 67, 43, 22 ]
24
[ "22-21=1", "67-43=24", "1*24=24" ]
Current State: 24:[21, 67, 43, 22], Operations: [] Exploring Operation: 22-21=1, Resulting Numbers: [67, 43, 1] Generated Node #2: [67, 43, 1] from Operation: 22-21=1 Current State: 24:[67, 43, 1], Operations: ['22-21=1'] Exploring Operation: 67-43=24, Resulting Numbers: [1, 24] Generated Node #3: [1, 24] from Operation: 67-43=24 Current State: 24:[1, 24], Operations: ['22-21=1', '67-43=24'] Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[21, 67, 43, 22], Operations: [] Exploring Operation: 67-21=46, Resulting Numbers: [43, 22, 46] Generated Node #0,0: 24:[43, 22, 46] Operation: 67-21=46 Exploring Operation: 67-22=45, Resulting Numbers: [21, 43, 45] Generated Node #0,1: 24:[21, 43, 45] Operation: 67-22=45 Exploring Operation: 43-21=22, Resulting Numbers: [67, 22, 22] Generated Node #0,2: 24:[67, 22, 22] Operation: 43-21=22 Exploring Operation: 67-43=24, Resulting Numbers: [21, 22, 24] Generated Node #0,3: 24:[21, 22, 24] Operation: 67-43=24 Exploring Operation: 43-22=21, Resulting Numbers: [21, 67, 21] Generated Node #0,4: 24:[21, 67, 21] Operation: 43-22=21 Moving to Node #0,3 Current State: 24:[21, 22, 24], Operations: ['67-43=24'] Exploring Operation: 24-21=3, Resulting Numbers: [22, 3] Generated Node #0,3,0: 24:[22, 3] Operation: 24-21=3 Exploring Operation: 21+24=45, Resulting Numbers: [22, 45] Generated Node #0,3,1: 24:[22, 45] Operation: 21+24=45 Exploring Operation: 22-21=1, Resulting Numbers: [24, 1] Generated Node #0,3,2: 24:[24, 1] Operation: 22-21=1 Exploring Operation: 24-22=2, Resulting Numbers: [21, 2] Generated Node #0,3,3: 24:[21, 2] Operation: 24-22=2 Exploring Operation: 21+22=43, Resulting Numbers: [24, 43] Generated Node #0,3,4: 24:[24, 43] Operation: 21+22=43 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 24:[24, 1], Operations: ['67-43=24', '22-21=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[21, 67, 43, 22], Operations: [] Exploring Operation: 67-43=24, Resulting Numbers: [21, 22, 24] Generated Node #0,3: 24:[21, 22, 24] Operation: 67-43=24 Moving to Node #0,3 Current State: 24:[21, 22, 24], Operations: ['67-43=24'] Exploring Operation: 22-21=1, Resulting Numbers: [24, 1] Generated Node #0,3,2: 24:[24, 1] Operation: 22-21=1 Moving to Node #0,3,2 Current State: 24:[24, 1], Operations: ['67-43=24', '22-21=1'] Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 51, 15, 93, 53 ]
76
[ "51-15=36", "93-53=40", "36+40=76" ]
Current State: 76:[51, 15, 93, 53], Operations: [] Exploring Operation: 51-15=36, Resulting Numbers: [93, 53, 36] Generated Node #2: [93, 53, 36] from Operation: 51-15=36 Current State: 76:[93, 53, 36], Operations: ['51-15=36'] Exploring Operation: 93-53=40, Resulting Numbers: [36, 40] Generated Node #3: [36, 40] from Operation: 93-53=40 Current State: 76:[36, 40], Operations: ['51-15=36', '93-53=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[51, 15, 93, 53], Operations: [] Exploring Operation: 93-53=40, Resulting Numbers: [51, 15, 40] Generated Node #0,0: 76:[51, 15, 40] Operation: 93-53=40 Exploring Operation: 53-51=2, Resulting Numbers: [15, 93, 2] Generated Node #0,1: 76:[15, 93, 2] Operation: 53-51=2 Exploring Operation: 93-51=42, Resulting Numbers: [15, 53, 42] Generated Node #0,2: 76:[15, 53, 42] Operation: 93-51=42 Moving to Node #0,0 Current State: 76:[51, 15, 40], Operations: ['93-53=40'] Exploring Operation: 51-15=36, Resulting Numbers: [40, 36] Generated Node #0,0,0: 76:[40, 36] Operation: 51-15=36 Exploring Operation: 51+15=66, Resulting Numbers: [40, 66] Generated Node #0,0,1: 76:[40, 66] Operation: 51+15=66 Exploring Operation: 51-40=11, Resulting Numbers: [15, 11] Generated Node #0,0,2: 76:[15, 11] Operation: 51-40=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[40, 36], Operations: ['93-53=40', '51-15=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[51, 15, 93, 53], Operations: [] Exploring Operation: 93-53=40, Resulting Numbers: [51, 15, 40] Generated Node #0,0: 76:[51, 15, 40] Operation: 93-53=40 Moving to Node #0,0 Current State: 76:[51, 15, 40], Operations: ['93-53=40'] Exploring Operation: 51-15=36, Resulting Numbers: [40, 36] Generated Node #0,0,0: 76:[40, 36] Operation: 51-15=36 Moving to Node #0,0,0 Current State: 76:[40, 36], Operations: ['93-53=40', '51-15=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 40, 96, 15, 16 ]
11
[ "40-16=24", "96/24=4", "15-4=11" ]
Current State: 11:[40, 96, 15, 16], Operations: [] Exploring Operation: 40-16=24, Resulting Numbers: [96, 15, 24] Generated Node #2: [96, 15, 24] from Operation: 40-16=24 Current State: 11:[96, 15, 24], Operations: ['40-16=24'] Exploring Operation: 96/24=4, Resulting Numbers: [15, 4] Generated Node #3: [15, 4] from Operation: 96/24=4 Current State: 11:[15, 4], Operations: ['40-16=24', '96/24=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[40, 96, 15, 16], Operations: [] Exploring Operation: 96/16=6, Resulting Numbers: [40, 15, 6] Generated Node #0,0: 11:[40, 15, 6] Operation: 96/16=6 Moving to Node #0,0 Current State: 11:[40, 15, 6], Operations: ['96/16=6'] Exploring Operation: 40-15=25, Resulting Numbers: [6, 25] Generated Node #0,0,0: 11:[6, 25] Operation: 40-15=25 Moving to Node #0,0,0 Current State: 11:[6, 25], Operations: ['96/16=6', '40-15=25'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,11 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 68, 5, 82, 77 ]
67
[ "82-5=77", "77/77=1", "68-1=67" ]
Current State: 67:[68, 5, 82, 77], Operations: [] Exploring Operation: 82-5=77, Resulting Numbers: [68, 77, 77] Generated Node #2: [68, 77, 77] from Operation: 82-5=77 Current State: 67:[68, 77, 77], Operations: ['82-5=77'] Exploring Operation: 77/77=1, Resulting Numbers: [68, 1] Generated Node #3: [68, 1] from Operation: 77/77=1 Current State: 67:[68, 1], Operations: ['82-5=77', '77/77=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[68, 5, 82, 77], Operations: [] Exploring Operation: 77-5=72, Resulting Numbers: [68, 82, 72] Generated Node #0,0: 67:[68, 82, 72] Operation: 77-5=72 Exploring Operation: 68-5=63, Resulting Numbers: [82, 77, 63] Generated Node #0,1: 67:[82, 77, 63] Operation: 68-5=63 Exploring Operation: 82-5=77, Resulting Numbers: [68, 77, 77] Generated Node #0,2: 67:[68, 77, 77] Operation: 82-5=77 Moving to Node #0,0 Current State: 67:[68, 82, 72], Operations: ['77-5=72'] Exploring Operation: 72-68=4, Resulting Numbers: [82, 4] Generated Node #0,0,0: 67:[82, 4] Operation: 72-68=4 Exploring Operation: 82-68=14, Resulting Numbers: [72, 14] Generated Node #0,0,1: 67:[72, 14] Operation: 82-68=14 Exploring Operation: 82-72=10, Resulting Numbers: [68, 10] Generated Node #0,0,2: 67:[68, 10] Operation: 82-72=10 Moving to Node #0,2 Current State: 67:[68, 77, 77], Operations: ['82-5=77'] Exploring Operation: 77/77=1, Resulting Numbers: [68, 1] Generated Node #0,2,0: 67:[68, 1] Operation: 77/77=1 Exploring Operation: 77-68=9, Resulting Numbers: [77, 9] Generated Node #0,2,1: 67:[77, 9] Operation: 77-68=9 Exploring Operation: 77-68=9, Resulting Numbers: [77, 9] Generated Node #0,2,2: 67:[77, 9] Operation: 77-68=9 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[68, 1], Operations: ['82-5=77', '77/77=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[68, 5, 82, 77], Operations: [] Exploring Operation: 82-5=77, Resulting Numbers: [68, 77, 77] Generated Node #0,2: 67:[68, 77, 77] Operation: 82-5=77 Moving to Node #0,2 Current State: 67:[68, 77, 77], Operations: ['82-5=77'] Exploring Operation: 77/77=1, Resulting Numbers: [68, 1] Generated Node #0,2,0: 67:[68, 1] Operation: 77/77=1 Moving to Node #0,2,0 Current State: 67:[68, 1], Operations: ['82-5=77', '77/77=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 19, 25, 68, 1 ]
62
[ "25-19=6", "68*1=68", "68-6=62" ]
Current State: 62:[19, 25, 68, 1], Operations: [] Exploring Operation: 25-19=6, Resulting Numbers: [68, 1, 6] Generated Node #2: [68, 1, 6] from Operation: 25-19=6 Current State: 62:[68, 1, 6], Operations: ['25-19=6'] Exploring Operation: 68*1=68, Resulting Numbers: [6, 68] Generated Node #3: [6, 68] from Operation: 68*1=68 Current State: 62:[6, 68], Operations: ['25-19=6', '68*1=68'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[19, 25, 68, 1], Operations: [] Exploring Operation: 19+25=44, Resulting Numbers: [68, 1, 44] Generated Node #0,0: 62:[68, 1, 44] Operation: 19+25=44 Exploring Operation: 25-19=6, Resulting Numbers: [68, 1, 6] Generated Node #0,1: 62:[68, 1, 6] Operation: 25-19=6 Exploring Operation: 68-19=49, Resulting Numbers: [25, 1, 49] Generated Node #0,2: 62:[25, 1, 49] Operation: 68-19=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[68, 1, 6], Operations: ['25-19=6'] Exploring Operation: 6-1=5, Resulting Numbers: [68, 5] Generated Node #0,1,0: 62:[68, 5] Operation: 6-1=5 Exploring Operation: 68-6=62, Resulting Numbers: [1, 62] Generated Node #0,1,1: 62:[1, 62] Operation: 68-6=62 Exploring Operation: 68-1=67, Resulting Numbers: [6, 67] Generated Node #0,1,2: 62:[6, 67] Operation: 68-1=67 Moving to Node #0,1,1 Current State: 62:[1, 62], Operations: ['25-19=6', '68-6=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[19, 25, 68, 1], Operations: [] Exploring Operation: 25-19=6, Resulting Numbers: [68, 1, 6] Generated Node #0,1: 62:[68, 1, 6] Operation: 25-19=6 Moving to Node #0,1 Current State: 62:[68, 1, 6], Operations: ['25-19=6'] Exploring Operation: 68-6=62, Resulting Numbers: [1, 62] Generated Node #0,1,1: 62:[1, 62] Operation: 68-6=62 Moving to Node #0,1,1 Current State: 62:[1, 62], Operations: ['25-19=6', '68-6=62'] Exploring Operation: 1*62=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 81, 73, 26, 49 ]
78
[ "81+49=130", "130/26=5", "73+5=78" ]
Current State: 78:[81, 73, 26, 49], Operations: [] Exploring Operation: 81+49=130, Resulting Numbers: [73, 26, 130] Generated Node #2: [73, 26, 130] from Operation: 81+49=130 Current State: 78:[73, 26, 130], Operations: ['81+49=130'] Exploring Operation: 130/26=5, Resulting Numbers: [73, 5] Generated Node #3: [73, 5] from Operation: 130/26=5 Current State: 78:[73, 5], Operations: ['81+49=130', '130/26=5'] Exploring Operation: 73+5=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[81, 73, 26, 49], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [81, 26, 24] Generated Node #0,0: 78:[81, 26, 24] Operation: 73-49=24 Exploring Operation: 81-49=32, Resulting Numbers: [73, 26, 32] Generated Node #0,1: 78:[73, 26, 32] Operation: 81-49=32 Exploring Operation: 26+49=75, Resulting Numbers: [81, 73, 75] Generated Node #0,2: 78:[81, 73, 75] Operation: 26+49=75 Exploring Operation: 49-26=23, Resulting Numbers: [81, 73, 23] Generated Node #0,3: 78:[81, 73, 23] Operation: 49-26=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[81, 26, 24], Operations: ['73-49=24'] Exploring Operation: 81-24=57, Resulting Numbers: [26, 57] Generated Node #0,0,0: 78:[26, 57] Operation: 81-24=57 Exploring Operation: 26-24=2, Resulting Numbers: [81, 2] Generated Node #0,0,1: 78:[81, 2] Operation: 26-24=2 Exploring Operation: 81-26=55, Resulting Numbers: [24, 55] Generated Node #0,0,2: 78:[24, 55] Operation: 81-26=55 Exploring Operation: 26+24=50, Resulting Numbers: [81, 50] Generated Node #0,0,3: 78:[81, 50] Operation: 26+24=50 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[81, 2], Operations: ['73-49=24', '26-24=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 81*2=162, Resulting Numbers: [162] 162,78 unequal: No Solution Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,78 unequal: No Solution No 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: 78:[81, 50], Operations: ['73-49=24', '26+24=50'] Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,78 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,78 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,78 unequal: No Solution No 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: 78:[26, 57], Operations: ['73-49=24', '81-24=57'] Exploring Operation: 57-26=31, Resulting Numbers: [31] 31,78 unequal: No Solution Exploring Operation: 26*57=1482, Resulting Numbers: [1482] 1482,78 unequal: No Solution Exploring Operation: 26+57=83, Resulting Numbers: [83] 83,78 unequal: No Solution No 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: 78:[24, 55], Operations: ['73-49=24', '81-26=55'] Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,78 unequal: No Solution Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,78 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: 78:[73, 26, 32], Operations: ['81-49=32'] Exploring Operation: 26+32=58, Resulting Numbers: [73, 58] Generated Node #0,1,0: 78:[73, 58] Operation: 26+32=58 Exploring Operation: 73-26=47, Resulting Numbers: [32, 47] Generated Node #0,1,1: 78:[32, 47] Operation: 73-26=47 Exploring Operation: 32-26=6, Resulting Numbers: [73, 6] Generated Node #0,1,2: 78:[73, 6] Operation: 32-26=6 Exploring Operation: 73-32=41, Resulting Numbers: [26, 41] Generated Node #0,1,3: 78:[26, 41] Operation: 73-32=41 Moving to Node #0,1,3 Current State: 78:[26, 41], Operations: ['81-49=32', '73-32=41'] Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 26*41=1066, Resulting Numbers: [1066] 1066,78 unequal: No Solution Exploring Operation: 26+41=67, Resulting Numbers: [67] 67,78 unequal: No Solution Moving to Node #0,1,2 Current State: 78:[73, 6], Operations: ['81-49=32', '32-26=6'] Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,78 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[32, 47], Operations: ['81-49=32', '73-26=47'] Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,78 unequal: No Solution Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[73, 58], Operations: ['81-49=32', '26+32=58'] Exploring Operation: 73*58=4234, Resulting Numbers: [4234] 4234,78 unequal: No Solution Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 73+58=131, Resulting Numbers: [131] 131,78 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 Current State: 78:[81, 73, 75], Operations: ['26+49=75'] Exploring Operation: 81-73=8, Resulting Numbers: [75, 8] Generated Node #0,2,0: 78:[75, 8] Operation: 81-73=8 Exploring Operation: 75-73=2, Resulting Numbers: [81, 2] Generated Node #0,2,1: 78:[81, 2] Operation: 75-73=2 Exploring Operation: 81-75=6, Resulting Numbers: [73, 6] Generated Node #0,2,2: 78:[73, 6] Operation: 81-75=6 Exploring Operation: 73+75=148, Resulting Numbers: [81, 148] Generated Node #0,2,3: 78:[81, 148] Operation: 73+75=148 Moving to Node #0,2,1 Current State: 78:[81, 2], Operations: ['26+49=75', '75-73=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,78 unequal: No Solution Exploring Operation: 81*2=162, Resulting Numbers: [162] 162,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[73, 6], Operations: ['26+49=75', '81-75=6'] Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,78 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[75, 8], Operations: ['26+49=75', '81-73=8'] Exploring Operation: 75-8=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 75+8=83, Resulting Numbers: [83] 83,78 unequal: No Solution Exploring Operation: 75*8=600, Resulting Numbers: [600] 600,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[81, 148], Operations: ['26+49=75', '73+75=148'] Exploring Operation: 148-81=67, Resulting Numbers: [67] 67,78 unequal: No Solution Exploring Operation: 81+148=229, Resulting Numbers: [229] 229,78 unequal: No Solution Exploring Operation: 81*148=11988, Resulting Numbers: [11988] 11988,78 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 Current State: 78:[81, 73, 23], Operations: ['49-26=23'] Exploring Operation: 81-73=8, Resulting Numbers: [23, 8] Generated Node #0,3,0: 78:[23, 8] Operation: 81-73=8 Exploring Operation: 73+23=96, Resulting Numbers: [81, 96] Generated Node #0,3,1: 78:[81, 96] Operation: 73+23=96 Exploring Operation: 81-23=58, Resulting Numbers: [73, 58] Generated Node #0,3,2: 78:[73, 58] Operation: 81-23=58 Exploring Operation: 73-23=50, Resulting Numbers: [81, 50] Generated Node #0,3,3: 78:[81, 50] Operation: 73-23=50 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 78:[23, 8], Operations: ['49-26=23', '81-73=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,78 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,78 unequal: No Solution No 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: 78:[81, 50], Operations: ['49-26=23', '73-23=50'] Exploring Operation: 81+50=131, Resulting Numbers: [131] 131,78 unequal: No Solution Exploring Operation: 81*50=4050, Resulting Numbers: [4050] 4050,78 unequal: No Solution Exploring Operation: 81-50=31, Resulting Numbers: [31] 31,78 unequal: No Solution No 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: 78:[81, 96], Operations: ['49-26=23', '73+23=96'] Exploring Operation: 81+96=177, Resulting Numbers: [177] 177,78 unequal: No Solution Exploring Operation: 96-81=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 81*96=7776, Resulting Numbers: [7776] 7776,78 unequal: No Solution No 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: 78:[73, 58], Operations: ['49-26=23', '81-23=58'] Exploring Operation: 73-58=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 73*58=4234, Resulting Numbers: [4234] 4234,78 unequal: No Solution Exploring Operation: 73+58=131, Resulting Numbers: [131] 131,78 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
[ 13, 70, 70, 99 ]
87
[ "99-13=86", "70/70=1", "86+1=87" ]
Current State: 87:[13, 70, 70, 99], Operations: [] Exploring Operation: 99-13=86, Resulting Numbers: [70, 70, 86] Generated Node #2: [70, 70, 86] from Operation: 99-13=86 Current State: 87:[70, 70, 86], Operations: ['99-13=86'] Exploring Operation: 70/70=1, Resulting Numbers: [86, 1] Generated Node #3: [86, 1] from Operation: 70/70=1 Current State: 87:[86, 1], Operations: ['99-13=86', '70/70=1'] Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[13, 70, 70, 99], Operations: [] Exploring Operation: 99-70=29, Resulting Numbers: [13, 70, 29] Generated Node #0,0: 87:[13, 70, 29] Operation: 99-70=29 Exploring Operation: 70/70=1, Resulting Numbers: [13, 99, 1] Generated Node #0,1: 87:[13, 99, 1] Operation: 70/70=1 Exploring Operation: 70-70=0, Resulting Numbers: [13, 99, 0] Generated Node #0,2: 87:[13, 99, 0] Operation: 70-70=0 Moving to Node #0,1 Current State: 87:[13, 99, 1], Operations: ['70/70=1'] Exploring Operation: 99-13=86, Resulting Numbers: [1, 86] Generated Node #0,1,0: 87:[1, 86] Operation: 99-13=86 Exploring Operation: 99-1=98, Resulting Numbers: [13, 98] Generated Node #0,1,1: 87:[13, 98] Operation: 99-1=98 Exploring Operation: 13-1=12, Resulting Numbers: [99, 12] Generated Node #0,1,2: 87:[99, 12] Operation: 13-1=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[1, 86], Operations: ['70/70=1', '99-13=86'] Exploring Operation: 1+86=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[13, 70, 70, 99], Operations: [] Exploring Operation: 70/70=1, Resulting Numbers: [13, 99, 1] Generated Node #0,1: 87:[13, 99, 1] Operation: 70/70=1 Moving to Node #0,1 Current State: 87:[13, 99, 1], Operations: ['70/70=1'] Exploring Operation: 99-13=86, Resulting Numbers: [1, 86] Generated Node #0,1,0: 87:[1, 86] Operation: 99-13=86 Moving to Node #0,1,0 Current State: 87:[1, 86], Operations: ['70/70=1', '99-13=86'] Exploring Operation: 1+86=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 21, 96, 17, 64 ]
36
[ "21+96=117", "17+64=81", "117-81=36" ]
Current State: 36:[21, 96, 17, 64], Operations: [] Exploring Operation: 21+96=117, Resulting Numbers: [17, 64, 117] Generated Node #2: [17, 64, 117] from Operation: 21+96=117 Current State: 36:[17, 64, 117], Operations: ['21+96=117'] Exploring Operation: 17+64=81, Resulting Numbers: [117, 81] Generated Node #3: [117, 81] from Operation: 17+64=81 Current State: 36:[117, 81], Operations: ['21+96=117', '17+64=81'] Exploring Operation: 117-81=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[21, 96, 17, 64], Operations: [] Exploring Operation: 64-21=43, Resulting Numbers: [96, 17, 43] Generated Node #0,0: 36:[96, 17, 43] Operation: 64-21=43 Exploring Operation: 96-64=32, Resulting Numbers: [21, 17, 32] Generated Node #0,1: 36:[21, 17, 32] Operation: 96-64=32 Exploring Operation: 96-17=79, Resulting Numbers: [21, 64, 79] Generated Node #0,2: 36:[21, 64, 79] Operation: 96-17=79 Exploring Operation: 96-21=75, Resulting Numbers: [17, 64, 75] Generated Node #0,3: 36:[17, 64, 75] Operation: 96-21=75 Moving to Node #0,1 Current State: 36:[21, 17, 32], Operations: ['96-64=32'] Exploring Operation: 32-17=15, Resulting Numbers: [21, 15] Generated Node #0,1,0: 36:[21, 15] Operation: 32-17=15 Exploring Operation: 32-21=11, Resulting Numbers: [17, 11] Generated Node #0,1,1: 36:[17, 11] Operation: 32-21=11 Exploring Operation: 21+17=38, Resulting Numbers: [32, 38] Generated Node #0,1,2: 36:[32, 38] Operation: 21+17=38 Exploring Operation: 21-17=4, Resulting Numbers: [32, 4] Generated Node #0,1,3: 36:[32, 4] Operation: 21-17=4 Moving to Node #0,3 Current State: 36:[17, 64, 75], Operations: ['96-21=75'] Exploring Operation: 17+64=81, Resulting Numbers: [75, 81] Generated Node #0,3,0: 36:[75, 81] Operation: 17+64=81 Exploring Operation: 75-17=58, Resulting Numbers: [64, 58] Generated Node #0,3,1: 36:[64, 58] Operation: 75-17=58 Exploring Operation: 75-64=11, Resulting Numbers: [17, 11] Generated Node #0,3,2: 36:[17, 11] Operation: 75-64=11 Exploring Operation: 64-17=47, Resulting Numbers: [75, 47] Generated Node #0,3,3: 36:[75, 47] Operation: 64-17=47 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 36:[17, 11], Operations: ['96-21=75', '75-64=11'] Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,36 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,36 unequal: No Solution No 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: 36:[64, 58], Operations: ['96-21=75', '75-17=58'] Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 64+58=122, Resulting Numbers: [122] 122,36 unequal: No Solution Exploring Operation: 64*58=3712, Resulting Numbers: [3712] 3712,36 unequal: No Solution No 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: 36:[75, 47], Operations: ['96-21=75', '64-17=47'] Exploring Operation: 75-47=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 75*47=3525, Resulting Numbers: [3525] 3525,36 unequal: No Solution Exploring Operation: 75+47=122, Resulting Numbers: [122] 122,36 unequal: No Solution No 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: 36:[75, 81], Operations: ['96-21=75', '17+64=81'] Exploring Operation: 75+81=156, Resulting Numbers: [156] 156,36 unequal: No Solution Exploring Operation: 81-75=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 75*81=6075, Resulting Numbers: [6075] 6075,36 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: 36:[96, 17, 43], Operations: ['64-21=43'] Exploring Operation: 43-17=26, Resulting Numbers: [96, 26] Generated Node #0,0,0: 36:[96, 26] Operation: 43-17=26 Exploring Operation: 96-43=53, Resulting Numbers: [17, 53] Generated Node #0,0,1: 36:[17, 53] Operation: 96-43=53 Exploring Operation: 96-17=79, Resulting Numbers: [43, 79] Generated Node #0,0,2: 36:[43, 79] Operation: 96-17=79 Exploring Operation: 96+17=113, Resulting Numbers: [43, 113] Generated Node #0,0,3: 36:[43, 113] Operation: 96+17=113 Moving to Node #0,2 Current State: 36:[21, 64, 79], Operations: ['96-17=79'] Exploring Operation: 79-64=15, Resulting Numbers: [21, 15] Generated Node #0,2,0: 36:[21, 15] Operation: 79-64=15 Exploring Operation: 64-21=43, Resulting Numbers: [79, 43] Generated Node #0,2,1: 36:[79, 43] Operation: 64-21=43 Exploring Operation: 79-21=58, Resulting Numbers: [64, 58] Generated Node #0,2,2: 36:[64, 58] Operation: 79-21=58 Exploring Operation: 21+64=85, Resulting Numbers: [79, 85] Generated Node #0,2,3: 36:[79, 85] Operation: 21+64=85 Moving to Node #0,1,1 Current State: 36:[17, 11], Operations: ['96-64=32', '32-21=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,36 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,36 unequal: No Solution Moving to Node #0,1,3 Current State: 36:[32, 4], Operations: ['96-64=32', '21-17=4'] Exploring Operation: 32*4=128, Resulting Numbers: [128] 128,36 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,36 unequal: No Solution Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[21, 96, 17, 64], Operations: [] Exploring Operation: 96-64=32, Resulting Numbers: [21, 17, 32] Generated Node #0,1: 36:[21, 17, 32] Operation: 96-64=32 Moving to Node #0,1 Current State: 36:[21, 17, 32], Operations: ['96-64=32'] Exploring Operation: 21-17=4, Resulting Numbers: [32, 4] Generated Node #0,1,3: 36:[32, 4] Operation: 21-17=4 Moving to Node #0,1,3 Current State: 36:[32, 4], Operations: ['96-64=32', '21-17=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.963542
hs_4
mult_heuristic
[ 49, 84, 45, 8 ]
11
[ "49+84=133", "133-45=88", "88/8=11" ]
Current State: 11:[49, 84, 45, 8], Operations: [] Exploring Operation: 49+84=133, Resulting Numbers: [45, 8, 133] Generated Node #2: [45, 8, 133] from Operation: 49+84=133 Current State: 11:[45, 8, 133], Operations: ['49+84=133'] Exploring Operation: 133-45=88, Resulting Numbers: [8, 88] Generated Node #3: [8, 88] from Operation: 133-45=88 Current State: 11:[8, 88], Operations: ['49+84=133', '133-45=88'] Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[49, 84, 45, 8], Operations: [] Exploring Operation: 84-49=35, Resulting Numbers: [45, 8, 35] Generated Node #0,0: 11:[45, 8, 35] Operation: 84-49=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[45, 8, 35], Operations: ['84-49=35'] Exploring Operation: 45-35=10, Resulting Numbers: [8, 10] Generated Node #0,0,0: 11:[8, 10] Operation: 45-35=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[8, 10], Operations: ['84-49=35', '45-35=10'] Exploring Operation: 8+10=18, Resulting Numbers: [18] 18,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 87, 8, 64, 69 ]
11
[ "87-64=23", "69/23=3", "8+3=11" ]
Current State: 11:[87, 8, 64, 69], Operations: [] Exploring Operation: 87-64=23, Resulting Numbers: [8, 69, 23] Generated Node #2: [8, 69, 23] from Operation: 87-64=23 Current State: 11:[8, 69, 23], Operations: ['87-64=23'] Exploring Operation: 69/23=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 69/23=3 Current State: 11:[8, 3], Operations: ['87-64=23', '69/23=3'] Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[87, 8, 64, 69], Operations: [] Exploring Operation: 87-69=18, Resulting Numbers: [8, 64, 18] Generated Node #0,0: 11:[8, 64, 18] Operation: 87-69=18 Moving to Node #0,0 Current State: 11:[8, 64, 18], Operations: ['87-69=18'] Exploring Operation: 64/8=8, Resulting Numbers: [18, 8] Generated Node #0,0,0: 11:[18, 8] Operation: 64/8=8 Moving to Node #0,0,0 Current State: 11:[18, 8], Operations: ['87-69=18', '64/8=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,11 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 15, 42, 20, 45 ]
75
[ "45-42=3", "20*3=60", "15+60=75" ]
Current State: 75:[15, 42, 20, 45], Operations: [] Exploring Operation: 45-42=3, Resulting Numbers: [15, 20, 3] Generated Node #2: [15, 20, 3] from Operation: 45-42=3 Current State: 75:[15, 20, 3], Operations: ['45-42=3'] Exploring Operation: 20*3=60, Resulting Numbers: [15, 60] Generated Node #3: [15, 60] from Operation: 20*3=60 Current State: 75:[15, 60], Operations: ['45-42=3', '20*3=60'] Exploring Operation: 15+60=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[15, 42, 20, 45], Operations: [] Exploring Operation: 45-42=3, Resulting Numbers: [15, 20, 3] Generated Node #0,0: 75:[15, 20, 3] Operation: 45-42=3 Moving to Node #0,0 Current State: 75:[15, 20, 3], Operations: ['45-42=3'] Exploring Operation: 20-15=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 75:[3, 5] Operation: 20-15=5 Moving to Node #0,0,0 Current State: 75:[3, 5], Operations: ['45-42=3', '20-15=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 20, 54, 54, 91 ]
72
[ "91-20=71", "54/54=1", "71+1=72" ]
Current State: 72:[20, 54, 54, 91], Operations: [] Exploring Operation: 91-20=71, Resulting Numbers: [54, 54, 71] Generated Node #2: [54, 54, 71] from Operation: 91-20=71 Current State: 72:[54, 54, 71], Operations: ['91-20=71'] Exploring Operation: 54/54=1, Resulting Numbers: [71, 1] Generated Node #3: [71, 1] from Operation: 54/54=1 Current State: 72:[71, 1], Operations: ['91-20=71', '54/54=1'] Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[20, 54, 54, 91], Operations: [] Exploring Operation: 91-54=37, Resulting Numbers: [20, 54, 37] Generated Node #0,0: 72:[20, 54, 37] Operation: 91-54=37 Exploring Operation: 91-54=37, Resulting Numbers: [20, 54, 37] Generated Node #0,1: 72:[20, 54, 37] Operation: 91-54=37 Moving to Node #0,0 Current State: 72:[20, 54, 37], Operations: ['91-54=37'] Exploring Operation: 20+54=74, Resulting Numbers: [37, 74] Generated Node #0,0,0: 72:[37, 74] Operation: 20+54=74 Exploring Operation: 54-20=34, Resulting Numbers: [37, 34] Generated Node #0,0,1: 72:[37, 34] Operation: 54-20=34 Moving to Node #0,1 Current State: 72:[20, 54, 37], Operations: ['91-54=37'] Exploring Operation: 54-20=34, Resulting Numbers: [37, 34] Generated Node #0,1,0: 72:[37, 34] Operation: 54-20=34 Exploring Operation: 20+54=74, Resulting Numbers: [37, 74] Generated Node #0,1,1: 72:[37, 74] Operation: 20+54=74 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[37, 34], Operations: ['91-54=37', '54-20=34'] Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,72 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 #0,1,1 Current State: 72:[37, 74], Operations: ['91-54=37', '20+54=74'] Exploring Operation: 74-37=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 74/37=2, Resulting Numbers: [2] 2,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 72:[37, 74], Operations: ['91-54=37', '20+54=74'] Exploring Operation: 74-37=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 74/37=2, Resulting Numbers: [2] 2,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[37, 34], Operations: ['91-54=37', '54-20=34'] Exploring Operation: 37+34=71, Resulting Numbers: [71] 71,72 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,72 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 3, 67, 61, 75 ]
31
[ "75/3=25", "67-61=6", "25+6=31" ]
Current State: 31:[3, 67, 61, 75], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [67, 61, 25] Generated Node #2: [67, 61, 25] from Operation: 75/3=25 Current State: 31:[67, 61, 25], Operations: ['75/3=25'] Exploring Operation: 67-61=6, Resulting Numbers: [25, 6] Generated Node #3: [25, 6] from Operation: 67-61=6 Current State: 31:[25, 6], Operations: ['75/3=25', '67-61=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[3, 67, 61, 75], Operations: [] Exploring Operation: 75/3=25, Resulting Numbers: [67, 61, 25] Generated Node #0,0: 31:[67, 61, 25] Operation: 75/3=25 Exploring Operation: 75-61=14, Resulting Numbers: [3, 67, 14] Generated Node #0,1: 31:[3, 67, 14] Operation: 75-61=14 Exploring Operation: 75-67=8, Resulting Numbers: [3, 61, 8] Generated Node #0,2: 31:[3, 61, 8] Operation: 75-67=8 Exploring Operation: 67-61=6, Resulting Numbers: [3, 75, 6] Generated Node #0,3: 31:[3, 75, 6] Operation: 67-61=6 Moving to Node #0,0 Current State: 31:[67, 61, 25], Operations: ['75/3=25'] Exploring Operation: 61-25=36, Resulting Numbers: [67, 36] Generated Node #0,0,0: 31:[67, 36] Operation: 61-25=36 Exploring Operation: 67-61=6, Resulting Numbers: [25, 6] Generated Node #0,0,1: 31:[25, 6] Operation: 67-61=6 Exploring Operation: 67-25=42, Resulting Numbers: [61, 42] Generated Node #0,0,2: 31:[61, 42] Operation: 67-25=42 Exploring Operation: 67+25=92, Resulting Numbers: [61, 92] Generated Node #0,0,3: 31:[61, 92] Operation: 67+25=92 Moving to Node #0,2 Current State: 31:[3, 61, 8], Operations: ['75-67=8'] Exploring Operation: 3*8=24, Resulting Numbers: [61, 24] Generated Node #0,2,0: 31:[61, 24] Operation: 3*8=24 Exploring Operation: 61-8=53, Resulting Numbers: [3, 53] Generated Node #0,2,1: 31:[3, 53] Operation: 61-8=53 Exploring Operation: 61-3=58, Resulting Numbers: [8, 58] Generated Node #0,2,2: 31:[8, 58] Operation: 61-3=58 Exploring Operation: 3+8=11, Resulting Numbers: [61, 11] Generated Node #0,2,3: 31:[61, 11] Operation: 3+8=11 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[61, 24], Operations: ['75-67=8', '3*8=24'] Exploring Operation: 61*24=1464, Resulting Numbers: [1464] 1464,31 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 61+24=85, Resulting Numbers: [85] 85,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[3, 53], Operations: ['75-67=8', '61-8=53'] Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,31 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 3*53=159, Resulting Numbers: [159] 159,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[8, 58], Operations: ['75-67=8', '61-3=58'] Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,31 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[61, 11], Operations: ['75-67=8', '3+8=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 61*11=671, Resulting Numbers: [671] 671,31 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 31:[3, 67, 14], Operations: ['75-61=14'] Exploring Operation: 3*14=42, Resulting Numbers: [67, 42] Generated Node #0,1,0: 31:[67, 42] Operation: 3*14=42 Exploring Operation: 67-3=64, Resulting Numbers: [14, 64] Generated Node #0,1,1: 31:[14, 64] Operation: 67-3=64 Exploring Operation: 3+14=17, Resulting Numbers: [67, 17] Generated Node #0,1,2: 31:[67, 17] Operation: 3+14=17 Exploring Operation: 67-14=53, Resulting Numbers: [3, 53] Generated Node #0,1,3: 31:[3, 53] Operation: 67-14=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[67, 42], Operations: ['75-61=14', '3*14=42'] Exploring Operation: 67*42=2814, Resulting Numbers: [2814] 2814,31 unequal: No Solution Exploring Operation: 67-42=25, Resulting Numbers: [25] 25,31 unequal: No Solution Exploring Operation: 67+42=109, Resulting Numbers: [109] 109,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[14, 64], Operations: ['75-61=14', '67-3=64'] Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,31 unequal: No Solution Exploring Operation: 14*64=896, Resulting Numbers: [896] 896,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[67, 17], Operations: ['75-61=14', '3+14=17'] Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,31 unequal: No Solution Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 31:[3, 53], Operations: ['75-61=14', '67-14=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 3*53=159, Resulting Numbers: [159] 159,31 unequal: No Solution Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 31:[3, 75, 6], Operations: ['67-61=6'] Exploring Operation: 75/3=25, Resulting Numbers: [6, 25] Generated Node #0,3,0: 31:[6, 25] Operation: 75/3=25 Exploring Operation: 3+6=9, Resulting Numbers: [75, 9] Generated Node #0,3,1: 31:[75, 9] Operation: 3+6=9 Exploring Operation: 75-3=72, Resulting Numbers: [6, 72] Generated Node #0,3,2: 31:[6, 72] Operation: 75-3=72 Exploring Operation: 3*6=18, Resulting Numbers: [75, 18] Generated Node #0,3,3: 31:[75, 18] Operation: 3*6=18 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[6, 25], Operations: ['67-61=6', '75/3=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[3, 67, 61, 75], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [3, 75, 6] Generated Node #0,3: 31:[3, 75, 6] Operation: 67-61=6 Moving to Node #0,3 Current State: 31:[3, 75, 6], Operations: ['67-61=6'] Exploring Operation: 75/3=25, Resulting Numbers: [6, 25] Generated Node #0,3,0: 31:[6, 25] Operation: 75/3=25 Moving to Node #0,3,0 Current State: 31:[6, 25], Operations: ['67-61=6', '75/3=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 65, 94, 93, 87 ]
31
[ "94-65=29", "93*29=2697", "2697/87=31" ]
Current State: 31:[65, 94, 93, 87], Operations: [] Exploring Operation: 94-65=29, Resulting Numbers: [93, 87, 29] Generated Node #2: [93, 87, 29] from Operation: 94-65=29 Current State: 31:[93, 87, 29], Operations: ['94-65=29'] Exploring Operation: 93*29=2697, Resulting Numbers: [87, 2697] Generated Node #3: [87, 2697] from Operation: 93*29=2697 Current State: 31:[87, 2697], Operations: ['94-65=29', '93*29=2697'] Exploring Operation: 2697/87=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[65, 94, 93, 87], Operations: [] Exploring Operation: 94-65=29, Resulting Numbers: [93, 87, 29] Generated Node #0,0: 31:[93, 87, 29] Operation: 94-65=29 Moving to Node #0,0 Current State: 31:[93, 87, 29], Operations: ['94-65=29'] Exploring Operation: 93-87=6, Resulting Numbers: [29, 6] Generated Node #0,0,0: 31:[29, 6] Operation: 93-87=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[29, 6], Operations: ['94-65=29', '93-87=6'] Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,31 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
[ 79, 77, 49, 11 ]
58
[ "79-77=2", "49+11=60", "60-2=58" ]
Current State: 58:[79, 77, 49, 11], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [49, 11, 2] Generated Node #2: [49, 11, 2] from Operation: 79-77=2 Current State: 58:[49, 11, 2], Operations: ['79-77=2'] Exploring Operation: 49+11=60, Resulting Numbers: [2, 60] Generated Node #3: [2, 60] from Operation: 49+11=60 Current State: 58:[2, 60], Operations: ['79-77=2', '49+11=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[79, 77, 49, 11], Operations: [] Exploring Operation: 77-49=28, Resulting Numbers: [79, 11, 28] Generated Node #0,0: 58:[79, 11, 28] Operation: 77-49=28 Exploring Operation: 79-49=30, Resulting Numbers: [77, 11, 30] Generated Node #0,1: 58:[77, 11, 30] Operation: 79-49=30 Exploring Operation: 77/11=7, Resulting Numbers: [79, 49, 7] Generated Node #0,2: 58:[79, 49, 7] Operation: 77/11=7 Exploring Operation: 79-77=2, Resulting Numbers: [49, 11, 2] Generated Node #0,3: 58:[49, 11, 2] Operation: 79-77=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[49, 11, 2], Operations: ['79-77=2'] Exploring Operation: 49+11=60, Resulting Numbers: [2, 60] Generated Node #0,3,0: 58:[2, 60] Operation: 49+11=60 Exploring Operation: 49+2=51, Resulting Numbers: [11, 51] Generated Node #0,3,1: 58:[11, 51] Operation: 49+2=51 Exploring Operation: 11*2=22, Resulting Numbers: [49, 22] Generated Node #0,3,2: 58:[49, 22] Operation: 11*2=22 Exploring Operation: 49-11=38, Resulting Numbers: [2, 38] Generated Node #0,3,3: 58:[2, 38] Operation: 49-11=38 Moving to Node #0,3,0 Current State: 58:[2, 60], Operations: ['79-77=2', '49+11=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,58 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,58 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[79, 77, 49, 11], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [49, 11, 2] Generated Node #0,3: 58:[49, 11, 2] Operation: 79-77=2 Moving to Node #0,3 Current State: 58:[49, 11, 2], Operations: ['79-77=2'] Exploring Operation: 49+11=60, Resulting Numbers: [2, 60] Generated Node #0,3,0: 58:[2, 60] Operation: 49+11=60 Moving to Node #0,3,0 Current State: 58:[2, 60], Operations: ['79-77=2', '49+11=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 41, 37, 69, 8 ]
57
[ "41-37=4", "69-8=61", "61-4=57" ]
Current State: 57:[41, 37, 69, 8], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [69, 8, 4] Generated Node #2: [69, 8, 4] from Operation: 41-37=4 Current State: 57:[69, 8, 4], Operations: ['41-37=4'] Exploring Operation: 69-8=61, Resulting Numbers: [4, 61] Generated Node #3: [4, 61] from Operation: 69-8=61 Current State: 57:[4, 61], Operations: ['41-37=4', '69-8=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[41, 37, 69, 8], Operations: [] Exploring Operation: 41+8=49, Resulting Numbers: [37, 69, 49] Generated Node #0,0: 57:[37, 69, 49] Operation: 41+8=49 Exploring Operation: 41-37=4, Resulting Numbers: [69, 8, 4] Generated Node #0,1: 57:[69, 8, 4] Operation: 41-37=4 Exploring Operation: 69-41=28, Resulting Numbers: [37, 8, 28] Generated Node #0,2: 57:[37, 8, 28] Operation: 69-41=28 Exploring Operation: 69-37=32, Resulting Numbers: [41, 8, 32] Generated Node #0,3: 57:[41, 8, 32] Operation: 69-37=32 Exploring Operation: 41+37=78, Resulting Numbers: [69, 8, 78] Generated Node #0,4: 57:[69, 8, 78] Operation: 41+37=78 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[69, 8, 4], Operations: ['41-37=4'] Exploring Operation: 69-4=65, Resulting Numbers: [8, 65] Generated Node #0,1,0: 57:[8, 65] Operation: 69-4=65 Exploring Operation: 69-8=61, Resulting Numbers: [4, 61] Generated Node #0,1,1: 57:[4, 61] Operation: 69-8=61 Exploring Operation: 8/4=2, Resulting Numbers: [69, 2] Generated Node #0,1,2: 57:[69, 2] Operation: 8/4=2 Exploring Operation: 8-4=4, Resulting Numbers: [69, 4] Generated Node #0,1,3: 57:[69, 4] Operation: 8-4=4 Exploring Operation: 8+4=12, Resulting Numbers: [69, 12] Generated Node #0,1,4: 57:[69, 12] Operation: 8+4=12 Moving to Node #0,1,1 Current State: 57:[4, 61], Operations: ['41-37=4', '69-8=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[41, 37, 69, 8], Operations: [] Exploring Operation: 41-37=4, Resulting Numbers: [69, 8, 4] Generated Node #0,1: 57:[69, 8, 4] Operation: 41-37=4 Moving to Node #0,1 Current State: 57:[69, 8, 4], Operations: ['41-37=4'] Exploring Operation: 69-8=61, Resulting Numbers: [4, 61] Generated Node #0,1,1: 57:[4, 61] Operation: 69-8=61 Moving to Node #0,1,1 Current State: 57:[4, 61], Operations: ['41-37=4', '69-8=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 27, 18, 43, 13 ]
84
[ "43+13=56", "27*56=1512", "1512/18=84" ]
Current State: 84:[27, 18, 43, 13], Operations: [] Exploring Operation: 43+13=56, Resulting Numbers: [27, 18, 56] Generated Node #2: [27, 18, 56] from Operation: 43+13=56 Current State: 84:[27, 18, 56], Operations: ['43+13=56'] Exploring Operation: 27*56=1512, Resulting Numbers: [18, 1512] Generated Node #3: [18, 1512] from Operation: 27*56=1512 Current State: 84:[18, 1512], Operations: ['43+13=56', '27*56=1512'] Exploring Operation: 1512/18=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[27, 18, 43, 13], Operations: [] Exploring Operation: 27+18=45, Resulting Numbers: [43, 13, 45] Generated Node #0,0: 84:[43, 13, 45] Operation: 27+18=45 Exploring Operation: 18-13=5, Resulting Numbers: [27, 43, 5] Generated Node #0,1: 84:[27, 43, 5] Operation: 18-13=5 Exploring Operation: 27-18=9, Resulting Numbers: [43, 13, 9] Generated Node #0,2: 84:[43, 13, 9] Operation: 27-18=9 Exploring Operation: 27-13=14, Resulting Numbers: [18, 43, 14] Generated Node #0,3: 84:[18, 43, 14] Operation: 27-13=14 Moving to Node #0,1 Current State: 84:[27, 43, 5], Operations: ['18-13=5'] Exploring Operation: 27-5=22, Resulting Numbers: [43, 22] Generated Node #0,1,0: 84:[43, 22] Operation: 27-5=22 Exploring Operation: 27+5=32, Resulting Numbers: [43, 32] Generated Node #0,1,1: 84:[43, 32] Operation: 27+5=32 Exploring Operation: 43-27=16, Resulting Numbers: [5, 16] Generated Node #0,1,2: 84:[5, 16] Operation: 43-27=16 Exploring Operation: 43-5=38, Resulting Numbers: [27, 38] Generated Node #0,1,3: 84:[27, 38] Operation: 43-5=38 Moving to Node #0,3 Current State: 84:[18, 43, 14], Operations: ['27-13=14'] Exploring Operation: 18-14=4, Resulting Numbers: [43, 4] Generated Node #0,3,0: 84:[43, 4] Operation: 18-14=4 Exploring Operation: 43-14=29, Resulting Numbers: [18, 29] Generated Node #0,3,1: 84:[18, 29] Operation: 43-14=29 Exploring Operation: 43-18=25, Resulting Numbers: [14, 25] Generated Node #0,3,2: 84:[14, 25] Operation: 43-18=25 Exploring Operation: 18+14=32, Resulting Numbers: [43, 32] Generated Node #0,3,3: 84:[43, 32] Operation: 18+14=32 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[43, 4], Operations: ['27-13=14', '18-14=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,84 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[14, 25], Operations: ['27-13=14', '43-18=25'] Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[18, 29], Operations: ['27-13=14', '43-14=29'] Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,84 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[43, 32], Operations: ['27-13=14', '18+14=32'] Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,84 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 84:[43, 13, 9], Operations: ['27-18=9'] Exploring Operation: 13+9=22, Resulting Numbers: [43, 22] Generated Node #0,2,0: 84:[43, 22] Operation: 13+9=22 Exploring Operation: 13-9=4, Resulting Numbers: [43, 4] Generated Node #0,2,1: 84:[43, 4] Operation: 13-9=4 Exploring Operation: 43-9=34, Resulting Numbers: [13, 34] Generated Node #0,2,2: 84:[13, 34] Operation: 43-9=34 Exploring Operation: 43-13=30, Resulting Numbers: [9, 30] Generated Node #0,2,3: 84:[9, 30] Operation: 43-13=30 Moving to Node #0,0 Current State: 84:[43, 13, 45], Operations: ['27+18=45'] Exploring Operation: 45-43=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 84:[13, 2] Operation: 45-43=2 Exploring Operation: 43+45=88, Resulting Numbers: [13, 88] Generated Node #0,0,1: 84:[13, 88] Operation: 43+45=88 Exploring Operation: 43-13=30, Resulting Numbers: [45, 30] Generated Node #0,0,2: 84:[45, 30] Operation: 43-13=30 Exploring Operation: 45-13=32, Resulting Numbers: [43, 32] Generated Node #0,0,3: 84:[43, 32] Operation: 45-13=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[13, 2], Operations: ['27+18=45', '45-43=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,84 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[13, 88], Operations: ['27+18=45', '43+45=88'] Exploring Operation: 13+88=101, Resulting Numbers: [101] 101,84 unequal: No Solution Exploring Operation: 13*88=1144, Resulting Numbers: [1144] 1144,84 unequal: No Solution Exploring Operation: 88-13=75, Resulting Numbers: [75] 75,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[45, 30], Operations: ['27+18=45', '43-13=30'] Exploring Operation: 45-30=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 45*30=1350, Resulting Numbers: [1350] 1350,84 unequal: No Solution Exploring Operation: 45+30=75, Resulting Numbers: [75] 75,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[43, 32], Operations: ['27+18=45', '45-13=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,84 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 84:[43, 4], Operations: ['27-18=9', '13-9=4'] Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,84 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[43, 22], Operations: ['27-18=9', '13+9=22'] Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,84 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[43, 22], Operations: ['18-13=5', '27-5=22'] Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[5, 16], Operations: ['18-13=5', '43-27=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,84 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[9, 30], Operations: ['27-18=9', '43-13=30'] Exploring Operation: 9+30=39, Resulting Numbers: [39] 39,84 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 9*30=270, Resulting Numbers: [270] 270,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[27, 38], Operations: ['18-13=5', '43-5=38'] Exploring Operation: 27+38=65, Resulting Numbers: [65] 65,84 unequal: No Solution Exploring Operation: 27*38=1026, Resulting Numbers: [1026] 1026,84 unequal: No Solution Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[43, 32], Operations: ['18-13=5', '27+5=32'] Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,84 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,84 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[13, 34], Operations: ['27-18=9', '43-9=34'] Exploring Operation: 13+34=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 13*34=442, Resulting Numbers: [442] 442,84 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 41, 50, 29 ]
69
[ "7+41=48", "50-29=21", "48+21=69" ]
Current State: 69:[7, 41, 50, 29], Operations: [] Exploring Operation: 7+41=48, Resulting Numbers: [50, 29, 48] Generated Node #2: [50, 29, 48] from Operation: 7+41=48 Current State: 69:[50, 29, 48], Operations: ['7+41=48'] Exploring Operation: 50-29=21, Resulting Numbers: [48, 21] Generated Node #3: [48, 21] from Operation: 50-29=21 Current State: 69:[48, 21], Operations: ['7+41=48', '50-29=21'] Exploring Operation: 48+21=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[7, 41, 50, 29], Operations: [] Exploring Operation: 41-29=12, Resulting Numbers: [7, 50, 12] Generated Node #0,0: 69:[7, 50, 12] Operation: 41-29=12 Exploring Operation: 50-41=9, Resulting Numbers: [7, 29, 9] Generated Node #0,1: 69:[7, 29, 9] Operation: 50-41=9 Exploring Operation: 41+50=91, Resulting Numbers: [7, 29, 91] Generated Node #0,2: 69:[7, 29, 91] Operation: 41+50=91 Exploring Operation: 41+29=70, Resulting Numbers: [7, 50, 70] Generated Node #0,3: 69:[7, 50, 70] Operation: 41+29=70 Exploring Operation: 50-29=21, Resulting Numbers: [7, 41, 21] Generated Node #0,4: 69:[7, 41, 21] Operation: 50-29=21 Moving to Node #0,1 Current State: 69:[7, 29, 9], Operations: ['50-41=9'] Exploring Operation: 7+9=16, Resulting Numbers: [29, 16] Generated Node #0,1,0: 69:[29, 16] Operation: 7+9=16 Exploring Operation: 29-9=20, Resulting Numbers: [7, 20] Generated Node #0,1,1: 69:[7, 20] Operation: 29-9=20 Exploring Operation: 7*9=63, Resulting Numbers: [29, 63] Generated Node #0,1,2: 69:[29, 63] Operation: 7*9=63 Exploring Operation: 9-7=2, Resulting Numbers: [29, 2] Generated Node #0,1,3: 69:[29, 2] Operation: 9-7=2 Exploring Operation: 29-7=22, Resulting Numbers: [9, 22] Generated Node #0,1,4: 69:[9, 22] Operation: 29-7=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[7, 20], Operations: ['50-41=9', '29-9=20'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,69 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[29, 2], Operations: ['50-41=9', '9-7=2'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 69:[9, 22], Operations: ['50-41=9', '29-7=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,69 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[29, 63], Operations: ['50-41=9', '7*9=63'] Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 29+63=92, Resulting Numbers: [92] 92,69 unequal: No Solution Exploring Operation: 29*63=1827, Resulting Numbers: [1827] 1827,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[29, 16], Operations: ['50-41=9', '7+9=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,69 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,69 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: 69:[7, 41, 21], Operations: ['50-29=21'] Exploring Operation: 41-7=34, Resulting Numbers: [21, 34] Generated Node #0,4,0: 69:[21, 34] Operation: 41-7=34 Exploring Operation: 41-21=20, Resulting Numbers: [7, 20] Generated Node #0,4,1: 69:[7, 20] Operation: 41-21=20 Exploring Operation: 21/7=3, Resulting Numbers: [41, 3] Generated Node #0,4,2: 69:[41, 3] Operation: 21/7=3 Exploring Operation: 41+21=62, Resulting Numbers: [7, 62] Generated Node #0,4,3: 69:[7, 62] Operation: 41+21=62 Exploring Operation: 7+41=48, Resulting Numbers: [21, 48] Generated Node #0,4,4: 69:[21, 48] Operation: 7+41=48 Moving to Node #0,3 Current State: 69:[7, 50, 70], Operations: ['41+29=70'] Exploring Operation: 70-50=20, Resulting Numbers: [7, 20] Generated Node #0,3,0: 69:[7, 20] Operation: 70-50=20 Exploring Operation: 7+50=57, Resulting Numbers: [70, 57] Generated Node #0,3,1: 69:[70, 57] Operation: 7+50=57 Exploring Operation: 70/7=10, Resulting Numbers: [50, 10] Generated Node #0,3,2: 69:[50, 10] Operation: 70/7=10 Exploring Operation: 70-7=63, Resulting Numbers: [50, 63] Generated Node #0,3,3: 69:[50, 63] Operation: 70-7=63 Exploring Operation: 50-7=43, Resulting Numbers: [70, 43] Generated Node #0,3,4: 69:[70, 43] Operation: 50-7=43 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[7, 20], Operations: ['41+29=70', '70-50=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,69 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 69:[70, 57], Operations: ['41+29=70', '7+50=57'] Exploring Operation: 70+57=127, Resulting Numbers: [127] 127,69 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 70*57=3990, Resulting Numbers: [3990] 3990,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 69:[70, 43], Operations: ['41+29=70', '50-7=43'] Exploring Operation: 70+43=113, Resulting Numbers: [113] 113,69 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 70*43=3010, Resulting Numbers: [3010] 3010,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[50, 63], Operations: ['41+29=70', '70-7=63'] Exploring Operation: 50+63=113, Resulting Numbers: [113] 113,69 unequal: No Solution Exploring Operation: 50*63=3150, Resulting Numbers: [3150] 3150,69 unequal: No Solution Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[50, 10], Operations: ['41+29=70', '70/7=10'] Exploring Operation: 50*10=500, Resulting Numbers: [500] 500,69 unequal: No Solution Exploring Operation: 50+10=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 50/10=5, Resulting Numbers: [5] 5,69 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: 69:[7, 50, 12], Operations: ['41-29=12'] Exploring Operation: 50+12=62, Resulting Numbers: [7, 62] Generated Node #0,0,0: 69:[7, 62] Operation: 50+12=62 Exploring Operation: 50-12=38, Resulting Numbers: [7, 38] Generated Node #0,0,1: 69:[7, 38] Operation: 50-12=38 Exploring Operation: 12-7=5, Resulting Numbers: [50, 5] Generated Node #0,0,2: 69:[50, 5] Operation: 12-7=5 Exploring Operation: 7+12=19, Resulting Numbers: [50, 19] Generated Node #0,0,3: 69:[50, 19] Operation: 7+12=19 Exploring Operation: 7+50=57, Resulting Numbers: [12, 57] Generated Node #0,0,4: 69:[12, 57] Operation: 7+50=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[7, 62], Operations: ['41-29=12', '50+12=62'] Exploring Operation: 7*62=434, Resulting Numbers: [434] 434,69 unequal: No Solution Exploring Operation: 62-7=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[7, 41, 50, 29], Operations: [] Exploring Operation: 41-29=12, Resulting Numbers: [7, 50, 12] Generated Node #0,0: 69:[7, 50, 12] Operation: 41-29=12 Moving to Node #0,0 Current State: 69:[7, 50, 12], Operations: ['41-29=12'] Exploring Operation: 50+12=62, Resulting Numbers: [7, 62] Generated Node #0,0,0: 69:[7, 62] Operation: 50+12=62 Moving to Node #0,0,0 Current State: 69:[7, 62], Operations: ['41-29=12', '50+12=62'] Exploring Operation: 7+62=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.945313
hs_5
mult_heuristic
[ 90, 2, 61, 9 ]
49
[ "90-61=29", "2*29=58", "58-9=49" ]
Current State: 49:[90, 2, 61, 9], Operations: [] Exploring Operation: 90-61=29, Resulting Numbers: [2, 9, 29] Generated Node #2: [2, 9, 29] from Operation: 90-61=29 Current State: 49:[2, 9, 29], Operations: ['90-61=29'] Exploring Operation: 2*29=58, Resulting Numbers: [9, 58] Generated Node #3: [9, 58] from Operation: 2*29=58 Current State: 49:[9, 58], Operations: ['90-61=29', '2*29=58'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[90, 2, 61, 9], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [2, 61, 10] Generated Node #0,0: 49:[2, 61, 10] Operation: 90/9=10 Exploring Operation: 90-61=29, Resulting Numbers: [2, 9, 29] Generated Node #0,1: 49:[2, 9, 29] Operation: 90-61=29 Exploring Operation: 90/2=45, Resulting Numbers: [61, 9, 45] Generated Node #0,2: 49:[61, 9, 45] Operation: 90/2=45 Exploring Operation: 90-9=81, Resulting Numbers: [2, 61, 81] Generated Node #0,3: 49:[2, 61, 81] Operation: 90-9=81 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[61, 9, 45], Operations: ['90/2=45'] Exploring Operation: 9+45=54, Resulting Numbers: [61, 54] Generated Node #0,2,0: 49:[61, 54] Operation: 9+45=54 Exploring Operation: 61-45=16, Resulting Numbers: [9, 16] Generated Node #0,2,1: 49:[9, 16] Operation: 61-45=16 Exploring Operation: 45/9=5, Resulting Numbers: [61, 5] Generated Node #0,2,2: 49:[61, 5] Operation: 45/9=5 Exploring Operation: 61-9=52, Resulting Numbers: [45, 52] Generated Node #0,2,3: 49:[45, 52] Operation: 61-9=52 Moving to Node #0,2,3 Current State: 49:[45, 52], Operations: ['90/2=45', '61-9=52'] Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 45+52=97, Resulting Numbers: [97] 97,49 unequal: No Solution Exploring Operation: 45*52=2340, Resulting Numbers: [2340] 2340,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[9, 16], Operations: ['90/2=45', '61-45=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,49 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,49 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[61, 5], Operations: ['90/2=45', '45/9=5'] Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 61*5=305, Resulting Numbers: [305] 305,49 unequal: No Solution Exploring Operation: 61+5=66, Resulting Numbers: [66] 66,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[61, 54], Operations: ['90/2=45', '9+45=54'] Exploring Operation: 61*54=3294, Resulting Numbers: [3294] 3294,49 unequal: No Solution Exploring Operation: 61-54=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 61+54=115, Resulting Numbers: [115] 115,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[2, 61, 10], Operations: ['90/9=10'] Exploring Operation: 61-10=51, Resulting Numbers: [2, 51] Generated Node #0,0,0: 49:[2, 51] Operation: 61-10=51 Exploring Operation: 10-2=8, Resulting Numbers: [61, 8] Generated Node #0,0,1: 49:[61, 8] Operation: 10-2=8 Exploring Operation: 61-2=59, Resulting Numbers: [10, 59] Generated Node #0,0,2: 49:[10, 59] Operation: 61-2=59 Exploring Operation: 10/2=5, Resulting Numbers: [61, 5] Generated Node #0,0,3: 49:[61, 5] Operation: 10/2=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[2, 51], Operations: ['90/9=10', '61-10=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,49 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[90, 2, 61, 9], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [2, 61, 10] Generated Node #0,0: 49:[2, 61, 10] Operation: 90/9=10 Moving to Node #0,0 Current State: 49:[2, 61, 10], Operations: ['90/9=10'] Exploring Operation: 61-10=51, Resulting Numbers: [2, 51] Generated Node #0,0,0: 49:[2, 51] Operation: 61-10=51 Moving to Node #0,0,0 Current State: 49:[2, 51], Operations: ['90/9=10', '61-10=51'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 54, 25, 52, 68 ]
59
[ "54-52=2", "68/2=34", "25+34=59" ]
Current State: 59:[54, 25, 52, 68], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [25, 68, 2] Generated Node #2: [25, 68, 2] from Operation: 54-52=2 Current State: 59:[25, 68, 2], Operations: ['54-52=2'] Exploring Operation: 68/2=34, Resulting Numbers: [25, 34] Generated Node #3: [25, 34] from Operation: 68/2=34 Current State: 59:[25, 34], Operations: ['54-52=2', '68/2=34'] Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[54, 25, 52, 68], Operations: [] Exploring Operation: 68-25=43, Resulting Numbers: [54, 52, 43] Generated Node #0,0: 59:[54, 52, 43] Operation: 68-25=43 Exploring Operation: 25+52=77, Resulting Numbers: [54, 68, 77] Generated Node #0,1: 59:[54, 68, 77] Operation: 25+52=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[54, 52, 43], Operations: ['68-25=43'] Exploring Operation: 52+43=95, Resulting Numbers: [54, 95] Generated Node #0,0,0: 59:[54, 95] Operation: 52+43=95 Exploring Operation: 54+43=97, Resulting Numbers: [52, 97] Generated Node #0,0,1: 59:[52, 97] Operation: 54+43=97 Moving to Node #0,0,0 Current State: 59:[54, 95], Operations: ['68-25=43', '52+43=95'] Exploring Operation: 95-54=41, Resulting Numbers: [41] 41,59 unequal: No Solution Exploring Operation: 54+95=149, Resulting Numbers: [149] 149,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[52, 97], Operations: ['68-25=43', '54+43=97'] Exploring Operation: 97-52=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 52+97=149, Resulting Numbers: [149] 149,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[54, 68, 77], Operations: ['25+52=77'] Exploring Operation: 77-68=9, Resulting Numbers: [54, 9] Generated Node #0,1,0: 59:[54, 9] Operation: 77-68=9 Exploring Operation: 77-54=23, Resulting Numbers: [68, 23] Generated Node #0,1,1: 59:[68, 23] Operation: 77-54=23 Moving to Node #0,1,1 Current State: 59:[68, 23], Operations: ['25+52=77', '77-54=23'] Exploring Operation: 68+23=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 68-23=45, Resulting Numbers: [45] 45,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[54, 9], Operations: ['25+52=77', '77-68=9'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic