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
[ 30, 51, 21, 34 ]
35
[ "51-30=21", "21/21=1", "34+1=35" ]
Current State: 35:[30, 51, 21, 34], Operations: [] Exploring Operation: 51-30=21, Resulting Numbers: [21, 34, 21] Generated Node #2: [21, 34, 21] from Operation: 51-30=21 Current State: 35:[21, 34, 21], Operations: ['51-30=21'] Exploring Operation: 21/21=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 21/21=1 Current State: 35:[34, 1], Operations: ['51-30=21', '21/21=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[30, 51, 21, 34], Operations: [] Exploring Operation: 30-21=9, Resulting Numbers: [51, 34, 9] Generated Node #0,0: 35:[51, 34, 9] Operation: 30-21=9 Exploring Operation: 51-21=30, Resulting Numbers: [30, 34, 30] Generated Node #0,1: 35:[30, 34, 30] Operation: 51-21=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[30, 34, 30], Operations: ['51-21=30'] Exploring Operation: 30/30=1, Resulting Numbers: [34, 1] Generated Node #0,1,0: 35:[34, 1] Operation: 30/30=1 Exploring Operation: 34-30=4, Resulting Numbers: [30, 4] Generated Node #0,1,1: 35:[30, 4] Operation: 34-30=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[34, 1], Operations: ['51-21=30', '30/30=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[30, 51, 21, 34], Operations: [] Exploring Operation: 51-21=30, Resulting Numbers: [30, 34, 30] Generated Node #0,1: 35:[30, 34, 30] Operation: 51-21=30 Moving to Node #0,1 Current State: 35:[30, 34, 30], Operations: ['51-21=30'] Exploring Operation: 30/30=1, Resulting Numbers: [34, 1] Generated Node #0,1,0: 35:[34, 1] Operation: 30/30=1 Moving to Node #0,1,0 Current State: 35:[34, 1], Operations: ['51-21=30', '30/30=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 31, 91, 54, 8 ]
89
[ "54+8=62", "62/31=2", "91-2=89" ]
Current State: 89:[31, 91, 54, 8], Operations: [] Exploring Operation: 54+8=62, Resulting Numbers: [31, 91, 62] Generated Node #2: [31, 91, 62] from Operation: 54+8=62 Current State: 89:[31, 91, 62], Operations: ['54+8=62'] Exploring Operation: 62/31=2, Resulting Numbers: [91, 2] Generated Node #3: [91, 2] from Operation: 62/31=2 Current State: 89:[91, 2], Operations: ['54+8=62', '62/31=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[31, 91, 54, 8], Operations: [] Exploring Operation: 91-8=83, Resulting Numbers: [31, 54, 83] Generated Node #0,0: 89:[31, 54, 83] Operation: 91-8=83 Exploring Operation: 31+54=85, Resulting Numbers: [91, 8, 85] Generated Node #0,1: 89:[91, 8, 85] Operation: 31+54=85 Exploring Operation: 31+8=39, Resulting Numbers: [91, 54, 39] Generated Node #0,2: 89:[91, 54, 39] Operation: 31+8=39 Exploring Operation: 31-8=23, Resulting Numbers: [91, 54, 23] Generated Node #0,3: 89:[91, 54, 23] Operation: 31-8=23 Exploring Operation: 54+8=62, Resulting Numbers: [31, 91, 62] Generated Node #0,4: 89:[31, 91, 62] Operation: 54+8=62 Moving to Node #0,1 Current State: 89:[91, 8, 85], Operations: ['31+54=85'] Exploring Operation: 91+8=99, Resulting Numbers: [85, 99] Generated Node #0,1,0: 89:[85, 99] Operation: 91+8=99 Exploring Operation: 8+85=93, Resulting Numbers: [91, 93] Generated Node #0,1,1: 89:[91, 93] Operation: 8+85=93 Exploring Operation: 91-8=83, Resulting Numbers: [85, 83] Generated Node #0,1,2: 89:[85, 83] Operation: 91-8=83 Exploring Operation: 91-85=6, Resulting Numbers: [8, 6] Generated Node #0,1,3: 89:[8, 6] Operation: 91-85=6 Exploring Operation: 85-8=77, Resulting Numbers: [91, 77] Generated Node #0,1,4: 89:[91, 77] Operation: 85-8=77 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[91, 93], Operations: ['31+54=85', '8+85=93'] Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,89 unequal: No Solution Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[85, 83], Operations: ['31+54=85', '91-8=83'] Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 85+83=168, Resulting Numbers: [168] 168,89 unequal: No Solution Exploring Operation: 85*83=7055, Resulting Numbers: [7055] 7055,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[85, 99], Operations: ['31+54=85', '91+8=99'] Exploring Operation: 85*99=8415, Resulting Numbers: [8415] 8415,89 unequal: No Solution Exploring Operation: 99-85=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 85+99=184, Resulting Numbers: [184] 184,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 89:[91, 77], Operations: ['31+54=85', '85-8=77'] Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,89 unequal: No Solution Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,89 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[8, 6], Operations: ['31+54=85', '91-85=6'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 89:[31, 91, 62], Operations: ['54+8=62'] Exploring Operation: 91-31=60, Resulting Numbers: [62, 60] Generated Node #0,4,0: 89:[62, 60] Operation: 91-31=60 Exploring Operation: 62/31=2, Resulting Numbers: [91, 2] Generated Node #0,4,1: 89:[91, 2] Operation: 62/31=2 Exploring Operation: 62-31=31, Resulting Numbers: [91, 31] Generated Node #0,4,2: 89:[91, 31] Operation: 62-31=31 Exploring Operation: 31+62=93, Resulting Numbers: [91, 93] Generated Node #0,4,3: 89:[91, 93] Operation: 31+62=93 Exploring Operation: 31+91=122, Resulting Numbers: [62, 122] Generated Node #0,4,4: 89:[62, 122] Operation: 31+91=122 Moving to Node #0,2 Current State: 89:[91, 54, 39], Operations: ['31+8=39'] Exploring Operation: 54-39=15, Resulting Numbers: [91, 15] Generated Node #0,2,0: 89:[91, 15] Operation: 54-39=15 Exploring Operation: 91-54=37, Resulting Numbers: [39, 37] Generated Node #0,2,1: 89:[39, 37] Operation: 91-54=37 Exploring Operation: 54+39=93, Resulting Numbers: [91, 93] Generated Node #0,2,2: 89:[91, 93] Operation: 54+39=93 Exploring Operation: 91+39=130, Resulting Numbers: [54, 130] Generated Node #0,2,3: 89:[54, 130] Operation: 91+39=130 Exploring Operation: 91-39=52, Resulting Numbers: [54, 52] Generated Node #0,2,4: 89:[54, 52] Operation: 91-39=52 Moving to Node #0,0 Current State: 89:[31, 54, 83], Operations: ['91-8=83'] Exploring Operation: 31+83=114, Resulting Numbers: [54, 114] Generated Node #0,0,0: 89:[54, 114] Operation: 31+83=114 Exploring Operation: 54-31=23, Resulting Numbers: [83, 23] Generated Node #0,0,1: 89:[83, 23] Operation: 54-31=23 Exploring Operation: 54+83=137, Resulting Numbers: [31, 137] Generated Node #0,0,2: 89:[31, 137] Operation: 54+83=137 Exploring Operation: 31+54=85, Resulting Numbers: [83, 85] Generated Node #0,0,3: 89:[83, 85] Operation: 31+54=85 Exploring Operation: 83-31=52, Resulting Numbers: [54, 52] Generated Node #0,0,4: 89:[54, 52] Operation: 83-31=52 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[83, 85], Operations: ['91-8=83', '31+54=85'] Exploring Operation: 83+85=168, Resulting Numbers: [168] 168,89 unequal: No Solution Exploring Operation: 85-83=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 83*85=7055, Resulting Numbers: [7055] 7055,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[54, 114], Operations: ['91-8=83', '31+83=114'] Exploring Operation: 54*114=6156, Resulting Numbers: [6156] 6156,89 unequal: No Solution Exploring Operation: 114-54=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 54+114=168, Resulting Numbers: [168] 168,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[83, 23], Operations: ['91-8=83', '54-31=23'] Exploring Operation: 83*23=1909, Resulting Numbers: [1909] 1909,89 unequal: No Solution Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 89:[54, 52], Operations: ['91-8=83', '83-31=52'] Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,89 unequal: No Solution Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[31, 137], Operations: ['91-8=83', '54+83=137'] Exploring Operation: 137-31=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 31+137=168, Resulting Numbers: [168] 168,89 unequal: No Solution Exploring Operation: 31*137=4247, Resulting Numbers: [4247] 4247,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 89:[91, 54, 23], Operations: ['31-8=23'] Exploring Operation: 91-54=37, Resulting Numbers: [23, 37] Generated Node #0,3,0: 89:[23, 37] Operation: 91-54=37 Exploring Operation: 91-23=68, Resulting Numbers: [54, 68] Generated Node #0,3,1: 89:[54, 68] Operation: 91-23=68 Exploring Operation: 54-23=31, Resulting Numbers: [91, 31] Generated Node #0,3,2: 89:[91, 31] Operation: 54-23=31 Exploring Operation: 54+23=77, Resulting Numbers: [91, 77] Generated Node #0,3,3: 89:[91, 77] Operation: 54+23=77 Exploring Operation: 91+23=114, Resulting Numbers: [54, 114] Generated Node #0,3,4: 89:[54, 114] Operation: 91+23=114 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 89:[91, 77], Operations: ['31-8=23', '54+23=77'] Exploring Operation: 91*77=7007, Resulting Numbers: [7007] 7007,89 unequal: No Solution Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 91+77=168, Resulting Numbers: [168] 168,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 89:[54, 68], Operations: ['31-8=23', '91-23=68'] Exploring Operation: 68-54=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 54*68=3672, Resulting Numbers: [3672] 3672,89 unequal: No Solution Exploring Operation: 54+68=122, Resulting Numbers: [122] 122,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 89:[91, 31], Operations: ['31-8=23', '54-23=31'] Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 91*31=2821, Resulting Numbers: [2821] 2821,89 unequal: No Solution Exploring Operation: 91+31=122, Resulting Numbers: [122] 122,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 89:[54, 114], Operations: ['31-8=23', '91+23=114'] Exploring Operation: 54+114=168, Resulting Numbers: [168] 168,89 unequal: No Solution Exploring Operation: 114-54=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 54*114=6156, Resulting Numbers: [6156] 6156,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 89:[23, 37], Operations: ['31-8=23', '91-54=37'] Exploring Operation: 23*37=851, Resulting Numbers: [851] 851,89 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,89 unequal: No Solution Exploring Operation: 23+37=60, Resulting Numbers: [60] 60,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 89:[91, 93], Operations: ['54+8=62', '31+62=93'] Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,89 unequal: No Solution Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[91, 93], Operations: ['31+8=39', '54+39=93'] Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,89 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[62, 60], Operations: ['54+8=62', '91-31=60'] Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 62*60=3720, Resulting Numbers: [3720] 3720,89 unequal: No Solution Exploring Operation: 62+60=122, Resulting Numbers: [122] 122,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[91, 31], Operations: ['54+8=62', '62-31=31'] Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 91+31=122, Resulting Numbers: [122] 122,89 unequal: No Solution Exploring Operation: 91*31=2821, Resulting Numbers: [2821] 2821,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[62, 122], Operations: ['54+8=62', '31+91=122'] Exploring Operation: 122-62=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 62*122=7564, Resulting Numbers: [7564] 7564,89 unequal: No Solution Exploring Operation: 62+122=184, Resulting Numbers: [184] 184,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[54, 52], Operations: ['31+8=39', '91-39=52'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,89 unequal: No Solution Exploring Operation: 54+52=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 54*52=2808, Resulting Numbers: [2808] 2808,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[91, 15], Operations: ['31+8=39', '54-39=15'] Exploring Operation: 91+15=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 91*15=1365, Resulting Numbers: [1365] 1365,89 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[54, 130], Operations: ['31+8=39', '91+39=130'] Exploring Operation: 130-54=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 54*130=7020, Resulting Numbers: [7020] 7020,89 unequal: No Solution Exploring Operation: 54+130=184, Resulting Numbers: [184] 184,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[91, 2], Operations: ['54+8=62', '62/31=2'] Exploring Operation: 91*2=182, Resulting Numbers: [182] 182,89 unequal: No Solution Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[31, 91, 54, 8], Operations: [] Exploring Operation: 54+8=62, Resulting Numbers: [31, 91, 62] Generated Node #0,4: 89:[31, 91, 62] Operation: 54+8=62 Moving to Node #0,4 Current State: 89:[31, 91, 62], Operations: ['54+8=62'] Exploring Operation: 62/31=2, Resulting Numbers: [91, 2] Generated Node #0,4,1: 89:[91, 2] Operation: 62/31=2 Moving to Node #0,4,1 Current State: 89:[91, 2], Operations: ['54+8=62', '62/31=2'] Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.907986
hs_5
sum_heuristic
[ 16, 57, 42, 33 ]
19
[ "57+42=99", "99/33=3", "16+3=19" ]
Current State: 19:[16, 57, 42, 33], Operations: [] Exploring Operation: 57+42=99, Resulting Numbers: [16, 33, 99] Generated Node #2: [16, 33, 99] from Operation: 57+42=99 Current State: 19:[16, 33, 99], Operations: ['57+42=99'] Exploring Operation: 99/33=3, Resulting Numbers: [16, 3] Generated Node #3: [16, 3] from Operation: 99/33=3 Current State: 19:[16, 3], Operations: ['57+42=99', '99/33=3'] Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[16, 57, 42, 33], Operations: [] Exploring Operation: 57-42=15, Resulting Numbers: [16, 33, 15] Generated Node #0,0: 19:[16, 33, 15] Operation: 57-42=15 Exploring Operation: 57-33=24, Resulting Numbers: [16, 42, 24] Generated Node #0,1: 19:[16, 42, 24] Operation: 57-33=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[16, 33, 15], Operations: ['57-42=15'] Exploring Operation: 33-15=18, Resulting Numbers: [16, 18] Generated Node #0,0,0: 19:[16, 18] Operation: 33-15=18 Exploring Operation: 33-16=17, Resulting Numbers: [15, 17] Generated Node #0,0,1: 19:[15, 17] Operation: 33-16=17 Moving to Node #0,0,0 Current State: 19:[16, 18], Operations: ['57-42=15', '33-15=18'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[15, 17], Operations: ['57-42=15', '33-16=17'] Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,19 unequal: No Solution No 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: 19:[16, 42, 24], Operations: ['57-33=24'] Exploring Operation: 42-16=26, Resulting Numbers: [24, 26] Generated Node #0,1,0: 19:[24, 26] Operation: 42-16=26 Exploring Operation: 42-24=18, Resulting Numbers: [16, 18] Generated Node #0,1,1: 19:[16, 18] Operation: 42-24=18 Moving to Node #0,1,1 Current State: 19:[16, 18], Operations: ['57-33=24', '42-24=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,19 unequal: No Solution Moving to Node #0,1,0 Current State: 19:[24, 26], Operations: ['57-33=24', '42-16=26'] Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,19 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
[ 68, 79, 29, 87 ]
47
[ "79-68=11", "87-29=58", "58-11=47" ]
Current State: 47:[68, 79, 29, 87], Operations: [] Exploring Operation: 79-68=11, Resulting Numbers: [29, 87, 11] Generated Node #2: [29, 87, 11] from Operation: 79-68=11 Current State: 47:[29, 87, 11], Operations: ['79-68=11'] Exploring Operation: 87-29=58, Resulting Numbers: [11, 58] Generated Node #3: [11, 58] from Operation: 87-29=58 Current State: 47:[11, 58], Operations: ['79-68=11', '87-29=58'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[68, 79, 29, 87], Operations: [] Exploring Operation: 87-68=19, Resulting Numbers: [79, 29, 19] Generated Node #0,0: 47:[79, 29, 19] Operation: 87-68=19 Exploring Operation: 87-29=58, Resulting Numbers: [68, 79, 58] Generated Node #0,1: 47:[68, 79, 58] Operation: 87-29=58 Exploring Operation: 68-29=39, Resulting Numbers: [79, 87, 39] Generated Node #0,2: 47:[79, 87, 39] Operation: 68-29=39 Exploring Operation: 87-79=8, Resulting Numbers: [68, 29, 8] Generated Node #0,3: 47:[68, 29, 8] Operation: 87-79=8 Exploring Operation: 79-29=50, Resulting Numbers: [68, 87, 50] Generated Node #0,4: 47:[68, 87, 50] Operation: 79-29=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[68, 79, 58], Operations: ['87-29=58'] Exploring Operation: 79-68=11, Resulting Numbers: [58, 11] Generated Node #0,1,0: 47:[58, 11] Operation: 79-68=11 Exploring Operation: 68+79=147, Resulting Numbers: [58, 147] Generated Node #0,1,1: 47:[58, 147] Operation: 68+79=147 Exploring Operation: 68+58=126, Resulting Numbers: [79, 126] Generated Node #0,1,2: 47:[79, 126] Operation: 68+58=126 Exploring Operation: 79-58=21, Resulting Numbers: [68, 21] Generated Node #0,1,3: 47:[68, 21] Operation: 79-58=21 Exploring Operation: 68-58=10, Resulting Numbers: [79, 10] Generated Node #0,1,4: 47:[79, 10] Operation: 68-58=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[58, 11], Operations: ['87-29=58', '79-68=11'] Exploring Operation: 58+11=69, Resulting Numbers: [69] 69,47 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[68, 79, 29, 87], Operations: [] Exploring Operation: 87-29=58, Resulting Numbers: [68, 79, 58] Generated Node #0,1: 47:[68, 79, 58] Operation: 87-29=58 Moving to Node #0,1 Current State: 47:[68, 79, 58], Operations: ['87-29=58'] Exploring Operation: 79-68=11, Resulting Numbers: [58, 11] Generated Node #0,1,0: 47:[58, 11] Operation: 79-68=11 Moving to Node #0,1,0 Current State: 47:[58, 11], Operations: ['87-29=58', '79-68=11'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 91, 86, 61, 77 ]
21
[ "91-86=5", "77-61=16", "5+16=21" ]
Current State: 21:[91, 86, 61, 77], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [61, 77, 5] Generated Node #2: [61, 77, 5] from Operation: 91-86=5 Current State: 21:[61, 77, 5], Operations: ['91-86=5'] Exploring Operation: 77-61=16, Resulting Numbers: [5, 16] Generated Node #3: [5, 16] from Operation: 77-61=16 Current State: 21:[5, 16], Operations: ['91-86=5', '77-61=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[91, 86, 61, 77], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [61, 77, 5] Generated Node #0,0: 21:[61, 77, 5] Operation: 91-86=5 Exploring Operation: 91-77=14, Resulting Numbers: [86, 61, 14] Generated Node #0,1: 21:[86, 61, 14] Operation: 91-77=14 Exploring Operation: 91-61=30, Resulting Numbers: [86, 77, 30] Generated Node #0,2: 21:[86, 77, 30] Operation: 91-61=30 Exploring Operation: 86-77=9, Resulting Numbers: [91, 61, 9] Generated Node #0,3: 21:[91, 61, 9] Operation: 86-77=9 Moving to Node #0,0 Current State: 21:[61, 77, 5], Operations: ['91-86=5'] Exploring Operation: 61+5=66, Resulting Numbers: [77, 66] Generated Node #0,0,0: 21:[77, 66] Operation: 61+5=66 Exploring Operation: 61-5=56, Resulting Numbers: [77, 56] Generated Node #0,0,1: 21:[77, 56] Operation: 61-5=56 Exploring Operation: 77-61=16, Resulting Numbers: [5, 16] Generated Node #0,0,2: 21:[5, 16] Operation: 77-61=16 Exploring Operation: 77-5=72, Resulting Numbers: [61, 72] Generated Node #0,0,3: 21:[61, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[5, 16], Operations: ['91-86=5', '77-61=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,21 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[91, 86, 61, 77], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [61, 77, 5] Generated Node #0,0: 21:[61, 77, 5] Operation: 91-86=5 Moving to Node #0,0 Current State: 21:[61, 77, 5], Operations: ['91-86=5'] Exploring Operation: 77-61=16, Resulting Numbers: [5, 16] Generated Node #0,0,2: 21:[5, 16] Operation: 77-61=16 Moving to Node #0,0,2 Current State: 21:[5, 16], Operations: ['91-86=5', '77-61=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 42, 94, 53, 24 ]
59
[ "42+94=136", "53+24=77", "136-77=59" ]
Current State: 59:[42, 94, 53, 24], Operations: [] Exploring Operation: 42+94=136, Resulting Numbers: [53, 24, 136] Generated Node #2: [53, 24, 136] from Operation: 42+94=136 Current State: 59:[53, 24, 136], Operations: ['42+94=136'] Exploring Operation: 53+24=77, Resulting Numbers: [136, 77] Generated Node #3: [136, 77] from Operation: 53+24=77 Current State: 59:[136, 77], Operations: ['42+94=136', '53+24=77'] Exploring Operation: 136-77=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[42, 94, 53, 24], Operations: [] Exploring Operation: 53+24=77, Resulting Numbers: [42, 94, 77] Generated Node #0,0: 59:[42, 94, 77] Operation: 53+24=77 Exploring Operation: 94-42=52, Resulting Numbers: [53, 24, 52] Generated Node #0,1: 59:[53, 24, 52] Operation: 94-42=52 Exploring Operation: 94-53=41, Resulting Numbers: [42, 24, 41] Generated Node #0,2: 59:[42, 24, 41] Operation: 94-53=41 Exploring Operation: 42+24=66, Resulting Numbers: [94, 53, 66] Generated Node #0,3: 59:[94, 53, 66] Operation: 42+24=66 Exploring Operation: 94-24=70, Resulting Numbers: [42, 53, 70] Generated Node #0,4: 59:[42, 53, 70] Operation: 94-24=70 Moving to Node #0,4 Current State: 59:[42, 53, 70], Operations: ['94-24=70'] Exploring Operation: 53-42=11, Resulting Numbers: [70, 11] Generated Node #0,4,0: 59:[70, 11] Operation: 53-42=11 Exploring Operation: 42+53=95, Resulting Numbers: [70, 95] Generated Node #0,4,1: 59:[70, 95] Operation: 42+53=95 Exploring Operation: 42+70=112, Resulting Numbers: [53, 112] Generated Node #0,4,2: 59:[53, 112] Operation: 42+70=112 Exploring Operation: 70-42=28, Resulting Numbers: [53, 28] Generated Node #0,4,3: 59:[53, 28] Operation: 70-42=28 Exploring Operation: 70-53=17, Resulting Numbers: [42, 17] Generated Node #0,4,4: 59:[42, 17] Operation: 70-53=17 Moving to Node #0,3 Current State: 59:[94, 53, 66], Operations: ['42+24=66'] Exploring Operation: 53+66=119, Resulting Numbers: [94, 119] Generated Node #0,3,0: 59:[94, 119] Operation: 53+66=119 Exploring Operation: 94-53=41, Resulting Numbers: [66, 41] Generated Node #0,3,1: 59:[66, 41] Operation: 94-53=41 Exploring Operation: 66-53=13, Resulting Numbers: [94, 13] Generated Node #0,3,2: 59:[94, 13] Operation: 66-53=13 Exploring Operation: 94+53=147, Resulting Numbers: [66, 147] Generated Node #0,3,3: 59:[66, 147] Operation: 94+53=147 Exploring Operation: 94-66=28, Resulting Numbers: [53, 28] Generated Node #0,3,4: 59:[53, 28] Operation: 94-66=28 Moving to Node #0,1 Current State: 59:[53, 24, 52], Operations: ['94-42=52'] Exploring Operation: 52-24=28, Resulting Numbers: [53, 28] Generated Node #0,1,0: 59:[53, 28] Operation: 52-24=28 Exploring Operation: 53+52=105, Resulting Numbers: [24, 105] Generated Node #0,1,1: 59:[24, 105] Operation: 53+52=105 Exploring Operation: 53+24=77, Resulting Numbers: [52, 77] Generated Node #0,1,2: 59:[52, 77] Operation: 53+24=77 Exploring Operation: 53-24=29, Resulting Numbers: [52, 29] Generated Node #0,1,3: 59:[52, 29] Operation: 53-24=29 Exploring Operation: 24+52=76, Resulting Numbers: [53, 76] Generated Node #0,1,4: 59:[53, 76] Operation: 24+52=76 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 59:[53, 76], Operations: ['94-42=52', '24+52=76'] Exploring Operation: 76-53=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 53+76=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 53*76=4028, Resulting Numbers: [4028] 4028,59 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:[52, 77], Operations: ['94-42=52', '53+24=77'] Exploring Operation: 52+77=129, Resulting Numbers: [129] 129,59 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 52*77=4004, Resulting Numbers: [4004] 4004,59 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 #0,1,0 Current State: 59:[53, 28], Operations: ['94-42=52', '52-24=28'] Exploring Operation: 53*28=1484, Resulting Numbers: [1484] 1484,59 unequal: No Solution Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 53+28=81, Resulting Numbers: [81] 81,59 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 #0,1,3 Current State: 59:[52, 29], Operations: ['94-42=52', '53-24=29'] Exploring Operation: 52+29=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 52-29=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 52*29=1508, Resulting Numbers: [1508] 1508,59 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:[24, 105], Operations: ['94-42=52', '53+52=105'] Exploring Operation: 24*105=2520, Resulting Numbers: [2520] 2520,59 unequal: No Solution Exploring Operation: 105-24=81, Resulting Numbers: [81] 81,59 unequal: No Solution Exploring Operation: 24+105=129, Resulting Numbers: [129] 129,59 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: 59:[42, 94, 77], Operations: ['53+24=77'] Exploring Operation: 94-77=17, Resulting Numbers: [42, 17] Generated Node #0,0,0: 59:[42, 17] Operation: 94-77=17 Exploring Operation: 42+77=119, Resulting Numbers: [94, 119] Generated Node #0,0,1: 59:[94, 119] Operation: 42+77=119 Exploring Operation: 77-42=35, Resulting Numbers: [94, 35] Generated Node #0,0,2: 59:[94, 35] Operation: 77-42=35 Exploring Operation: 42+94=136, Resulting Numbers: [77, 136] Generated Node #0,0,3: 59:[77, 136] Operation: 42+94=136 Exploring Operation: 94-42=52, Resulting Numbers: [77, 52] Generated Node #0,0,4: 59:[77, 52] Operation: 94-42=52 Moving to Node #0,2 Current State: 59:[42, 24, 41], Operations: ['94-53=41'] Exploring Operation: 42+24=66, Resulting Numbers: [41, 66] Generated Node #0,2,0: 59:[41, 66] Operation: 42+24=66 Exploring Operation: 41-24=17, Resulting Numbers: [42, 17] Generated Node #0,2,1: 59:[42, 17] Operation: 41-24=17 Exploring Operation: 42-24=18, Resulting Numbers: [41, 18] Generated Node #0,2,2: 59:[41, 18] Operation: 42-24=18 Exploring Operation: 42+41=83, Resulting Numbers: [24, 83] Generated Node #0,2,3: 59:[24, 83] Operation: 42+41=83 Exploring Operation: 24+41=65, Resulting Numbers: [42, 65] Generated Node #0,2,4: 59:[42, 65] Operation: 24+41=65 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 59:[42, 65], Operations: ['94-53=41', '24+41=65'] Exploring Operation: 42+65=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 65-42=23, Resulting Numbers: [23] 23,59 unequal: No Solution Exploring Operation: 42*65=2730, Resulting Numbers: [2730] 2730,59 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:[41, 66], Operations: ['94-53=41', '42+24=66'] Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,59 unequal: No Solution Exploring Operation: 41+66=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 41*66=2706, Resulting Numbers: [2706] 2706,59 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:[42, 17], Operations: ['94-53=41', '41-24=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[42, 94, 53, 24], Operations: [] Exploring Operation: 94-53=41, Resulting Numbers: [42, 24, 41] Generated Node #0,2: 59:[42, 24, 41] Operation: 94-53=41 Moving to Node #0,2 Current State: 59:[42, 24, 41], Operations: ['94-53=41'] Exploring Operation: 41-24=17, Resulting Numbers: [42, 17] Generated Node #0,2,1: 59:[42, 17] Operation: 41-24=17 Moving to Node #0,2,1 Current State: 59:[42, 17], Operations: ['94-53=41', '41-24=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
sum_heuristic
[ 84, 2, 93, 22 ]
40
[ "93-84=9", "2*9=18", "22+18=40" ]
Current State: 40:[84, 2, 93, 22], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [2, 22, 9] Generated Node #2: [2, 22, 9] from Operation: 93-84=9 Current State: 40:[2, 22, 9], Operations: ['93-84=9'] Exploring Operation: 2*9=18, Resulting Numbers: [22, 18] Generated Node #3: [22, 18] from Operation: 2*9=18 Current State: 40:[22, 18], Operations: ['93-84=9', '2*9=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[84, 2, 93, 22], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [2, 22, 9] Generated Node #0,0: 40:[2, 22, 9] Operation: 93-84=9 Moving to Node #0,0 Current State: 40:[2, 22, 9], Operations: ['93-84=9'] Exploring Operation: 22-2=20, Resulting Numbers: [9, 20] Generated Node #0,0,0: 40:[9, 20] Operation: 22-2=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[9, 20], Operations: ['93-84=9', '22-2=20'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,40 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
[ 27, 46, 24, 16 ]
94
[ "27-24=3", "16*3=48", "46+48=94" ]
Current State: 94:[27, 46, 24, 16], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [46, 16, 3] Generated Node #2: [46, 16, 3] from Operation: 27-24=3 Current State: 94:[46, 16, 3], Operations: ['27-24=3'] Exploring Operation: 16*3=48, Resulting Numbers: [46, 48] Generated Node #3: [46, 48] from Operation: 16*3=48 Current State: 94:[46, 48], Operations: ['27-24=3', '16*3=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[27, 46, 24, 16], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [46, 16, 3] Generated Node #0,0: 94:[46, 16, 3] Operation: 27-24=3 Exploring Operation: 27+24=51, Resulting Numbers: [46, 16, 51] Generated Node #0,1: 94:[46, 16, 51] Operation: 27+24=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[46, 16, 3], Operations: ['27-24=3'] Exploring Operation: 16-3=13, Resulting Numbers: [46, 13] Generated Node #0,0,0: 94:[46, 13] Operation: 16-3=13 Exploring Operation: 16*3=48, Resulting Numbers: [46, 48] Generated Node #0,0,1: 94:[46, 48] Operation: 16*3=48 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[46, 48], Operations: ['27-24=3', '16*3=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[27, 46, 24, 16], Operations: [] Exploring Operation: 27-24=3, Resulting Numbers: [46, 16, 3] Generated Node #0,0: 94:[46, 16, 3] Operation: 27-24=3 Moving to Node #0,0 Current State: 94:[46, 16, 3], Operations: ['27-24=3'] Exploring Operation: 16*3=48, Resulting Numbers: [46, 48] Generated Node #0,0,1: 94:[46, 48] Operation: 16*3=48 Moving to Node #0,0,1 Current State: 94:[46, 48], Operations: ['27-24=3', '16*3=48'] Exploring Operation: 46+48=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 4, 39, 93, 96 ]
33
[ "4*39=156", "93+96=189", "189-156=33" ]
Current State: 33:[4, 39, 93, 96], Operations: [] Exploring Operation: 4*39=156, Resulting Numbers: [93, 96, 156] Generated Node #2: [93, 96, 156] from Operation: 4*39=156 Current State: 33:[93, 96, 156], Operations: ['4*39=156'] Exploring Operation: 93+96=189, Resulting Numbers: [156, 189] Generated Node #3: [156, 189] from Operation: 93+96=189 Current State: 33:[156, 189], Operations: ['4*39=156', '93+96=189'] Exploring Operation: 189-156=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[4, 39, 93, 96], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [4, 39, 3] Generated Node #0,0: 33:[4, 39, 3] Operation: 96-93=3 Moving to Node #0,0 Current State: 33:[4, 39, 3], Operations: ['96-93=3'] Exploring Operation: 39-4=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 33:[3, 35] Operation: 39-4=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[3, 35], Operations: ['96-93=3', '39-4=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 96, 64, 36, 76 ]
52
[ "64*36=2304", "2304/96=24", "76-24=52" ]
Current State: 52:[96, 64, 36, 76], Operations: [] Exploring Operation: 64*36=2304, Resulting Numbers: [96, 76, 2304] Generated Node #2: [96, 76, 2304] from Operation: 64*36=2304 Current State: 52:[96, 76, 2304], Operations: ['64*36=2304'] Exploring Operation: 2304/96=24, Resulting Numbers: [76, 24] Generated Node #3: [76, 24] from Operation: 2304/96=24 Current State: 52:[76, 24], Operations: ['64*36=2304', '2304/96=24'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[96, 64, 36, 76], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [64, 36, 20] Generated Node #0,0: 52:[64, 36, 20] Operation: 96-76=20 Exploring Operation: 96-64=32, Resulting Numbers: [36, 76, 32] Generated Node #0,1: 52:[36, 76, 32] Operation: 96-64=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[64, 36, 20], Operations: ['96-76=20'] Exploring Operation: 36-20=16, Resulting Numbers: [64, 16] Generated Node #0,0,0: 52:[64, 16] Operation: 36-20=16 Exploring Operation: 64-36=28, Resulting Numbers: [20, 28] Generated Node #0,0,1: 52:[20, 28] Operation: 64-36=28 Moving to Node #0,0,1 Current State: 52:[20, 28], Operations: ['96-76=20', '64-36=28'] Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[64, 16], Operations: ['96-76=20', '36-20=16'] Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,52 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[36, 76, 32], Operations: ['96-64=32'] Exploring Operation: 76-32=44, Resulting Numbers: [36, 44] Generated Node #0,1,0: 52:[36, 44] Operation: 76-32=44 Exploring Operation: 76-36=40, Resulting Numbers: [32, 40] Generated Node #0,1,1: 52:[32, 40] Operation: 76-36=40 Moving to Node #0,1,0 Current State: 52:[36, 44], Operations: ['96-64=32', '76-32=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[32, 40], Operations: ['96-64=32', '76-36=40'] Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,52 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
[ 43, 42, 23, 28 ]
52
[ "43-42=1", "23+28=51", "1+51=52" ]
Current State: 52:[43, 42, 23, 28], Operations: [] Exploring Operation: 43-42=1, Resulting Numbers: [23, 28, 1] Generated Node #2: [23, 28, 1] from Operation: 43-42=1 Current State: 52:[23, 28, 1], Operations: ['43-42=1'] Exploring Operation: 23+28=51, Resulting Numbers: [1, 51] Generated Node #3: [1, 51] from Operation: 23+28=51 Current State: 52:[1, 51], Operations: ['43-42=1', '23+28=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[43, 42, 23, 28], Operations: [] Exploring Operation: 43-42=1, Resulting Numbers: [23, 28, 1] Generated Node #0,0: 52:[23, 28, 1] Operation: 43-42=1 Exploring Operation: 42-28=14, Resulting Numbers: [43, 23, 14] Generated Node #0,1: 52:[43, 23, 14] Operation: 42-28=14 Exploring Operation: 43-28=15, Resulting Numbers: [42, 23, 15] Generated Node #0,2: 52:[42, 23, 15] Operation: 43-28=15 Exploring Operation: 42-23=19, Resulting Numbers: [43, 28, 19] Generated Node #0,3: 52:[43, 28, 19] Operation: 42-23=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[23, 28, 1], Operations: ['43-42=1'] Exploring Operation: 23+1=24, Resulting Numbers: [28, 24] Generated Node #0,0,0: 52:[28, 24] Operation: 23+1=24 Exploring Operation: 23+28=51, Resulting Numbers: [1, 51] Generated Node #0,0,1: 52:[1, 51] Operation: 23+28=51 Exploring Operation: 28-1=27, Resulting Numbers: [23, 27] Generated Node #0,0,2: 52:[23, 27] Operation: 28-1=27 Exploring Operation: 28-23=5, Resulting Numbers: [1, 5] Generated Node #0,0,3: 52:[1, 5] Operation: 28-23=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[1, 51], Operations: ['43-42=1', '23+28=51'] Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,52 unequal: No Solution Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[43, 42, 23, 28], Operations: [] Exploring Operation: 43-42=1, Resulting Numbers: [23, 28, 1] Generated Node #0,0: 52:[23, 28, 1] Operation: 43-42=1 Moving to Node #0,0 Current State: 52:[23, 28, 1], Operations: ['43-42=1'] Exploring Operation: 23+28=51, Resulting Numbers: [1, 51] Generated Node #0,0,1: 52:[1, 51] Operation: 23+28=51 Moving to Node #0,0,1 Current State: 52:[1, 51], Operations: ['43-42=1', '23+28=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 68, 90, 10, 81 ]
93
[ "90-68=22", "81-10=71", "22+71=93" ]
Current State: 93:[68, 90, 10, 81], Operations: [] Exploring Operation: 90-68=22, Resulting Numbers: [10, 81, 22] Generated Node #2: [10, 81, 22] from Operation: 90-68=22 Current State: 93:[10, 81, 22], Operations: ['90-68=22'] Exploring Operation: 81-10=71, Resulting Numbers: [22, 71] Generated Node #3: [22, 71] from Operation: 81-10=71 Current State: 93:[22, 71], Operations: ['90-68=22', '81-10=71'] Exploring Operation: 22+71=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[68, 90, 10, 81], Operations: [] Exploring Operation: 10+81=91, Resulting Numbers: [68, 90, 91] Generated Node #0,0: 93:[68, 90, 91] Operation: 10+81=91 Exploring Operation: 81-68=13, Resulting Numbers: [90, 10, 13] Generated Node #0,1: 93:[90, 10, 13] Operation: 81-68=13 Exploring Operation: 68+10=78, Resulting Numbers: [90, 81, 78] Generated Node #0,2: 93:[90, 81, 78] Operation: 68+10=78 Exploring Operation: 90-68=22, Resulting Numbers: [10, 81, 22] Generated Node #0,3: 93:[10, 81, 22] Operation: 90-68=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[90, 10, 13], Operations: ['81-68=13'] Exploring Operation: 90/10=9, Resulting Numbers: [13, 9] Generated Node #0,1,0: 93:[13, 9] Operation: 90/10=9 Exploring Operation: 10+13=23, Resulting Numbers: [90, 23] Generated Node #0,1,1: 93:[90, 23] Operation: 10+13=23 Exploring Operation: 13-10=3, Resulting Numbers: [90, 3] Generated Node #0,1,2: 93:[90, 3] Operation: 13-10=3 Exploring Operation: 90+10=100, Resulting Numbers: [13, 100] Generated Node #0,1,3: 93:[13, 100] Operation: 90+10=100 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[90, 3], Operations: ['81-68=13', '13-10=3'] Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[68, 90, 10, 81], Operations: [] Exploring Operation: 81-68=13, Resulting Numbers: [90, 10, 13] Generated Node #0,1: 93:[90, 10, 13] Operation: 81-68=13 Moving to Node #0,1 Current State: 93:[90, 10, 13], Operations: ['81-68=13'] Exploring Operation: 13-10=3, Resulting Numbers: [90, 3] Generated Node #0,1,2: 93:[90, 3] Operation: 13-10=3 Moving to Node #0,1,2 Current State: 93:[90, 3], Operations: ['81-68=13', '13-10=3'] Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 88, 99, 65, 52 ]
24
[ "99-88=11", "65-52=13", "11+13=24" ]
Current State: 24:[88, 99, 65, 52], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [65, 52, 11] Generated Node #2: [65, 52, 11] from Operation: 99-88=11 Current State: 24:[65, 52, 11], Operations: ['99-88=11'] Exploring Operation: 65-52=13, Resulting Numbers: [11, 13] Generated Node #3: [11, 13] from Operation: 65-52=13 Current State: 24:[11, 13], Operations: ['99-88=11', '65-52=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[88, 99, 65, 52], Operations: [] Exploring Operation: 99-65=34, Resulting Numbers: [88, 52, 34] Generated Node #0,0: 24:[88, 52, 34] Operation: 99-65=34 Exploring Operation: 99-88=11, Resulting Numbers: [65, 52, 11] Generated Node #0,1: 24:[65, 52, 11] Operation: 99-88=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[65, 52, 11], Operations: ['99-88=11'] Exploring Operation: 65-11=54, Resulting Numbers: [52, 54] Generated Node #0,1,0: 24:[52, 54] Operation: 65-11=54 Exploring Operation: 65-52=13, Resulting Numbers: [11, 13] Generated Node #0,1,1: 24:[11, 13] Operation: 65-52=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 24:[11, 13], Operations: ['99-88=11', '65-52=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[88, 99, 65, 52], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [65, 52, 11] Generated Node #0,1: 24:[65, 52, 11] Operation: 99-88=11 Moving to Node #0,1 Current State: 24:[65, 52, 11], Operations: ['99-88=11'] Exploring Operation: 65-52=13, Resulting Numbers: [11, 13] Generated Node #0,1,1: 24:[11, 13] Operation: 65-52=13 Moving to Node #0,1,1 Current State: 24:[11, 13], Operations: ['99-88=11', '65-52=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 72, 16, 7, 39 ]
79
[ "72-39=33", "16*7=112", "112-33=79" ]
Current State: 79:[72, 16, 7, 39], Operations: [] Exploring Operation: 72-39=33, Resulting Numbers: [16, 7, 33] Generated Node #2: [16, 7, 33] from Operation: 72-39=33 Current State: 79:[16, 7, 33], Operations: ['72-39=33'] Exploring Operation: 16*7=112, Resulting Numbers: [33, 112] Generated Node #3: [33, 112] from Operation: 16*7=112 Current State: 79:[33, 112], Operations: ['72-39=33', '16*7=112'] Exploring Operation: 112-33=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[72, 16, 7, 39], Operations: [] Exploring Operation: 16*7=112, Resulting Numbers: [72, 39, 112] Generated Node #0,0: 79:[72, 39, 112] Operation: 16*7=112 Moving to Node #0,0 Current State: 79:[72, 39, 112], Operations: ['16*7=112'] Exploring Operation: 112-39=73, Resulting Numbers: [72, 73] Generated Node #0,0,0: 79:[72, 73] Operation: 112-39=73 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[72, 73], Operations: ['16*7=112', '112-39=73'] Exploring Operation: 72+73=145, Resulting Numbers: [145] 145,79 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
[ 70, 91, 18, 36 ]
33
[ "91-70=21", "18+36=54", "54-21=33" ]
Current State: 33:[70, 91, 18, 36], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [18, 36, 21] Generated Node #2: [18, 36, 21] from Operation: 91-70=21 Current State: 33:[18, 36, 21], Operations: ['91-70=21'] Exploring Operation: 18+36=54, Resulting Numbers: [21, 54] Generated Node #3: [21, 54] from Operation: 18+36=54 Current State: 33:[21, 54], Operations: ['91-70=21', '18+36=54'] Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[70, 91, 18, 36], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [18, 36, 21] Generated Node #0,0: 33:[18, 36, 21] Operation: 91-70=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[18, 36, 21], Operations: ['91-70=21'] Exploring Operation: 21-18=3, Resulting Numbers: [36, 3] Generated Node #0,0,0: 33:[36, 3] Operation: 21-18=3 Moving to Node #0,0,0 Current State: 33:[36, 3], Operations: ['91-70=21', '21-18=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[70, 91, 18, 36], Operations: [] Exploring Operation: 91-70=21, Resulting Numbers: [18, 36, 21] Generated Node #0,0: 33:[18, 36, 21] Operation: 91-70=21 Moving to Node #0,0 Current State: 33:[18, 36, 21], Operations: ['91-70=21'] Exploring Operation: 21-18=3, Resulting Numbers: [36, 3] Generated Node #0,0,0: 33:[36, 3] Operation: 21-18=3 Moving to Node #0,0,0 Current State: 33:[36, 3], Operations: ['91-70=21', '21-18=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 8, 96, 78, 47 ]
98
[ "47-8=39", "78/39=2", "96+2=98" ]
Current State: 98:[8, 96, 78, 47], Operations: [] Exploring Operation: 47-8=39, Resulting Numbers: [96, 78, 39] Generated Node #2: [96, 78, 39] from Operation: 47-8=39 Current State: 98:[96, 78, 39], Operations: ['47-8=39'] Exploring Operation: 78/39=2, Resulting Numbers: [96, 2] Generated Node #3: [96, 2] from Operation: 78/39=2 Current State: 98:[96, 2], Operations: ['47-8=39', '78/39=2'] Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[8, 96, 78, 47], Operations: [] Exploring Operation: 96-47=49, Resulting Numbers: [8, 78, 49] Generated Node #0,0: 98:[8, 78, 49] Operation: 96-47=49 Exploring Operation: 96-78=18, Resulting Numbers: [8, 47, 18] Generated Node #0,1: 98:[8, 47, 18] Operation: 96-78=18 Exploring Operation: 8+78=86, Resulting Numbers: [96, 47, 86] Generated Node #0,2: 98:[96, 47, 86] Operation: 8+78=86 Exploring Operation: 96/8=12, Resulting Numbers: [78, 47, 12] Generated Node #0,3: 98:[78, 47, 12] Operation: 96/8=12 Exploring Operation: 78-47=31, Resulting Numbers: [8, 96, 31] Generated Node #0,4: 98:[8, 96, 31] Operation: 78-47=31 Moving to Node #0,1 Current State: 98:[8, 47, 18], Operations: ['96-78=18'] Exploring Operation: 47-8=39, Resulting Numbers: [18, 39] Generated Node #0,1,0: 98:[18, 39] Operation: 47-8=39 Exploring Operation: 8+18=26, Resulting Numbers: [47, 26] Generated Node #0,1,1: 98:[47, 26] Operation: 8+18=26 Exploring Operation: 18-8=10, Resulting Numbers: [47, 10] Generated Node #0,1,2: 98:[47, 10] Operation: 18-8=10 Exploring Operation: 47-18=29, Resulting Numbers: [8, 29] Generated Node #0,1,3: 98:[8, 29] Operation: 47-18=29 Exploring Operation: 8+47=55, Resulting Numbers: [18, 55] Generated Node #0,1,4: 98:[18, 55] Operation: 8+47=55 Moving to Node #0,2 Current State: 98:[96, 47, 86], Operations: ['8+78=86'] Exploring Operation: 47+86=133, Resulting Numbers: [96, 133] Generated Node #0,2,0: 98:[96, 133] Operation: 47+86=133 Exploring Operation: 96-86=10, Resulting Numbers: [47, 10] Generated Node #0,2,1: 98:[47, 10] Operation: 96-86=10 Exploring Operation: 86-47=39, Resulting Numbers: [96, 39] Generated Node #0,2,2: 98:[96, 39] Operation: 86-47=39 Exploring Operation: 96+47=143, Resulting Numbers: [86, 143] Generated Node #0,2,3: 98:[86, 143] Operation: 96+47=143 Exploring Operation: 96-47=49, Resulting Numbers: [86, 49] Generated Node #0,2,4: 98:[86, 49] Operation: 96-47=49 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 98:[47, 10], Operations: ['8+78=86', '96-86=10'] Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,98 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 98:[96, 39], Operations: ['8+78=86', '86-47=39'] Exploring Operation: 96+39=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 96*39=3744, Resulting Numbers: [3744] 3744,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 98:[86, 49], Operations: ['8+78=86', '96-47=49'] Exploring Operation: 86+49=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 86*49=4214, Resulting Numbers: [4214] 4214,98 unequal: No Solution Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 98:[96, 133], Operations: ['8+78=86', '47+86=133'] Exploring Operation: 96*133=12768, Resulting Numbers: [12768] 12768,98 unequal: No Solution Exploring Operation: 133-96=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 96+133=229, Resulting Numbers: [229] 229,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 98:[86, 143], Operations: ['8+78=86', '96+47=143'] Exploring Operation: 86+143=229, Resulting Numbers: [229] 229,98 unequal: No Solution Exploring Operation: 86*143=12298, Resulting Numbers: [12298] 12298,98 unequal: No Solution Exploring Operation: 143-86=57, Resulting Numbers: [57] 57,98 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: 98:[8, 96, 31], Operations: ['78-47=31'] Exploring Operation: 8+31=39, Resulting Numbers: [96, 39] Generated Node #0,4,0: 98:[96, 39] Operation: 8+31=39 Exploring Operation: 96/8=12, Resulting Numbers: [31, 12] Generated Node #0,4,1: 98:[31, 12] Operation: 96/8=12 Exploring Operation: 96-31=65, Resulting Numbers: [8, 65] Generated Node #0,4,2: 98:[8, 65] Operation: 96-31=65 Exploring Operation: 31-8=23, Resulting Numbers: [96, 23] Generated Node #0,4,3: 98:[96, 23] Operation: 31-8=23 Exploring Operation: 8+96=104, Resulting Numbers: [31, 104] Generated Node #0,4,4: 98:[31, 104] Operation: 8+96=104 Moving to Node #0,0 Current State: 98:[8, 78, 49], Operations: ['96-47=49'] Exploring Operation: 8+78=86, Resulting Numbers: [49, 86] Generated Node #0,0,0: 98:[49, 86] Operation: 8+78=86 Exploring Operation: 78-8=70, Resulting Numbers: [49, 70] Generated Node #0,0,1: 98:[49, 70] Operation: 78-8=70 Exploring Operation: 49-8=41, Resulting Numbers: [78, 41] Generated Node #0,0,2: 98:[78, 41] Operation: 49-8=41 Exploring Operation: 8+49=57, Resulting Numbers: [78, 57] Generated Node #0,0,3: 98:[78, 57] Operation: 8+49=57 Exploring Operation: 78-49=29, Resulting Numbers: [8, 29] Generated Node #0,0,4: 98:[8, 29] Operation: 78-49=29 Moving to Node #0,3 Current State: 98:[78, 47, 12], Operations: ['96/8=12'] Exploring Operation: 78-47=31, Resulting Numbers: [12, 31] Generated Node #0,3,0: 98:[12, 31] Operation: 78-47=31 Exploring Operation: 78+47=125, Resulting Numbers: [12, 125] Generated Node #0,3,1: 98:[12, 125] Operation: 78+47=125 Exploring Operation: 47+12=59, Resulting Numbers: [78, 59] Generated Node #0,3,2: 98:[78, 59] Operation: 47+12=59 Exploring Operation: 78+12=90, Resulting Numbers: [47, 90] Generated Node #0,3,3: 98:[47, 90] Operation: 78+12=90 Exploring Operation: 78-12=66, Resulting Numbers: [47, 66] Generated Node #0,3,4: 98:[47, 66] Operation: 78-12=66 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 98:[47, 90], Operations: ['96/8=12', '78+12=90'] Exploring Operation: 90-47=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 47+90=137, Resulting Numbers: [137] 137,98 unequal: No Solution Exploring Operation: 47*90=4230, Resulting Numbers: [4230] 4230,98 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 #0,3,0 Current State: 98:[12, 31], Operations: ['96/8=12', '78-47=31'] Exploring Operation: 12+31=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 12*31=372, Resulting Numbers: [372] 372,98 unequal: No Solution Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,98 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 #0,3,4 Current State: 98:[47, 66], Operations: ['96/8=12', '78-12=66'] Exploring Operation: 47*66=3102, Resulting Numbers: [3102] 3102,98 unequal: No Solution Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,98 unequal: No Solution Exploring Operation: 47+66=113, Resulting Numbers: [113] 113,98 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 #0,3,1 Current State: 98:[12, 125], Operations: ['96/8=12', '78+47=125'] Exploring Operation: 125-12=113, Resulting Numbers: [113] 113,98 unequal: No Solution Exploring Operation: 12+125=137, Resulting Numbers: [137] 137,98 unequal: No Solution Exploring Operation: 12*125=1500, Resulting Numbers: [1500] 1500,98 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 #0,3,2 Current State: 98:[78, 59], Operations: ['96/8=12', '47+12=59'] Exploring Operation: 78-59=19, Resulting Numbers: [19] 19,98 unequal: No Solution Exploring Operation: 78*59=4602, Resulting Numbers: [4602] 4602,98 unequal: No Solution Exploring Operation: 78+59=137, Resulting Numbers: [137] 137,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 98:[47, 10], Operations: ['96-78=18', '18-8=10'] Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 47*10=470, Resulting Numbers: [470] 470,98 unequal: No Solution Exploring Operation: 47+10=57, Resulting Numbers: [57] 57,98 unequal: No Solution Moving to Node #0,1,4 Current State: 98:[18, 55], Operations: ['96-78=18', '8+47=55'] Exploring Operation: 18*55=990, Resulting Numbers: [990] 990,98 unequal: No Solution Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 18+55=73, Resulting Numbers: [73] 73,98 unequal: No Solution Moving to Node #0,4,3 Current State: 98:[96, 23], Operations: ['78-47=31', '31-8=23'] Exploring Operation: 96+23=119, Resulting Numbers: [119] 119,98 unequal: No Solution Exploring Operation: 96*23=2208, Resulting Numbers: [2208] 2208,98 unequal: No Solution Exploring Operation: 96-23=73, Resulting Numbers: [73] 73,98 unequal: No Solution Moving to Node #0,4,0 Current State: 98:[96, 39], Operations: ['78-47=31', '8+31=39'] Exploring Operation: 96-39=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 96+39=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 96*39=3744, Resulting Numbers: [3744] 3744,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[49, 86], Operations: ['96-47=49', '8+78=86'] Exploring Operation: 49+86=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 49*86=4214, Resulting Numbers: [4214] 4214,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[18, 39], Operations: ['96-78=18', '47-8=39'] Exploring Operation: 18*39=702, Resulting Numbers: [702] 702,98 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 18+39=57, Resulting Numbers: [57] 57,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[47, 26], Operations: ['96-78=18', '8+18=26'] Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,98 unequal: No Solution Moving to Node #0,0,4 Current State: 98:[8, 29], Operations: ['96-47=49', '78-49=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[8, 29], Operations: ['96-78=18', '47-18=29'] Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,98 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,98 unequal: No Solution Moving to Node #0,4,2 Current State: 98:[8, 65], Operations: ['78-47=31', '96-31=65'] Exploring Operation: 8+65=73, Resulting Numbers: [73] 73,98 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,98 unequal: No Solution Exploring Operation: 8*65=520, Resulting Numbers: [520] 520,98 unequal: No Solution Moving to Node #0,4,1 Current State: 98:[31, 12], Operations: ['78-47=31', '96/8=12'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,98 unequal: No Solution Exploring Operation: 31*12=372, Resulting Numbers: [372] 372,98 unequal: No Solution Exploring Operation: 31+12=43, Resulting Numbers: [43] 43,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[49, 70], Operations: ['96-47=49', '78-8=70'] Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,98 unequal: No Solution Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,98 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,98 unequal: No Solution Moving to Node #0,4,4 Current State: 98:[31, 104], Operations: ['78-47=31', '8+96=104'] Exploring Operation: 31*104=3224, Resulting Numbers: [3224] 3224,98 unequal: No Solution Exploring Operation: 31+104=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 104-31=73, Resulting Numbers: [73] 73,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[78, 41], Operations: ['96-47=49', '49-8=41'] Exploring Operation: 78*41=3198, Resulting Numbers: [3198] 3198,98 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 78+41=119, Resulting Numbers: [119] 119,98 unequal: No Solution Moving to Node #0,0,3 Current State: 98:[78, 57], Operations: ['96-47=49', '8+49=57'] Exploring Operation: 78*57=4446, Resulting Numbers: [4446] 4446,98 unequal: No Solution Exploring Operation: 78+57=135, Resulting Numbers: [135] 135,98 unequal: No Solution Exploring Operation: 78-57=21, Resulting Numbers: [21] 21,98 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 3, 27, 98, 18 ]
50
[ "3+27=30", "98-18=80", "80-30=50" ]
Current State: 50:[3, 27, 98, 18], Operations: [] Exploring Operation: 3+27=30, Resulting Numbers: [98, 18, 30] Generated Node #2: [98, 18, 30] from Operation: 3+27=30 Current State: 50:[98, 18, 30], Operations: ['3+27=30'] Exploring Operation: 98-18=80, Resulting Numbers: [30, 80] Generated Node #3: [30, 80] from Operation: 98-18=80 Current State: 50:[30, 80], Operations: ['3+27=30', '98-18=80'] Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[3, 27, 98, 18], Operations: [] Exploring Operation: 18/3=6, Resulting Numbers: [27, 98, 6] Generated Node #0,0: 50:[27, 98, 6] Operation: 18/3=6 Exploring Operation: 98-27=71, Resulting Numbers: [3, 18, 71] Generated Node #0,1: 50:[3, 18, 71] Operation: 98-27=71 Exploring Operation: 27-18=9, Resulting Numbers: [3, 98, 9] Generated Node #0,2: 50:[3, 98, 9] Operation: 27-18=9 Exploring Operation: 98-18=80, Resulting Numbers: [3, 27, 80] Generated Node #0,3: 50:[3, 27, 80] Operation: 98-18=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[3, 18, 71], Operations: ['98-27=71'] Exploring Operation: 3+18=21, Resulting Numbers: [71, 21] Generated Node #0,1,0: 50:[71, 21] Operation: 3+18=21 Exploring Operation: 18/3=6, Resulting Numbers: [71, 6] Generated Node #0,1,1: 50:[71, 6] Operation: 18/3=6 Exploring Operation: 71-18=53, Resulting Numbers: [3, 53] Generated Node #0,1,2: 50:[3, 53] Operation: 71-18=53 Exploring Operation: 3*18=54, Resulting Numbers: [71, 54] Generated Node #0,1,3: 50:[71, 54] Operation: 3*18=54 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 50:[3, 53], Operations: ['98-27=71', '71-18=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[3, 27, 98, 18], Operations: [] Exploring Operation: 98-27=71, Resulting Numbers: [3, 18, 71] Generated Node #0,1: 50:[3, 18, 71] Operation: 98-27=71 Moving to Node #0,1 Current State: 50:[3, 18, 71], Operations: ['98-27=71'] Exploring Operation: 71-18=53, Resulting Numbers: [3, 53] Generated Node #0,1,2: 50:[3, 53] Operation: 71-18=53 Moving to Node #0,1,2 Current State: 50:[3, 53], Operations: ['98-27=71', '71-18=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 94, 85, 67, 78 ]
20
[ "94-85=9", "78-67=11", "9+11=20" ]
Current State: 20:[94, 85, 67, 78], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [67, 78, 9] Generated Node #2: [67, 78, 9] from Operation: 94-85=9 Current State: 20:[67, 78, 9], Operations: ['94-85=9'] Exploring Operation: 78-67=11, Resulting Numbers: [9, 11] Generated Node #3: [9, 11] from Operation: 78-67=11 Current State: 20:[9, 11], Operations: ['94-85=9', '78-67=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[94, 85, 67, 78], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [67, 78, 9] Generated Node #0,0: 20:[67, 78, 9] Operation: 94-85=9 Exploring Operation: 85-78=7, Resulting Numbers: [94, 67, 7] Generated Node #0,1: 20:[94, 67, 7] Operation: 85-78=7 Exploring Operation: 94-78=16, Resulting Numbers: [85, 67, 16] Generated Node #0,2: 20:[85, 67, 16] Operation: 94-78=16 Moving to Node #0,0 Current State: 20:[67, 78, 9], Operations: ['94-85=9'] Exploring Operation: 78-67=11, Resulting Numbers: [9, 11] Generated Node #0,0,0: 20:[9, 11] Operation: 78-67=11 Exploring Operation: 67-9=58, Resulting Numbers: [78, 58] Generated Node #0,0,1: 20:[78, 58] Operation: 67-9=58 Exploring Operation: 78-9=69, Resulting Numbers: [67, 69] Generated Node #0,0,2: 20:[67, 69] Operation: 78-9=69 Moving to Node #0,2 Current State: 20:[85, 67, 16], Operations: ['94-78=16'] Exploring Operation: 67-16=51, Resulting Numbers: [85, 51] Generated Node #0,2,0: 20:[85, 51] Operation: 67-16=51 Exploring Operation: 85-16=69, Resulting Numbers: [67, 69] Generated Node #0,2,1: 20:[67, 69] Operation: 85-16=69 Exploring Operation: 85-67=18, Resulting Numbers: [16, 18] Generated Node #0,2,2: 20:[16, 18] Operation: 85-67=18 Moving to Node #0,1 Current State: 20:[94, 67, 7], Operations: ['85-78=7'] Exploring Operation: 67-7=60, Resulting Numbers: [94, 60] Generated Node #0,1,0: 20:[94, 60] Operation: 67-7=60 Exploring Operation: 94-67=27, Resulting Numbers: [7, 27] Generated Node #0,1,1: 20:[7, 27] Operation: 94-67=27 Exploring Operation: 94-7=87, Resulting Numbers: [67, 87] Generated Node #0,1,2: 20:[67, 87] Operation: 94-7=87 Moving to Node #0,0,0 Current State: 20:[9, 11], Operations: ['94-85=9', '78-67=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,20 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,20 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[94, 85, 67, 78], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [67, 78, 9] Generated Node #0,0: 20:[67, 78, 9] Operation: 94-85=9 Moving to Node #0,0 Current State: 20:[67, 78, 9], Operations: ['94-85=9'] Exploring Operation: 78-67=11, Resulting Numbers: [9, 11] Generated Node #0,0,0: 20:[9, 11] Operation: 78-67=11 Moving to Node #0,0,0 Current State: 20:[9, 11], Operations: ['94-85=9', '78-67=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 52, 79, 3, 83 ]
45
[ "52+79=131", "3+83=86", "131-86=45" ]
Current State: 45:[52, 79, 3, 83], Operations: [] Exploring Operation: 52+79=131, Resulting Numbers: [3, 83, 131] Generated Node #2: [3, 83, 131] from Operation: 52+79=131 Current State: 45:[3, 83, 131], Operations: ['52+79=131'] Exploring Operation: 3+83=86, Resulting Numbers: [131, 86] Generated Node #3: [131, 86] from Operation: 3+83=86 Current State: 45:[131, 86], Operations: ['52+79=131', '3+83=86'] Exploring Operation: 131-86=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[52, 79, 3, 83], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [52, 3, 4] Generated Node #0,0: 45:[52, 3, 4] Operation: 83-79=4 Exploring Operation: 83-52=31, Resulting Numbers: [79, 3, 31] Generated Node #0,1: 45:[79, 3, 31] Operation: 83-52=31 Exploring Operation: 79-52=27, Resulting Numbers: [3, 83, 27] Generated Node #0,2: 45:[3, 83, 27] Operation: 79-52=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[52, 3, 4], Operations: ['83-79=4'] Exploring Operation: 52-4=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 45:[3, 48] Operation: 52-4=48 Exploring Operation: 52/4=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 45:[3, 13] Operation: 52/4=13 Exploring Operation: 52-3=49, Resulting Numbers: [4, 49] Generated Node #0,0,2: 45:[4, 49] Operation: 52-3=49 Moving to Node #0,0,1 Current State: 45:[3, 13], Operations: ['83-79=4', '52/4=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[3, 48], Operations: ['83-79=4', '52-4=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,45 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[52, 79, 3, 83], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [52, 3, 4] Generated Node #0,0: 45:[52, 3, 4] Operation: 83-79=4 Moving to Node #0,0 Current State: 45:[52, 3, 4], Operations: ['83-79=4'] Exploring Operation: 52-4=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 45:[3, 48] Operation: 52-4=48 Moving to Node #0,0,0 Current State: 45:[3, 48], Operations: ['83-79=4', '52-4=48'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 1, 4, 59, 65 ]
20
[ "1+59=60", "65-60=5", "4*5=20" ]
Current State: 20:[1, 4, 59, 65], Operations: [] Exploring Operation: 1+59=60, Resulting Numbers: [4, 65, 60] Generated Node #2: [4, 65, 60] from Operation: 1+59=60 Current State: 20:[4, 65, 60], Operations: ['1+59=60'] Exploring Operation: 65-60=5, Resulting Numbers: [4, 5] Generated Node #3: [4, 5] from Operation: 65-60=5 Current State: 20:[4, 5], Operations: ['1+59=60', '65-60=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[1, 4, 59, 65], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [1, 4, 6] Generated Node #0,0: 20:[1, 4, 6] Operation: 65-59=6 Exploring Operation: 59-4=55, Resulting Numbers: [1, 65, 55] Generated Node #0,1: 20:[1, 65, 55] Operation: 59-4=55 Moving to Node #0,0 Current State: 20:[1, 4, 6], Operations: ['65-59=6'] Exploring Operation: 6-1=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 20:[4, 5] Operation: 6-1=5 Exploring Operation: 1+4=5, Resulting Numbers: [6, 5] Generated Node #0,0,1: 20:[6, 5] Operation: 1+4=5 Moving to Node #0,1 Current State: 20:[1, 65, 55], Operations: ['59-4=55'] Exploring Operation: 65-1=64, Resulting Numbers: [55, 64] Generated Node #0,1,0: 20:[55, 64] Operation: 65-1=64 Exploring Operation: 65-55=10, Resulting Numbers: [1, 10] Generated Node #0,1,1: 20:[1, 10] Operation: 65-55=10 Moving to Node #0,0,0 Current State: 20:[4, 5], Operations: ['65-59=6', '6-1=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[1, 4, 59, 65], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [1, 4, 6] Generated Node #0,0: 20:[1, 4, 6] Operation: 65-59=6 Moving to Node #0,0 Current State: 20:[1, 4, 6], Operations: ['65-59=6'] Exploring Operation: 6-1=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 20:[4, 5] Operation: 6-1=5 Moving to Node #0,0,0 Current State: 20:[4, 5], Operations: ['65-59=6', '6-1=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 4, 64, 58, 37 ]
39
[ "64-4=60", "58-37=21", "60-21=39" ]
Current State: 39:[4, 64, 58, 37], Operations: [] Exploring Operation: 64-4=60, Resulting Numbers: [58, 37, 60] Generated Node #2: [58, 37, 60] from Operation: 64-4=60 Current State: 39:[58, 37, 60], Operations: ['64-4=60'] Exploring Operation: 58-37=21, Resulting Numbers: [60, 21] Generated Node #3: [60, 21] from Operation: 58-37=21 Current State: 39:[60, 21], Operations: ['64-4=60', '58-37=21'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[4, 64, 58, 37], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [58, 37, 16] Generated Node #0,0: 39:[58, 37, 16] Operation: 64/4=16 Exploring Operation: 58-37=21, Resulting Numbers: [4, 64, 21] Generated Node #0,1: 39:[4, 64, 21] Operation: 58-37=21 Exploring Operation: 64-4=60, Resulting Numbers: [58, 37, 60] Generated Node #0,2: 39:[58, 37, 60] Operation: 64-4=60 Exploring Operation: 64-58=6, Resulting Numbers: [4, 37, 6] Generated Node #0,3: 39:[4, 37, 6] Operation: 64-58=6 Exploring Operation: 64-37=27, Resulting Numbers: [4, 58, 27] Generated Node #0,4: 39:[4, 58, 27] Operation: 64-37=27 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[4, 37, 6], Operations: ['64-58=6'] Exploring Operation: 4+6=10, Resulting Numbers: [37, 10] Generated Node #0,3,0: 39:[37, 10] Operation: 4+6=10 Exploring Operation: 6-4=2, Resulting Numbers: [37, 2] Generated Node #0,3,1: 39:[37, 2] Operation: 6-4=2 Exploring Operation: 37+6=43, Resulting Numbers: [4, 43] Generated Node #0,3,2: 39:[4, 43] Operation: 37+6=43 Exploring Operation: 4+37=41, Resulting Numbers: [6, 41] Generated Node #0,3,3: 39:[6, 41] Operation: 4+37=41 Exploring Operation: 37-4=33, Resulting Numbers: [6, 33] Generated Node #0,3,4: 39:[6, 33] Operation: 37-4=33 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 39:[37, 2], Operations: ['64-58=6', '6-4=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[4, 64, 58, 37], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [4, 37, 6] Generated Node #0,3: 39:[4, 37, 6] Operation: 64-58=6 Moving to Node #0,3 Current State: 39:[4, 37, 6], Operations: ['64-58=6'] Exploring Operation: 6-4=2, Resulting Numbers: [37, 2] Generated Node #0,3,1: 39:[37, 2] Operation: 6-4=2 Moving to Node #0,3,1 Current State: 39:[37, 2], Operations: ['64-58=6', '6-4=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 24, 5, 93, 81 ]
72
[ "24+81=105", "105/5=21", "93-21=72" ]
Current State: 72:[24, 5, 93, 81], Operations: [] Exploring Operation: 24+81=105, Resulting Numbers: [5, 93, 105] Generated Node #2: [5, 93, 105] from Operation: 24+81=105 Current State: 72:[5, 93, 105], Operations: ['24+81=105'] Exploring Operation: 105/5=21, Resulting Numbers: [93, 21] Generated Node #3: [93, 21] from Operation: 105/5=21 Current State: 72:[93, 21], Operations: ['24+81=105', '105/5=21'] Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[24, 5, 93, 81], Operations: [] Exploring Operation: 93-81=12, Resulting Numbers: [24, 5, 12] Generated Node #0,0: 72:[24, 5, 12] Operation: 93-81=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[24, 5, 12], Operations: ['93-81=12'] Exploring Operation: 24-5=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 72:[12, 19] Operation: 24-5=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[12, 19], Operations: ['93-81=12', '24-5=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 47, 51, 90, 51 ]
47
[ "51-51=0", "90*0=0", "47+0=47" ]
Current State: 47:[47, 51, 90, 51], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [47, 90, 0] Generated Node #2: [47, 90, 0] from Operation: 51-51=0 Current State: 47:[47, 90, 0], Operations: ['51-51=0'] Exploring Operation: 90*0=0, Resulting Numbers: [47, 0] Generated Node #3: [47, 0] from Operation: 90*0=0 Current State: 47:[47, 0], Operations: ['51-51=0', '90*0=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[47, 51, 90, 51], Operations: [] Exploring Operation: 90-51=39, Resulting Numbers: [47, 51, 39] Generated Node #0,0: 47:[47, 51, 39] Operation: 90-51=39 Exploring Operation: 90-51=39, Resulting Numbers: [47, 51, 39] Generated Node #0,1: 47:[47, 51, 39] Operation: 90-51=39 Exploring Operation: 90-47=43, Resulting Numbers: [51, 51, 43] Generated Node #0,2: 47:[51, 51, 43] Operation: 90-47=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[47, 51, 39], Operations: ['90-51=39'] Exploring Operation: 51-39=12, Resulting Numbers: [47, 12] Generated Node #0,0,0: 47:[47, 12] Operation: 51-39=12 Exploring Operation: 47+39=86, Resulting Numbers: [51, 86] Generated Node #0,0,1: 47:[51, 86] Operation: 47+39=86 Exploring Operation: 47-39=8, Resulting Numbers: [51, 8] Generated Node #0,0,2: 47:[51, 8] Operation: 47-39=8 Moving to Node #0,0,0 Current State: 47:[47, 12], Operations: ['90-51=39', '51-39=12'] Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,47 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[51, 86], Operations: ['90-51=39', '47+39=86'] Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,47 unequal: No Solution Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[51, 8], Operations: ['90-51=39', '47-39=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[47, 51, 39], Operations: ['90-51=39'] Exploring Operation: 47+39=86, Resulting Numbers: [51, 86] Generated Node #0,1,0: 47:[51, 86] Operation: 47+39=86 Exploring Operation: 47-39=8, Resulting Numbers: [51, 8] Generated Node #0,1,1: 47:[51, 8] Operation: 47-39=8 Exploring Operation: 51-39=12, Resulting Numbers: [47, 12] Generated Node #0,1,2: 47:[47, 12] Operation: 51-39=12 Moving to Node #0,1,2 Current State: 47:[47, 12], Operations: ['90-51=39', '51-39=12'] Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 47*12=564, Resulting Numbers: [564] 564,47 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[51, 86], Operations: ['90-51=39', '47+39=86'] Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,47 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,47 unequal: No Solution Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[51, 8], Operations: ['90-51=39', '47-39=8'] Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[51, 51, 43], Operations: ['90-47=43'] Exploring Operation: 51-43=8, Resulting Numbers: [51, 8] Generated Node #0,2,0: 47:[51, 8] Operation: 51-43=8 Exploring Operation: 51/51=1, Resulting Numbers: [43, 1] Generated Node #0,2,1: 47:[43, 1] Operation: 51/51=1 Exploring Operation: 51-43=8, Resulting Numbers: [51, 8] Generated Node #0,2,2: 47:[51, 8] Operation: 51-43=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 47:[51, 8], Operations: ['90-47=43', '51-43=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution No 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: 47:[51, 8], Operations: ['90-47=43', '51-43=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,47 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,47 unequal: No Solution No 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: 47:[43, 1], Operations: ['90-47=43', '51/51=1'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,47 unequal: No Solution Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,47 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 79, 54, 16, 4 ]
36
[ "79-54=25", "25-16=9", "4*9=36" ]
Current State: 36:[79, 54, 16, 4], Operations: [] Exploring Operation: 79-54=25, Resulting Numbers: [16, 4, 25] Generated Node #2: [16, 4, 25] from Operation: 79-54=25 Current State: 36:[16, 4, 25], Operations: ['79-54=25'] Exploring Operation: 25-16=9, Resulting Numbers: [4, 9] Generated Node #3: [4, 9] from Operation: 25-16=9 Current State: 36:[4, 9], Operations: ['79-54=25', '25-16=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[79, 54, 16, 4], Operations: [] Exploring Operation: 79-16=63, Resulting Numbers: [54, 4, 63] Generated Node #0,0: 36:[54, 4, 63] Operation: 79-16=63 Exploring Operation: 54-4=50, Resulting Numbers: [79, 16, 50] Generated Node #0,1: 36:[79, 16, 50] Operation: 54-4=50 Exploring Operation: 79-4=75, Resulting Numbers: [54, 16, 75] Generated Node #0,2: 36:[54, 16, 75] Operation: 79-4=75 Exploring Operation: 54-16=38, Resulting Numbers: [79, 4, 38] Generated Node #0,3: 36:[79, 4, 38] Operation: 54-16=38 Exploring Operation: 79-54=25, Resulting Numbers: [16, 4, 25] Generated Node #0,4: 36:[16, 4, 25] Operation: 79-54=25 Moving to Node #0,4 Current State: 36:[16, 4, 25], Operations: ['79-54=25'] Exploring Operation: 16-4=12, Resulting Numbers: [25, 12] Generated Node #0,4,0: 36:[25, 12] Operation: 16-4=12 Exploring Operation: 25-16=9, Resulting Numbers: [4, 9] Generated Node #0,4,1: 36:[4, 9] Operation: 25-16=9 Exploring Operation: 16/4=4, Resulting Numbers: [25, 4] Generated Node #0,4,2: 36:[25, 4] Operation: 16/4=4 Exploring Operation: 25-4=21, Resulting Numbers: [16, 21] Generated Node #0,4,3: 36:[16, 21] Operation: 25-4=21 Exploring Operation: 16+25=41, Resulting Numbers: [4, 41] Generated Node #0,4,4: 36:[4, 41] Operation: 16+25=41 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 36:[4, 9], Operations: ['79-54=25', '25-16=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[79, 54, 16, 4], Operations: [] Exploring Operation: 79-54=25, Resulting Numbers: [16, 4, 25] Generated Node #0,4: 36:[16, 4, 25] Operation: 79-54=25 Moving to Node #0,4 Current State: 36:[16, 4, 25], Operations: ['79-54=25'] Exploring Operation: 25-16=9, Resulting Numbers: [4, 9] Generated Node #0,4,1: 36:[4, 9] Operation: 25-16=9 Moving to Node #0,4,1 Current State: 36:[4, 9], Operations: ['79-54=25', '25-16=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 90, 59, 21, 16 ]
95
[ "59+21=80", "80/16=5", "90+5=95" ]
Current State: 95:[90, 59, 21, 16], Operations: [] Exploring Operation: 59+21=80, Resulting Numbers: [90, 16, 80] Generated Node #2: [90, 16, 80] from Operation: 59+21=80 Current State: 95:[90, 16, 80], Operations: ['59+21=80'] Exploring Operation: 80/16=5, Resulting Numbers: [90, 5] Generated Node #3: [90, 5] from Operation: 80/16=5 Current State: 95:[90, 5], Operations: ['59+21=80', '80/16=5'] Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[90, 59, 21, 16], Operations: [] Exploring Operation: 59-16=43, Resulting Numbers: [90, 21, 43] Generated Node #0,0: 95:[90, 21, 43] Operation: 59-16=43 Exploring Operation: 59+21=80, Resulting Numbers: [90, 16, 80] Generated Node #0,1: 95:[90, 16, 80] Operation: 59+21=80 Exploring Operation: 59-21=38, Resulting Numbers: [90, 16, 38] Generated Node #0,2: 95:[90, 16, 38] Operation: 59-21=38 Exploring Operation: 90-59=31, Resulting Numbers: [21, 16, 31] Generated Node #0,3: 95:[21, 16, 31] Operation: 90-59=31 Exploring Operation: 59+16=75, Resulting Numbers: [90, 21, 75] Generated Node #0,4: 95:[90, 21, 75] Operation: 59+16=75 Moving to Node #0,3 Current State: 95:[21, 16, 31], Operations: ['90-59=31'] Exploring Operation: 31-16=15, Resulting Numbers: [21, 15] Generated Node #0,3,0: 95:[21, 15] Operation: 31-16=15 Exploring Operation: 21-16=5, Resulting Numbers: [31, 5] Generated Node #0,3,1: 95:[31, 5] Operation: 21-16=5 Exploring Operation: 16+31=47, Resulting Numbers: [21, 47] Generated Node #0,3,2: 95:[21, 47] Operation: 16+31=47 Exploring Operation: 31-21=10, Resulting Numbers: [16, 10] Generated Node #0,3,3: 95:[16, 10] Operation: 31-21=10 Exploring Operation: 21+16=37, Resulting Numbers: [31, 37] Generated Node #0,3,4: 95:[31, 37] Operation: 21+16=37 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 95:[21, 15], Operations: ['90-59=31', '31-16=15'] Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 95:[16, 10], Operations: ['90-59=31', '31-21=10'] Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,95 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 95:[31, 5], Operations: ['90-59=31', '21-16=5'] Exploring Operation: 31*5=155, Resulting Numbers: [155] 155,95 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,95 unequal: No Solution Exploring Operation: 31+5=36, Resulting Numbers: [36] 36,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 95:[21, 47], Operations: ['90-59=31', '16+31=47'] Exploring Operation: 21*47=987, Resulting Numbers: [987] 987,95 unequal: No Solution Exploring Operation: 21+47=68, Resulting Numbers: [68] 68,95 unequal: No Solution Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 95:[31, 37], Operations: ['90-59=31', '21+16=37'] Exploring Operation: 31*37=1147, Resulting Numbers: [1147] 1147,95 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 31+37=68, Resulting Numbers: [68] 68,95 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: 95:[90, 16, 80], Operations: ['59+21=80'] Exploring Operation: 16+80=96, Resulting Numbers: [90, 96] Generated Node #0,1,0: 95:[90, 96] Operation: 16+80=96 Exploring Operation: 80/16=5, Resulting Numbers: [90, 5] Generated Node #0,1,1: 95:[90, 5] Operation: 80/16=5 Exploring Operation: 90+16=106, Resulting Numbers: [80, 106] Generated Node #0,1,2: 95:[80, 106] Operation: 90+16=106 Exploring Operation: 90-80=10, Resulting Numbers: [16, 10] Generated Node #0,1,3: 95:[16, 10] Operation: 90-80=10 Exploring Operation: 90-16=74, Resulting Numbers: [80, 74] Generated Node #0,1,4: 95:[80, 74] Operation: 90-16=74 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[90, 5], Operations: ['59+21=80', '80/16=5'] Exploring Operation: 90*5=450, Resulting Numbers: [450] 450,95 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,95 unequal: No Solution Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[90, 59, 21, 16], Operations: [] Exploring Operation: 59+21=80, Resulting Numbers: [90, 16, 80] Generated Node #0,1: 95:[90, 16, 80] Operation: 59+21=80 Moving to Node #0,1 Current State: 95:[90, 16, 80], Operations: ['59+21=80'] Exploring Operation: 80/16=5, Resulting Numbers: [90, 5] Generated Node #0,1,1: 95:[90, 5] Operation: 80/16=5 Moving to Node #0,1,1 Current State: 95:[90, 5], Operations: ['59+21=80', '80/16=5'] Exploring Operation: 90+5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 15, 68, 71, 38 ]
50
[ "15+68=83", "71-38=33", "83-33=50" ]
Current State: 50:[15, 68, 71, 38], Operations: [] Exploring Operation: 15+68=83, Resulting Numbers: [71, 38, 83] Generated Node #2: [71, 38, 83] from Operation: 15+68=83 Current State: 50:[71, 38, 83], Operations: ['15+68=83'] Exploring Operation: 71-38=33, Resulting Numbers: [83, 33] Generated Node #3: [83, 33] from Operation: 71-38=33 Current State: 50:[83, 33], Operations: ['15+68=83', '71-38=33'] Exploring Operation: 83-33=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[15, 68, 71, 38], Operations: [] Exploring Operation: 68-15=53, Resulting Numbers: [71, 38, 53] Generated Node #0,0: 50:[71, 38, 53] Operation: 68-15=53 Exploring Operation: 68-38=30, Resulting Numbers: [15, 71, 30] Generated Node #0,1: 50:[15, 71, 30] Operation: 68-38=30 Exploring Operation: 71-68=3, Resulting Numbers: [15, 38, 3] Generated Node #0,2: 50:[15, 38, 3] Operation: 71-68=3 Exploring Operation: 71-38=33, Resulting Numbers: [15, 68, 33] Generated Node #0,3: 50:[15, 68, 33] Operation: 71-38=33 Start Sub Search at level 1: Moving to Node #0,2 Current State: 50:[15, 38, 3], Operations: ['71-68=3'] Exploring Operation: 15-3=12, Resulting Numbers: [38, 12] Generated Node #0,2,0: 50:[38, 12] Operation: 15-3=12 Exploring Operation: 38-15=23, Resulting Numbers: [3, 23] Generated Node #0,2,1: 50:[3, 23] Operation: 38-15=23 Exploring Operation: 15+38=53, Resulting Numbers: [3, 53] Generated Node #0,2,2: 50:[3, 53] Operation: 15+38=53 Exploring Operation: 15/3=5, Resulting Numbers: [38, 5] Generated Node #0,2,3: 50:[38, 5] Operation: 15/3=5 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 50:[3, 23], Operations: ['71-68=3', '38-15=23'] Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,50 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,50 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,50 unequal: No Solution No 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: 50:[3, 53], Operations: ['71-68=3', '15+38=53'] Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,50 unequal: No Solution Exploring Operation: 3*53=159, Resulting Numbers: [159] 159,50 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[15, 68, 71, 38], Operations: [] Exploring Operation: 71-68=3, Resulting Numbers: [15, 38, 3] Generated Node #0,2: 50:[15, 38, 3] Operation: 71-68=3 Moving to Node #0,2 Current State: 50:[15, 38, 3], Operations: ['71-68=3'] Exploring Operation: 15+38=53, Resulting Numbers: [3, 53] Generated Node #0,2,2: 50:[3, 53] Operation: 15+38=53 Moving to Node #0,2,2 Current State: 50:[3, 53], Operations: ['71-68=3', '15+38=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 88, 58, 50, 54 ]
86
[ "58+50=108", "108/54=2", "88-2=86" ]
Current State: 86:[88, 58, 50, 54], Operations: [] Exploring Operation: 58+50=108, Resulting Numbers: [88, 54, 108] Generated Node #2: [88, 54, 108] from Operation: 58+50=108 Current State: 86:[88, 54, 108], Operations: ['58+50=108'] Exploring Operation: 108/54=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 108/54=2 Current State: 86:[88, 2], Operations: ['58+50=108', '108/54=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[88, 58, 50, 54], Operations: [] Exploring Operation: 58-54=4, Resulting Numbers: [88, 50, 4] Generated Node #0,0: 86:[88, 50, 4] Operation: 58-54=4 Exploring Operation: 54-50=4, Resulting Numbers: [88, 58, 4] Generated Node #0,1: 86:[88, 58, 4] Operation: 54-50=4 Exploring Operation: 58-50=8, Resulting Numbers: [88, 54, 8] Generated Node #0,2: 86:[88, 54, 8] Operation: 58-50=8 Moving to Node #0,0 Current State: 86:[88, 50, 4], Operations: ['58-54=4'] Exploring Operation: 50-4=46, Resulting Numbers: [88, 46] Generated Node #0,0,0: 86:[88, 46] Operation: 50-4=46 Exploring Operation: 88-50=38, Resulting Numbers: [4, 38] Generated Node #0,0,1: 86:[4, 38] Operation: 88-50=38 Exploring Operation: 88-4=84, Resulting Numbers: [50, 84] Generated Node #0,0,2: 86:[50, 84] Operation: 88-4=84 Moving to Node #0,1 Current State: 86:[88, 58, 4], Operations: ['54-50=4'] Exploring Operation: 58-4=54, Resulting Numbers: [88, 54] Generated Node #0,1,0: 86:[88, 54] Operation: 58-4=54 Exploring Operation: 88-58=30, Resulting Numbers: [4, 30] Generated Node #0,1,1: 86:[4, 30] Operation: 88-58=30 Exploring Operation: 88-4=84, Resulting Numbers: [58, 84] Generated Node #0,1,2: 86:[58, 84] Operation: 88-4=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[88, 54], Operations: ['54-50=4', '58-4=54'] Exploring Operation: 88-54=34, Resulting Numbers: [34] 34,86 unequal: No Solution Exploring Operation: 88+54=142, Resulting Numbers: [142] 142,86 unequal: No Solution Exploring Operation: 88*54=4752, Resulting Numbers: [4752] 4752,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[4, 30], Operations: ['54-50=4', '88-58=30'] Exploring Operation: 4+30=34, Resulting Numbers: [34] 34,86 unequal: No Solution Exploring Operation: 4*30=120, Resulting Numbers: [120] 120,86 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[58, 84], Operations: ['54-50=4', '88-4=84'] Exploring Operation: 58+84=142, Resulting Numbers: [142] 142,86 unequal: No Solution Exploring Operation: 58*84=4872, Resulting Numbers: [4872] 4872,86 unequal: No Solution Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[88, 54, 8], Operations: ['58-50=8'] Exploring Operation: 88-54=34, Resulting Numbers: [8, 34] Generated Node #0,2,0: 86:[8, 34] Operation: 88-54=34 Exploring Operation: 54-8=46, Resulting Numbers: [88, 46] Generated Node #0,2,1: 86:[88, 46] Operation: 54-8=46 Exploring Operation: 88-8=80, Resulting Numbers: [54, 80] Generated Node #0,2,2: 86:[54, 80] Operation: 88-8=80 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[88, 46], Operations: ['58-50=8', '54-8=46'] Exploring Operation: 88+46=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 88*46=4048, Resulting Numbers: [4048] 4048,86 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 #0,2,0 Current State: 86:[8, 34], Operations: ['58-50=8', '88-54=34'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,86 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,86 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,86 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:[54, 80], Operations: ['58-50=8', '88-8=80'] Exploring Operation: 54*80=4320, Resulting Numbers: [4320] 4320,86 unequal: No Solution Exploring Operation: 54+80=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 80-54=26, Resulting Numbers: [26] 26,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 86:[88, 46], Operations: ['58-54=4', '50-4=46'] Exploring Operation: 88+46=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 88*46=4048, Resulting Numbers: [4048] 4048,86 unequal: No Solution Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[4, 38], Operations: ['58-54=4', '88-50=38'] Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,86 unequal: No Solution Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,86 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[50, 84], Operations: ['58-54=4', '88-4=84'] Exploring Operation: 50+84=134, Resulting Numbers: [134] 134,86 unequal: No Solution Exploring Operation: 50*84=4200, Resulting Numbers: [4200] 4200,86 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,86 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 53, 61, 14, 65 ]
62
[ "61+65=126", "126/14=9", "53+9=62" ]
Current State: 62:[53, 61, 14, 65], Operations: [] Exploring Operation: 61+65=126, Resulting Numbers: [53, 14, 126] Generated Node #2: [53, 14, 126] from Operation: 61+65=126 Current State: 62:[53, 14, 126], Operations: ['61+65=126'] Exploring Operation: 126/14=9, Resulting Numbers: [53, 9] Generated Node #3: [53, 9] from Operation: 126/14=9 Current State: 62:[53, 9], Operations: ['61+65=126', '126/14=9'] Exploring Operation: 53+9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[53, 61, 14, 65], Operations: [] Exploring Operation: 61-53=8, Resulting Numbers: [14, 65, 8] Generated Node #0,0: 62:[14, 65, 8] Operation: 61-53=8 Exploring Operation: 53+14=67, Resulting Numbers: [61, 65, 67] Generated Node #0,1: 62:[61, 65, 67] Operation: 53+14=67 Exploring Operation: 53-14=39, Resulting Numbers: [61, 65, 39] Generated Node #0,2: 62:[61, 65, 39] Operation: 53-14=39 Exploring Operation: 65-14=51, Resulting Numbers: [53, 61, 51] Generated Node #0,3: 62:[53, 61, 51] Operation: 65-14=51 Moving to Node #0,1 Current State: 62:[61, 65, 67], Operations: ['53+14=67'] Exploring Operation: 65-61=4, Resulting Numbers: [67, 4] Generated Node #0,1,0: 62:[67, 4] Operation: 65-61=4 Exploring Operation: 61+65=126, Resulting Numbers: [67, 126] Generated Node #0,1,1: 62:[67, 126] Operation: 61+65=126 Exploring Operation: 67-61=6, Resulting Numbers: [65, 6] Generated Node #0,1,2: 62:[65, 6] Operation: 67-61=6 Exploring Operation: 67-65=2, Resulting Numbers: [61, 2] Generated Node #0,1,3: 62:[61, 2] Operation: 67-65=2 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[61, 2], Operations: ['53+14=67', '67-65=2'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[67, 4], Operations: ['53+14=67', '65-61=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 67+4=71, Resulting Numbers: [71] 71,62 unequal: No Solution Exploring Operation: 67*4=268, Resulting Numbers: [268] 268,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[65, 6], Operations: ['53+14=67', '67-61=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,62 unequal: No Solution Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[67, 126], Operations: ['53+14=67', '61+65=126'] Exploring Operation: 126-67=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 67*126=8442, Resulting Numbers: [8442] 8442,62 unequal: No Solution Exploring Operation: 67+126=193, Resulting Numbers: [193] 193,62 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: 62:[61, 65, 39], Operations: ['53-14=39'] Exploring Operation: 61+39=100, Resulting Numbers: [65, 100] Generated Node #0,2,0: 62:[65, 100] Operation: 61+39=100 Exploring Operation: 65-39=26, Resulting Numbers: [61, 26] Generated Node #0,2,1: 62:[61, 26] Operation: 65-39=26 Exploring Operation: 65-61=4, Resulting Numbers: [39, 4] Generated Node #0,2,2: 62:[39, 4] Operation: 65-61=4 Exploring Operation: 61-39=22, Resulting Numbers: [65, 22] Generated Node #0,2,3: 62:[65, 22] Operation: 61-39=22 Moving to Node #0,3 Current State: 62:[53, 61, 51], Operations: ['65-14=51'] Exploring Operation: 61-53=8, Resulting Numbers: [51, 8] Generated Node #0,3,0: 62:[51, 8] Operation: 61-53=8 Exploring Operation: 61-51=10, Resulting Numbers: [53, 10] Generated Node #0,3,1: 62:[53, 10] Operation: 61-51=10 Exploring Operation: 53-51=2, Resulting Numbers: [61, 2] Generated Node #0,3,2: 62:[61, 2] Operation: 53-51=2 Exploring Operation: 53+51=104, Resulting Numbers: [61, 104] Generated Node #0,3,3: 62:[61, 104] Operation: 53+51=104 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[61, 2], Operations: ['65-14=51', '53-51=2'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,62 unequal: No Solution Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[51, 8], Operations: ['65-14=51', '61-53=8'] Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,62 unequal: No Solution Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 62:[53, 10], Operations: ['65-14=51', '61-51=10'] Exploring Operation: 53-10=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 53+10=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 53*10=530, Resulting Numbers: [530] 530,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 62:[61, 104], Operations: ['65-14=51', '53+51=104'] Exploring Operation: 104-61=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 61*104=6344, Resulting Numbers: [6344] 6344,62 unequal: No Solution Exploring Operation: 61+104=165, Resulting Numbers: [165] 165,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 62:[14, 65, 8], Operations: ['61-53=8'] Exploring Operation: 65-14=51, Resulting Numbers: [8, 51] Generated Node #0,0,0: 62:[8, 51] Operation: 65-14=51 Exploring Operation: 14+8=22, Resulting Numbers: [65, 22] Generated Node #0,0,1: 62:[65, 22] Operation: 14+8=22 Exploring Operation: 14-8=6, Resulting Numbers: [65, 6] Generated Node #0,0,2: 62:[65, 6] Operation: 14-8=6 Exploring Operation: 65-8=57, Resulting Numbers: [14, 57] Generated Node #0,0,3: 62:[14, 57] Operation: 65-8=57 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[65, 6], Operations: ['61-53=8', '14-8=6'] Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,62 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[65, 22], Operations: ['61-53=8', '14+8=22'] Exploring Operation: 65+22=87, Resulting Numbers: [87] 87,62 unequal: No Solution Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 65*22=1430, Resulting Numbers: [1430] 1430,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[8, 51], Operations: ['61-53=8', '65-14=51'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,62 unequal: No Solution Exploring Operation: 8+51=59, Resulting Numbers: [59] 59,62 unequal: No Solution Exploring Operation: 8*51=408, Resulting Numbers: [408] 408,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 62:[14, 57], Operations: ['61-53=8', '65-8=57'] Exploring Operation: 14*57=798, Resulting Numbers: [798] 798,62 unequal: No Solution Exploring Operation: 14+57=71, Resulting Numbers: [71] 71,62 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,62 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: 62:[61, 26], Operations: ['53-14=39', '65-39=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,62 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[39, 4], Operations: ['53-14=39', '65-61=4'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,62 unequal: No Solution Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[65, 22], Operations: ['53-14=39', '61-39=22'] Exploring Operation: 65+22=87, Resulting Numbers: [87] 87,62 unequal: No Solution Exploring Operation: 65*22=1430, Resulting Numbers: [1430] 1430,62 unequal: No Solution Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[65, 100], Operations: ['53-14=39', '61+39=100'] Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,62 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,62 unequal: No Solution Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,62 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 7, 87, 93, 98 ]
20
[ "98/7=14", "93-87=6", "14+6=20" ]
Current State: 20:[7, 87, 93, 98], Operations: [] Exploring Operation: 98/7=14, Resulting Numbers: [87, 93, 14] Generated Node #2: [87, 93, 14] from Operation: 98/7=14 Current State: 20:[87, 93, 14], Operations: ['98/7=14'] Exploring Operation: 93-87=6, Resulting Numbers: [14, 6] Generated Node #3: [14, 6] from Operation: 93-87=6 Current State: 20:[14, 6], Operations: ['98/7=14', '93-87=6'] Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[7, 87, 93, 98], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [7, 98, 6] Generated Node #0,0: 20:[7, 98, 6] Operation: 93-87=6 Exploring Operation: 98-93=5, Resulting Numbers: [7, 87, 5] Generated Node #0,1: 20:[7, 87, 5] Operation: 98-93=5 Exploring Operation: 98-87=11, Resulting Numbers: [7, 93, 11] Generated Node #0,2: 20:[7, 93, 11] Operation: 98-87=11 Exploring Operation: 98/7=14, Resulting Numbers: [87, 93, 14] Generated Node #0,3: 20:[87, 93, 14] Operation: 98/7=14 Exploring Operation: 87-7=80, Resulting Numbers: [93, 98, 80] Generated Node #0,4: 20:[93, 98, 80] Operation: 87-7=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[7, 87, 5], Operations: ['98-93=5'] Exploring Operation: 7+5=12, Resulting Numbers: [87, 12] Generated Node #0,1,0: 20:[87, 12] Operation: 7+5=12 Exploring Operation: 7+87=94, Resulting Numbers: [5, 94] Generated Node #0,1,1: 20:[5, 94] Operation: 7+87=94 Exploring Operation: 87-7=80, Resulting Numbers: [5, 80] Generated Node #0,1,2: 20:[5, 80] Operation: 87-7=80 Exploring Operation: 87-5=82, Resulting Numbers: [7, 82] Generated Node #0,1,3: 20:[7, 82] Operation: 87-5=82 Exploring Operation: 7-5=2, Resulting Numbers: [87, 2] Generated Node #0,1,4: 20:[87, 2] Operation: 7-5=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 20:[5, 80], Operations: ['98-93=5', '87-7=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,20 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,20 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 20:[7, 82], Operations: ['98-93=5', '87-5=82'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,20 unequal: No Solution Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 20:[87, 2], Operations: ['98-93=5', '7-5=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,20 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[87, 12], Operations: ['98-93=5', '7+5=12'] Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,20 unequal: No Solution Exploring Operation: 87*12=1044, Resulting Numbers: [1044] 1044,20 unequal: No Solution Exploring Operation: 87+12=99, Resulting Numbers: [99] 99,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[5, 94], Operations: ['98-93=5', '7+87=94'] Exploring Operation: 5+94=99, Resulting Numbers: [99] 99,20 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 5*94=470, Resulting Numbers: [470] 470,20 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: 20:[7, 93, 11], Operations: ['98-87=11'] Exploring Operation: 7+93=100, Resulting Numbers: [11, 100] Generated Node #0,2,0: 20:[11, 100] Operation: 7+93=100 Exploring Operation: 7+11=18, Resulting Numbers: [93, 18] Generated Node #0,2,1: 20:[93, 18] Operation: 7+11=18 Exploring Operation: 11-7=4, Resulting Numbers: [93, 4] Generated Node #0,2,2: 20:[93, 4] Operation: 11-7=4 Exploring Operation: 93-11=82, Resulting Numbers: [7, 82] Generated Node #0,2,3: 20:[7, 82] Operation: 93-11=82 Exploring Operation: 93-7=86, Resulting Numbers: [11, 86] Generated Node #0,2,4: 20:[11, 86] Operation: 93-7=86 Moving to Node #0,2,3 Current State: 20:[7, 82], Operations: ['98-87=11', '93-11=82'] Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,20 unequal: No Solution Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,20 unequal: No Solution Moving to Node #0,2,4 Current State: 20:[11, 86], Operations: ['98-87=11', '93-7=86'] Exploring Operation: 11+86=97, Resulting Numbers: [97] 97,20 unequal: No Solution Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,20 unequal: No Solution Exploring Operation: 11*86=946, Resulting Numbers: [946] 946,20 unequal: No Solution Moving to Node #0,2,2 Current State: 20:[93, 4], Operations: ['98-87=11', '11-7=4'] Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 93*4=372, Resulting Numbers: [372] 372,20 unequal: No Solution Exploring Operation: 93+4=97, Resulting Numbers: [97] 97,20 unequal: No Solution Moving to Node #0,2,1 Current State: 20:[93, 18], Operations: ['98-87=11', '7+11=18'] Exploring Operation: 93+18=111, Resulting Numbers: [111] 111,20 unequal: No Solution Exploring Operation: 93*18=1674, Resulting Numbers: [1674] 1674,20 unequal: No Solution Exploring Operation: 93-18=75, Resulting Numbers: [75] 75,20 unequal: No Solution Moving to Node #0,2,0 Current State: 20:[11, 100], Operations: ['98-87=11', '7+93=100'] Exploring Operation: 100-11=89, Resulting Numbers: [89] 89,20 unequal: No Solution Exploring Operation: 11*100=1100, Resulting Numbers: [1100] 1100,20 unequal: No Solution Exploring Operation: 11+100=111, Resulting Numbers: [111] 111,20 unequal: No Solution No 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: 20:[7, 98, 6], Operations: ['93-87=6'] Exploring Operation: 7+6=13, Resulting Numbers: [98, 13] Generated Node #0,0,0: 20:[98, 13] Operation: 7+6=13 Exploring Operation: 98/7=14, Resulting Numbers: [6, 14] Generated Node #0,0,1: 20:[6, 14] Operation: 98/7=14 Exploring Operation: 98-7=91, Resulting Numbers: [6, 91] Generated Node #0,0,2: 20:[6, 91] Operation: 98-7=91 Exploring Operation: 98-6=92, Resulting Numbers: [7, 92] Generated Node #0,0,3: 20:[7, 92] Operation: 98-6=92 Exploring Operation: 7-6=1, Resulting Numbers: [98, 1] Generated Node #0,0,4: 20:[98, 1] Operation: 7-6=1 Moving to Node #0,0,1 Current State: 20:[6, 14], Operations: ['93-87=6', '98/7=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,20 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[7, 87, 93, 98], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [7, 98, 6] Generated Node #0,0: 20:[7, 98, 6] Operation: 93-87=6 Moving to Node #0,0 Current State: 20:[7, 98, 6], Operations: ['93-87=6'] Exploring Operation: 98/7=14, Resulting Numbers: [6, 14] Generated Node #0,0,1: 20:[6, 14] Operation: 98/7=14 Moving to Node #0,0,1 Current State: 20:[6, 14], Operations: ['93-87=6', '98/7=14'] Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 39, 45, 69, 26 ]
39
[ "39*45=1755", "69*26=1794", "1794-1755=39" ]
Current State: 39:[39, 45, 69, 26], Operations: [] Exploring Operation: 39*45=1755, Resulting Numbers: [69, 26, 1755] Generated Node #2: [69, 26, 1755] from Operation: 39*45=1755 Current State: 39:[69, 26, 1755], Operations: ['39*45=1755'] Exploring Operation: 69*26=1794, Resulting Numbers: [1755, 1794] Generated Node #3: [1755, 1794] from Operation: 69*26=1794 Current State: 39:[1755, 1794], Operations: ['39*45=1755', '69*26=1794'] Exploring Operation: 1794-1755=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[39, 45, 69, 26], Operations: [] Exploring Operation: 39-26=13, Resulting Numbers: [45, 69, 13] Generated Node #0,0: 39:[45, 69, 13] Operation: 39-26=13 Exploring Operation: 69-45=24, Resulting Numbers: [39, 26, 24] Generated Node #0,1: 39:[39, 26, 24] Operation: 69-45=24 Exploring Operation: 69-39=30, Resulting Numbers: [45, 26, 30] Generated Node #0,2: 39:[45, 26, 30] Operation: 69-39=30 Exploring Operation: 69-26=43, Resulting Numbers: [39, 45, 43] Generated Node #0,3: 39:[39, 45, 43] Operation: 69-26=43 Exploring Operation: 45-26=19, Resulting Numbers: [39, 69, 19] Generated Node #0,4: 39:[39, 69, 19] Operation: 45-26=19 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[39, 45, 43], Operations: ['69-26=43'] Exploring Operation: 39+45=84, Resulting Numbers: [43, 84] Generated Node #0,3,0: 39:[43, 84] Operation: 39+45=84 Exploring Operation: 45-43=2, Resulting Numbers: [39, 2] Generated Node #0,3,1: 39:[39, 2] Operation: 45-43=2 Exploring Operation: 45-39=6, Resulting Numbers: [43, 6] Generated Node #0,3,2: 39:[43, 6] Operation: 45-39=6 Exploring Operation: 43-39=4, Resulting Numbers: [45, 4] Generated Node #0,3,3: 39:[45, 4] Operation: 43-39=4 Exploring Operation: 39+43=82, Resulting Numbers: [45, 82] Generated Node #0,3,4: 39:[45, 82] Operation: 39+43=82 Moving to Node #0,3,1 Current State: 39:[39, 2], Operations: ['69-26=43', '45-43=2'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[45, 4], Operations: ['69-26=43', '43-39=4'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[43, 6], Operations: ['69-26=43', '45-39=6'] Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[43, 84], Operations: ['69-26=43', '39+45=84'] Exploring Operation: 84-43=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 43+84=127, Resulting Numbers: [127] 127,39 unequal: No Solution Exploring Operation: 43*84=3612, Resulting Numbers: [3612] 3612,39 unequal: No Solution Moving to Node #0,3,4 Current State: 39:[45, 82], Operations: ['69-26=43', '39+43=82'] Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,39 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,39 unequal: No Solution No 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: 39:[39, 26, 24], Operations: ['69-45=24'] Exploring Operation: 39-24=15, Resulting Numbers: [26, 15] Generated Node #0,1,0: 39:[26, 15] Operation: 39-24=15 Exploring Operation: 26+24=50, Resulting Numbers: [39, 50] Generated Node #0,1,1: 39:[39, 50] Operation: 26+24=50 Exploring Operation: 26-24=2, Resulting Numbers: [39, 2] Generated Node #0,1,2: 39:[39, 2] Operation: 26-24=2 Exploring Operation: 39-26=13, Resulting Numbers: [24, 13] Generated Node #0,1,3: 39:[24, 13] Operation: 39-26=13 Exploring Operation: 39+26=65, Resulting Numbers: [24, 65] Generated Node #0,1,4: 39:[24, 65] Operation: 39+26=65 Moving to Node #0,1,2 Current State: 39:[39, 2], Operations: ['69-45=24', '26-24=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,39 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[24, 13], Operations: ['69-45=24', '39-26=13'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,39 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[39, 50], Operations: ['69-45=24', '26+24=50'] Exploring Operation: 39*50=1950, Resulting Numbers: [1950] 1950,39 unequal: No Solution Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 39+50=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[26, 15], Operations: ['69-45=24', '39-24=15'] Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,39 unequal: No Solution Moving to Node #0,1,4 Current State: 39:[24, 65], Operations: ['69-45=24', '39+26=65'] Exploring Operation: 24+65=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 24*65=1560, Resulting Numbers: [1560] 1560,39 unequal: No Solution No 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: 39:[45, 26, 30], Operations: ['69-39=30'] Exploring Operation: 26+30=56, Resulting Numbers: [45, 56] Generated Node #0,2,0: 39:[45, 56] Operation: 26+30=56 Exploring Operation: 45-30=15, Resulting Numbers: [26, 15] Generated Node #0,2,1: 39:[26, 15] Operation: 45-30=15 Exploring Operation: 30-26=4, Resulting Numbers: [45, 4] Generated Node #0,2,2: 39:[45, 4] Operation: 30-26=4 Exploring Operation: 45+26=71, Resulting Numbers: [30, 71] Generated Node #0,2,3: 39:[30, 71] Operation: 45+26=71 Exploring Operation: 45-26=19, Resulting Numbers: [30, 19] Generated Node #0,2,4: 39:[30, 19] Operation: 45-26=19 Moving to Node #0,2,2 Current State: 39:[45, 4], Operations: ['69-39=30', '30-26=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,39 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,39 unequal: No Solution Moving to Node #0,2,4 Current State: 39:[30, 19], Operations: ['69-39=30', '45-26=19'] Exploring Operation: 30+19=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 30*19=570, Resulting Numbers: [570] 570,39 unequal: No Solution Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[26, 15], Operations: ['69-39=30', '45-30=15'] Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 26*15=390, Resulting Numbers: [390] 390,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[45, 56], Operations: ['69-39=30', '26+30=56'] Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,39 unequal: No Solution Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,39 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[30, 71], Operations: ['69-39=30', '45+26=71'] Exploring Operation: 30+71=101, Resulting Numbers: [101] 101,39 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,39 unequal: No Solution Exploring Operation: 30*71=2130, Resulting Numbers: [2130] 2130,39 unequal: No Solution No 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: 39:[45, 69, 13], Operations: ['39-26=13'] Exploring Operation: 45-13=32, Resulting Numbers: [69, 32] Generated Node #0,0,0: 39:[69, 32] Operation: 45-13=32 Exploring Operation: 45+13=58, Resulting Numbers: [69, 58] Generated Node #0,0,1: 39:[69, 58] Operation: 45+13=58 Exploring Operation: 69+13=82, Resulting Numbers: [45, 82] Generated Node #0,0,2: 39:[45, 82] Operation: 69+13=82 Exploring Operation: 69-45=24, Resulting Numbers: [13, 24] Generated Node #0,0,3: 39:[13, 24] Operation: 69-45=24 Exploring Operation: 69-13=56, Resulting Numbers: [45, 56] Generated Node #0,0,4: 39:[45, 56] Operation: 69-13=56 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 39:[13, 24], Operations: ['39-26=13', '69-45=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,39 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,39 unequal: No Solution No 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: 39:[45, 56], Operations: ['39-26=13', '69-13=56'] Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,39 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,39 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,39 unequal: No Solution No 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: 39:[69, 32], Operations: ['39-26=13', '45-13=32'] Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,39 unequal: No Solution Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,39 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,39 unequal: No Solution No 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: 39:[69, 58], Operations: ['39-26=13', '45+13=58'] Exploring Operation: 69*58=4002, Resulting Numbers: [4002] 4002,39 unequal: No Solution Exploring Operation: 69+58=127, Resulting Numbers: [127] 127,39 unequal: No Solution Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,39 unequal: No Solution No 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: 39:[45, 82], Operations: ['39-26=13', '69+13=82'] Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,39 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,39 unequal: No Solution Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,39 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: 39:[39, 69, 19], Operations: ['45-26=19'] Exploring Operation: 69+19=88, Resulting Numbers: [39, 88] Generated Node #0,4,0: 39:[39, 88] Operation: 69+19=88 Exploring Operation: 69-19=50, Resulting Numbers: [39, 50] Generated Node #0,4,1: 39:[39, 50] Operation: 69-19=50 Exploring Operation: 39-19=20, Resulting Numbers: [69, 20] Generated Node #0,4,2: 39:[69, 20] Operation: 39-19=20 Exploring Operation: 69-39=30, Resulting Numbers: [19, 30] Generated Node #0,4,3: 39:[19, 30] Operation: 69-39=30 Exploring Operation: 39+19=58, Resulting Numbers: [69, 58] Generated Node #0,4,4: 39:[69, 58] Operation: 39+19=58 Moving to Node #0,4,1 Current State: 39:[39, 50], Operations: ['45-26=19', '69-19=50'] Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 39*50=1950, Resulting Numbers: [1950] 1950,39 unequal: No Solution Exploring Operation: 39+50=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[19, 30], Operations: ['45-26=19', '69-39=30'] Exploring Operation: 19+30=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 19*30=570, Resulting Numbers: [570] 570,39 unequal: No Solution Moving to Node #0,4,2 Current State: 39:[69, 20], Operations: ['45-26=19', '39-19=20'] Exploring Operation: 69*20=1380, Resulting Numbers: [1380] 1380,39 unequal: No Solution Exploring Operation: 69+20=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,39 unequal: No Solution Moving to Node #0,4,0 Current State: 39:[39, 88], Operations: ['45-26=19', '69+19=88'] Exploring Operation: 39+88=127, Resulting Numbers: [127] 127,39 unequal: No Solution Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,39 unequal: No Solution Exploring Operation: 39*88=3432, Resulting Numbers: [3432] 3432,39 unequal: No Solution Moving to Node #0,4,4 Current State: 39:[69, 58], Operations: ['45-26=19', '39+19=58'] Exploring Operation: 69*58=4002, Resulting Numbers: [4002] 4002,39 unequal: No Solution Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 69+58=127, Resulting Numbers: [127] 127,39 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
[ 56, 69, 7, 7 ]
27
[ "69-56=13", "7+7=14", "13+14=27" ]
Current State: 27:[56, 69, 7, 7], Operations: [] Exploring Operation: 69-56=13, Resulting Numbers: [7, 7, 13] Generated Node #2: [7, 7, 13] from Operation: 69-56=13 Current State: 27:[7, 7, 13], Operations: ['69-56=13'] Exploring Operation: 7+7=14, Resulting Numbers: [13, 14] Generated Node #3: [13, 14] from Operation: 7+7=14 Current State: 27:[13, 14], Operations: ['69-56=13', '7+7=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[56, 69, 7, 7], Operations: [] Exploring Operation: 69-56=13, Resulting Numbers: [7, 7, 13] Generated Node #0,0: 27:[7, 7, 13] Operation: 69-56=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[7, 7, 13], Operations: ['69-56=13'] Exploring Operation: 13-7=6, Resulting Numbers: [7, 6] Generated Node #0,0,0: 27:[7, 6] Operation: 13-7=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[7, 6], Operations: ['69-56=13', '13-7=6'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,27 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
[ 66, 31, 35, 54 ]
53
[ "66-31=35", "35/35=1", "54-1=53" ]
Current State: 53:[66, 31, 35, 54], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [35, 54, 35] Generated Node #2: [35, 54, 35] from Operation: 66-31=35 Current State: 53:[35, 54, 35], Operations: ['66-31=35'] Exploring Operation: 35/35=1, Resulting Numbers: [54, 1] Generated Node #3: [54, 1] from Operation: 35/35=1 Current State: 53:[54, 1], Operations: ['66-31=35', '35/35=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[66, 31, 35, 54], Operations: [] Exploring Operation: 66-31=35, Resulting Numbers: [35, 54, 35] Generated Node #0,0: 53:[35, 54, 35] Operation: 66-31=35 Exploring Operation: 31+35=66, Resulting Numbers: [66, 54, 66] Generated Node #0,1: 53:[66, 54, 66] Operation: 31+35=66 Exploring Operation: 54-31=23, Resulting Numbers: [66, 35, 23] Generated Node #0,2: 53:[66, 35, 23] Operation: 54-31=23 Exploring Operation: 66-35=31, Resulting Numbers: [31, 54, 31] Generated Node #0,3: 53:[31, 54, 31] Operation: 66-35=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[66, 54, 66], Operations: ['31+35=66'] Exploring Operation: 66/66=1, Resulting Numbers: [54, 1] Generated Node #0,1,0: 53:[54, 1] Operation: 66/66=1 Exploring Operation: 66-66=0, Resulting Numbers: [54, 0] Generated Node #0,1,1: 53:[54, 0] Operation: 66-66=0 Exploring Operation: 66-54=12, Resulting Numbers: [66, 12] Generated Node #0,1,2: 53:[66, 12] Operation: 66-54=12 Exploring Operation: 66-54=12, Resulting Numbers: [66, 12] Generated Node #0,1,3: 53:[66, 12] Operation: 66-54=12 Moving to Node #0,1,0 Current State: 53:[54, 1], Operations: ['31+35=66', '66/66=1'] Exploring Operation: 54*1=54, Resulting Numbers: [54] 54,53 unequal: No Solution Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[66, 31, 35, 54], Operations: [] Exploring Operation: 31+35=66, Resulting Numbers: [66, 54, 66] Generated Node #0,1: 53:[66, 54, 66] Operation: 31+35=66 Moving to Node #0,1 Current State: 53:[66, 54, 66], Operations: ['31+35=66'] Exploring Operation: 66/66=1, Resulting Numbers: [54, 1] Generated Node #0,1,0: 53:[54, 1] Operation: 66/66=1 Moving to Node #0,1,0 Current State: 53:[54, 1], Operations: ['31+35=66', '66/66=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 3, 58, 29, 50 ]
82
[ "3+58=61", "50-29=21", "61+21=82" ]
Current State: 82:[3, 58, 29, 50], Operations: [] Exploring Operation: 3+58=61, Resulting Numbers: [29, 50, 61] Generated Node #2: [29, 50, 61] from Operation: 3+58=61 Current State: 82:[29, 50, 61], Operations: ['3+58=61'] Exploring Operation: 50-29=21, Resulting Numbers: [61, 21] Generated Node #3: [61, 21] from Operation: 50-29=21 Current State: 82:[61, 21], Operations: ['3+58=61', '50-29=21'] Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[3, 58, 29, 50], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [3, 50, 2] Generated Node #0,0: 82:[3, 50, 2] Operation: 58/29=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[3, 50, 2], Operations: ['58/29=2'] Exploring Operation: 50-3=47, Resulting Numbers: [2, 47] Generated Node #0,0,0: 82:[2, 47] Operation: 50-3=47 Moving to Node #0,0,0 Current State: 82:[2, 47], Operations: ['58/29=2', '50-3=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 26, 12, 72, 10 ]
18
[ "26-12=14", "14-10=4", "72/4=18" ]
Current State: 18:[26, 12, 72, 10], Operations: [] Exploring Operation: 26-12=14, Resulting Numbers: [72, 10, 14] Generated Node #2: [72, 10, 14] from Operation: 26-12=14 Current State: 18:[72, 10, 14], Operations: ['26-12=14'] Exploring Operation: 14-10=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 14-10=4 Current State: 18:[72, 4], Operations: ['26-12=14', '14-10=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[26, 12, 72, 10], Operations: [] Exploring Operation: 72/12=6, Resulting Numbers: [26, 10, 6] Generated Node #0,0: 18:[26, 10, 6] Operation: 72/12=6 Exploring Operation: 72-26=46, Resulting Numbers: [12, 10, 46] Generated Node #0,1: 18:[12, 10, 46] Operation: 72-26=46 Moving to Node #0,0 Current State: 18:[26, 10, 6], Operations: ['72/12=6'] Exploring Operation: 26-6=20, Resulting Numbers: [10, 20] Generated Node #0,0,0: 18:[10, 20] Operation: 26-6=20 Exploring Operation: 26-10=16, Resulting Numbers: [6, 16] Generated Node #0,0,1: 18:[6, 16] Operation: 26-10=16 Moving to Node #0,1 Current State: 18:[12, 10, 46], Operations: ['72-26=46'] Exploring Operation: 46-10=36, Resulting Numbers: [12, 36] Generated Node #0,1,0: 18:[12, 36] Operation: 46-10=36 Exploring Operation: 46-12=34, Resulting Numbers: [10, 34] Generated Node #0,1,1: 18:[10, 34] Operation: 46-12=34 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[10, 34], Operations: ['72-26=46', '46-12=34'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 10+34=44, Resulting Numbers: [44] 44,18 unequal: No Solution No 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: 18:[12, 36], Operations: ['72-26=46', '46-10=36'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,18 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: 18:[6, 16], Operations: ['72/12=6', '26-10=16'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[10, 20], Operations: ['72/12=6', '26-6=20'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,18 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 30, 73, 27, 51 ]
56
[ "30-27=3", "51/3=17", "73-17=56" ]
Current State: 56:[30, 73, 27, 51], Operations: [] Exploring Operation: 30-27=3, Resulting Numbers: [73, 51, 3] Generated Node #2: [73, 51, 3] from Operation: 30-27=3 Current State: 56:[73, 51, 3], Operations: ['30-27=3'] Exploring Operation: 51/3=17, Resulting Numbers: [73, 17] Generated Node #3: [73, 17] from Operation: 51/3=17 Current State: 56:[73, 17], Operations: ['30-27=3', '51/3=17'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[30, 73, 27, 51], Operations: [] Exploring Operation: 73-30=43, Resulting Numbers: [27, 51, 43] Generated Node #0,0: 56:[27, 51, 43] Operation: 73-30=43 Exploring Operation: 30-27=3, Resulting Numbers: [73, 51, 3] Generated Node #0,1: 56:[73, 51, 3] Operation: 30-27=3 Exploring Operation: 30+27=57, Resulting Numbers: [73, 51, 57] Generated Node #0,2: 56:[73, 51, 57] Operation: 30+27=57 Exploring Operation: 73-27=46, Resulting Numbers: [30, 51, 46] Generated Node #0,3: 56:[30, 51, 46] Operation: 73-27=46 Exploring Operation: 73-51=22, Resulting Numbers: [30, 27, 22] Generated Node #0,4: 56:[30, 27, 22] Operation: 73-51=22 Start Sub Search at level 1: Moving to Node #0,4 Current State: 56:[30, 27, 22], Operations: ['73-51=22'] Exploring Operation: 30-27=3, Resulting Numbers: [22, 3] Generated Node #0,4,0: 56:[22, 3] Operation: 30-27=3 Exploring Operation: 30+27=57, Resulting Numbers: [22, 57] Generated Node #0,4,1: 56:[22, 57] Operation: 30+27=57 Exploring Operation: 30-22=8, Resulting Numbers: [27, 8] Generated Node #0,4,2: 56:[27, 8] Operation: 30-22=8 Exploring Operation: 27-22=5, Resulting Numbers: [30, 5] Generated Node #0,4,3: 56:[30, 5] Operation: 27-22=5 Exploring Operation: 30+22=52, Resulting Numbers: [27, 52] Generated Node #0,4,4: 56:[27, 52] Operation: 30+22=52 Moving to Node #0,4,2 Current State: 56:[27, 8], Operations: ['73-51=22', '30-22=8'] Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,56 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,56 unequal: No Solution Moving to Node #0,4,3 Current State: 56:[30, 5], Operations: ['73-51=22', '27-22=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,56 unequal: No Solution Moving to Node #0,4,4 Current State: 56:[27, 52], Operations: ['73-51=22', '30+22=52'] Exploring Operation: 27+52=79, Resulting Numbers: [79] 79,56 unequal: No Solution Exploring Operation: 52-27=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 27*52=1404, Resulting Numbers: [1404] 1404,56 unequal: No Solution Moving to Node #0,4,0 Current State: 56:[22, 3], Operations: ['73-51=22', '30-27=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,56 unequal: No Solution Moving to Node #0,4,1 Current State: 56:[22, 57], Operations: ['73-51=22', '30+27=57'] Exploring Operation: 22+57=79, Resulting Numbers: [79] 79,56 unequal: No Solution Exploring Operation: 22*57=1254, Resulting Numbers: [1254] 1254,56 unequal: No Solution Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[30, 51, 46], Operations: ['73-27=46'] Exploring Operation: 51-46=5, Resulting Numbers: [30, 5] Generated Node #0,3,0: 56:[30, 5] Operation: 51-46=5 Exploring Operation: 30+51=81, Resulting Numbers: [46, 81] Generated Node #0,3,1: 56:[46, 81] Operation: 30+51=81 Exploring Operation: 30+46=76, Resulting Numbers: [51, 76] Generated Node #0,3,2: 56:[51, 76] Operation: 30+46=76 Exploring Operation: 51-30=21, Resulting Numbers: [46, 21] Generated Node #0,3,3: 56:[46, 21] Operation: 51-30=21 Exploring Operation: 46-30=16, Resulting Numbers: [51, 16] Generated Node #0,3,4: 56:[51, 16] Operation: 46-30=16 Moving to Node #0,3,0 Current State: 56:[30, 5], Operations: ['73-27=46', '51-46=5'] Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,56 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,56 unequal: No Solution Moving to Node #0,3,4 Current State: 56:[51, 16], Operations: ['73-27=46', '46-30=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,56 unequal: No Solution Moving to Node #0,3,3 Current State: 56:[46, 21], Operations: ['73-27=46', '51-30=21'] Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,56 unequal: No Solution Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[51, 76], Operations: ['73-27=46', '30+46=76'] Exploring Operation: 51*76=3876, Resulting Numbers: [3876] 3876,56 unequal: No Solution Exploring Operation: 76-51=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 51+76=127, Resulting Numbers: [127] 127,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[46, 81], Operations: ['73-27=46', '30+51=81'] Exploring Operation: 81-46=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 46+81=127, Resulting Numbers: [127] 127,56 unequal: No Solution Exploring Operation: 46*81=3726, Resulting Numbers: [3726] 3726,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[27, 51, 43], Operations: ['73-30=43'] Exploring Operation: 27+51=78, Resulting Numbers: [43, 78] Generated Node #0,0,0: 56:[43, 78] Operation: 27+51=78 Exploring Operation: 51-43=8, Resulting Numbers: [27, 8] Generated Node #0,0,1: 56:[27, 8] Operation: 51-43=8 Exploring Operation: 43-27=16, Resulting Numbers: [51, 16] Generated Node #0,0,2: 56:[51, 16] Operation: 43-27=16 Exploring Operation: 51-27=24, Resulting Numbers: [43, 24] Generated Node #0,0,3: 56:[43, 24] Operation: 51-27=24 Exploring Operation: 27+43=70, Resulting Numbers: [51, 70] Generated Node #0,0,4: 56:[51, 70] Operation: 27+43=70 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[27, 8], Operations: ['73-30=43', '51-43=8'] Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,56 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 56:[51, 16], Operations: ['73-30=43', '43-27=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 56:[43, 24], Operations: ['73-30=43', '51-27=24'] Exploring Operation: 43+24=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 43*24=1032, Resulting Numbers: [1032] 1032,56 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 56:[51, 70], Operations: ['73-30=43', '27+43=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[43, 78], Operations: ['73-30=43', '27+51=78'] Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,56 unequal: No Solution Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,56 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: 56:[73, 51, 3], Operations: ['30-27=3'] Exploring Operation: 73+3=76, Resulting Numbers: [51, 76] Generated Node #0,1,0: 56:[51, 76] Operation: 73+3=76 Exploring Operation: 51+3=54, Resulting Numbers: [73, 54] Generated Node #0,1,1: 56:[73, 54] Operation: 51+3=54 Exploring Operation: 73-3=70, Resulting Numbers: [51, 70] Generated Node #0,1,2: 56:[51, 70] Operation: 73-3=70 Exploring Operation: 51/3=17, Resulting Numbers: [73, 17] Generated Node #0,1,3: 56:[73, 17] Operation: 51/3=17 Exploring Operation: 73-51=22, Resulting Numbers: [3, 22] Generated Node #0,1,4: 56:[3, 22] Operation: 73-51=22 Moving to Node #0,1,4 Current State: 56:[3, 22], Operations: ['30-27=3', '73-51=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[51, 70], Operations: ['30-27=3', '73-3=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 51*70=3570, Resulting Numbers: [3570] 3570,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[73, 54], Operations: ['30-27=3', '51+3=54'] Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,56 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,56 unequal: No Solution Moving to Node #0,1,3 Current State: 56:[73, 17], Operations: ['30-27=3', '51/3=17'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[30, 73, 27, 51], Operations: [] Exploring Operation: 30-27=3, Resulting Numbers: [73, 51, 3] Generated Node #0,1: 56:[73, 51, 3] Operation: 30-27=3 Moving to Node #0,1 Current State: 56:[73, 51, 3], Operations: ['30-27=3'] Exploring Operation: 51/3=17, Resulting Numbers: [73, 17] Generated Node #0,1,3: 56:[73, 17] Operation: 51/3=17 Moving to Node #0,1,3 Current State: 56:[73, 17], Operations: ['30-27=3', '51/3=17'] Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.925347
hs_5
sum_heuristic
[ 72, 63, 57, 48 ]
80
[ "63+57=120", "48*120=5760", "5760/72=80" ]
Current State: 80:[72, 63, 57, 48], Operations: [] Exploring Operation: 63+57=120, Resulting Numbers: [72, 48, 120] Generated Node #2: [72, 48, 120] from Operation: 63+57=120 Current State: 80:[72, 48, 120], Operations: ['63+57=120'] Exploring Operation: 48*120=5760, Resulting Numbers: [72, 5760] Generated Node #3: [72, 5760] from Operation: 48*120=5760 Current State: 80:[72, 5760], Operations: ['63+57=120', '48*120=5760'] Exploring Operation: 5760/72=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[72, 63, 57, 48], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [72, 48, 6] Generated Node #0,0: 80:[72, 48, 6] Operation: 63-57=6 Exploring Operation: 72-63=9, Resulting Numbers: [57, 48, 9] Generated Node #0,1: 80:[57, 48, 9] Operation: 72-63=9 Moving to Node #0,0 Current State: 80:[72, 48, 6], Operations: ['63-57=6'] Exploring Operation: 48/6=8, Resulting Numbers: [72, 8] Generated Node #0,0,0: 80:[72, 8] Operation: 48/6=8 Exploring Operation: 72-48=24, Resulting Numbers: [6, 24] Generated Node #0,0,1: 80:[6, 24] Operation: 72-48=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[6, 24], Operations: ['63-57=6', '72-48=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[72, 8], Operations: ['63-57=6', '48/6=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[72, 63, 57, 48], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [72, 48, 6] Generated Node #0,0: 80:[72, 48, 6] Operation: 63-57=6 Moving to Node #0,0 Current State: 80:[72, 48, 6], Operations: ['63-57=6'] Exploring Operation: 48/6=8, Resulting Numbers: [72, 8] Generated Node #0,0,0: 80:[72, 8] Operation: 48/6=8 Moving to Node #0,0,0 Current State: 80:[72, 8], Operations: ['63-57=6', '48/6=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 43, 65, 91, 62 ]
79
[ "43+65=108", "91-62=29", "108-29=79" ]
Current State: 79:[43, 65, 91, 62], Operations: [] Exploring Operation: 43+65=108, Resulting Numbers: [91, 62, 108] Generated Node #2: [91, 62, 108] from Operation: 43+65=108 Current State: 79:[91, 62, 108], Operations: ['43+65=108'] Exploring Operation: 91-62=29, Resulting Numbers: [108, 29] Generated Node #3: [108, 29] from Operation: 91-62=29 Current State: 79:[108, 29], Operations: ['43+65=108', '91-62=29'] Exploring Operation: 108-29=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[43, 65, 91, 62], Operations: [] Exploring Operation: 43+62=105, Resulting Numbers: [65, 91, 105] Generated Node #0,0: 79:[65, 91, 105] Operation: 43+62=105 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[65, 91, 105], Operations: ['43+62=105'] Exploring Operation: 105-65=40, Resulting Numbers: [91, 40] Generated Node #0,0,0: 79:[91, 40] Operation: 105-65=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[91, 40], Operations: ['43+62=105', '105-65=40'] Exploring Operation: 91-40=51, Resulting Numbers: [51] 51,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 66, 3, 5 ]
68
[ "66-6=60", "3+5=8", "60+8=68" ]
Current State: 68:[6, 66, 3, 5], Operations: [] Exploring Operation: 66-6=60, Resulting Numbers: [3, 5, 60] Generated Node #2: [3, 5, 60] from Operation: 66-6=60 Current State: 68:[3, 5, 60], Operations: ['66-6=60'] Exploring Operation: 3+5=8, Resulting Numbers: [60, 8] Generated Node #3: [60, 8] from Operation: 3+5=8 Current State: 68:[60, 8], Operations: ['66-6=60', '3+5=8'] Exploring Operation: 60+8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[6, 66, 3, 5], Operations: [] Exploring Operation: 6/3=2, Resulting Numbers: [66, 5, 2] Generated Node #0,0: 68:[66, 5, 2] Operation: 6/3=2 Exploring Operation: 6*3=18, Resulting Numbers: [66, 5, 18] Generated Node #0,1: 68:[66, 5, 18] Operation: 6*3=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[66, 5, 2], Operations: ['6/3=2'] Exploring Operation: 66+2=68, Resulting Numbers: [5, 68] Generated Node #0,0,0: 68:[5, 68] Operation: 66+2=68 Exploring Operation: 66/2=33, Resulting Numbers: [5, 33] Generated Node #0,0,1: 68:[5, 33] Operation: 66/2=33 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[5, 68], Operations: ['6/3=2', '66+2=68'] Exploring Operation: 5+68=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 68-5=63, Resulting Numbers: [63] 63,68 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 #0,0,1 Current State: 68:[5, 33], Operations: ['6/3=2', '66/2=33'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 5+33=38, Resulting Numbers: [38] 38,68 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 #0,1 Current State: 68:[66, 5, 18], Operations: ['6*3=18'] Exploring Operation: 18-5=13, Resulting Numbers: [66, 13] Generated Node #0,1,0: 68:[66, 13] Operation: 18-5=13 Exploring Operation: 66+5=71, Resulting Numbers: [18, 71] Generated Node #0,1,1: 68:[18, 71] Operation: 66+5=71 Moving to Node #0,1,1 Current State: 68:[18, 71], Operations: ['6*3=18', '66+5=71'] Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 18+71=89, Resulting Numbers: [89] 89,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[66, 13], Operations: ['6*3=18', '18-5=13'] Exploring Operation: 66-13=53, Resulting Numbers: [53] 53,68 unequal: No Solution Exploring Operation: 66+13=79, Resulting Numbers: [79] 79,68 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
[ 42, 60, 31, 12 ]
16
[ "42-31=11", "60/12=5", "11+5=16" ]
Current State: 16:[42, 60, 31, 12], Operations: [] Exploring Operation: 42-31=11, Resulting Numbers: [60, 12, 11] Generated Node #2: [60, 12, 11] from Operation: 42-31=11 Current State: 16:[60, 12, 11], Operations: ['42-31=11'] Exploring Operation: 60/12=5, Resulting Numbers: [11, 5] Generated Node #3: [11, 5] from Operation: 60/12=5 Current State: 16:[11, 5], Operations: ['42-31=11', '60/12=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[42, 60, 31, 12], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [42, 31, 5] Generated Node #0,0: 16:[42, 31, 5] Operation: 60/12=5 Exploring Operation: 60-42=18, Resulting Numbers: [31, 12, 18] Generated Node #0,1: 16:[31, 12, 18] Operation: 60-42=18 Moving to Node #0,1 Current State: 16:[31, 12, 18], Operations: ['60-42=18'] Exploring Operation: 31-12=19, Resulting Numbers: [18, 19] Generated Node #0,1,0: 16:[18, 19] Operation: 31-12=19 Exploring Operation: 31-18=13, Resulting Numbers: [12, 13] Generated Node #0,1,1: 16:[12, 13] Operation: 31-18=13 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[18, 19], Operations: ['60-42=18', '31-12=19'] Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,16 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,16 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:[12, 13], Operations: ['60-42=18', '31-18=13'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,16 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: 16:[42, 31, 5], Operations: ['60/12=5'] Exploring Operation: 42-31=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 16:[5, 11] Operation: 42-31=11 Exploring Operation: 42-5=37, Resulting Numbers: [31, 37] Generated Node #0,0,1: 16:[31, 37] Operation: 42-5=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[5, 11], Operations: ['60/12=5', '42-31=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[42, 60, 31, 12], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [42, 31, 5] Generated Node #0,0: 16:[42, 31, 5] Operation: 60/12=5 Moving to Node #0,0 Current State: 16:[42, 31, 5], Operations: ['60/12=5'] Exploring Operation: 42-31=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 16:[5, 11] Operation: 42-31=11 Moving to Node #0,0,0 Current State: 16:[5, 11], Operations: ['60/12=5', '42-31=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 4, 51, 86, 6 ]
36
[ "4+86=90", "90/6=15", "51-15=36" ]
Current State: 36:[4, 51, 86, 6], Operations: [] Exploring Operation: 4+86=90, Resulting Numbers: [51, 6, 90] Generated Node #2: [51, 6, 90] from Operation: 4+86=90 Current State: 36:[51, 6, 90], Operations: ['4+86=90'] Exploring Operation: 90/6=15, Resulting Numbers: [51, 15] Generated Node #3: [51, 15] from Operation: 90/6=15 Current State: 36:[51, 15], Operations: ['4+86=90', '90/6=15'] Exploring Operation: 51-15=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[4, 51, 86, 6], Operations: [] Exploring Operation: 86-6=80, Resulting Numbers: [4, 51, 80] Generated Node #0,0: 36:[4, 51, 80] Operation: 86-6=80 Exploring Operation: 51-6=45, Resulting Numbers: [4, 86, 45] Generated Node #0,1: 36:[4, 86, 45] Operation: 51-6=45 Exploring Operation: 86-51=35, Resulting Numbers: [4, 6, 35] Generated Node #0,2: 36:[4, 6, 35] Operation: 86-51=35 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[4, 6, 35], Operations: ['86-51=35'] Exploring Operation: 6-4=2, Resulting Numbers: [35, 2] Generated Node #0,2,0: 36:[35, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [35, 10] Generated Node #0,2,1: 36:[35, 10] Operation: 4+6=10 Exploring Operation: 4+35=39, Resulting Numbers: [6, 39] Generated Node #0,2,2: 36:[6, 39] Operation: 4+35=39 Moving to Node #0,2,0 Current State: 36:[35, 2], Operations: ['86-51=35', '6-4=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,36 unequal: No Solution Moving to Node #0,2,1 Current State: 36:[35, 10], Operations: ['86-51=35', '4+6=10'] Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,36 unequal: No Solution Exploring Operation: 35*10=350, Resulting Numbers: [350] 350,36 unequal: No Solution Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,36 unequal: No Solution Moving to Node #0,2,2 Current State: 36:[6, 39], Operations: ['86-51=35', '4+35=39'] Exploring Operation: 6*39=234, Resulting Numbers: [234] 234,36 unequal: No Solution Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 6+39=45, Resulting Numbers: [45] 45,36 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 Current State: 36:[4, 51, 80], Operations: ['86-6=80'] Exploring Operation: 80-51=29, Resulting Numbers: [4, 29] Generated Node #0,0,0: 36:[4, 29] Operation: 80-51=29 Exploring Operation: 80/4=20, Resulting Numbers: [51, 20] Generated Node #0,0,1: 36:[51, 20] Operation: 80/4=20 Exploring Operation: 51-4=47, Resulting Numbers: [80, 47] Generated Node #0,0,2: 36:[80, 47] Operation: 51-4=47 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[4, 29], Operations: ['86-6=80', '80-51=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,36 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,36 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,36 unequal: No Solution No 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: 36:[51, 20], Operations: ['86-6=80', '80/4=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,36 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,36 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,36 unequal: No Solution No 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: 36:[80, 47], Operations: ['86-6=80', '51-4=47'] Exploring Operation: 80*47=3760, Resulting Numbers: [3760] 3760,36 unequal: No Solution Exploring Operation: 80-47=33, Resulting Numbers: [33] 33,36 unequal: No Solution Exploring Operation: 80+47=127, Resulting Numbers: [127] 127,36 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: 36:[4, 86, 45], Operations: ['51-6=45'] Exploring Operation: 86-4=82, Resulting Numbers: [45, 82] Generated Node #0,1,0: 36:[45, 82] Operation: 86-4=82 Exploring Operation: 45-4=41, Resulting Numbers: [86, 41] Generated Node #0,1,1: 36:[86, 41] Operation: 45-4=41 Exploring Operation: 86-45=41, Resulting Numbers: [4, 41] Generated Node #0,1,2: 36:[4, 41] Operation: 86-45=41 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 36:[4, 41], Operations: ['51-6=45', '86-45=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,36 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,36 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,36 unequal: No Solution No 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: 36:[45, 82], Operations: ['51-6=45', '86-4=82'] Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,36 unequal: No Solution Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,36 unequal: No Solution No 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: 36:[86, 41], Operations: ['51-6=45', '45-4=41'] Exploring Operation: 86*41=3526, Resulting Numbers: [3526] 3526,36 unequal: No Solution Exploring Operation: 86+41=127, Resulting Numbers: [127] 127,36 unequal: No Solution Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 75, 29, 91, 99 ]
13
[ "75+29=104", "99-91=8", "104/8=13" ]
Current State: 13:[75, 29, 91, 99], Operations: [] Exploring Operation: 75+29=104, Resulting Numbers: [91, 99, 104] Generated Node #2: [91, 99, 104] from Operation: 75+29=104 Current State: 13:[91, 99, 104], Operations: ['75+29=104'] Exploring Operation: 99-91=8, Resulting Numbers: [104, 8] Generated Node #3: [104, 8] from Operation: 99-91=8 Current State: 13:[104, 8], Operations: ['75+29=104', '99-91=8'] Exploring Operation: 104/8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[75, 29, 91, 99], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [75, 29, 8] Generated Node #0,0: 13:[75, 29, 8] Operation: 99-91=8 Exploring Operation: 91-75=16, Resulting Numbers: [29, 99, 16] Generated Node #0,1: 13:[29, 99, 16] Operation: 91-75=16 Moving to Node #0,0 Current State: 13:[75, 29, 8], Operations: ['99-91=8'] Exploring Operation: 75-8=67, Resulting Numbers: [29, 67] Generated Node #0,0,0: 13:[29, 67] Operation: 75-8=67 Exploring Operation: 75-29=46, Resulting Numbers: [8, 46] Generated Node #0,0,1: 13:[8, 46] Operation: 75-29=46 Moving to Node #0,1 Current State: 13:[29, 99, 16], Operations: ['91-75=16'] Exploring Operation: 29-16=13, Resulting Numbers: [99, 13] Generated Node #0,1,0: 13:[99, 13] Operation: 29-16=13 Exploring Operation: 99-29=70, Resulting Numbers: [16, 70] Generated Node #0,1,1: 13:[16, 70] Operation: 99-29=70 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[16, 70], Operations: ['91-75=16', '99-29=70'] Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,13 unequal: No Solution Exploring Operation: 16+70=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[99, 13], Operations: ['91-75=16', '29-16=13'] Exploring Operation: 99+13=112, Resulting Numbers: [112] 112,13 unequal: No Solution Exploring Operation: 99-13=86, Resulting Numbers: [86] 86,13 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: 13:[8, 46], Operations: ['99-91=8', '75-29=46'] Exploring Operation: 8+46=54, Resulting Numbers: [54] 54,13 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,13 unequal: No Solution Moving to Node #0,0,0 Current State: 13:[29, 67], Operations: ['99-91=8', '75-8=67'] Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,13 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 13, 2, 11, 14 ]
21
[ "14-13=1", "2*11=22", "22-1=21" ]
Current State: 21:[13, 2, 11, 14], Operations: [] Exploring Operation: 14-13=1, Resulting Numbers: [2, 11, 1] Generated Node #2: [2, 11, 1] from Operation: 14-13=1 Current State: 21:[2, 11, 1], Operations: ['14-13=1'] Exploring Operation: 2*11=22, Resulting Numbers: [1, 22] Generated Node #3: [1, 22] from Operation: 2*11=22 Current State: 21:[1, 22], Operations: ['14-13=1', '2*11=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[13, 2, 11, 14], Operations: [] Exploring Operation: 13+11=24, Resulting Numbers: [2, 14, 24] Generated Node #0,0: 21:[2, 14, 24] Operation: 13+11=24 Exploring Operation: 14-13=1, Resulting Numbers: [2, 11, 1] Generated Node #0,1: 21:[2, 11, 1] Operation: 14-13=1 Exploring Operation: 14-11=3, Resulting Numbers: [13, 2, 3] Generated Node #0,2: 21:[13, 2, 3] Operation: 14-11=3 Exploring Operation: 13-11=2, Resulting Numbers: [2, 14, 2] Generated Node #0,3: 21:[2, 14, 2] Operation: 13-11=2 Exploring Operation: 14/2=7, Resulting Numbers: [13, 11, 7] Generated Node #0,4: 21:[13, 11, 7] Operation: 14/2=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[2, 11, 1], Operations: ['14-13=1'] Exploring Operation: 11-2=9, Resulting Numbers: [1, 9] Generated Node #0,1,0: 21:[1, 9] Operation: 11-2=9 Exploring Operation: 2*1=2, Resulting Numbers: [11, 2] Generated Node #0,1,1: 21:[11, 2] Operation: 2*1=2 Exploring Operation: 11-1=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 21:[2, 10] Operation: 11-1=10 Exploring Operation: 2*11=22, Resulting Numbers: [1, 22] Generated Node #0,1,3: 21:[1, 22] Operation: 2*11=22 Exploring Operation: 2+1=3, Resulting Numbers: [11, 3] Generated Node #0,1,4: 21:[11, 3] Operation: 2+1=3 Moving to Node #0,1,3 Current State: 21:[1, 22], Operations: ['14-13=1', '2*11=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,21 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[13, 2, 11, 14], Operations: [] Exploring Operation: 14-13=1, Resulting Numbers: [2, 11, 1] Generated Node #0,1: 21:[2, 11, 1] Operation: 14-13=1 Moving to Node #0,1 Current State: 21:[2, 11, 1], Operations: ['14-13=1'] Exploring Operation: 2*11=22, Resulting Numbers: [1, 22] Generated Node #0,1,3: 21:[1, 22] Operation: 2*11=22 Moving to Node #0,1,3 Current State: 21:[1, 22], Operations: ['14-13=1', '2*11=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 89, 98, 17, 6 ]
93
[ "98-89=9", "17*6=102", "102-9=93" ]
Current State: 93:[89, 98, 17, 6], Operations: [] Exploring Operation: 98-89=9, Resulting Numbers: [17, 6, 9] Generated Node #2: [17, 6, 9] from Operation: 98-89=9 Current State: 93:[17, 6, 9], Operations: ['98-89=9'] Exploring Operation: 17*6=102, Resulting Numbers: [9, 102] Generated Node #3: [9, 102] from Operation: 17*6=102 Current State: 93:[9, 102], Operations: ['98-89=9', '17*6=102'] Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[89, 98, 17, 6], Operations: [] Exploring Operation: 17-6=11, Resulting Numbers: [89, 98, 11] Generated Node #0,0: 93:[89, 98, 11] Operation: 17-6=11 Exploring Operation: 17*6=102, Resulting Numbers: [89, 98, 102] Generated Node #0,1: 93:[89, 98, 102] Operation: 17*6=102 Exploring Operation: 17+6=23, Resulting Numbers: [89, 98, 23] Generated Node #0,2: 93:[89, 98, 23] Operation: 17+6=23 Moving to Node #0,0 Current State: 93:[89, 98, 11], Operations: ['17-6=11'] Exploring Operation: 98-11=87, Resulting Numbers: [89, 87] Generated Node #0,0,0: 93:[89, 87] Operation: 98-11=87 Exploring Operation: 98-89=9, Resulting Numbers: [11, 9] Generated Node #0,0,1: 93:[11, 9] Operation: 98-89=9 Exploring Operation: 89+11=100, Resulting Numbers: [98, 100] Generated Node #0,0,2: 93:[98, 100] Operation: 89+11=100 Moving to Node #0,2 Current State: 93:[89, 98, 23], Operations: ['17+6=23'] Exploring Operation: 98-23=75, Resulting Numbers: [89, 75] Generated Node #0,2,0: 93:[89, 75] Operation: 98-23=75 Exploring Operation: 98-89=9, Resulting Numbers: [23, 9] Generated Node #0,2,1: 93:[23, 9] Operation: 98-89=9 Exploring Operation: 89+23=112, Resulting Numbers: [98, 112] Generated Node #0,2,2: 93:[98, 112] Operation: 89+23=112 Moving to Node #0,1 Current State: 93:[89, 98, 102], Operations: ['17*6=102'] Exploring Operation: 102-98=4, Resulting Numbers: [89, 4] Generated Node #0,1,0: 93:[89, 4] Operation: 102-98=4 Exploring Operation: 102-89=13, Resulting Numbers: [98, 13] Generated Node #0,1,1: 93:[98, 13] Operation: 102-89=13 Exploring Operation: 98-89=9, Resulting Numbers: [102, 9] Generated Node #0,1,2: 93:[102, 9] Operation: 98-89=9 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[89, 4], Operations: ['17*6=102', '102-98=4'] Exploring Operation: 89*4=356, Resulting Numbers: [356] 356,93 unequal: No Solution Exploring Operation: 89+4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[89, 98, 17, 6], Operations: [] Exploring Operation: 17*6=102, Resulting Numbers: [89, 98, 102] Generated Node #0,1: 93:[89, 98, 102] Operation: 17*6=102 Moving to Node #0,1 Current State: 93:[89, 98, 102], Operations: ['17*6=102'] Exploring Operation: 102-98=4, Resulting Numbers: [89, 4] Generated Node #0,1,0: 93:[89, 4] Operation: 102-98=4 Moving to Node #0,1,0 Current State: 93:[89, 4], Operations: ['17*6=102', '102-98=4'] Exploring Operation: 89+4=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 47, 93, 29, 62 ]
12
[ "47-29=18", "62*18=1116", "1116/93=12" ]
Current State: 12:[47, 93, 29, 62], Operations: [] Exploring Operation: 47-29=18, Resulting Numbers: [93, 62, 18] Generated Node #2: [93, 62, 18] from Operation: 47-29=18 Current State: 12:[93, 62, 18], Operations: ['47-29=18'] Exploring Operation: 62*18=1116, Resulting Numbers: [93, 1116] Generated Node #3: [93, 1116] from Operation: 62*18=1116 Current State: 12:[93, 1116], Operations: ['47-29=18', '62*18=1116'] Exploring Operation: 1116/93=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[47, 93, 29, 62], Operations: [] Exploring Operation: 93-47=46, Resulting Numbers: [29, 62, 46] Generated Node #0,0: 12:[29, 62, 46] Operation: 93-47=46 Exploring Operation: 62-47=15, Resulting Numbers: [93, 29, 15] Generated Node #0,1: 12:[93, 29, 15] Operation: 62-47=15 Exploring Operation: 93-62=31, Resulting Numbers: [47, 29, 31] Generated Node #0,2: 12:[47, 29, 31] Operation: 93-62=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[47, 29, 31], Operations: ['93-62=31'] Exploring Operation: 47-29=18, Resulting Numbers: [31, 18] Generated Node #0,2,0: 12:[31, 18] Operation: 47-29=18 Exploring Operation: 31-29=2, Resulting Numbers: [47, 2] Generated Node #0,2,1: 12:[47, 2] Operation: 31-29=2 Exploring Operation: 47-31=16, Resulting Numbers: [29, 16] Generated Node #0,2,2: 12:[29, 16] Operation: 47-31=16 Moving to Node #0,2,2 Current State: 12:[29, 16], Operations: ['93-62=31', '47-31=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,12 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[31, 18], Operations: ['93-62=31', '47-29=18'] Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,12 unequal: No Solution Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,12 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[47, 2], Operations: ['93-62=31', '31-29=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,12 unequal: No Solution Exploring Operation: 47+2=49, Resulting Numbers: [49] 49,12 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,12 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 Current State: 12:[29, 62, 46], Operations: ['93-47=46'] Exploring Operation: 62-46=16, Resulting Numbers: [29, 16] Generated Node #0,0,0: 12:[29, 16] Operation: 62-46=16 Exploring Operation: 62-29=33, Resulting Numbers: [46, 33] Generated Node #0,0,1: 12:[46, 33] Operation: 62-29=33 Exploring Operation: 46-29=17, Resulting Numbers: [62, 17] Generated Node #0,0,2: 12:[62, 17] Operation: 46-29=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[29, 16], Operations: ['93-47=46', '62-46=16'] Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,12 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,12 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,12 unequal: No Solution No 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: 12:[46, 33], Operations: ['93-47=46', '62-29=33'] Exploring Operation: 46*33=1518, Resulting Numbers: [1518] 1518,12 unequal: No Solution Exploring Operation: 46-33=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 46+33=79, Resulting Numbers: [79] 79,12 unequal: No Solution No 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: 12:[62, 17], Operations: ['93-47=46', '46-29=17'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,12 unequal: No Solution Exploring Operation: 62+17=79, Resulting Numbers: [79] 79,12 unequal: No Solution Exploring Operation: 62*17=1054, Resulting Numbers: [1054] 1054,12 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: 12:[93, 29, 15], Operations: ['62-47=15'] Exploring Operation: 29-15=14, Resulting Numbers: [93, 14] Generated Node #0,1,0: 12:[93, 14] Operation: 29-15=14 Exploring Operation: 93-29=64, Resulting Numbers: [15, 64] Generated Node #0,1,1: 12:[15, 64] Operation: 93-29=64 Exploring Operation: 93-15=78, Resulting Numbers: [29, 78] Generated Node #0,1,2: 12:[29, 78] Operation: 93-15=78 Moving to Node #0,1,1 Current State: 12:[15, 64], Operations: ['62-47=15', '93-29=64'] Exploring Operation: 15+64=79, Resulting Numbers: [79] 79,12 unequal: No Solution Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,12 unequal: No Solution Exploring Operation: 15*64=960, Resulting Numbers: [960] 960,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[93, 14], Operations: ['62-47=15', '29-15=14'] Exploring Operation: 93-14=79, Resulting Numbers: [79] 79,12 unequal: No Solution Exploring Operation: 93+14=107, Resulting Numbers: [107] 107,12 unequal: No Solution Exploring Operation: 93*14=1302, Resulting Numbers: [1302] 1302,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[29, 78], Operations: ['62-47=15', '93-15=78'] Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,12 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,12 unequal: No Solution Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,12 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
[ 27, 33, 30, 68 ]
38
[ "27+33=60", "30+68=98", "98-60=38" ]
Current State: 38:[27, 33, 30, 68], Operations: [] Exploring Operation: 27+33=60, Resulting Numbers: [30, 68, 60] Generated Node #2: [30, 68, 60] from Operation: 27+33=60 Current State: 38:[30, 68, 60], Operations: ['27+33=60'] Exploring Operation: 30+68=98, Resulting Numbers: [60, 98] Generated Node #3: [60, 98] from Operation: 30+68=98 Current State: 38:[60, 98], Operations: ['27+33=60', '30+68=98'] Exploring Operation: 98-60=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[27, 33, 30, 68], Operations: [] Exploring Operation: 68-30=38, Resulting Numbers: [27, 33, 38] Generated Node #0,0: 38:[27, 33, 38] Operation: 68-30=38 Exploring Operation: 68-27=41, Resulting Numbers: [33, 30, 41] Generated Node #0,1: 38:[33, 30, 41] Operation: 68-27=41 Exploring Operation: 30-27=3, Resulting Numbers: [33, 68, 3] Generated Node #0,2: 38:[33, 68, 3] Operation: 30-27=3 Exploring Operation: 68-33=35, Resulting Numbers: [27, 30, 35] Generated Node #0,3: 38:[27, 30, 35] Operation: 68-33=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[27, 33, 38], Operations: ['68-30=38'] Exploring Operation: 38-33=5, Resulting Numbers: [27, 5] Generated Node #0,0,0: 38:[27, 5] Operation: 38-33=5 Exploring Operation: 38-27=11, Resulting Numbers: [33, 11] Generated Node #0,0,1: 38:[33, 11] Operation: 38-27=11 Exploring Operation: 33-27=6, Resulting Numbers: [38, 6] Generated Node #0,0,2: 38:[38, 6] Operation: 33-27=6 Exploring Operation: 27+33=60, Resulting Numbers: [38, 60] Generated Node #0,0,3: 38:[38, 60] Operation: 27+33=60 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[38, 6], Operations: ['68-30=38', '33-27=6'] Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,38 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,38 unequal: No Solution No 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: 38:[27, 5], Operations: ['68-30=38', '38-33=5'] Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,38 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,38 unequal: No Solution No 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: 38:[33, 11], Operations: ['68-30=38', '38-27=11'] Exploring Operation: 33*11=363, Resulting Numbers: [363] 363,38 unequal: No Solution Exploring Operation: 33+11=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 33/11=3, Resulting Numbers: [3] 3,38 unequal: No Solution No 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: 38:[38, 60], Operations: ['68-30=38', '27+33=60'] Exploring Operation: 38*60=2280, Resulting Numbers: [2280] 2280,38 unequal: No Solution Exploring Operation: 38+60=98, Resulting Numbers: [98] 98,38 unequal: No Solution Exploring Operation: 60-38=22, Resulting Numbers: [22] 22,38 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: 38:[33, 30, 41], Operations: ['68-27=41'] Exploring Operation: 41-30=11, Resulting Numbers: [33, 11] Generated Node #0,1,0: 38:[33, 11] Operation: 41-30=11 Exploring Operation: 33+30=63, Resulting Numbers: [41, 63] Generated Node #0,1,1: 38:[41, 63] Operation: 33+30=63 Exploring Operation: 41-33=8, Resulting Numbers: [30, 8] Generated Node #0,1,2: 38:[30, 8] Operation: 41-33=8 Exploring Operation: 33-30=3, Resulting Numbers: [41, 3] Generated Node #0,1,3: 38:[41, 3] Operation: 33-30=3 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 38:[41, 3], Operations: ['68-27=41', '33-30=3'] Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,38 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[27, 33, 30, 68], Operations: [] Exploring Operation: 68-27=41, Resulting Numbers: [33, 30, 41] Generated Node #0,1: 38:[33, 30, 41] Operation: 68-27=41 Moving to Node #0,1 Current State: 38:[33, 30, 41], Operations: ['68-27=41'] Exploring Operation: 33-30=3, Resulting Numbers: [41, 3] Generated Node #0,1,3: 38:[41, 3] Operation: 33-30=3 Moving to Node #0,1,3 Current State: 38:[41, 3], Operations: ['68-27=41', '33-30=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 50, 84, 80, 16 ]
62
[ "84-50=34", "80+16=96", "96-34=62" ]
Current State: 62:[50, 84, 80, 16], Operations: [] Exploring Operation: 84-50=34, Resulting Numbers: [80, 16, 34] Generated Node #2: [80, 16, 34] from Operation: 84-50=34 Current State: 62:[80, 16, 34], Operations: ['84-50=34'] Exploring Operation: 80+16=96, Resulting Numbers: [34, 96] Generated Node #3: [34, 96] from Operation: 80+16=96 Current State: 62:[34, 96], Operations: ['84-50=34', '80+16=96'] Exploring Operation: 96-34=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[50, 84, 80, 16], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [50, 16, 4] Generated Node #0,0: 62:[50, 16, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[50, 16, 4], Operations: ['84-80=4'] Exploring Operation: 50-16=34, Resulting Numbers: [4, 34] Generated Node #0,0,0: 62:[4, 34] Operation: 50-16=34 Moving to Node #0,0,0 Current State: 62:[4, 34], Operations: ['84-80=4', '50-16=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,62 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
[ 96, 22, 97, 50 ]
28
[ "97-96=1", "50-22=28", "1*28=28" ]
Current State: 28:[96, 22, 97, 50], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [22, 50, 1] Generated Node #2: [22, 50, 1] from Operation: 97-96=1 Current State: 28:[22, 50, 1], Operations: ['97-96=1'] Exploring Operation: 50-22=28, Resulting Numbers: [1, 28] Generated Node #3: [1, 28] from Operation: 50-22=28 Current State: 28:[1, 28], Operations: ['97-96=1', '50-22=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[96, 22, 97, 50], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [22, 50, 1] Generated Node #0,0: 28:[22, 50, 1] Operation: 97-96=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[22, 50, 1], Operations: ['97-96=1'] Exploring Operation: 50-22=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 50-22=28 Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['97-96=1', '50-22=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[96, 22, 97, 50], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [22, 50, 1] Generated Node #0,0: 28:[22, 50, 1] Operation: 97-96=1 Moving to Node #0,0 Current State: 28:[22, 50, 1], Operations: ['97-96=1'] Exploring Operation: 50-22=28, Resulting Numbers: [1, 28] Generated Node #0,0,0: 28:[1, 28] Operation: 50-22=28 Moving to Node #0,0,0 Current State: 28:[1, 28], Operations: ['97-96=1', '50-22=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 70, 73, 78, 9 ]
17
[ "73-70=3", "78/3=26", "26-9=17" ]
Current State: 17:[70, 73, 78, 9], Operations: [] Exploring Operation: 73-70=3, Resulting Numbers: [78, 9, 3] Generated Node #2: [78, 9, 3] from Operation: 73-70=3 Current State: 17:[78, 9, 3], Operations: ['73-70=3'] Exploring Operation: 78/3=26, Resulting Numbers: [9, 26] Generated Node #3: [9, 26] from Operation: 78/3=26 Current State: 17:[9, 26], Operations: ['73-70=3', '78/3=26'] Exploring Operation: 26-9=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[70, 73, 78, 9], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [73, 9, 8] Generated Node #0,0: 17:[73, 9, 8] Operation: 78-70=8 Moving to Node #0,0 Current State: 17:[73, 9, 8], Operations: ['78-70=8'] Exploring Operation: 73-9=64, Resulting Numbers: [8, 64] Generated Node #0,0,0: 17:[8, 64] Operation: 73-9=64 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[8, 64], Operations: ['78-70=8', '73-9=64'] Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 72, 34, 6, 2 ]
61
[ "72+6=78", "34/2=17", "78-17=61" ]
Current State: 61:[72, 34, 6, 2], Operations: [] Exploring Operation: 72+6=78, Resulting Numbers: [34, 2, 78] Generated Node #2: [34, 2, 78] from Operation: 72+6=78 Current State: 61:[34, 2, 78], Operations: ['72+6=78'] Exploring Operation: 34/2=17, Resulting Numbers: [78, 17] Generated Node #3: [78, 17] from Operation: 34/2=17 Current State: 61:[78, 17], Operations: ['72+6=78', '34/2=17'] Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[72, 34, 6, 2], Operations: [] Exploring Operation: 34*2=68, Resulting Numbers: [72, 6, 68] Generated Node #0,0: 61:[72, 6, 68] Operation: 34*2=68 Exploring Operation: 72-6=66, Resulting Numbers: [34, 2, 66] Generated Node #0,1: 61:[34, 2, 66] Operation: 72-6=66 Exploring Operation: 6*2=12, Resulting Numbers: [72, 34, 12] Generated Node #0,2: 61:[72, 34, 12] Operation: 6*2=12 Moving to Node #0,0 Current State: 61:[72, 6, 68], Operations: ['34*2=68'] Exploring Operation: 72+6=78, Resulting Numbers: [68, 78] Generated Node #0,0,0: 61:[68, 78] Operation: 72+6=78 Exploring Operation: 68-6=62, Resulting Numbers: [72, 62] Generated Node #0,0,1: 61:[72, 62] Operation: 68-6=62 Exploring Operation: 72-6=66, Resulting Numbers: [68, 66] Generated Node #0,0,2: 61:[68, 66] Operation: 72-6=66 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[72, 62], Operations: ['34*2=68', '68-6=62'] Exploring Operation: 72*62=4464, Resulting Numbers: [4464] 4464,61 unequal: No Solution Exploring Operation: 72+62=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 72-62=10, Resulting Numbers: [10] 10,61 unequal: No Solution No 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: 61:[68, 66], Operations: ['34*2=68', '72-6=66'] Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 68+66=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 68*66=4488, Resulting Numbers: [4488] 4488,61 unequal: No Solution No 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: 61:[68, 78], Operations: ['34*2=68', '72+6=78'] Exploring Operation: 78-68=10, Resulting Numbers: [10] 10,61 unequal: No Solution Exploring Operation: 68+78=146, Resulting Numbers: [146] 146,61 unequal: No Solution Exploring Operation: 68*78=5304, Resulting Numbers: [5304] 5304,61 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: 61:[72, 34, 12], Operations: ['6*2=12'] Exploring Operation: 72+12=84, Resulting Numbers: [34, 84] Generated Node #0,2,0: 61:[34, 84] Operation: 72+12=84 Exploring Operation: 34+12=46, Resulting Numbers: [72, 46] Generated Node #0,2,1: 61:[72, 46] Operation: 34+12=46 Exploring Operation: 72-12=60, Resulting Numbers: [34, 60] Generated Node #0,2,2: 61:[34, 60] Operation: 72-12=60 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 61:[72, 46], Operations: ['6*2=12', '34+12=46'] Exploring Operation: 72-46=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 72*46=3312, Resulting Numbers: [3312] 3312,61 unequal: No Solution Exploring Operation: 72+46=118, Resulting Numbers: [118] 118,61 unequal: No Solution No 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: 61:[34, 60], Operations: ['6*2=12', '72-12=60'] Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,61 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,61 unequal: No Solution No 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: 61:[34, 84], Operations: ['6*2=12', '72+12=84'] Exploring Operation: 34*84=2856, Resulting Numbers: [2856] 2856,61 unequal: No Solution Exploring Operation: 84-34=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 34+84=118, Resulting Numbers: [118] 118,61 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: 61:[34, 2, 66], Operations: ['72-6=66'] Exploring Operation: 66-2=64, Resulting Numbers: [34, 64] Generated Node #0,1,0: 61:[34, 64] Operation: 66-2=64 Exploring Operation: 34+2=36, Resulting Numbers: [66, 36] Generated Node #0,1,1: 61:[66, 36] Operation: 34+2=36 Exploring Operation: 34*2=68, Resulting Numbers: [66, 68] Generated Node #0,1,2: 61:[66, 68] Operation: 34*2=68 Moving to Node #0,1,2 Current State: 61:[66, 68], Operations: ['72-6=66', '34*2=68'] Exploring Operation: 66+68=134, Resulting Numbers: [134] 134,61 unequal: No Solution Exploring Operation: 68-66=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 66*68=4488, Resulting Numbers: [4488] 4488,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[34, 64], Operations: ['72-6=66', '66-2=64'] Exploring Operation: 34+64=98, Resulting Numbers: [98] 98,61 unequal: No Solution Exploring Operation: 34*64=2176, Resulting Numbers: [2176] 2176,61 unequal: No Solution Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[66, 36], Operations: ['72-6=66', '34+2=36'] Exploring Operation: 66*36=2376, Resulting Numbers: [2376] 2376,61 unequal: No Solution Exploring Operation: 66+36=102, Resulting Numbers: [102] 102,61 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,61 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 2, 58, 97, 79 ]
30
[ "97+79=176", "176/2=88", "88-58=30" ]
Current State: 30:[2, 58, 97, 79], Operations: [] Exploring Operation: 97+79=176, Resulting Numbers: [2, 58, 176] Generated Node #2: [2, 58, 176] from Operation: 97+79=176 Current State: 30:[2, 58, 176], Operations: ['97+79=176'] Exploring Operation: 176/2=88, Resulting Numbers: [58, 88] Generated Node #3: [58, 88] from Operation: 176/2=88 Current State: 30:[58, 88], Operations: ['97+79=176', '176/2=88'] Exploring Operation: 88-58=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[2, 58, 97, 79], Operations: [] Exploring Operation: 79-58=21, Resulting Numbers: [2, 97, 21] Generated Node #0,0: 30:[2, 97, 21] Operation: 79-58=21 Exploring Operation: 97-58=39, Resulting Numbers: [2, 79, 39] Generated Node #0,1: 30:[2, 79, 39] Operation: 97-58=39 Exploring Operation: 97-79=18, Resulting Numbers: [2, 58, 18] Generated Node #0,2: 30:[2, 58, 18] Operation: 97-79=18 Moving to Node #0,2 Current State: 30:[2, 58, 18], Operations: ['97-79=18'] Exploring Operation: 58-18=40, Resulting Numbers: [2, 40] Generated Node #0,2,0: 30:[2, 40] Operation: 58-18=40 Exploring Operation: 58-2=56, Resulting Numbers: [18, 56] Generated Node #0,2,1: 30:[18, 56] Operation: 58-2=56 Exploring Operation: 58/2=29, Resulting Numbers: [18, 29] Generated Node #0,2,2: 30:[18, 29] Operation: 58/2=29 Moving to Node #0,1 Current State: 30:[2, 79, 39], Operations: ['97-58=39'] Exploring Operation: 79-2=77, Resulting Numbers: [39, 77] Generated Node #0,1,0: 30:[39, 77] Operation: 79-2=77 Exploring Operation: 79-39=40, Resulting Numbers: [2, 40] Generated Node #0,1,1: 30:[2, 40] Operation: 79-39=40 Exploring Operation: 39-2=37, Resulting Numbers: [79, 37] Generated Node #0,1,2: 30:[79, 37] Operation: 39-2=37 Moving to Node #0,0 Current State: 30:[2, 97, 21], Operations: ['79-58=21'] Exploring Operation: 21-2=19, Resulting Numbers: [97, 19] Generated Node #0,0,0: 30:[97, 19] Operation: 21-2=19 Exploring Operation: 97-2=95, Resulting Numbers: [21, 95] Generated Node #0,0,1: 30:[21, 95] Operation: 97-2=95 Exploring Operation: 97-21=76, Resulting Numbers: [2, 76] Generated Node #0,0,2: 30:[2, 76] Operation: 97-21=76 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[2, 76], Operations: ['79-58=21', '97-21=76'] Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,30 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[97, 19], Operations: ['79-58=21', '21-2=19'] Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,30 unequal: No Solution Exploring Operation: 97+19=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 97*19=1843, Resulting Numbers: [1843] 1843,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[21, 95], Operations: ['79-58=21', '97-2=95'] Exploring Operation: 21*95=1995, Resulting Numbers: [1995] 1995,30 unequal: No Solution Exploring Operation: 21+95=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 95-21=74, Resulting Numbers: [74] 74,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 30:[18, 29], Operations: ['97-79=18', '58/2=29'] Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,30 unequal: No Solution Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[2, 40], Operations: ['97-79=18', '58-18=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[2, 40], Operations: ['97-58=39', '79-39=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[18, 56], Operations: ['97-79=18', '58-2=56'] Exploring Operation: 18*56=1008, Resulting Numbers: [1008] 1008,30 unequal: No Solution Exploring Operation: 18+56=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[79, 37], Operations: ['97-58=39', '39-2=37'] Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,30 unequal: No Solution Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,30 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[39, 77], Operations: ['97-58=39', '79-2=77'] Exploring Operation: 39*77=3003, Resulting Numbers: [3003] 3003,30 unequal: No Solution Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 39+77=116, Resulting Numbers: [116] 116,30 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 15, 71, 22, 63 ]
62
[ "22-15=7", "63/7=9", "71-9=62" ]
Current State: 62:[15, 71, 22, 63], Operations: [] Exploring Operation: 22-15=7, Resulting Numbers: [71, 63, 7] Generated Node #2: [71, 63, 7] from Operation: 22-15=7 Current State: 62:[71, 63, 7], Operations: ['22-15=7'] Exploring Operation: 63/7=9, Resulting Numbers: [71, 9] Generated Node #3: [71, 9] from Operation: 63/7=9 Current State: 62:[71, 9], Operations: ['22-15=7', '63/7=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[15, 71, 22, 63], Operations: [] Exploring Operation: 15+22=37, Resulting Numbers: [71, 63, 37] Generated Node #0,0: 62:[71, 63, 37] Operation: 15+22=37 Exploring Operation: 71-15=56, Resulting Numbers: [22, 63, 56] Generated Node #0,1: 62:[22, 63, 56] Operation: 71-15=56 Exploring Operation: 71-22=49, Resulting Numbers: [15, 63, 49] Generated Node #0,2: 62:[15, 63, 49] Operation: 71-22=49 Exploring Operation: 22-15=7, Resulting Numbers: [71, 63, 7] Generated Node #0,3: 62:[71, 63, 7] Operation: 22-15=7 Moving to Node #0,3 Current State: 62:[71, 63, 7], Operations: ['22-15=7'] Exploring Operation: 63-7=56, Resulting Numbers: [71, 56] Generated Node #0,3,0: 62:[71, 56] Operation: 63-7=56 Exploring Operation: 71-63=8, Resulting Numbers: [7, 8] Generated Node #0,3,1: 62:[7, 8] Operation: 71-63=8 Exploring Operation: 71-7=64, Resulting Numbers: [63, 64] Generated Node #0,3,2: 62:[63, 64] Operation: 71-7=64 Exploring Operation: 63/7=9, Resulting Numbers: [71, 9] Generated Node #0,3,3: 62:[71, 9] Operation: 63/7=9 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[63, 64], Operations: ['22-15=7', '71-7=64'] Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 62:[7, 8], Operations: ['22-15=7', '71-63=8'] Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[71, 56], Operations: ['22-15=7', '63-7=56'] Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,62 unequal: No Solution Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 62:[71, 9], Operations: ['22-15=7', '63/7=9'] Exploring Operation: 71+9=80, Resulting Numbers: [80] 80,62 unequal: No Solution Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[15, 71, 22, 63], Operations: [] Exploring Operation: 22-15=7, Resulting Numbers: [71, 63, 7] Generated Node #0,3: 62:[71, 63, 7] Operation: 22-15=7 Moving to Node #0,3 Current State: 62:[71, 63, 7], Operations: ['22-15=7'] Exploring Operation: 63/7=9, Resulting Numbers: [71, 9] Generated Node #0,3,3: 62:[71, 9] Operation: 63/7=9 Moving to Node #0,3,3 Current State: 62:[71, 9], Operations: ['22-15=7', '63/7=9'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 3, 32, 2, 76 ]
10
[ "3*32=96", "96-76=20", "20/2=10" ]
Current State: 10:[3, 32, 2, 76], Operations: [] Exploring Operation: 3*32=96, Resulting Numbers: [2, 76, 96] Generated Node #2: [2, 76, 96] from Operation: 3*32=96 Current State: 10:[2, 76, 96], Operations: ['3*32=96'] Exploring Operation: 96-76=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 96-76=20 Current State: 10:[2, 20], Operations: ['3*32=96', '96-76=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[3, 32, 2, 76], Operations: [] Exploring Operation: 76/2=38, Resulting Numbers: [3, 32, 38] Generated Node #0,0: 10:[3, 32, 38] Operation: 76/2=38 Exploring Operation: 76-32=44, Resulting Numbers: [3, 2, 44] Generated Node #0,1: 10:[3, 2, 44] Operation: 76-32=44 Exploring Operation: 32/2=16, Resulting Numbers: [3, 76, 16] Generated Node #0,2: 10:[3, 76, 16] Operation: 32/2=16 Exploring Operation: 32-3=29, Resulting Numbers: [2, 76, 29] Generated Node #0,3: 10:[2, 76, 29] Operation: 32-3=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[3, 2, 44], Operations: ['76-32=44'] Exploring Operation: 3+2=5, Resulting Numbers: [44, 5] Generated Node #0,1,0: 10:[44, 5] Operation: 3+2=5 Exploring Operation: 44-3=41, Resulting Numbers: [2, 41] Generated Node #0,1,1: 10:[2, 41] Operation: 44-3=41 Exploring Operation: 44/2=22, Resulting Numbers: [3, 22] Generated Node #0,1,2: 10:[3, 22] Operation: 44/2=22 Exploring Operation: 44-2=42, Resulting Numbers: [3, 42] Generated Node #0,1,3: 10:[3, 42] Operation: 44-2=42 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 10:[3, 22], Operations: ['76-32=44', '44/2=22'] Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,10 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,10 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,10 unequal: No Solution No 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: 10:[2, 41], Operations: ['76-32=44', '44-3=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,10 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,10 unequal: No Solution No 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: 10:[3, 42], Operations: ['76-32=44', '44-2=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,10 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,10 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,10 unequal: No Solution No 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: 10:[44, 5], Operations: ['76-32=44', '3+2=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 44*5=220, Resulting Numbers: [220] 220,10 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: 10:[3, 32, 38], Operations: ['76/2=38'] Exploring Operation: 32-3=29, Resulting Numbers: [38, 29] Generated Node #0,0,0: 10:[38, 29] Operation: 32-3=29 Exploring Operation: 38-3=35, Resulting Numbers: [32, 35] Generated Node #0,0,1: 10:[32, 35] Operation: 38-3=35 Exploring Operation: 3+32=35, Resulting Numbers: [38, 35] Generated Node #0,0,2: 10:[38, 35] Operation: 3+32=35 Exploring Operation: 38-32=6, Resulting Numbers: [3, 6] Generated Node #0,0,3: 10:[3, 6] Operation: 38-32=6 Moving to Node #0,0,3 Current State: 10:[3, 6], Operations: ['76/2=38', '38-32=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[32, 35], Operations: ['76/2=38', '38-3=35'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 32*35=1120, Resulting Numbers: [1120] 1120,10 unequal: No Solution Exploring Operation: 32+35=67, Resulting Numbers: [67] 67,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[38, 29], Operations: ['76/2=38', '32-3=29'] Exploring Operation: 38*29=1102, Resulting Numbers: [1102] 1102,10 unequal: No Solution Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,10 unequal: No Solution Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[38, 35], Operations: ['76/2=38', '3+32=35'] Exploring Operation: 38+35=73, Resulting Numbers: [73] 73,10 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 38*35=1330, Resulting Numbers: [1330] 1330,10 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 #0,2 Current State: 10:[3, 76, 16], Operations: ['32/2=16'] Exploring Operation: 76-16=60, Resulting Numbers: [3, 60] Generated Node #0,2,0: 10:[3, 60] Operation: 76-16=60 Exploring Operation: 16-3=13, Resulting Numbers: [76, 13] Generated Node #0,2,1: 10:[76, 13] Operation: 16-3=13 Exploring Operation: 76-3=73, Resulting Numbers: [16, 73] Generated Node #0,2,2: 10:[16, 73] Operation: 76-3=73 Exploring Operation: 3+76=79, Resulting Numbers: [16, 79] Generated Node #0,2,3: 10:[16, 79] Operation: 3+76=79 Moving to Node #0,2,0 Current State: 10:[3, 60], Operations: ['32/2=16', '76-16=60'] Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,10 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[16, 73], Operations: ['32/2=16', '76-3=73'] Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 16*73=1168, Resulting Numbers: [1168] 1168,10 unequal: No Solution Exploring Operation: 16+73=89, Resulting Numbers: [89] 89,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[76, 13], Operations: ['32/2=16', '16-3=13'] Exploring Operation: 76-13=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 76+13=89, Resulting Numbers: [89] 89,10 unequal: No Solution Exploring Operation: 76*13=988, Resulting Numbers: [988] 988,10 unequal: No Solution Moving to Node #0,2,3 Current State: 10:[16, 79], Operations: ['32/2=16', '3+76=79'] Exploring Operation: 16*79=1264, Resulting Numbers: [1264] 1264,10 unequal: No Solution Exploring Operation: 16+79=95, Resulting Numbers: [95] 95,10 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,10 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 #0,3 Current State: 10:[2, 76, 29], Operations: ['32-3=29'] Exploring Operation: 29-2=27, Resulting Numbers: [76, 27] Generated Node #0,3,0: 10:[76, 27] Operation: 29-2=27 Exploring Operation: 76-29=47, Resulting Numbers: [2, 47] Generated Node #0,3,1: 10:[2, 47] Operation: 76-29=47 Exploring Operation: 76-2=74, Resulting Numbers: [29, 74] Generated Node #0,3,2: 10:[29, 74] Operation: 76-2=74 Exploring Operation: 76/2=38, Resulting Numbers: [29, 38] Generated Node #0,3,3: 10:[29, 38] Operation: 76/2=38 Moving to Node #0,3,1 Current State: 10:[2, 47], Operations: ['32-3=29', '76-29=47'] Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,10 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,10 unequal: No Solution Moving to Node #0,3,3 Current State: 10:[29, 38], Operations: ['32-3=29', '76/2=38'] Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 29+38=67, Resulting Numbers: [67] 67,10 unequal: No Solution Exploring Operation: 29*38=1102, Resulting Numbers: [1102] 1102,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[29, 74], Operations: ['32-3=29', '76-2=74'] Exploring Operation: 29*74=2146, Resulting Numbers: [2146] 2146,10 unequal: No Solution Exploring Operation: 29+74=103, Resulting Numbers: [103] 103,10 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,10 unequal: No Solution Moving to Node #0,3,0 Current State: 10:[76, 27], Operations: ['32-3=29', '29-2=27'] Exploring Operation: 76+27=103, Resulting Numbers: [103] 103,10 unequal: No Solution Exploring Operation: 76*27=2052, Resulting Numbers: [2052] 2052,10 unequal: No Solution Exploring Operation: 76-27=49, Resulting Numbers: [49] 49,10 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
[ 16, 70, 21, 57 ]
90
[ "70-16=54", "57-21=36", "54+36=90" ]
Current State: 90:[16, 70, 21, 57], Operations: [] Exploring Operation: 70-16=54, Resulting Numbers: [21, 57, 54] Generated Node #2: [21, 57, 54] from Operation: 70-16=54 Current State: 90:[21, 57, 54], Operations: ['70-16=54'] Exploring Operation: 57-21=36, Resulting Numbers: [54, 36] Generated Node #3: [54, 36] from Operation: 57-21=36 Current State: 90:[54, 36], Operations: ['70-16=54', '57-21=36'] Exploring Operation: 54+36=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[16, 70, 21, 57], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [16, 57, 49] Generated Node #0,0: 90:[16, 57, 49] Operation: 70-21=49 Exploring Operation: 16+70=86, Resulting Numbers: [21, 57, 86] Generated Node #0,1: 90:[21, 57, 86] Operation: 16+70=86 Exploring Operation: 70+21=91, Resulting Numbers: [16, 57, 91] Generated Node #0,2: 90:[16, 57, 91] Operation: 70+21=91 Exploring Operation: 70-57=13, Resulting Numbers: [16, 21, 13] Generated Node #0,3: 90:[16, 21, 13] Operation: 70-57=13 Moving to Node #0,3 Current State: 90:[16, 21, 13], Operations: ['70-57=13'] Exploring Operation: 21-13=8, Resulting Numbers: [16, 8] Generated Node #0,3,0: 90:[16, 8] Operation: 21-13=8 Exploring Operation: 21-16=5, Resulting Numbers: [13, 5] Generated Node #0,3,1: 90:[13, 5] Operation: 21-16=5 Exploring Operation: 16-13=3, Resulting Numbers: [21, 3] Generated Node #0,3,2: 90:[21, 3] Operation: 16-13=3 Exploring Operation: 16+13=29, Resulting Numbers: [21, 29] Generated Node #0,3,3: 90:[21, 29] Operation: 16+13=29 Moving to Node #0,2 Current State: 90:[16, 57, 91], Operations: ['70+21=91'] Exploring Operation: 16+57=73, Resulting Numbers: [91, 73] Generated Node #0,2,0: 90:[91, 73] Operation: 16+57=73 Exploring Operation: 57-16=41, Resulting Numbers: [91, 41] Generated Node #0,2,1: 90:[91, 41] Operation: 57-16=41 Exploring Operation: 91-57=34, Resulting Numbers: [16, 34] Generated Node #0,2,2: 90:[16, 34] Operation: 91-57=34 Exploring Operation: 91-16=75, Resulting Numbers: [57, 75] Generated Node #0,2,3: 90:[57, 75] Operation: 91-16=75 Moving to Node #0,0 Current State: 90:[16, 57, 49], Operations: ['70-21=49'] Exploring Operation: 49-16=33, Resulting Numbers: [57, 33] Generated Node #0,0,0: 90:[57, 33] Operation: 49-16=33 Exploring Operation: 57+49=106, Resulting Numbers: [16, 106] Generated Node #0,0,1: 90:[16, 106] Operation: 57+49=106 Exploring Operation: 57-16=41, Resulting Numbers: [49, 41] Generated Node #0,0,2: 90:[49, 41] Operation: 57-16=41 Exploring Operation: 57-49=8, Resulting Numbers: [16, 8] Generated Node #0,0,3: 90:[16, 8] Operation: 57-49=8 Moving to Node #0,1 Current State: 90:[21, 57, 86], Operations: ['16+70=86'] Exploring Operation: 21+57=78, Resulting Numbers: [86, 78] Generated Node #0,1,0: 90:[86, 78] Operation: 21+57=78 Exploring Operation: 86-57=29, Resulting Numbers: [21, 29] Generated Node #0,1,1: 90:[21, 29] Operation: 86-57=29 Exploring Operation: 21+86=107, Resulting Numbers: [57, 107] Generated Node #0,1,2: 90:[57, 107] Operation: 21+86=107 Exploring Operation: 57-21=36, Resulting Numbers: [86, 36] Generated Node #0,1,3: 90:[86, 36] Operation: 57-21=36 Moving to Node #0,3,0 Current State: 90:[16, 8], Operations: ['70-57=13', '21-13=8'] Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,90 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[13, 5], Operations: ['70-57=13', '21-16=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[16, 8], Operations: ['70-21=49', '57-49=8'] Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,90 unequal: No Solution Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[21, 3], Operations: ['70-57=13', '16-13=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[21, 29], Operations: ['16+70=86', '86-57=29'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[21, 29], Operations: ['70-57=13', '16+13=29'] Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 21+29=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 21*29=609, Resulting Numbers: [609] 609,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[16, 34], Operations: ['70+21=91', '91-57=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,90 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[91, 41], Operations: ['70+21=91', '57-16=41'] Exploring Operation: 91*41=3731, Resulting Numbers: [3731] 3731,90 unequal: No Solution Exploring Operation: 91+41=132, Resulting Numbers: [132] 132,90 unequal: No Solution Exploring Operation: 91-41=50, Resulting Numbers: [50] 50,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[49, 41], Operations: ['70-21=49', '57-16=41'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,90 unequal: No Solution Exploring Operation: 49*41=2009, Resulting Numbers: [2009] 2009,90 unequal: No Solution Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[16, 70, 21, 57], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [16, 57, 49] Generated Node #0,0: 90:[16, 57, 49] Operation: 70-21=49 Moving to Node #0,0 Current State: 90:[16, 57, 49], Operations: ['70-21=49'] Exploring Operation: 57-16=41, Resulting Numbers: [49, 41] Generated Node #0,0,2: 90:[49, 41] Operation: 57-16=41 Moving to Node #0,0,2 Current State: 90:[49, 41], Operations: ['70-21=49', '57-16=41'] Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
0.953125
hs_4
mult_heuristic
[ 86, 43, 77, 12 ]
63
[ "86/43=2", "77-12=65", "65-2=63" ]
Current State: 63:[86, 43, 77, 12], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [77, 12, 2] Generated Node #2: [77, 12, 2] from Operation: 86/43=2 Current State: 63:[77, 12, 2], Operations: ['86/43=2'] Exploring Operation: 77-12=65, Resulting Numbers: [2, 65] Generated Node #3: [2, 65] from Operation: 77-12=65 Current State: 63:[2, 65], Operations: ['86/43=2', '77-12=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[86, 43, 77, 12], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [77, 12, 2] Generated Node #0,0: 63:[77, 12, 2] Operation: 86/43=2 Exploring Operation: 86-77=9, Resulting Numbers: [43, 12, 9] Generated Node #0,1: 63:[43, 12, 9] Operation: 86-77=9 Exploring Operation: 86-43=43, Resulting Numbers: [77, 12, 43] Generated Node #0,2: 63:[77, 12, 43] Operation: 86-43=43 Exploring Operation: 77-43=34, Resulting Numbers: [86, 12, 34] Generated Node #0,3: 63:[86, 12, 34] Operation: 77-43=34 Moving to Node #0,0 Current State: 63:[77, 12, 2], Operations: ['86/43=2'] Exploring Operation: 77-12=65, Resulting Numbers: [2, 65] Generated Node #0,0,0: 63:[2, 65] Operation: 77-12=65 Exploring Operation: 12/2=6, Resulting Numbers: [77, 6] Generated Node #0,0,1: 63:[77, 6] Operation: 12/2=6 Exploring Operation: 12-2=10, Resulting Numbers: [77, 10] Generated Node #0,0,2: 63:[77, 10] Operation: 12-2=10 Exploring Operation: 77-2=75, Resulting Numbers: [12, 75] Generated Node #0,0,3: 63:[12, 75] Operation: 77-2=75 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[2, 65], Operations: ['86/43=2', '77-12=65'] Exploring Operation: 2*65=130, Resulting Numbers: [130] 130,63 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[86, 43, 77, 12], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [77, 12, 2] Generated Node #0,0: 63:[77, 12, 2] Operation: 86/43=2 Moving to Node #0,0 Current State: 63:[77, 12, 2], Operations: ['86/43=2'] Exploring Operation: 77-12=65, Resulting Numbers: [2, 65] Generated Node #0,0,0: 63:[2, 65] Operation: 77-12=65 Moving to Node #0,0,0 Current State: 63:[2, 65], Operations: ['86/43=2', '77-12=65'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 55, 2, 7, 20 ]
84
[ "55+2=57", "7+20=27", "57+27=84" ]
Current State: 84:[55, 2, 7, 20], Operations: [] Exploring Operation: 55+2=57, Resulting Numbers: [7, 20, 57] Generated Node #2: [7, 20, 57] from Operation: 55+2=57 Current State: 84:[7, 20, 57], Operations: ['55+2=57'] Exploring Operation: 7+20=27, Resulting Numbers: [57, 27] Generated Node #3: [57, 27] from Operation: 7+20=27 Current State: 84:[57, 27], Operations: ['55+2=57', '7+20=27'] Exploring Operation: 57+27=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[55, 2, 7, 20], Operations: [] Exploring Operation: 55-20=35, Resulting Numbers: [2, 7, 35] Generated Node #0,0: 84:[2, 7, 35] Operation: 55-20=35 Exploring Operation: 55-7=48, Resulting Numbers: [2, 20, 48] Generated Node #0,1: 84:[2, 20, 48] Operation: 55-7=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[2, 7, 35], Operations: ['55-20=35'] Exploring Operation: 35-7=28, Resulting Numbers: [2, 28] Generated Node #0,0,0: 84:[2, 28] Operation: 35-7=28 Exploring Operation: 7+35=42, Resulting Numbers: [2, 42] Generated Node #0,0,1: 84:[2, 42] Operation: 7+35=42 Moving to Node #0,0,0 Current State: 84:[2, 28], Operations: ['55-20=35', '35-7=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,84 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[2, 42], Operations: ['55-20=35', '7+35=42'] Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[55, 2, 7, 20], Operations: [] Exploring Operation: 55-20=35, Resulting Numbers: [2, 7, 35] Generated Node #0,0: 84:[2, 7, 35] Operation: 55-20=35 Moving to Node #0,0 Current State: 84:[2, 7, 35], Operations: ['55-20=35'] Exploring Operation: 7+35=42, Resulting Numbers: [2, 42] Generated Node #0,0,1: 84:[2, 42] Operation: 7+35=42 Moving to Node #0,0,1 Current State: 84:[2, 42], Operations: ['55-20=35', '7+35=42'] Exploring Operation: 2*42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 34, 19, 1, 38 ]
24
[ "34-19=15", "1+38=39", "39-15=24" ]
Current State: 24:[34, 19, 1, 38], Operations: [] Exploring Operation: 34-19=15, Resulting Numbers: [1, 38, 15] Generated Node #2: [1, 38, 15] from Operation: 34-19=15 Current State: 24:[1, 38, 15], Operations: ['34-19=15'] Exploring Operation: 1+38=39, Resulting Numbers: [15, 39] Generated Node #3: [15, 39] from Operation: 1+38=39 Current State: 24:[15, 39], Operations: ['34-19=15', '1+38=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[34, 19, 1, 38], Operations: [] Exploring Operation: 38/19=2, Resulting Numbers: [34, 1, 2] Generated Node #0,0: 24:[34, 1, 2] Operation: 38/19=2 Exploring Operation: 38-34=4, Resulting Numbers: [19, 1, 4] Generated Node #0,1: 24:[19, 1, 4] Operation: 38-34=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[19, 1, 4], Operations: ['38-34=4'] Exploring Operation: 19+1=20, Resulting Numbers: [4, 20] Generated Node #0,1,0: 24:[4, 20] Operation: 19+1=20 Exploring Operation: 19+4=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 24:[1, 23] Operation: 19+4=23 Moving to Node #0,1,1 Current State: 24:[1, 23], Operations: ['38-34=4', '19+4=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[34, 19, 1, 38], Operations: [] Exploring Operation: 38-34=4, Resulting Numbers: [19, 1, 4] Generated Node #0,1: 24:[19, 1, 4] Operation: 38-34=4 Moving to Node #0,1 Current State: 24:[19, 1, 4], Operations: ['38-34=4'] Exploring Operation: 19+4=23, Resulting Numbers: [1, 23] Generated Node #0,1,1: 24:[1, 23] Operation: 19+4=23 Moving to Node #0,1,1 Current State: 24:[1, 23], Operations: ['38-34=4', '19+4=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 8, 64, 28, 78 ]
34
[ "8+64=72", "28+78=106", "106-72=34" ]
Current State: 34:[8, 64, 28, 78], Operations: [] Exploring Operation: 8+64=72, Resulting Numbers: [28, 78, 72] Generated Node #2: [28, 78, 72] from Operation: 8+64=72 Current State: 34:[28, 78, 72], Operations: ['8+64=72'] Exploring Operation: 28+78=106, Resulting Numbers: [72, 106] Generated Node #3: [72, 106] from Operation: 28+78=106 Current State: 34:[72, 106], Operations: ['8+64=72', '28+78=106'] Exploring Operation: 106-72=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[8, 64, 28, 78], Operations: [] Exploring Operation: 78-28=50, Resulting Numbers: [8, 64, 50] Generated Node #0,0: 34:[8, 64, 50] Operation: 78-28=50 Exploring Operation: 64-8=56, Resulting Numbers: [28, 78, 56] Generated Node #0,1: 34:[28, 78, 56] Operation: 64-8=56 Exploring Operation: 64/8=8, Resulting Numbers: [28, 78, 8] Generated Node #0,2: 34:[28, 78, 8] Operation: 64/8=8 Exploring Operation: 64-28=36, Resulting Numbers: [8, 78, 36] Generated Node #0,3: 34:[8, 78, 36] Operation: 64-28=36 Exploring Operation: 78-64=14, Resulting Numbers: [8, 28, 14] Generated Node #0,4: 34:[8, 28, 14] Operation: 78-64=14 Start Sub Search at level 1: Moving to Node #0,4 Current State: 34:[8, 28, 14], Operations: ['78-64=14'] Exploring Operation: 28-14=14, Resulting Numbers: [8, 14] Generated Node #0,4,0: 34:[8, 14] Operation: 28-14=14 Exploring Operation: 28-8=20, Resulting Numbers: [14, 20] Generated Node #0,4,1: 34:[14, 20] Operation: 28-8=20 Exploring Operation: 14-8=6, Resulting Numbers: [28, 6] Generated Node #0,4,2: 34:[28, 6] Operation: 14-8=6 Exploring Operation: 8+28=36, Resulting Numbers: [14, 36] Generated Node #0,4,3: 34:[14, 36] Operation: 8+28=36 Exploring Operation: 28/14=2, Resulting Numbers: [8, 2] Generated Node #0,4,4: 34:[8, 2] Operation: 28/14=2 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 34:[14, 36], Operations: ['78-64=14', '8+28=36'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,34 unequal: No Solution Exploring Operation: 14*36=504, Resulting Numbers: [504] 504,34 unequal: No Solution Exploring Operation: 14+36=50, Resulting Numbers: [50] 50,34 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 #0,4,1 Current State: 34:[14, 20], Operations: ['78-64=14', '28-8=20'] Exploring Operation: 14*20=280, Resulting Numbers: [280] 280,34 unequal: No Solution Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[8, 64, 28, 78], Operations: [] Exploring Operation: 78-64=14, Resulting Numbers: [8, 28, 14] Generated Node #0,4: 34:[8, 28, 14] Operation: 78-64=14 Moving to Node #0,4 Current State: 34:[8, 28, 14], Operations: ['78-64=14'] Exploring Operation: 28-8=20, Resulting Numbers: [14, 20] Generated Node #0,4,1: 34:[14, 20] Operation: 28-8=20 Moving to Node #0,4,1 Current State: 34:[14, 20], Operations: ['78-64=14', '28-8=20'] Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 24, 38, 27, 2 ]
87
[ "24+38=62", "27-2=25", "62+25=87" ]
Current State: 87:[24, 38, 27, 2], Operations: [] Exploring Operation: 24+38=62, Resulting Numbers: [27, 2, 62] Generated Node #2: [27, 2, 62] from Operation: 24+38=62 Current State: 87:[27, 2, 62], Operations: ['24+38=62'] Exploring Operation: 27-2=25, Resulting Numbers: [62, 25] Generated Node #3: [62, 25] from Operation: 27-2=25 Current State: 87:[62, 25], Operations: ['24+38=62', '27-2=25'] Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[24, 38, 27, 2], Operations: [] Exploring Operation: 38-24=14, Resulting Numbers: [27, 2, 14] Generated Node #0,0: 87:[27, 2, 14] Operation: 38-24=14 Exploring Operation: 24+2=26, Resulting Numbers: [38, 27, 26] Generated Node #0,1: 87:[38, 27, 26] Operation: 24+2=26 Exploring Operation: 27-24=3, Resulting Numbers: [38, 2, 3] Generated Node #0,2: 87:[38, 2, 3] Operation: 27-24=3 Moving to Node #0,2 Current State: 87:[38, 2, 3], Operations: ['27-24=3'] Exploring Operation: 38/2=19, Resulting Numbers: [3, 19] Generated Node #0,2,0: 87:[3, 19] Operation: 38/2=19 Exploring Operation: 38-2=36, Resulting Numbers: [3, 36] Generated Node #0,2,1: 87:[3, 36] Operation: 38-2=36 Exploring Operation: 38-3=35, Resulting Numbers: [2, 35] Generated Node #0,2,2: 87:[2, 35] Operation: 38-3=35 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[3, 36], Operations: ['27-24=3', '38-2=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[2, 35], Operations: ['27-24=3', '38-3=35'] Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[3, 19], Operations: ['27-24=3', '38/2=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,87 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,87 unequal: No Solution Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,87 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: 87:[27, 2, 14], Operations: ['38-24=14'] Exploring Operation: 14/2=7, Resulting Numbers: [27, 7] Generated Node #0,0,0: 87:[27, 7] Operation: 14/2=7 Exploring Operation: 2*14=28, Resulting Numbers: [27, 28] Generated Node #0,0,1: 87:[27, 28] Operation: 2*14=28 Exploring Operation: 27+2=29, Resulting Numbers: [14, 29] Generated Node #0,0,2: 87:[14, 29] Operation: 27+2=29 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[27, 28], Operations: ['38-24=14', '2*14=28'] Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,87 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,87 unequal: No Solution Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[27, 7], Operations: ['38-24=14', '14/2=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,87 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[14, 29], Operations: ['38-24=14', '27+2=29'] Exploring Operation: 14*29=406, Resulting Numbers: [406] 406,87 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,87 unequal: No Solution Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,87 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: 87:[38, 27, 26], Operations: ['24+2=26'] Exploring Operation: 27-26=1, Resulting Numbers: [38, 1] Generated Node #0,1,0: 87:[38, 1] Operation: 27-26=1 Exploring Operation: 38-26=12, Resulting Numbers: [27, 12] Generated Node #0,1,1: 87:[27, 12] Operation: 38-26=12 Exploring Operation: 38-27=11, Resulting Numbers: [26, 11] Generated Node #0,1,2: 87:[26, 11] Operation: 38-27=11 Moving to Node #0,1,0 Current State: 87:[38, 1], Operations: ['24+2=26', '27-26=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,87 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[27, 12], Operations: ['24+2=26', '38-26=12'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,87 unequal: No Solution Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,87 unequal: No Solution Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[26, 11], Operations: ['24+2=26', '38-27=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,87 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,87 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,87 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 5, 14, 7, 23 ]
12
[ "14-7=7", "5*7=35", "35-23=12" ]
Current State: 12:[5, 14, 7, 23], Operations: [] Exploring Operation: 14-7=7, Resulting Numbers: [5, 23, 7] Generated Node #2: [5, 23, 7] from Operation: 14-7=7 Current State: 12:[5, 23, 7], Operations: ['14-7=7'] Exploring Operation: 5*7=35, Resulting Numbers: [23, 35] Generated Node #3: [23, 35] from Operation: 5*7=35 Current State: 12:[23, 35], Operations: ['14-7=7', '5*7=35'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[5, 14, 7, 23], Operations: [] Exploring Operation: 23-14=9, Resulting Numbers: [5, 7, 9] Generated Node #0,0: 12:[5, 7, 9] Operation: 23-14=9 Moving to Node #0,0 Current State: 12:[5, 7, 9], Operations: ['23-14=9'] Exploring Operation: 9-5=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 12:[7, 4] Operation: 9-5=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[7, 4], Operations: ['23-14=9', '9-5=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,12 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
[ 47, 86, 82, 2 ]
41
[ "86-47=39", "82-2=80", "80-39=41" ]
Current State: 41:[47, 86, 82, 2], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [82, 2, 39] Generated Node #2: [82, 2, 39] from Operation: 86-47=39 Current State: 41:[82, 2, 39], Operations: ['86-47=39'] Exploring Operation: 82-2=80, Resulting Numbers: [39, 80] Generated Node #3: [39, 80] from Operation: 82-2=80 Current State: 41:[39, 80], Operations: ['86-47=39', '82-2=80'] Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[47, 86, 82, 2], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [47, 86, 41] Generated Node #0,0: 41:[47, 86, 41] Operation: 82/2=41 Exploring Operation: 86/2=43, Resulting Numbers: [47, 82, 43] Generated Node #0,1: 41:[47, 82, 43] Operation: 86/2=43 Exploring Operation: 86-47=39, Resulting Numbers: [82, 2, 39] Generated Node #0,2: 41:[82, 2, 39] Operation: 86-47=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[47, 82, 43], Operations: ['86/2=43'] Exploring Operation: 82-43=39, Resulting Numbers: [47, 39] Generated Node #0,1,0: 41:[47, 39] Operation: 82-43=39 Exploring Operation: 82-47=35, Resulting Numbers: [43, 35] Generated Node #0,1,1: 41:[43, 35] Operation: 82-47=35 Exploring Operation: 47-43=4, Resulting Numbers: [82, 4] Generated Node #0,1,2: 41:[82, 4] Operation: 47-43=4 Moving to Node #0,1,0 Current State: 41:[47, 39], Operations: ['86/2=43', '82-43=39'] Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,41 unequal: No Solution Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[43, 35], Operations: ['86/2=43', '82-47=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,41 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,41 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[82, 4], Operations: ['86/2=43', '47-43=4'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,41 unequal: No Solution Exploring Operation: 82+4=86, Resulting Numbers: [86] 86,41 unequal: No Solution Exploring Operation: 82*4=328, Resulting Numbers: [328] 328,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[47, 86, 41], Operations: ['82/2=41'] Exploring Operation: 86-41=45, Resulting Numbers: [47, 45] Generated Node #0,0,0: 41:[47, 45] Operation: 86-41=45 Exploring Operation: 47-41=6, Resulting Numbers: [86, 6] Generated Node #0,0,1: 41:[86, 6] Operation: 47-41=6 Exploring Operation: 86-47=39, Resulting Numbers: [41, 39] Generated Node #0,0,2: 41:[41, 39] Operation: 86-47=39 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[41, 39], Operations: ['82/2=41', '86-47=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,41 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[47, 45], Operations: ['82/2=41', '86-41=45'] Exploring Operation: 47+45=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 47*45=2115, Resulting Numbers: [2115] 2115,41 unequal: No Solution Exploring Operation: 47-45=2, Resulting Numbers: [2] 2,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[86, 6], Operations: ['82/2=41', '47-41=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,41 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[82, 2, 39], Operations: ['86-47=39'] Exploring Operation: 82-39=43, Resulting Numbers: [2, 43] Generated Node #0,2,0: 41:[2, 43] Operation: 82-39=43 Exploring Operation: 82-2=80, Resulting Numbers: [39, 80] Generated Node #0,2,1: 41:[39, 80] Operation: 82-2=80 Exploring Operation: 82/2=41, Resulting Numbers: [39, 41] Generated Node #0,2,2: 41:[39, 41] Operation: 82/2=41 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[39, 41], Operations: ['86-47=39', '82/2=41'] Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 39*41=1599, Resulting Numbers: [1599] 1599,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[2, 43], Operations: ['86-47=39', '82-39=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[47, 86, 82, 2], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [82, 2, 39] Generated Node #0,2: 41:[82, 2, 39] Operation: 86-47=39 Moving to Node #0,2 Current State: 41:[82, 2, 39], Operations: ['86-47=39'] Exploring Operation: 82-39=43, Resulting Numbers: [2, 43] Generated Node #0,2,0: 41:[2, 43] Operation: 82-39=43 Moving to Node #0,2,0 Current State: 41:[2, 43], Operations: ['86-47=39', '82-39=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_3
sum_heuristic
[ 53, 29, 94, 53 ]
94
[ "53-53=0", "29*0=0", "94+0=94" ]
Current State: 94:[53, 29, 94, 53], Operations: [] Exploring Operation: 53-53=0, Resulting Numbers: [29, 94, 0] Generated Node #2: [29, 94, 0] from Operation: 53-53=0 Current State: 94:[29, 94, 0], Operations: ['53-53=0'] Exploring Operation: 29*0=0, Resulting Numbers: [94, 0] Generated Node #3: [94, 0] from Operation: 29*0=0 Current State: 94:[94, 0], Operations: ['53-53=0', '29*0=0'] Exploring Operation: 94+0=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[53, 29, 94, 53], Operations: [] Exploring Operation: 53/53=1, Resulting Numbers: [29, 94, 1] Generated Node #0,0: 94:[29, 94, 1] Operation: 53/53=1 Exploring Operation: 53+29=82, Resulting Numbers: [94, 53, 82] Generated Node #0,1: 94:[94, 53, 82] Operation: 53+29=82 Exploring Operation: 29+53=82, Resulting Numbers: [53, 94, 82] Generated Node #0,2: 94:[53, 94, 82] Operation: 29+53=82 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[94, 53, 82], Operations: ['53+29=82'] Exploring Operation: 94-82=12, Resulting Numbers: [53, 12] Generated Node #0,1,0: 94:[53, 12] Operation: 94-82=12 Exploring Operation: 94-53=41, Resulting Numbers: [82, 41] Generated Node #0,1,1: 94:[82, 41] Operation: 94-53=41 Exploring Operation: 82-53=29, Resulting Numbers: [94, 29] Generated Node #0,1,2: 94:[94, 29] Operation: 82-53=29 Moving to Node #0,1,0 Current State: 94:[53, 12], Operations: ['53+29=82', '94-82=12'] Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[82, 41], Operations: ['53+29=82', '94-53=41'] Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[94, 29], Operations: ['53+29=82', '82-53=29'] Exploring Operation: 94*29=2726, Resulting Numbers: [2726] 2726,94 unequal: No Solution Exploring Operation: 94+29=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[53, 94, 82], Operations: ['29+53=82'] Exploring Operation: 94-82=12, Resulting Numbers: [53, 12] Generated Node #0,2,0: 94:[53, 12] Operation: 94-82=12 Exploring Operation: 94-53=41, Resulting Numbers: [82, 41] Generated Node #0,2,1: 94:[82, 41] Operation: 94-53=41 Exploring Operation: 82-53=29, Resulting Numbers: [94, 29] Generated Node #0,2,2: 94:[94, 29] Operation: 82-53=29 Moving to Node #0,2,0 Current State: 94:[53, 12], Operations: ['29+53=82', '94-82=12'] Exploring Operation: 53*12=636, Resulting Numbers: [636] 636,94 unequal: No Solution Exploring Operation: 53+12=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[82, 41], Operations: ['29+53=82', '94-53=41'] Exploring Operation: 82-41=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 82+41=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 82/41=2, Resulting Numbers: [2] 2,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[94, 29], Operations: ['29+53=82', '82-53=29'] Exploring Operation: 94+29=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 94*29=2726, Resulting Numbers: [2726] 2726,94 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[29, 94, 1], Operations: ['53/53=1'] Exploring Operation: 29/1=29, Resulting Numbers: [94, 29] Generated Node #0,0,0: 94:[94, 29] Operation: 29/1=29 Exploring Operation: 29*1=29, Resulting Numbers: [94, 29] Generated Node #0,0,1: 94:[94, 29] Operation: 29*1=29 Exploring Operation: 29+1=30, Resulting Numbers: [94, 30] Generated Node #0,0,2: 94:[94, 30] Operation: 29+1=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[94, 30], Operations: ['53/53=1', '29+1=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,94 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,94 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[94, 29], Operations: ['53/53=1', '29/1=29'] Exploring Operation: 94+29=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 94*29=2726, Resulting Numbers: [2726] 2726,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[94, 29], Operations: ['53/53=1', '29*1=29'] Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,94 unequal: No Solution Exploring Operation: 94*29=2726, Resulting Numbers: [2726] 2726,94 unequal: No Solution Exploring Operation: 94+29=123, Resulting Numbers: [123] 123,94 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
[ 65, 79, 83, 48 ]
77
[ "83-79=4", "48/4=12", "65+12=77" ]
Current State: 77:[65, 79, 83, 48], Operations: [] Exploring Operation: 83-79=4, Resulting Numbers: [65, 48, 4] Generated Node #2: [65, 48, 4] from Operation: 83-79=4 Current State: 77:[65, 48, 4], Operations: ['83-79=4'] Exploring Operation: 48/4=12, Resulting Numbers: [65, 12] Generated Node #3: [65, 12] from Operation: 48/4=12 Current State: 77:[65, 12], Operations: ['83-79=4', '48/4=12'] Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[65, 79, 83, 48], Operations: [] Exploring Operation: 79-65=14, Resulting Numbers: [83, 48, 14] Generated Node #0,0: 77:[83, 48, 14] Operation: 79-65=14 Exploring Operation: 83-65=18, Resulting Numbers: [79, 48, 18] Generated Node #0,1: 77:[79, 48, 18] Operation: 83-65=18 Exploring Operation: 65-48=17, Resulting Numbers: [79, 83, 17] Generated Node #0,2: 77:[79, 83, 17] Operation: 65-48=17 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[79, 83, 17], Operations: ['65-48=17'] Exploring Operation: 79-17=62, Resulting Numbers: [83, 62] Generated Node #0,2,0: 77:[83, 62] Operation: 79-17=62 Exploring Operation: 83-17=66, Resulting Numbers: [79, 66] Generated Node #0,2,1: 77:[79, 66] Operation: 83-17=66 Exploring Operation: 83-79=4, Resulting Numbers: [17, 4] Generated Node #0,2,2: 77:[17, 4] Operation: 83-79=4 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[17, 4], Operations: ['65-48=17', '83-79=4'] Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[79, 66], Operations: ['65-48=17', '83-17=66'] Exploring Operation: 79*66=5214, Resulting Numbers: [5214] 5214,77 unequal: No Solution Exploring Operation: 79+66=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[83, 62], Operations: ['65-48=17', '79-17=62'] Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 83*62=5146, Resulting Numbers: [5146] 5146,77 unequal: No Solution Exploring Operation: 83+62=145, Resulting Numbers: [145] 145,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[83, 48, 14], Operations: ['79-65=14'] Exploring Operation: 48+14=62, Resulting Numbers: [83, 62] Generated Node #0,0,0: 77:[83, 62] Operation: 48+14=62 Exploring Operation: 48-14=34, Resulting Numbers: [83, 34] Generated Node #0,0,1: 77:[83, 34] Operation: 48-14=34 Exploring Operation: 83-48=35, Resulting Numbers: [14, 35] Generated Node #0,0,2: 77:[14, 35] Operation: 83-48=35 Moving to Node #0,0,0 Current State: 77:[83, 62], Operations: ['79-65=14', '48+14=62'] Exploring Operation: 83*62=5146, Resulting Numbers: [5146] 5146,77 unequal: No Solution Exploring Operation: 83+62=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[14, 35], Operations: ['79-65=14', '83-48=35'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,77 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[83, 34], Operations: ['79-65=14', '48-14=34'] Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,77 unequal: No Solution Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,77 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[79, 48, 18], Operations: ['83-65=18'] Exploring Operation: 48-18=30, Resulting Numbers: [79, 30] Generated Node #0,1,0: 77:[79, 30] Operation: 48-18=30 Exploring Operation: 48+18=66, Resulting Numbers: [79, 66] Generated Node #0,1,1: 77:[79, 66] Operation: 48+18=66 Exploring Operation: 79-48=31, Resulting Numbers: [18, 31] Generated Node #0,1,2: 77:[18, 31] Operation: 79-48=31 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[79, 66], Operations: ['83-65=18', '48+18=66'] Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 79+66=145, Resulting Numbers: [145] 145,77 unequal: No Solution Exploring Operation: 79*66=5214, Resulting Numbers: [5214] 5214,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[79, 30], Operations: ['83-65=18', '48-18=30'] Exploring Operation: 79+30=109, Resulting Numbers: [109] 109,77 unequal: No Solution Exploring Operation: 79*30=2370, Resulting Numbers: [2370] 2370,77 unequal: No Solution Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 77:[18, 31], Operations: ['83-65=18', '79-48=31'] Exploring Operation: 18+31=49, Resulting Numbers: [49] 49,77 unequal: No Solution Exploring Operation: 18*31=558, Resulting Numbers: [558] 558,77 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 95, 2, 27, 74 ]
89
[ "95*2=190", "27+74=101", "190-101=89" ]
Current State: 89:[95, 2, 27, 74], Operations: [] Exploring Operation: 95*2=190, Resulting Numbers: [27, 74, 190] Generated Node #2: [27, 74, 190] from Operation: 95*2=190 Current State: 89:[27, 74, 190], Operations: ['95*2=190'] Exploring Operation: 27+74=101, Resulting Numbers: [190, 101] Generated Node #3: [190, 101] from Operation: 27+74=101 Current State: 89:[190, 101], Operations: ['95*2=190', '27+74=101'] Exploring Operation: 190-101=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[95, 2, 27, 74], Operations: [] Exploring Operation: 95-2=93, Resulting Numbers: [27, 74, 93] Generated Node #0,0: 89:[27, 74, 93] Operation: 95-2=93 Exploring Operation: 2+27=29, Resulting Numbers: [95, 74, 29] Generated Node #0,1: 89:[95, 74, 29] Operation: 2+27=29 Exploring Operation: 2*27=54, Resulting Numbers: [95, 74, 54] Generated Node #0,2: 89:[95, 74, 54] Operation: 2*27=54 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[95, 74, 54], Operations: ['2*27=54'] Exploring Operation: 95+54=149, Resulting Numbers: [74, 149] Generated Node #0,2,0: 89:[74, 149] Operation: 95+54=149 Exploring Operation: 95-54=41, Resulting Numbers: [74, 41] Generated Node #0,2,1: 89:[74, 41] Operation: 95-54=41 Exploring Operation: 74+54=128, Resulting Numbers: [95, 128] Generated Node #0,2,2: 89:[95, 128] Operation: 74+54=128 Moving to Node #0,2,2 Current State: 89:[95, 128], Operations: ['2*27=54', '74+54=128'] Exploring Operation: 128-95=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 95+128=223, Resulting Numbers: [223] 223,89 unequal: No Solution Exploring Operation: 95*128=12160, Resulting Numbers: [12160] 12160,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[74, 41], Operations: ['2*27=54', '95-54=41'] Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,89 unequal: No Solution Exploring Operation: 74*41=3034, Resulting Numbers: [3034] 3034,89 unequal: No Solution Exploring Operation: 74+41=115, Resulting Numbers: [115] 115,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[74, 149], Operations: ['2*27=54', '95+54=149'] Exploring Operation: 149-74=75, Resulting Numbers: [75] 75,89 unequal: No Solution Exploring Operation: 74*149=11026, Resulting Numbers: [11026] 11026,89 unequal: No Solution Exploring Operation: 74+149=223, Resulting Numbers: [223] 223,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[27, 74, 93], Operations: ['95-2=93'] Exploring Operation: 93-27=66, Resulting Numbers: [74, 66] Generated Node #0,0,0: 89:[74, 66] Operation: 93-27=66 Exploring Operation: 74-27=47, Resulting Numbers: [93, 47] Generated Node #0,0,1: 89:[93, 47] Operation: 74-27=47 Exploring Operation: 27+74=101, Resulting Numbers: [93, 101] Generated Node #0,0,2: 89:[93, 101] Operation: 27+74=101 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[93, 101], Operations: ['95-2=93', '27+74=101'] Exploring Operation: 93+101=194, Resulting Numbers: [194] 194,89 unequal: No Solution Exploring Operation: 101-93=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 93*101=9393, Resulting Numbers: [9393] 9393,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[74, 66], Operations: ['95-2=93', '93-27=66'] Exploring Operation: 74+66=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 74*66=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[93, 47], Operations: ['95-2=93', '74-27=47'] Exploring Operation: 93*47=4371, Resulting Numbers: [4371] 4371,89 unequal: No Solution Exploring Operation: 93+47=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 93-47=46, Resulting Numbers: [46] 46,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[95, 74, 29], Operations: ['2+27=29'] Exploring Operation: 95-29=66, Resulting Numbers: [74, 66] Generated Node #0,1,0: 89:[74, 66] Operation: 95-29=66 Exploring Operation: 74+29=103, Resulting Numbers: [95, 103] Generated Node #0,1,1: 89:[95, 103] Operation: 74+29=103 Exploring Operation: 95+29=124, Resulting Numbers: [74, 124] Generated Node #0,1,2: 89:[74, 124] Operation: 95+29=124 Moving to Node #0,1,1 Current State: 89:[95, 103], Operations: ['2+27=29', '74+29=103'] Exploring Operation: 95*103=9785, Resulting Numbers: [9785] 9785,89 unequal: No Solution Exploring Operation: 103-95=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 95+103=198, Resulting Numbers: [198] 198,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[74, 66], Operations: ['2+27=29', '95-29=66'] Exploring Operation: 74-66=8, Resulting Numbers: [8] 8,89 unequal: No Solution Exploring Operation: 74+66=140, Resulting Numbers: [140] 140,89 unequal: No Solution Exploring Operation: 74*66=4884, Resulting Numbers: [4884] 4884,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[74, 124], Operations: ['2+27=29', '95+29=124'] Exploring Operation: 74*124=9176, Resulting Numbers: [9176] 9176,89 unequal: No Solution Exploring Operation: 74+124=198, Resulting Numbers: [198] 198,89 unequal: No Solution Exploring Operation: 124-74=50, Resulting Numbers: [50] 50,89 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
[ 7, 60, 17, 47 ]
97
[ "7+60=67", "47-17=30", "67+30=97" ]
Current State: 97:[7, 60, 17, 47], Operations: [] Exploring Operation: 7+60=67, Resulting Numbers: [17, 47, 67] Generated Node #2: [17, 47, 67] from Operation: 7+60=67 Current State: 97:[17, 47, 67], Operations: ['7+60=67'] Exploring Operation: 47-17=30, Resulting Numbers: [67, 30] Generated Node #3: [67, 30] from Operation: 47-17=30 Current State: 97:[67, 30], Operations: ['7+60=67', '47-17=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[7, 60, 17, 47], Operations: [] Exploring Operation: 7+17=24, Resulting Numbers: [60, 47, 24] Generated Node #0,0: 97:[60, 47, 24] Operation: 7+17=24 Exploring Operation: 7+60=67, Resulting Numbers: [17, 47, 67] Generated Node #0,1: 97:[17, 47, 67] Operation: 7+60=67 Exploring Operation: 7*17=119, Resulting Numbers: [60, 47, 119] Generated Node #0,2: 97:[60, 47, 119] Operation: 7*17=119 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[60, 47, 119], Operations: ['7*17=119'] Exploring Operation: 119-60=59, Resulting Numbers: [47, 59] Generated Node #0,2,0: 97:[47, 59] Operation: 119-60=59 Exploring Operation: 60+47=107, Resulting Numbers: [119, 107] Generated Node #0,2,1: 97:[119, 107] Operation: 60+47=107 Exploring Operation: 119-47=72, Resulting Numbers: [60, 72] Generated Node #0,2,2: 97:[60, 72] Operation: 119-47=72 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[119, 107], Operations: ['7*17=119', '60+47=107'] Exploring Operation: 119+107=226, Resulting Numbers: [226] 226,97 unequal: No Solution Exploring Operation: 119-107=12, Resulting Numbers: [12] 12,97 unequal: No Solution Exploring Operation: 119*107=12733, Resulting Numbers: [12733] 12733,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[60, 72], Operations: ['7*17=119', '119-47=72'] Exploring Operation: 60+72=132, Resulting Numbers: [132] 132,97 unequal: No Solution Exploring Operation: 60*72=4320, Resulting Numbers: [4320] 4320,97 unequal: No Solution Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[47, 59], Operations: ['7*17=119', '119-60=59'] Exploring Operation: 47*59=2773, Resulting Numbers: [2773] 2773,97 unequal: No Solution Exploring Operation: 47+59=106, Resulting Numbers: [106] 106,97 unequal: No Solution Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[60, 47, 24], Operations: ['7+17=24'] Exploring Operation: 60+24=84, Resulting Numbers: [47, 84] Generated Node #0,0,0: 97:[47, 84] Operation: 60+24=84 Exploring Operation: 60+47=107, Resulting Numbers: [24, 107] Generated Node #0,0,1: 97:[24, 107] Operation: 60+47=107 Exploring Operation: 47+24=71, Resulting Numbers: [60, 71] Generated Node #0,0,2: 97:[60, 71] Operation: 47+24=71 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[47, 84], Operations: ['7+17=24', '60+24=84'] Exploring Operation: 47+84=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 47*84=3948, Resulting Numbers: [3948] 3948,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[60, 71], Operations: ['7+17=24', '47+24=71'] Exploring Operation: 60*71=4260, Resulting Numbers: [4260] 4260,97 unequal: No Solution Exploring Operation: 60+71=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 71-60=11, Resulting Numbers: [11] 11,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[24, 107], Operations: ['7+17=24', '60+47=107'] Exploring Operation: 24+107=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 24*107=2568, Resulting Numbers: [2568] 2568,97 unequal: No Solution Exploring Operation: 107-24=83, Resulting Numbers: [83] 83,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[17, 47, 67], Operations: ['7+60=67'] Exploring Operation: 17+47=64, Resulting Numbers: [67, 64] Generated Node #0,1,0: 97:[67, 64] Operation: 17+47=64 Exploring Operation: 17+67=84, Resulting Numbers: [47, 84] Generated Node #0,1,1: 97:[47, 84] Operation: 17+67=84 Exploring Operation: 47-17=30, Resulting Numbers: [67, 30] Generated Node #0,1,2: 97:[67, 30] Operation: 47-17=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[67, 64], Operations: ['7+60=67', '17+47=64'] Exploring Operation: 67+64=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 67-64=3, Resulting Numbers: [3] 3,97 unequal: No Solution Exploring Operation: 67*64=4288, Resulting Numbers: [4288] 4288,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[47, 84], Operations: ['7+60=67', '17+67=84'] Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,97 unequal: No Solution Exploring Operation: 47*84=3948, Resulting Numbers: [3948] 3948,97 unequal: No Solution Exploring Operation: 47+84=131, Resulting Numbers: [131] 131,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[67, 30], Operations: ['7+60=67', '47-17=30'] Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,97 unequal: No Solution Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[7, 60, 17, 47], Operations: [] Exploring Operation: 7+60=67, Resulting Numbers: [17, 47, 67] Generated Node #0,1: 97:[17, 47, 67] Operation: 7+60=67 Moving to Node #0,1 Current State: 97:[17, 47, 67], Operations: ['7+60=67'] Exploring Operation: 47-17=30, Resulting Numbers: [67, 30] Generated Node #0,1,2: 97:[67, 30] Operation: 47-17=30 Moving to Node #0,1,2 Current State: 97:[67, 30], Operations: ['7+60=67', '47-17=30'] Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.963542
hs_3
sum_heuristic
[ 7, 80, 72, 12 ]
81
[ "7+80=87", "72/12=6", "87-6=81" ]
Current State: 81:[7, 80, 72, 12], Operations: [] Exploring Operation: 7+80=87, Resulting Numbers: [72, 12, 87] Generated Node #2: [72, 12, 87] from Operation: 7+80=87 Current State: 81:[72, 12, 87], Operations: ['7+80=87'] Exploring Operation: 72/12=6, Resulting Numbers: [87, 6] Generated Node #3: [87, 6] from Operation: 72/12=6 Current State: 81:[87, 6], Operations: ['7+80=87', '72/12=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[7, 80, 72, 12], Operations: [] Exploring Operation: 7+72=79, Resulting Numbers: [80, 12, 79] Generated Node #0,0: 81:[80, 12, 79] Operation: 7+72=79 Exploring Operation: 80-72=8, Resulting Numbers: [7, 12, 8] Generated Node #0,1: 81:[7, 12, 8] Operation: 80-72=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[80, 12, 79], Operations: ['7+72=79'] Exploring Operation: 80-79=1, Resulting Numbers: [12, 1] Generated Node #0,0,0: 81:[12, 1] Operation: 80-79=1 Exploring Operation: 12+79=91, Resulting Numbers: [80, 91] Generated Node #0,0,1: 81:[80, 91] Operation: 12+79=91 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[12, 1], Operations: ['7+72=79', '80-79=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,81 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,81 unequal: No Solution No 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: 81:[80, 91], Operations: ['7+72=79', '12+79=91'] Exploring Operation: 80+91=171, Resulting Numbers: [171] 171,81 unequal: No Solution Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,81 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: 81:[7, 12, 8], Operations: ['80-72=8'] Exploring Operation: 12-8=4, Resulting Numbers: [7, 4] Generated Node #0,1,0: 81:[7, 4] Operation: 12-8=4 Exploring Operation: 12-7=5, Resulting Numbers: [8, 5] Generated Node #0,1,1: 81:[8, 5] Operation: 12-7=5 Moving to Node #0,1,0 Current State: 81:[7, 4], Operations: ['80-72=8', '12-8=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[8, 5], Operations: ['80-72=8', '12-7=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,81 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
[ 16, 60, 45, 93 ]
94
[ "60-16=44", "45+93=138", "138-44=94" ]
Current State: 94:[16, 60, 45, 93], Operations: [] Exploring Operation: 60-16=44, Resulting Numbers: [45, 93, 44] Generated Node #2: [45, 93, 44] from Operation: 60-16=44 Current State: 94:[45, 93, 44], Operations: ['60-16=44'] Exploring Operation: 45+93=138, Resulting Numbers: [44, 138] Generated Node #3: [44, 138] from Operation: 45+93=138 Current State: 94:[44, 138], Operations: ['60-16=44', '45+93=138'] Exploring Operation: 138-44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[16, 60, 45, 93], Operations: [] Exploring Operation: 60-45=15, Resulting Numbers: [16, 93, 15] Generated Node #0,0: 94:[16, 93, 15] Operation: 60-45=15 Exploring Operation: 60+45=105, Resulting Numbers: [16, 93, 105] Generated Node #0,1: 94:[16, 93, 105] Operation: 60+45=105 Exploring Operation: 16+45=61, Resulting Numbers: [60, 93, 61] Generated Node #0,2: 94:[60, 93, 61] Operation: 16+45=61 Exploring Operation: 16+60=76, Resulting Numbers: [45, 93, 76] Generated Node #0,3: 94:[45, 93, 76] Operation: 16+60=76 Exploring Operation: 60-16=44, Resulting Numbers: [45, 93, 44] Generated Node #0,4: 94:[45, 93, 44] Operation: 60-16=44 Moving to Node #0,4 Current State: 94:[45, 93, 44], Operations: ['60-16=44'] Exploring Operation: 93-44=49, Resulting Numbers: [45, 49] Generated Node #0,4,0: 94:[45, 49] Operation: 93-44=49 Exploring Operation: 93+44=137, Resulting Numbers: [45, 137] Generated Node #0,4,1: 94:[45, 137] Operation: 93+44=137 Exploring Operation: 45-44=1, Resulting Numbers: [93, 1] Generated Node #0,4,2: 94:[93, 1] Operation: 45-44=1 Exploring Operation: 45+44=89, Resulting Numbers: [93, 89] Generated Node #0,4,3: 94:[93, 89] Operation: 45+44=89 Exploring Operation: 93-45=48, Resulting Numbers: [44, 48] Generated Node #0,4,4: 94:[44, 48] Operation: 93-45=48 Moving to Node #0,3 Current State: 94:[45, 93, 76], Operations: ['16+60=76'] Exploring Operation: 93-76=17, Resulting Numbers: [45, 17] Generated Node #0,3,0: 94:[45, 17] Operation: 93-76=17 Exploring Operation: 45+93=138, Resulting Numbers: [76, 138] Generated Node #0,3,1: 94:[76, 138] Operation: 45+93=138 Exploring Operation: 76-45=31, Resulting Numbers: [93, 31] Generated Node #0,3,2: 94:[93, 31] Operation: 76-45=31 Exploring Operation: 93-45=48, Resulting Numbers: [76, 48] Generated Node #0,3,3: 94:[76, 48] Operation: 93-45=48 Exploring Operation: 45+76=121, Resulting Numbers: [93, 121] Generated Node #0,3,4: 94:[93, 121] Operation: 45+76=121 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 94:[45, 17], Operations: ['16+60=76', '93-76=17'] Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 94:[93, 31], Operations: ['16+60=76', '76-45=31'] Exploring Operation: 93+31=124, Resulting Numbers: [124] 124,94 unequal: No Solution Exploring Operation: 93*31=2883, Resulting Numbers: [2883] 2883,94 unequal: No Solution Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 94:[76, 48], Operations: ['16+60=76', '93-45=48'] Exploring Operation: 76*48=3648, Resulting Numbers: [3648] 3648,94 unequal: No Solution Exploring Operation: 76-48=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 76+48=124, Resulting Numbers: [124] 124,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 94:[93, 121], Operations: ['16+60=76', '45+76=121'] Exploring Operation: 121-93=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 93*121=11253, Resulting Numbers: [11253] 11253,94 unequal: No Solution Exploring Operation: 93+121=214, Resulting Numbers: [214] 214,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 94:[76, 138], Operations: ['16+60=76', '45+93=138'] Exploring Operation: 76*138=10488, Resulting Numbers: [10488] 10488,94 unequal: No Solution Exploring Operation: 138-76=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 76+138=214, Resulting Numbers: [214] 214,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 94:[16, 93, 105], Operations: ['60+45=105'] Exploring Operation: 16+105=121, Resulting Numbers: [93, 121] Generated Node #0,1,0: 94:[93, 121] Operation: 16+105=121 Exploring Operation: 93-16=77, Resulting Numbers: [105, 77] Generated Node #0,1,1: 94:[105, 77] Operation: 93-16=77 Exploring Operation: 16+93=109, Resulting Numbers: [105, 109] Generated Node #0,1,2: 94:[105, 109] Operation: 16+93=109 Exploring Operation: 105-93=12, Resulting Numbers: [16, 12] Generated Node #0,1,3: 94:[16, 12] Operation: 105-93=12 Exploring Operation: 105-16=89, Resulting Numbers: [93, 89] Generated Node #0,1,4: 94:[93, 89] Operation: 105-16=89 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 94:[93, 89], Operations: ['60+45=105', '105-16=89'] Exploring Operation: 93+89=182, Resulting Numbers: [182] 182,94 unequal: No Solution Exploring Operation: 93*89=8277, Resulting Numbers: [8277] 8277,94 unequal: No Solution Exploring Operation: 93-89=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 94:[16, 12], Operations: ['60+45=105', '105-93=12'] Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 94:[105, 109], Operations: ['60+45=105', '16+93=109'] Exploring Operation: 105+109=214, Resulting Numbers: [214] 214,94 unequal: No Solution Exploring Operation: 109-105=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 105*109=11445, Resulting Numbers: [11445] 11445,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[93, 121], Operations: ['60+45=105', '16+105=121'] Exploring Operation: 93*121=11253, Resulting Numbers: [11253] 11253,94 unequal: No Solution Exploring Operation: 121-93=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 93+121=214, Resulting Numbers: [214] 214,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[105, 77], Operations: ['60+45=105', '93-16=77'] Exploring Operation: 105+77=182, Resulting Numbers: [182] 182,94 unequal: No Solution Exploring Operation: 105*77=8085, Resulting Numbers: [8085] 8085,94 unequal: No Solution Exploring Operation: 105-77=28, Resulting Numbers: [28] 28,94 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: 94:[16, 93, 15], Operations: ['60-45=15'] Exploring Operation: 93-16=77, Resulting Numbers: [15, 77] Generated Node #0,0,0: 94:[15, 77] Operation: 93-16=77 Exploring Operation: 16-15=1, Resulting Numbers: [93, 1] Generated Node #0,0,1: 94:[93, 1] Operation: 16-15=1 Exploring Operation: 16+93=109, Resulting Numbers: [15, 109] Generated Node #0,0,2: 94:[15, 109] Operation: 16+93=109 Exploring Operation: 16+15=31, Resulting Numbers: [93, 31] Generated Node #0,0,3: 94:[93, 31] Operation: 16+15=31 Exploring Operation: 93+15=108, Resulting Numbers: [16, 108] Generated Node #0,0,4: 94:[16, 108] Operation: 93+15=108 Moving to Node #0,2 Current State: 94:[60, 93, 61], Operations: ['16+45=61'] Exploring Operation: 61-60=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 94:[93, 1] Operation: 61-60=1 Exploring Operation: 93-60=33, Resulting Numbers: [61, 33] Generated Node #0,2,1: 94:[61, 33] Operation: 93-60=33 Exploring Operation: 93-61=32, Resulting Numbers: [60, 32] Generated Node #0,2,2: 94:[60, 32] Operation: 93-61=32 Exploring Operation: 60+61=121, Resulting Numbers: [93, 121] Generated Node #0,2,3: 94:[93, 121] Operation: 60+61=121 Exploring Operation: 60+93=153, Resulting Numbers: [61, 153] Generated Node #0,2,4: 94:[61, 153] Operation: 60+93=153 Moving to Node #0,4,2 Current State: 94:[93, 1], Operations: ['60-16=44', '45-44=1'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,94 unequal: No Solution Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[16, 60, 45, 93], Operations: [] Exploring Operation: 60-16=44, Resulting Numbers: [45, 93, 44] Generated Node #0,4: 94:[45, 93, 44] Operation: 60-16=44 Moving to Node #0,4 Current State: 94:[45, 93, 44], Operations: ['60-16=44'] Exploring Operation: 45-44=1, Resulting Numbers: [93, 1] Generated Node #0,4,2: 94:[93, 1] Operation: 45-44=1 Moving to Node #0,4,2 Current State: 94:[93, 1], Operations: ['60-16=44', '45-44=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 83, 8, 17, 18 ]
92
[ "83+8=91", "18-17=1", "91+1=92" ]
Current State: 92:[83, 8, 17, 18], Operations: [] Exploring Operation: 83+8=91, Resulting Numbers: [17, 18, 91] Generated Node #2: [17, 18, 91] from Operation: 83+8=91 Current State: 92:[17, 18, 91], Operations: ['83+8=91'] Exploring Operation: 18-17=1, Resulting Numbers: [91, 1] Generated Node #3: [91, 1] from Operation: 18-17=1 Current State: 92:[91, 1], Operations: ['83+8=91', '18-17=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[83, 8, 17, 18], Operations: [] Exploring Operation: 83+8=91, Resulting Numbers: [17, 18, 91] Generated Node #0,0: 92:[17, 18, 91] Operation: 83+8=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[17, 18, 91], Operations: ['83+8=91'] Exploring Operation: 18-17=1, Resulting Numbers: [91, 1] Generated Node #0,0,0: 92:[91, 1] Operation: 18-17=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[91, 1], Operations: ['83+8=91', '18-17=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[83, 8, 17, 18], Operations: [] Exploring Operation: 83+8=91, Resulting Numbers: [17, 18, 91] Generated Node #0,0: 92:[17, 18, 91] Operation: 83+8=91 Moving to Node #0,0 Current State: 92:[17, 18, 91], Operations: ['83+8=91'] Exploring Operation: 18-17=1, Resulting Numbers: [91, 1] Generated Node #0,0,0: 92:[91, 1] Operation: 18-17=1 Moving to Node #0,0,0 Current State: 92:[91, 1], Operations: ['83+8=91', '18-17=1'] Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 8, 45, 59, 18 ]
94
[ "8+45=53", "59-18=41", "53+41=94" ]
Current State: 94:[8, 45, 59, 18], Operations: [] Exploring Operation: 8+45=53, Resulting Numbers: [59, 18, 53] Generated Node #2: [59, 18, 53] from Operation: 8+45=53 Current State: 94:[59, 18, 53], Operations: ['8+45=53'] Exploring Operation: 59-18=41, Resulting Numbers: [53, 41] Generated Node #3: [53, 41] from Operation: 59-18=41 Current State: 94:[53, 41], Operations: ['8+45=53', '59-18=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[8, 45, 59, 18], Operations: [] Exploring Operation: 59+18=77, Resulting Numbers: [8, 45, 77] Generated Node #0,0: 94:[8, 45, 77] Operation: 59+18=77 Exploring Operation: 59-18=41, Resulting Numbers: [8, 45, 41] Generated Node #0,1: 94:[8, 45, 41] Operation: 59-18=41 Exploring Operation: 59-8=51, Resulting Numbers: [45, 18, 51] Generated Node #0,2: 94:[45, 18, 51] Operation: 59-8=51 Exploring Operation: 18-8=10, Resulting Numbers: [45, 59, 10] Generated Node #0,3: 94:[45, 59, 10] Operation: 18-8=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[8, 45, 41], Operations: ['59-18=41'] Exploring Operation: 8+41=49, Resulting Numbers: [45, 49] Generated Node #0,1,0: 94:[45, 49] Operation: 8+41=49 Exploring Operation: 45+41=86, Resulting Numbers: [8, 86] Generated Node #0,1,1: 94:[8, 86] Operation: 45+41=86 Exploring Operation: 8+45=53, Resulting Numbers: [41, 53] Generated Node #0,1,2: 94:[41, 53] Operation: 8+45=53 Exploring Operation: 45-41=4, Resulting Numbers: [8, 4] Generated Node #0,1,3: 94:[8, 4] Operation: 45-41=4 Moving to Node #0,1,0 Current State: 94:[45, 49], Operations: ['59-18=41', '8+41=49'] Exploring Operation: 45*49=2205, Resulting Numbers: [2205] 2205,94 unequal: No Solution Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[8, 45, 59, 18], Operations: [] Exploring Operation: 59-18=41, Resulting Numbers: [8, 45, 41] Generated Node #0,1: 94:[8, 45, 41] Operation: 59-18=41 Moving to Node #0,1 Current State: 94:[8, 45, 41], Operations: ['59-18=41'] Exploring Operation: 8+41=49, Resulting Numbers: [45, 49] Generated Node #0,1,0: 94:[45, 49] Operation: 8+41=49 Moving to Node #0,1,0 Current State: 94:[45, 49], Operations: ['59-18=41', '8+41=49'] Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 15, 69, 3, 23 ]
47
[ "15*3=45", "69+23=92", "92-45=47" ]
Current State: 47:[15, 69, 3, 23], Operations: [] Exploring Operation: 15*3=45, Resulting Numbers: [69, 23, 45] Generated Node #2: [69, 23, 45] from Operation: 15*3=45 Current State: 47:[69, 23, 45], Operations: ['15*3=45'] Exploring Operation: 69+23=92, Resulting Numbers: [45, 92] Generated Node #3: [45, 92] from Operation: 69+23=92 Current State: 47:[45, 92], Operations: ['15*3=45', '69+23=92'] Exploring Operation: 92-45=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[15, 69, 3, 23], Operations: [] Exploring Operation: 15*3=45, Resulting Numbers: [69, 23, 45] Generated Node #0,0: 47:[69, 23, 45] Operation: 15*3=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[69, 23, 45], Operations: ['15*3=45'] Exploring Operation: 69-23=46, Resulting Numbers: [45, 46] Generated Node #0,0,0: 47:[45, 46] Operation: 69-23=46 Moving to Node #0,0,0 Current State: 47:[45, 46], Operations: ['15*3=45', '69-23=46'] Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,47 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
[ 78, 6, 87, 29 ]
16
[ "78/6=13", "87/29=3", "13+3=16" ]
Current State: 16:[78, 6, 87, 29], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [87, 29, 13] Generated Node #2: [87, 29, 13] from Operation: 78/6=13 Current State: 16:[87, 29, 13], Operations: ['78/6=13'] Exploring Operation: 87/29=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 87/29=3 Current State: 16:[13, 3], Operations: ['78/6=13', '87/29=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[78, 6, 87, 29], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [6, 29, 9] Generated Node #0,0: 16:[6, 29, 9] Operation: 87-78=9 Exploring Operation: 87/29=3, Resulting Numbers: [78, 6, 3] Generated Node #0,1: 16:[78, 6, 3] Operation: 87/29=3 Exploring Operation: 78-29=49, Resulting Numbers: [6, 87, 49] Generated Node #0,2: 16:[6, 87, 49] Operation: 78-29=49 Exploring Operation: 78/6=13, Resulting Numbers: [87, 29, 13] Generated Node #0,3: 16:[87, 29, 13] Operation: 78/6=13 Exploring Operation: 87-29=58, Resulting Numbers: [78, 6, 58] Generated Node #0,4: 16:[78, 6, 58] Operation: 87-29=58 Moving to Node #0,0 Current State: 16:[6, 29, 9], Operations: ['87-78=9'] Exploring Operation: 6+9=15, Resulting Numbers: [29, 15] Generated Node #0,0,0: 16:[29, 15] Operation: 6+9=15 Exploring Operation: 29-9=20, Resulting Numbers: [6, 20] Generated Node #0,0,1: 16:[6, 20] Operation: 29-9=20 Exploring Operation: 6+29=35, Resulting Numbers: [9, 35] Generated Node #0,0,2: 16:[9, 35] Operation: 6+29=35 Exploring Operation: 29-6=23, Resulting Numbers: [9, 23] Generated Node #0,0,3: 16:[9, 23] Operation: 29-6=23 Exploring Operation: 9-6=3, Resulting Numbers: [29, 3] Generated Node #0,0,4: 16:[29, 3] Operation: 9-6=3 Moving to Node #0,1 Current State: 16:[78, 6, 3], Operations: ['87/29=3'] Exploring Operation: 78/6=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 16:[3, 13] Operation: 78/6=13 Exploring Operation: 78/3=26, Resulting Numbers: [6, 26] Generated Node #0,1,1: 16:[6, 26] Operation: 78/3=26 Exploring Operation: 78-6=72, Resulting Numbers: [3, 72] Generated Node #0,1,2: 16:[3, 72] Operation: 78-6=72 Exploring Operation: 78-3=75, Resulting Numbers: [6, 75] Generated Node #0,1,3: 16:[6, 75] Operation: 78-3=75 Exploring Operation: 6/3=2, Resulting Numbers: [78, 2] Generated Node #0,1,4: 16:[78, 2] Operation: 6/3=2 Moving to Node #0,3 Current State: 16:[87, 29, 13], Operations: ['78/6=13'] Exploring Operation: 87-13=74, Resulting Numbers: [29, 74] Generated Node #0,3,0: 16:[29, 74] Operation: 87-13=74 Exploring Operation: 87/29=3, Resulting Numbers: [13, 3] Generated Node #0,3,1: 16:[13, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [13, 58] Generated Node #0,3,2: 16:[13, 58] Operation: 87-29=58 Exploring Operation: 87+13=100, Resulting Numbers: [29, 100] Generated Node #0,3,3: 16:[29, 100] Operation: 87+13=100 Exploring Operation: 29-13=16, Resulting Numbers: [87, 16] Generated Node #0,3,4: 16:[87, 16] Operation: 29-13=16 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 16:[13, 3], Operations: ['78/6=13', '87/29=3'] Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,16 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[78, 6, 87, 29], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [87, 29, 13] Generated Node #0,3: 16:[87, 29, 13] Operation: 78/6=13 Moving to Node #0,3 Current State: 16:[87, 29, 13], Operations: ['78/6=13'] Exploring Operation: 87/29=3, Resulting Numbers: [13, 3] Generated Node #0,3,1: 16:[13, 3] Operation: 87/29=3 Moving to Node #0,3,1 Current State: 16:[13, 3], Operations: ['78/6=13', '87/29=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 67, 13, 29, 5 ]
20
[ "67-13=54", "29+5=34", "54-34=20" ]
Current State: 20:[67, 13, 29, 5], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [29, 5, 54] Generated Node #2: [29, 5, 54] from Operation: 67-13=54 Current State: 20:[29, 5, 54], Operations: ['67-13=54'] Exploring Operation: 29+5=34, Resulting Numbers: [54, 34] Generated Node #3: [54, 34] from Operation: 29+5=34 Current State: 20:[54, 34], Operations: ['67-13=54', '29+5=34'] Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[67, 13, 29, 5], Operations: [] Exploring Operation: 29-5=24, Resulting Numbers: [67, 13, 24] Generated Node #0,0: 20:[67, 13, 24] Operation: 29-5=24 Exploring Operation: 67-29=38, Resulting Numbers: [13, 5, 38] Generated Node #0,1: 20:[13, 5, 38] Operation: 67-29=38 Exploring Operation: 29-13=16, Resulting Numbers: [67, 5, 16] Generated Node #0,2: 20:[67, 5, 16] Operation: 29-13=16 Exploring Operation: 67-13=54, Resulting Numbers: [29, 5, 54] Generated Node #0,3: 20:[29, 5, 54] Operation: 67-13=54 Exploring Operation: 67-5=62, Resulting Numbers: [13, 29, 62] Generated Node #0,4: 20:[13, 29, 62] Operation: 67-5=62 Moving to Node #0,1 Current State: 20:[13, 5, 38], Operations: ['67-29=38'] Exploring Operation: 38-13=25, Resulting Numbers: [5, 25] Generated Node #0,1,0: 20:[5, 25] Operation: 38-13=25 Exploring Operation: 38-5=33, Resulting Numbers: [13, 33] Generated Node #0,1,1: 20:[13, 33] Operation: 38-5=33 Exploring Operation: 13+5=18, Resulting Numbers: [38, 18] Generated Node #0,1,2: 20:[38, 18] Operation: 13+5=18 Exploring Operation: 13-5=8, Resulting Numbers: [38, 8] Generated Node #0,1,3: 20:[38, 8] Operation: 13-5=8 Exploring Operation: 5+38=43, Resulting Numbers: [13, 43] Generated Node #0,1,4: 20:[13, 43] Operation: 5+38=43 Moving to Node #0,3 Current State: 20:[29, 5, 54], Operations: ['67-13=54'] Exploring Operation: 5+54=59, Resulting Numbers: [29, 59] Generated Node #0,3,0: 20:[29, 59] Operation: 5+54=59 Exploring Operation: 54-29=25, Resulting Numbers: [5, 25] Generated Node #0,3,1: 20:[5, 25] Operation: 54-29=25 Exploring Operation: 29-5=24, Resulting Numbers: [54, 24] Generated Node #0,3,2: 20:[54, 24] Operation: 29-5=24 Exploring Operation: 29+5=34, Resulting Numbers: [54, 34] Generated Node #0,3,3: 20:[54, 34] Operation: 29+5=34 Exploring Operation: 54-5=49, Resulting Numbers: [29, 49] Generated Node #0,3,4: 20:[29, 49] Operation: 54-5=49 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 20:[5, 25], Operations: ['67-13=54', '54-29=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,20 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[67, 13, 29, 5], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [29, 5, 54] Generated Node #0,3: 20:[29, 5, 54] Operation: 67-13=54 Moving to Node #0,3 Current State: 20:[29, 5, 54], Operations: ['67-13=54'] Exploring Operation: 54-29=25, Resulting Numbers: [5, 25] Generated Node #0,3,1: 20:[5, 25] Operation: 54-29=25 Moving to Node #0,3,1 Current State: 20:[5, 25], Operations: ['67-13=54', '54-29=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 38, 76, 90, 2 ]
46
[ "76/38=2", "90+2=92", "92/2=46" ]
Current State: 46:[38, 76, 90, 2], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [90, 2, 2] Generated Node #2: [90, 2, 2] from Operation: 76/38=2 Current State: 46:[90, 2, 2], Operations: ['76/38=2'] Exploring Operation: 90+2=92, Resulting Numbers: [92] 92,46 equal: Goal Reached Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[38, 76, 90, 2], Operations: [] Exploring Operation: 90-76=14, Resulting Numbers: [38, 2, 14] Generated Node #0,0: 46:[38, 2, 14] Operation: 90-76=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[38, 2, 14], Operations: ['90-76=14'] Exploring Operation: 38-14=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 46:[2, 24] Operation: 38-14=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[2, 24], Operations: ['90-76=14', '38-14=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 89, 39, 35, 12 ]
81
[ "89+39=128", "35+12=47", "128-47=81" ]
Current State: 81:[89, 39, 35, 12], Operations: [] Exploring Operation: 89+39=128, Resulting Numbers: [35, 12, 128] Generated Node #2: [35, 12, 128] from Operation: 89+39=128 Current State: 81:[35, 12, 128], Operations: ['89+39=128'] Exploring Operation: 35+12=47, Resulting Numbers: [128, 47] Generated Node #3: [128, 47] from Operation: 35+12=47 Current State: 81:[128, 47], Operations: ['89+39=128', '35+12=47'] Exploring Operation: 128-47=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[89, 39, 35, 12], Operations: [] Exploring Operation: 39-35=4, Resulting Numbers: [89, 12, 4] Generated Node #0,0: 81:[89, 12, 4] Operation: 39-35=4 Exploring Operation: 39-12=27, Resulting Numbers: [89, 35, 27] Generated Node #0,1: 81:[89, 35, 27] Operation: 39-12=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[89, 12, 4], Operations: ['39-35=4'] Exploring Operation: 89-4=85, Resulting Numbers: [12, 85] Generated Node #0,0,0: 81:[12, 85] Operation: 89-4=85 Exploring Operation: 89-12=77, Resulting Numbers: [4, 77] Generated Node #0,0,1: 81:[4, 77] Operation: 89-12=77 Moving to Node #0,0,1 Current State: 81:[4, 77], Operations: ['39-35=4', '89-12=77'] Exploring Operation: 4+77=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[89, 39, 35, 12], Operations: [] Exploring Operation: 39-35=4, Resulting Numbers: [89, 12, 4] Generated Node #0,0: 81:[89, 12, 4] Operation: 39-35=4 Moving to Node #0,0 Current State: 81:[89, 12, 4], Operations: ['39-35=4'] Exploring Operation: 89-12=77, Resulting Numbers: [4, 77] Generated Node #0,0,1: 81:[4, 77] Operation: 89-12=77 Moving to Node #0,0,1 Current State: 81:[4, 77], Operations: ['39-35=4', '89-12=77'] Exploring Operation: 4+77=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 83, 61, 67, 33 ]
12
[ "83-61=22", "67-33=34", "34-22=12" ]
Current State: 12:[83, 61, 67, 33], Operations: [] Exploring Operation: 83-61=22, Resulting Numbers: [67, 33, 22] Generated Node #2: [67, 33, 22] from Operation: 83-61=22 Current State: 12:[67, 33, 22], Operations: ['83-61=22'] Exploring Operation: 67-33=34, Resulting Numbers: [22, 34] Generated Node #3: [22, 34] from Operation: 67-33=34 Current State: 12:[22, 34], Operations: ['83-61=22', '67-33=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[83, 61, 67, 33], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [61, 33, 16] Generated Node #0,0: 12:[61, 33, 16] Operation: 83-67=16 Exploring Operation: 83-61=22, Resulting Numbers: [67, 33, 22] Generated Node #0,1: 12:[67, 33, 22] Operation: 83-61=22 Exploring Operation: 67-61=6, Resulting Numbers: [83, 33, 6] Generated Node #0,2: 12:[83, 33, 6] Operation: 67-61=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[61, 33, 16], Operations: ['83-67=16'] Exploring Operation: 61-16=45, Resulting Numbers: [33, 45] Generated Node #0,0,0: 12:[33, 45] Operation: 61-16=45 Exploring Operation: 61-33=28, Resulting Numbers: [16, 28] Generated Node #0,0,1: 12:[16, 28] Operation: 61-33=28 Exploring Operation: 33-16=17, Resulting Numbers: [61, 17] Generated Node #0,0,2: 12:[61, 17] Operation: 33-16=17 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[16, 28], Operations: ['83-67=16', '61-33=28'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[83, 61, 67, 33], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [61, 33, 16] Generated Node #0,0: 12:[61, 33, 16] Operation: 83-67=16 Moving to Node #0,0 Current State: 12:[61, 33, 16], Operations: ['83-67=16'] Exploring Operation: 61-33=28, Resulting Numbers: [16, 28] Generated Node #0,0,1: 12:[16, 28] Operation: 61-33=28 Moving to Node #0,0,1 Current State: 12:[16, 28], Operations: ['83-67=16', '61-33=28'] Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 64, 83, 91, 68 ]
42
[ "83-64=19", "91-68=23", "19+23=42" ]
Current State: 42:[64, 83, 91, 68], Operations: [] Exploring Operation: 83-64=19, Resulting Numbers: [91, 68, 19] Generated Node #2: [91, 68, 19] from Operation: 83-64=19 Current State: 42:[91, 68, 19], Operations: ['83-64=19'] Exploring Operation: 91-68=23, Resulting Numbers: [19, 23] Generated Node #3: [19, 23] from Operation: 91-68=23 Current State: 42:[19, 23], Operations: ['83-64=19', '91-68=23'] Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[64, 83, 91, 68], Operations: [] Exploring Operation: 91-83=8, Resulting Numbers: [64, 68, 8] Generated Node #0,0: 42:[64, 68, 8] Operation: 91-83=8 Exploring Operation: 91-68=23, Resulting Numbers: [64, 83, 23] Generated Node #0,1: 42:[64, 83, 23] Operation: 91-68=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[64, 68, 8], Operations: ['91-83=8'] Exploring Operation: 68-64=4, Resulting Numbers: [8, 4] Generated Node #0,0,0: 42:[8, 4] Operation: 68-64=4 Exploring Operation: 64/8=8, Resulting Numbers: [68, 8] Generated Node #0,0,1: 42:[68, 8] Operation: 64/8=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[8, 4], Operations: ['91-83=8', '68-64=4'] Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,42 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 #0,0,1 Current State: 42:[68, 8], Operations: ['91-83=8', '64/8=8'] Exploring Operation: 68+8=76, Resulting Numbers: [76] 76,42 unequal: No Solution Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,42 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 #0,1 Current State: 42:[64, 83, 23], Operations: ['91-68=23'] Exploring Operation: 83-23=60, Resulting Numbers: [64, 60] Generated Node #0,1,0: 42:[64, 60] Operation: 83-23=60 Exploring Operation: 83-64=19, Resulting Numbers: [23, 19] Generated Node #0,1,1: 42:[23, 19] Operation: 83-64=19 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[23, 19], Operations: ['91-68=23', '83-64=19'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,42 unequal: No Solution Exploring Operation: 23+19=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[64, 83, 91, 68], Operations: [] Exploring Operation: 91-68=23, Resulting Numbers: [64, 83, 23] Generated Node #0,1: 42:[64, 83, 23] Operation: 91-68=23 Moving to Node #0,1 Current State: 42:[64, 83, 23], Operations: ['91-68=23'] Exploring Operation: 83-64=19, Resulting Numbers: [23, 19] Generated Node #0,1,1: 42:[23, 19] Operation: 83-64=19 Moving to Node #0,1,1 Current State: 42:[23, 19], Operations: ['91-68=23', '83-64=19'] Exploring Operation: 23+19=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 80, 57, 23, 57 ]
23
[ "57-57=0", "80*0=0", "23+0=23" ]
Current State: 23:[80, 57, 23, 57], Operations: [] Exploring Operation: 57-57=0, Resulting Numbers: [80, 23, 0] Generated Node #2: [80, 23, 0] from Operation: 57-57=0 Current State: 23:[80, 23, 0], Operations: ['57-57=0'] Exploring Operation: 80*0=0, Resulting Numbers: [23, 0] Generated Node #3: [23, 0] from Operation: 80*0=0 Current State: 23:[23, 0], Operations: ['57-57=0', '80*0=0'] Exploring Operation: 23+0=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[80, 57, 23, 57], Operations: [] Exploring Operation: 80-57=23, Resulting Numbers: [23, 57, 23] Generated Node #0,0: 23:[23, 57, 23] Operation: 80-57=23 Exploring Operation: 80-57=23, Resulting Numbers: [57, 23, 23] Generated Node #0,1: 23:[57, 23, 23] Operation: 80-57=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[23, 57, 23], Operations: ['80-57=23'] Exploring Operation: 57-23=34, Resulting Numbers: [23, 34] Generated Node #0,0,0: 23:[23, 34] Operation: 57-23=34 Exploring Operation: 57-23=34, Resulting Numbers: [23, 34] Generated Node #0,0,1: 23:[23, 34] Operation: 57-23=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[23, 34], Operations: ['80-57=23', '57-23=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[23, 34], Operations: ['80-57=23', '57-23=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[57, 23, 23], Operations: ['80-57=23'] Exploring Operation: 57-23=34, Resulting Numbers: [23, 34] Generated Node #0,1,0: 23:[23, 34] Operation: 57-23=34 Exploring Operation: 57-23=34, Resulting Numbers: [23, 34] Generated Node #0,1,1: 23:[23, 34] Operation: 57-23=34 Moving to Node #0,1,0 Current State: 23:[23, 34], Operations: ['80-57=23', '57-23=34'] Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[23, 34], Operations: ['80-57=23', '57-23=34'] Exploring Operation: 23+34=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 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
[ 28, 15, 4, 33 ]
89
[ "28+15=43", "4*33=132", "132-43=89" ]
Current State: 89:[28, 15, 4, 33], Operations: [] Exploring Operation: 28+15=43, Resulting Numbers: [4, 33, 43] Generated Node #2: [4, 33, 43] from Operation: 28+15=43 Current State: 89:[4, 33, 43], Operations: ['28+15=43'] Exploring Operation: 4*33=132, Resulting Numbers: [43, 132] Generated Node #3: [43, 132] from Operation: 4*33=132 Current State: 89:[43, 132], Operations: ['28+15=43', '4*33=132'] Exploring Operation: 132-43=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[28, 15, 4, 33], Operations: [] Exploring Operation: 28*4=112, Resulting Numbers: [15, 33, 112] Generated Node #0,0: 89:[15, 33, 112] Operation: 28*4=112 Exploring Operation: 4*33=132, Resulting Numbers: [28, 15, 132] Generated Node #0,1: 89:[28, 15, 132] Operation: 4*33=132 Exploring Operation: 15*4=60, Resulting Numbers: [28, 33, 60] Generated Node #0,2: 89:[28, 33, 60] Operation: 15*4=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[28, 33, 60], Operations: ['15*4=60'] Exploring Operation: 28+60=88, Resulting Numbers: [33, 88] Generated Node #0,2,0: 89:[33, 88] Operation: 28+60=88 Exploring Operation: 33+60=93, Resulting Numbers: [28, 93] Generated Node #0,2,1: 89:[28, 93] Operation: 33+60=93 Exploring Operation: 28+33=61, Resulting Numbers: [60, 61] Generated Node #0,2,2: 89:[60, 61] Operation: 28+33=61 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 89:[33, 88], Operations: ['15*4=60', '28+60=88'] Exploring Operation: 33*88=2904, Resulting Numbers: [2904] 2904,89 unequal: No Solution Exploring Operation: 33+88=121, Resulting Numbers: [121] 121,89 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 89:[60, 61], Operations: ['15*4=60', '28+33=61'] Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 60*61=3660, Resulting Numbers: [3660] 3660,89 unequal: No Solution Exploring Operation: 60+61=121, Resulting Numbers: [121] 121,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 89:[28, 93], Operations: ['15*4=60', '33+60=93'] Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,89 unequal: No Solution Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,89 unequal: No Solution Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[15, 33, 112], Operations: ['28*4=112'] Exploring Operation: 112-33=79, Resulting Numbers: [15, 79] Generated Node #0,0,0: 89:[15, 79] Operation: 112-33=79 Exploring Operation: 15+33=48, Resulting Numbers: [112, 48] Generated Node #0,0,1: 89:[112, 48] Operation: 15+33=48 Exploring Operation: 112-15=97, Resulting Numbers: [33, 97] Generated Node #0,0,2: 89:[33, 97] Operation: 112-15=97 Moving to Node #0,0,1 Current State: 89:[112, 48], Operations: ['28*4=112', '15+33=48'] Exploring Operation: 112*48=5376, Resulting Numbers: [5376] 5376,89 unequal: No Solution Exploring Operation: 112+48=160, Resulting Numbers: [160] 160,89 unequal: No Solution Exploring Operation: 112-48=64, Resulting Numbers: [64] 64,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[33, 97], Operations: ['28*4=112', '112-15=97'] Exploring Operation: 33+97=130, Resulting Numbers: [130] 130,89 unequal: No Solution Exploring Operation: 97-33=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 33*97=3201, Resulting Numbers: [3201] 3201,89 unequal: No Solution Moving to Node #0,0,0 Current State: 89:[15, 79], Operations: ['28*4=112', '112-33=79'] Exploring Operation: 15+79=94, Resulting Numbers: [94] 94,89 unequal: No Solution Exploring Operation: 15*79=1185, Resulting Numbers: [1185] 1185,89 unequal: No Solution Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[28, 15, 132], Operations: ['4*33=132'] Exploring Operation: 28+15=43, Resulting Numbers: [132, 43] Generated Node #0,1,0: 89:[132, 43] Operation: 28+15=43 Exploring Operation: 132-28=104, Resulting Numbers: [15, 104] Generated Node #0,1,1: 89:[15, 104] Operation: 132-28=104 Exploring Operation: 132-15=117, Resulting Numbers: [28, 117] Generated Node #0,1,2: 89:[28, 117] Operation: 132-15=117 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[132, 43], Operations: ['4*33=132', '28+15=43'] Exploring Operation: 132+43=175, Resulting Numbers: [175] 175,89 unequal: No Solution Exploring Operation: 132*43=5676, Resulting Numbers: [5676] 5676,89 unequal: No Solution Exploring Operation: 132-43=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[28, 15, 4, 33], Operations: [] Exploring Operation: 4*33=132, Resulting Numbers: [28, 15, 132] Generated Node #0,1: 89:[28, 15, 132] Operation: 4*33=132 Moving to Node #0,1 Current State: 89:[28, 15, 132], Operations: ['4*33=132'] Exploring Operation: 28+15=43, Resulting Numbers: [132, 43] Generated Node #0,1,0: 89:[132, 43] Operation: 28+15=43 Moving to Node #0,1,0 Current State: 89:[132, 43], Operations: ['4*33=132', '28+15=43'] Exploring Operation: 132-43=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_3
sum_heuristic
[ 11, 99, 13, 17 ]
84
[ "99-11=88", "17-13=4", "88-4=84" ]
Current State: 84:[11, 99, 13, 17], Operations: [] Exploring Operation: 99-11=88, Resulting Numbers: [13, 17, 88] Generated Node #2: [13, 17, 88] from Operation: 99-11=88 Current State: 84:[13, 17, 88], Operations: ['99-11=88'] Exploring Operation: 17-13=4, Resulting Numbers: [88, 4] Generated Node #3: [88, 4] from Operation: 17-13=4 Current State: 84:[88, 4], Operations: ['99-11=88', '17-13=4'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[11, 99, 13, 17], Operations: [] Exploring Operation: 99-13=86, Resulting Numbers: [11, 17, 86] Generated Node #0,0: 84:[11, 17, 86] Operation: 99-13=86 Exploring Operation: 99/11=9, Resulting Numbers: [13, 17, 9] Generated Node #0,1: 84:[13, 17, 9] Operation: 99/11=9 Exploring Operation: 99-17=82, Resulting Numbers: [11, 13, 82] Generated Node #0,2: 84:[11, 13, 82] Operation: 99-17=82 Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[11, 13, 82], Operations: ['99-17=82'] Exploring Operation: 11+82=93, Resulting Numbers: [13, 93] Generated Node #0,2,0: 84:[13, 93] Operation: 11+82=93 Exploring Operation: 11+13=24, Resulting Numbers: [82, 24] Generated Node #0,2,1: 84:[82, 24] Operation: 11+13=24 Exploring Operation: 13-11=2, Resulting Numbers: [82, 2] Generated Node #0,2,2: 84:[82, 2] Operation: 13-11=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 84:[82, 2], Operations: ['99-17=82', '13-11=2'] Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,84 unequal: No Solution Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[11, 99, 13, 17], Operations: [] Exploring Operation: 99-17=82, Resulting Numbers: [11, 13, 82] Generated Node #0,2: 84:[11, 13, 82] Operation: 99-17=82 Moving to Node #0,2 Current State: 84:[11, 13, 82], Operations: ['99-17=82'] Exploring Operation: 13-11=2, Resulting Numbers: [82, 2] Generated Node #0,2,2: 84:[82, 2] Operation: 13-11=2 Moving to Node #0,2,2 Current State: 84:[82, 2], Operations: ['99-17=82', '13-11=2'] Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 70, 16, 63, 1 ]
66
[ "63+1=64", "64/16=4", "70-4=66" ]
Current State: 66:[70, 16, 63, 1], Operations: [] Exploring Operation: 63+1=64, Resulting Numbers: [70, 16, 64] Generated Node #2: [70, 16, 64] from Operation: 63+1=64 Current State: 66:[70, 16, 64], Operations: ['63+1=64'] Exploring Operation: 64/16=4, Resulting Numbers: [70, 4] Generated Node #3: [70, 4] from Operation: 64/16=4 Current State: 66:[70, 4], Operations: ['63+1=64', '64/16=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[70, 16, 63, 1], Operations: [] Exploring Operation: 70-1=69, Resulting Numbers: [16, 63, 69] Generated Node #0,0: 66:[16, 63, 69] Operation: 70-1=69 Exploring Operation: 16-1=15, Resulting Numbers: [70, 63, 15] Generated Node #0,1: 66:[70, 63, 15] Operation: 16-1=15 Exploring Operation: 70*1=70, Resulting Numbers: [16, 63, 70] Generated Node #0,2: 66:[16, 63, 70] Operation: 70*1=70 Exploring Operation: 63+1=64, Resulting Numbers: [70, 16, 64] Generated Node #0,3: 66:[70, 16, 64] Operation: 63+1=64 Exploring Operation: 70-63=7, Resulting Numbers: [16, 1, 7] Generated Node #0,4: 66:[16, 1, 7] Operation: 70-63=7 Moving to Node #0,4 Current State: 66:[16, 1, 7], Operations: ['70-63=7'] Exploring Operation: 16-7=9, Resulting Numbers: [1, 9] Generated Node #0,4,0: 66:[1, 9] Operation: 16-7=9 Exploring Operation: 16+1=17, Resulting Numbers: [7, 17] Generated Node #0,4,1: 66:[7, 17] Operation: 16+1=17 Exploring Operation: 16+7=23, Resulting Numbers: [1, 23] Generated Node #0,4,2: 66:[1, 23] Operation: 16+7=23 Exploring Operation: 7-1=6, Resulting Numbers: [16, 6] Generated Node #0,4,3: 66:[16, 6] Operation: 7-1=6 Exploring Operation: 16-1=15, Resulting Numbers: [7, 15] Generated Node #0,4,4: 66:[7, 15] Operation: 16-1=15 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 66:[1, 23], Operations: ['70-63=7', '16+7=23'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,66 unequal: No Solution Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,66 unequal: No Solution No 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: 66:[1, 9], Operations: ['70-63=7', '16-7=9'] Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,66 unequal: No Solution No 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: 66:[16, 6], Operations: ['70-63=7', '7-1=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,66 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,66 unequal: No Solution No 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: 66:[7, 15], Operations: ['70-63=7', '16-1=15'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,66 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,66 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,66 unequal: No Solution No 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: 66:[7, 17], Operations: ['70-63=7', '16+1=17'] Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,66 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,66 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: 66:[70, 63, 15], Operations: ['16-1=15'] Exploring Operation: 63+15=78, Resulting Numbers: [70, 78] Generated Node #0,1,0: 66:[70, 78] Operation: 63+15=78 Exploring Operation: 70+15=85, Resulting Numbers: [63, 85] Generated Node #0,1,1: 66:[63, 85] Operation: 70+15=85 Exploring Operation: 70-15=55, Resulting Numbers: [63, 55] Generated Node #0,1,2: 66:[63, 55] Operation: 70-15=55 Exploring Operation: 70-63=7, Resulting Numbers: [15, 7] Generated Node #0,1,3: 66:[15, 7] Operation: 70-63=7 Exploring Operation: 63-15=48, Resulting Numbers: [70, 48] Generated Node #0,1,4: 66:[70, 48] Operation: 63-15=48 Moving to Node #0,0 Current State: 66:[16, 63, 69], Operations: ['70-1=69'] Exploring Operation: 63-16=47, Resulting Numbers: [69, 47] Generated Node #0,0,0: 66:[69, 47] Operation: 63-16=47 Exploring Operation: 16+69=85, Resulting Numbers: [63, 85] Generated Node #0,0,1: 66:[63, 85] Operation: 16+69=85 Exploring Operation: 16+63=79, Resulting Numbers: [69, 79] Generated Node #0,0,2: 66:[69, 79] Operation: 16+63=79 Exploring Operation: 69-63=6, Resulting Numbers: [16, 6] Generated Node #0,0,3: 66:[16, 6] Operation: 69-63=6 Exploring Operation: 69-16=53, Resulting Numbers: [63, 53] Generated Node #0,0,4: 66:[63, 53] Operation: 69-16=53 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 66:[16, 6], Operations: ['70-1=69', '69-63=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,66 unequal: No Solution No 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: 66:[69, 79], Operations: ['70-1=69', '16+63=79'] Exploring Operation: 69+79=148, Resulting Numbers: [148] 148,66 unequal: No Solution Exploring Operation: 69*79=5451, Resulting Numbers: [5451] 5451,66 unequal: No Solution Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,66 unequal: No Solution No 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: 66:[63, 53], Operations: ['70-1=69', '69-16=53'] Exploring Operation: 63*53=3339, Resulting Numbers: [3339] 3339,66 unequal: No Solution Exploring Operation: 63-53=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 63+53=116, Resulting Numbers: [116] 116,66 unequal: No Solution No 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: 66:[69, 47], Operations: ['70-1=69', '63-16=47'] Exploring Operation: 69+47=116, Resulting Numbers: [116] 116,66 unequal: No Solution Exploring Operation: 69*47=3243, Resulting Numbers: [3243] 3243,66 unequal: No Solution Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,66 unequal: No Solution No 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: 66:[63, 85], Operations: ['70-1=69', '16+69=85'] Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 63*85=5355, Resulting Numbers: [5355] 5355,66 unequal: No Solution Exploring Operation: 63+85=148, Resulting Numbers: [148] 148,66 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: 66:[70, 16, 64], Operations: ['63+1=64'] Exploring Operation: 70-64=6, Resulting Numbers: [16, 6] Generated Node #0,3,0: 66:[16, 6] Operation: 70-64=6 Exploring Operation: 64/16=4, Resulting Numbers: [70, 4] Generated Node #0,3,1: 66:[70, 4] Operation: 64/16=4 Exploring Operation: 64-16=48, Resulting Numbers: [70, 48] Generated Node #0,3,2: 66:[70, 48] Operation: 64-16=48 Exploring Operation: 70-16=54, Resulting Numbers: [64, 54] Generated Node #0,3,3: 66:[64, 54] Operation: 70-16=54 Exploring Operation: 16+64=80, Resulting Numbers: [70, 80] Generated Node #0,3,4: 66:[70, 80] Operation: 16+64=80 Moving to Node #0,2 Current State: 66:[16, 63, 70], Operations: ['70*1=70'] Exploring Operation: 70-16=54, Resulting Numbers: [63, 54] Generated Node #0,2,0: 66:[63, 54] Operation: 70-16=54 Exploring Operation: 63-16=47, Resulting Numbers: [70, 47] Generated Node #0,2,1: 66:[70, 47] Operation: 63-16=47 Exploring Operation: 16+63=79, Resulting Numbers: [70, 79] Generated Node #0,2,2: 66:[70, 79] Operation: 16+63=79 Exploring Operation: 70-63=7, Resulting Numbers: [16, 7] Generated Node #0,2,3: 66:[16, 7] Operation: 70-63=7 Exploring Operation: 16+70=86, Resulting Numbers: [63, 86] Generated Node #0,2,4: 66:[63, 86] Operation: 16+70=86 Moving to Node #0,1,3 Current State: 66:[15, 7], Operations: ['16-1=15', '70-63=7'] Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,66 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,66 unequal: No Solution Moving to Node #0,3,0 Current State: 66:[16, 6], Operations: ['63+1=64', '70-64=6'] Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,66 unequal: No Solution Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,66 unequal: No Solution Moving to Node #0,3,1 Current State: 66:[70, 4], Operations: ['63+1=64', '64/16=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,66 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[70, 16, 63, 1], Operations: [] Exploring Operation: 63+1=64, Resulting Numbers: [70, 16, 64] Generated Node #0,3: 66:[70, 16, 64] Operation: 63+1=64 Moving to Node #0,3 Current State: 66:[70, 16, 64], Operations: ['63+1=64'] Exploring Operation: 64/16=4, Resulting Numbers: [70, 4] Generated Node #0,3,1: 66:[70, 4] Operation: 64/16=4 Moving to Node #0,3,1 Current State: 66:[70, 4], Operations: ['63+1=64', '64/16=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
0.935764
hs_5
mult_heuristic
[ 95, 85, 81, 5 ]
45
[ "95+85=180", "180/5=36", "81-36=45" ]
Current State: 45:[95, 85, 81, 5], Operations: [] Exploring Operation: 95+85=180, Resulting Numbers: [81, 5, 180] Generated Node #2: [81, 5, 180] from Operation: 95+85=180 Current State: 45:[81, 5, 180], Operations: ['95+85=180'] Exploring Operation: 180/5=36, Resulting Numbers: [81, 36] Generated Node #3: [81, 36] from Operation: 180/5=36 Current State: 45:[81, 36], Operations: ['95+85=180', '180/5=36'] Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[95, 85, 81, 5], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [95, 5, 4] Generated Node #0,0: 45:[95, 5, 4] Operation: 85-81=4 Exploring Operation: 95-81=14, Resulting Numbers: [85, 5, 14] Generated Node #0,1: 45:[85, 5, 14] Operation: 95-81=14 Exploring Operation: 95-85=10, Resulting Numbers: [81, 5, 10] Generated Node #0,2: 45:[81, 5, 10] Operation: 95-85=10 Moving to Node #0,2 Current State: 45:[81, 5, 10], Operations: ['95-85=10'] Exploring Operation: 81-10=71, Resulting Numbers: [5, 71] Generated Node #0,2,0: 45:[5, 71] Operation: 81-10=71 Exploring Operation: 5+10=15, Resulting Numbers: [81, 15] Generated Node #0,2,1: 45:[81, 15] Operation: 5+10=15 Exploring Operation: 81-5=76, Resulting Numbers: [10, 76] Generated Node #0,2,2: 45:[10, 76] Operation: 81-5=76 Moving to Node #0,1 Current State: 45:[85, 5, 14], Operations: ['95-81=14'] Exploring Operation: 85-14=71, Resulting Numbers: [5, 71] Generated Node #0,1,0: 45:[5, 71] Operation: 85-14=71 Exploring Operation: 85/5=17, Resulting Numbers: [14, 17] Generated Node #0,1,1: 45:[14, 17] Operation: 85/5=17 Exploring Operation: 85-5=80, Resulting Numbers: [14, 80] Generated Node #0,1,2: 45:[14, 80] Operation: 85-5=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[14, 17], Operations: ['95-81=14', '85/5=17'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,45 unequal: No Solution Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[5, 71], Operations: ['95-81=14', '85-14=71'] Exploring Operation: 5*71=355, Resulting Numbers: [355] 355,45 unequal: No Solution Exploring Operation: 5+71=76, Resulting Numbers: [76] 76,45 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[14, 80], Operations: ['95-81=14', '85-5=80'] Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 14+80=94, Resulting Numbers: [94] 94,45 unequal: No Solution Exploring Operation: 14*80=1120, Resulting Numbers: [1120] 1120,45 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: 45:[95, 5, 4], Operations: ['85-81=4'] Exploring Operation: 95/5=19, Resulting Numbers: [4, 19] Generated Node #0,0,0: 45:[4, 19] Operation: 95/5=19 Exploring Operation: 95-5=90, Resulting Numbers: [4, 90] Generated Node #0,0,1: 45:[4, 90] Operation: 95-5=90 Exploring Operation: 95-4=91, Resulting Numbers: [5, 91] Generated Node #0,0,2: 45:[5, 91] Operation: 95-4=91 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[4, 19], Operations: ['85-81=4', '95/5=19'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,45 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,45 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[4, 90], Operations: ['85-81=4', '95-5=90'] Exploring Operation: 4+90=94, Resulting Numbers: [94] 94,45 unequal: No Solution Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 4*90=360, Resulting Numbers: [360] 360,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[5, 91], Operations: ['85-81=4', '95-4=91'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 5+91=96, Resulting Numbers: [96] 96,45 unequal: No Solution Exploring Operation: 5*91=455, Resulting Numbers: [455] 455,45 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: 45:[5, 71], Operations: ['95-85=10', '81-10=71'] Exploring Operation: 5*71=355, Resulting Numbers: [355] 355,45 unequal: No Solution Exploring Operation: 5+71=76, Resulting Numbers: [76] 76,45 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[10, 76], Operations: ['95-85=10', '81-5=76'] Exploring Operation: 10+76=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 10*76=760, Resulting Numbers: [760] 760,45 unequal: No Solution Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[81, 15], Operations: ['95-85=10', '5+10=15'] Exploring Operation: 81+15=96, Resulting Numbers: [96] 96,45 unequal: No Solution Exploring Operation: 81*15=1215, Resulting Numbers: [1215] 1215,45 unequal: No Solution Exploring Operation: 81-15=66, Resulting Numbers: [66] 66,45 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 25, 98, 99, 14 ]
76
[ "25*98=2450", "2450/14=175", "175-99=76" ]
Current State: 76:[25, 98, 99, 14], Operations: [] Exploring Operation: 25*98=2450, Resulting Numbers: [99, 14, 2450] Generated Node #2: [99, 14, 2450] from Operation: 25*98=2450 Current State: 76:[99, 14, 2450], Operations: ['25*98=2450'] Exploring Operation: 2450/14=175, Resulting Numbers: [99, 175] Generated Node #3: [99, 175] from Operation: 2450/14=175 Current State: 76:[99, 175], Operations: ['25*98=2450', '2450/14=175'] Exploring Operation: 175-99=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[25, 98, 99, 14], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [25, 14, 1] Generated Node #0,0: 76:[25, 14, 1] Operation: 99-98=1 Exploring Operation: 99-25=74, Resulting Numbers: [98, 14, 74] Generated Node #0,1: 76:[98, 14, 74] Operation: 99-25=74 Moving to Node #0,0 Current State: 76:[25, 14, 1], Operations: ['99-98=1'] Exploring Operation: 25+14=39, Resulting Numbers: [1, 39] Generated Node #0,0,0: 76:[1, 39] Operation: 25+14=39 Exploring Operation: 25-14=11, Resulting Numbers: [1, 11] Generated Node #0,0,1: 76:[1, 11] Operation: 25-14=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[1, 39], Operations: ['99-98=1', '25+14=39'] Exploring Operation: 1*39=39, Resulting Numbers: [39] 39,76 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 76:[1, 11], Operations: ['99-98=1', '25-14=11'] Exploring Operation: 1+11=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 76:[98, 14, 74], Operations: ['99-25=74'] Exploring Operation: 98/14=7, Resulting Numbers: [74, 7] Generated Node #0,1,0: 76:[74, 7] Operation: 98/14=7 Exploring Operation: 98-14=84, Resulting Numbers: [74, 84] Generated Node #0,1,1: 76:[74, 84] Operation: 98-14=84 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 76:[74, 7], Operations: ['99-25=74', '98/14=7'] Exploring Operation: 74-7=67, Resulting Numbers: [67] 67,76 unequal: No Solution Exploring Operation: 74+7=81, Resulting Numbers: [81] 81,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 76:[74, 84], Operations: ['99-25=74', '98-14=84'] Exploring Operation: 84-74=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 74+84=158, Resulting Numbers: [158] 158,76 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
[ 54, 80, 52, 15 ]
97
[ "54+80=134", "52-15=37", "134-37=97" ]
Current State: 97:[54, 80, 52, 15], Operations: [] Exploring Operation: 54+80=134, Resulting Numbers: [52, 15, 134] Generated Node #2: [52, 15, 134] from Operation: 54+80=134 Current State: 97:[52, 15, 134], Operations: ['54+80=134'] Exploring Operation: 52-15=37, Resulting Numbers: [134, 37] Generated Node #3: [134, 37] from Operation: 52-15=37 Current State: 97:[134, 37], Operations: ['54+80=134', '52-15=37'] Exploring Operation: 134-37=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[54, 80, 52, 15], Operations: [] Exploring Operation: 80+15=95, Resulting Numbers: [54, 52, 95] Generated Node #0,0: 97:[54, 52, 95] Operation: 80+15=95 Exploring Operation: 54+15=69, Resulting Numbers: [80, 52, 69] Generated Node #0,1: 97:[80, 52, 69] Operation: 54+15=69 Exploring Operation: 52+15=67, Resulting Numbers: [54, 80, 67] Generated Node #0,2: 97:[54, 80, 67] Operation: 52+15=67 Exploring Operation: 54+52=106, Resulting Numbers: [80, 15, 106] Generated Node #0,3: 97:[80, 15, 106] Operation: 54+52=106 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[54, 52, 95], Operations: ['80+15=95'] Exploring Operation: 54+52=106, Resulting Numbers: [95, 106] Generated Node #0,0,0: 97:[95, 106] Operation: 54+52=106 Exploring Operation: 54-52=2, Resulting Numbers: [95, 2] Generated Node #0,0,1: 97:[95, 2] Operation: 54-52=2 Exploring Operation: 52+95=147, Resulting Numbers: [54, 147] Generated Node #0,0,2: 97:[54, 147] Operation: 52+95=147 Exploring Operation: 54+95=149, Resulting Numbers: [52, 149] Generated Node #0,0,3: 97:[52, 149] Operation: 54+95=149 Moving to Node #0,0,0 Current State: 97:[95, 106], Operations: ['80+15=95', '54+52=106'] Exploring Operation: 106-95=11, Resulting Numbers: [11] 11,97 unequal: No Solution Exploring Operation: 95+106=201, Resulting Numbers: [201] 201,97 unequal: No Solution Exploring Operation: 95*106=10070, Resulting Numbers: [10070] 10070,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[54, 147], Operations: ['80+15=95', '52+95=147'] Exploring Operation: 54*147=7938, Resulting Numbers: [7938] 7938,97 unequal: No Solution Exploring Operation: 54+147=201, Resulting Numbers: [201] 201,97 unequal: No Solution Exploring Operation: 147-54=93, Resulting Numbers: [93] 93,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[52, 149], Operations: ['80+15=95', '54+95=149'] Exploring Operation: 52*149=7748, Resulting Numbers: [7748] 7748,97 unequal: No Solution Exploring Operation: 52+149=201, Resulting Numbers: [201] 201,97 unequal: No Solution Exploring Operation: 149-52=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[54, 80, 52, 15], Operations: [] Exploring Operation: 80+15=95, Resulting Numbers: [54, 52, 95] Generated Node #0,0: 97:[54, 52, 95] Operation: 80+15=95 Moving to Node #0,0 Current State: 97:[54, 52, 95], Operations: ['80+15=95'] Exploring Operation: 54+95=149, Resulting Numbers: [52, 149] Generated Node #0,0,3: 97:[52, 149] Operation: 54+95=149 Moving to Node #0,0,3 Current State: 97:[52, 149], Operations: ['80+15=95', '54+95=149'] Exploring Operation: 149-52=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 52, 87, 21, 88 ]
72
[ "52+87=139", "88-21=67", "139-67=72" ]
Current State: 72:[52, 87, 21, 88], Operations: [] Exploring Operation: 52+87=139, Resulting Numbers: [21, 88, 139] Generated Node #2: [21, 88, 139] from Operation: 52+87=139 Current State: 72:[21, 88, 139], Operations: ['52+87=139'] Exploring Operation: 88-21=67, Resulting Numbers: [139, 67] Generated Node #3: [139, 67] from Operation: 88-21=67 Current State: 72:[139, 67], Operations: ['52+87=139', '88-21=67'] Exploring Operation: 139-67=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[52, 87, 21, 88], Operations: [] Exploring Operation: 88-52=36, Resulting Numbers: [87, 21, 36] Generated Node #0,0: 72:[87, 21, 36] Operation: 88-52=36 Moving to Node #0,0 Current State: 72:[87, 21, 36], Operations: ['88-52=36'] Exploring Operation: 87-21=66, Resulting Numbers: [36, 66] Generated Node #0,0,0: 72:[36, 66] Operation: 87-21=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[36, 66], Operations: ['88-52=36', '87-21=66'] Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,72 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
[ 8, 81, 78, 65 ]
89
[ "81-78=3", "8*3=24", "65+24=89" ]
Current State: 89:[8, 81, 78, 65], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [8, 65, 3] Generated Node #2: [8, 65, 3] from Operation: 81-78=3 Current State: 89:[8, 65, 3], Operations: ['81-78=3'] Exploring Operation: 8*3=24, Resulting Numbers: [65, 24] Generated Node #3: [65, 24] from Operation: 8*3=24 Current State: 89:[65, 24], Operations: ['81-78=3', '8*3=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[8, 81, 78, 65], Operations: [] Exploring Operation: 78-8=70, Resulting Numbers: [81, 65, 70] Generated Node #0,0: 89:[81, 65, 70] Operation: 78-8=70 Exploring Operation: 8+78=86, Resulting Numbers: [81, 65, 86] Generated Node #0,1: 89:[81, 65, 86] Operation: 8+78=86 Exploring Operation: 8+65=73, Resulting Numbers: [81, 78, 73] Generated Node #0,2: 89:[81, 78, 73] Operation: 8+65=73 Exploring Operation: 8+81=89, Resulting Numbers: [78, 65, 89] Generated Node #0,3: 89:[78, 65, 89] Operation: 8+81=89 Exploring Operation: 81-8=73, Resulting Numbers: [78, 65, 73] Generated Node #0,4: 89:[78, 65, 73] Operation: 81-8=73 Moving to Node #0,1 Current State: 89:[81, 65, 86], Operations: ['8+78=86'] Exploring Operation: 86-65=21, Resulting Numbers: [81, 21] Generated Node #0,1,0: 89:[81, 21] Operation: 86-65=21 Exploring Operation: 81+65=146, Resulting Numbers: [86, 146] Generated Node #0,1,1: 89:[86, 146] Operation: 81+65=146 Exploring Operation: 65+86=151, Resulting Numbers: [81, 151] Generated Node #0,1,2: 89:[81, 151] Operation: 65+86=151 Exploring Operation: 81-65=16, Resulting Numbers: [86, 16] Generated Node #0,1,3: 89:[86, 16] Operation: 81-65=16 Exploring Operation: 81+86=167, Resulting Numbers: [65, 167] Generated Node #0,1,4: 89:[65, 167] Operation: 81+86=167 Moving to Node #0,3 Current State: 89:[78, 65, 89], Operations: ['8+81=89'] Exploring Operation: 78-65=13, Resulting Numbers: [89, 13] Generated Node #0,3,0: 89:[89, 13] Operation: 78-65=13 Exploring Operation: 65+89=154, Resulting Numbers: [78, 154] Generated Node #0,3,1: 89:[78, 154] Operation: 65+89=154 Exploring Operation: 78+89=167, Resulting Numbers: [65, 167] Generated Node #0,3,2: 89:[65, 167] Operation: 78+89=167 Exploring Operation: 89-65=24, Resulting Numbers: [78, 24] Generated Node #0,3,3: 89:[78, 24] Operation: 89-65=24 Exploring Operation: 78+65=143, Resulting Numbers: [89, 143] Generated Node #0,3,4: 89:[89, 143] Operation: 78+65=143 Moving to Node #0,2 Current State: 89:[81, 78, 73], Operations: ['8+65=73'] Exploring Operation: 81-73=8, Resulting Numbers: [78, 8] Generated Node #0,2,0: 89:[78, 8] Operation: 81-73=8 Exploring Operation: 78+73=151, Resulting Numbers: [81, 151] Generated Node #0,2,1: 89:[81, 151] Operation: 78+73=151 Exploring Operation: 81+73=154, Resulting Numbers: [78, 154] Generated Node #0,2,2: 89:[78, 154] Operation: 81+73=154 Exploring Operation: 81+78=159, Resulting Numbers: [73, 159] Generated Node #0,2,3: 89:[73, 159] Operation: 81+78=159 Exploring Operation: 78-73=5, Resulting Numbers: [81, 5] Generated Node #0,2,4: 89:[81, 5] Operation: 78-73=5 Moving to Node #0,0 Current State: 89:[81, 65, 70], Operations: ['78-8=70'] Exploring Operation: 81+70=151, Resulting Numbers: [65, 151] Generated Node #0,0,0: 89:[65, 151] Operation: 81+70=151 Exploring Operation: 65+70=135, Resulting Numbers: [81, 135] Generated Node #0,0,1: 89:[81, 135] Operation: 65+70=135 Exploring Operation: 70-65=5, Resulting Numbers: [81, 5] Generated Node #0,0,2: 89:[81, 5] Operation: 70-65=5 Exploring Operation: 81+65=146, Resulting Numbers: [70, 146] Generated Node #0,0,3: 89:[70, 146] Operation: 81+65=146 Exploring Operation: 81-65=16, Resulting Numbers: [70, 16] Generated Node #0,0,4: 89:[70, 16] Operation: 81-65=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[81, 135], Operations: ['78-8=70', '65+70=135'] Exploring Operation: 135-81=54, Resulting Numbers: [54] 54,89 unequal: No Solution Exploring Operation: 81*135=10935, Resulting Numbers: [10935] 10935,89 unequal: No Solution Exploring Operation: 81+135=216, Resulting Numbers: [216] 216,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[70, 146], Operations: ['78-8=70', '81+65=146'] Exploring Operation: 146-70=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 70+146=216, Resulting Numbers: [216] 216,89 unequal: No Solution Exploring Operation: 70*146=10220, Resulting Numbers: [10220] 10220,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[65, 151], Operations: ['78-8=70', '81+70=151'] Exploring Operation: 65+151=216, Resulting Numbers: [216] 216,89 unequal: No Solution Exploring Operation: 151-65=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 65*151=9815, Resulting Numbers: [9815] 9815,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[81, 5], Operations: ['78-8=70', '70-65=5'] Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,89 unequal: No Solution Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 89:[70, 16], Operations: ['78-8=70', '81-65=16'] Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 70*16=1120, Resulting Numbers: [1120] 1120,89 unequal: No Solution Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 89:[78, 65, 73], Operations: ['81-8=73'] Exploring Operation: 65+73=138, Resulting Numbers: [78, 138] Generated Node #0,4,0: 89:[78, 138] Operation: 65+73=138 Exploring Operation: 78-65=13, Resulting Numbers: [73, 13] Generated Node #0,4,1: 89:[73, 13] Operation: 78-65=13 Exploring Operation: 78+73=151, Resulting Numbers: [65, 151] Generated Node #0,4,2: 89:[65, 151] Operation: 78+73=151 Exploring Operation: 73-65=8, Resulting Numbers: [78, 8] Generated Node #0,4,3: 89:[78, 8] Operation: 73-65=8 Exploring Operation: 78+65=143, Resulting Numbers: [73, 143] Generated Node #0,4,4: 89:[73, 143] Operation: 78+65=143 Moving to Node #0,3,4 Current State: 89:[89, 143], Operations: ['8+81=89', '78+65=143'] Exploring Operation: 89*143=12727, Resulting Numbers: [12727] 12727,89 unequal: No Solution Exploring Operation: 143-89=54, Resulting Numbers: [54] 54,89 unequal: No Solution Exploring Operation: 89+143=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[86, 146], Operations: ['8+78=86', '81+65=146'] Exploring Operation: 86*146=12556, Resulting Numbers: [12556] 12556,89 unequal: No Solution Exploring Operation: 146-86=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 86+146=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,4,0 Current State: 89:[78, 138], Operations: ['81-8=73', '65+73=138'] Exploring Operation: 138-78=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 78+138=216, Resulting Numbers: [216] 216,89 unequal: No Solution Exploring Operation: 78*138=10764, Resulting Numbers: [10764] 10764,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[81, 151], Operations: ['8+65=73', '78+73=151'] Exploring Operation: 81*151=12231, Resulting Numbers: [12231] 12231,89 unequal: No Solution Exploring Operation: 151-81=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 81+151=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[81, 151], Operations: ['8+78=86', '65+86=151'] Exploring Operation: 81*151=12231, Resulting Numbers: [12231] 12231,89 unequal: No Solution Exploring Operation: 151-81=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 81+151=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,4,4 Current State: 89:[73, 143], Operations: ['81-8=73', '78+65=143'] Exploring Operation: 143-73=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 73*143=10439, Resulting Numbers: [10439] 10439,89 unequal: No Solution Exploring Operation: 73+143=216, Resulting Numbers: [216] 216,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[89, 13], Operations: ['8+81=89', '78-65=13'] Exploring Operation: 89+13=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 89*13=1157, Resulting Numbers: [1157] 1157,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[81, 21], Operations: ['8+78=86', '86-65=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,89 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[78, 154], Operations: ['8+65=73', '81+73=154'] Exploring Operation: 154-78=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 78*154=12012, Resulting Numbers: [12012] 12012,89 unequal: No Solution Exploring Operation: 78+154=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[78, 24], Operations: ['8+81=89', '89-65=24'] Exploring Operation: 78-24=54, Resulting Numbers: [54] 54,89 unequal: No Solution Exploring Operation: 78+24=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 78*24=1872, Resulting Numbers: [1872] 1872,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[86, 16], Operations: ['8+78=86', '81-65=16'] Exploring Operation: 86*16=1376, Resulting Numbers: [1376] 1376,89 unequal: No Solution Exploring Operation: 86-16=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 86+16=102, Resulting Numbers: [102] 102,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[78, 154], Operations: ['8+81=89', '65+89=154'] Exploring Operation: 154-78=76, Resulting Numbers: [76] 76,89 unequal: No Solution Exploring Operation: 78*154=12012, Resulting Numbers: [12012] 12012,89 unequal: No Solution Exploring Operation: 78+154=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[73, 159], Operations: ['8+65=73', '81+78=159'] Exploring Operation: 73*159=11607, Resulting Numbers: [11607] 11607,89 unequal: No Solution Exploring Operation: 159-73=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 73+159=232, Resulting Numbers: [232] 232,89 unequal: No Solution Moving to Node #0,4,2 Current State: 89:[65, 151], Operations: ['81-8=73', '78+73=151'] Exploring Operation: 151-65=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 65+151=216, Resulting Numbers: [216] 216,89 unequal: No Solution Exploring Operation: 65*151=9815, Resulting Numbers: [9815] 9815,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[81, 5], Operations: ['8+65=73', '78-73=5'] Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,89 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[78, 8], Operations: ['8+65=73', '81-73=8'] Exploring Operation: 78-8=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 78*8=624, Resulting Numbers: [624] 624,89 unequal: No Solution Exploring Operation: 78+8=86, Resulting Numbers: [86] 86,89 unequal: No Solution Moving to Node #0,4,3 Current State: 89:[78, 8], Operations: ['81-8=73', '73-65=8'] Exploring Operation: 78-8=70, Resulting Numbers: [70] 70,89 unequal: No Solution Exploring Operation: 78+8=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 78*8=624, Resulting Numbers: [624] 624,89 unequal: No Solution Moving to Node #0,4,1 Current State: 89:[73, 13], Operations: ['81-8=73', '78-65=13'] Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,89 unequal: No Solution Exploring Operation: 73*13=949, Resulting Numbers: [949] 949,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[65, 167], Operations: ['8+81=89', '78+89=167'] Exploring Operation: 65*167=10855, Resulting Numbers: [10855] 10855,89 unequal: No Solution Exploring Operation: 65+167=232, Resulting Numbers: [232] 232,89 unequal: No Solution Exploring Operation: 167-65=102, Resulting Numbers: [102] 102,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[65, 167], Operations: ['8+78=86', '81+86=167'] Exploring Operation: 65+167=232, Resulting Numbers: [232] 232,89 unequal: No Solution Exploring Operation: 167-65=102, Resulting Numbers: [102] 102,89 unequal: No Solution Exploring Operation: 65*167=10855, Resulting Numbers: [10855] 10855,89 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 23, 22, 32, 62 ]
95
[ "23-22=1", "32+62=94", "1+94=95" ]
Current State: 95:[23, 22, 32, 62], Operations: [] Exploring Operation: 23-22=1, Resulting Numbers: [32, 62, 1] Generated Node #2: [32, 62, 1] from Operation: 23-22=1 Current State: 95:[32, 62, 1], Operations: ['23-22=1'] Exploring Operation: 32+62=94, Resulting Numbers: [1, 94] Generated Node #3: [1, 94] from Operation: 32+62=94 Current State: 95:[1, 94], Operations: ['23-22=1', '32+62=94'] Exploring Operation: 1+94=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[23, 22, 32, 62], Operations: [] Exploring Operation: 22+62=84, Resulting Numbers: [23, 32, 84] Generated Node #0,0: 95:[23, 32, 84] Operation: 22+62=84 Exploring Operation: 23+62=85, Resulting Numbers: [22, 32, 85] Generated Node #0,1: 95:[22, 32, 85] Operation: 23+62=85 Exploring Operation: 32+62=94, Resulting Numbers: [23, 22, 94] Generated Node #0,2: 95:[23, 22, 94] Operation: 32+62=94 Exploring Operation: 62-32=30, Resulting Numbers: [23, 22, 30] Generated Node #0,3: 95:[23, 22, 30] Operation: 62-32=30 Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[23, 22, 94], Operations: ['32+62=94'] Exploring Operation: 23+22=45, Resulting Numbers: [94, 45] Generated Node #0,2,0: 95:[94, 45] Operation: 23+22=45 Exploring Operation: 23+94=117, Resulting Numbers: [22, 117] Generated Node #0,2,1: 95:[22, 117] Operation: 23+94=117 Exploring Operation: 23-22=1, Resulting Numbers: [94, 1] Generated Node #0,2,2: 95:[94, 1] Operation: 23-22=1 Exploring Operation: 22+94=116, Resulting Numbers: [23, 116] Generated Node #0,2,3: 95:[23, 116] Operation: 22+94=116 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 95:[94, 1], Operations: ['32+62=94', '23-22=1'] Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,95 unequal: No Solution Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,95 unequal: No Solution Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,95 unequal: No Solution Exploring Operation: 94+1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[23, 22, 32, 62], Operations: [] Exploring Operation: 32+62=94, Resulting Numbers: [23, 22, 94] Generated Node #0,2: 95:[23, 22, 94] Operation: 32+62=94 Moving to Node #0,2 Current State: 95:[23, 22, 94], Operations: ['32+62=94'] Exploring Operation: 23-22=1, Resulting Numbers: [94, 1] Generated Node #0,2,2: 95:[94, 1] Operation: 23-22=1 Moving to Node #0,2,2 Current State: 95:[94, 1], Operations: ['32+62=94', '23-22=1'] Exploring Operation: 94+1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 66, 32, 35, 26 ]
95
[ "66-32=34", "35+26=61", "34+61=95" ]
Current State: 95:[66, 32, 35, 26], Operations: [] Exploring Operation: 66-32=34, Resulting Numbers: [35, 26, 34] Generated Node #2: [35, 26, 34] from Operation: 66-32=34 Current State: 95:[35, 26, 34], Operations: ['66-32=34'] Exploring Operation: 35+26=61, Resulting Numbers: [34, 61] Generated Node #3: [34, 61] from Operation: 35+26=61 Current State: 95:[34, 61], Operations: ['66-32=34', '35+26=61'] Exploring Operation: 34+61=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[66, 32, 35, 26], Operations: [] Exploring Operation: 66+32=98, Resulting Numbers: [35, 26, 98] Generated Node #0,0: 95:[35, 26, 98] Operation: 66+32=98 Exploring Operation: 66-35=31, Resulting Numbers: [32, 26, 31] Generated Node #0,1: 95:[32, 26, 31] Operation: 66-35=31 Exploring Operation: 66+35=101, Resulting Numbers: [32, 26, 101] Generated Node #0,2: 95:[32, 26, 101] Operation: 66+35=101 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[35, 26, 98], Operations: ['66+32=98'] Exploring Operation: 35+26=61, Resulting Numbers: [98, 61] Generated Node #0,0,0: 95:[98, 61] Operation: 35+26=61 Exploring Operation: 35-26=9, Resulting Numbers: [98, 9] Generated Node #0,0,1: 95:[98, 9] Operation: 35-26=9 Exploring Operation: 98-35=63, Resulting Numbers: [26, 63] Generated Node #0,0,2: 95:[26, 63] Operation: 98-35=63 Moving to Node #0,0,1 Current State: 95:[98, 9], Operations: ['66+32=98', '35-26=9'] Exploring Operation: 98*9=882, Resulting Numbers: [882] 882,95 unequal: No Solution Exploring Operation: 98-9=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 98+9=107, Resulting Numbers: [107] 107,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[98, 61], Operations: ['66+32=98', '35+26=61'] Exploring Operation: 98*61=5978, Resulting Numbers: [5978] 5978,95 unequal: No Solution Exploring Operation: 98+61=159, Resulting Numbers: [159] 159,95 unequal: No Solution Exploring Operation: 98-61=37, Resulting Numbers: [37] 37,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[26, 63], Operations: ['66+32=98', '98-35=63'] Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,95 unequal: No Solution Exploring Operation: 26*63=1638, Resulting Numbers: [1638] 1638,95 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[32, 26, 101], Operations: ['66+35=101'] Exploring Operation: 101-26=75, Resulting Numbers: [32, 75] Generated Node #0,2,0: 95:[32, 75] Operation: 101-26=75 Exploring Operation: 32-26=6, Resulting Numbers: [101, 6] Generated Node #0,2,1: 95:[101, 6] Operation: 32-26=6 Exploring Operation: 101-32=69, Resulting Numbers: [26, 69] Generated Node #0,2,2: 95:[26, 69] Operation: 101-32=69 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 95:[101, 6], Operations: ['66+35=101', '32-26=6'] Exploring Operation: 101-6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[66, 32, 35, 26], Operations: [] Exploring Operation: 66+35=101, Resulting Numbers: [32, 26, 101] Generated Node #0,2: 95:[32, 26, 101] Operation: 66+35=101 Moving to Node #0,2 Current State: 95:[32, 26, 101], Operations: ['66+35=101'] Exploring Operation: 32-26=6, Resulting Numbers: [101, 6] Generated Node #0,2,1: 95:[101, 6] Operation: 32-26=6 Moving to Node #0,2,1 Current State: 95:[101, 6], Operations: ['66+35=101', '32-26=6'] Exploring Operation: 101-6=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 10, 92, 81, 15 ]
40
[ "92-81=11", "15-11=4", "10*4=40" ]
Current State: 40:[10, 92, 81, 15], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [10, 15, 11] Generated Node #2: [10, 15, 11] from Operation: 92-81=11 Current State: 40:[10, 15, 11], Operations: ['92-81=11'] Exploring Operation: 15-11=4, Resulting Numbers: [10, 4] Generated Node #3: [10, 4] from Operation: 15-11=4 Current State: 40:[10, 4], Operations: ['92-81=11', '15-11=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[10, 92, 81, 15], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [10, 15, 11] Generated Node #0,0: 40:[10, 15, 11] Operation: 92-81=11 Exploring Operation: 92-15=77, Resulting Numbers: [10, 81, 77] Generated Node #0,1: 40:[10, 81, 77] Operation: 92-15=77 Exploring Operation: 81-15=66, Resulting Numbers: [10, 92, 66] Generated Node #0,2: 40:[10, 92, 66] Operation: 81-15=66 Moving to Node #0,0 Current State: 40:[10, 15, 11], Operations: ['92-81=11'] Exploring Operation: 10+15=25, Resulting Numbers: [11, 25] Generated Node #0,0,0: 40:[11, 25] Operation: 10+15=25 Exploring Operation: 15-10=5, Resulting Numbers: [11, 5] Generated Node #0,0,1: 40:[11, 5] Operation: 15-10=5 Exploring Operation: 15-11=4, Resulting Numbers: [10, 4] Generated Node #0,0,2: 40:[10, 4] Operation: 15-11=4 Moving to Node #0,1 Current State: 40:[10, 81, 77], Operations: ['92-15=77'] Exploring Operation: 81-77=4, Resulting Numbers: [10, 4] Generated Node #0,1,0: 40:[10, 4] Operation: 81-77=4 Exploring Operation: 77-10=67, Resulting Numbers: [81, 67] Generated Node #0,1,1: 40:[81, 67] Operation: 77-10=67 Exploring Operation: 81-10=71, Resulting Numbers: [77, 71] Generated Node #0,1,2: 40:[77, 71] Operation: 81-10=71 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[10, 4], Operations: ['92-15=77', '81-77=4'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,40 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[10, 92, 81, 15], Operations: [] Exploring Operation: 92-15=77, Resulting Numbers: [10, 81, 77] Generated Node #0,1: 40:[10, 81, 77] Operation: 92-15=77 Moving to Node #0,1 Current State: 40:[10, 81, 77], Operations: ['92-15=77'] Exploring Operation: 81-77=4, Resulting Numbers: [10, 4] Generated Node #0,1,0: 40:[10, 4] Operation: 81-77=4 Moving to Node #0,1,0 Current State: 40:[10, 4], Operations: ['92-15=77', '81-77=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 82, 2, 27, 38 ]
36
[ "82-27=55", "38/2=19", "55-19=36" ]
Current State: 36:[82, 2, 27, 38], Operations: [] Exploring Operation: 82-27=55, Resulting Numbers: [2, 38, 55] Generated Node #2: [2, 38, 55] from Operation: 82-27=55 Current State: 36:[2, 38, 55], Operations: ['82-27=55'] Exploring Operation: 38/2=19, Resulting Numbers: [55, 19] Generated Node #3: [55, 19] from Operation: 38/2=19 Current State: 36:[55, 19], Operations: ['82-27=55', '38/2=19'] Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[82, 2, 27, 38], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [27, 38, 41] Generated Node #0,0: 36:[27, 38, 41] Operation: 82/2=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[27, 38, 41], Operations: ['82/2=41'] Exploring Operation: 41-27=14, Resulting Numbers: [38, 14] Generated Node #0,0,0: 36:[38, 14] Operation: 41-27=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[38, 14], Operations: ['82/2=41', '41-27=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,36 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
[ 1, 3, 11, 79 ]
83
[ "1+11=12", "12/3=4", "79+4=83" ]
Current State: 83:[1, 3, 11, 79], Operations: [] Exploring Operation: 1+11=12, Resulting Numbers: [3, 79, 12] Generated Node #2: [3, 79, 12] from Operation: 1+11=12 Current State: 83:[3, 79, 12], Operations: ['1+11=12'] Exploring Operation: 12/3=4, Resulting Numbers: [79, 4] Generated Node #3: [79, 4] from Operation: 12/3=4 Current State: 83:[79, 4], Operations: ['1+11=12', '12/3=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[1, 3, 11, 79], Operations: [] Exploring Operation: 3*11=33, Resulting Numbers: [1, 79, 33] Generated Node #0,0: 83:[1, 79, 33] Operation: 3*11=33 Exploring Operation: 1+3=4, Resulting Numbers: [11, 79, 4] Generated Node #0,1: 83:[11, 79, 4] Operation: 1+3=4 Moving to Node #0,0 Current State: 83:[1, 79, 33], Operations: ['3*11=33'] Exploring Operation: 1+33=34, Resulting Numbers: [79, 34] Generated Node #0,0,0: 83:[79, 34] Operation: 1+33=34 Exploring Operation: 1+79=80, Resulting Numbers: [33, 80] Generated Node #0,0,1: 83:[33, 80] Operation: 1+79=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[79, 34], Operations: ['3*11=33', '1+33=34'] Exploring Operation: 79+34=113, Resulting Numbers: [113] 113,83 unequal: No Solution Exploring Operation: 79-34=45, Resulting Numbers: [45] 45,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[33, 80], Operations: ['3*11=33', '1+79=80'] Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 33+80=113, Resulting Numbers: [113] 113,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[11, 79, 4], Operations: ['1+3=4'] Exploring Operation: 11*4=44, Resulting Numbers: [79, 44] Generated Node #0,1,0: 83:[79, 44] Operation: 11*4=44 Exploring Operation: 11+4=15, Resulting Numbers: [79, 15] Generated Node #0,1,1: 83:[79, 15] Operation: 11+4=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[79, 44], Operations: ['1+3=4', '11*4=44'] Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,83 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[79, 15], Operations: ['1+3=4', '11+4=15'] Exploring Operation: 79+15=94, Resulting Numbers: [94] 94,83 unequal: No Solution Exploring Operation: 79-15=64, Resulting Numbers: [64] 64,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 13, 40, 9, 36 ]
19
[ "13-9=4", "40+36=76", "76/4=19" ]
Current State: 19:[13, 40, 9, 36], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [40, 36, 4] Generated Node #2: [40, 36, 4] from Operation: 13-9=4 Current State: 19:[40, 36, 4], Operations: ['13-9=4'] Exploring Operation: 40+36=76, Resulting Numbers: [4, 76] Generated Node #3: [4, 76] from Operation: 40+36=76 Current State: 19:[4, 76], Operations: ['13-9=4', '40+36=76'] Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[13, 40, 9, 36], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [13, 9, 4] Generated Node #0,0: 19:[13, 9, 4] Operation: 40-36=4 Moving to Node #0,0 Current State: 19:[13, 9, 4], Operations: ['40-36=4'] Exploring Operation: 13+4=17, Resulting Numbers: [9, 17] Generated Node #0,0,0: 19:[9, 17] Operation: 13+4=17 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[9, 17], Operations: ['40-36=4', '13+4=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,19 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
[ 10, 90, 26, 20 ]
58
[ "20/10=2", "90+26=116", "116/2=58" ]
Current State: 58:[10, 90, 26, 20], Operations: [] Exploring Operation: 20/10=2, Resulting Numbers: [90, 26, 2] Generated Node #2: [90, 26, 2] from Operation: 20/10=2 Current State: 58:[90, 26, 2], Operations: ['20/10=2'] Exploring Operation: 90+26=116, Resulting Numbers: [2, 116] Generated Node #3: [2, 116] from Operation: 90+26=116 Current State: 58:[2, 116], Operations: ['20/10=2', '90+26=116'] Exploring Operation: 116/2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[10, 90, 26, 20], Operations: [] Exploring Operation: 90-20=70, Resulting Numbers: [10, 26, 70] Generated Node #0,0: 58:[10, 26, 70] Operation: 90-20=70 Exploring Operation: 90-26=64, Resulting Numbers: [10, 20, 64] Generated Node #0,1: 58:[10, 20, 64] Operation: 90-26=64 Exploring Operation: 90/10=9, Resulting Numbers: [26, 20, 9] Generated Node #0,2: 58:[26, 20, 9] Operation: 90/10=9 Exploring Operation: 20/10=2, Resulting Numbers: [90, 26, 2] Generated Node #0,3: 58:[90, 26, 2] Operation: 20/10=2 Exploring Operation: 90-10=80, Resulting Numbers: [26, 20, 80] Generated Node #0,4: 58:[26, 20, 80] Operation: 90-10=80 Moving to Node #0,2 Current State: 58:[26, 20, 9], Operations: ['90/10=9'] Exploring Operation: 20-9=11, Resulting Numbers: [26, 11] Generated Node #0,2,0: 58:[26, 11] Operation: 20-9=11 Exploring Operation: 26+20=46, Resulting Numbers: [9, 46] Generated Node #0,2,1: 58:[9, 46] Operation: 26+20=46 Exploring Operation: 26+9=35, Resulting Numbers: [20, 35] Generated Node #0,2,2: 58:[20, 35] Operation: 26+9=35 Exploring Operation: 20+9=29, Resulting Numbers: [26, 29] Generated Node #0,2,3: 58:[26, 29] Operation: 20+9=29 Exploring Operation: 26-20=6, Resulting Numbers: [9, 6] Generated Node #0,2,4: 58:[9, 6] Operation: 26-20=6 Moving to Node #0,1 Current State: 58:[10, 20, 64], Operations: ['90-26=64'] Exploring Operation: 64-10=54, Resulting Numbers: [20, 54] Generated Node #0,1,0: 58:[20, 54] Operation: 64-10=54 Exploring Operation: 20/10=2, Resulting Numbers: [64, 2] Generated Node #0,1,1: 58:[64, 2] Operation: 20/10=2 Exploring Operation: 64-20=44, Resulting Numbers: [10, 44] Generated Node #0,1,2: 58:[10, 44] Operation: 64-20=44 Exploring Operation: 20-10=10, Resulting Numbers: [64, 10] Generated Node #0,1,3: 58:[64, 10] Operation: 20-10=10 Exploring Operation: 10+20=30, Resulting Numbers: [64, 30] Generated Node #0,1,4: 58:[64, 30] Operation: 10+20=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 58:[64, 2], Operations: ['90-26=64', '20/10=2'] Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,58 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,58 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,58 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,58 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 #0,1,4 Current State: 58:[64, 30], Operations: ['90-26=64', '10+20=30'] Exploring Operation: 64*30=1920, Resulting Numbers: [1920] 1920,58 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,58 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 #0,1,0 Current State: 58:[20, 54], Operations: ['90-26=64', '64-10=54'] Exploring Operation: 20*54=1080, Resulting Numbers: [1080] 1080,58 unequal: No Solution Exploring Operation: 20+54=74, Resulting Numbers: [74] 74,58 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,58 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 #0,1,3 Current State: 58:[64, 10], Operations: ['90-26=64', '20-10=10'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,58 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,58 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 #0,1,2 Current State: 58:[10, 44], Operations: ['90-26=64', '64-20=44'] Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,58 unequal: No Solution Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,58 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: 58:[10, 26, 70], Operations: ['90-20=70'] Exploring Operation: 10+26=36, Resulting Numbers: [70, 36] Generated Node #0,0,0: 58:[70, 36] Operation: 10+26=36 Exploring Operation: 70-26=44, Resulting Numbers: [10, 44] Generated Node #0,0,1: 58:[10, 44] Operation: 70-26=44 Exploring Operation: 70-10=60, Resulting Numbers: [26, 60] Generated Node #0,0,2: 58:[26, 60] Operation: 70-10=60 Exploring Operation: 70/10=7, Resulting Numbers: [26, 7] Generated Node #0,0,3: 58:[26, 7] Operation: 70/10=7 Exploring Operation: 26-10=16, Resulting Numbers: [70, 16] Generated Node #0,0,4: 58:[70, 16] Operation: 26-10=16 Moving to Node #0,4 Current State: 58:[26, 20, 80], Operations: ['90-10=80'] Exploring Operation: 26+20=46, Resulting Numbers: [80, 46] Generated Node #0,4,0: 58:[80, 46] Operation: 26+20=46 Exploring Operation: 26-20=6, Resulting Numbers: [80, 6] Generated Node #0,4,1: 58:[80, 6] Operation: 26-20=6 Exploring Operation: 80-20=60, Resulting Numbers: [26, 60] Generated Node #0,4,2: 58:[26, 60] Operation: 80-20=60 Exploring Operation: 80-26=54, Resulting Numbers: [20, 54] Generated Node #0,4,3: 58:[20, 54] Operation: 80-26=54 Exploring Operation: 80/20=4, Resulting Numbers: [26, 4] Generated Node #0,4,4: 58:[26, 4] Operation: 80/20=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 58:[26, 60], Operations: ['90-10=80', '80-20=60'] Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,58 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,58 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 #0,4,4 Current State: 58:[26, 4], Operations: ['90-10=80', '80/20=4'] Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,58 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,58 unequal: No Solution Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,58 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 #0,4,3 Current State: 58:[20, 54], Operations: ['90-10=80', '80-26=54'] Exploring Operation: 20*54=1080, Resulting Numbers: [1080] 1080,58 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 20+54=74, Resulting Numbers: [74] 74,58 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 #0,4,1 Current State: 58:[80, 6], Operations: ['90-10=80', '26-20=6'] Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,58 unequal: No Solution Exploring Operation: 80*6=480, Resulting Numbers: [480] 480,58 unequal: No Solution Exploring Operation: 80+6=86, Resulting Numbers: [86] 86,58 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 #0,4,0 Current State: 58:[80, 46], Operations: ['90-10=80', '26+20=46'] Exploring Operation: 80*46=3680, Resulting Numbers: [3680] 3680,58 unequal: No Solution Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,58 unequal: No Solution Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,58 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: 58:[90, 26, 2], Operations: ['20/10=2'] Exploring Operation: 90-26=64, Resulting Numbers: [2, 64] Generated Node #0,3,0: 58:[2, 64] Operation: 90-26=64 Exploring Operation: 26+2=28, Resulting Numbers: [90, 28] Generated Node #0,3,1: 58:[90, 28] Operation: 26+2=28 Exploring Operation: 90+2=92, Resulting Numbers: [26, 92] Generated Node #0,3,2: 58:[26, 92] Operation: 90+2=92 Exploring Operation: 90-2=88, Resulting Numbers: [26, 88] Generated Node #0,3,3: 58:[26, 88] Operation: 90-2=88 Exploring Operation: 90/2=45, Resulting Numbers: [26, 45] Generated Node #0,3,4: 58:[26, 45] Operation: 90/2=45 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 58:[2, 64], Operations: ['20/10=2', '90-26=64'] Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,58 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,58 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,58 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,58 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 #0,3,4 Current State: 58:[26, 45], Operations: ['20/10=2', '90/2=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,58 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,58 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,58 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 #0,3,1 Current State: 58:[90, 28], Operations: ['20/10=2', '26+2=28'] Exploring Operation: 90*28=2520, Resulting Numbers: [2520] 2520,58 unequal: No Solution Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,58 unequal: No Solution Exploring Operation: 90+28=118, Resulting Numbers: [118] 118,58 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 #0,3,3 Current State: 58:[26, 88], Operations: ['20/10=2', '90-2=88'] Exploring Operation: 26*88=2288, Resulting Numbers: [2288] 2288,58 unequal: No Solution Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,58 unequal: No Solution Exploring Operation: 26+88=114, Resulting Numbers: [114] 114,58 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 #0,3,2 Current State: 58:[26, 92], Operations: ['20/10=2', '90+2=92'] Exploring Operation: 26+92=118, Resulting Numbers: [118] 118,58 unequal: No Solution Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,58 unequal: No Solution Exploring Operation: 26*92=2392, Resulting Numbers: [2392] 2392,58 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: 58:[26, 29], Operations: ['90/10=9', '20+9=29'] Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,58 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[26, 60], Operations: ['90-20=70', '70-10=60'] Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,58 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,58 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,58 unequal: No Solution Moving to Node #0,0,3 Current State: 58:[26, 7], Operations: ['90-20=70', '70/10=7'] Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,58 unequal: No Solution Exploring Operation: 26+7=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,58 unequal: No Solution Moving to Node #0,2,4 Current State: 58:[9, 6], Operations: ['90/10=9', '26-20=6'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 9+6=15, Resulting Numbers: [15] 15,58 unequal: No Solution Exploring Operation: 9*6=54, Resulting Numbers: [54] 54,58 unequal: No Solution Moving to Node #0,2,0 Current State: 58:[26, 11], Operations: ['90/10=9', '20-9=11'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,58 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,58 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,58 unequal: No Solution Moving to Node #0,2,2 Current State: 58:[20, 35], Operations: ['90/10=9', '26+9=35'] Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,58 unequal: No Solution Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,58 unequal: No Solution Moving to Node #0,2,1 Current State: 58:[9, 46], Operations: ['90/10=9', '26+20=46'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,58 unequal: No Solution Exploring Operation: 9+46=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 9*46=414, Resulting Numbers: [414] 414,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[70, 36], Operations: ['90-20=70', '10+26=36'] Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,58 unequal: No Solution Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[10, 44], Operations: ['90-20=70', '70-26=44'] Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,58 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,58 unequal: No Solution Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,58 unequal: No Solution Moving to Node #0,0,4 Current State: 58:[70, 16], Operations: ['90-20=70', '26-10=16'] Exploring Operation: 70+16=86, Resulting Numbers: [86] 86,58 unequal: No Solution Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,58 unequal: No Solution Exploring Operation: 70*16=1120, Resulting Numbers: [1120] 1120,58 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 22, 20, 68, 31 ]
90
[ "68+31=99", "20*99=1980", "1980/22=90" ]
Current State: 90:[22, 20, 68, 31], Operations: [] Exploring Operation: 68+31=99, Resulting Numbers: [22, 20, 99] Generated Node #2: [22, 20, 99] from Operation: 68+31=99 Current State: 90:[22, 20, 99], Operations: ['68+31=99'] Exploring Operation: 20*99=1980, Resulting Numbers: [22, 1980] Generated Node #3: [22, 1980] from Operation: 20*99=1980 Current State: 90:[22, 1980], Operations: ['68+31=99', '20*99=1980'] Exploring Operation: 1980/22=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[22, 20, 68, 31], Operations: [] Exploring Operation: 22+68=90, Resulting Numbers: [20, 31, 90] Generated Node #0,0: 90:[20, 31, 90] Operation: 22+68=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[20, 31, 90], Operations: ['22+68=90'] Exploring Operation: 31-20=11, Resulting Numbers: [90, 11] Generated Node #0,0,0: 90:[90, 11] Operation: 31-20=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[90, 11], Operations: ['22+68=90', '31-20=11'] Exploring Operation: 90+11=101, Resulting Numbers: [101] 101,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 53, 19, 54, 49 ]
67
[ "53+19=72", "54-49=5", "72-5=67" ]
Current State: 67:[53, 19, 54, 49], Operations: [] Exploring Operation: 53+19=72, Resulting Numbers: [54, 49, 72] Generated Node #2: [54, 49, 72] from Operation: 53+19=72 Current State: 67:[54, 49, 72], Operations: ['53+19=72'] Exploring Operation: 54-49=5, Resulting Numbers: [72, 5] Generated Node #3: [72, 5] from Operation: 54-49=5 Current State: 67:[72, 5], Operations: ['53+19=72', '54-49=5'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[53, 19, 54, 49], Operations: [] Exploring Operation: 53-19=34, Resulting Numbers: [54, 49, 34] Generated Node #0,0: 67:[54, 49, 34] Operation: 53-19=34 Exploring Operation: 19+54=73, Resulting Numbers: [53, 49, 73] Generated Node #0,1: 67:[53, 49, 73] Operation: 19+54=73 Exploring Operation: 53+19=72, Resulting Numbers: [54, 49, 72] Generated Node #0,2: 67:[54, 49, 72] Operation: 53+19=72 Exploring Operation: 19+49=68, Resulting Numbers: [53, 54, 68] Generated Node #0,3: 67:[53, 54, 68] Operation: 19+49=68 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[53, 54, 68], Operations: ['19+49=68'] Exploring Operation: 53+54=107, Resulting Numbers: [68, 107] Generated Node #0,3,0: 67:[68, 107] Operation: 53+54=107 Exploring Operation: 53+68=121, Resulting Numbers: [54, 121] Generated Node #0,3,1: 67:[54, 121] Operation: 53+68=121 Exploring Operation: 54-53=1, Resulting Numbers: [68, 1] Generated Node #0,3,2: 67:[68, 1] Operation: 54-53=1 Exploring Operation: 68-53=15, Resulting Numbers: [54, 15] Generated Node #0,3,3: 67:[54, 15] Operation: 68-53=15 Moving to Node #0,3,0 Current State: 67:[68, 107], Operations: ['19+49=68', '53+54=107'] Exploring Operation: 68+107=175, Resulting Numbers: [175] 175,67 unequal: No Solution Exploring Operation: 107-68=39, Resulting Numbers: [39] 39,67 unequal: No Solution Exploring Operation: 68*107=7276, Resulting Numbers: [7276] 7276,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[54, 15], Operations: ['19+49=68', '68-53=15'] Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,67 unequal: No Solution Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[68, 1], Operations: ['19+49=68', '54-53=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,67 unequal: No Solution Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[53, 19, 54, 49], Operations: [] Exploring Operation: 19+49=68, Resulting Numbers: [53, 54, 68] Generated Node #0,3: 67:[53, 54, 68] Operation: 19+49=68 Moving to Node #0,3 Current State: 67:[53, 54, 68], Operations: ['19+49=68'] Exploring Operation: 54-53=1, Resulting Numbers: [68, 1] Generated Node #0,3,2: 67:[68, 1] Operation: 54-53=1 Moving to Node #0,3,2 Current State: 67:[68, 1], Operations: ['19+49=68', '54-53=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 82, 20, 24, 19 ]
59
[ "82+20=102", "24+19=43", "102-43=59" ]
Current State: 59:[82, 20, 24, 19], Operations: [] Exploring Operation: 82+20=102, Resulting Numbers: [24, 19, 102] Generated Node #2: [24, 19, 102] from Operation: 82+20=102 Current State: 59:[24, 19, 102], Operations: ['82+20=102'] Exploring Operation: 24+19=43, Resulting Numbers: [102, 43] Generated Node #3: [102, 43] from Operation: 24+19=43 Current State: 59:[102, 43], Operations: ['82+20=102', '24+19=43'] Exploring Operation: 102-43=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[82, 20, 24, 19], Operations: [] Exploring Operation: 20+19=39, Resulting Numbers: [82, 24, 39] Generated Node #0,0: 59:[82, 24, 39] Operation: 20+19=39 Exploring Operation: 20+24=44, Resulting Numbers: [82, 19, 44] Generated Node #0,1: 59:[82, 19, 44] Operation: 20+24=44 Exploring Operation: 82-19=63, Resulting Numbers: [20, 24, 63] Generated Node #0,2: 59:[20, 24, 63] Operation: 82-19=63 Exploring Operation: 82-20=62, Resulting Numbers: [24, 19, 62] Generated Node #0,3: 59:[24, 19, 62] Operation: 82-20=62 Exploring Operation: 24+19=43, Resulting Numbers: [82, 20, 43] Generated Node #0,4: 59:[82, 20, 43] Operation: 24+19=43 Moving to Node #0,0 Current State: 59:[82, 24, 39], Operations: ['20+19=39'] Exploring Operation: 24+39=63, Resulting Numbers: [82, 63] Generated Node #0,0,0: 59:[82, 63] Operation: 24+39=63 Exploring Operation: 82-24=58, Resulting Numbers: [39, 58] Generated Node #0,0,1: 59:[39, 58] Operation: 82-24=58 Exploring Operation: 82+24=106, Resulting Numbers: [39, 106] Generated Node #0,0,2: 59:[39, 106] Operation: 82+24=106 Exploring Operation: 39-24=15, Resulting Numbers: [82, 15] Generated Node #0,0,3: 59:[82, 15] Operation: 39-24=15 Exploring Operation: 82-39=43, Resulting Numbers: [24, 43] Generated Node #0,0,4: 59:[24, 43] Operation: 82-39=43 Moving to Node #0,2 Current State: 59:[20, 24, 63], Operations: ['82-19=63'] Exploring Operation: 24-20=4, Resulting Numbers: [63, 4] Generated Node #0,2,0: 59:[63, 4] Operation: 24-20=4 Exploring Operation: 63-24=39, Resulting Numbers: [20, 39] Generated Node #0,2,1: 59:[20, 39] Operation: 63-24=39 Exploring Operation: 63-20=43, Resulting Numbers: [24, 43] Generated Node #0,2,2: 59:[24, 43] Operation: 63-20=43 Exploring Operation: 20+24=44, Resulting Numbers: [63, 44] Generated Node #0,2,3: 59:[63, 44] Operation: 20+24=44 Exploring Operation: 20+63=83, Resulting Numbers: [24, 83] Generated Node #0,2,4: 59:[24, 83] Operation: 20+63=83 Moving to Node #0,4 Current State: 59:[82, 20, 43], Operations: ['24+19=43'] Exploring Operation: 20+43=63, Resulting Numbers: [82, 63] Generated Node #0,4,0: 59:[82, 63] Operation: 20+43=63 Exploring Operation: 82-20=62, Resulting Numbers: [43, 62] Generated Node #0,4,1: 59:[43, 62] Operation: 82-20=62 Exploring Operation: 82+20=102, Resulting Numbers: [43, 102] Generated Node #0,4,2: 59:[43, 102] Operation: 82+20=102 Exploring Operation: 43-20=23, Resulting Numbers: [82, 23] Generated Node #0,4,3: 59:[82, 23] Operation: 43-20=23 Exploring Operation: 82-43=39, Resulting Numbers: [20, 39] Generated Node #0,4,4: 59:[20, 39] Operation: 82-43=39 Moving to Node #0,1 Current State: 59:[82, 19, 44], Operations: ['20+24=44'] Exploring Operation: 44-19=25, Resulting Numbers: [82, 25] Generated Node #0,1,0: 59:[82, 25] Operation: 44-19=25 Exploring Operation: 82-44=38, Resulting Numbers: [19, 38] Generated Node #0,1,1: 59:[19, 38] Operation: 82-44=38 Exploring Operation: 82-19=63, Resulting Numbers: [44, 63] Generated Node #0,1,2: 59:[44, 63] Operation: 82-19=63 Exploring Operation: 19+44=63, Resulting Numbers: [82, 63] Generated Node #0,1,3: 59:[82, 63] Operation: 19+44=63 Exploring Operation: 82+19=101, Resulting Numbers: [44, 101] Generated Node #0,1,4: 59:[44, 101] Operation: 82+19=101 Moving to Node #0,3 Current State: 59:[24, 19, 62], Operations: ['82-20=62'] Exploring Operation: 24+19=43, Resulting Numbers: [62, 43] Generated Node #0,3,0: 59:[62, 43] Operation: 24+19=43 Exploring Operation: 62-19=43, Resulting Numbers: [24, 43] Generated Node #0,3,1: 59:[24, 43] Operation: 62-19=43 Exploring Operation: 19+62=81, Resulting Numbers: [24, 81] Generated Node #0,3,2: 59:[24, 81] Operation: 19+62=81 Exploring Operation: 24-19=5, Resulting Numbers: [62, 5] Generated Node #0,3,3: 59:[62, 5] Operation: 24-19=5 Exploring Operation: 62-24=38, Resulting Numbers: [19, 38] Generated Node #0,3,4: 59:[19, 38] Operation: 62-24=38 Moving to Node #0,2,3 Current State: 59:[63, 44], Operations: ['82-19=63', '20+24=44'] Exploring Operation: 63+44=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 63*44=2772, Resulting Numbers: [2772] 2772,59 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,4,1 Current State: 59:[43, 62], Operations: ['24+19=43', '82-20=62'] Exploring Operation: 43*62=2666, Resulting Numbers: [2666] 2666,59 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 43+62=105, Resulting Numbers: [105] 105,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[62, 43], Operations: ['82-20=62', '24+19=43'] Exploring Operation: 62*43=2666, Resulting Numbers: [2666] 2666,59 unequal: No Solution Exploring Operation: 62-43=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 62+43=105, Resulting Numbers: [105] 105,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[44, 63], Operations: ['20+24=44', '82-19=63'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,59 unequal: No Solution Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[39, 58], Operations: ['20+19=39', '82-24=58'] Exploring Operation: 39*58=2262, Resulting Numbers: [2262] 2262,59 unequal: No Solution Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,59 unequal: No Solution Exploring Operation: 58-39=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[82, 63], Operations: ['24+19=43', '20+43=63'] Exploring Operation: 82-63=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 82*63=5166, Resulting Numbers: [5166] 5166,59 unequal: No Solution Exploring Operation: 82+63=145, Resulting Numbers: [145] 145,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[82, 63], Operations: ['20+19=39', '24+39=63'] Exploring Operation: 82-63=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 82*63=5166, Resulting Numbers: [5166] 5166,59 unequal: No Solution Exploring Operation: 82+63=145, Resulting Numbers: [145] 145,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[82, 63], Operations: ['20+24=44', '19+44=63'] Exploring Operation: 82*63=5166, Resulting Numbers: [5166] 5166,59 unequal: No Solution Exploring Operation: 82+63=145, Resulting Numbers: [145] 145,59 unequal: No Solution Exploring Operation: 82-63=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[24, 43], Operations: ['82-19=63', '63-20=43'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,59 unequal: No Solution Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[24, 43], Operations: ['20+19=39', '82-39=43'] Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,59 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,59 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[24, 43], Operations: ['82-20=62', '62-19=43'] Exploring Operation: 24+43=67, Resulting Numbers: [67] 67,59 unequal: No Solution Exploring Operation: 24*43=1032, Resulting Numbers: [1032] 1032,59 unequal: No Solution Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[24, 81], Operations: ['82-20=62', '19+62=81'] Exploring Operation: 24+81=105, Resulting Numbers: [105] 105,59 unequal: No Solution Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 24*81=1944, Resulting Numbers: [1944] 1944,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[82, 25], Operations: ['20+24=44', '44-19=25'] Exploring Operation: 82+25=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 82*25=2050, Resulting Numbers: [2050] 2050,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[44, 101], Operations: ['20+24=44', '82+19=101'] Exploring Operation: 44*101=4444, Resulting Numbers: [4444] 4444,59 unequal: No Solution Exploring Operation: 101-44=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 44+101=145, Resulting Numbers: [145] 145,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[62, 5], Operations: ['82-20=62', '24-19=5'] Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,59 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,59 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,59 unequal: No Solution Moving to Node #0,4,4 Current State: 59:[20, 39], Operations: ['24+19=43', '82-43=39'] Exploring Operation: 20*39=780, Resulting Numbers: [780] 780,59 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[82, 20, 24, 19], Operations: [] Exploring Operation: 24+19=43, Resulting Numbers: [82, 20, 43] Generated Node #0,4: 59:[82, 20, 43] Operation: 24+19=43 Moving to Node #0,4 Current State: 59:[82, 20, 43], Operations: ['24+19=43'] Exploring Operation: 82-43=39, Resulting Numbers: [20, 39] Generated Node #0,4,4: 59:[20, 39] Operation: 82-43=39 Moving to Node #0,4,4 Current State: 59:[20, 39], Operations: ['24+19=43', '82-43=39'] Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.929688
hs_5
sum_heuristic
[ 60, 92, 64, 60 ]
36
[ "92-60=32", "64-60=4", "32+4=36" ]
Current State: 36:[60, 92, 64, 60], Operations: [] Exploring Operation: 92-60=32, Resulting Numbers: [64, 32] Generated Node #2: [64, 32] from Operation: 92-60=32 Current State: 36:[64, 32], Operations: ['92-60=32'] Exploring Operation: 64-60=4, Resulting Numbers: [32, 4] Generated Node #3: [32, 4] from Operation: 64-60=4 Current State: 36:[32, 4], Operations: ['92-60=32', '64-60=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[60, 92, 64, 60], Operations: [] Exploring Operation: 92-60=32, Resulting Numbers: [60, 64, 32] Generated Node #0,0: 36:[60, 64, 32] Operation: 92-60=32 Exploring Operation: 92-60=32, Resulting Numbers: [64, 60, 32] Generated Node #0,1: 36:[64, 60, 32] Operation: 92-60=32 Exploring Operation: 92-64=28, Resulting Numbers: [60, 60, 28] Generated Node #0,2: 36:[60, 60, 28] Operation: 92-64=28 Exploring Operation: 64-60=4, Resulting Numbers: [92, 60, 4] Generated Node #0,3: 36:[92, 60, 4] Operation: 64-60=4 Exploring Operation: 64-60=4, Resulting Numbers: [60, 92, 4] Generated Node #0,4: 36:[60, 92, 4] Operation: 64-60=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[60, 64, 32], Operations: ['92-60=32'] Exploring Operation: 64/32=2, Resulting Numbers: [60, 2] Generated Node #0,0,0: 36:[60, 2] Operation: 64/32=2 Exploring Operation: 64-60=4, Resulting Numbers: [32, 4] Generated Node #0,0,1: 36:[32, 4] Operation: 64-60=4 Exploring Operation: 60-32=28, Resulting Numbers: [64, 28] Generated Node #0,0,2: 36:[64, 28] Operation: 60-32=28 Exploring Operation: 64-32=32, Resulting Numbers: [60, 32] Generated Node #0,0,3: 36:[60, 32] Operation: 64-32=32 Exploring Operation: 60+32=92, Resulting Numbers: [64, 92] Generated Node #0,0,4: 36:[64, 92] Operation: 60+32=92 Moving to Node #0,0,1 Current State: 36:[32, 4], Operations: ['92-60=32', '64-60=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[60, 92, 64, 60], Operations: [] Exploring Operation: 92-60=32, Resulting Numbers: [60, 64, 32] Generated Node #0,0: 36:[60, 64, 32] Operation: 92-60=32 Moving to Node #0,0 Current State: 36:[60, 64, 32], Operations: ['92-60=32'] Exploring Operation: 64-60=4, Resulting Numbers: [32, 4] Generated Node #0,0,1: 36:[32, 4] Operation: 64-60=4 Moving to Node #0,0,1 Current State: 36:[32, 4], Operations: ['92-60=32', '64-60=4'] Exploring Operation: 32+4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 10, 81, 30, 32 ]
93
[ "10+81=91", "32-30=2", "91+2=93" ]
Current State: 93:[10, 81, 30, 32], Operations: [] Exploring Operation: 10+81=91, Resulting Numbers: [30, 32, 91] Generated Node #2: [30, 32, 91] from Operation: 10+81=91 Current State: 93:[30, 32, 91], Operations: ['10+81=91'] Exploring Operation: 32-30=2, Resulting Numbers: [91, 2] Generated Node #3: [91, 2] from Operation: 32-30=2 Current State: 93:[91, 2], Operations: ['10+81=91', '32-30=2'] Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[10, 81, 30, 32], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [10, 81, 2] Generated Node #0,0: 93:[10, 81, 2] Operation: 32-30=2 Exploring Operation: 10+81=91, Resulting Numbers: [30, 32, 91] Generated Node #0,1: 93:[30, 32, 91] Operation: 10+81=91 Exploring Operation: 10+30=40, Resulting Numbers: [81, 32, 40] Generated Node #0,2: 93:[81, 32, 40] Operation: 10+30=40 Exploring Operation: 32-10=22, Resulting Numbers: [81, 30, 22] Generated Node #0,3: 93:[81, 30, 22] Operation: 32-10=22 Exploring Operation: 30/10=3, Resulting Numbers: [81, 32, 3] Generated Node #0,4: 93:[81, 32, 3] Operation: 30/10=3 Moving to Node #0,1 Current State: 93:[30, 32, 91], Operations: ['10+81=91'] Exploring Operation: 91-30=61, Resulting Numbers: [32, 61] Generated Node #0,1,0: 93:[32, 61] Operation: 91-30=61 Exploring Operation: 32-30=2, Resulting Numbers: [91, 2] Generated Node #0,1,1: 93:[91, 2] Operation: 32-30=2 Exploring Operation: 32+91=123, Resulting Numbers: [30, 123] Generated Node #0,1,2: 93:[30, 123] Operation: 32+91=123 Exploring Operation: 30+91=121, Resulting Numbers: [32, 121] Generated Node #0,1,3: 93:[32, 121] Operation: 30+91=121 Exploring Operation: 91-32=59, Resulting Numbers: [30, 59] Generated Node #0,1,4: 93:[30, 59] Operation: 91-32=59 Moving to Node #0,4 Current State: 93:[81, 32, 3], Operations: ['30/10=3'] Exploring Operation: 32*3=96, Resulting Numbers: [81, 96] Generated Node #0,4,0: 93:[81, 96] Operation: 32*3=96 Exploring Operation: 81+3=84, Resulting Numbers: [32, 84] Generated Node #0,4,1: 93:[32, 84] Operation: 81+3=84 Exploring Operation: 81-3=78, Resulting Numbers: [32, 78] Generated Node #0,4,2: 93:[32, 78] Operation: 81-3=78 Exploring Operation: 81/3=27, Resulting Numbers: [32, 27] Generated Node #0,4,3: 93:[32, 27] Operation: 81/3=27 Exploring Operation: 32-3=29, Resulting Numbers: [81, 29] Generated Node #0,4,4: 93:[81, 29] Operation: 32-3=29 Moving to Node #0,0 Current State: 93:[10, 81, 2], Operations: ['32-30=2'] Exploring Operation: 10/2=5, Resulting Numbers: [81, 5] Generated Node #0,0,0: 93:[81, 5] Operation: 10/2=5 Exploring Operation: 10+2=12, Resulting Numbers: [81, 12] Generated Node #0,0,1: 93:[81, 12] Operation: 10+2=12 Exploring Operation: 81+2=83, Resulting Numbers: [10, 83] Generated Node #0,0,2: 93:[10, 83] Operation: 81+2=83 Exploring Operation: 10+81=91, Resulting Numbers: [2, 91] Generated Node #0,0,3: 93:[2, 91] Operation: 10+81=91 Exploring Operation: 10-2=8, Resulting Numbers: [81, 8] Generated Node #0,0,4: 93:[81, 8] Operation: 10-2=8 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[2, 91], Operations: ['32-30=2', '10+81=91'] Exploring Operation: 2*91=182, Resulting Numbers: [182] 182,93 unequal: No Solution Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[10, 81, 30, 32], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [10, 81, 2] Generated Node #0,0: 93:[10, 81, 2] Operation: 32-30=2 Moving to Node #0,0 Current State: 93:[10, 81, 2], Operations: ['32-30=2'] Exploring Operation: 10+81=91, Resulting Numbers: [2, 91] Generated Node #0,0,3: 93:[2, 91] Operation: 10+81=91 Moving to Node #0,0,3 Current State: 93:[2, 91], Operations: ['32-30=2', '10+81=91'] Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 98, 5, 97, 42 ]
38
[ "98-5=93", "97-42=55", "93-55=38" ]
Current State: 38:[98, 5, 97, 42], Operations: [] Exploring Operation: 98-5=93, Resulting Numbers: [97, 42, 93] Generated Node #2: [97, 42, 93] from Operation: 98-5=93 Current State: 38:[97, 42, 93], Operations: ['98-5=93'] Exploring Operation: 97-42=55, Resulting Numbers: [93, 55] Generated Node #3: [93, 55] from Operation: 97-42=55 Current State: 38:[93, 55], Operations: ['98-5=93', '97-42=55'] Exploring Operation: 93-55=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[98, 5, 97, 42], Operations: [] Exploring Operation: 98-42=56, Resulting Numbers: [5, 97, 56] Generated Node #0,0: 38:[5, 97, 56] Operation: 98-42=56 Exploring Operation: 98-97=1, Resulting Numbers: [5, 42, 1] Generated Node #0,1: 38:[5, 42, 1] Operation: 98-97=1 Moving to Node #0,1 Current State: 38:[5, 42, 1], Operations: ['98-97=1'] Exploring Operation: 42-5=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 38:[1, 37] Operation: 42-5=37 Exploring Operation: 5-1=4, Resulting Numbers: [42, 4] Generated Node #0,1,1: 38:[42, 4] Operation: 5-1=4 Moving to Node #0,0 Current State: 38:[5, 97, 56], Operations: ['98-42=56'] Exploring Operation: 97-5=92, Resulting Numbers: [56, 92] Generated Node #0,0,0: 38:[56, 92] Operation: 97-5=92 Exploring Operation: 97-56=41, Resulting Numbers: [5, 41] Generated Node #0,0,1: 38:[5, 41] Operation: 97-56=41 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[5, 41], Operations: ['98-42=56', '97-56=41'] Exploring Operation: 5+41=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[56, 92], Operations: ['98-42=56', '97-5=92'] Exploring Operation: 92-56=36, Resulting Numbers: [36] 36,38 unequal: No Solution Exploring Operation: 56+92=148, Resulting Numbers: [148] 148,38 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: 38:[1, 37], Operations: ['98-97=1', '42-5=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[98, 5, 97, 42], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [5, 42, 1] Generated Node #0,1: 38:[5, 42, 1] Operation: 98-97=1 Moving to Node #0,1 Current State: 38:[5, 42, 1], Operations: ['98-97=1'] Exploring Operation: 42-5=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 38:[1, 37] Operation: 42-5=37 Moving to Node #0,1,0 Current State: 38:[1, 37], Operations: ['98-97=1', '42-5=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 36, 24, 38, 17 ]
48
[ "36-17=19", "24*38=912", "912/19=48" ]
Current State: 48:[36, 24, 38, 17], Operations: [] Exploring Operation: 36-17=19, Resulting Numbers: [24, 38, 19] Generated Node #2: [24, 38, 19] from Operation: 36-17=19 Current State: 48:[24, 38, 19], Operations: ['36-17=19'] Exploring Operation: 24*38=912, Resulting Numbers: [19, 912] Generated Node #3: [19, 912] from Operation: 24*38=912 Current State: 48:[19, 912], Operations: ['36-17=19', '24*38=912'] Exploring Operation: 912/19=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[36, 24, 38, 17], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [24, 17, 2] Generated Node #0,0: 48:[24, 17, 2] Operation: 38-36=2 Exploring Operation: 36+17=53, Resulting Numbers: [24, 38, 53] Generated Node #0,1: 48:[24, 38, 53] Operation: 36+17=53 Exploring Operation: 36-17=19, Resulting Numbers: [24, 38, 19] Generated Node #0,2: 48:[24, 38, 19] Operation: 36-17=19 Exploring Operation: 38-24=14, Resulting Numbers: [36, 17, 14] Generated Node #0,3: 48:[36, 17, 14] Operation: 38-24=14 Exploring Operation: 36-24=12, Resulting Numbers: [38, 17, 12] Generated Node #0,4: 48:[38, 17, 12] Operation: 36-24=12 Moving to Node #0,0 Current State: 48:[24, 17, 2], Operations: ['38-36=2'] Exploring Operation: 24+2=26, Resulting Numbers: [17, 26] Generated Node #0,0,0: 48:[17, 26] Operation: 24+2=26 Exploring Operation: 24*2=48, Resulting Numbers: [17, 48] Generated Node #0,0,1: 48:[17, 48] Operation: 24*2=48 Exploring Operation: 24/2=12, Resulting Numbers: [17, 12] Generated Node #0,0,2: 48:[17, 12] Operation: 24/2=12 Exploring Operation: 17-2=15, Resulting Numbers: [24, 15] Generated Node #0,0,3: 48:[24, 15] Operation: 17-2=15 Exploring Operation: 24-17=7, Resulting Numbers: [2, 7] Generated Node #0,0,4: 48:[2, 7] Operation: 24-17=7 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[17, 48], Operations: ['38-36=2', '24*2=48'] Exploring Operation: 17*48=816, Resulting Numbers: [816] 816,48 unequal: No Solution Exploring Operation: 17+48=65, Resulting Numbers: [65] 65,48 unequal: No Solution Exploring Operation: 48-17=31, Resulting Numbers: [31] 31,48 unequal: No Solution No 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: 48:[17, 12], Operations: ['38-36=2', '24/2=12'] Exploring Operation: 17*12=204, Resulting Numbers: [204] 204,48 unequal: No Solution Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,48 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,48 unequal: No Solution No 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: 48:[24, 15], Operations: ['38-36=2', '17-2=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,48 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,48 unequal: No Solution No 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: 48:[2, 7], Operations: ['38-36=2', '24-17=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,48 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,48 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,48 unequal: No Solution No 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: 48:[17, 26], Operations: ['38-36=2', '24+2=26'] Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,48 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,48 unequal: No Solution Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,48 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: 48:[38, 17, 12], Operations: ['36-24=12'] Exploring Operation: 38-17=21, Resulting Numbers: [12, 21] Generated Node #0,4,0: 48:[12, 21] Operation: 38-17=21 Exploring Operation: 38+12=50, Resulting Numbers: [17, 50] Generated Node #0,4,1: 48:[17, 50] Operation: 38+12=50 Exploring Operation: 38+17=55, Resulting Numbers: [12, 55] Generated Node #0,4,2: 48:[12, 55] Operation: 38+17=55 Exploring Operation: 38-12=26, Resulting Numbers: [17, 26] Generated Node #0,4,3: 48:[17, 26] Operation: 38-12=26 Exploring Operation: 17-12=5, Resulting Numbers: [38, 5] Generated Node #0,4,4: 48:[38, 5] Operation: 17-12=5 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 48:[12, 21], Operations: ['36-24=12', '38-17=21'] Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,48 unequal: No Solution Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,48 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,48 unequal: No Solution No 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: 48:[17, 50], Operations: ['36-24=12', '38+12=50'] Exploring Operation: 17*50=850, Resulting Numbers: [850] 850,48 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,48 unequal: No Solution Exploring Operation: 17+50=67, Resulting Numbers: [67] 67,48 unequal: No Solution No 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: 48:[17, 26], Operations: ['36-24=12', '38-12=26'] Exploring Operation: 17*26=442, Resulting Numbers: [442] 442,48 unequal: No Solution Exploring Operation: 17+26=43, Resulting Numbers: [43] 43,48 unequal: No Solution Exploring Operation: 26-17=9, Resulting Numbers: [9] 9,48 unequal: No Solution No 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: 48:[12, 55], Operations: ['36-24=12', '38+17=55'] Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,48 unequal: No Solution Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,48 unequal: No Solution No 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: 48:[38, 5], Operations: ['36-24=12', '17-12=5'] Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,48 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,48 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,48 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: 48:[24, 38, 19], Operations: ['36-17=19'] Exploring Operation: 38-24=14, Resulting Numbers: [19, 14] Generated Node #0,2,0: 48:[19, 14] Operation: 38-24=14 Exploring Operation: 38+19=57, Resulting Numbers: [24, 57] Generated Node #0,2,1: 48:[24, 57] Operation: 38+19=57 Exploring Operation: 38/19=2, Resulting Numbers: [24, 2] Generated Node #0,2,2: 48:[24, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [24, 19] Generated Node #0,2,3: 48:[24, 19] Operation: 38-19=19 Exploring Operation: 24-19=5, Resulting Numbers: [38, 5] Generated Node #0,2,4: 48:[38, 5] Operation: 24-19=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 48:[24, 2], Operations: ['36-17=19', '38/19=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[36, 24, 38, 17], Operations: [] Exploring Operation: 36-17=19, Resulting Numbers: [24, 38, 19] Generated Node #0,2: 48:[24, 38, 19] Operation: 36-17=19 Moving to Node #0,2 Current State: 48:[24, 38, 19], Operations: ['36-17=19'] Exploring Operation: 38/19=2, Resulting Numbers: [24, 2] Generated Node #0,2,2: 48:[24, 2] Operation: 38/19=2 Moving to Node #0,2,2 Current State: 48:[24, 2], Operations: ['36-17=19', '38/19=2'] Exploring Operation: 24*2=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.952257
hs_5
mult_heuristic
[ 39, 21, 34, 2 ]
54
[ "39-21=18", "34+2=36", "18+36=54" ]
Current State: 54:[39, 21, 34, 2], Operations: [] Exploring Operation: 39-21=18, Resulting Numbers: [34, 2, 18] Generated Node #2: [34, 2, 18] from Operation: 39-21=18 Current State: 54:[34, 2, 18], Operations: ['39-21=18'] Exploring Operation: 34+2=36, Resulting Numbers: [18, 36] Generated Node #3: [18, 36] from Operation: 34+2=36 Current State: 54:[18, 36], Operations: ['39-21=18', '34+2=36'] Exploring Operation: 18+36=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[39, 21, 34, 2], Operations: [] Exploring Operation: 39-21=18, Resulting Numbers: [34, 2, 18] Generated Node #0,0: 54:[34, 2, 18] Operation: 39-21=18 Exploring Operation: 39-34=5, Resulting Numbers: [21, 2, 5] Generated Node #0,1: 54:[21, 2, 5] Operation: 39-34=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[21, 2, 5], Operations: ['39-34=5'] Exploring Operation: 21-2=19, Resulting Numbers: [5, 19] Generated Node #0,1,0: 54:[5, 19] Operation: 21-2=19 Exploring Operation: 21+5=26, Resulting Numbers: [2, 26] Generated Node #0,1,1: 54:[2, 26] Operation: 21+5=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[2, 26], Operations: ['39-34=5', '21+5=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[5, 19], Operations: ['39-34=5', '21-2=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[34, 2, 18], Operations: ['39-21=18'] Exploring Operation: 34/2=17, Resulting Numbers: [18, 17] Generated Node #0,0,0: 54:[18, 17] Operation: 34/2=17 Exploring Operation: 34+18=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 54:[2, 52] Operation: 34+18=52 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[18, 17], Operations: ['39-21=18', '34/2=17'] Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,54 unequal: No Solution Exploring Operation: 18+17=35, Resulting Numbers: [35] 35,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[2, 52], Operations: ['39-21=18', '34+18=52'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,54 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[39, 21, 34, 2], Operations: [] Exploring Operation: 39-21=18, Resulting Numbers: [34, 2, 18] Generated Node #0,0: 54:[34, 2, 18] Operation: 39-21=18 Moving to Node #0,0 Current State: 54:[34, 2, 18], Operations: ['39-21=18'] Exploring Operation: 34+18=52, Resulting Numbers: [2, 52] Generated Node #0,0,1: 54:[2, 52] Operation: 34+18=52 Moving to Node #0,0,1 Current State: 54:[2, 52], Operations: ['39-21=18', '34+18=52'] Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 9, 30, 6, 66 ]
64
[ "9+6=15", "30/15=2", "66-2=64" ]
Current State: 64:[9, 30, 6, 66], Operations: [] Exploring Operation: 9+6=15, Resulting Numbers: [30, 66, 15] Generated Node #2: [30, 66, 15] from Operation: 9+6=15 Current State: 64:[30, 66, 15], Operations: ['9+6=15'] Exploring Operation: 30/15=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 30/15=2 Current State: 64:[66, 2], Operations: ['9+6=15', '30/15=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[9, 30, 6, 66], Operations: [] Exploring Operation: 66/6=11, Resulting Numbers: [9, 30, 11] Generated Node #0,0: 64:[9, 30, 11] Operation: 66/6=11 Exploring Operation: 30/6=5, Resulting Numbers: [9, 66, 5] Generated Node #0,1: 64:[9, 66, 5] Operation: 30/6=5 Exploring Operation: 9-6=3, Resulting Numbers: [30, 66, 3] Generated Node #0,2: 64:[30, 66, 3] Operation: 9-6=3 Exploring Operation: 9+6=15, Resulting Numbers: [30, 66, 15] Generated Node #0,3: 64:[30, 66, 15] Operation: 9+6=15 Moving to Node #0,1 Current State: 64:[9, 66, 5], Operations: ['30/6=5'] Exploring Operation: 66-9=57, Resulting Numbers: [5, 57] Generated Node #0,1,0: 64:[5, 57] Operation: 66-9=57 Exploring Operation: 66-5=61, Resulting Numbers: [9, 61] Generated Node #0,1,1: 64:[9, 61] Operation: 66-5=61 Exploring Operation: 9+5=14, Resulting Numbers: [66, 14] Generated Node #0,1,2: 64:[66, 14] Operation: 9+5=14 Exploring Operation: 9-5=4, Resulting Numbers: [66, 4] Generated Node #0,1,3: 64:[66, 4] Operation: 9-5=4 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[66, 4], Operations: ['30/6=5', '9-5=4'] Exploring Operation: 66-4=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 66*4=264, Resulting Numbers: [264] 264,64 unequal: No Solution Exploring Operation: 66+4=70, Resulting Numbers: [70] 70,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[9, 61], Operations: ['30/6=5', '66-5=61'] Exploring Operation: 9+61=70, Resulting Numbers: [70] 70,64 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,64 unequal: No Solution Exploring Operation: 9*61=549, Resulting Numbers: [549] 549,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[66, 14], Operations: ['30/6=5', '9+5=14'] Exploring Operation: 66+14=80, Resulting Numbers: [80] 80,64 unequal: No Solution Exploring Operation: 66*14=924, Resulting Numbers: [924] 924,64 unequal: No Solution Exploring Operation: 66-14=52, Resulting Numbers: [52] 52,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 64:[5, 57], Operations: ['30/6=5', '66-9=57'] Exploring Operation: 5+57=62, Resulting Numbers: [62] 62,64 unequal: No Solution Exploring Operation: 57-5=52, Resulting Numbers: [52] 52,64 unequal: No Solution Exploring Operation: 5*57=285, Resulting Numbers: [285] 285,64 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: 64:[30, 66, 15], Operations: ['9+6=15'] Exploring Operation: 30-15=15, Resulting Numbers: [66, 15] Generated Node #0,3,0: 64:[66, 15] Operation: 30-15=15 Exploring Operation: 30/15=2, Resulting Numbers: [66, 2] Generated Node #0,3,1: 64:[66, 2] Operation: 30/15=2 Exploring Operation: 30+15=45, Resulting Numbers: [66, 45] Generated Node #0,3,2: 64:[66, 45] Operation: 30+15=45 Exploring Operation: 66-30=36, Resulting Numbers: [15, 36] Generated Node #0,3,3: 64:[15, 36] Operation: 66-30=36 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 64:[66, 2], Operations: ['9+6=15', '30/15=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[9, 30, 6, 66], Operations: [] Exploring Operation: 9+6=15, Resulting Numbers: [30, 66, 15] Generated Node #0,3: 64:[30, 66, 15] Operation: 9+6=15 Moving to Node #0,3 Current State: 64:[30, 66, 15], Operations: ['9+6=15'] Exploring Operation: 30/15=2, Resulting Numbers: [66, 2] Generated Node #0,3,1: 64:[66, 2] Operation: 30/15=2 Moving to Node #0,3,1 Current State: 64:[66, 2], Operations: ['9+6=15', '30/15=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic