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
[ 35, 51, 2, 91 ]
24
[ "35+91=126", "51*2=102", "126-102=24" ]
Current State: 24:[35, 51, 2, 91], Operations: [] Exploring Operation: 35+91=126, Resulting Numbers: [51, 2, 126] Generated Node #2: [51, 2, 126] from Operation: 35+91=126 Current State: 24:[51, 2, 126], Operations: ['35+91=126'] Exploring Operation: 51*2=102, Resulting Numbers: [126, 102] Generated Node #3: [126, 102] from Operation: 51*2=102 Current State: 24:[126, 102], Operations: ['35+91=126', '51*2=102'] Exploring Operation: 126-102=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[35, 51, 2, 91], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [2, 91, 16] Generated Node #0,0: 24:[2, 91, 16] Operation: 51-35=16 Exploring Operation: 91-35=56, Resulting Numbers: [51, 2, 56] Generated Node #0,1: 24:[51, 2, 56] Operation: 91-35=56 Exploring Operation: 91-51=40, Resulting Numbers: [35, 2, 40] Generated Node #0,2: 24:[35, 2, 40] Operation: 91-51=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[35, 2, 40], Operations: ['91-51=40'] Exploring Operation: 35-2=33, Resulting Numbers: [40, 33] Generated Node #0,2,0: 24:[40, 33] Operation: 35-2=33 Exploring Operation: 40-35=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 24:[2, 5] Operation: 40-35=5 Exploring Operation: 40/2=20, Resulting Numbers: [35, 20] Generated Node #0,2,2: 24:[35, 20] Operation: 40/2=20 Moving to Node #0,2,1 Current State: 24:[2, 5], Operations: ['91-51=40', '40-35=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[35, 20], Operations: ['91-51=40', '40/2=20'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,24 unequal: No Solution Exploring Operation: 35+20=55, Resulting Numbers: [55] 55,24 unequal: No Solution Exploring Operation: 35*20=700, Resulting Numbers: [700] 700,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[40, 33], Operations: ['91-51=40', '35-2=33'] Exploring Operation: 40+33=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 40*33=1320, Resulting Numbers: [1320] 1320,24 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[51, 2, 56], Operations: ['91-35=56'] Exploring Operation: 56/2=28, Resulting Numbers: [51, 28] Generated Node #0,1,0: 24:[51, 28] Operation: 56/2=28 Exploring Operation: 56-51=5, Resulting Numbers: [2, 5] Generated Node #0,1,1: 24:[2, 5] Operation: 56-51=5 Exploring Operation: 51-2=49, Resulting Numbers: [56, 49] Generated Node #0,1,2: 24:[56, 49] Operation: 51-2=49 Moving to Node #0,1,1 Current State: 24:[2, 5], Operations: ['91-35=56', '56-51=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,24 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[51, 28], Operations: ['91-35=56', '56/2=28'] Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 51*28=1428, Resulting Numbers: [1428] 1428,24 unequal: No Solution Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[56, 49], Operations: ['91-35=56', '51-2=49'] Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,24 unequal: No Solution Exploring Operation: 56+49=105, Resulting Numbers: [105] 105,24 unequal: No Solution Exploring Operation: 56*49=2744, Resulting Numbers: [2744] 2744,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[2, 91, 16], Operations: ['51-35=16'] Exploring Operation: 91-16=75, Resulting Numbers: [2, 75] Generated Node #0,0,0: 24:[2, 75] Operation: 91-16=75 Exploring Operation: 16/2=8, Resulting Numbers: [91, 8] Generated Node #0,0,1: 24:[91, 8] Operation: 16/2=8 Exploring Operation: 91-2=89, Resulting Numbers: [16, 89] Generated Node #0,0,2: 24:[16, 89] Operation: 91-2=89 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[2, 75], Operations: ['51-35=16', '91-16=75'] Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,24 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 2*75=150, Resulting Numbers: [150] 150,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[91, 8], Operations: ['51-35=16', '16/2=8'] Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,24 unequal: No Solution Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,24 unequal: No Solution Exploring Operation: 91*8=728, Resulting Numbers: [728] 728,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 24:[16, 89], Operations: ['51-35=16', '91-2=89'] Exploring Operation: 16*89=1424, Resulting Numbers: [1424] 1424,24 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 16+89=105, Resulting Numbers: [105] 105,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 5, 15, 6, 45 ]
72
[ "15+45=60", "60/5=12", "6*12=72" ]
Current State: 72:[5, 15, 6, 45], Operations: [] Exploring Operation: 15+45=60, Resulting Numbers: [5, 6, 60] Generated Node #2: [5, 6, 60] from Operation: 15+45=60 Current State: 72:[5, 6, 60], Operations: ['15+45=60'] Exploring Operation: 60/5=12, Resulting Numbers: [6, 12] Generated Node #3: [6, 12] from Operation: 60/5=12 Current State: 72:[6, 12], Operations: ['15+45=60', '60/5=12'] Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[5, 15, 6, 45], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [15, 6, 40] Generated Node #0,0: 72:[15, 6, 40] Operation: 45-5=40 Exploring Operation: 45-15=30, Resulting Numbers: [5, 6, 30] Generated Node #0,1: 72:[5, 6, 30] Operation: 45-15=30 Exploring Operation: 45/5=9, Resulting Numbers: [15, 6, 9] Generated Node #0,2: 72:[15, 6, 9] Operation: 45/5=9 Exploring Operation: 45/15=3, Resulting Numbers: [5, 6, 3] Generated Node #0,3: 72:[5, 6, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[5, 6, 3], Operations: ['45/15=3'] Exploring Operation: 6-5=1, Resulting Numbers: [3, 1] Generated Node #0,3,0: 72:[3, 1] Operation: 6-5=1 Exploring Operation: 5+3=8, Resulting Numbers: [6, 8] Generated Node #0,3,1: 72:[6, 8] Operation: 5+3=8 Exploring Operation: 5+6=11, Resulting Numbers: [3, 11] Generated Node #0,3,2: 72:[3, 11] Operation: 5+6=11 Exploring Operation: 5-3=2, Resulting Numbers: [6, 2] Generated Node #0,3,3: 72:[6, 2] Operation: 5-3=2 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[6, 8], Operations: ['45/15=3', '5+3=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 72:[6, 2], Operations: ['45/15=3', '5-3=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[3, 1], Operations: ['45/15=3', '6-5=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,72 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 72:[3, 11], Operations: ['45/15=3', '5+6=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,72 unequal: No Solution Exploring Operation: 3+11=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[15, 6, 9], Operations: ['45/5=9'] Exploring Operation: 15+9=24, Resulting Numbers: [6, 24] Generated Node #0,2,0: 72:[6, 24] Operation: 15+9=24 Exploring Operation: 15+6=21, Resulting Numbers: [9, 21] Generated Node #0,2,1: 72:[9, 21] Operation: 15+6=21 Exploring Operation: 15-9=6, Resulting Numbers: [6, 6] Generated Node #0,2,2: 72:[6, 6] Operation: 15-9=6 Exploring Operation: 15-6=9, Resulting Numbers: [9, 9] Generated Node #0,2,3: 72:[9, 9] Operation: 15-6=9 Moving to Node #0,2,0 Current State: 72:[6, 24], Operations: ['45/5=9', '15+9=24'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,72 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[9, 9], Operations: ['45/5=9', '15-6=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 9-9=0, Resulting Numbers: [0] 0,72 unequal: No Solution Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[6, 6], Operations: ['45/5=9', '15-9=6'] Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,72 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[9, 21], Operations: ['45/5=9', '15+6=21'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,72 unequal: No Solution Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[15, 6, 40], Operations: ['45-5=40'] Exploring Operation: 15+6=21, Resulting Numbers: [40, 21] Generated Node #0,0,0: 72:[40, 21] Operation: 15+6=21 Exploring Operation: 40-15=25, Resulting Numbers: [6, 25] Generated Node #0,0,1: 72:[6, 25] Operation: 40-15=25 Exploring Operation: 40-6=34, Resulting Numbers: [15, 34] Generated Node #0,0,2: 72:[15, 34] Operation: 40-6=34 Exploring Operation: 15-6=9, Resulting Numbers: [40, 9] Generated Node #0,0,3: 72:[40, 9] Operation: 15-6=9 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[6, 25], Operations: ['45-5=40', '40-15=25'] Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,72 unequal: No Solution Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 72:[40, 9], Operations: ['45-5=40', '15-6=9'] Exploring Operation: 40+9=49, Resulting Numbers: [49] 49,72 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 40*9=360, Resulting Numbers: [360] 360,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[15, 34], Operations: ['45-5=40', '40-6=34'] Exploring Operation: 15*34=510, Resulting Numbers: [510] 510,72 unequal: No Solution Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,72 unequal: No Solution Exploring Operation: 15+34=49, Resulting Numbers: [49] 49,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[40, 21], Operations: ['45-5=40', '15+6=21'] Exploring Operation: 40+21=61, Resulting Numbers: [61] 61,72 unequal: No Solution Exploring Operation: 40*21=840, Resulting Numbers: [840] 840,72 unequal: No Solution Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[5, 6, 30], Operations: ['45-15=30'] Exploring Operation: 6+30=36, Resulting Numbers: [5, 36] Generated Node #0,1,0: 72:[5, 36] Operation: 6+30=36 Exploring Operation: 30-5=25, Resulting Numbers: [6, 25] Generated Node #0,1,1: 72:[6, 25] Operation: 30-5=25 Exploring Operation: 5+30=35, Resulting Numbers: [6, 35] Generated Node #0,1,2: 72:[6, 35] Operation: 5+30=35 Exploring Operation: 30/5=6, Resulting Numbers: [6, 6] Generated Node #0,1,3: 72:[6, 6] Operation: 30/5=6 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 72:[6, 6], Operations: ['45-15=30', '30/5=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,72 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,72 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,72 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[5, 36], Operations: ['45-15=30', '6+30=36'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,72 unequal: No Solution Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[6, 25], Operations: ['45-15=30', '30-5=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,72 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[6, 35], Operations: ['45-15=30', '5+30=35'] Exploring Operation: 6*35=210, Resulting Numbers: [210] 210,72 unequal: No Solution Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,72 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 89, 26, 47, 64 ]
98
[ "89+26=115", "64-47=17", "115-17=98" ]
Current State: 98:[89, 26, 47, 64], Operations: [] Exploring Operation: 89+26=115, Resulting Numbers: [47, 64, 115] Generated Node #2: [47, 64, 115] from Operation: 89+26=115 Current State: 98:[47, 64, 115], Operations: ['89+26=115'] Exploring Operation: 64-47=17, Resulting Numbers: [115, 17] Generated Node #3: [115, 17] from Operation: 64-47=17 Current State: 98:[115, 17], Operations: ['89+26=115', '64-47=17'] Exploring Operation: 115-17=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[89, 26, 47, 64], Operations: [] Exploring Operation: 64-47=17, Resulting Numbers: [89, 26, 17] Generated Node #0,0: 98:[89, 26, 17] Operation: 64-47=17 Exploring Operation: 26+64=90, Resulting Numbers: [89, 47, 90] Generated Node #0,1: 98:[89, 47, 90] Operation: 26+64=90 Exploring Operation: 64-26=38, Resulting Numbers: [89, 47, 38] Generated Node #0,2: 98:[89, 47, 38] Operation: 64-26=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[89, 47, 90], Operations: ['26+64=90'] Exploring Operation: 90-47=43, Resulting Numbers: [89, 43] Generated Node #0,1,0: 98:[89, 43] Operation: 90-47=43 Exploring Operation: 89-47=42, Resulting Numbers: [90, 42] Generated Node #0,1,1: 98:[90, 42] Operation: 89-47=42 Exploring Operation: 90-89=1, Resulting Numbers: [47, 1] Generated Node #0,1,2: 98:[47, 1] Operation: 90-89=1 Moving to Node #0,1,2 Current State: 98:[47, 1], Operations: ['26+64=90', '90-89=1'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,98 unequal: No Solution Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,98 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[89, 43], Operations: ['26+64=90', '90-47=43'] Exploring Operation: 89+43=132, Resulting Numbers: [132] 132,98 unequal: No Solution Exploring Operation: 89*43=3827, Resulting Numbers: [3827] 3827,98 unequal: No Solution Exploring Operation: 89-43=46, Resulting Numbers: [46] 46,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[90, 42], Operations: ['26+64=90', '89-47=42'] Exploring Operation: 90*42=3780, Resulting Numbers: [3780] 3780,98 unequal: No Solution Exploring Operation: 90+42=132, Resulting Numbers: [132] 132,98 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,98 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 Current State: 98:[89, 47, 38], Operations: ['64-26=38'] Exploring Operation: 47-38=9, Resulting Numbers: [89, 9] Generated Node #0,2,0: 98:[89, 9] Operation: 47-38=9 Exploring Operation: 89-38=51, Resulting Numbers: [47, 51] Generated Node #0,2,1: 98:[47, 51] Operation: 89-38=51 Exploring Operation: 89-47=42, Resulting Numbers: [38, 42] Generated Node #0,2,2: 98:[38, 42] Operation: 89-47=42 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 98:[47, 51], Operations: ['64-26=38', '89-38=51'] Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,98 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,98 unequal: No Solution Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[89, 26, 47, 64], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [89, 47, 38] Generated Node #0,2: 98:[89, 47, 38] Operation: 64-26=38 Moving to Node #0,2 Current State: 98:[89, 47, 38], Operations: ['64-26=38'] Exploring Operation: 89-38=51, Resulting Numbers: [47, 51] Generated Node #0,2,1: 98:[47, 51] Operation: 89-38=51 Moving to Node #0,2,1 Current State: 98:[47, 51], Operations: ['64-26=38', '89-38=51'] Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 33, 36, 59, 15 ]
47
[ "36-33=3", "59-15=44", "3+44=47" ]
Current State: 47:[33, 36, 59, 15], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [59, 15, 3] Generated Node #2: [59, 15, 3] from Operation: 36-33=3 Current State: 47:[59, 15, 3], Operations: ['36-33=3'] Exploring Operation: 59-15=44, Resulting Numbers: [3, 44] Generated Node #3: [3, 44] from Operation: 59-15=44 Current State: 47:[3, 44], Operations: ['36-33=3', '59-15=44'] Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[33, 36, 59, 15], Operations: [] Exploring Operation: 36-15=21, Resulting Numbers: [33, 59, 21] Generated Node #0,0: 47:[33, 59, 21] Operation: 36-15=21 Exploring Operation: 59-15=44, Resulting Numbers: [33, 36, 44] Generated Node #0,1: 47:[33, 36, 44] Operation: 59-15=44 Exploring Operation: 33-15=18, Resulting Numbers: [36, 59, 18] Generated Node #0,2: 47:[36, 59, 18] Operation: 33-15=18 Exploring Operation: 33+15=48, Resulting Numbers: [36, 59, 48] Generated Node #0,3: 47:[36, 59, 48] Operation: 33+15=48 Exploring Operation: 36+15=51, Resulting Numbers: [33, 59, 51] Generated Node #0,4: 47:[33, 59, 51] Operation: 36+15=51 Moving to Node #0,3 Current State: 47:[36, 59, 48], Operations: ['33+15=48'] Exploring Operation: 59-48=11, Resulting Numbers: [36, 11] Generated Node #0,3,0: 47:[36, 11] Operation: 59-48=11 Exploring Operation: 59-36=23, Resulting Numbers: [48, 23] Generated Node #0,3,1: 47:[48, 23] Operation: 59-36=23 Exploring Operation: 36+48=84, Resulting Numbers: [59, 84] Generated Node #0,3,2: 47:[59, 84] Operation: 36+48=84 Exploring Operation: 36+59=95, Resulting Numbers: [48, 95] Generated Node #0,3,3: 47:[48, 95] Operation: 36+59=95 Exploring Operation: 48-36=12, Resulting Numbers: [59, 12] Generated Node #0,3,4: 47:[59, 12] Operation: 48-36=12 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[48, 23], Operations: ['33+15=48', '59-36=23'] Exploring Operation: 48+23=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 48*23=1104, Resulting Numbers: [1104] 1104,47 unequal: No Solution Exploring Operation: 48-23=25, Resulting Numbers: [25] 25,47 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 #0,3,0 Current State: 47:[36, 11], Operations: ['33+15=48', '59-48=11'] Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,47 unequal: No Solution Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,47 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[33, 36, 59, 15], Operations: [] Exploring Operation: 33+15=48, Resulting Numbers: [36, 59, 48] Generated Node #0,3: 47:[36, 59, 48] Operation: 33+15=48 Moving to Node #0,3 Current State: 47:[36, 59, 48], Operations: ['33+15=48'] Exploring Operation: 59-48=11, Resulting Numbers: [36, 11] Generated Node #0,3,0: 47:[36, 11] Operation: 59-48=11 Moving to Node #0,3,0 Current State: 47:[36, 11], Operations: ['33+15=48', '59-48=11'] Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 82, 85, 5, 87 ]
60
[ "87-82=5", "5*5=25", "85-25=60" ]
Current State: 60:[82, 85, 5, 87], Operations: [] Exploring Operation: 87-82=5, Resulting Numbers: [85, 5, 5] Generated Node #2: [85, 5, 5] from Operation: 87-82=5 Current State: 60:[85, 5, 5], Operations: ['87-82=5'] Exploring Operation: 5*5=25, Resulting Numbers: [85, 25] Generated Node #3: [85, 25] from Operation: 5*5=25 Current State: 60:[85, 25], Operations: ['87-82=5', '5*5=25'] Exploring Operation: 85-25=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[82, 85, 5, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [82, 5, 2] Generated Node #0,0: 60:[82, 5, 2] Operation: 87-85=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[82, 5, 2], Operations: ['87-85=2'] Exploring Operation: 82/2=41, Resulting Numbers: [5, 41] Generated Node #0,0,0: 60:[5, 41] Operation: 82/2=41 Moving to Node #0,0,0 Current State: 60:[5, 41], Operations: ['87-85=2', '82/2=41'] Exploring Operation: 41-5=36, Resulting Numbers: [36] 36,60 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
[ 1, 14, 51, 42 ]
55
[ "1+51=52", "42/14=3", "52+3=55" ]
Current State: 55:[1, 14, 51, 42], Operations: [] Exploring Operation: 1+51=52, Resulting Numbers: [14, 42, 52] Generated Node #2: [14, 42, 52] from Operation: 1+51=52 Current State: 55:[14, 42, 52], Operations: ['1+51=52'] Exploring Operation: 42/14=3, Resulting Numbers: [52, 3] Generated Node #3: [52, 3] from Operation: 42/14=3 Current State: 55:[52, 3], Operations: ['1+51=52', '42/14=3'] Exploring Operation: 52+3=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[1, 14, 51, 42], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [1, 51, 3] Generated Node #0,0: 55:[1, 51, 3] Operation: 42/14=3 Exploring Operation: 51-42=9, Resulting Numbers: [1, 14, 9] Generated Node #0,1: 55:[1, 14, 9] Operation: 51-42=9 Exploring Operation: 14+42=56, Resulting Numbers: [1, 51, 56] Generated Node #0,2: 55:[1, 51, 56] Operation: 14+42=56 Moving to Node #0,1 Current State: 55:[1, 14, 9], Operations: ['51-42=9'] Exploring Operation: 14-9=5, Resulting Numbers: [1, 5] Generated Node #0,1,0: 55:[1, 5] Operation: 14-9=5 Exploring Operation: 14-1=13, Resulting Numbers: [9, 13] Generated Node #0,1,1: 55:[9, 13] Operation: 14-1=13 Exploring Operation: 1+9=10, Resulting Numbers: [14, 10] Generated Node #0,1,2: 55:[14, 10] Operation: 1+9=10 Moving to Node #0,2 Current State: 55:[1, 51, 56], Operations: ['14+42=56'] Exploring Operation: 1+51=52, Resulting Numbers: [56, 52] Generated Node #0,2,0: 55:[56, 52] Operation: 1+51=52 Exploring Operation: 56-1=55, Resulting Numbers: [51, 55] Generated Node #0,2,1: 55:[51, 55] Operation: 56-1=55 Exploring Operation: 56-51=5, Resulting Numbers: [1, 5] Generated Node #0,2,2: 55:[1, 5] Operation: 56-51=5 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 55:[56, 52], Operations: ['14+42=56', '1+51=52'] Exploring Operation: 56-52=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 56+52=108, Resulting Numbers: [108] 108,55 unequal: No Solution Exploring Operation: 56*52=2912, Resulting Numbers: [2912] 2912,55 unequal: No Solution No 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: 55:[51, 55], Operations: ['14+42=56', '56-1=55'] Exploring Operation: 55-51=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 51+55=106, Resulting Numbers: [106] 106,55 unequal: No Solution Exploring Operation: 51*55=2805, Resulting Numbers: [2805] 2805,55 unequal: No Solution No 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: 55:[1, 5], Operations: ['14+42=56', '56-51=5'] Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,55 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,55 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: 55:[1, 51, 3], Operations: ['42/14=3'] Exploring Operation: 51+3=54, Resulting Numbers: [1, 54] Generated Node #0,0,0: 55:[1, 54] Operation: 51+3=54 Exploring Operation: 1+3=4, Resulting Numbers: [51, 4] Generated Node #0,0,1: 55:[51, 4] Operation: 1+3=4 Exploring Operation: 1+51=52, Resulting Numbers: [3, 52] Generated Node #0,0,2: 55:[3, 52] Operation: 1+51=52 Moving to Node #0,1,0 Current State: 55:[1, 5], Operations: ['51-42=9', '14-9=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[14, 10], Operations: ['51-42=9', '1+9=10'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 14*10=140, Resulting Numbers: [140] 140,55 unequal: No Solution Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[9, 13], Operations: ['51-42=9', '14-1=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,55 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[3, 52], Operations: ['42/14=3', '1+51=52'] Exploring Operation: 52-3=49, Resulting Numbers: [49] 49,55 unequal: No Solution Exploring Operation: 3*52=156, Resulting Numbers: [156] 156,55 unequal: No Solution Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[1, 14, 51, 42], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [1, 51, 3] Generated Node #0,0: 55:[1, 51, 3] Operation: 42/14=3 Moving to Node #0,0 Current State: 55:[1, 51, 3], Operations: ['42/14=3'] Exploring Operation: 1+51=52, Resulting Numbers: [3, 52] Generated Node #0,0,2: 55:[3, 52] Operation: 1+51=52 Moving to Node #0,0,2 Current State: 55:[3, 52], Operations: ['42/14=3', '1+51=52'] Exploring Operation: 3+52=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 85, 73, 56, 60 ]
65
[ "73-56=17", "85/17=5", "60+5=65" ]
Current State: 65:[85, 73, 56, 60], Operations: [] Exploring Operation: 73-56=17, Resulting Numbers: [85, 60, 17] Generated Node #2: [85, 60, 17] from Operation: 73-56=17 Current State: 65:[85, 60, 17], Operations: ['73-56=17'] Exploring Operation: 85/17=5, Resulting Numbers: [60, 5] Generated Node #3: [60, 5] from Operation: 85/17=5 Current State: 65:[60, 5], Operations: ['73-56=17', '85/17=5'] Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[85, 73, 56, 60], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [56, 60, 12] Generated Node #0,0: 65:[56, 60, 12] Operation: 85-73=12 Moving to Node #0,0 Current State: 65:[56, 60, 12], Operations: ['85-73=12'] Exploring Operation: 60-56=4, Resulting Numbers: [12, 4] Generated Node #0,0,0: 65:[12, 4] Operation: 60-56=4 Moving to Node #0,0,0 Current State: 65:[12, 4], Operations: ['85-73=12', '60-56=4'] Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,65 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 13, 15, 28, 45 ]
45
[ "13+15=28", "28+45=73", "73-28=45" ]
Current State: 45:[13, 15, 28, 45], Operations: [] Exploring Operation: 13+15=28, Resulting Numbers: [28, 45, 28] Generated Node #2: [28, 45, 28] from Operation: 13+15=28 Current State: 45:[28, 45, 28], Operations: ['13+15=28'] Exploring Operation: 28+45=73, Resulting Numbers: [73] 73,45 equal: Goal Reached Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[13, 15, 28, 45], Operations: [] Exploring Operation: 28-13=15, Resulting Numbers: [15, 45, 15] Generated Node #0,0: 45:[15, 45, 15] Operation: 28-13=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[15, 45, 15], Operations: ['28-13=15'] Exploring Operation: 45/15=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 45:[15, 3] Operation: 45/15=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[15, 3], Operations: ['28-13=15', '45/15=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[13, 15, 28, 45], Operations: [] Exploring Operation: 28-13=15, Resulting Numbers: [15, 45, 15] Generated Node #0,0: 45:[15, 45, 15] Operation: 28-13=15 Moving to Node #0,0 Current State: 45:[15, 45, 15], Operations: ['28-13=15'] Exploring Operation: 45/15=3, Resulting Numbers: [15, 3] Generated Node #0,0,0: 45:[15, 3] Operation: 45/15=3 Moving to Node #0,0,0 Current State: 45:[15, 3], Operations: ['28-13=15', '45/15=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 87, 72, 8 ]
71
[ "87-7=80", "72/8=9", "80-9=71" ]
Current State: 71:[7, 87, 72, 8], Operations: [] Exploring Operation: 87-7=80, Resulting Numbers: [72, 8, 80] Generated Node #2: [72, 8, 80] from Operation: 87-7=80 Current State: 71:[72, 8, 80], Operations: ['87-7=80'] Exploring Operation: 72/8=9, Resulting Numbers: [80, 9] Generated Node #3: [80, 9] from Operation: 72/8=9 Current State: 71:[80, 9], Operations: ['87-7=80', '72/8=9'] Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[7, 87, 72, 8], Operations: [] Exploring Operation: 7*8=56, Resulting Numbers: [87, 72, 56] Generated Node #0,0: 71:[87, 72, 56] Operation: 7*8=56 Moving to Node #0,0 Current State: 71:[87, 72, 56], Operations: ['7*8=56'] Exploring Operation: 87-56=31, Resulting Numbers: [72, 31] Generated Node #0,0,0: 71:[72, 31] Operation: 87-56=31 Moving to Node #0,0,0 Current State: 71:[72, 31], Operations: ['7*8=56', '87-56=31'] Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,71 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 79, 66, 16, 82 ]
85
[ "79-66=13", "16+82=98", "98-13=85" ]
Current State: 85:[79, 66, 16, 82], Operations: [] Exploring Operation: 79-66=13, Resulting Numbers: [16, 82, 13] Generated Node #2: [16, 82, 13] from Operation: 79-66=13 Current State: 85:[16, 82, 13], Operations: ['79-66=13'] Exploring Operation: 16+82=98, Resulting Numbers: [13, 98] Generated Node #3: [13, 98] from Operation: 16+82=98 Current State: 85:[13, 98], Operations: ['79-66=13', '16+82=98'] Exploring Operation: 98-13=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[79, 66, 16, 82], Operations: [] Exploring Operation: 66+16=82, Resulting Numbers: [79, 82, 82] Generated Node #0,0: 85:[79, 82, 82] Operation: 66+16=82 Exploring Operation: 79-66=13, Resulting Numbers: [16, 82, 13] Generated Node #0,1: 85:[16, 82, 13] Operation: 79-66=13 Exploring Operation: 82-79=3, Resulting Numbers: [66, 16, 3] Generated Node #0,2: 85:[66, 16, 3] Operation: 82-79=3 Exploring Operation: 82-66=16, Resulting Numbers: [79, 16, 16] Generated Node #0,3: 85:[79, 16, 16] Operation: 82-66=16 Moving to Node #0,1 Current State: 85:[16, 82, 13], Operations: ['79-66=13'] Exploring Operation: 82+13=95, Resulting Numbers: [16, 95] Generated Node #0,1,0: 85:[16, 95] Operation: 82+13=95 Exploring Operation: 16+13=29, Resulting Numbers: [82, 29] Generated Node #0,1,1: 85:[82, 29] Operation: 16+13=29 Exploring Operation: 16-13=3, Resulting Numbers: [82, 3] Generated Node #0,1,2: 85:[82, 3] Operation: 16-13=3 Exploring Operation: 16+82=98, Resulting Numbers: [13, 98] Generated Node #0,1,3: 85:[13, 98] Operation: 16+82=98 Moving to Node #0,3 Current State: 85:[79, 16, 16], Operations: ['82-66=16'] Exploring Operation: 16/16=1, Resulting Numbers: [79, 1] Generated Node #0,3,0: 85:[79, 1] Operation: 16/16=1 Exploring Operation: 79+16=95, Resulting Numbers: [16, 95] Generated Node #0,3,1: 85:[16, 95] Operation: 79+16=95 Exploring Operation: 79+16=95, Resulting Numbers: [16, 95] Generated Node #0,3,2: 85:[16, 95] Operation: 79+16=95 Exploring Operation: 16-16=0, Resulting Numbers: [79, 0] Generated Node #0,3,3: 85:[79, 0] Operation: 16-16=0 Moving to Node #0,0 Current State: 85:[79, 82, 82], Operations: ['66+16=82'] Exploring Operation: 82-79=3, Resulting Numbers: [82, 3] Generated Node #0,0,0: 85:[82, 3] Operation: 82-79=3 Exploring Operation: 82-82=0, Resulting Numbers: [79, 0] Generated Node #0,0,1: 85:[79, 0] Operation: 82-82=0 Exploring Operation: 82-79=3, Resulting Numbers: [82, 3] Generated Node #0,0,2: 85:[82, 3] Operation: 82-79=3 Exploring Operation: 82/82=1, Resulting Numbers: [79, 1] Generated Node #0,0,3: 85:[79, 1] Operation: 82/82=1 Moving to Node #0,2 Current State: 85:[66, 16, 3], Operations: ['82-79=3'] Exploring Operation: 66+3=69, Resulting Numbers: [16, 69] Generated Node #0,2,0: 85:[16, 69] Operation: 66+3=69 Exploring Operation: 16+3=19, Resulting Numbers: [66, 19] Generated Node #0,2,1: 85:[66, 19] Operation: 16+3=19 Exploring Operation: 66+16=82, Resulting Numbers: [3, 82] Generated Node #0,2,2: 85:[3, 82] Operation: 66+16=82 Exploring Operation: 66/3=22, Resulting Numbers: [16, 22] Generated Node #0,2,3: 85:[16, 22] Operation: 66/3=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 85:[3, 82], Operations: ['82-79=3', '66+16=82'] Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,85 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,85 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[79, 66, 16, 82], Operations: [] Exploring Operation: 82-79=3, Resulting Numbers: [66, 16, 3] Generated Node #0,2: 85:[66, 16, 3] Operation: 82-79=3 Moving to Node #0,2 Current State: 85:[66, 16, 3], Operations: ['82-79=3'] Exploring Operation: 66+16=82, Resulting Numbers: [3, 82] Generated Node #0,2,2: 85:[3, 82] Operation: 66+16=82 Moving to Node #0,2,2 Current State: 85:[3, 82], Operations: ['82-79=3', '66+16=82'] Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_4
sum_heuristic
[ 31, 33, 56, 81 ]
27
[ "33-31=2", "81-56=25", "2+25=27" ]
Current State: 27:[31, 33, 56, 81], Operations: [] Exploring Operation: 33-31=2, Resulting Numbers: [56, 81, 2] Generated Node #2: [56, 81, 2] from Operation: 33-31=2 Current State: 27:[56, 81, 2], Operations: ['33-31=2'] Exploring Operation: 81-56=25, Resulting Numbers: [2, 25] Generated Node #3: [2, 25] from Operation: 81-56=25 Current State: 27:[2, 25], Operations: ['33-31=2', '81-56=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[31, 33, 56, 81], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [33, 81, 25] Generated Node #0,0: 27:[33, 81, 25] Operation: 56-31=25 Exploring Operation: 81-56=25, Resulting Numbers: [31, 33, 25] Generated Node #0,1: 27:[31, 33, 25] Operation: 81-56=25 Exploring Operation: 81-33=48, Resulting Numbers: [31, 56, 48] Generated Node #0,2: 27:[31, 56, 48] Operation: 81-33=48 Exploring Operation: 81-31=50, Resulting Numbers: [33, 56, 50] Generated Node #0,3: 27:[33, 56, 50] Operation: 81-31=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[31, 33, 25], Operations: ['81-56=25'] Exploring Operation: 31-25=6, Resulting Numbers: [33, 6] Generated Node #0,1,0: 27:[33, 6] Operation: 31-25=6 Exploring Operation: 33-25=8, Resulting Numbers: [31, 8] Generated Node #0,1,1: 27:[31, 8] Operation: 33-25=8 Exploring Operation: 33-31=2, Resulting Numbers: [25, 2] Generated Node #0,1,2: 27:[25, 2] Operation: 33-31=2 Exploring Operation: 31+25=56, Resulting Numbers: [33, 56] Generated Node #0,1,3: 27:[33, 56] Operation: 31+25=56 Moving to Node #0,1,2 Current State: 27:[25, 2], Operations: ['81-56=25', '33-31=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,27 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,27 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[31, 33, 56, 81], Operations: [] Exploring Operation: 81-56=25, Resulting Numbers: [31, 33, 25] Generated Node #0,1: 27:[31, 33, 25] Operation: 81-56=25 Moving to Node #0,1 Current State: 27:[31, 33, 25], Operations: ['81-56=25'] Exploring Operation: 33-31=2, Resulting Numbers: [25, 2] Generated Node #0,1,2: 27:[25, 2] Operation: 33-31=2 Moving to Node #0,1,2 Current State: 27:[25, 2], Operations: ['81-56=25', '33-31=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 36, 9, 23, 21 ]
90
[ "36+9=45", "23-21=2", "45*2=90" ]
Current State: 90:[36, 9, 23, 21], Operations: [] Exploring Operation: 36+9=45, Resulting Numbers: [23, 21, 45] Generated Node #2: [23, 21, 45] from Operation: 36+9=45 Current State: 90:[23, 21, 45], Operations: ['36+9=45'] Exploring Operation: 23-21=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 23-21=2 Current State: 90:[45, 2], Operations: ['36+9=45', '23-21=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[36, 9, 23, 21], Operations: [] Exploring Operation: 36-23=13, Resulting Numbers: [9, 21, 13] Generated Node #0,0: 90:[9, 21, 13] Operation: 36-23=13 Exploring Operation: 36-21=15, Resulting Numbers: [9, 23, 15] Generated Node #0,1: 90:[9, 23, 15] Operation: 36-21=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[9, 21, 13], Operations: ['36-23=13'] Exploring Operation: 21-13=8, Resulting Numbers: [9, 8] Generated Node #0,0,0: 90:[9, 8] Operation: 21-13=8 Exploring Operation: 9+21=30, Resulting Numbers: [13, 30] Generated Node #0,0,1: 90:[13, 30] Operation: 9+21=30 Moving to Node #0,0,0 Current State: 90:[9, 8], Operations: ['36-23=13', '21-13=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[13, 30], Operations: ['36-23=13', '9+21=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,90 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[9, 23, 15], Operations: ['36-21=15'] Exploring Operation: 23-9=14, Resulting Numbers: [15, 14] Generated Node #0,1,0: 90:[15, 14] Operation: 23-9=14 Exploring Operation: 23-15=8, Resulting Numbers: [9, 8] Generated Node #0,1,1: 90:[9, 8] Operation: 23-15=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[15, 14], Operations: ['36-21=15', '23-9=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,90 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[9, 8], Operations: ['36-21=15', '23-15=8'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 25, 61, 19, 45 ]
28
[ "61-25=36", "19+45=64", "64-36=28" ]
Current State: 28:[25, 61, 19, 45], Operations: [] Exploring Operation: 61-25=36, Resulting Numbers: [19, 45, 36] Generated Node #2: [19, 45, 36] from Operation: 61-25=36 Current State: 28:[19, 45, 36], Operations: ['61-25=36'] Exploring Operation: 19+45=64, Resulting Numbers: [36, 64] Generated Node #3: [36, 64] from Operation: 19+45=64 Current State: 28:[36, 64], Operations: ['61-25=36', '19+45=64'] Exploring Operation: 64-36=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[25, 61, 19, 45], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [25, 19, 16] Generated Node #0,0: 28:[25, 19, 16] Operation: 61-45=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[25, 19, 16], Operations: ['61-45=16'] Exploring Operation: 25-19=6, Resulting Numbers: [16, 6] Generated Node #0,0,0: 28:[16, 6] Operation: 25-19=6 Moving to Node #0,0,0 Current State: 28:[16, 6], Operations: ['61-45=16', '25-19=6'] Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,28 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
[ 57, 44, 91, 43 ]
34
[ "91-57=34", "44-43=1", "34*1=34" ]
Current State: 34:[57, 44, 91, 43], Operations: [] Exploring Operation: 91-57=34, Resulting Numbers: [44, 43, 34] Generated Node #2: [44, 43, 34] from Operation: 91-57=34 Current State: 34:[44, 43, 34], Operations: ['91-57=34'] Exploring Operation: 44-43=1, Resulting Numbers: [34, 1] Generated Node #3: [34, 1] from Operation: 44-43=1 Current State: 34:[34, 1], Operations: ['91-57=34', '44-43=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[57, 44, 91, 43], Operations: [] Exploring Operation: 57-44=13, Resulting Numbers: [91, 43, 13] Generated Node #0,0: 34:[91, 43, 13] Operation: 57-44=13 Exploring Operation: 91-43=48, Resulting Numbers: [57, 44, 48] Generated Node #0,1: 34:[57, 44, 48] Operation: 91-43=48 Exploring Operation: 91-57=34, Resulting Numbers: [44, 43, 34] Generated Node #0,2: 34:[44, 43, 34] Operation: 91-57=34 Exploring Operation: 91-44=47, Resulting Numbers: [57, 43, 47] Generated Node #0,3: 34:[57, 43, 47] Operation: 91-44=47 Moving to Node #0,2 Current State: 34:[44, 43, 34], Operations: ['91-57=34'] Exploring Operation: 44-43=1, Resulting Numbers: [34, 1] Generated Node #0,2,0: 34:[34, 1] Operation: 44-43=1 Exploring Operation: 44-34=10, Resulting Numbers: [43, 10] Generated Node #0,2,1: 34:[43, 10] Operation: 44-34=10 Exploring Operation: 43-34=9, Resulting Numbers: [44, 9] Generated Node #0,2,2: 34:[44, 9] Operation: 43-34=9 Exploring Operation: 44+43=87, Resulting Numbers: [34, 87] Generated Node #0,2,3: 34:[34, 87] Operation: 44+43=87 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[34, 1], Operations: ['91-57=34', '44-43=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[57, 44, 91, 43], Operations: [] Exploring Operation: 91-57=34, Resulting Numbers: [44, 43, 34] Generated Node #0,2: 34:[44, 43, 34] Operation: 91-57=34 Moving to Node #0,2 Current State: 34:[44, 43, 34], Operations: ['91-57=34'] Exploring Operation: 44-43=1, Resulting Numbers: [34, 1] Generated Node #0,2,0: 34:[34, 1] Operation: 44-43=1 Moving to Node #0,2,0 Current State: 34:[34, 1], Operations: ['91-57=34', '44-43=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 14, 39, 79, 13 ]
31
[ "14+79=93", "39/13=3", "93/3=31" ]
Current State: 31:[14, 39, 79, 13], Operations: [] Exploring Operation: 14+79=93, Resulting Numbers: [39, 13, 93] Generated Node #2: [39, 13, 93] from Operation: 14+79=93 Current State: 31:[39, 13, 93], Operations: ['14+79=93'] Exploring Operation: 39/13=3, Resulting Numbers: [93, 3] Generated Node #3: [93, 3] from Operation: 39/13=3 Current State: 31:[93, 3], Operations: ['14+79=93', '39/13=3'] Exploring Operation: 93/3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[14, 39, 79, 13], Operations: [] Exploring Operation: 79-14=65, Resulting Numbers: [39, 13, 65] Generated Node #0,0: 31:[39, 13, 65] Operation: 79-14=65 Exploring Operation: 79-39=40, Resulting Numbers: [14, 13, 40] Generated Node #0,1: 31:[14, 13, 40] Operation: 79-39=40 Exploring Operation: 39-13=26, Resulting Numbers: [14, 79, 26] Generated Node #0,2: 31:[14, 79, 26] Operation: 39-13=26 Exploring Operation: 14+13=27, Resulting Numbers: [39, 79, 27] Generated Node #0,3: 31:[39, 79, 27] Operation: 14+13=27 Exploring Operation: 79-13=66, Resulting Numbers: [14, 39, 66] Generated Node #0,4: 31:[14, 39, 66] Operation: 79-13=66 Moving to Node #0,1 Current State: 31:[14, 13, 40], Operations: ['79-39=40'] Exploring Operation: 14-13=1, Resulting Numbers: [40, 1] Generated Node #0,1,0: 31:[40, 1] Operation: 14-13=1 Exploring Operation: 13+40=53, Resulting Numbers: [14, 53] Generated Node #0,1,1: 31:[14, 53] Operation: 13+40=53 Exploring Operation: 40-13=27, Resulting Numbers: [14, 27] Generated Node #0,1,2: 31:[14, 27] Operation: 40-13=27 Exploring Operation: 14+13=27, Resulting Numbers: [40, 27] Generated Node #0,1,3: 31:[40, 27] Operation: 14+13=27 Exploring Operation: 40-14=26, Resulting Numbers: [13, 26] Generated Node #0,1,4: 31:[13, 26] Operation: 40-14=26 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 31:[40, 27], Operations: ['79-39=40', '14+13=27'] Exploring Operation: 40*27=1080, Resulting Numbers: [1080] 1080,31 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 40+27=67, Resulting Numbers: [67] 67,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 31:[14, 27], Operations: ['79-39=40', '40-13=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 31:[13, 26], Operations: ['79-39=40', '40-14=26'] Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,31 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 31:[40, 1], Operations: ['79-39=40', '14-13=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,31 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 40+1=41, Resulting Numbers: [41] 41,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[14, 53], Operations: ['79-39=40', '13+40=53'] Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,31 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 31:[39, 79, 27], Operations: ['14+13=27'] Exploring Operation: 79-27=52, Resulting Numbers: [39, 52] Generated Node #0,3,0: 31:[39, 52] Operation: 79-27=52 Exploring Operation: 79-39=40, Resulting Numbers: [27, 40] Generated Node #0,3,1: 31:[27, 40] Operation: 79-39=40 Exploring Operation: 79+27=106, Resulting Numbers: [39, 106] Generated Node #0,3,2: 31:[39, 106] Operation: 79+27=106 Exploring Operation: 39+27=66, Resulting Numbers: [79, 66] Generated Node #0,3,3: 31:[79, 66] Operation: 39+27=66 Exploring Operation: 39-27=12, Resulting Numbers: [79, 12] Generated Node #0,3,4: 31:[79, 12] Operation: 39-27=12 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[27, 40], Operations: ['14+13=27', '79-39=40'] Exploring Operation: 27*40=1080, Resulting Numbers: [1080] 1080,31 unequal: No Solution Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[39, 52], Operations: ['14+13=27', '79-27=52'] Exploring Operation: 39+52=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 39*52=2028, Resulting Numbers: [2028] 2028,31 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 31:[79, 12], Operations: ['14+13=27', '39-27=12'] Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 79*12=948, Resulting Numbers: [948] 948,31 unequal: No Solution Exploring Operation: 79+12=91, Resulting Numbers: [91] 91,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[39, 106], Operations: ['14+13=27', '79+27=106'] Exploring Operation: 39+106=145, Resulting Numbers: [145] 145,31 unequal: No Solution Exploring Operation: 106-39=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 39*106=4134, Resulting Numbers: [4134] 4134,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[79, 66], Operations: ['14+13=27', '39+27=66'] Exploring Operation: 79+66=145, Resulting Numbers: [145] 145,31 unequal: No Solution Exploring Operation: 79*66=5214, Resulting Numbers: [5214] 5214,31 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,31 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: 31:[39, 13, 65], Operations: ['79-14=65'] Exploring Operation: 39+13=52, Resulting Numbers: [65, 52] Generated Node #0,0,0: 31:[65, 52] Operation: 39+13=52 Exploring Operation: 65-39=26, Resulting Numbers: [13, 26] Generated Node #0,0,1: 31:[13, 26] Operation: 65-39=26 Exploring Operation: 39-13=26, Resulting Numbers: [65, 26] Generated Node #0,0,2: 31:[65, 26] Operation: 39-13=26 Exploring Operation: 65/13=5, Resulting Numbers: [39, 5] Generated Node #0,0,3: 31:[39, 5] Operation: 65/13=5 Exploring Operation: 65-13=52, Resulting Numbers: [39, 52] Generated Node #0,0,4: 31:[39, 52] Operation: 65-13=52 Moving to Node #0,4 Current State: 31:[14, 39, 66], Operations: ['79-13=66'] Exploring Operation: 14+39=53, Resulting Numbers: [66, 53] Generated Node #0,4,0: 31:[66, 53] Operation: 14+39=53 Exploring Operation: 39-14=25, Resulting Numbers: [66, 25] Generated Node #0,4,1: 31:[66, 25] Operation: 39-14=25 Exploring Operation: 66-14=52, Resulting Numbers: [39, 52] Generated Node #0,4,2: 31:[39, 52] Operation: 66-14=52 Exploring Operation: 14+66=80, Resulting Numbers: [39, 80] Generated Node #0,4,3: 31:[39, 80] Operation: 14+66=80 Exploring Operation: 66-39=27, Resulting Numbers: [14, 27] Generated Node #0,4,4: 31:[14, 27] Operation: 66-39=27 Moving to Node #0,2 Current State: 31:[14, 79, 26], Operations: ['39-13=26'] Exploring Operation: 26-14=12, Resulting Numbers: [79, 12] Generated Node #0,2,0: 31:[79, 12] Operation: 26-14=12 Exploring Operation: 79-14=65, Resulting Numbers: [26, 65] Generated Node #0,2,1: 31:[26, 65] Operation: 79-14=65 Exploring Operation: 14+79=93, Resulting Numbers: [26, 93] Generated Node #0,2,2: 31:[26, 93] Operation: 14+79=93 Exploring Operation: 14+26=40, Resulting Numbers: [79, 40] Generated Node #0,2,3: 31:[79, 40] Operation: 14+26=40 Exploring Operation: 79-26=53, Resulting Numbers: [14, 53] Generated Node #0,2,4: 31:[14, 53] Operation: 79-26=53 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[26, 65], Operations: ['39-13=26', '79-14=65'] Exploring Operation: 26+65=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 26*65=1690, Resulting Numbers: [1690] 1690,31 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 31:[14, 53], Operations: ['39-13=26', '79-26=53'] Exploring Operation: 14+53=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 53-14=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 14*53=742, Resulting Numbers: [742] 742,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[79, 40], Operations: ['39-13=26', '14+26=40'] Exploring Operation: 79*40=3160, Resulting Numbers: [3160] 3160,31 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,31 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[79, 12], Operations: ['39-13=26', '26-14=12'] Exploring Operation: 79*12=948, Resulting Numbers: [948] 948,31 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 79+12=91, Resulting Numbers: [91] 91,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[26, 93], Operations: ['39-13=26', '14+79=93'] Exploring Operation: 26*93=2418, Resulting Numbers: [2418] 2418,31 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,31 unequal: No Solution Exploring Operation: 26+93=119, Resulting Numbers: [119] 119,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 31:[14, 27], Operations: ['79-13=66', '66-39=27'] Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,31 unequal: No Solution Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[13, 26], Operations: ['79-14=65', '65-39=26'] Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,31 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,31 unequal: No Solution Moving to Node #0,4,2 Current State: 31:[39, 52], Operations: ['79-13=66', '66-14=52'] Exploring Operation: 39*52=2028, Resulting Numbers: [2028] 2028,31 unequal: No Solution Exploring Operation: 39+52=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,31 unequal: No Solution Moving to Node #0,0,4 Current State: 31:[39, 52], Operations: ['79-14=65', '65-13=52'] Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 39+52=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 39*52=2028, Resulting Numbers: [2028] 2028,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[39, 5], Operations: ['79-14=65', '65/13=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[65, 26], Operations: ['79-14=65', '39-13=26'] Exploring Operation: 65+26=91, Resulting Numbers: [91] 91,31 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 65*26=1690, Resulting Numbers: [1690] 1690,31 unequal: No Solution Moving to Node #0,4,1 Current State: 31:[66, 25], Operations: ['79-13=66', '39-14=25'] Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 66*25=1650, Resulting Numbers: [1650] 1650,31 unequal: No Solution Exploring Operation: 66+25=91, Resulting Numbers: [91] 91,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[65, 52], Operations: ['79-14=65', '39+13=52'] Exploring Operation: 65*52=3380, Resulting Numbers: [3380] 3380,31 unequal: No Solution Exploring Operation: 65-52=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 65+52=117, Resulting Numbers: [117] 117,31 unequal: No Solution Moving to Node #0,4,3 Current State: 31:[39, 80], Operations: ['79-13=66', '14+66=80'] Exploring Operation: 39*80=3120, Resulting Numbers: [3120] 3120,31 unequal: No Solution Exploring Operation: 39+80=119, Resulting Numbers: [119] 119,31 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,31 unequal: No Solution Moving to Node #0,4,0 Current State: 31:[66, 53], Operations: ['79-13=66', '14+39=53'] Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,31 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,31 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 37, 96, 27, 25 ]
61
[ "96-37=59", "27-25=2", "59+2=61" ]
Current State: 61:[37, 96, 27, 25], Operations: [] Exploring Operation: 96-37=59, Resulting Numbers: [27, 25, 59] Generated Node #2: [27, 25, 59] from Operation: 96-37=59 Current State: 61:[27, 25, 59], Operations: ['96-37=59'] Exploring Operation: 27-25=2, Resulting Numbers: [59, 2] Generated Node #3: [59, 2] from Operation: 27-25=2 Current State: 61:[59, 2], Operations: ['96-37=59', '27-25=2'] Exploring Operation: 59+2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[37, 96, 27, 25], Operations: [] Exploring Operation: 96-25=71, Resulting Numbers: [37, 27, 71] Generated Node #0,0: 61:[37, 27, 71] Operation: 96-25=71 Exploring Operation: 96-27=69, Resulting Numbers: [37, 25, 69] Generated Node #0,1: 61:[37, 25, 69] Operation: 96-27=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[37, 27, 71], Operations: ['96-25=71'] Exploring Operation: 37+27=64, Resulting Numbers: [71, 64] Generated Node #0,0,0: 61:[71, 64] Operation: 37+27=64 Exploring Operation: 71-27=44, Resulting Numbers: [37, 44] Generated Node #0,0,1: 61:[37, 44] Operation: 71-27=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[71, 64], Operations: ['96-25=71', '37+27=64'] Exploring Operation: 71+64=135, Resulting Numbers: [135] 135,61 unequal: No Solution Exploring Operation: 71-64=7, Resulting Numbers: [7] 7,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[37, 44], Operations: ['96-25=71', '71-27=44'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,61 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: 61:[37, 25, 69], Operations: ['96-27=69'] Exploring Operation: 69-25=44, Resulting Numbers: [37, 44] Generated Node #0,1,0: 61:[37, 44] Operation: 69-25=44 Exploring Operation: 37+25=62, Resulting Numbers: [69, 62] Generated Node #0,1,1: 61:[69, 62] Operation: 37+25=62 Moving to Node #0,1,1 Current State: 61:[69, 62], Operations: ['96-27=69', '37+25=62'] Exploring Operation: 69-62=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 69+62=131, Resulting Numbers: [131] 131,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[37, 44], Operations: ['96-27=69', '69-25=44'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,61 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
[ 8, 67, 11, 6 ]
87
[ "8+6=14", "11*14=154", "154-67=87" ]
Current State: 87:[8, 67, 11, 6], Operations: [] Exploring Operation: 8+6=14, Resulting Numbers: [67, 11, 14] Generated Node #2: [67, 11, 14] from Operation: 8+6=14 Current State: 87:[67, 11, 14], Operations: ['8+6=14'] Exploring Operation: 11*14=154, Resulting Numbers: [67, 154] Generated Node #3: [67, 154] from Operation: 11*14=154 Current State: 87:[67, 154], Operations: ['8+6=14', '11*14=154'] Exploring Operation: 154-67=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[8, 67, 11, 6], Operations: [] Exploring Operation: 67+11=78, Resulting Numbers: [8, 6, 78] Generated Node #0,0: 87:[8, 6, 78] Operation: 67+11=78 Exploring Operation: 67+6=73, Resulting Numbers: [8, 11, 73] Generated Node #0,1: 87:[8, 11, 73] Operation: 67+6=73 Exploring Operation: 11-8=3, Resulting Numbers: [67, 6, 3] Generated Node #0,2: 87:[67, 6, 3] Operation: 11-8=3 Exploring Operation: 8*11=88, Resulting Numbers: [67, 6, 88] Generated Node #0,3: 87:[67, 6, 88] Operation: 8*11=88 Exploring Operation: 8+67=75, Resulting Numbers: [11, 6, 75] Generated Node #0,4: 87:[11, 6, 75] Operation: 8+67=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[8, 6, 78], Operations: ['67+11=78'] Exploring Operation: 6+78=84, Resulting Numbers: [8, 84] Generated Node #0,0,0: 87:[8, 84] Operation: 6+78=84 Exploring Operation: 8+78=86, Resulting Numbers: [6, 86] Generated Node #0,0,1: 87:[6, 86] Operation: 8+78=86 Exploring Operation: 78/6=13, Resulting Numbers: [8, 13] Generated Node #0,0,2: 87:[8, 13] Operation: 78/6=13 Exploring Operation: 8+6=14, Resulting Numbers: [78, 14] Generated Node #0,0,3: 87:[78, 14] Operation: 8+6=14 Exploring Operation: 8-6=2, Resulting Numbers: [78, 2] Generated Node #0,0,4: 87:[78, 2] Operation: 8-6=2 Moving to Node #0,0,1 Current State: 87:[6, 86], Operations: ['67+11=78', '8+78=86'] Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,87 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,87 unequal: No Solution Moving to Node #0,0,0 Current State: 87:[8, 84], Operations: ['67+11=78', '6+78=84'] Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 8*84=672, Resulting Numbers: [672] 672,87 unequal: No Solution Exploring Operation: 8+84=92, Resulting Numbers: [92] 92,87 unequal: No Solution Moving to Node #0,0,4 Current State: 87:[78, 2], Operations: ['67+11=78', '8-6=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,87 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[8, 13], Operations: ['67+11=78', '78/6=13'] Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,87 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,87 unequal: No Solution Moving to Node #0,0,3 Current State: 87:[78, 14], Operations: ['67+11=78', '8+6=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,87 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 Current State: 87:[67, 6, 3], Operations: ['11-8=3'] Exploring Operation: 6-3=3, Resulting Numbers: [67, 3] Generated Node #0,2,0: 87:[67, 3] Operation: 6-3=3 Exploring Operation: 67+3=70, Resulting Numbers: [6, 70] Generated Node #0,2,1: 87:[6, 70] Operation: 67+3=70 Exploring Operation: 6/3=2, Resulting Numbers: [67, 2] Generated Node #0,2,2: 87:[67, 2] Operation: 6/3=2 Exploring Operation: 67+6=73, Resulting Numbers: [3, 73] Generated Node #0,2,3: 87:[3, 73] Operation: 67+6=73 Exploring Operation: 67-6=61, Resulting Numbers: [3, 61] Generated Node #0,2,4: 87:[3, 61] Operation: 67-6=61 Moving to Node #0,2,3 Current State: 87:[3, 73], Operations: ['11-8=3', '67+6=73'] Exploring Operation: 3*73=219, Resulting Numbers: [219] 219,87 unequal: No Solution Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[6, 70], Operations: ['11-8=3', '67+3=70'] Exploring Operation: 6+70=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 6*70=420, Resulting Numbers: [420] 420,87 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[67, 3], Operations: ['11-8=3', '6-3=3'] Exploring Operation: 67+3=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 67*3=201, Resulting Numbers: [201] 201,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[67, 2], Operations: ['11-8=3', '6/3=2'] Exploring Operation: 67*2=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,87 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,87 unequal: No Solution Moving to Node #0,2,4 Current State: 87:[3, 61], Operations: ['11-8=3', '67-6=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,87 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 #0,4 Current State: 87:[11, 6, 75], Operations: ['8+67=75'] Exploring Operation: 11-6=5, Resulting Numbers: [75, 5] Generated Node #0,4,0: 87:[75, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [75, 17] Generated Node #0,4,1: 87:[75, 17] Operation: 11+6=17 Exploring Operation: 11+75=86, Resulting Numbers: [6, 86] Generated Node #0,4,2: 87:[6, 86] Operation: 11+75=86 Exploring Operation: 75-11=64, Resulting Numbers: [6, 64] Generated Node #0,4,3: 87:[6, 64] Operation: 75-11=64 Exploring Operation: 6+75=81, Resulting Numbers: [11, 81] Generated Node #0,4,4: 87:[11, 81] Operation: 6+75=81 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 87:[6, 86], Operations: ['8+67=75', '11+75=86'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 6+86=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 6*86=516, Resulting Numbers: [516] 516,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 87:[75, 5], Operations: ['8+67=75', '11-6=5'] Exploring Operation: 75*5=375, Resulting Numbers: [375] 375,87 unequal: No Solution Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 87:[11, 81], Operations: ['8+67=75', '6+75=81'] Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,87 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 87:[75, 17], Operations: ['8+67=75', '11+6=17'] Exploring Operation: 75*17=1275, Resulting Numbers: [1275] 1275,87 unequal: No Solution Exploring Operation: 75+17=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 87:[6, 64], Operations: ['8+67=75', '75-11=64'] Exploring Operation: 6+64=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 6*64=384, Resulting Numbers: [384] 384,87 unequal: No Solution Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[67, 6, 88], Operations: ['8*11=88'] Exploring Operation: 67-6=61, Resulting Numbers: [88, 61] Generated Node #0,3,0: 87:[88, 61] Operation: 67-6=61 Exploring Operation: 67+6=73, Resulting Numbers: [88, 73] Generated Node #0,3,1: 87:[88, 73] Operation: 67+6=73 Exploring Operation: 6+88=94, Resulting Numbers: [67, 94] Generated Node #0,3,2: 87:[67, 94] Operation: 6+88=94 Exploring Operation: 88-67=21, Resulting Numbers: [6, 21] Generated Node #0,3,3: 87:[6, 21] Operation: 88-67=21 Exploring Operation: 88-6=82, Resulting Numbers: [67, 82] Generated Node #0,3,4: 87:[67, 82] Operation: 88-6=82 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[6, 21], Operations: ['8*11=88', '88-67=21'] Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,87 unequal: No Solution Exploring Operation: 6*21=126, Resulting Numbers: [126] 126,87 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[88, 73], Operations: ['8*11=88', '67+6=73'] Exploring Operation: 88*73=6424, Resulting Numbers: [6424] 6424,87 unequal: No Solution Exploring Operation: 88+73=161, Resulting Numbers: [161] 161,87 unequal: No Solution Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 87:[67, 82], Operations: ['8*11=88', '88-6=82'] Exploring Operation: 67*82=5494, Resulting Numbers: [5494] 5494,87 unequal: No Solution Exploring Operation: 67+82=149, Resulting Numbers: [149] 149,87 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[88, 61], Operations: ['8*11=88', '67-6=61'] Exploring Operation: 88+61=149, Resulting Numbers: [149] 149,87 unequal: No Solution Exploring Operation: 88*61=5368, Resulting Numbers: [5368] 5368,87 unequal: No Solution Exploring Operation: 88-61=27, Resulting Numbers: [27] 27,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[67, 94], Operations: ['8*11=88', '6+88=94'] Exploring Operation: 67+94=161, Resulting Numbers: [161] 161,87 unequal: No Solution Exploring Operation: 67*94=6298, Resulting Numbers: [6298] 6298,87 unequal: No Solution Exploring Operation: 94-67=27, Resulting Numbers: [27] 27,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[8, 11, 73], Operations: ['67+6=73'] Exploring Operation: 11-8=3, Resulting Numbers: [73, 3] Generated Node #0,1,0: 87:[73, 3] Operation: 11-8=3 Exploring Operation: 8+73=81, Resulting Numbers: [11, 81] Generated Node #0,1,1: 87:[11, 81] Operation: 8+73=81 Exploring Operation: 8*11=88, Resulting Numbers: [73, 88] Generated Node #0,1,2: 87:[73, 88] Operation: 8*11=88 Exploring Operation: 8+11=19, Resulting Numbers: [73, 19] Generated Node #0,1,3: 87:[73, 19] Operation: 8+11=19 Exploring Operation: 11+73=84, Resulting Numbers: [8, 84] Generated Node #0,1,4: 87:[8, 84] Operation: 11+73=84 Moving to Node #0,1,4 Current State: 87:[8, 84], Operations: ['67+6=73', '11+73=84'] Exploring Operation: 8*84=672, Resulting Numbers: [672] 672,87 unequal: No Solution Exploring Operation: 8+84=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 84-8=76, Resulting Numbers: [76] 76,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[11, 81], Operations: ['67+6=73', '8+73=81'] Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[73, 3], Operations: ['67+6=73', '11-8=3'] Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,87 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,87 unequal: No Solution Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[73, 88], Operations: ['67+6=73', '8*11=88'] Exploring Operation: 73+88=161, Resulting Numbers: [161] 161,87 unequal: No Solution Exploring Operation: 73*88=6424, Resulting Numbers: [6424] 6424,87 unequal: No Solution Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[73, 19], Operations: ['67+6=73', '8+11=19'] Exploring Operation: 73+19=92, Resulting Numbers: [92] 92,87 unequal: No Solution Exploring Operation: 73*19=1387, Resulting Numbers: [1387] 1387,87 unequal: No Solution Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,87 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
[ 71, 17, 90, 84 ]
42
[ "71+17=88", "90-88=2", "84/2=42" ]
Current State: 42:[71, 17, 90, 84], Operations: [] Exploring Operation: 71+17=88, Resulting Numbers: [90, 84, 88] Generated Node #2: [90, 84, 88] from Operation: 71+17=88 Current State: 42:[90, 84, 88], Operations: ['71+17=88'] Exploring Operation: 90-88=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 90-88=2 Current State: 42:[84, 2], Operations: ['71+17=88', '90-88=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[71, 17, 90, 84], Operations: [] Exploring Operation: 84-71=13, Resulting Numbers: [17, 90, 13] Generated Node #0,0: 42:[17, 90, 13] Operation: 84-71=13 Exploring Operation: 71-17=54, Resulting Numbers: [90, 84, 54] Generated Node #0,1: 42:[90, 84, 54] Operation: 71-17=54 Exploring Operation: 90-71=19, Resulting Numbers: [17, 84, 19] Generated Node #0,2: 42:[17, 84, 19] Operation: 90-71=19 Exploring Operation: 90-84=6, Resulting Numbers: [71, 17, 6] Generated Node #0,3: 42:[71, 17, 6] Operation: 90-84=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[71, 17, 6], Operations: ['90-84=6'] Exploring Operation: 17+6=23, Resulting Numbers: [71, 23] Generated Node #0,3,0: 42:[71, 23] Operation: 17+6=23 Exploring Operation: 71-17=54, Resulting Numbers: [6, 54] Generated Node #0,3,1: 42:[6, 54] Operation: 71-17=54 Exploring Operation: 71-6=65, Resulting Numbers: [17, 65] Generated Node #0,3,2: 42:[17, 65] Operation: 71-6=65 Exploring Operation: 17-6=11, Resulting Numbers: [71, 11] Generated Node #0,3,3: 42:[71, 11] Operation: 17-6=11 Moving to Node #0,3,1 Current State: 42:[6, 54], Operations: ['90-84=6', '71-17=54'] Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,42 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[17, 65], Operations: ['90-84=6', '71-6=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,42 unequal: No Solution Exploring Operation: 17*65=1105, Resulting Numbers: [1105] 1105,42 unequal: No Solution Moving to Node #0,3,0 Current State: 42:[71, 23], Operations: ['90-84=6', '17+6=23'] Exploring Operation: 71*23=1633, Resulting Numbers: [1633] 1633,42 unequal: No Solution Exploring Operation: 71+23=94, Resulting Numbers: [94] 94,42 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[71, 11], Operations: ['90-84=6', '17-6=11'] Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,42 unequal: No Solution Exploring Operation: 71*11=781, Resulting Numbers: [781] 781,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[17, 84, 19], Operations: ['90-71=19'] Exploring Operation: 19-17=2, Resulting Numbers: [84, 2] Generated Node #0,2,0: 42:[84, 2] Operation: 19-17=2 Exploring Operation: 17+19=36, Resulting Numbers: [84, 36] Generated Node #0,2,1: 42:[84, 36] Operation: 17+19=36 Exploring Operation: 84-19=65, Resulting Numbers: [17, 65] Generated Node #0,2,2: 42:[17, 65] Operation: 84-19=65 Exploring Operation: 84-17=67, Resulting Numbers: [19, 67] Generated Node #0,2,3: 42:[19, 67] Operation: 84-17=67 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 42:[17, 65], Operations: ['90-71=19', '84-19=65'] Exploring Operation: 17*65=1105, Resulting Numbers: [1105] 1105,42 unequal: No Solution Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,42 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 #0,2,3 Current State: 42:[19, 67], Operations: ['90-71=19', '84-17=67'] Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,42 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,42 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,42 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 #0,2,0 Current State: 42:[84, 2], Operations: ['90-71=19', '19-17=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,42 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,42 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,42 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[71, 17, 90, 84], Operations: [] Exploring Operation: 90-71=19, Resulting Numbers: [17, 84, 19] Generated Node #0,2: 42:[17, 84, 19] Operation: 90-71=19 Moving to Node #0,2 Current State: 42:[17, 84, 19], Operations: ['90-71=19'] Exploring Operation: 19-17=2, Resulting Numbers: [84, 2] Generated Node #0,2,0: 42:[84, 2] Operation: 19-17=2 Moving to Node #0,2,0 Current State: 42:[84, 2], Operations: ['90-71=19', '19-17=2'] Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 61, 62, 20, 32 ]
52
[ "62-61=1", "20+32=52", "1*52=52" ]
Current State: 52:[61, 62, 20, 32], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [20, 32, 1] Generated Node #2: [20, 32, 1] from Operation: 62-61=1 Current State: 52:[20, 32, 1], Operations: ['62-61=1'] Exploring Operation: 20+32=52, Resulting Numbers: [1, 52] Generated Node #3: [1, 52] from Operation: 20+32=52 Current State: 52:[1, 52], Operations: ['62-61=1', '20+32=52'] Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[61, 62, 20, 32], Operations: [] Exploring Operation: 61-32=29, Resulting Numbers: [62, 20, 29] Generated Node #0,0: 52:[62, 20, 29] Operation: 61-32=29 Exploring Operation: 62-61=1, Resulting Numbers: [20, 32, 1] Generated Node #0,1: 52:[20, 32, 1] Operation: 62-61=1 Exploring Operation: 62-32=30, Resulting Numbers: [61, 20, 30] Generated Node #0,2: 52:[61, 20, 30] Operation: 62-32=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[20, 32, 1], Operations: ['62-61=1'] Exploring Operation: 32-20=12, Resulting Numbers: [1, 12] Generated Node #0,1,0: 52:[1, 12] Operation: 32-20=12 Exploring Operation: 20+1=21, Resulting Numbers: [32, 21] Generated Node #0,1,1: 52:[32, 21] Operation: 20+1=21 Exploring Operation: 20+32=52, Resulting Numbers: [1, 52] Generated Node #0,1,2: 52:[1, 52] Operation: 20+32=52 Moving to Node #0,1,2 Current State: 52:[1, 52], Operations: ['62-61=1', '20+32=52'] Exploring Operation: 1+52=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[61, 62, 20, 32], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [20, 32, 1] Generated Node #0,1: 52:[20, 32, 1] Operation: 62-61=1 Moving to Node #0,1 Current State: 52:[20, 32, 1], Operations: ['62-61=1'] Exploring Operation: 20+32=52, Resulting Numbers: [1, 52] Generated Node #0,1,2: 52:[1, 52] Operation: 20+32=52 Moving to Node #0,1,2 Current State: 52:[1, 52], Operations: ['62-61=1', '20+32=52'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 58, 36, 66, 55 ]
33
[ "58-36=22", "66-55=11", "22+11=33" ]
Current State: 33:[58, 36, 66, 55], Operations: [] Exploring Operation: 58-36=22, Resulting Numbers: [66, 55, 22] Generated Node #2: [66, 55, 22] from Operation: 58-36=22 Current State: 33:[66, 55, 22], Operations: ['58-36=22'] Exploring Operation: 66-55=11, Resulting Numbers: [22, 11] Generated Node #3: [22, 11] from Operation: 66-55=11 Current State: 33:[22, 11], Operations: ['58-36=22', '66-55=11'] Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[58, 36, 66, 55], Operations: [] Exploring Operation: 66-58=8, Resulting Numbers: [36, 55, 8] Generated Node #0,0: 33:[36, 55, 8] Operation: 66-58=8 Moving to Node #0,0 Current State: 33:[36, 55, 8], Operations: ['66-58=8'] Exploring Operation: 55-36=19, Resulting Numbers: [8, 19] Generated Node #0,0,0: 33:[8, 19] Operation: 55-36=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[8, 19], Operations: ['66-58=8', '55-36=19'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 52, 54, 62, 11 ]
53
[ "54-52=2", "62-11=51", "2+51=53" ]
Current State: 53:[52, 54, 62, 11], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [62, 11, 2] Generated Node #2: [62, 11, 2] from Operation: 54-52=2 Current State: 53:[62, 11, 2], Operations: ['54-52=2'] Exploring Operation: 62-11=51, Resulting Numbers: [2, 51] Generated Node #3: [2, 51] from Operation: 62-11=51 Current State: 53:[2, 51], Operations: ['54-52=2', '62-11=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[52, 54, 62, 11], Operations: [] Exploring Operation: 62-11=51, Resulting Numbers: [52, 54, 51] Generated Node #0,0: 53:[52, 54, 51] Operation: 62-11=51 Moving to Node #0,0 Current State: 53:[52, 54, 51], Operations: ['62-11=51'] Exploring Operation: 52+51=103, Resulting Numbers: [54, 103] Generated Node #0,0,0: 53:[54, 103] Operation: 52+51=103 Moving to Node #0,0,0 Current State: 53:[54, 103], Operations: ['62-11=51', '52+51=103'] Exploring Operation: 103-54=49, Resulting Numbers: [49] 49,53 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 62, 15, 72, 60 ]
12
[ "62+15=77", "77-72=5", "60/5=12" ]
Current State: 12:[62, 15, 72, 60], Operations: [] Exploring Operation: 62+15=77, Resulting Numbers: [72, 60, 77] Generated Node #2: [72, 60, 77] from Operation: 62+15=77 Current State: 12:[72, 60, 77], Operations: ['62+15=77'] Exploring Operation: 77-72=5, Resulting Numbers: [60, 5] Generated Node #3: [60, 5] from Operation: 77-72=5 Current State: 12:[60, 5], Operations: ['62+15=77', '77-72=5'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[62, 15, 72, 60], Operations: [] Exploring Operation: 72-60=12, Resulting Numbers: [62, 15, 12] Generated Node #0,0: 12:[62, 15, 12] Operation: 72-60=12 Exploring Operation: 62-60=2, Resulting Numbers: [15, 72, 2] Generated Node #0,1: 12:[15, 72, 2] Operation: 62-60=2 Exploring Operation: 72-62=10, Resulting Numbers: [15, 60, 10] Generated Node #0,2: 12:[15, 60, 10] Operation: 72-62=10 Moving to Node #0,0 Current State: 12:[62, 15, 12], Operations: ['72-60=12'] Exploring Operation: 62-12=50, Resulting Numbers: [15, 50] Generated Node #0,0,0: 12:[15, 50] Operation: 62-12=50 Exploring Operation: 15-12=3, Resulting Numbers: [62, 3] Generated Node #0,0,1: 12:[62, 3] Operation: 15-12=3 Exploring Operation: 62-15=47, Resulting Numbers: [12, 47] Generated Node #0,0,2: 12:[12, 47] Operation: 62-15=47 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[12, 47], Operations: ['72-60=12', '62-15=47'] Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[15, 50], Operations: ['72-60=12', '62-12=50'] Exploring Operation: 15*50=750, Resulting Numbers: [750] 750,12 unequal: No Solution Exploring Operation: 15+50=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[62, 3], Operations: ['72-60=12', '15-12=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,12 unequal: No Solution Exploring Operation: 62*3=186, Resulting Numbers: [186] 186,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 12:[15, 60, 10], Operations: ['72-62=10'] Exploring Operation: 60/15=4, Resulting Numbers: [10, 4] Generated Node #0,2,0: 12:[10, 4] Operation: 60/15=4 Exploring Operation: 60-15=45, Resulting Numbers: [10, 45] Generated Node #0,2,1: 12:[10, 45] Operation: 60-15=45 Exploring Operation: 60/10=6, Resulting Numbers: [15, 6] Generated Node #0,2,2: 12:[15, 6] Operation: 60/10=6 Moving to Node #0,1 Current State: 12:[15, 72, 2], Operations: ['62-60=2'] Exploring Operation: 72-15=57, Resulting Numbers: [2, 57] Generated Node #0,1,0: 12:[2, 57] Operation: 72-15=57 Exploring Operation: 15-2=13, Resulting Numbers: [72, 13] Generated Node #0,1,1: 12:[72, 13] Operation: 15-2=13 Exploring Operation: 72/2=36, Resulting Numbers: [15, 36] Generated Node #0,1,2: 12:[15, 36] Operation: 72/2=36 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 12:[15, 36], Operations: ['62-60=2', '72/2=36'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 15+36=51, Resulting Numbers: [51] 51,12 unequal: No Solution Exploring Operation: 15*36=540, Resulting Numbers: [540] 540,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[2, 57], Operations: ['62-60=2', '72-15=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,12 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[72, 13], Operations: ['62-60=2', '15-2=13'] Exploring Operation: 72+13=85, Resulting Numbers: [85] 85,12 unequal: No Solution Exploring Operation: 72-13=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 72*13=936, Resulting Numbers: [936] 936,12 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: 12:[10, 4], Operations: ['72-62=10', '60/15=4'] Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[15, 6], Operations: ['72-62=10', '60/10=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[10, 45], Operations: ['72-62=10', '60-15=45'] Exploring Operation: 10+45=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,12 unequal: No Solution Exploring Operation: 10*45=450, Resulting Numbers: [450] 450,12 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 69, 36, 68, 6 ]
29
[ "69-36=33", "68-6=62", "62-33=29" ]
Current State: 29:[69, 36, 68, 6], Operations: [] Exploring Operation: 69-36=33, Resulting Numbers: [68, 6, 33] Generated Node #2: [68, 6, 33] from Operation: 69-36=33 Current State: 29:[68, 6, 33], Operations: ['69-36=33'] Exploring Operation: 68-6=62, Resulting Numbers: [33, 62] Generated Node #3: [33, 62] from Operation: 68-6=62 Current State: 29:[33, 62], Operations: ['69-36=33', '68-6=62'] Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[69, 36, 68, 6], Operations: [] Exploring Operation: 69-36=33, Resulting Numbers: [68, 6, 33] Generated Node #0,0: 29:[68, 6, 33] Operation: 69-36=33 Exploring Operation: 69-68=1, Resulting Numbers: [36, 6, 1] Generated Node #0,1: 29:[36, 6, 1] Operation: 69-68=1 Exploring Operation: 68-36=32, Resulting Numbers: [69, 6, 32] Generated Node #0,2: 29:[69, 6, 32] Operation: 68-36=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[36, 6, 1], Operations: ['69-68=1'] Exploring Operation: 6+1=7, Resulting Numbers: [36, 7] Generated Node #0,1,0: 29:[36, 7] Operation: 6+1=7 Exploring Operation: 36-6=30, Resulting Numbers: [1, 30] Generated Node #0,1,1: 29:[1, 30] Operation: 36-6=30 Exploring Operation: 36-1=35, Resulting Numbers: [6, 35] Generated Node #0,1,2: 29:[6, 35] Operation: 36-1=35 Moving to Node #0,1,0 Current State: 29:[36, 7], Operations: ['69-68=1', '6+1=7'] Exploring Operation: 36*7=252, Resulting Numbers: [252] 252,29 unequal: No Solution Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[69, 36, 68, 6], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [36, 6, 1] Generated Node #0,1: 29:[36, 6, 1] Operation: 69-68=1 Moving to Node #0,1 Current State: 29:[36, 6, 1], Operations: ['69-68=1'] Exploring Operation: 6+1=7, Resulting Numbers: [36, 7] Generated Node #0,1,0: 29:[36, 7] Operation: 6+1=7 Moving to Node #0,1,0 Current State: 29:[36, 7], Operations: ['69-68=1', '6+1=7'] Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 14, 89, 85, 40 ]
50
[ "89-14=75", "85+40=125", "125-75=50" ]
Current State: 50:[14, 89, 85, 40], Operations: [] Exploring Operation: 89-14=75, Resulting Numbers: [85, 40, 75] Generated Node #2: [85, 40, 75] from Operation: 89-14=75 Current State: 50:[85, 40, 75], Operations: ['89-14=75'] Exploring Operation: 85+40=125, Resulting Numbers: [75, 125] Generated Node #3: [75, 125] from Operation: 85+40=125 Current State: 50:[75, 125], Operations: ['89-14=75', '85+40=125'] Exploring Operation: 125-75=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[14, 89, 85, 40], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [14, 40, 4] Generated Node #0,0: 50:[14, 40, 4] Operation: 89-85=4 Exploring Operation: 89-40=49, Resulting Numbers: [14, 85, 49] Generated Node #0,1: 50:[14, 85, 49] Operation: 89-40=49 Exploring Operation: 89-14=75, Resulting Numbers: [85, 40, 75] Generated Node #0,2: 50:[85, 40, 75] Operation: 89-14=75 Exploring Operation: 85-40=45, Resulting Numbers: [14, 89, 45] Generated Node #0,3: 50:[14, 89, 45] Operation: 85-40=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[14, 40, 4], Operations: ['89-85=4'] Exploring Operation: 40/4=10, Resulting Numbers: [14, 10] Generated Node #0,0,0: 50:[14, 10] Operation: 40/4=10 Exploring Operation: 14+40=54, Resulting Numbers: [4, 54] Generated Node #0,0,1: 50:[4, 54] Operation: 14+40=54 Exploring Operation: 40-14=26, Resulting Numbers: [4, 26] Generated Node #0,0,2: 50:[4, 26] Operation: 40-14=26 Exploring Operation: 14-4=10, Resulting Numbers: [40, 10] Generated Node #0,0,3: 50:[40, 10] Operation: 14-4=10 Moving to Node #0,0,2 Current State: 50:[4, 26], Operations: ['89-85=4', '40-14=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,50 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,50 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[14, 10], Operations: ['89-85=4', '40/4=10'] Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 14*10=140, Resulting Numbers: [140] 140,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[4, 54], Operations: ['89-85=4', '14+40=54'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[14, 89, 85, 40], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [14, 40, 4] Generated Node #0,0: 50:[14, 40, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 50:[14, 40, 4], Operations: ['89-85=4'] Exploring Operation: 14+40=54, Resulting Numbers: [4, 54] Generated Node #0,0,1: 50:[4, 54] Operation: 14+40=54 Moving to Node #0,0,1 Current State: 50:[4, 54], Operations: ['89-85=4', '14+40=54'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 21, 2, 95, 83 ]
29
[ "83-21=62", "2*62=124", "124-95=29" ]
Current State: 29:[21, 2, 95, 83], Operations: [] Exploring Operation: 83-21=62, Resulting Numbers: [2, 95, 62] Generated Node #2: [2, 95, 62] from Operation: 83-21=62 Current State: 29:[2, 95, 62], Operations: ['83-21=62'] Exploring Operation: 2*62=124, Resulting Numbers: [95, 124] Generated Node #3: [95, 124] from Operation: 2*62=124 Current State: 29:[95, 124], Operations: ['83-21=62', '2*62=124'] Exploring Operation: 124-95=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[21, 2, 95, 83], Operations: [] Exploring Operation: 95-83=12, Resulting Numbers: [21, 2, 12] Generated Node #0,0: 29:[21, 2, 12] Operation: 95-83=12 Exploring Operation: 21+2=23, Resulting Numbers: [95, 83, 23] Generated Node #0,1: 29:[95, 83, 23] Operation: 21+2=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[21, 2, 12], Operations: ['95-83=12'] Exploring Operation: 2*12=24, Resulting Numbers: [21, 24] Generated Node #0,0,0: 29:[21, 24] Operation: 2*12=24 Exploring Operation: 21+2=23, Resulting Numbers: [12, 23] Generated Node #0,0,1: 29:[12, 23] Operation: 21+2=23 Moving to Node #0,0,0 Current State: 29:[21, 24], Operations: ['95-83=12', '2*12=24'] Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,29 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[12, 23], Operations: ['95-83=12', '21+2=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,29 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[95, 83, 23], Operations: ['21+2=23'] Exploring Operation: 95-23=72, Resulting Numbers: [83, 72] Generated Node #0,1,0: 29:[83, 72] Operation: 95-23=72 Exploring Operation: 95-83=12, Resulting Numbers: [23, 12] Generated Node #0,1,1: 29:[23, 12] Operation: 95-83=12 Moving to Node #0,1,1 Current State: 29:[23, 12], Operations: ['21+2=23', '95-83=12'] Exploring Operation: 23+12=35, Resulting Numbers: [35] 35,29 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[83, 72], Operations: ['21+2=23', '95-23=72'] Exploring Operation: 83+72=155, Resulting Numbers: [155] 155,29 unequal: No Solution Exploring Operation: 83-72=11, Resulting Numbers: [11] 11,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 6, 18, 6, 65 ]
83
[ "6+18=24", "65-6=59", "24+59=83" ]
Current State: 83:[6, 18, 6, 65], Operations: [] Exploring Operation: 6+18=24, Resulting Numbers: [65, 24] Generated Node #2: [65, 24] from Operation: 6+18=24 Current State: 83:[65, 24], Operations: ['6+18=24'] Exploring Operation: 65-6=59, Resulting Numbers: [24, 59] Generated Node #3: [24, 59] from Operation: 65-6=59 Current State: 83:[24, 59], Operations: ['6+18=24', '65-6=59'] Exploring Operation: 24+59=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[6, 18, 6, 65], Operations: [] Exploring Operation: 6*18=108, Resulting Numbers: [6, 65, 108] Generated Node #0,0: 83:[6, 65, 108] Operation: 6*18=108 Exploring Operation: 18*6=108, Resulting Numbers: [6, 65, 108] Generated Node #0,1: 83:[6, 65, 108] Operation: 18*6=108 Moving to Node #0,0 Current State: 83:[6, 65, 108], Operations: ['6*18=108'] Exploring Operation: 108-6=102, Resulting Numbers: [65, 102] Generated Node #0,0,0: 83:[65, 102] Operation: 108-6=102 Exploring Operation: 6+65=71, Resulting Numbers: [108, 71] Generated Node #0,0,1: 83:[108, 71] Operation: 6+65=71 Moving to Node #0,1 Current State: 83:[6, 65, 108], Operations: ['18*6=108'] Exploring Operation: 108-6=102, Resulting Numbers: [65, 102] Generated Node #0,1,0: 83:[65, 102] Operation: 108-6=102 Exploring Operation: 6+65=71, Resulting Numbers: [108, 71] Generated Node #0,1,1: 83:[108, 71] Operation: 6+65=71 Moving to Node #0,0,0 Current State: 83:[65, 102], Operations: ['6*18=108', '108-6=102'] Exploring Operation: 102-65=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 65+102=167, Resulting Numbers: [167] 167,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[65, 102], Operations: ['18*6=108', '108-6=102'] Exploring Operation: 102-65=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 65+102=167, Resulting Numbers: [167] 167,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[108, 71], Operations: ['6*18=108', '6+65=71'] Exploring Operation: 108-71=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 108+71=179, Resulting Numbers: [179] 179,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[108, 71], Operations: ['18*6=108', '6+65=71'] Exploring Operation: 108+71=179, Resulting Numbers: [179] 179,83 unequal: No Solution Exploring Operation: 108-71=37, Resulting Numbers: [37] 37,83 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 95, 38, 92, 4 ]
38
[ "95-92=3", "4-3=1", "38*1=38" ]
Current State: 38:[95, 38, 92, 4], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [38, 4, 3] Generated Node #2: [38, 4, 3] from Operation: 95-92=3 Current State: 38:[38, 4, 3], Operations: ['95-92=3'] Exploring Operation: 4-3=1, Resulting Numbers: [38, 1] Generated Node #3: [38, 1] from Operation: 4-3=1 Current State: 38:[38, 1], Operations: ['95-92=3', '4-3=1'] Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[95, 38, 92, 4], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [38, 4, 3] Generated Node #0,0: 38:[38, 4, 3] Operation: 95-92=3 Exploring Operation: 95-38=57, Resulting Numbers: [92, 4, 57] Generated Node #0,1: 38:[92, 4, 57] Operation: 95-38=57 Exploring Operation: 92/4=23, Resulting Numbers: [95, 38, 23] Generated Node #0,2: 38:[95, 38, 23] Operation: 92/4=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[38, 4, 3], Operations: ['95-92=3'] Exploring Operation: 4-3=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 4-3=1 Exploring Operation: 38-4=34, Resulting Numbers: [3, 34] Generated Node #0,0,1: 38:[3, 34] Operation: 38-4=34 Exploring Operation: 38+4=42, Resulting Numbers: [3, 42] Generated Node #0,0,2: 38:[3, 42] Operation: 38+4=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['95-92=3', '4-3=1'] Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,38 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[95, 38, 92, 4], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [38, 4, 3] Generated Node #0,0: 38:[38, 4, 3] Operation: 95-92=3 Moving to Node #0,0 Current State: 38:[38, 4, 3], Operations: ['95-92=3'] Exploring Operation: 4-3=1, Resulting Numbers: [38, 1] Generated Node #0,0,0: 38:[38, 1] Operation: 4-3=1 Moving to Node #0,0,0 Current State: 38:[38, 1], Operations: ['95-92=3', '4-3=1'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 20, 90, 6, 40 ]
27
[ "40-20=20", "90*6=540", "540/20=27" ]
Current State: 27:[20, 90, 6, 40], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [90, 6, 20] Generated Node #2: [90, 6, 20] from Operation: 40-20=20 Current State: 27:[90, 6, 20], Operations: ['40-20=20'] Exploring Operation: 90*6=540, Resulting Numbers: [20, 540] Generated Node #3: [20, 540] from Operation: 90*6=540 Current State: 27:[20, 540], Operations: ['40-20=20', '90*6=540'] Exploring Operation: 540/20=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[20, 90, 6, 40], Operations: [] Exploring Operation: 90-40=50, Resulting Numbers: [20, 6, 50] Generated Node #0,0: 27:[20, 6, 50] Operation: 90-40=50 Exploring Operation: 90/6=15, Resulting Numbers: [20, 40, 15] Generated Node #0,1: 27:[20, 40, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[20, 40, 15], Operations: ['90/6=15'] Exploring Operation: 40/20=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 27:[15, 2] Operation: 40/20=2 Exploring Operation: 40-15=25, Resulting Numbers: [20, 25] Generated Node #0,1,1: 27:[20, 25] Operation: 40-15=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[15, 2], Operations: ['90/6=15', '40/20=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,27 unequal: No Solution No 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: 27:[20, 25], Operations: ['90/6=15', '40-15=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,27 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[20, 6, 50], Operations: ['90-40=50'] Exploring Operation: 50-20=30, Resulting Numbers: [6, 30] Generated Node #0,0,0: 27:[6, 30] Operation: 50-20=30 Exploring Operation: 20+6=26, Resulting Numbers: [50, 26] Generated Node #0,0,1: 27:[50, 26] Operation: 20+6=26 Moving to Node #0,0,0 Current State: 27:[6, 30], Operations: ['90-40=50', '50-20=30'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[50, 26], Operations: ['90-40=50', '20+6=26'] Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 50+26=76, Resulting Numbers: [76] 76,27 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
[ 95, 34, 96, 36 ]
70
[ "96-95=1", "34+36=70", "1*70=70" ]
Current State: 70:[95, 34, 96, 36], Operations: [] Exploring Operation: 96-95=1, Resulting Numbers: [34, 36, 1] Generated Node #2: [34, 36, 1] from Operation: 96-95=1 Current State: 70:[34, 36, 1], Operations: ['96-95=1'] Exploring Operation: 34+36=70, Resulting Numbers: [1, 70] Generated Node #3: [1, 70] from Operation: 34+36=70 Current State: 70:[1, 70], Operations: ['96-95=1', '34+36=70'] Exploring Operation: 1*70=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[95, 34, 96, 36], Operations: [] Exploring Operation: 96-34=62, Resulting Numbers: [95, 36, 62] Generated Node #0,0: 70:[95, 36, 62] Operation: 96-34=62 Exploring Operation: 96-95=1, Resulting Numbers: [34, 36, 1] Generated Node #0,1: 70:[34, 36, 1] Operation: 96-95=1 Moving to Node #0,1 Current State: 70:[34, 36, 1], Operations: ['96-95=1'] Exploring Operation: 36-34=2, Resulting Numbers: [1, 2] Generated Node #0,1,0: 70:[1, 2] Operation: 36-34=2 Exploring Operation: 34+36=70, Resulting Numbers: [1, 70] Generated Node #0,1,1: 70:[1, 70] Operation: 34+36=70 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[1, 2], Operations: ['96-95=1', '36-34=2'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 70:[1, 70], Operations: ['96-95=1', '34+36=70'] Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[95, 34, 96, 36], Operations: [] Exploring Operation: 96-95=1, Resulting Numbers: [34, 36, 1] Generated Node #0,1: 70:[34, 36, 1] Operation: 96-95=1 Moving to Node #0,1 Current State: 70:[34, 36, 1], Operations: ['96-95=1'] Exploring Operation: 34+36=70, Resulting Numbers: [1, 70] Generated Node #0,1,1: 70:[1, 70] Operation: 34+36=70 Moving to Node #0,1,1 Current State: 70:[1, 70], Operations: ['96-95=1', '34+36=70'] Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 97, 8, 93, 79 ]
67
[ "97+8=105", "93+79=172", "172-105=67" ]
Current State: 67:[97, 8, 93, 79], Operations: [] Exploring Operation: 97+8=105, Resulting Numbers: [93, 79, 105] Generated Node #2: [93, 79, 105] from Operation: 97+8=105 Current State: 67:[93, 79, 105], Operations: ['97+8=105'] Exploring Operation: 93+79=172, Resulting Numbers: [105, 172] Generated Node #3: [105, 172] from Operation: 93+79=172 Current State: 67:[105, 172], Operations: ['97+8=105', '93+79=172'] Exploring Operation: 172-105=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[97, 8, 93, 79], Operations: [] Exploring Operation: 93-8=85, Resulting Numbers: [97, 79, 85] Generated Node #0,0: 67:[97, 79, 85] Operation: 93-8=85 Exploring Operation: 97-8=89, Resulting Numbers: [93, 79, 89] Generated Node #0,1: 67:[93, 79, 89] Operation: 97-8=89 Moving to Node #0,0 Current State: 67:[97, 79, 85], Operations: ['93-8=85'] Exploring Operation: 97-79=18, Resulting Numbers: [85, 18] Generated Node #0,0,0: 67:[85, 18] Operation: 97-79=18 Exploring Operation: 97-85=12, Resulting Numbers: [79, 12] Generated Node #0,0,1: 67:[79, 12] Operation: 97-85=12 Moving to Node #0,1 Current State: 67:[93, 79, 89], Operations: ['97-8=89'] Exploring Operation: 93-79=14, Resulting Numbers: [89, 14] Generated Node #0,1,0: 67:[89, 14] Operation: 93-79=14 Exploring Operation: 93-89=4, Resulting Numbers: [79, 4] Generated Node #0,1,1: 67:[79, 4] Operation: 93-89=4 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[89, 14], Operations: ['97-8=89', '93-79=14'] Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,67 unequal: No Solution Exploring Operation: 89+14=103, Resulting Numbers: [103] 103,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[79, 4], Operations: ['97-8=89', '93-89=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,67 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 67:[85, 18], Operations: ['93-8=85', '97-79=18'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[97, 8, 93, 79], Operations: [] Exploring Operation: 93-8=85, Resulting Numbers: [97, 79, 85] Generated Node #0,0: 67:[97, 79, 85] Operation: 93-8=85 Moving to Node #0,0 Current State: 67:[97, 79, 85], Operations: ['93-8=85'] Exploring Operation: 97-79=18, Resulting Numbers: [85, 18] Generated Node #0,0,0: 67:[85, 18] Operation: 97-79=18 Moving to Node #0,0,0 Current State: 67:[85, 18], Operations: ['93-8=85', '97-79=18'] Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 66, 59, 69, 47 ]
15
[ "66-59=7", "69-47=22", "22-7=15" ]
Current State: 15:[66, 59, 69, 47], Operations: [] Exploring Operation: 66-59=7, Resulting Numbers: [69, 47, 7] Generated Node #2: [69, 47, 7] from Operation: 66-59=7 Current State: 15:[69, 47, 7], Operations: ['66-59=7'] Exploring Operation: 69-47=22, Resulting Numbers: [7, 22] Generated Node #3: [7, 22] from Operation: 69-47=22 Current State: 15:[7, 22], Operations: ['66-59=7', '69-47=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[66, 59, 69, 47], Operations: [] Exploring Operation: 69-59=10, Resulting Numbers: [66, 47, 10] Generated Node #0,0: 15:[66, 47, 10] Operation: 69-59=10 Exploring Operation: 69-66=3, Resulting Numbers: [59, 47, 3] Generated Node #0,1: 15:[59, 47, 3] Operation: 69-66=3 Exploring Operation: 66-59=7, Resulting Numbers: [69, 47, 7] Generated Node #0,2: 15:[69, 47, 7] Operation: 66-59=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[59, 47, 3], Operations: ['69-66=3'] Exploring Operation: 47-3=44, Resulting Numbers: [59, 44] Generated Node #0,1,0: 15:[59, 44] Operation: 47-3=44 Exploring Operation: 59-47=12, Resulting Numbers: [3, 12] Generated Node #0,1,1: 15:[3, 12] Operation: 59-47=12 Exploring Operation: 59-3=56, Resulting Numbers: [47, 56] Generated Node #0,1,2: 15:[47, 56] Operation: 59-3=56 Moving to Node #0,1,1 Current State: 15:[3, 12], Operations: ['69-66=3', '59-47=12'] Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[66, 59, 69, 47], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [59, 47, 3] Generated Node #0,1: 15:[59, 47, 3] Operation: 69-66=3 Moving to Node #0,1 Current State: 15:[59, 47, 3], Operations: ['69-66=3'] Exploring Operation: 59-47=12, Resulting Numbers: [3, 12] Generated Node #0,1,1: 15:[3, 12] Operation: 59-47=12 Moving to Node #0,1,1 Current State: 15:[3, 12], Operations: ['69-66=3', '59-47=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 79, 3, 58, 15 ]
26
[ "79-58=21", "15/3=5", "21+5=26" ]
Current State: 26:[79, 3, 58, 15], Operations: [] Exploring Operation: 79-58=21, Resulting Numbers: [3, 15, 21] Generated Node #2: [3, 15, 21] from Operation: 79-58=21 Current State: 26:[3, 15, 21], Operations: ['79-58=21'] Exploring Operation: 15/3=5, Resulting Numbers: [21, 5] Generated Node #3: [21, 5] from Operation: 15/3=5 Current State: 26:[21, 5], Operations: ['79-58=21', '15/3=5'] Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[79, 3, 58, 15], Operations: [] Exploring Operation: 79-15=64, Resulting Numbers: [3, 58, 64] Generated Node #0,0: 26:[3, 58, 64] Operation: 79-15=64 Exploring Operation: 58-15=43, Resulting Numbers: [79, 3, 43] Generated Node #0,1: 26:[79, 3, 43] Operation: 58-15=43 Exploring Operation: 79-3=76, Resulting Numbers: [58, 15, 76] Generated Node #0,2: 26:[58, 15, 76] Operation: 79-3=76 Exploring Operation: 79-58=21, Resulting Numbers: [3, 15, 21] Generated Node #0,3: 26:[3, 15, 21] Operation: 79-58=21 Moving to Node #0,3 Current State: 26:[3, 15, 21], Operations: ['79-58=21'] Exploring Operation: 15-3=12, Resulting Numbers: [21, 12] Generated Node #0,3,0: 26:[21, 12] Operation: 15-3=12 Exploring Operation: 21-3=18, Resulting Numbers: [15, 18] Generated Node #0,3,1: 26:[15, 18] Operation: 21-3=18 Exploring Operation: 21-15=6, Resulting Numbers: [3, 6] Generated Node #0,3,2: 26:[3, 6] Operation: 21-15=6 Exploring Operation: 3+21=24, Resulting Numbers: [15, 24] Generated Node #0,3,3: 26:[15, 24] Operation: 3+21=24 Moving to Node #0,1 Current State: 26:[79, 3, 43], Operations: ['58-15=43'] Exploring Operation: 79+3=82, Resulting Numbers: [43, 82] Generated Node #0,1,0: 26:[43, 82] Operation: 79+3=82 Exploring Operation: 79-43=36, Resulting Numbers: [3, 36] Generated Node #0,1,1: 26:[3, 36] Operation: 79-43=36 Exploring Operation: 43-3=40, Resulting Numbers: [79, 40] Generated Node #0,1,2: 26:[79, 40] Operation: 43-3=40 Exploring Operation: 79-3=76, Resulting Numbers: [43, 76] Generated Node #0,1,3: 26:[43, 76] Operation: 79-3=76 Moving to Node #0,0 Current State: 26:[3, 58, 64], Operations: ['79-15=64'] Exploring Operation: 64-3=61, Resulting Numbers: [58, 61] Generated Node #0,0,0: 26:[58, 61] Operation: 64-3=61 Exploring Operation: 64-58=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 26:[3, 6] Operation: 64-58=6 Exploring Operation: 3+58=61, Resulting Numbers: [64, 61] Generated Node #0,0,2: 26:[64, 61] Operation: 3+58=61 Exploring Operation: 58-3=55, Resulting Numbers: [64, 55] Generated Node #0,0,3: 26:[64, 55] Operation: 58-3=55 Moving to Node #0,2 Current State: 26:[58, 15, 76], Operations: ['79-3=76'] Exploring Operation: 76-58=18, Resulting Numbers: [15, 18] Generated Node #0,2,0: 26:[15, 18] Operation: 76-58=18 Exploring Operation: 58-15=43, Resulting Numbers: [76, 43] Generated Node #0,2,1: 26:[76, 43] Operation: 58-15=43 Exploring Operation: 58+15=73, Resulting Numbers: [76, 73] Generated Node #0,2,2: 26:[76, 73] Operation: 58+15=73 Exploring Operation: 76-15=61, Resulting Numbers: [58, 61] Generated Node #0,2,3: 26:[58, 61] Operation: 76-15=61 Moving to Node #0,3,3 Current State: 26:[15, 24], Operations: ['79-58=21', '3+21=24'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,26 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,26 unequal: No Solution Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,26 unequal: No Solution Moving to Node #0,3,2 Current State: 26:[3, 6], Operations: ['79-58=21', '21-15=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,26 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,0,1 Current State: 26:[3, 6], Operations: ['79-15=64', '64-58=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,26 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,3,0 Current State: 26:[21, 12], Operations: ['79-58=21', '15-3=12'] Exploring Operation: 21*12=252, Resulting Numbers: [252] 252,26 unequal: No Solution Exploring Operation: 21+12=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[15, 18], Operations: ['79-3=76', '76-58=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,26 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,26 unequal: No Solution Moving to Node #0,3,1 Current State: 26:[15, 18], Operations: ['79-58=21', '21-3=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,26 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[3, 36], Operations: ['58-15=43', '79-43=36'] Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,26 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,26 unequal: No Solution Moving to Node #0,1,3 Current State: 26:[43, 76], Operations: ['58-15=43', '79-3=76'] Exploring Operation: 43+76=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 43*76=3268, Resulting Numbers: [3268] 3268,26 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[76, 43], Operations: ['79-3=76', '58-15=43'] Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,26 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,26 unequal: No Solution Moving to Node #0,1,2 Current State: 26:[79, 40], Operations: ['58-15=43', '43-3=40'] Exploring Operation: 79*40=3160, Resulting Numbers: [3160] 3160,26 unequal: No Solution Exploring Operation: 79+40=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 79-40=39, Resulting Numbers: [39] 39,26 unequal: No Solution Moving to Node #0,0,3 Current State: 26:[64, 55], Operations: ['79-15=64', '58-3=55'] Exploring Operation: 64*55=3520, Resulting Numbers: [3520] 3520,26 unequal: No Solution Exploring Operation: 64+55=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,26 unequal: No Solution Moving to Node #0,0,0 Current State: 26:[58, 61], Operations: ['79-15=64', '64-3=61'] Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,26 unequal: No Solution Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[58, 61], Operations: ['79-3=76', '76-15=61'] Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,26 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[64, 61], Operations: ['79-15=64', '3+58=61'] Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,26 unequal: No Solution Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,26 unequal: No Solution Moving to Node #0,1,0 Current State: 26:[43, 82], Operations: ['58-15=43', '79+3=82'] Exploring Operation: 82-43=39, Resulting Numbers: [39] 39,26 unequal: No Solution Exploring Operation: 43+82=125, Resulting Numbers: [125] 125,26 unequal: No Solution Exploring Operation: 43*82=3526, Resulting Numbers: [3526] 3526,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[76, 73], Operations: ['79-3=76', '58+15=73'] Exploring Operation: 76+73=149, Resulting Numbers: [149] 149,26 unequal: No Solution Exploring Operation: 76-73=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 76*73=5548, Resulting Numbers: [5548] 5548,26 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 52, 2, 5 ]
85
[ "23+52=75", "2*5=10", "75+10=85" ]
Current State: 85:[23, 52, 2, 5], Operations: [] Exploring Operation: 23+52=75, Resulting Numbers: [2, 5, 75] Generated Node #2: [2, 5, 75] from Operation: 23+52=75 Current State: 85:[2, 5, 75], Operations: ['23+52=75'] Exploring Operation: 2*5=10, Resulting Numbers: [75, 10] Generated Node #3: [75, 10] from Operation: 2*5=10 Current State: 85:[75, 10], Operations: ['23+52=75', '2*5=10'] Exploring Operation: 75+10=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[23, 52, 2, 5], Operations: [] Exploring Operation: 23+52=75, Resulting Numbers: [2, 5, 75] Generated Node #0,0: 85:[2, 5, 75] Operation: 23+52=75 Exploring Operation: 52-23=29, Resulting Numbers: [2, 5, 29] Generated Node #0,1: 85:[2, 5, 29] Operation: 52-23=29 Exploring Operation: 52/2=26, Resulting Numbers: [23, 5, 26] Generated Node #0,2: 85:[23, 5, 26] Operation: 52/2=26 Exploring Operation: 52*2=104, Resulting Numbers: [23, 5, 104] Generated Node #0,3: 85:[23, 5, 104] Operation: 52*2=104 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[2, 5, 75], Operations: ['23+52=75'] Exploring Operation: 2+75=77, Resulting Numbers: [5, 77] Generated Node #0,0,0: 85:[5, 77] Operation: 2+75=77 Exploring Operation: 5+75=80, Resulting Numbers: [2, 80] Generated Node #0,0,1: 85:[2, 80] Operation: 5+75=80 Exploring Operation: 2+5=7, Resulting Numbers: [75, 7] Generated Node #0,0,2: 85:[75, 7] Operation: 2+5=7 Exploring Operation: 75/5=15, Resulting Numbers: [2, 15] Generated Node #0,0,3: 85:[2, 15] Operation: 75/5=15 Moving to Node #0,0,3 Current State: 85:[2, 15], Operations: ['23+52=75', '75/5=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[2, 80], Operations: ['23+52=75', '5+75=80'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,85 unequal: No Solution Exploring Operation: 2+80=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 80-2=78, Resulting Numbers: [78] 78,85 unequal: No Solution Exploring Operation: 2*80=160, Resulting Numbers: [160] 160,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[5, 77], Operations: ['23+52=75', '2+75=77'] Exploring Operation: 5+77=82, Resulting Numbers: [82] 82,85 unequal: No Solution Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,85 unequal: No Solution Exploring Operation: 5*77=385, Resulting Numbers: [385] 385,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[75, 7], Operations: ['23+52=75', '2+5=7'] Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,85 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,85 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[2, 5, 29], Operations: ['52-23=29'] Exploring Operation: 2+5=7, Resulting Numbers: [29, 7] Generated Node #0,1,0: 85:[29, 7] Operation: 2+5=7 Exploring Operation: 29-2=27, Resulting Numbers: [5, 27] Generated Node #0,1,1: 85:[5, 27] Operation: 29-2=27 Exploring Operation: 5-2=3, Resulting Numbers: [29, 3] Generated Node #0,1,2: 85:[29, 3] Operation: 5-2=3 Exploring Operation: 29-5=24, Resulting Numbers: [2, 24] Generated Node #0,1,3: 85:[2, 24] Operation: 29-5=24 Moving to Node #0,1,1 Current State: 85:[5, 27], Operations: ['52-23=29', '29-2=27'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,85 unequal: No Solution Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[2, 24], Operations: ['52-23=29', '29-5=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[29, 3], Operations: ['52-23=29', '5-2=3'] Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[29, 7], Operations: ['52-23=29', '2+5=7'] Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 29*7=203, Resulting Numbers: [203] 203,85 unequal: No Solution Exploring Operation: 29+7=36, Resulting Numbers: [36] 36,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[23, 5, 26], Operations: ['52/2=26'] Exploring Operation: 23-5=18, Resulting Numbers: [26, 18] Generated Node #0,2,0: 85:[26, 18] Operation: 23-5=18 Exploring Operation: 26-23=3, Resulting Numbers: [5, 3] Generated Node #0,2,1: 85:[5, 3] Operation: 26-23=3 Exploring Operation: 26-5=21, Resulting Numbers: [23, 21] Generated Node #0,2,2: 85:[23, 21] Operation: 26-5=21 Exploring Operation: 23+5=28, Resulting Numbers: [26, 28] Generated Node #0,2,3: 85:[26, 28] Operation: 23+5=28 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 85:[5, 3], Operations: ['52/2=26', '26-23=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,85 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,85 unequal: No Solution No 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: 85:[26, 18], Operations: ['52/2=26', '23-5=18'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,85 unequal: No Solution Exploring Operation: 26*18=468, Resulting Numbers: [468] 468,85 unequal: No Solution No 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: 85:[23, 21], Operations: ['52/2=26', '26-5=21'] Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,85 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 85:[26, 28], Operations: ['52/2=26', '23+5=28'] Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,85 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 85:[23, 5, 104], Operations: ['52*2=104'] Exploring Operation: 104-23=81, Resulting Numbers: [5, 81] Generated Node #0,3,0: 85:[5, 81] Operation: 104-23=81 Exploring Operation: 104-5=99, Resulting Numbers: [23, 99] Generated Node #0,3,1: 85:[23, 99] Operation: 104-5=99 Exploring Operation: 23+5=28, Resulting Numbers: [104, 28] Generated Node #0,3,2: 85:[104, 28] Operation: 23+5=28 Exploring Operation: 23-5=18, Resulting Numbers: [104, 18] Generated Node #0,3,3: 85:[104, 18] Operation: 23-5=18 Moving to Node #0,3,0 Current State: 85:[5, 81], Operations: ['52*2=104', '104-23=81'] Exploring Operation: 5*81=405, Resulting Numbers: [405] 405,85 unequal: No Solution Exploring Operation: 5+81=86, Resulting Numbers: [86] 86,85 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[104, 18], Operations: ['52*2=104', '23-5=18'] Exploring Operation: 104-18=86, Resulting Numbers: [86] 86,85 unequal: No Solution Exploring Operation: 104*18=1872, Resulting Numbers: [1872] 1872,85 unequal: No Solution Exploring Operation: 104+18=122, Resulting Numbers: [122] 122,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[23, 99], Operations: ['52*2=104', '104-5=99'] Exploring Operation: 23*99=2277, Resulting Numbers: [2277] 2277,85 unequal: No Solution Exploring Operation: 23+99=122, Resulting Numbers: [122] 122,85 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[104, 28], Operations: ['52*2=104', '23+5=28'] Exploring Operation: 104+28=132, Resulting Numbers: [132] 132,85 unequal: No Solution Exploring Operation: 104*28=2912, Resulting Numbers: [2912] 2912,85 unequal: No Solution Exploring Operation: 104-28=76, Resulting Numbers: [76] 76,85 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
[ 45, 93, 14, 2 ]
10
[ "45+93=138", "2+138=140", "140/14=10" ]
Current State: 10:[45, 93, 14, 2], Operations: [] Exploring Operation: 45+93=138, Resulting Numbers: [14, 2, 138] Generated Node #2: [14, 2, 138] from Operation: 45+93=138 Current State: 10:[14, 2, 138], Operations: ['45+93=138'] Exploring Operation: 2+138=140, Resulting Numbers: [14, 140] Generated Node #3: [14, 140] from Operation: 2+138=140 Current State: 10:[14, 140], Operations: ['45+93=138', '2+138=140'] Exploring Operation: 140/14=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[45, 93, 14, 2], Operations: [] Exploring Operation: 93-14=79, Resulting Numbers: [45, 2, 79] Generated Node #0,0: 10:[45, 2, 79] Operation: 93-14=79 Exploring Operation: 45-14=31, Resulting Numbers: [93, 2, 31] Generated Node #0,1: 10:[93, 2, 31] Operation: 45-14=31 Exploring Operation: 93-45=48, Resulting Numbers: [14, 2, 48] Generated Node #0,2: 10:[14, 2, 48] Operation: 93-45=48 Moving to Node #0,2 Current State: 10:[14, 2, 48], Operations: ['93-45=48'] Exploring Operation: 48/2=24, Resulting Numbers: [14, 24] Generated Node #0,2,0: 10:[14, 24] Operation: 48/2=24 Exploring Operation: 14-2=12, Resulting Numbers: [48, 12] Generated Node #0,2,1: 10:[48, 12] Operation: 14-2=12 Exploring Operation: 48-14=34, Resulting Numbers: [2, 34] Generated Node #0,2,2: 10:[2, 34] Operation: 48-14=34 Moving to Node #0,0 Current State: 10:[45, 2, 79], Operations: ['93-14=79'] Exploring Operation: 79-45=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 10:[2, 34] Operation: 79-45=34 Exploring Operation: 79-2=77, Resulting Numbers: [45, 77] Generated Node #0,0,1: 10:[45, 77] Operation: 79-2=77 Exploring Operation: 45-2=43, Resulting Numbers: [79, 43] Generated Node #0,0,2: 10:[79, 43] Operation: 45-2=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[2, 34], Operations: ['93-14=79', '79-45=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 10:[45, 77], Operations: ['93-14=79', '79-2=77'] Exploring Operation: 45+77=122, Resulting Numbers: [122] 122,10 unequal: No Solution Exploring Operation: 45*77=3465, Resulting Numbers: [3465] 3465,10 unequal: No Solution Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[79, 43], Operations: ['93-14=79', '45-2=43'] Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,10 unequal: No Solution Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,10 unequal: No Solution Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,10 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: 10:[93, 2, 31], Operations: ['45-14=31'] Exploring Operation: 93/31=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 10:[2, 3] Operation: 93/31=3 Exploring Operation: 93-2=91, Resulting Numbers: [31, 91] Generated Node #0,1,1: 10:[31, 91] Operation: 93-2=91 Exploring Operation: 93-31=62, Resulting Numbers: [2, 62] Generated Node #0,1,2: 10:[2, 62] Operation: 93-31=62 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[2, 3], Operations: ['45-14=31', '93/31=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[2, 62], Operations: ['45-14=31', '93-31=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,10 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,10 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[31, 91], Operations: ['45-14=31', '93-2=91'] Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,10 unequal: No Solution Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,10 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,10 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: 10:[14, 24], Operations: ['93-45=48', '48/2=24'] Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,10 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[45, 93, 14, 2], Operations: [] Exploring Operation: 93-45=48, Resulting Numbers: [14, 2, 48] Generated Node #0,2: 10:[14, 2, 48] Operation: 93-45=48 Moving to Node #0,2 Current State: 10:[14, 2, 48], Operations: ['93-45=48'] Exploring Operation: 48/2=24, Resulting Numbers: [14, 24] Generated Node #0,2,0: 10:[14, 24] Operation: 48/2=24 Moving to Node #0,2,0 Current State: 10:[14, 24], Operations: ['93-45=48', '48/2=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.96875
hs_3
sum_heuristic
[ 32, 55, 52, 61 ]
90
[ "55-32=23", "52+61=113", "113-23=90" ]
Current State: 90:[32, 55, 52, 61], Operations: [] Exploring Operation: 55-32=23, Resulting Numbers: [52, 61, 23] Generated Node #2: [52, 61, 23] from Operation: 55-32=23 Current State: 90:[52, 61, 23], Operations: ['55-32=23'] Exploring Operation: 52+61=113, Resulting Numbers: [23, 113] Generated Node #3: [23, 113] from Operation: 52+61=113 Current State: 90:[23, 113], Operations: ['55-32=23', '52+61=113'] Exploring Operation: 113-23=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[32, 55, 52, 61], Operations: [] Exploring Operation: 61-55=6, Resulting Numbers: [32, 52, 6] Generated Node #0,0: 90:[32, 52, 6] Operation: 61-55=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[32, 52, 6], Operations: ['61-55=6'] Exploring Operation: 52-32=20, Resulting Numbers: [6, 20] Generated Node #0,0,0: 90:[6, 20] Operation: 52-32=20 Moving to Node #0,0,0 Current State: 90:[6, 20], Operations: ['61-55=6', '52-32=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 13, 95, 48, 63 ]
97
[ "95-13=82", "63-48=15", "82+15=97" ]
Current State: 97:[13, 95, 48, 63], Operations: [] Exploring Operation: 95-13=82, Resulting Numbers: [48, 63, 82] Generated Node #2: [48, 63, 82] from Operation: 95-13=82 Current State: 97:[48, 63, 82], Operations: ['95-13=82'] Exploring Operation: 63-48=15, Resulting Numbers: [82, 15] Generated Node #3: [82, 15] from Operation: 63-48=15 Current State: 97:[82, 15], Operations: ['95-13=82', '63-48=15'] Exploring Operation: 82+15=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[13, 95, 48, 63], Operations: [] Exploring Operation: 13+48=61, Resulting Numbers: [95, 63, 61] Generated Node #0,0: 97:[95, 63, 61] Operation: 13+48=61 Exploring Operation: 13+95=108, Resulting Numbers: [48, 63, 108] Generated Node #0,1: 97:[48, 63, 108] Operation: 13+95=108 Exploring Operation: 13+63=76, Resulting Numbers: [95, 48, 76] Generated Node #0,2: 97:[95, 48, 76] Operation: 13+63=76 Moving to Node #0,0 Current State: 97:[95, 63, 61], Operations: ['13+48=61'] Exploring Operation: 95+63=158, Resulting Numbers: [61, 158] Generated Node #0,0,0: 97:[61, 158] Operation: 95+63=158 Exploring Operation: 63+61=124, Resulting Numbers: [95, 124] Generated Node #0,0,1: 97:[95, 124] Operation: 63+61=124 Exploring Operation: 95+61=156, Resulting Numbers: [63, 156] Generated Node #0,0,2: 97:[63, 156] Operation: 95+61=156 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[95, 124], Operations: ['13+48=61', '63+61=124'] Exploring Operation: 95+124=219, Resulting Numbers: [219] 219,97 unequal: No Solution Exploring Operation: 95*124=11780, Resulting Numbers: [11780] 11780,97 unequal: No Solution Exploring Operation: 124-95=29, Resulting Numbers: [29] 29,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 97:[63, 156], Operations: ['13+48=61', '95+61=156'] Exploring Operation: 63*156=9828, Resulting Numbers: [9828] 9828,97 unequal: No Solution Exploring Operation: 156-63=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 63+156=219, Resulting Numbers: [219] 219,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[61, 158], Operations: ['13+48=61', '95+63=158'] Exploring Operation: 158-61=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[13, 95, 48, 63], Operations: [] Exploring Operation: 13+48=61, Resulting Numbers: [95, 63, 61] Generated Node #0,0: 97:[95, 63, 61] Operation: 13+48=61 Moving to Node #0,0 Current State: 97:[95, 63, 61], Operations: ['13+48=61'] Exploring Operation: 95+63=158, Resulting Numbers: [61, 158] Generated Node #0,0,0: 97:[61, 158] Operation: 95+63=158 Moving to Node #0,0,0 Current State: 97:[61, 158], Operations: ['13+48=61', '95+63=158'] Exploring Operation: 158-61=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 76, 18, 12, 20 ]
82
[ "20-18=2", "12/2=6", "76+6=82" ]
Current State: 82:[76, 18, 12, 20], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [76, 12, 2] Generated Node #2: [76, 12, 2] from Operation: 20-18=2 Current State: 82:[76, 12, 2], Operations: ['20-18=2'] Exploring Operation: 12/2=6, Resulting Numbers: [76, 6] Generated Node #3: [76, 6] from Operation: 12/2=6 Current State: 82:[76, 6], Operations: ['20-18=2', '12/2=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[76, 18, 12, 20], Operations: [] Exploring Operation: 18+20=38, Resulting Numbers: [76, 12, 38] Generated Node #0,0: 82:[76, 12, 38] Operation: 18+20=38 Exploring Operation: 20-18=2, Resulting Numbers: [76, 12, 2] Generated Node #0,1: 82:[76, 12, 2] Operation: 20-18=2 Moving to Node #0,1 Current State: 82:[76, 12, 2], Operations: ['20-18=2'] Exploring Operation: 76+12=88, Resulting Numbers: [2, 88] Generated Node #0,1,0: 82:[2, 88] Operation: 76+12=88 Exploring Operation: 12/2=6, Resulting Numbers: [76, 6] Generated Node #0,1,1: 82:[76, 6] Operation: 12/2=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 82:[2, 88], Operations: ['20-18=2', '76+12=88'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,82 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 82:[76, 6], Operations: ['20-18=2', '12/2=6'] Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[76, 18, 12, 20], Operations: [] Exploring Operation: 20-18=2, Resulting Numbers: [76, 12, 2] Generated Node #0,1: 82:[76, 12, 2] Operation: 20-18=2 Moving to Node #0,1 Current State: 82:[76, 12, 2], Operations: ['20-18=2'] Exploring Operation: 12/2=6, Resulting Numbers: [76, 6] Generated Node #0,1,1: 82:[76, 6] Operation: 12/2=6 Moving to Node #0,1,1 Current State: 82:[76, 6], Operations: ['20-18=2', '12/2=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 38, 4, 37, 11 ]
31
[ "38+37=75", "4*11=44", "75-44=31" ]
Current State: 31:[38, 4, 37, 11], Operations: [] Exploring Operation: 38+37=75, Resulting Numbers: [4, 11, 75] Generated Node #2: [4, 11, 75] from Operation: 38+37=75 Current State: 31:[4, 11, 75], Operations: ['38+37=75'] Exploring Operation: 4*11=44, Resulting Numbers: [75, 44] Generated Node #3: [75, 44] from Operation: 4*11=44 Current State: 31:[75, 44], Operations: ['38+37=75', '4*11=44'] Exploring Operation: 75-44=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[38, 4, 37, 11], Operations: [] Exploring Operation: 4*11=44, Resulting Numbers: [38, 37, 44] Generated Node #0,0: 31:[38, 37, 44] Operation: 4*11=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[38, 37, 44], Operations: ['4*11=44'] Exploring Operation: 44-38=6, Resulting Numbers: [37, 6] Generated Node #0,0,0: 31:[37, 6] Operation: 44-38=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[37, 6], Operations: ['4*11=44', '44-38=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[38, 4, 37, 11], Operations: [] Exploring Operation: 4*11=44, Resulting Numbers: [38, 37, 44] Generated Node #0,0: 31:[38, 37, 44] Operation: 4*11=44 Moving to Node #0,0 Current State: 31:[38, 37, 44], Operations: ['4*11=44'] Exploring Operation: 44-38=6, Resulting Numbers: [37, 6] Generated Node #0,0,0: 31:[37, 6] Operation: 44-38=6 Moving to Node #0,0,0 Current State: 31:[37, 6], Operations: ['4*11=44', '44-38=6'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 44, 16, 3, 69 ]
44
[ "44-16=28", "3+69=72", "72-28=44" ]
Current State: 44:[44, 16, 3, 69], Operations: [] Exploring Operation: 44-16=28, Resulting Numbers: [3, 69, 28] Generated Node #2: [3, 69, 28] from Operation: 44-16=28 Current State: 44:[3, 69, 28], Operations: ['44-16=28'] Exploring Operation: 3+69=72, Resulting Numbers: [28, 72] Generated Node #3: [28, 72] from Operation: 3+69=72 Current State: 44:[28, 72], Operations: ['44-16=28', '3+69=72'] Exploring Operation: 72-28=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[44, 16, 3, 69], Operations: [] Exploring Operation: 69-16=53, Resulting Numbers: [44, 3, 53] Generated Node #0,0: 44:[44, 3, 53] Operation: 69-16=53 Exploring Operation: 69-44=25, Resulting Numbers: [16, 3, 25] Generated Node #0,1: 44:[16, 3, 25] Operation: 69-44=25 Exploring Operation: 69/3=23, Resulting Numbers: [44, 16, 23] Generated Node #0,2: 44:[44, 16, 23] Operation: 69/3=23 Exploring Operation: 69-3=66, Resulting Numbers: [44, 16, 66] Generated Node #0,3: 44:[44, 16, 66] Operation: 69-3=66 Exploring Operation: 16-3=13, Resulting Numbers: [44, 69, 13] Generated Node #0,4: 44:[44, 69, 13] Operation: 16-3=13 Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[44, 16, 23], Operations: ['69/3=23'] Exploring Operation: 44-23=21, Resulting Numbers: [16, 21] Generated Node #0,2,0: 44:[16, 21] Operation: 44-23=21 Exploring Operation: 44+16=60, Resulting Numbers: [23, 60] Generated Node #0,2,1: 44:[23, 60] Operation: 44+16=60 Exploring Operation: 16+23=39, Resulting Numbers: [44, 39] Generated Node #0,2,2: 44:[44, 39] Operation: 16+23=39 Exploring Operation: 23-16=7, Resulting Numbers: [44, 7] Generated Node #0,2,3: 44:[44, 7] Operation: 23-16=7 Exploring Operation: 44-16=28, Resulting Numbers: [23, 28] Generated Node #0,2,4: 44:[23, 28] Operation: 44-16=28 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[44, 7], Operations: ['69/3=23', '23-16=7'] Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,44 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,44 unequal: No Solution Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[44, 39], Operations: ['69/3=23', '16+23=39'] Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[16, 21], Operations: ['69/3=23', '44-23=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,44 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 44:[23, 28], Operations: ['69/3=23', '44-16=28'] Exploring Operation: 28-23=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 23+28=51, Resulting Numbers: [51] 51,44 unequal: No Solution Exploring Operation: 23*28=644, Resulting Numbers: [644] 644,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[23, 60], Operations: ['69/3=23', '44+16=60'] Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,44 unequal: No Solution Exploring Operation: 23+60=83, Resulting Numbers: [83] 83,44 unequal: No Solution Exploring Operation: 23*60=1380, Resulting Numbers: [1380] 1380,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[16, 3, 25], Operations: ['69-44=25'] Exploring Operation: 16-3=13, Resulting Numbers: [25, 13] Generated Node #0,1,0: 44:[25, 13] Operation: 16-3=13 Exploring Operation: 25-16=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 44:[3, 9] Operation: 25-16=9 Exploring Operation: 16+3=19, Resulting Numbers: [25, 19] Generated Node #0,1,2: 44:[25, 19] Operation: 16+3=19 Exploring Operation: 16+25=41, Resulting Numbers: [3, 41] Generated Node #0,1,3: 44:[3, 41] Operation: 16+25=41 Exploring Operation: 25-3=22, Resulting Numbers: [16, 22] Generated Node #0,1,4: 44:[16, 22] Operation: 25-3=22 Moving to Node #0,1,1 Current State: 44:[3, 9], Operations: ['69-44=25', '25-16=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,44 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,44 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[3, 41], Operations: ['69-44=25', '16+25=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,44 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[44, 16, 3, 69], Operations: [] Exploring Operation: 69-44=25, Resulting Numbers: [16, 3, 25] Generated Node #0,1: 44:[16, 3, 25] Operation: 69-44=25 Moving to Node #0,1 Current State: 44:[16, 3, 25], Operations: ['69-44=25'] Exploring Operation: 16+25=41, Resulting Numbers: [3, 41] Generated Node #0,1,3: 44:[3, 41] Operation: 16+25=41 Moving to Node #0,1,3 Current State: 44:[3, 41], Operations: ['69-44=25', '16+25=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 85, 5, 63, 78 ]
45
[ "85-78=7", "5*63=315", "315/7=45" ]
Current State: 45:[85, 5, 63, 78], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [5, 63, 7] Generated Node #2: [5, 63, 7] from Operation: 85-78=7 Current State: 45:[5, 63, 7], Operations: ['85-78=7'] Exploring Operation: 5*63=315, Resulting Numbers: [7, 315] Generated Node #3: [7, 315] from Operation: 5*63=315 Current State: 45:[7, 315], Operations: ['85-78=7', '5*63=315'] Exploring Operation: 315/7=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[85, 5, 63, 78], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [5, 63, 7] Generated Node #0,0: 45:[5, 63, 7] Operation: 85-78=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[5, 63, 7], Operations: ['85-78=7'] Exploring Operation: 63/7=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 45:[5, 9] Operation: 63/7=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[5, 9], Operations: ['85-78=7', '63/7=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[85, 5, 63, 78], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [5, 63, 7] Generated Node #0,0: 45:[5, 63, 7] Operation: 85-78=7 Moving to Node #0,0 Current State: 45:[5, 63, 7], Operations: ['85-78=7'] Exploring Operation: 63/7=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 45:[5, 9] Operation: 63/7=9 Moving to Node #0,0,0 Current State: 45:[5, 9], Operations: ['85-78=7', '63/7=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 11, 37, 32, 16 ]
85
[ "37*32=1184", "1184/16=74", "11+74=85" ]
Current State: 85:[11, 37, 32, 16], Operations: [] Exploring Operation: 37*32=1184, Resulting Numbers: [11, 16, 1184] Generated Node #2: [11, 16, 1184] from Operation: 37*32=1184 Current State: 85:[11, 16, 1184], Operations: ['37*32=1184'] Exploring Operation: 1184/16=74, Resulting Numbers: [11, 74] Generated Node #3: [11, 74] from Operation: 1184/16=74 Current State: 85:[11, 74], Operations: ['37*32=1184', '1184/16=74'] Exploring Operation: 11+74=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[11, 37, 32, 16], Operations: [] Exploring Operation: 37+32=69, Resulting Numbers: [11, 16, 69] Generated Node #0,0: 85:[11, 16, 69] Operation: 37+32=69 Exploring Operation: 32-11=21, Resulting Numbers: [37, 16, 21] Generated Node #0,1: 85:[37, 16, 21] Operation: 32-11=21 Exploring Operation: 37-16=21, Resulting Numbers: [11, 32, 21] Generated Node #0,2: 85:[11, 32, 21] Operation: 37-16=21 Exploring Operation: 37-32=5, Resulting Numbers: [11, 16, 5] Generated Node #0,3: 85:[11, 16, 5] Operation: 37-32=5 Exploring Operation: 37-11=26, Resulting Numbers: [32, 16, 26] Generated Node #0,4: 85:[32, 16, 26] Operation: 37-11=26 Moving to Node #0,3 Current State: 85:[11, 16, 5], Operations: ['37-32=5'] Exploring Operation: 16+5=21, Resulting Numbers: [11, 21] Generated Node #0,3,0: 85:[11, 21] Operation: 16+5=21 Exploring Operation: 16-11=5, Resulting Numbers: [5, 5] Generated Node #0,3,1: 85:[5, 5] Operation: 16-11=5 Exploring Operation: 11-5=6, Resulting Numbers: [16, 6] Generated Node #0,3,2: 85:[16, 6] Operation: 11-5=6 Exploring Operation: 11+5=16, Resulting Numbers: [16, 16] Generated Node #0,3,3: 85:[16, 16] Operation: 11+5=16 Exploring Operation: 11+16=27, Resulting Numbers: [5, 27] Generated Node #0,3,4: 85:[5, 27] Operation: 11+16=27 Moving to Node #0,0 Current State: 85:[11, 16, 69], Operations: ['37+32=69'] Exploring Operation: 16+69=85, Resulting Numbers: [11, 85] Generated Node #0,0,0: 85:[11, 85] Operation: 16+69=85 Exploring Operation: 69-11=58, Resulting Numbers: [16, 58] Generated Node #0,0,1: 85:[16, 58] Operation: 69-11=58 Exploring Operation: 11+69=80, Resulting Numbers: [16, 80] Generated Node #0,0,2: 85:[16, 80] Operation: 11+69=80 Exploring Operation: 16-11=5, Resulting Numbers: [69, 5] Generated Node #0,0,3: 85:[69, 5] Operation: 16-11=5 Exploring Operation: 11+16=27, Resulting Numbers: [69, 27] Generated Node #0,0,4: 85:[69, 27] Operation: 11+16=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[11, 85], Operations: ['37+32=69', '16+69=85'] Exploring Operation: 11*85=935, Resulting Numbers: [935] 935,85 unequal: No Solution Exploring Operation: 85-11=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 11+85=96, Resulting Numbers: [96] 96,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 85:[16, 80], Operations: ['37+32=69', '11+69=80'] Exploring Operation: 16+80=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,85 unequal: No Solution Exploring Operation: 16*80=1280, Resulting Numbers: [1280] 1280,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 85:[69, 5], Operations: ['37+32=69', '16-11=5'] Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 69*5=345, Resulting Numbers: [345] 345,85 unequal: No Solution Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 85:[69, 27], Operations: ['37+32=69', '11+16=27'] Exploring Operation: 69-27=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 69+27=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 69*27=1863, Resulting Numbers: [1863] 1863,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[16, 58], Operations: ['37+32=69', '69-11=58'] Exploring Operation: 16+58=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 16*58=928, Resulting Numbers: [928] 928,85 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: 85:[37, 16, 21], Operations: ['32-11=21'] Exploring Operation: 37+16=53, Resulting Numbers: [21, 53] Generated Node #0,1,0: 85:[21, 53] Operation: 37+16=53 Exploring Operation: 37-16=21, Resulting Numbers: [21, 21] Generated Node #0,1,1: 85:[21, 21] Operation: 37-16=21 Exploring Operation: 21-16=5, Resulting Numbers: [37, 5] Generated Node #0,1,2: 85:[37, 5] Operation: 21-16=5 Exploring Operation: 37-21=16, Resulting Numbers: [16, 16] Generated Node #0,1,3: 85:[16, 16] Operation: 37-21=16 Exploring Operation: 37+21=58, Resulting Numbers: [16, 58] Generated Node #0,1,4: 85:[16, 58] Operation: 37+21=58 Moving to Node #0,2 Current State: 85:[11, 32, 21], Operations: ['37-16=21'] Exploring Operation: 32-21=11, Resulting Numbers: [11, 11] Generated Node #0,2,0: 85:[11, 11] Operation: 32-21=11 Exploring Operation: 32-11=21, Resulting Numbers: [21, 21] Generated Node #0,2,1: 85:[21, 21] Operation: 32-11=21 Exploring Operation: 11+21=32, Resulting Numbers: [32, 32] Generated Node #0,2,2: 85:[32, 32] Operation: 11+21=32 Exploring Operation: 11+32=43, Resulting Numbers: [21, 43] Generated Node #0,2,3: 85:[21, 43] Operation: 11+32=43 Exploring Operation: 21-11=10, Resulting Numbers: [32, 10] Generated Node #0,2,4: 85:[32, 10] Operation: 21-11=10 Moving to Node #0,4 Current State: 85:[32, 16, 26], Operations: ['37-11=26'] Exploring Operation: 26-16=10, Resulting Numbers: [32, 10] Generated Node #0,4,0: 85:[32, 10] Operation: 26-16=10 Exploring Operation: 32-26=6, Resulting Numbers: [16, 6] Generated Node #0,4,1: 85:[16, 6] Operation: 32-26=6 Exploring Operation: 32/16=2, Resulting Numbers: [26, 2] Generated Node #0,4,2: 85:[26, 2] Operation: 32/16=2 Exploring Operation: 32+26=58, Resulting Numbers: [16, 58] Generated Node #0,4,3: 85:[16, 58] Operation: 32+26=58 Exploring Operation: 32-16=16, Resulting Numbers: [26, 16] Generated Node #0,4,4: 85:[26, 16] Operation: 32-16=16 Moving to Node #0,3,1 Current State: 85:[5, 5], Operations: ['37-32=5', '16-11=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[16, 16], Operations: ['37-32=5', '11+5=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,85 unequal: No Solution Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[16, 16], Operations: ['32-11=21', '37-21=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,85 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[16, 6], Operations: ['37-32=5', '11-5=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[16, 6], Operations: ['37-11=26', '32-26=6'] Exploring Operation: 16*6=96, Resulting Numbers: [96] 96,85 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 16+6=22, Resulting Numbers: [22] 22,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[21, 21], Operations: ['32-11=21', '37-16=21'] Exploring Operation: 21*21=441, Resulting Numbers: [441] 441,85 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[21, 21], Operations: ['37-16=21', '32-11=21'] Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 21*21=441, Resulting Numbers: [441] 441,85 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,3,4 Current State: 85:[5, 27], Operations: ['37-32=5', '11+16=27'] Exploring Operation: 5+27=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 5*27=135, Resulting Numbers: [135] 135,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[11, 21], Operations: ['37-32=5', '16+5=21'] Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,85 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[26, 16], Operations: ['37-11=26', '32-16=16'] Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[11, 11], Operations: ['37-16=21', '32-21=11'] Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,85 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[26, 2], Operations: ['37-11=26', '32/16=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,85 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,85 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,85 unequal: No Solution Moving to Node #0,4,0 Current State: 85:[32, 10], Operations: ['37-11=26', '26-16=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,85 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[32, 10], Operations: ['37-16=21', '21-11=10'] Exploring Operation: 32*10=320, Resulting Numbers: [320] 320,85 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[37, 5], Operations: ['32-11=21', '21-16=5'] Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,85 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,85 unequal: No Solution Moving to Node #0,1,4 Current State: 85:[16, 58], Operations: ['32-11=21', '37+21=58'] Exploring Operation: 16*58=928, Resulting Numbers: [928] 928,85 unequal: No Solution Exploring Operation: 16+58=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[16, 58], Operations: ['37-11=26', '32+26=58'] Exploring Operation: 16*58=928, Resulting Numbers: [928] 928,85 unequal: No Solution Exploring Operation: 16+58=74, Resulting Numbers: [74] 74,85 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[21, 43], Operations: ['37-16=21', '11+32=43'] Exploring Operation: 21+43=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 21*43=903, Resulting Numbers: [903] 903,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[32, 32], Operations: ['37-16=21', '11+21=32'] Exploring Operation: 32+32=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 32*32=1024, Resulting Numbers: [1024] 1024,85 unequal: No Solution Exploring Operation: 32/32=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 32-32=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[21, 53], Operations: ['32-11=21', '37+16=53'] Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,85 unequal: No Solution Exploring Operation: 21*53=1113, Resulting Numbers: [1113] 1113,85 unequal: No Solution Exploring Operation: 21+53=74, Resulting Numbers: [74] 74,85 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 30, 82, 4, 32 ]
45
[ "82-30=52", "52/4=13", "32+13=45" ]
Current State: 45:[30, 82, 4, 32], Operations: [] Exploring Operation: 82-30=52, Resulting Numbers: [4, 32, 52] Generated Node #2: [4, 32, 52] from Operation: 82-30=52 Current State: 45:[4, 32, 52], Operations: ['82-30=52'] Exploring Operation: 52/4=13, Resulting Numbers: [32, 13] Generated Node #3: [32, 13] from Operation: 52/4=13 Current State: 45:[32, 13], Operations: ['82-30=52', '52/4=13'] Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[30, 82, 4, 32], Operations: [] Exploring Operation: 82-32=50, Resulting Numbers: [30, 4, 50] Generated Node #0,0: 45:[30, 4, 50] Operation: 82-32=50 Exploring Operation: 82-30=52, Resulting Numbers: [4, 32, 52] Generated Node #0,1: 45:[4, 32, 52] Operation: 82-30=52 Moving to Node #0,0 Current State: 45:[30, 4, 50], Operations: ['82-32=50'] Exploring Operation: 50-30=20, Resulting Numbers: [4, 20] Generated Node #0,0,0: 45:[4, 20] Operation: 50-30=20 Exploring Operation: 30+4=34, Resulting Numbers: [50, 34] Generated Node #0,0,1: 45:[50, 34] Operation: 30+4=34 Moving to Node #0,1 Current State: 45:[4, 32, 52], Operations: ['82-30=52'] Exploring Operation: 52-32=20, Resulting Numbers: [4, 20] Generated Node #0,1,0: 45:[4, 20] Operation: 52-32=20 Exploring Operation: 32/4=8, Resulting Numbers: [52, 8] Generated Node #0,1,1: 45:[52, 8] Operation: 32/4=8 Moving to Node #0,0,0 Current State: 45:[4, 20], Operations: ['82-32=50', '50-30=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[4, 20], Operations: ['82-30=52', '52-32=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[52, 8], Operations: ['82-30=52', '32/4=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[50, 34], Operations: ['82-32=50', '30+4=34'] Exploring Operation: 50+34=84, Resulting Numbers: [84] 84,45 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,45 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 18, 98, 45, 18 ]
89
[ "18+98=116", "45-18=27", "116-27=89" ]
Current State: 89:[18, 98, 45, 18], Operations: [] Exploring Operation: 18+98=116, Resulting Numbers: [45, 116] Generated Node #2: [45, 116] from Operation: 18+98=116 Current State: 89:[45, 116], Operations: ['18+98=116'] Exploring Operation: 45-18=27, Resulting Numbers: [116, 27] Generated Node #3: [116, 27] from Operation: 45-18=27 Current State: 89:[116, 27], Operations: ['18+98=116', '45-18=27'] Exploring Operation: 116-27=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[18, 98, 45, 18], Operations: [] Exploring Operation: 18+18=36, Resulting Numbers: [98, 45, 36] Generated Node #0,0: 89:[98, 45, 36] Operation: 18+18=36 Exploring Operation: 45+18=63, Resulting Numbers: [18, 98, 63] Generated Node #0,1: 89:[18, 98, 63] Operation: 45+18=63 Exploring Operation: 98-18=80, Resulting Numbers: [45, 18, 80] Generated Node #0,2: 89:[45, 18, 80] Operation: 98-18=80 Exploring Operation: 18+45=63, Resulting Numbers: [98, 18, 63] Generated Node #0,3: 89:[98, 18, 63] Operation: 18+45=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[98, 45, 36], Operations: ['18+18=36'] Exploring Operation: 98+36=134, Resulting Numbers: [45, 134] Generated Node #0,0,0: 89:[45, 134] Operation: 98+36=134 Exploring Operation: 98-45=53, Resulting Numbers: [36, 53] Generated Node #0,0,1: 89:[36, 53] Operation: 98-45=53 Exploring Operation: 98-36=62, Resulting Numbers: [45, 62] Generated Node #0,0,2: 89:[45, 62] Operation: 98-36=62 Exploring Operation: 45+36=81, Resulting Numbers: [98, 81] Generated Node #0,0,3: 89:[98, 81] Operation: 45+36=81 Moving to Node #0,0,3 Current State: 89:[98, 81], Operations: ['18+18=36', '45+36=81'] Exploring Operation: 98+81=179, Resulting Numbers: [179] 179,89 unequal: No Solution Exploring Operation: 98*81=7938, Resulting Numbers: [7938] 7938,89 unequal: No Solution Exploring Operation: 98-81=17, Resulting Numbers: [17] 17,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[45, 62], Operations: ['18+18=36', '98-36=62'] Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,89 unequal: No Solution Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,89 unequal: No Solution Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[36, 53], Operations: ['18+18=36', '98-45=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[18, 98, 45, 18], Operations: [] Exploring Operation: 18+18=36, Resulting Numbers: [98, 45, 36] Generated Node #0,0: 89:[98, 45, 36] Operation: 18+18=36 Moving to Node #0,0 Current State: 89:[98, 45, 36], Operations: ['18+18=36'] Exploring Operation: 98-45=53, Resulting Numbers: [36, 53] Generated Node #0,0,1: 89:[36, 53] Operation: 98-45=53 Moving to Node #0,0,1 Current State: 89:[36, 53], Operations: ['18+18=36', '98-45=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 48, 46, 20, 22 ]
64
[ "48-46=2", "22*2=44", "20+44=64" ]
Current State: 64:[48, 46, 20, 22], Operations: [] Exploring Operation: 48-46=2, Resulting Numbers: [20, 22, 2] Generated Node #2: [20, 22, 2] from Operation: 48-46=2 Current State: 64:[20, 22, 2], Operations: ['48-46=2'] Exploring Operation: 22*2=44, Resulting Numbers: [20, 44] Generated Node #3: [20, 44] from Operation: 22*2=44 Current State: 64:[20, 44], Operations: ['48-46=2', '22*2=44'] Exploring Operation: 20+44=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[48, 46, 20, 22], Operations: [] Exploring Operation: 48+22=70, Resulting Numbers: [46, 20, 70] Generated Node #0,0: 64:[46, 20, 70] Operation: 48+22=70 Exploring Operation: 48+20=68, Resulting Numbers: [46, 22, 68] Generated Node #0,1: 64:[46, 22, 68] Operation: 48+20=68 Exploring Operation: 48-20=28, Resulting Numbers: [46, 22, 28] Generated Node #0,2: 64:[46, 22, 28] Operation: 48-20=28 Exploring Operation: 48-46=2, Resulting Numbers: [20, 22, 2] Generated Node #0,3: 64:[20, 22, 2] Operation: 48-46=2 Moving to Node #0,3 Current State: 64:[20, 22, 2], Operations: ['48-46=2'] Exploring Operation: 22/2=11, Resulting Numbers: [20, 11] Generated Node #0,3,0: 64:[20, 11] Operation: 22/2=11 Exploring Operation: 22-20=2, Resulting Numbers: [2, 2] Generated Node #0,3,1: 64:[2, 2] Operation: 22-20=2 Exploring Operation: 20-2=18, Resulting Numbers: [22, 18] Generated Node #0,3,2: 64:[22, 18] Operation: 20-2=18 Exploring Operation: 20/2=10, Resulting Numbers: [22, 10] Generated Node #0,3,3: 64:[22, 10] Operation: 20/2=10 Moving to Node #0,1 Current State: 64:[46, 22, 68], Operations: ['48+20=68'] Exploring Operation: 46-22=24, Resulting Numbers: [68, 24] Generated Node #0,1,0: 64:[68, 24] Operation: 46-22=24 Exploring Operation: 68-22=46, Resulting Numbers: [46, 46] Generated Node #0,1,1: 64:[46, 46] Operation: 68-22=46 Exploring Operation: 68-46=22, Resulting Numbers: [22, 22] Generated Node #0,1,2: 64:[22, 22] Operation: 68-46=22 Exploring Operation: 46+22=68, Resulting Numbers: [68, 68] Generated Node #0,1,3: 64:[68, 68] Operation: 46+22=68 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[68, 68], Operations: ['48+20=68', '46+22=68'] Exploring Operation: 68*68=4624, Resulting Numbers: [4624] 4624,64 unequal: No Solution Exploring Operation: 68/68=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 68-68=0, Resulting Numbers: [0] 0,64 unequal: No Solution Exploring Operation: 68+68=136, Resulting Numbers: [136] 136,64 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:[68, 24], Operations: ['48+20=68', '46-22=24'] Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,64 unequal: No Solution Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,64 unequal: No Solution Exploring Operation: 68*24=1632, Resulting Numbers: [1632] 1632,64 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:[22, 22], Operations: ['48+20=68', '68-46=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,64 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,64 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,64 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:[46, 46], Operations: ['48+20=68', '68-22=46'] Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,64 unequal: No Solution Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,64 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,64 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,64 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: 64:[46, 20, 70], Operations: ['48+22=70'] Exploring Operation: 70-20=50, Resulting Numbers: [46, 50] Generated Node #0,0,0: 64:[46, 50] Operation: 70-20=50 Exploring Operation: 46+20=66, Resulting Numbers: [70, 66] Generated Node #0,0,1: 64:[70, 66] Operation: 46+20=66 Exploring Operation: 46-20=26, Resulting Numbers: [70, 26] Generated Node #0,0,2: 64:[70, 26] Operation: 46-20=26 Exploring Operation: 70-46=24, Resulting Numbers: [20, 24] Generated Node #0,0,3: 64:[20, 24] Operation: 70-46=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[70, 66], Operations: ['48+22=70', '46+20=66'] Exploring Operation: 70-66=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 70+66=136, Resulting Numbers: [136] 136,64 unequal: No Solution Exploring Operation: 70*66=4620, Resulting Numbers: [4620] 4620,64 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 #0,0,2 Current State: 64:[70, 26], Operations: ['48+22=70', '46-20=26'] Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,64 unequal: No Solution Exploring Operation: 70*26=1820, Resulting Numbers: [1820] 1820,64 unequal: No Solution Exploring Operation: 70+26=96, Resulting Numbers: [96] 96,64 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 #0,0,3 Current State: 64:[20, 24], Operations: ['48+22=70', '70-46=24'] Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,64 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,64 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,64 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 #0,0,0 Current State: 64:[46, 50], Operations: ['48+22=70', '70-20=50'] Exploring Operation: 46+50=96, Resulting Numbers: [96] 96,64 unequal: No Solution Exploring Operation: 46*50=2300, Resulting Numbers: [2300] 2300,64 unequal: No Solution Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,64 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: 64:[46, 22, 28], Operations: ['48-20=28'] Exploring Operation: 46-22=24, Resulting Numbers: [28, 24] Generated Node #0,2,0: 64:[28, 24] Operation: 46-22=24 Exploring Operation: 46+28=74, Resulting Numbers: [22, 74] Generated Node #0,2,1: 64:[22, 74] Operation: 46+28=74 Exploring Operation: 46-28=18, Resulting Numbers: [22, 18] Generated Node #0,2,2: 64:[22, 18] Operation: 46-28=18 Exploring Operation: 46+22=68, Resulting Numbers: [28, 68] Generated Node #0,2,3: 64:[28, 68] Operation: 46+22=68 Moving to Node #0,3,1 Current State: 64:[2, 2], Operations: ['48-46=2', '22-20=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,64 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,64 unequal: No Solution Moving to Node #0,3,0 Current State: 64:[20, 11], Operations: ['48-46=2', '22/2=11'] Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,64 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,64 unequal: No Solution Moving to Node #0,3,2 Current State: 64:[22, 18], Operations: ['48-46=2', '20-2=18'] Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,64 unequal: No Solution Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,64 unequal: No Solution Moving to Node #0,2,3 Current State: 64:[28, 68], Operations: ['48-20=28', '46+22=68'] Exploring Operation: 68-28=40, Resulting Numbers: [40] 40,64 unequal: No Solution Exploring Operation: 28*68=1904, Resulting Numbers: [1904] 1904,64 unequal: No Solution Exploring Operation: 28+68=96, Resulting Numbers: [96] 96,64 unequal: No Solution Moving to Node #0,2,2 Current State: 64:[22, 18], Operations: ['48-20=28', '46-28=18'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,64 unequal: No Solution Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,64 unequal: No Solution Moving to Node #0,3,3 Current State: 64:[22, 10], Operations: ['48-46=2', '20/2=10'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 22*10=220, Resulting Numbers: [220] 220,64 unequal: No Solution Exploring Operation: 22+10=32, Resulting Numbers: [32] 32,64 unequal: No Solution Moving to Node #0,2,0 Current State: 64:[28, 24], Operations: ['48-20=28', '46-22=24'] Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,64 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,64 unequal: No Solution Moving to Node #0,2,1 Current State: 64:[22, 74], Operations: ['48-20=28', '46+28=74'] Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,64 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,64 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,64 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 87, 95, 28, 87 ]
68
[ "87/87=1", "95-28=67", "1+67=68" ]
Current State: 68:[87, 95, 28, 87], Operations: [] Exploring Operation: 87/87=1, Resulting Numbers: [95, 28, 1] Generated Node #2: [95, 28, 1] from Operation: 87/87=1 Current State: 68:[95, 28, 1], Operations: ['87/87=1'] Exploring Operation: 95-28=67, Resulting Numbers: [1, 67] Generated Node #3: [1, 67] from Operation: 95-28=67 Current State: 68:[1, 67], Operations: ['87/87=1', '95-28=67'] Exploring Operation: 1+67=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[87, 95, 28, 87], Operations: [] Exploring Operation: 95-87=8, Resulting Numbers: [28, 87, 8] Generated Node #0,0: 68:[28, 87, 8] Operation: 95-87=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[28, 87, 8], Operations: ['95-87=8'] Exploring Operation: 87-28=59, Resulting Numbers: [8, 59] Generated Node #0,0,0: 68:[8, 59] Operation: 87-28=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[8, 59], Operations: ['95-87=8', '87-28=59'] Exploring Operation: 8+59=67, Resulting Numbers: [67] 67,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 94, 22, 33, 40 ]
43
[ "94+22=116", "33+40=73", "116-73=43" ]
Current State: 43:[94, 22, 33, 40], Operations: [] Exploring Operation: 94+22=116, Resulting Numbers: [33, 40, 116] Generated Node #2: [33, 40, 116] from Operation: 94+22=116 Current State: 43:[33, 40, 116], Operations: ['94+22=116'] Exploring Operation: 33+40=73, Resulting Numbers: [116, 73] Generated Node #3: [116, 73] from Operation: 33+40=73 Current State: 43:[116, 73], Operations: ['94+22=116', '33+40=73'] Exploring Operation: 116-73=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[94, 22, 33, 40], Operations: [] Exploring Operation: 94-40=54, Resulting Numbers: [22, 33, 54] Generated Node #0,0: 43:[22, 33, 54] Operation: 94-40=54 Exploring Operation: 94-33=61, Resulting Numbers: [22, 40, 61] Generated Node #0,1: 43:[22, 40, 61] Operation: 94-33=61 Exploring Operation: 94-22=72, Resulting Numbers: [33, 40, 72] Generated Node #0,2: 43:[33, 40, 72] Operation: 94-22=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[22, 33, 54], Operations: ['94-40=54'] Exploring Operation: 22+33=55, Resulting Numbers: [54, 55] Generated Node #0,0,0: 43:[54, 55] Operation: 22+33=55 Exploring Operation: 33-22=11, Resulting Numbers: [54, 11] Generated Node #0,0,1: 43:[54, 11] Operation: 33-22=11 Exploring Operation: 54-22=32, Resulting Numbers: [33, 32] Generated Node #0,0,2: 43:[33, 32] Operation: 54-22=32 Moving to Node #0,0,2 Current State: 43:[33, 32], Operations: ['94-40=54', '54-22=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,43 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[54, 55], Operations: ['94-40=54', '22+33=55'] Exploring Operation: 54+55=109, Resulting Numbers: [109] 109,43 unequal: No Solution Exploring Operation: 54*55=2970, Resulting Numbers: [2970] 2970,43 unequal: No Solution Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[54, 11], Operations: ['94-40=54', '33-22=11'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[94, 22, 33, 40], Operations: [] Exploring Operation: 94-40=54, Resulting Numbers: [22, 33, 54] Generated Node #0,0: 43:[22, 33, 54] Operation: 94-40=54 Moving to Node #0,0 Current State: 43:[22, 33, 54], Operations: ['94-40=54'] Exploring Operation: 33-22=11, Resulting Numbers: [54, 11] Generated Node #0,0,1: 43:[54, 11] Operation: 33-22=11 Moving to Node #0,0,1 Current State: 43:[54, 11], Operations: ['94-40=54', '33-22=11'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 29, 28, 30, 42 ]
71
[ "29-28=1", "30+42=72", "72-1=71" ]
Current State: 71:[29, 28, 30, 42], Operations: [] Exploring Operation: 29-28=1, Resulting Numbers: [30, 42, 1] Generated Node #2: [30, 42, 1] from Operation: 29-28=1 Current State: 71:[30, 42, 1], Operations: ['29-28=1'] Exploring Operation: 30+42=72, Resulting Numbers: [1, 72] Generated Node #3: [1, 72] from Operation: 30+42=72 Current State: 71:[1, 72], Operations: ['29-28=1', '30+42=72'] Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[29, 28, 30, 42], Operations: [] Exploring Operation: 29+42=71, Resulting Numbers: [28, 30, 71] Generated Node #0,0: 71:[28, 30, 71] Operation: 29+42=71 Exploring Operation: 29+30=59, Resulting Numbers: [28, 42, 59] Generated Node #0,1: 71:[28, 42, 59] Operation: 29+30=59 Exploring Operation: 29+28=57, Resulting Numbers: [30, 42, 57] Generated Node #0,2: 71:[30, 42, 57] Operation: 29+28=57 Moving to Node #0,0 Current State: 71:[28, 30, 71], Operations: ['29+42=71'] Exploring Operation: 30-28=2, Resulting Numbers: [71, 2] Generated Node #0,0,0: 71:[71, 2] Operation: 30-28=2 Exploring Operation: 28+71=99, Resulting Numbers: [30, 99] Generated Node #0,0,1: 71:[30, 99] Operation: 28+71=99 Exploring Operation: 28+30=58, Resulting Numbers: [71, 58] Generated Node #0,0,2: 71:[71, 58] Operation: 28+30=58 Moving to Node #0,1 Current State: 71:[28, 42, 59], Operations: ['29+30=59'] Exploring Operation: 28+59=87, Resulting Numbers: [42, 87] Generated Node #0,1,0: 71:[42, 87] Operation: 28+59=87 Exploring Operation: 42-28=14, Resulting Numbers: [59, 14] Generated Node #0,1,1: 71:[59, 14] Operation: 42-28=14 Exploring Operation: 28+42=70, Resulting Numbers: [59, 70] Generated Node #0,1,2: 71:[59, 70] Operation: 28+42=70 Moving to Node #0,2 Current State: 71:[30, 42, 57], Operations: ['29+28=57'] Exploring Operation: 42+57=99, Resulting Numbers: [30, 99] Generated Node #0,2,0: 71:[30, 99] Operation: 42+57=99 Exploring Operation: 30+42=72, Resulting Numbers: [57, 72] Generated Node #0,2,1: 71:[57, 72] Operation: 30+42=72 Exploring Operation: 30+57=87, Resulting Numbers: [42, 87] Generated Node #0,2,2: 71:[42, 87] Operation: 30+57=87 Moving to Node #0,0,2 Current State: 71:[71, 58], Operations: ['29+42=71', '28+30=58'] Exploring Operation: 71-58=13, Resulting Numbers: [13] 13,71 unequal: No Solution Exploring Operation: 71*58=4118, Resulting Numbers: [4118] 4118,71 unequal: No Solution Exploring Operation: 71+58=129, Resulting Numbers: [129] 129,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[59, 70], Operations: ['29+30=59', '28+42=70'] Exploring Operation: 70-59=11, Resulting Numbers: [11] 11,71 unequal: No Solution Exploring Operation: 59+70=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 59*70=4130, Resulting Numbers: [4130] 4130,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[57, 72], Operations: ['29+28=57', '30+42=72'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,71 unequal: No Solution Exploring Operation: 57+72=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 57*72=4104, Resulting Numbers: [4104] 4104,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[42, 87], Operations: ['29+30=59', '28+59=87'] Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,71 unequal: No Solution Exploring Operation: 42*87=3654, Resulting Numbers: [3654] 3654,71 unequal: No Solution Exploring Operation: 42+87=129, Resulting Numbers: [129] 129,71 unequal: No Solution Moving to Node #0,2,2 Current State: 71:[42, 87], Operations: ['29+28=57', '30+57=87'] Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,71 unequal: No Solution Exploring Operation: 42*87=3654, Resulting Numbers: [3654] 3654,71 unequal: No Solution Exploring Operation: 42+87=129, Resulting Numbers: [129] 129,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[30, 99], Operations: ['29+42=71', '28+71=99'] Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,71 unequal: No Solution Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[59, 14], Operations: ['29+30=59', '42-28=14'] Exploring Operation: 59*14=826, Resulting Numbers: [826] 826,71 unequal: No Solution Exploring Operation: 59+14=73, Resulting Numbers: [73] 73,71 unequal: No Solution Exploring Operation: 59-14=45, Resulting Numbers: [45] 45,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[30, 99], Operations: ['29+28=57', '42+57=99'] Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,71 unequal: No Solution Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,71 unequal: No Solution Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[71, 2], Operations: ['29+42=71', '30-28=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,71 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 15, 15, 1, 60 ]
18
[ "15-1=14", "60/15=4", "14+4=18" ]
Current State: 18:[15, 15, 1, 60], Operations: [] Exploring Operation: 15-1=14, Resulting Numbers: [60, 14] Generated Node #2: [60, 14] from Operation: 15-1=14 Current State: 18:[60, 14], Operations: ['15-1=14'] Exploring Operation: 60/15=4, Resulting Numbers: [14, 4] Generated Node #3: [14, 4] from Operation: 60/15=4 Current State: 18:[14, 4], Operations: ['15-1=14', '60/15=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[15, 15, 1, 60], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [15, 1, 4] Generated Node #0,0: 18:[15, 1, 4] Operation: 60/15=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[15, 1, 4], Operations: ['60/15=4'] Exploring Operation: 15+4=19, Resulting Numbers: [1, 19] Generated Node #0,0,0: 18:[1, 19] Operation: 15+4=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[1, 19], Operations: ['60/15=4', '15+4=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[15, 15, 1, 60], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [15, 1, 4] Generated Node #0,0: 18:[15, 1, 4] Operation: 60/15=4 Moving to Node #0,0 Current State: 18:[15, 1, 4], Operations: ['60/15=4'] Exploring Operation: 15+4=19, Resulting Numbers: [1, 19] Generated Node #0,0,0: 18:[1, 19] Operation: 15+4=19 Moving to Node #0,0,0 Current State: 18:[1, 19], Operations: ['60/15=4', '15+4=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 95, 16, 26, 40 ]
97
[ "95+16=111", "40-26=14", "111-14=97" ]
Current State: 97:[95, 16, 26, 40], Operations: [] Exploring Operation: 95+16=111, Resulting Numbers: [26, 40, 111] Generated Node #2: [26, 40, 111] from Operation: 95+16=111 Current State: 97:[26, 40, 111], Operations: ['95+16=111'] Exploring Operation: 40-26=14, Resulting Numbers: [111, 14] Generated Node #3: [111, 14] from Operation: 40-26=14 Current State: 97:[111, 14], Operations: ['95+16=111', '40-26=14'] Exploring Operation: 111-14=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[95, 16, 26, 40], Operations: [] Exploring Operation: 95-16=79, Resulting Numbers: [26, 40, 79] Generated Node #0,0: 97:[26, 40, 79] Operation: 95-16=79 Exploring Operation: 16+26=42, Resulting Numbers: [95, 40, 42] Generated Node #0,1: 97:[95, 40, 42] Operation: 16+26=42 Exploring Operation: 26+40=66, Resulting Numbers: [95, 16, 66] Generated Node #0,2: 97:[95, 16, 66] Operation: 26+40=66 Exploring Operation: 95+16=111, Resulting Numbers: [26, 40, 111] Generated Node #0,3: 97:[26, 40, 111] Operation: 95+16=111 Exploring Operation: 16+40=56, Resulting Numbers: [95, 26, 56] Generated Node #0,4: 97:[95, 26, 56] Operation: 16+40=56 Moving to Node #0,1 Current State: 97:[95, 40, 42], Operations: ['16+26=42'] Exploring Operation: 42-40=2, Resulting Numbers: [95, 2] Generated Node #0,1,0: 97:[95, 2] Operation: 42-40=2 Exploring Operation: 95+40=135, Resulting Numbers: [42, 135] Generated Node #0,1,1: 97:[42, 135] Operation: 95+40=135 Exploring Operation: 95+42=137, Resulting Numbers: [40, 137] Generated Node #0,1,2: 97:[40, 137] Operation: 95+42=137 Exploring Operation: 40+42=82, Resulting Numbers: [95, 82] Generated Node #0,1,3: 97:[95, 82] Operation: 40+42=82 Exploring Operation: 95-40=55, Resulting Numbers: [42, 55] Generated Node #0,1,4: 97:[42, 55] Operation: 95-40=55 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[95, 82], Operations: ['16+26=42', '40+42=82'] Exploring Operation: 95*82=7790, Resulting Numbers: [7790] 7790,97 unequal: No Solution Exploring Operation: 95-82=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 95+82=177, Resulting Numbers: [177] 177,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[42, 135], Operations: ['16+26=42', '95+40=135'] Exploring Operation: 42+135=177, Resulting Numbers: [177] 177,97 unequal: No Solution Exploring Operation: 42*135=5670, Resulting Numbers: [5670] 5670,97 unequal: No Solution Exploring Operation: 135-42=93, Resulting Numbers: [93] 93,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[95, 2], Operations: ['16+26=42', '42-40=2'] Exploring Operation: 95*2=190, Resulting Numbers: [190] 190,97 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,97 unequal: No Solution Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[95, 16, 26, 40], Operations: [] Exploring Operation: 16+26=42, Resulting Numbers: [95, 40, 42] Generated Node #0,1: 97:[95, 40, 42] Operation: 16+26=42 Moving to Node #0,1 Current State: 97:[95, 40, 42], Operations: ['16+26=42'] Exploring Operation: 42-40=2, Resulting Numbers: [95, 2] Generated Node #0,1,0: 97:[95, 2] Operation: 42-40=2 Moving to Node #0,1,0 Current State: 97:[95, 2], Operations: ['16+26=42', '42-40=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 78, 75, 57, 54 ]
63
[ "78*54=4212", "75*57=4275", "4275-4212=63" ]
Current State: 63:[78, 75, 57, 54], Operations: [] Exploring Operation: 78*54=4212, Resulting Numbers: [75, 57, 4212] Generated Node #2: [75, 57, 4212] from Operation: 78*54=4212 Current State: 63:[75, 57, 4212], Operations: ['78*54=4212'] Exploring Operation: 75*57=4275, Resulting Numbers: [4212, 4275] Generated Node #3: [4212, 4275] from Operation: 75*57=4275 Current State: 63:[4212, 4275], Operations: ['78*54=4212', '75*57=4275'] Exploring Operation: 4275-4212=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[78, 75, 57, 54], Operations: [] Exploring Operation: 78-57=21, Resulting Numbers: [75, 54, 21] Generated Node #0,0: 63:[75, 54, 21] Operation: 78-57=21 Exploring Operation: 78-75=3, Resulting Numbers: [57, 54, 3] Generated Node #0,1: 63:[57, 54, 3] Operation: 78-75=3 Exploring Operation: 78-54=24, Resulting Numbers: [75, 57, 24] Generated Node #0,2: 63:[75, 57, 24] Operation: 78-54=24 Moving to Node #0,1 Current State: 63:[57, 54, 3], Operations: ['78-75=3'] Exploring Operation: 57/3=19, Resulting Numbers: [54, 19] Generated Node #0,1,0: 63:[54, 19] Operation: 57/3=19 Exploring Operation: 54/3=18, Resulting Numbers: [57, 18] Generated Node #0,1,1: 63:[57, 18] Operation: 54/3=18 Exploring Operation: 57-54=3, Resulting Numbers: [3, 3] Generated Node #0,1,2: 63:[3, 3] Operation: 57-54=3 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[3, 3], Operations: ['78-75=3', '57-54=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[57, 18], Operations: ['78-75=3', '54/3=18'] Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,63 unequal: No Solution Exploring Operation: 57+18=75, Resulting Numbers: [75] 75,63 unequal: No Solution Exploring Operation: 57*18=1026, Resulting Numbers: [1026] 1026,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[54, 19], Operations: ['78-75=3', '57/3=19'] Exploring Operation: 54+19=73, Resulting Numbers: [73] 73,63 unequal: No Solution Exploring Operation: 54-19=35, Resulting Numbers: [35] 35,63 unequal: No Solution Exploring Operation: 54*19=1026, Resulting Numbers: [1026] 1026,63 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: 63:[75, 54, 21], Operations: ['78-57=21'] Exploring Operation: 75-21=54, Resulting Numbers: [54, 54] Generated Node #0,0,0: 63:[54, 54] Operation: 75-21=54 Exploring Operation: 75-54=21, Resulting Numbers: [21, 21] Generated Node #0,0,1: 63:[21, 21] Operation: 75-54=21 Exploring Operation: 54+21=75, Resulting Numbers: [75, 75] Generated Node #0,0,2: 63:[75, 75] Operation: 54+21=75 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[21, 21], Operations: ['78-57=21', '75-54=21'] Exploring Operation: 21-21=0, Resulting Numbers: [0] 0,63 unequal: No Solution Exploring Operation: 21/21=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 21+21=42, Resulting Numbers: [42] 42,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[54, 54], Operations: ['78-57=21', '75-21=54'] Exploring Operation: 54/54=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 54+54=108, Resulting Numbers: [108] 108,63 unequal: No Solution Exploring Operation: 54-54=0, Resulting Numbers: [0] 0,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[75, 75], Operations: ['78-57=21', '54+21=75'] Exploring Operation: 75/75=1, Resulting Numbers: [1] 1,63 unequal: No Solution Exploring Operation: 75+75=150, Resulting Numbers: [150] 150,63 unequal: No Solution Exploring Operation: 75-75=0, Resulting Numbers: [0] 0,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 63:[75, 57, 24], Operations: ['78-54=24'] Exploring Operation: 75-57=18, Resulting Numbers: [24, 18] Generated Node #0,2,0: 63:[24, 18] Operation: 75-57=18 Exploring Operation: 57-24=33, Resulting Numbers: [75, 33] Generated Node #0,2,1: 63:[75, 33] Operation: 57-24=33 Exploring Operation: 75-24=51, Resulting Numbers: [57, 51] Generated Node #0,2,2: 63:[57, 51] Operation: 75-24=51 Moving to Node #0,2,0 Current State: 63:[24, 18], Operations: ['78-54=24', '75-57=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[57, 51], Operations: ['78-54=24', '75-24=51'] Exploring Operation: 57*51=2907, Resulting Numbers: [2907] 2907,63 unequal: No Solution Exploring Operation: 57+51=108, Resulting Numbers: [108] 108,63 unequal: No Solution Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[75, 33], Operations: ['78-54=24', '57-24=33'] Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,63 unequal: No Solution Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,63 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,63 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 19, 36, 68, 36 ]
87
[ "19+36=55", "68-36=32", "55+32=87" ]
Current State: 87:[19, 36, 68, 36], Operations: [] Exploring Operation: 19+36=55, Resulting Numbers: [68, 55] Generated Node #2: [68, 55] from Operation: 19+36=55 Current State: 87:[68, 55], Operations: ['19+36=55'] Exploring Operation: 68-36=32, Resulting Numbers: [55, 32] Generated Node #3: [55, 32] from Operation: 68-36=32 Current State: 87:[55, 32], Operations: ['19+36=55', '68-36=32'] Exploring Operation: 55+32=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[19, 36, 68, 36], Operations: [] Exploring Operation: 36/36=1, Resulting Numbers: [19, 68, 1] Generated Node #0,0: 87:[19, 68, 1] Operation: 36/36=1 Exploring Operation: 68-36=32, Resulting Numbers: [19, 36, 32] Generated Node #0,1: 87:[19, 36, 32] Operation: 68-36=32 Exploring Operation: 19+68=87, Resulting Numbers: [36, 36, 87] Generated Node #0,2: 87:[36, 36, 87] Operation: 19+68=87 Exploring Operation: 68-36=32, Resulting Numbers: [19, 36, 32] Generated Node #0,3: 87:[19, 36, 32] Operation: 68-36=32 Moving to Node #0,2 Current State: 87:[36, 36, 87], Operations: ['19+68=87'] Exploring Operation: 36/36=1, Resulting Numbers: [87, 1] Generated Node #0,2,0: 87:[87, 1] Operation: 36/36=1 Exploring Operation: 36-36=0, Resulting Numbers: [87, 0] Generated Node #0,2,1: 87:[87, 0] Operation: 36-36=0 Exploring Operation: 36+36=72, Resulting Numbers: [87, 72] Generated Node #0,2,2: 87:[87, 72] Operation: 36+36=72 Exploring Operation: 87-36=51, Resulting Numbers: [36, 51] Generated Node #0,2,3: 87:[36, 51] Operation: 87-36=51 Moving to Node #0,3 Current State: 87:[19, 36, 32], Operations: ['68-36=32'] Exploring Operation: 32-19=13, Resulting Numbers: [36, 13] Generated Node #0,3,0: 87:[36, 13] Operation: 32-19=13 Exploring Operation: 36-19=17, Resulting Numbers: [32, 17] Generated Node #0,3,1: 87:[32, 17] Operation: 36-19=17 Exploring Operation: 36-32=4, Resulting Numbers: [19, 4] Generated Node #0,3,2: 87:[19, 4] Operation: 36-32=4 Exploring Operation: 19+36=55, Resulting Numbers: [32, 55] Generated Node #0,3,3: 87:[32, 55] Operation: 19+36=55 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 87:[19, 4], Operations: ['68-36=32', '36-32=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,87 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,87 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,87 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 #0,3,1 Current State: 87:[32, 17], Operations: ['68-36=32', '36-19=17'] Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,87 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,87 unequal: No Solution Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,87 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 #0,3,0 Current State: 87:[36, 13], Operations: ['68-36=32', '32-19=13'] Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,87 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,87 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 #0,3,3 Current State: 87:[32, 55], Operations: ['68-36=32', '19+36=55'] Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,87 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[19, 36, 68, 36], Operations: [] Exploring Operation: 68-36=32, Resulting Numbers: [19, 36, 32] Generated Node #0,3: 87:[19, 36, 32] Operation: 68-36=32 Moving to Node #0,3 Current State: 87:[19, 36, 32], Operations: ['68-36=32'] Exploring Operation: 19+36=55, Resulting Numbers: [32, 55] Generated Node #0,3,3: 87:[32, 55] Operation: 19+36=55 Moving to Node #0,3,3 Current State: 87:[32, 55], Operations: ['68-36=32', '19+36=55'] Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_4
sum_heuristic
[ 72, 32, 24, 64 ]
12
[ "72*32=2304", "2304/64=36", "36-24=12" ]
Current State: 12:[72, 32, 24, 64], Operations: [] Exploring Operation: 72*32=2304, Resulting Numbers: [24, 64, 2304] Generated Node #2: [24, 64, 2304] from Operation: 72*32=2304 Current State: 12:[24, 64, 2304], Operations: ['72*32=2304'] Exploring Operation: 2304/64=36, Resulting Numbers: [24, 36] Generated Node #3: [24, 36] from Operation: 2304/64=36 Current State: 12:[24, 36], Operations: ['72*32=2304', '2304/64=36'] Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[72, 32, 24, 64], Operations: [] Exploring Operation: 72-64=8, Resulting Numbers: [32, 24, 8] Generated Node #0,0: 12:[32, 24, 8] Operation: 72-64=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[32, 24, 8], Operations: ['72-64=8'] Exploring Operation: 32-24=8, Resulting Numbers: [8, 8] Generated Node #0,0,0: 12:[8, 8] Operation: 32-24=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[8, 8], Operations: ['72-64=8', '32-24=8'] Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,12 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 No solution found.
0
hs_1
sum_heuristic
[ 40, 86, 12, 98 ]
12
[ "86-40=46", "98+46=144", "144/12=12" ]
Current State: 12:[40, 86, 12, 98], Operations: [] Exploring Operation: 86-40=46, Resulting Numbers: [12, 98, 46] Generated Node #2: [12, 98, 46] from Operation: 86-40=46 Current State: 12:[12, 98, 46], Operations: ['86-40=46'] Exploring Operation: 98+46=144, Resulting Numbers: [12, 144] Generated Node #3: [12, 144] from Operation: 98+46=144 Current State: 12:[12, 144], Operations: ['86-40=46', '98+46=144'] Exploring Operation: 144/12=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[40, 86, 12, 98], Operations: [] Exploring Operation: 98-40=58, Resulting Numbers: [86, 12, 58] Generated Node #0,0: 12:[86, 12, 58] Operation: 98-40=58 Exploring Operation: 98-86=12, Resulting Numbers: [40, 12, 12] Generated Node #0,1: 12:[40, 12, 12] Operation: 98-86=12 Exploring Operation: 86-40=46, Resulting Numbers: [12, 98, 46] Generated Node #0,2: 12:[12, 98, 46] Operation: 86-40=46 Moving to Node #0,1 Current State: 12:[40, 12, 12], Operations: ['98-86=12'] Exploring Operation: 40-12=28, Resulting Numbers: [12, 28] Generated Node #0,1,0: 12:[12, 28] Operation: 40-12=28 Exploring Operation: 12/12=1, Resulting Numbers: [40, 1] Generated Node #0,1,1: 12:[40, 1] Operation: 12/12=1 Exploring Operation: 40-12=28, Resulting Numbers: [12, 28] Generated Node #0,1,2: 12:[12, 28] Operation: 40-12=28 Moving to Node #0,0 Current State: 12:[86, 12, 58], Operations: ['98-40=58'] Exploring Operation: 86-12=74, Resulting Numbers: [58, 74] Generated Node #0,0,0: 12:[58, 74] Operation: 86-12=74 Exploring Operation: 86-58=28, Resulting Numbers: [12, 28] Generated Node #0,0,1: 12:[12, 28] Operation: 86-58=28 Exploring Operation: 58-12=46, Resulting Numbers: [86, 46] Generated Node #0,0,2: 12:[86, 46] Operation: 58-12=46 Moving to Node #0,2 Current State: 12:[12, 98, 46], Operations: ['86-40=46'] Exploring Operation: 98-46=52, Resulting Numbers: [12, 52] Generated Node #0,2,0: 12:[12, 52] Operation: 98-46=52 Exploring Operation: 98-12=86, Resulting Numbers: [46, 86] Generated Node #0,2,1: 12:[46, 86] Operation: 98-12=86 Exploring Operation: 46-12=34, Resulting Numbers: [98, 34] Generated Node #0,2,2: 12:[98, 34] Operation: 46-12=34 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 12:[12, 52], Operations: ['86-40=46', '98-46=52'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,12 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,12 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 #0,2,1 Current State: 12:[46, 86], Operations: ['86-40=46', '98-12=86'] Exploring Operation: 86-46=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 46*86=3956, Resulting Numbers: [3956] 3956,12 unequal: No Solution Exploring Operation: 46+86=132, Resulting Numbers: [132] 132,12 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 #0,2,2 Current State: 12:[98, 34], Operations: ['86-40=46', '46-12=34'] Exploring Operation: 98+34=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 98-34=64, Resulting Numbers: [64] 64,12 unequal: No Solution Exploring Operation: 98*34=3332, Resulting Numbers: [3332] 3332,12 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: 12:[12, 28], Operations: ['98-86=12', '40-12=28'] Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,12 unequal: No Solution Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[12, 28], Operations: ['98-86=12', '40-12=28'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[12, 28], Operations: ['98-40=58', '86-58=28'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 12+28=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 12*28=336, Resulting Numbers: [336] 336,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[40, 1], Operations: ['98-86=12', '12/12=1'] Exploring Operation: 40*1=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 40/1=40, Resulting Numbers: [40] 40,12 unequal: No Solution Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[86, 46], Operations: ['98-40=58', '58-12=46'] Exploring Operation: 86+46=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 86*46=3956, Resulting Numbers: [3956] 3956,12 unequal: No Solution Exploring Operation: 86-46=40, Resulting Numbers: [40] 40,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[58, 74], Operations: ['98-40=58', '86-12=74'] Exploring Operation: 74-58=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 58+74=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 58*74=4292, Resulting Numbers: [4292] 4292,12 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 27, 85, 54, 39 ]
44
[ "54/27=2", "85-39=46", "46-2=44" ]
Current State: 44:[27, 85, 54, 39], Operations: [] Exploring Operation: 54/27=2, Resulting Numbers: [85, 39, 2] Generated Node #2: [85, 39, 2] from Operation: 54/27=2 Current State: 44:[85, 39, 2], Operations: ['54/27=2'] Exploring Operation: 85-39=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 85-39=46 Current State: 44:[2, 46], Operations: ['54/27=2', '85-39=46'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[27, 85, 54, 39], Operations: [] Exploring Operation: 85-39=46, Resulting Numbers: [27, 54, 46] Generated Node #0,0: 44:[27, 54, 46] Operation: 85-39=46 Exploring Operation: 85-54=31, Resulting Numbers: [27, 39, 31] Generated Node #0,1: 44:[27, 39, 31] Operation: 85-54=31 Moving to Node #0,0 Current State: 44:[27, 54, 46], Operations: ['85-39=46'] Exploring Operation: 54/27=2, Resulting Numbers: [46, 2] Generated Node #0,0,0: 44:[46, 2] Operation: 54/27=2 Exploring Operation: 54-27=27, Resulting Numbers: [46, 27] Generated Node #0,0,1: 44:[46, 27] Operation: 54-27=27 Moving to Node #0,1 Current State: 44:[27, 39, 31], Operations: ['85-54=31'] Exploring Operation: 39-31=8, Resulting Numbers: [27, 8] Generated Node #0,1,0: 44:[27, 8] Operation: 39-31=8 Exploring Operation: 31-27=4, Resulting Numbers: [39, 4] Generated Node #0,1,1: 44:[39, 4] Operation: 31-27=4 Moving to Node #0,0,0 Current State: 44:[46, 2], Operations: ['85-39=46', '54/27=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[27, 85, 54, 39], Operations: [] Exploring Operation: 85-39=46, Resulting Numbers: [27, 54, 46] Generated Node #0,0: 44:[27, 54, 46] Operation: 85-39=46 Moving to Node #0,0 Current State: 44:[27, 54, 46], Operations: ['85-39=46'] Exploring Operation: 54/27=2, Resulting Numbers: [46, 2] Generated Node #0,0,0: 44:[46, 2] Operation: 54/27=2 Moving to Node #0,0,0 Current State: 44:[46, 2], Operations: ['85-39=46', '54/27=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 32, 2, 5, 30 ]
100
[ "32*5=160", "2*30=60", "160-60=100" ]
Current State: 100:[32, 2, 5, 30], Operations: [] Exploring Operation: 32*5=160, Resulting Numbers: [2, 30, 160] Generated Node #2: [2, 30, 160] from Operation: 32*5=160 Current State: 100:[2, 30, 160], Operations: ['32*5=160'] Exploring Operation: 2*30=60, Resulting Numbers: [160, 60] Generated Node #3: [160, 60] from Operation: 2*30=60 Current State: 100:[160, 60], Operations: ['32*5=160', '2*30=60'] Exploring Operation: 160-60=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[32, 2, 5, 30], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [2, 5, 2] Generated Node #0,0: 100:[2, 5, 2] Operation: 32-30=2 Moving to Node #0,0 Current State: 100:[2, 5, 2], Operations: ['32-30=2'] Exploring Operation: 2*5=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 100:[2, 10] Operation: 2*5=10 Moving to Node #0,0,0 Current State: 100:[2, 10], Operations: ['32-30=2', '2*5=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 71, 5, 8, 14 ]
11
[ "71-5=66", "14-8=6", "66/6=11" ]
Current State: 11:[71, 5, 8, 14], Operations: [] Exploring Operation: 71-5=66, Resulting Numbers: [8, 14, 66] Generated Node #2: [8, 14, 66] from Operation: 71-5=66 Current State: 11:[8, 14, 66], Operations: ['71-5=66'] Exploring Operation: 14-8=6, Resulting Numbers: [66, 6] Generated Node #3: [66, 6] from Operation: 14-8=6 Current State: 11:[66, 6], Operations: ['71-5=66', '14-8=6'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[71, 5, 8, 14], Operations: [] Exploring Operation: 71-14=57, Resulting Numbers: [5, 8, 57] Generated Node #0,0: 11:[5, 8, 57] Operation: 71-14=57 Moving to Node #0,0 Current State: 11:[5, 8, 57], Operations: ['71-14=57'] Exploring Operation: 57-5=52, Resulting Numbers: [8, 52] Generated Node #0,0,0: 11:[8, 52] Operation: 57-5=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[8, 52], Operations: ['71-14=57', '57-5=52'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,11 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
[ 78, 77, 99, 85 ]
29
[ "78+77=155", "99+85=184", "184-155=29" ]
Current State: 29:[78, 77, 99, 85], Operations: [] Exploring Operation: 78+77=155, Resulting Numbers: [99, 85, 155] Generated Node #2: [99, 85, 155] from Operation: 78+77=155 Current State: 29:[99, 85, 155], Operations: ['78+77=155'] Exploring Operation: 99+85=184, Resulting Numbers: [155, 184] Generated Node #3: [155, 184] from Operation: 99+85=184 Current State: 29:[155, 184], Operations: ['78+77=155', '99+85=184'] Exploring Operation: 184-155=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[78, 77, 99, 85], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [77, 85, 21] Generated Node #0,0: 29:[77, 85, 21] Operation: 99-78=21 Exploring Operation: 99-77=22, Resulting Numbers: [78, 85, 22] Generated Node #0,1: 29:[78, 85, 22] Operation: 99-77=22 Exploring Operation: 85-78=7, Resulting Numbers: [77, 99, 7] Generated Node #0,2: 29:[77, 99, 7] Operation: 85-78=7 Exploring Operation: 99-85=14, Resulting Numbers: [78, 77, 14] Generated Node #0,3: 29:[78, 77, 14] Operation: 99-85=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[77, 85, 21], Operations: ['99-78=21'] Exploring Operation: 85-77=8, Resulting Numbers: [21, 8] Generated Node #0,0,0: 29:[21, 8] Operation: 85-77=8 Exploring Operation: 77+21=98, Resulting Numbers: [85, 98] Generated Node #0,0,1: 29:[85, 98] Operation: 77+21=98 Exploring Operation: 85-21=64, Resulting Numbers: [77, 64] Generated Node #0,0,2: 29:[77, 64] Operation: 85-21=64 Exploring Operation: 77-21=56, Resulting Numbers: [85, 56] Generated Node #0,0,3: 29:[85, 56] Operation: 77-21=56 Moving to Node #0,0,0 Current State: 29:[21, 8], Operations: ['99-78=21', '85-77=8'] Exploring Operation: 21*8=168, Resulting Numbers: [168] 168,29 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[78, 77, 99, 85], Operations: [] Exploring Operation: 99-78=21, Resulting Numbers: [77, 85, 21] Generated Node #0,0: 29:[77, 85, 21] Operation: 99-78=21 Moving to Node #0,0 Current State: 29:[77, 85, 21], Operations: ['99-78=21'] Exploring Operation: 85-77=8, Resulting Numbers: [21, 8] Generated Node #0,0,0: 29:[21, 8] Operation: 85-77=8 Moving to Node #0,0,0 Current State: 29:[21, 8], Operations: ['99-78=21', '85-77=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 3, 52, 14, 97 ]
56
[ "3+52=55", "14+97=111", "111-55=56" ]
Current State: 56:[3, 52, 14, 97], Operations: [] Exploring Operation: 3+52=55, Resulting Numbers: [14, 97, 55] Generated Node #2: [14, 97, 55] from Operation: 3+52=55 Current State: 56:[14, 97, 55], Operations: ['3+52=55'] Exploring Operation: 14+97=111, Resulting Numbers: [55, 111] Generated Node #3: [55, 111] from Operation: 14+97=111 Current State: 56:[55, 111], Operations: ['3+52=55', '14+97=111'] Exploring Operation: 111-55=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[3, 52, 14, 97], Operations: [] Exploring Operation: 3+52=55, Resulting Numbers: [14, 97, 55] Generated Node #0,0: 56:[14, 97, 55] Operation: 3+52=55 Exploring Operation: 97-14=83, Resulting Numbers: [3, 52, 83] Generated Node #0,1: 56:[3, 52, 83] Operation: 97-14=83 Exploring Operation: 97-52=45, Resulting Numbers: [3, 14, 45] Generated Node #0,2: 56:[3, 14, 45] Operation: 97-52=45 Exploring Operation: 97-3=94, Resulting Numbers: [52, 14, 94] Generated Node #0,3: 56:[52, 14, 94] Operation: 97-3=94 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[3, 14, 45], Operations: ['97-52=45'] Exploring Operation: 45/3=15, Resulting Numbers: [14, 15] Generated Node #0,2,0: 56:[14, 15] Operation: 45/3=15 Exploring Operation: 45-14=31, Resulting Numbers: [3, 31] Generated Node #0,2,1: 56:[3, 31] Operation: 45-14=31 Exploring Operation: 3+45=48, Resulting Numbers: [14, 48] Generated Node #0,2,2: 56:[14, 48] Operation: 3+45=48 Exploring Operation: 14+45=59, Resulting Numbers: [3, 59] Generated Node #0,2,3: 56:[3, 59] Operation: 14+45=59 Moving to Node #0,2,0 Current State: 56:[14, 15], Operations: ['97-52=45', '45/3=15'] Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,56 unequal: No Solution Exploring Operation: 14+15=29, Resulting Numbers: [29] 29,56 unequal: No Solution Exploring Operation: 14*15=210, Resulting Numbers: [210] 210,56 unequal: No Solution Moving to Node #0,2,3 Current State: 56:[3, 59], Operations: ['97-52=45', '14+45=59'] Exploring Operation: 3*59=177, Resulting Numbers: [177] 177,56 unequal: No Solution Exploring Operation: 3+59=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[3, 52, 14, 97], Operations: [] Exploring Operation: 97-52=45, Resulting Numbers: [3, 14, 45] Generated Node #0,2: 56:[3, 14, 45] Operation: 97-52=45 Moving to Node #0,2 Current State: 56:[3, 14, 45], Operations: ['97-52=45'] Exploring Operation: 14+45=59, Resulting Numbers: [3, 59] Generated Node #0,2,3: 56:[3, 59] Operation: 14+45=59 Moving to Node #0,2,3 Current State: 56:[3, 59], Operations: ['97-52=45', '14+45=59'] Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 24, 43, 65, 46 ]
86
[ "24+43=67", "65-46=19", "67+19=86" ]
Current State: 86:[24, 43, 65, 46], Operations: [] Exploring Operation: 24+43=67, Resulting Numbers: [65, 46, 67] Generated Node #2: [65, 46, 67] from Operation: 24+43=67 Current State: 86:[65, 46, 67], Operations: ['24+43=67'] Exploring Operation: 65-46=19, Resulting Numbers: [67, 19] Generated Node #3: [67, 19] from Operation: 65-46=19 Current State: 86:[67, 19], Operations: ['24+43=67', '65-46=19'] Exploring Operation: 67+19=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[24, 43, 65, 46], Operations: [] Exploring Operation: 65-24=41, Resulting Numbers: [43, 46, 41] Generated Node #0,0: 86:[43, 46, 41] Operation: 65-24=41 Exploring Operation: 43-24=19, Resulting Numbers: [65, 46, 19] Generated Node #0,1: 86:[65, 46, 19] Operation: 43-24=19 Exploring Operation: 24+65=89, Resulting Numbers: [43, 46, 89] Generated Node #0,2: 86:[43, 46, 89] Operation: 24+65=89 Exploring Operation: 65-46=19, Resulting Numbers: [24, 43, 19] Generated Node #0,3: 86:[24, 43, 19] Operation: 65-46=19 Exploring Operation: 24+46=70, Resulting Numbers: [43, 65, 70] Generated Node #0,4: 86:[43, 65, 70] Operation: 24+46=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[43, 46, 41], Operations: ['65-24=41'] Exploring Operation: 43-41=2, Resulting Numbers: [46, 2] Generated Node #0,0,0: 86:[46, 2] Operation: 43-41=2 Exploring Operation: 46+41=87, Resulting Numbers: [43, 87] Generated Node #0,0,1: 86:[43, 87] Operation: 46+41=87 Exploring Operation: 46-43=3, Resulting Numbers: [41, 3] Generated Node #0,0,2: 86:[41, 3] Operation: 46-43=3 Exploring Operation: 46-41=5, Resulting Numbers: [43, 5] Generated Node #0,0,3: 86:[43, 5] Operation: 46-41=5 Exploring Operation: 43+46=89, Resulting Numbers: [41, 89] Generated Node #0,0,4: 86:[41, 89] Operation: 43+46=89 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[43, 87], Operations: ['65-24=41', '46+41=87'] Exploring Operation: 43*87=3741, Resulting Numbers: [3741] 3741,86 unequal: No Solution Exploring Operation: 87-43=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 43+87=130, Resulting Numbers: [130] 130,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[46, 2], Operations: ['65-24=41', '43-41=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,86 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[41, 3], Operations: ['65-24=41', '46-43=3'] Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,86 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,86 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[43, 5], Operations: ['65-24=41', '46-41=5'] Exploring Operation: 43*5=215, Resulting Numbers: [215] 215,86 unequal: No Solution Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 86:[41, 89], Operations: ['65-24=41', '43+46=89'] Exploring Operation: 89-41=48, Resulting Numbers: [48] 48,86 unequal: No Solution Exploring Operation: 41+89=130, Resulting Numbers: [130] 130,86 unequal: No Solution Exploring Operation: 41*89=3649, Resulting Numbers: [3649] 3649,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[43, 46, 89], Operations: ['24+65=89'] Exploring Operation: 46-43=3, Resulting Numbers: [89, 3] Generated Node #0,2,0: 86:[89, 3] Operation: 46-43=3 Exploring Operation: 89-43=46, Resulting Numbers: [46, 46] Generated Node #0,2,1: 86:[46, 46] Operation: 89-43=46 Exploring Operation: 43+89=132, Resulting Numbers: [46, 132] Generated Node #0,2,2: 86:[46, 132] Operation: 43+89=132 Exploring Operation: 43+46=89, Resulting Numbers: [89, 89] Generated Node #0,2,3: 86:[89, 89] Operation: 43+46=89 Exploring Operation: 89-46=43, Resulting Numbers: [43, 43] Generated Node #0,2,4: 86:[43, 43] Operation: 89-46=43 Moving to Node #0,2,4 Current State: 86:[43, 43], Operations: ['24+65=89', '89-46=43'] Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[24, 43, 65, 46], Operations: [] Exploring Operation: 24+65=89, Resulting Numbers: [43, 46, 89] Generated Node #0,2: 86:[43, 46, 89] Operation: 24+65=89 Moving to Node #0,2 Current State: 86:[43, 46, 89], Operations: ['24+65=89'] Exploring Operation: 89-46=43, Resulting Numbers: [43, 43] Generated Node #0,2,4: 86:[43, 43] Operation: 89-46=43 Moving to Node #0,2,4 Current State: 86:[43, 43], Operations: ['24+65=89', '89-46=43'] Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_5
sum_heuristic
[ 74, 2, 47, 77 ]
88
[ "74+47=121", "121-77=44", "2*44=88" ]
Current State: 88:[74, 2, 47, 77], Operations: [] Exploring Operation: 74+47=121, Resulting Numbers: [2, 77, 121] Generated Node #2: [2, 77, 121] from Operation: 74+47=121 Current State: 88:[2, 77, 121], Operations: ['74+47=121'] Exploring Operation: 121-77=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 121-77=44 Current State: 88:[2, 44], Operations: ['74+47=121', '121-77=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[74, 2, 47, 77], Operations: [] Exploring Operation: 74-47=27, Resulting Numbers: [2, 77, 27] Generated Node #0,0: 88:[2, 77, 27] Operation: 74-47=27 Exploring Operation: 77-74=3, Resulting Numbers: [2, 47, 3] Generated Node #0,1: 88:[2, 47, 3] Operation: 77-74=3 Moving to Node #0,1 Current State: 88:[2, 47, 3], Operations: ['77-74=3'] Exploring Operation: 47-2=45, Resulting Numbers: [3, 45] Generated Node #0,1,0: 88:[3, 45] Operation: 47-2=45 Exploring Operation: 47-3=44, Resulting Numbers: [2, 44] Generated Node #0,1,1: 88:[2, 44] Operation: 47-3=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[2, 44], Operations: ['77-74=3', '47-3=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[74, 2, 47, 77], Operations: [] Exploring Operation: 77-74=3, Resulting Numbers: [2, 47, 3] Generated Node #0,1: 88:[2, 47, 3] Operation: 77-74=3 Moving to Node #0,1 Current State: 88:[2, 47, 3], Operations: ['77-74=3'] Exploring Operation: 47-3=44, Resulting Numbers: [2, 44] Generated Node #0,1,1: 88:[2, 44] Operation: 47-3=44 Moving to Node #0,1,1 Current State: 88:[2, 44], Operations: ['77-74=3', '47-3=44'] Exploring Operation: 2*44=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 44, 82, 10, 86 ]
69
[ "44+86=130", "130/10=13", "82-13=69" ]
Current State: 69:[44, 82, 10, 86], Operations: [] Exploring Operation: 44+86=130, Resulting Numbers: [82, 10, 130] Generated Node #2: [82, 10, 130] from Operation: 44+86=130 Current State: 69:[82, 10, 130], Operations: ['44+86=130'] Exploring Operation: 130/10=13, Resulting Numbers: [82, 13] Generated Node #3: [82, 13] from Operation: 130/10=13 Current State: 69:[82, 13], Operations: ['44+86=130', '130/10=13'] Exploring Operation: 82-13=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[44, 82, 10, 86], Operations: [] Exploring Operation: 86-44=42, Resulting Numbers: [82, 10, 42] Generated Node #0,0: 69:[82, 10, 42] Operation: 86-44=42 Exploring Operation: 44-10=34, Resulting Numbers: [82, 86, 34] Generated Node #0,1: 69:[82, 86, 34] Operation: 44-10=34 Exploring Operation: 82-44=38, Resulting Numbers: [10, 86, 38] Generated Node #0,2: 69:[10, 86, 38] Operation: 82-44=38 Exploring Operation: 86-82=4, Resulting Numbers: [44, 10, 4] Generated Node #0,3: 69:[44, 10, 4] Operation: 86-82=4 Exploring Operation: 82-10=72, Resulting Numbers: [44, 86, 72] Generated Node #0,4: 69:[44, 86, 72] Operation: 82-10=72 Moving to Node #0,3 Current State: 69:[44, 10, 4], Operations: ['86-82=4'] Exploring Operation: 44+10=54, Resulting Numbers: [4, 54] Generated Node #0,3,0: 69:[4, 54] Operation: 44+10=54 Exploring Operation: 44/4=11, Resulting Numbers: [10, 11] Generated Node #0,3,1: 69:[10, 11] Operation: 44/4=11 Exploring Operation: 10-4=6, Resulting Numbers: [44, 6] Generated Node #0,3,2: 69:[44, 6] Operation: 10-4=6 Exploring Operation: 44-4=40, Resulting Numbers: [10, 40] Generated Node #0,3,3: 69:[10, 40] Operation: 44-4=40 Exploring Operation: 44-10=34, Resulting Numbers: [4, 34] Generated Node #0,3,4: 69:[4, 34] Operation: 44-10=34 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 69:[4, 34], Operations: ['86-82=4', '44-10=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,69 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 69:[10, 11], Operations: ['86-82=4', '44/4=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[4, 54], Operations: ['86-82=4', '44+10=54'] Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,69 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[44, 6], Operations: ['86-82=4', '10-4=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[10, 40], Operations: ['86-82=4', '44-4=40'] Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,69 unequal: No Solution Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[10, 86, 38], Operations: ['82-44=38'] Exploring Operation: 10+38=48, Resulting Numbers: [86, 48] Generated Node #0,2,0: 69:[86, 48] Operation: 10+38=48 Exploring Operation: 38-10=28, Resulting Numbers: [86, 28] Generated Node #0,2,1: 69:[86, 28] Operation: 38-10=28 Exploring Operation: 86-10=76, Resulting Numbers: [38, 76] Generated Node #0,2,2: 69:[38, 76] Operation: 86-10=76 Exploring Operation: 10+86=96, Resulting Numbers: [38, 96] Generated Node #0,2,3: 69:[38, 96] Operation: 10+86=96 Exploring Operation: 86-38=48, Resulting Numbers: [10, 48] Generated Node #0,2,4: 69:[10, 48] Operation: 86-38=48 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[86, 28], Operations: ['82-44=38', '38-10=28'] Exploring Operation: 86-28=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 86+28=114, Resulting Numbers: [114] 114,69 unequal: No Solution Exploring Operation: 86*28=2408, Resulting Numbers: [2408] 2408,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[38, 76], Operations: ['82-44=38', '86-10=76'] Exploring Operation: 76-38=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 38*76=2888, Resulting Numbers: [2888] 2888,69 unequal: No Solution Exploring Operation: 76/38=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 38+76=114, Resulting Numbers: [114] 114,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 69:[10, 48], Operations: ['82-44=38', '86-38=48'] Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 10*48=480, Resulting Numbers: [480] 480,69 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[86, 48], Operations: ['82-44=38', '10+38=48'] Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 86+48=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 86*48=4128, Resulting Numbers: [4128] 4128,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[38, 96], Operations: ['82-44=38', '10+86=96'] Exploring Operation: 38+96=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 38*96=3648, Resulting Numbers: [3648] 3648,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 69:[82, 10, 42], Operations: ['86-44=42'] Exploring Operation: 42-10=32, Resulting Numbers: [82, 32] Generated Node #0,0,0: 69:[82, 32] Operation: 42-10=32 Exploring Operation: 82-42=40, Resulting Numbers: [10, 40] Generated Node #0,0,1: 69:[10, 40] Operation: 82-42=40 Exploring Operation: 82-10=72, Resulting Numbers: [42, 72] Generated Node #0,0,2: 69:[42, 72] Operation: 82-10=72 Exploring Operation: 82+10=92, Resulting Numbers: [42, 92] Generated Node #0,0,3: 69:[42, 92] Operation: 82+10=92 Exploring Operation: 10+42=52, Resulting Numbers: [82, 52] Generated Node #0,0,4: 69:[82, 52] Operation: 10+42=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[82, 32], Operations: ['86-44=42', '42-10=32'] Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 82*32=2624, Resulting Numbers: [2624] 2624,69 unequal: No Solution Exploring Operation: 82+32=114, Resulting Numbers: [114] 114,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[42, 72], Operations: ['86-44=42', '82-10=72'] Exploring Operation: 42+72=114, Resulting Numbers: [114] 114,69 unequal: No Solution Exploring Operation: 42*72=3024, Resulting Numbers: [3024] 3024,69 unequal: No Solution Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[10, 40], Operations: ['86-44=42', '82-42=40'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 10+40=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 10*40=400, Resulting Numbers: [400] 400,69 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 69:[82, 52], Operations: ['86-44=42', '10+42=52'] Exploring Operation: 82+52=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 82*52=4264, Resulting Numbers: [4264] 4264,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[42, 92], Operations: ['86-44=42', '82+10=92'] Exploring Operation: 42+92=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 42*92=3864, Resulting Numbers: [3864] 3864,69 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: 69:[82, 86, 34], Operations: ['44-10=34'] Exploring Operation: 82-34=48, Resulting Numbers: [86, 48] Generated Node #0,1,0: 69:[86, 48] Operation: 82-34=48 Exploring Operation: 86-34=52, Resulting Numbers: [82, 52] Generated Node #0,1,1: 69:[82, 52] Operation: 86-34=52 Exploring Operation: 82+34=116, Resulting Numbers: [86, 116] Generated Node #0,1,2: 69:[86, 116] Operation: 82+34=116 Exploring Operation: 86+34=120, Resulting Numbers: [82, 120] Generated Node #0,1,3: 69:[82, 120] Operation: 86+34=120 Exploring Operation: 86-82=4, Resulting Numbers: [34, 4] Generated Node #0,1,4: 69:[34, 4] Operation: 86-82=4 Moving to Node #0,4 Current State: 69:[44, 86, 72], Operations: ['82-10=72'] Exploring Operation: 86-72=14, Resulting Numbers: [44, 14] Generated Node #0,4,0: 69:[44, 14] Operation: 86-72=14 Exploring Operation: 72-44=28, Resulting Numbers: [86, 28] Generated Node #0,4,1: 69:[86, 28] Operation: 72-44=28 Exploring Operation: 86-44=42, Resulting Numbers: [72, 42] Generated Node #0,4,2: 69:[72, 42] Operation: 86-44=42 Exploring Operation: 44+86=130, Resulting Numbers: [72, 130] Generated Node #0,4,3: 69:[72, 130] Operation: 44+86=130 Exploring Operation: 44+72=116, Resulting Numbers: [86, 116] Generated Node #0,4,4: 69:[86, 116] Operation: 44+72=116 Moving to Node #0,1,4 Current State: 69:[34, 4], Operations: ['44-10=34', '86-82=4'] Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 34*4=136, Resulting Numbers: [136] 136,69 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,69 unequal: No Solution Moving to Node #0,4,1 Current State: 69:[86, 28], Operations: ['82-10=72', '72-44=28'] Exploring Operation: 86-28=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 86*28=2408, Resulting Numbers: [2408] 2408,69 unequal: No Solution Exploring Operation: 86+28=114, Resulting Numbers: [114] 114,69 unequal: No Solution Moving to Node #0,4,2 Current State: 69:[72, 42], Operations: ['82-10=72', '86-44=42'] Exploring Operation: 72+42=114, Resulting Numbers: [114] 114,69 unequal: No Solution Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 72*42=3024, Resulting Numbers: [3024] 3024,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[82, 52], Operations: ['44-10=34', '86-34=52'] Exploring Operation: 82*52=4264, Resulting Numbers: [4264] 4264,69 unequal: No Solution Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 82+52=134, Resulting Numbers: [134] 134,69 unequal: No Solution Moving to Node #0,4,0 Current State: 69:[44, 14], Operations: ['82-10=72', '86-72=14'] Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,69 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[86, 48], Operations: ['44-10=34', '82-34=48'] Exploring Operation: 86-48=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 86+48=134, Resulting Numbers: [134] 134,69 unequal: No Solution Exploring Operation: 86*48=4128, Resulting Numbers: [4128] 4128,69 unequal: No Solution Moving to Node #0,4,3 Current State: 69:[72, 130], Operations: ['82-10=72', '44+86=130'] Exploring Operation: 72+130=202, Resulting Numbers: [202] 202,69 unequal: No Solution Exploring Operation: 72*130=9360, Resulting Numbers: [9360] 9360,69 unequal: No Solution Exploring Operation: 130-72=58, Resulting Numbers: [58] 58,69 unequal: No Solution Moving to Node #0,4,4 Current State: 69:[86, 116], Operations: ['82-10=72', '44+72=116'] Exploring Operation: 86+116=202, Resulting Numbers: [202] 202,69 unequal: No Solution Exploring Operation: 86*116=9976, Resulting Numbers: [9976] 9976,69 unequal: No Solution Exploring Operation: 116-86=30, Resulting Numbers: [30] 30,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[82, 120], Operations: ['44-10=34', '86+34=120'] Exploring Operation: 120-82=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 82*120=9840, Resulting Numbers: [9840] 9840,69 unequal: No Solution Exploring Operation: 82+120=202, Resulting Numbers: [202] 202,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[86, 116], Operations: ['44-10=34', '82+34=116'] Exploring Operation: 86+116=202, Resulting Numbers: [202] 202,69 unequal: No Solution Exploring Operation: 116-86=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 86*116=9976, Resulting Numbers: [9976] 9976,69 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 68, 67, 3, 40 ]
43
[ "68-67=1", "3+40=43", "1*43=43" ]
Current State: 43:[68, 67, 3, 40], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [3, 40, 1] Generated Node #2: [3, 40, 1] from Operation: 68-67=1 Current State: 43:[3, 40, 1], Operations: ['68-67=1'] Exploring Operation: 3+40=43, Resulting Numbers: [1, 43] Generated Node #3: [1, 43] from Operation: 3+40=43 Current State: 43:[1, 43], Operations: ['68-67=1', '3+40=43'] Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[68, 67, 3, 40], Operations: [] Exploring Operation: 67-3=64, Resulting Numbers: [68, 40, 64] Generated Node #0,0: 43:[68, 40, 64] Operation: 67-3=64 Exploring Operation: 68-3=65, Resulting Numbers: [67, 40, 65] Generated Node #0,1: 43:[67, 40, 65] Operation: 68-3=65 Moving to Node #0,0 Current State: 43:[68, 40, 64], Operations: ['67-3=64'] Exploring Operation: 68-40=28, Resulting Numbers: [64, 28] Generated Node #0,0,0: 43:[64, 28] Operation: 68-40=28 Exploring Operation: 68-64=4, Resulting Numbers: [40, 4] Generated Node #0,0,1: 43:[40, 4] Operation: 68-64=4 Moving to Node #0,1 Current State: 43:[67, 40, 65], Operations: ['68-3=65'] Exploring Operation: 65-40=25, Resulting Numbers: [67, 25] Generated Node #0,1,0: 43:[67, 25] Operation: 65-40=25 Exploring Operation: 67-40=27, Resulting Numbers: [65, 27] Generated Node #0,1,1: 43:[65, 27] Operation: 67-40=27 Moving to Node #0,0,0 Current State: 43:[64, 28], Operations: ['67-3=64', '68-40=28'] Exploring Operation: 64+28=92, Resulting Numbers: [92] 92,43 unequal: No Solution Exploring Operation: 64-28=36, Resulting Numbers: [36] 36,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[65, 27], Operations: ['68-3=65', '67-40=27'] Exploring Operation: 65+27=92, Resulting Numbers: [92] 92,43 unequal: No Solution Exploring Operation: 65-27=38, Resulting Numbers: [38] 38,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[40, 4], Operations: ['67-3=64', '68-64=4'] Exploring Operation: 40+4=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[67, 25], Operations: ['68-3=65', '65-40=25'] Exploring Operation: 67+25=92, Resulting Numbers: [92] 92,43 unequal: No Solution Exploring Operation: 67-25=42, Resulting Numbers: [42] 42,43 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 80, 92, 14, 93 ]
95
[ "92-80=12", "14+93=107", "107-12=95" ]
Current State: 95:[80, 92, 14, 93], Operations: [] Exploring Operation: 92-80=12, Resulting Numbers: [14, 93, 12] Generated Node #2: [14, 93, 12] from Operation: 92-80=12 Current State: 95:[14, 93, 12], Operations: ['92-80=12'] Exploring Operation: 14+93=107, Resulting Numbers: [12, 107] Generated Node #3: [12, 107] from Operation: 14+93=107 Current State: 95:[12, 107], Operations: ['92-80=12', '14+93=107'] Exploring Operation: 107-12=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[80, 92, 14, 93], Operations: [] Exploring Operation: 93-80=13, Resulting Numbers: [92, 14, 13] Generated Node #0,0: 95:[92, 14, 13] Operation: 93-80=13 Exploring Operation: 80+14=94, Resulting Numbers: [92, 93, 94] Generated Node #0,1: 95:[92, 93, 94] Operation: 80+14=94 Exploring Operation: 92-80=12, Resulting Numbers: [14, 93, 12] Generated Node #0,2: 95:[14, 93, 12] Operation: 92-80=12 Moving to Node #0,1 Current State: 95:[92, 93, 94], Operations: ['80+14=94'] Exploring Operation: 93-92=1, Resulting Numbers: [94, 1] Generated Node #0,1,0: 95:[94, 1] Operation: 93-92=1 Exploring Operation: 94-93=1, Resulting Numbers: [92, 1] Generated Node #0,1,1: 95:[92, 1] Operation: 94-93=1 Exploring Operation: 94-92=2, Resulting Numbers: [93, 2] Generated Node #0,1,2: 95:[93, 2] Operation: 94-92=2 Moving to Node #0,0 Current State: 95:[92, 14, 13], Operations: ['93-80=13'] Exploring Operation: 14-13=1, Resulting Numbers: [92, 1] Generated Node #0,0,0: 95:[92, 1] Operation: 14-13=1 Exploring Operation: 14+13=27, Resulting Numbers: [92, 27] Generated Node #0,0,1: 95:[92, 27] Operation: 14+13=27 Exploring Operation: 92+13=105, Resulting Numbers: [14, 105] Generated Node #0,0,2: 95:[14, 105] Operation: 92+13=105 Moving to Node #0,2 Current State: 95:[14, 93, 12], Operations: ['92-80=12'] Exploring Operation: 14-12=2, Resulting Numbers: [93, 2] Generated Node #0,2,0: 95:[93, 2] Operation: 14-12=2 Exploring Operation: 93+12=105, Resulting Numbers: [14, 105] Generated Node #0,2,1: 95:[14, 105] Operation: 93+12=105 Exploring Operation: 14+12=26, Resulting Numbers: [93, 26] Generated Node #0,2,2: 95:[93, 26] Operation: 14+12=26 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[93, 2], Operations: ['92-80=12', '14-12=2'] Exploring Operation: 93*2=186, Resulting Numbers: [186] 186,95 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,95 unequal: No Solution Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[80, 92, 14, 93], Operations: [] Exploring Operation: 92-80=12, Resulting Numbers: [14, 93, 12] Generated Node #0,2: 95:[14, 93, 12] Operation: 92-80=12 Moving to Node #0,2 Current State: 95:[14, 93, 12], Operations: ['92-80=12'] Exploring Operation: 14-12=2, Resulting Numbers: [93, 2] Generated Node #0,2,0: 95:[93, 2] Operation: 14-12=2 Moving to Node #0,2,0 Current State: 95:[93, 2], Operations: ['92-80=12', '14-12=2'] Exploring Operation: 93+2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 36, 13, 23, 89 ]
88
[ "36-13=23", "23/23=1", "89-1=88" ]
Current State: 88:[36, 13, 23, 89], Operations: [] Exploring Operation: 36-13=23, Resulting Numbers: [23, 89, 23] Generated Node #2: [23, 89, 23] from Operation: 36-13=23 Current State: 88:[23, 89, 23], Operations: ['36-13=23'] Exploring Operation: 23/23=1, Resulting Numbers: [89, 1] Generated Node #3: [89, 1] from Operation: 23/23=1 Current State: 88:[89, 1], Operations: ['36-13=23', '23/23=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[36, 13, 23, 89], Operations: [] Exploring Operation: 36-13=23, Resulting Numbers: [23, 89, 23] Generated Node #0,0: 88:[23, 89, 23] Operation: 36-13=23 Exploring Operation: 36-23=13, Resulting Numbers: [13, 89, 13] Generated Node #0,1: 88:[13, 89, 13] Operation: 36-23=13 Moving to Node #0,0 Current State: 88:[23, 89, 23], Operations: ['36-13=23'] Exploring Operation: 23/23=1, Resulting Numbers: [89, 1] Generated Node #0,0,0: 88:[89, 1] Operation: 23/23=1 Exploring Operation: 23+23=46, Resulting Numbers: [89, 46] Generated Node #0,0,1: 88:[89, 46] Operation: 23+23=46 Moving to Node #0,1 Current State: 88:[13, 89, 13], Operations: ['36-23=13'] Exploring Operation: 13-13=0, Resulting Numbers: [89, 0] Generated Node #0,1,0: 88:[89, 0] Operation: 13-13=0 Exploring Operation: 13/13=1, Resulting Numbers: [89, 1] Generated Node #0,1,1: 88:[89, 1] Operation: 13/13=1 Moving to Node #0,0,0 Current State: 88:[89, 1], Operations: ['36-13=23', '23/23=1'] Exploring Operation: 89*1=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[36, 13, 23, 89], Operations: [] Exploring Operation: 36-13=23, Resulting Numbers: [23, 89, 23] Generated Node #0,0: 88:[23, 89, 23] Operation: 36-13=23 Moving to Node #0,0 Current State: 88:[23, 89, 23], Operations: ['36-13=23'] Exploring Operation: 23/23=1, Resulting Numbers: [89, 1] Generated Node #0,0,0: 88:[89, 1] Operation: 23/23=1 Moving to Node #0,0,0 Current State: 88:[89, 1], Operations: ['36-13=23', '23/23=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 2, 23, 24, 73 ]
28
[ "23-2=21", "73-24=49", "49-21=28" ]
Current State: 28:[2, 23, 24, 73], Operations: [] Exploring Operation: 23-2=21, Resulting Numbers: [24, 73, 21] Generated Node #2: [24, 73, 21] from Operation: 23-2=21 Current State: 28:[24, 73, 21], Operations: ['23-2=21'] Exploring Operation: 73-24=49, Resulting Numbers: [21, 49] Generated Node #3: [21, 49] from Operation: 73-24=49 Current State: 28:[21, 49], Operations: ['23-2=21', '73-24=49'] Exploring Operation: 49-21=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[2, 23, 24, 73], Operations: [] Exploring Operation: 73-24=49, Resulting Numbers: [2, 23, 49] Generated Node #0,0: 28:[2, 23, 49] Operation: 73-24=49 Exploring Operation: 73-23=50, Resulting Numbers: [2, 24, 50] Generated Node #0,1: 28:[2, 24, 50] Operation: 73-23=50 Exploring Operation: 24-23=1, Resulting Numbers: [2, 73, 1] Generated Node #0,2: 28:[2, 73, 1] Operation: 24-23=1 Moving to Node #0,0 Current State: 28:[2, 23, 49], Operations: ['73-24=49'] Exploring Operation: 49-23=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 28:[2, 26] Operation: 49-23=26 Exploring Operation: 2+23=25, Resulting Numbers: [49, 25] Generated Node #0,0,1: 28:[49, 25] Operation: 2+23=25 Exploring Operation: 49-2=47, Resulting Numbers: [23, 47] Generated Node #0,0,2: 28:[23, 47] Operation: 49-2=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 28:[2, 26], Operations: ['73-24=49', '49-23=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[2, 23, 24, 73], Operations: [] Exploring Operation: 73-24=49, Resulting Numbers: [2, 23, 49] Generated Node #0,0: 28:[2, 23, 49] Operation: 73-24=49 Moving to Node #0,0 Current State: 28:[2, 23, 49], Operations: ['73-24=49'] Exploring Operation: 49-23=26, Resulting Numbers: [2, 26] Generated Node #0,0,0: 28:[2, 26] Operation: 49-23=26 Moving to Node #0,0,0 Current State: 28:[2, 26], Operations: ['73-24=49', '49-23=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 24, 24, 77, 9 ]
56
[ "24*77=1848", "24+9=33", "1848/33=56" ]
Current State: 56:[24, 24, 77, 9], Operations: [] Exploring Operation: 24*77=1848, Resulting Numbers: [9, 1848] Generated Node #2: [9, 1848] from Operation: 24*77=1848 Current State: 56:[9, 1848], Operations: ['24*77=1848'] Exploring Operation: 24+9=33, Resulting Numbers: [1848, 33] Generated Node #3: [1848, 33] from Operation: 24+9=33 Current State: 56:[1848, 33], Operations: ['24*77=1848', '24+9=33'] Exploring Operation: 1848/33=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[24, 24, 77, 9], Operations: [] Exploring Operation: 24-24=0, Resulting Numbers: [77, 9, 0] Generated Node #0,0: 56:[77, 9, 0] Operation: 24-24=0 Exploring Operation: 24/24=1, Resulting Numbers: [77, 9, 1] Generated Node #0,1: 56:[77, 9, 1] Operation: 24/24=1 Exploring Operation: 77-24=53, Resulting Numbers: [24, 9, 53] Generated Node #0,2: 56:[24, 9, 53] Operation: 77-24=53 Exploring Operation: 77-24=53, Resulting Numbers: [24, 9, 53] Generated Node #0,3: 56:[24, 9, 53] Operation: 77-24=53 Exploring Operation: 77-9=68, Resulting Numbers: [24, 24, 68] Generated Node #0,4: 56:[24, 24, 68] Operation: 77-9=68 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[24, 9, 53], Operations: ['77-24=53'] Exploring Operation: 24+9=33, Resulting Numbers: [53, 33] Generated Node #0,2,0: 56:[53, 33] Operation: 24+9=33 Exploring Operation: 24-9=15, Resulting Numbers: [53, 15] Generated Node #0,2,1: 56:[53, 15] Operation: 24-9=15 Exploring Operation: 9+53=62, Resulting Numbers: [24, 62] Generated Node #0,2,2: 56:[24, 62] Operation: 9+53=62 Exploring Operation: 53-24=29, Resulting Numbers: [9, 29] Generated Node #0,2,3: 56:[9, 29] Operation: 53-24=29 Exploring Operation: 53-9=44, Resulting Numbers: [24, 44] Generated Node #0,2,4: 56:[24, 44] Operation: 53-9=44 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 56:[9, 29], Operations: ['77-24=53', '53-24=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,56 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 #0,2,1 Current State: 56:[53, 15], Operations: ['77-24=53', '24-9=15'] Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 53*15=795, Resulting Numbers: [795] 795,56 unequal: No Solution Exploring Operation: 53+15=68, Resulting Numbers: [68] 68,56 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 #0,2,0 Current State: 56:[53, 33], Operations: ['77-24=53', '24+9=33'] Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,56 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,56 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 #0,2,2 Current State: 56:[24, 62], Operations: ['77-24=53', '9+53=62'] Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,56 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,56 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 #0,2,4 Current State: 56:[24, 44], Operations: ['77-24=53', '53-9=44'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,56 unequal: No Solution Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,56 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 #0,3 Current State: 56:[24, 9, 53], Operations: ['77-24=53'] Exploring Operation: 24-9=15, Resulting Numbers: [53, 15] Generated Node #0,3,0: 56:[53, 15] Operation: 24-9=15 Exploring Operation: 9+53=62, Resulting Numbers: [24, 62] Generated Node #0,3,1: 56:[24, 62] Operation: 9+53=62 Exploring Operation: 53-9=44, Resulting Numbers: [24, 44] Generated Node #0,3,2: 56:[24, 44] Operation: 53-9=44 Exploring Operation: 53-24=29, Resulting Numbers: [9, 29] Generated Node #0,3,3: 56:[9, 29] Operation: 53-24=29 Exploring Operation: 24+9=33, Resulting Numbers: [53, 33] Generated Node #0,3,4: 56:[53, 33] Operation: 24+9=33 Moving to Node #0,3,3 Current State: 56:[9, 29], Operations: ['77-24=53', '53-24=29'] Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,56 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,56 unequal: No Solution Moving to Node #0,3,0 Current State: 56:[53, 15], Operations: ['77-24=53', '24-9=15'] Exploring Operation: 53*15=795, Resulting Numbers: [795] 795,56 unequal: No Solution Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,56 unequal: No Solution Exploring Operation: 53+15=68, Resulting Numbers: [68] 68,56 unequal: No Solution Moving to Node #0,3,4 Current State: 56:[53, 33], Operations: ['77-24=53', '24+9=33'] Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,56 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,56 unequal: No Solution Moving to Node #0,3,1 Current State: 56:[24, 62], Operations: ['77-24=53', '9+53=62'] Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,56 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,56 unequal: No Solution Moving to Node #0,3,2 Current State: 56:[24, 44], Operations: ['77-24=53', '53-9=44'] Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,56 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 #0,4 Current State: 56:[24, 24, 68], Operations: ['77-9=68'] Exploring Operation: 24/24=1, Resulting Numbers: [68, 1] Generated Node #0,4,0: 56:[68, 1] Operation: 24/24=1 Exploring Operation: 68-24=44, Resulting Numbers: [24, 44] Generated Node #0,4,1: 56:[24, 44] Operation: 68-24=44 Exploring Operation: 24+24=48, Resulting Numbers: [68, 48] Generated Node #0,4,2: 56:[68, 48] Operation: 24+24=48 Exploring Operation: 24-24=0, Resulting Numbers: [68, 0] Generated Node #0,4,3: 56:[68, 0] Operation: 24-24=0 Exploring Operation: 68-24=44, Resulting Numbers: [24, 44] Generated Node #0,4,4: 56:[24, 44] Operation: 68-24=44 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 56:[68, 1], Operations: ['77-9=68', '24/24=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,56 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 #0,4,3 Current State: 56:[68, 0], Operations: ['77-9=68', '24-24=0'] Exploring Operation: 68-0=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 68*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 68+0=68, Resulting Numbers: [68] 68,56 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 #0,4,1 Current State: 56:[24, 44], Operations: ['77-9=68', '68-24=44'] Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,56 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,56 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 #0,4,4 Current State: 56:[24, 44], Operations: ['77-9=68', '68-24=44'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,56 unequal: No Solution Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,56 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 #0,4,2 Current State: 56:[68, 48], Operations: ['77-9=68', '24+24=48'] Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 68+48=116, Resulting Numbers: [116] 116,56 unequal: No Solution Exploring Operation: 68*48=3264, Resulting Numbers: [3264] 3264,56 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:[77, 9, 1], Operations: ['24/24=1'] Exploring Operation: 77*1=77, Resulting Numbers: [9, 77] Generated Node #0,1,0: 56:[9, 77] Operation: 77*1=77 Exploring Operation: 77-9=68, Resulting Numbers: [1, 68] Generated Node #0,1,1: 56:[1, 68] Operation: 77-9=68 Exploring Operation: 77-1=76, Resulting Numbers: [9, 76] Generated Node #0,1,2: 56:[9, 76] Operation: 77-1=76 Exploring Operation: 9-1=8, Resulting Numbers: [77, 8] Generated Node #0,1,3: 56:[77, 8] Operation: 9-1=8 Exploring Operation: 77/1=77, Resulting Numbers: [9, 77] Generated Node #0,1,4: 56:[9, 77] Operation: 77/1=77 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 56:[1, 68], Operations: ['24/24=1', '77-9=68'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 1+68=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 1*68=68, Resulting Numbers: [68] 68,56 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 #0,1,2 Current State: 56:[9, 76], Operations: ['24/24=1', '77-1=76'] Exploring Operation: 76-9=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 9+76=85, Resulting Numbers: [85] 85,56 unequal: No Solution Exploring Operation: 9*76=684, Resulting Numbers: [684] 684,56 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 #0,1,3 Current State: 56:[77, 8], Operations: ['24/24=1', '9-1=8'] Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,56 unequal: No Solution Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,56 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 #0,1,0 Current State: 56:[9, 77], Operations: ['24/24=1', '77*1=77'] Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,56 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,56 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 #0,1,4 Current State: 56:[9, 77], Operations: ['24/24=1', '77/1=77'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,56 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 #0,0 Current State: 56:[77, 9, 0], Operations: ['24-24=0'] Exploring Operation: 77-0=77, Resulting Numbers: [9, 77] Generated Node #0,0,0: 56:[9, 77] Operation: 77-0=77 Exploring Operation: 9+0=9, Resulting Numbers: [77, 9] Generated Node #0,0,1: 56:[77, 9] Operation: 9+0=9 Exploring Operation: 77*0=0, Resulting Numbers: [9, 0] Generated Node #0,0,2: 56:[9, 0] Operation: 77*0=0 Exploring Operation: 77-9=68, Resulting Numbers: [0, 68] Generated Node #0,0,3: 56:[0, 68] Operation: 77-9=68 Exploring Operation: 77+0=77, Resulting Numbers: [9, 77] Generated Node #0,0,4: 56:[9, 77] Operation: 77+0=77 Moving to Node #0,0,2 Current State: 56:[9, 0], Operations: ['24-24=0', '77*0=0'] Exploring Operation: 9+0=9, Resulting Numbers: [9] 9,56 unequal: No Solution Exploring Operation: 9-0=9, Resulting Numbers: [9] 9,56 unequal: No Solution Exploring Operation: 9*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Moving to Node #0,0,3 Current State: 56:[0, 68], Operations: ['24-24=0', '77-9=68'] Exploring Operation: 0*68=0, Resulting Numbers: [0] 0,56 unequal: No Solution Exploring Operation: 0+68=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 68-0=68, Resulting Numbers: [68] 68,56 unequal: No Solution Moving to Node #0,0,0 Current State: 56:[9, 77], Operations: ['24-24=0', '77-0=77'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,56 unequal: No Solution Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[77, 9], Operations: ['24-24=0', '9+0=9'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,56 unequal: No Solution Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,56 unequal: No Solution Moving to Node #0,0,4 Current State: 56:[9, 77], Operations: ['24-24=0', '77+0=77'] Exploring Operation: 9*77=693, Resulting Numbers: [693] 693,56 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,56 unequal: No Solution Exploring Operation: 9+77=86, Resulting Numbers: [86] 86,56 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
[ 82, 28, 69, 2 ]
17
[ "82-28=54", "69+2=71", "71-54=17" ]
Current State: 17:[82, 28, 69, 2], Operations: [] Exploring Operation: 82-28=54, Resulting Numbers: [69, 2, 54] Generated Node #2: [69, 2, 54] from Operation: 82-28=54 Current State: 17:[69, 2, 54], Operations: ['82-28=54'] Exploring Operation: 69+2=71, Resulting Numbers: [54, 71] Generated Node #3: [54, 71] from Operation: 69+2=71 Current State: 17:[54, 71], Operations: ['82-28=54', '69+2=71'] Exploring Operation: 71-54=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[82, 28, 69, 2], Operations: [] Exploring Operation: 69-28=41, Resulting Numbers: [82, 2, 41] Generated Node #0,0: 17:[82, 2, 41] Operation: 69-28=41 Exploring Operation: 82/2=41, Resulting Numbers: [28, 69, 41] Generated Node #0,1: 17:[28, 69, 41] Operation: 82/2=41 Exploring Operation: 82-69=13, Resulting Numbers: [28, 2, 13] Generated Node #0,2: 17:[28, 2, 13] Operation: 82-69=13 Exploring Operation: 82-28=54, Resulting Numbers: [69, 2, 54] Generated Node #0,3: 17:[69, 2, 54] Operation: 82-28=54 Moving to Node #0,2 Current State: 17:[28, 2, 13], Operations: ['82-69=13'] Exploring Operation: 28-2=26, Resulting Numbers: [13, 26] Generated Node #0,2,0: 17:[13, 26] Operation: 28-2=26 Exploring Operation: 28/2=14, Resulting Numbers: [13, 14] Generated Node #0,2,1: 17:[13, 14] Operation: 28/2=14 Exploring Operation: 2+13=15, Resulting Numbers: [28, 15] Generated Node #0,2,2: 17:[28, 15] Operation: 2+13=15 Exploring Operation: 28+2=30, Resulting Numbers: [13, 30] Generated Node #0,2,3: 17:[13, 30] Operation: 28+2=30 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 17:[13, 14], Operations: ['82-69=13', '28/2=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,17 unequal: No Solution Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,17 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[13, 26], Operations: ['82-69=13', '28-2=26'] Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,17 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,17 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 17:[28, 15], Operations: ['82-69=13', '2+13=15'] Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,17 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 17:[13, 30], Operations: ['82-69=13', '28+2=30'] Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,17 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[82, 28, 69, 2], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [28, 2, 13] Generated Node #0,2: 17:[28, 2, 13] Operation: 82-69=13 Moving to Node #0,2 Current State: 17:[28, 2, 13], Operations: ['82-69=13'] Exploring Operation: 28+2=30, Resulting Numbers: [13, 30] Generated Node #0,2,3: 17:[13, 30] Operation: 28+2=30 Moving to Node #0,2,3 Current State: 17:[13, 30], Operations: ['82-69=13', '28+2=30'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 60, 52, 65, 82 ]
25
[ "60-52=8", "82-65=17", "8+17=25" ]
Current State: 25:[60, 52, 65, 82], Operations: [] Exploring Operation: 60-52=8, Resulting Numbers: [65, 82, 8] Generated Node #2: [65, 82, 8] from Operation: 60-52=8 Current State: 25:[65, 82, 8], Operations: ['60-52=8'] Exploring Operation: 82-65=17, Resulting Numbers: [8, 17] Generated Node #3: [8, 17] from Operation: 82-65=17 Current State: 25:[8, 17], Operations: ['60-52=8', '82-65=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[60, 52, 65, 82], Operations: [] Exploring Operation: 82-60=22, Resulting Numbers: [52, 65, 22] Generated Node #0,0: 25:[52, 65, 22] Operation: 82-60=22 Exploring Operation: 65-60=5, Resulting Numbers: [52, 82, 5] Generated Node #0,1: 25:[52, 82, 5] Operation: 65-60=5 Exploring Operation: 82-52=30, Resulting Numbers: [60, 65, 30] Generated Node #0,2: 25:[60, 65, 30] Operation: 82-52=30 Exploring Operation: 82-65=17, Resulting Numbers: [60, 52, 17] Generated Node #0,3: 25:[60, 52, 17] Operation: 82-65=17 Exploring Operation: 60-52=8, Resulting Numbers: [65, 82, 8] Generated Node #0,4: 25:[65, 82, 8] Operation: 60-52=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[52, 65, 22], Operations: ['82-60=22'] Exploring Operation: 52+22=74, Resulting Numbers: [65, 74] Generated Node #0,0,0: 25:[65, 74] Operation: 52+22=74 Exploring Operation: 65-22=43, Resulting Numbers: [52, 43] Generated Node #0,0,1: 25:[52, 43] Operation: 65-22=43 Exploring Operation: 52-22=30, Resulting Numbers: [65, 30] Generated Node #0,0,2: 25:[65, 30] Operation: 52-22=30 Exploring Operation: 65+22=87, Resulting Numbers: [52, 87] Generated Node #0,0,3: 25:[52, 87] Operation: 65+22=87 Exploring Operation: 65-52=13, Resulting Numbers: [22, 13] Generated Node #0,0,4: 25:[22, 13] Operation: 65-52=13 Moving to Node #0,0,4 Current State: 25:[22, 13], Operations: ['82-60=22', '65-52=13'] Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 22*13=286, Resulting Numbers: [286] 286,25 unequal: No Solution Exploring Operation: 22+13=35, Resulting Numbers: [35] 35,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[65, 30], Operations: ['82-60=22', '52-22=30'] Exploring Operation: 65-30=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 65*30=1950, Resulting Numbers: [1950] 1950,25 unequal: No Solution Exploring Operation: 65+30=95, Resulting Numbers: [95] 95,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[52, 43], Operations: ['82-60=22', '65-22=43'] Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,25 unequal: No Solution Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[65, 74], Operations: ['82-60=22', '52+22=74'] Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 65*74=4810, Resulting Numbers: [4810] 4810,25 unequal: No Solution Exploring Operation: 65+74=139, Resulting Numbers: [139] 139,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[52, 87], Operations: ['82-60=22', '65+22=87'] Exploring Operation: 52*87=4524, Resulting Numbers: [4524] 4524,25 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 52+87=139, Resulting Numbers: [139] 139,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[60, 52, 17], Operations: ['82-65=17'] Exploring Operation: 60-52=8, Resulting Numbers: [17, 8] Generated Node #0,3,0: 25:[17, 8] Operation: 60-52=8 Exploring Operation: 60+17=77, Resulting Numbers: [52, 77] Generated Node #0,3,1: 25:[52, 77] Operation: 60+17=77 Exploring Operation: 60-17=43, Resulting Numbers: [52, 43] Generated Node #0,3,2: 25:[52, 43] Operation: 60-17=43 Exploring Operation: 52+17=69, Resulting Numbers: [60, 69] Generated Node #0,3,3: 25:[60, 69] Operation: 52+17=69 Exploring Operation: 52-17=35, Resulting Numbers: [60, 35] Generated Node #0,3,4: 25:[60, 35] Operation: 52-17=35 Moving to Node #0,3,0 Current State: 25:[17, 8], Operations: ['82-65=17', '60-52=8'] Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,25 unequal: No Solution Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[60, 52, 65, 82], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [60, 52, 17] Generated Node #0,3: 25:[60, 52, 17] Operation: 82-65=17 Moving to Node #0,3 Current State: 25:[60, 52, 17], Operations: ['82-65=17'] Exploring Operation: 60-52=8, Resulting Numbers: [17, 8] Generated Node #0,3,0: 25:[17, 8] Operation: 60-52=8 Moving to Node #0,3,0 Current State: 25:[17, 8], Operations: ['82-65=17', '60-52=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 10, 9, 61, 29 ]
39
[ "10*29=290", "61+290=351", "351/9=39" ]
Current State: 39:[10, 9, 61, 29], Operations: [] Exploring Operation: 10*29=290, Resulting Numbers: [9, 61, 290] Generated Node #2: [9, 61, 290] from Operation: 10*29=290 Current State: 39:[9, 61, 290], Operations: ['10*29=290'] Exploring Operation: 61+290=351, Resulting Numbers: [9, 351] Generated Node #3: [9, 351] from Operation: 61+290=351 Current State: 39:[9, 351], Operations: ['10*29=290', '61+290=351'] Exploring Operation: 351/9=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[10, 9, 61, 29], Operations: [] Exploring Operation: 9+29=38, Resulting Numbers: [10, 61, 38] Generated Node #0,0: 39:[10, 61, 38] Operation: 9+29=38 Exploring Operation: 10+29=39, Resulting Numbers: [9, 61, 39] Generated Node #0,1: 39:[9, 61, 39] Operation: 10+29=39 Exploring Operation: 61-10=51, Resulting Numbers: [9, 29, 51] Generated Node #0,2: 39:[9, 29, 51] Operation: 61-10=51 Exploring Operation: 61-29=32, Resulting Numbers: [10, 9, 32] Generated Node #0,3: 39:[10, 9, 32] Operation: 61-29=32 Exploring Operation: 61-9=52, Resulting Numbers: [10, 29, 52] Generated Node #0,4: 39:[10, 29, 52] Operation: 61-9=52 Moving to Node #0,3 Current State: 39:[10, 9, 32], Operations: ['61-29=32'] Exploring Operation: 10+9=19, Resulting Numbers: [32, 19] Generated Node #0,3,0: 39:[32, 19] Operation: 10+9=19 Exploring Operation: 9+32=41, Resulting Numbers: [10, 41] Generated Node #0,3,1: 39:[10, 41] Operation: 9+32=41 Exploring Operation: 10+32=42, Resulting Numbers: [9, 42] Generated Node #0,3,2: 39:[9, 42] Operation: 10+32=42 Exploring Operation: 10-9=1, Resulting Numbers: [32, 1] Generated Node #0,3,3: 39:[32, 1] Operation: 10-9=1 Exploring Operation: 32-10=22, Resulting Numbers: [9, 22] Generated Node #0,3,4: 39:[9, 22] Operation: 32-10=22 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[10, 41], Operations: ['61-29=32', '9+32=41'] Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 10*41=410, Resulting Numbers: [410] 410,39 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 #0,3,2 Current State: 39:[9, 42], Operations: ['61-29=32', '10+32=42'] Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,39 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,39 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,39 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 #0,3,3 Current State: 39:[32, 1], Operations: ['61-29=32', '10-9=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,39 unequal: No Solution Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,39 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 #0,3,0 Current State: 39:[32, 19], Operations: ['61-29=32', '10+9=19'] Exploring Operation: 32*19=608, Resulting Numbers: [608] 608,39 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,39 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 #0,3,4 Current State: 39:[9, 22], Operations: ['61-29=32', '32-10=22'] Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,39 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,39 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: 39:[9, 61, 39], Operations: ['10+29=39'] Exploring Operation: 9+61=70, Resulting Numbers: [39, 70] Generated Node #0,1,0: 39:[39, 70] Operation: 9+61=70 Exploring Operation: 9+39=48, Resulting Numbers: [61, 48] Generated Node #0,1,1: 39:[61, 48] Operation: 9+39=48 Exploring Operation: 39-9=30, Resulting Numbers: [61, 30] Generated Node #0,1,2: 39:[61, 30] Operation: 39-9=30 Exploring Operation: 61-9=52, Resulting Numbers: [39, 52] Generated Node #0,1,3: 39:[39, 52] Operation: 61-9=52 Exploring Operation: 61-39=22, Resulting Numbers: [9, 22] Generated Node #0,1,4: 39:[9, 22] Operation: 61-39=22 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 39:[39, 52], Operations: ['10+29=39', '61-9=52'] Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 39+52=91, Resulting Numbers: [91] 91,39 unequal: No Solution Exploring Operation: 39*52=2028, Resulting Numbers: [2028] 2028,39 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 #0,1,4 Current State: 39:[9, 22], Operations: ['10+29=39', '61-39=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,39 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,39 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 #0,1,0 Current State: 39:[39, 70], Operations: ['10+29=39', '9+61=70'] Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,39 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 #0,1,1 Current State: 39:[61, 48], Operations: ['10+29=39', '9+39=48'] Exploring Operation: 61+48=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 61*48=2928, Resulting Numbers: [2928] 2928,39 unequal: No Solution Exploring Operation: 61-48=13, Resulting Numbers: [13] 13,39 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 #0,1,2 Current State: 39:[61, 30], Operations: ['10+29=39', '39-9=30'] Exploring Operation: 61*30=1830, Resulting Numbers: [1830] 1830,39 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,39 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: 39:[10, 29, 52], Operations: ['61-9=52'] Exploring Operation: 52-10=42, Resulting Numbers: [29, 42] Generated Node #0,4,0: 39:[29, 42] Operation: 52-10=42 Exploring Operation: 10+29=39, Resulting Numbers: [52, 39] Generated Node #0,4,1: 39:[52, 39] Operation: 10+29=39 Exploring Operation: 29-10=19, Resulting Numbers: [52, 19] Generated Node #0,4,2: 39:[52, 19] Operation: 29-10=19 Exploring Operation: 10+52=62, Resulting Numbers: [29, 62] Generated Node #0,4,3: 39:[29, 62] Operation: 10+52=62 Exploring Operation: 52-29=23, Resulting Numbers: [10, 23] Generated Node #0,4,4: 39:[10, 23] Operation: 52-29=23 Moving to Node #0,0 Current State: 39:[10, 61, 38], Operations: ['9+29=38'] Exploring Operation: 38-10=28, Resulting Numbers: [61, 28] Generated Node #0,0,0: 39:[61, 28] Operation: 38-10=28 Exploring Operation: 61-10=51, Resulting Numbers: [38, 51] Generated Node #0,0,1: 39:[38, 51] Operation: 61-10=51 Exploring Operation: 10+38=48, Resulting Numbers: [61, 48] Generated Node #0,0,2: 39:[61, 48] Operation: 10+38=48 Exploring Operation: 10+61=71, Resulting Numbers: [38, 71] Generated Node #0,0,3: 39:[38, 71] Operation: 10+61=71 Exploring Operation: 61-38=23, Resulting Numbers: [10, 23] Generated Node #0,0,4: 39:[10, 23] Operation: 61-38=23 Moving to Node #0,2 Current State: 39:[9, 29, 51], Operations: ['61-10=51'] Exploring Operation: 29-9=20, Resulting Numbers: [51, 20] Generated Node #0,2,0: 39:[51, 20] Operation: 29-9=20 Exploring Operation: 9+51=60, Resulting Numbers: [29, 60] Generated Node #0,2,1: 39:[29, 60] Operation: 9+51=60 Exploring Operation: 51-9=42, Resulting Numbers: [29, 42] Generated Node #0,2,2: 39:[29, 42] Operation: 51-9=42 Exploring Operation: 9+29=38, Resulting Numbers: [51, 38] Generated Node #0,2,3: 39:[51, 38] Operation: 9+29=38 Exploring Operation: 51-29=22, Resulting Numbers: [9, 22] Generated Node #0,2,4: 39:[9, 22] Operation: 51-29=22 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[29, 42], Operations: ['61-10=51', '51-9=42'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,39 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 #0,2,3 Current State: 39:[51, 38], Operations: ['61-10=51', '9+29=38'] Exploring Operation: 51*38=1938, Resulting Numbers: [1938] 1938,39 unequal: No Solution Exploring Operation: 51+38=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,39 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 #0,2,4 Current State: 39:[9, 22], Operations: ['61-10=51', '51-29=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,39 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,39 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 #0,2,0 Current State: 39:[51, 20], Operations: ['61-10=51', '29-9=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,39 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 #0,2,1 Current State: 39:[29, 60], Operations: ['61-10=51', '9+51=60'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 29*60=1740, Resulting Numbers: [1740] 1740,39 unequal: No Solution Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 39:[29, 42], Operations: ['61-9=52', '52-10=42'] Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,39 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,39 unequal: No Solution Moving to Node #0,4,4 Current State: 39:[10, 23], Operations: ['61-9=52', '52-29=23'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[10, 23], Operations: ['9+29=38', '61-38=23'] Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[38, 51], Operations: ['9+29=38', '61-10=51'] Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,39 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,39 unequal: No Solution Moving to Node #0,4,1 Current State: 39:[52, 39], Operations: ['61-9=52', '10+29=39'] Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,39 unequal: No Solution Exploring Operation: 52+39=91, Resulting Numbers: [91] 91,39 unequal: No Solution Exploring Operation: 52*39=2028, Resulting Numbers: [2028] 2028,39 unequal: No Solution Moving to Node #0,4,2 Current State: 39:[52, 19], Operations: ['61-9=52', '29-10=19'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,39 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[61, 48], Operations: ['9+29=38', '10+38=48'] Exploring Operation: 61+48=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 61*48=2928, Resulting Numbers: [2928] 2928,39 unequal: No Solution Exploring Operation: 61-48=13, Resulting Numbers: [13] 13,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[61, 28], Operations: ['9+29=38', '38-10=28'] Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 61*28=1708, Resulting Numbers: [1708] 1708,39 unequal: No Solution Exploring Operation: 61+28=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,4,3 Current State: 39:[29, 62], Operations: ['61-9=52', '10+52=62'] Exploring Operation: 29*62=1798, Resulting Numbers: [1798] 1798,39 unequal: No Solution Exploring Operation: 62-29=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 29+62=91, Resulting Numbers: [91] 91,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[38, 71], Operations: ['9+29=38', '10+61=71'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 38+71=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 38*71=2698, Resulting Numbers: [2698] 2698,39 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 53, 78, 18, 2 ]
83
[ "78-18=60", "60/2=30", "53+30=83" ]
Current State: 83:[53, 78, 18, 2], Operations: [] Exploring Operation: 78-18=60, Resulting Numbers: [53, 2, 60] Generated Node #2: [53, 2, 60] from Operation: 78-18=60 Current State: 83:[53, 2, 60], Operations: ['78-18=60'] Exploring Operation: 60/2=30, Resulting Numbers: [53, 30] Generated Node #3: [53, 30] from Operation: 60/2=30 Current State: 83:[53, 30], Operations: ['78-18=60', '60/2=30'] Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[53, 78, 18, 2], Operations: [] Exploring Operation: 53+18=71, Resulting Numbers: [78, 2, 71] Generated Node #0,0: 83:[78, 2, 71] Operation: 53+18=71 Exploring Operation: 18*2=36, Resulting Numbers: [53, 78, 36] Generated Node #0,1: 83:[53, 78, 36] Operation: 18*2=36 Exploring Operation: 53+2=55, Resulting Numbers: [78, 18, 55] Generated Node #0,2: 83:[78, 18, 55] Operation: 53+2=55 Exploring Operation: 53*2=106, Resulting Numbers: [78, 18, 106] Generated Node #0,3: 83:[78, 18, 106] Operation: 53*2=106 Moving to Node #0,1 Current State: 83:[53, 78, 36], Operations: ['18*2=36'] Exploring Operation: 78-36=42, Resulting Numbers: [53, 42] Generated Node #0,1,0: 83:[53, 42] Operation: 78-36=42 Exploring Operation: 53+36=89, Resulting Numbers: [78, 89] Generated Node #0,1,1: 83:[78, 89] Operation: 53+36=89 Exploring Operation: 78+36=114, Resulting Numbers: [53, 114] Generated Node #0,1,2: 83:[53, 114] Operation: 78+36=114 Exploring Operation: 53-36=17, Resulting Numbers: [78, 17] Generated Node #0,1,3: 83:[78, 17] Operation: 53-36=17 Moving to Node #0,3 Current State: 83:[78, 18, 106], Operations: ['53*2=106'] Exploring Operation: 106-18=88, Resulting Numbers: [78, 88] Generated Node #0,3,0: 83:[78, 88] Operation: 106-18=88 Exploring Operation: 18+106=124, Resulting Numbers: [78, 124] Generated Node #0,3,1: 83:[78, 124] Operation: 18+106=124 Exploring Operation: 78+18=96, Resulting Numbers: [106, 96] Generated Node #0,3,2: 83:[106, 96] Operation: 78+18=96 Exploring Operation: 78-18=60, Resulting Numbers: [106, 60] Generated Node #0,3,3: 83:[106, 60] Operation: 78-18=60 Moving to Node #0,2 Current State: 83:[78, 18, 55], Operations: ['53+2=55'] Exploring Operation: 78-18=60, Resulting Numbers: [55, 60] Generated Node #0,2,0: 83:[55, 60] Operation: 78-18=60 Exploring Operation: 18+55=73, Resulting Numbers: [78, 73] Generated Node #0,2,1: 83:[78, 73] Operation: 18+55=73 Exploring Operation: 78+18=96, Resulting Numbers: [55, 96] Generated Node #0,2,2: 83:[55, 96] Operation: 78+18=96 Exploring Operation: 55-18=37, Resulting Numbers: [78, 37] Generated Node #0,2,3: 83:[78, 37] Operation: 55-18=37 Moving to Node #0,0 Current State: 83:[78, 2, 71], Operations: ['53+18=71'] Exploring Operation: 2+71=73, Resulting Numbers: [78, 73] Generated Node #0,0,0: 83:[78, 73] Operation: 2+71=73 Exploring Operation: 71-2=69, Resulting Numbers: [78, 69] Generated Node #0,0,1: 83:[78, 69] Operation: 71-2=69 Exploring Operation: 78+2=80, Resulting Numbers: [71, 80] Generated Node #0,0,2: 83:[71, 80] Operation: 78+2=80 Exploring Operation: 78-2=76, Resulting Numbers: [71, 76] Generated Node #0,0,3: 83:[71, 76] Operation: 78-2=76 Moving to Node #0,3,0 Current State: 83:[78, 88], Operations: ['53*2=106', '106-18=88'] Exploring Operation: 88-78=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 78+88=166, Resulting Numbers: [166] 166,83 unequal: No Solution Exploring Operation: 78*88=6864, Resulting Numbers: [6864] 6864,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[78, 89], Operations: ['18*2=36', '53+36=89'] Exploring Operation: 78*89=6942, Resulting Numbers: [6942] 6942,83 unequal: No Solution Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,83 unequal: No Solution Exploring Operation: 78+89=167, Resulting Numbers: [167] 167,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[78, 73], Operations: ['53+18=71', '2+71=73'] Exploring Operation: 78*73=5694, Resulting Numbers: [5694] 5694,83 unequal: No Solution Exploring Operation: 78+73=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 78-73=5, Resulting Numbers: [5] 5,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[71, 80], Operations: ['53+18=71', '78+2=80'] Exploring Operation: 71*80=5680, Resulting Numbers: [5680] 5680,83 unequal: No Solution Exploring Operation: 71+80=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[78, 73], Operations: ['53+2=55', '18+55=73'] Exploring Operation: 78+73=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 78*73=5694, Resulting Numbers: [5694] 5694,83 unequal: No Solution Exploring Operation: 78-73=5, Resulting Numbers: [5] 5,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[78, 69], Operations: ['53+18=71', '71-2=69'] Exploring Operation: 78*69=5382, Resulting Numbers: [5382] 5382,83 unequal: No Solution Exploring Operation: 78-69=9, Resulting Numbers: [9] 9,83 unequal: No Solution Exploring Operation: 78+69=147, Resulting Numbers: [147] 147,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[71, 76], Operations: ['53+18=71', '78-2=76'] Exploring Operation: 76-71=5, Resulting Numbers: [5] 5,83 unequal: No Solution Exploring Operation: 71+76=147, Resulting Numbers: [147] 147,83 unequal: No Solution Exploring Operation: 71*76=5396, Resulting Numbers: [5396] 5396,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[106, 96], Operations: ['53*2=106', '78+18=96'] Exploring Operation: 106*96=10176, Resulting Numbers: [10176] 10176,83 unequal: No Solution Exploring Operation: 106-96=10, Resulting Numbers: [10] 10,83 unequal: No Solution Exploring Operation: 106+96=202, Resulting Numbers: [202] 202,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[55, 96], Operations: ['53+2=55', '78+18=96'] Exploring Operation: 96-55=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 55*96=5280, Resulting Numbers: [5280] 5280,83 unequal: No Solution Exploring Operation: 55+96=151, Resulting Numbers: [151] 151,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[78, 124], Operations: ['53*2=106', '18+106=124'] Exploring Operation: 124-78=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 78*124=9672, Resulting Numbers: [9672] 9672,83 unequal: No Solution Exploring Operation: 78+124=202, Resulting Numbers: [202] 202,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[106, 60], Operations: ['53*2=106', '78-18=60'] Exploring Operation: 106+60=166, Resulting Numbers: [166] 166,83 unequal: No Solution Exploring Operation: 106-60=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 106*60=6360, Resulting Numbers: [6360] 6360,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[55, 60], Operations: ['53+2=55', '78-18=60'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,83 unequal: No Solution Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,83 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[78, 37], Operations: ['53+2=55', '55-18=37'] Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 78*37=2886, Resulting Numbers: [2886] 2886,83 unequal: No Solution Exploring Operation: 78+37=115, Resulting Numbers: [115] 115,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[53, 114], Operations: ['18*2=36', '78+36=114'] Exploring Operation: 53+114=167, Resulting Numbers: [167] 167,83 unequal: No Solution Exploring Operation: 53*114=6042, Resulting Numbers: [6042] 6042,83 unequal: No Solution Exploring Operation: 114-53=61, Resulting Numbers: [61] 61,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[53, 42], Operations: ['18*2=36', '78-36=42'] Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,83 unequal: No Solution Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,83 unequal: No Solution Exploring Operation: 53*42=2226, Resulting Numbers: [2226] 2226,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[78, 17], Operations: ['18*2=36', '53-36=17'] Exploring Operation: 78*17=1326, Resulting Numbers: [1326] 1326,83 unequal: No Solution Exploring Operation: 78-17=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 78+17=95, Resulting Numbers: [95] 95,83 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 30, 42, 82, 80 ]
30
[ "30+82=112", "42*80=3360", "3360/112=30" ]
Current State: 30:[30, 42, 82, 80], Operations: [] Exploring Operation: 30+82=112, Resulting Numbers: [42, 80, 112] Generated Node #2: [42, 80, 112] from Operation: 30+82=112 Current State: 30:[42, 80, 112], Operations: ['30+82=112'] Exploring Operation: 42*80=3360, Resulting Numbers: [112, 3360] Generated Node #3: [112, 3360] from Operation: 42*80=3360 Current State: 30:[112, 3360], Operations: ['30+82=112', '42*80=3360'] Exploring Operation: 3360/112=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[30, 42, 82, 80], Operations: [] Exploring Operation: 82-80=2, Resulting Numbers: [30, 42, 2] Generated Node #0,0: 30:[30, 42, 2] Operation: 82-80=2 Exploring Operation: 80-42=38, Resulting Numbers: [30, 82, 38] Generated Node #0,1: 30:[30, 82, 38] Operation: 80-42=38 Exploring Operation: 82-42=40, Resulting Numbers: [30, 80, 40] Generated Node #0,2: 30:[30, 80, 40] Operation: 82-42=40 Moving to Node #0,0 Current State: 30:[30, 42, 2], Operations: ['82-80=2'] Exploring Operation: 42-30=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 30:[2, 12] Operation: 42-30=12 Exploring Operation: 42-2=40, Resulting Numbers: [30, 40] Generated Node #0,0,1: 30:[30, 40] Operation: 42-2=40 Exploring Operation: 42/2=21, Resulting Numbers: [30, 21] Generated Node #0,0,2: 30:[30, 21] Operation: 42/2=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[2, 12], Operations: ['82-80=2', '42-30=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,30 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 #0,0,2 Current State: 30:[30, 21], Operations: ['82-80=2', '42/2=21'] Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 30+21=51, Resulting Numbers: [51] 51,30 unequal: No Solution Exploring Operation: 30*21=630, Resulting Numbers: [630] 630,30 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:[30, 40], Operations: ['82-80=2', '42-2=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[30, 82, 38], Operations: ['80-42=38'] Exploring Operation: 38-30=8, Resulting Numbers: [82, 8] Generated Node #0,1,0: 30:[82, 8] Operation: 38-30=8 Exploring Operation: 82-38=44, Resulting Numbers: [30, 44] Generated Node #0,1,1: 30:[30, 44] Operation: 82-38=44 Exploring Operation: 82-30=52, Resulting Numbers: [38, 52] Generated Node #0,1,2: 30:[38, 52] Operation: 82-30=52 Moving to Node #0,2 Current State: 30:[30, 80, 40], Operations: ['82-42=40'] Exploring Operation: 80/40=2, Resulting Numbers: [30, 2] Generated Node #0,2,0: 30:[30, 2] Operation: 80/40=2 Exploring Operation: 80-30=50, Resulting Numbers: [40, 50] Generated Node #0,2,1: 30:[40, 50] Operation: 80-30=50 Exploring Operation: 80-40=40, Resulting Numbers: [30, 40] Generated Node #0,2,2: 30:[30, 40] Operation: 80-40=40 Moving to Node #0,2,0 Current State: 30:[30, 2], Operations: ['82-42=40', '80/40=2'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 30+2=32, Resulting Numbers: [32] 32,30 unequal: No Solution Moving to Node #0,2,2 Current State: 30:[30, 40], Operations: ['82-42=40', '80-40=40'] Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 30*40=1200, Resulting Numbers: [1200] 1200,30 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[30, 44], Operations: ['80-42=38', '82-38=44'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,30 unequal: No Solution Moving to Node #0,2,1 Current State: 30:[40, 50], Operations: ['82-42=40', '80-30=50'] Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,30 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[38, 52], Operations: ['80-42=38', '82-30=52'] Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,30 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[82, 8], Operations: ['80-42=38', '38-30=8'] Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,30 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,30 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,30 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 27, 88, 51, 90 ]
80
[ "88-27=61", "51+90=141", "141-61=80" ]
Current State: 80:[27, 88, 51, 90], Operations: [] Exploring Operation: 88-27=61, Resulting Numbers: [51, 90, 61] Generated Node #2: [51, 90, 61] from Operation: 88-27=61 Current State: 80:[51, 90, 61], Operations: ['88-27=61'] Exploring Operation: 51+90=141, Resulting Numbers: [61, 141] Generated Node #3: [61, 141] from Operation: 51+90=141 Current State: 80:[61, 141], Operations: ['88-27=61', '51+90=141'] Exploring Operation: 141-61=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[27, 88, 51, 90], Operations: [] Exploring Operation: 90-51=39, Resulting Numbers: [27, 88, 39] Generated Node #0,0: 80:[27, 88, 39] Operation: 90-51=39 Exploring Operation: 90-88=2, Resulting Numbers: [27, 51, 2] Generated Node #0,1: 80:[27, 51, 2] Operation: 90-88=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[27, 88, 39], Operations: ['90-51=39'] Exploring Operation: 39-27=12, Resulting Numbers: [88, 12] Generated Node #0,0,0: 80:[88, 12] Operation: 39-27=12 Exploring Operation: 88-39=49, Resulting Numbers: [27, 49] Generated Node #0,0,1: 80:[27, 49] Operation: 88-39=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[88, 12], Operations: ['90-51=39', '39-27=12'] Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,80 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[27, 49], Operations: ['90-51=39', '88-39=49'] Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,80 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[27, 51, 2], Operations: ['90-88=2'] Exploring Operation: 51-27=24, Resulting Numbers: [2, 24] Generated Node #0,1,0: 80:[2, 24] Operation: 51-27=24 Exploring Operation: 27+51=78, Resulting Numbers: [2, 78] Generated Node #0,1,1: 80:[2, 78] Operation: 27+51=78 Moving to Node #0,1,1 Current State: 80:[2, 78], Operations: ['90-88=2', '27+51=78'] Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[27, 88, 51, 90], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [27, 51, 2] Generated Node #0,1: 80:[27, 51, 2] Operation: 90-88=2 Moving to Node #0,1 Current State: 80:[27, 51, 2], Operations: ['90-88=2'] Exploring Operation: 27+51=78, Resulting Numbers: [2, 78] Generated Node #0,1,1: 80:[2, 78] Operation: 27+51=78 Moving to Node #0,1,1 Current State: 80:[2, 78], Operations: ['90-88=2', '27+51=78'] Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 34, 26, 70, 27 ]
36
[ "70-34=36", "27-26=1", "36*1=36" ]
Current State: 36:[34, 26, 70, 27], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [26, 27, 36] Generated Node #2: [26, 27, 36] from Operation: 70-34=36 Current State: 36:[26, 27, 36], Operations: ['70-34=36'] Exploring Operation: 27-26=1, Resulting Numbers: [36, 1] Generated Node #3: [36, 1] from Operation: 27-26=1 Current State: 36:[36, 1], Operations: ['70-34=36', '27-26=1'] Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[34, 26, 70, 27], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [26, 27, 36] Generated Node #0,0: 36:[26, 27, 36] Operation: 70-34=36 Moving to Node #0,0 Current State: 36:[26, 27, 36], Operations: ['70-34=36'] Exploring Operation: 27-26=1, Resulting Numbers: [36, 1] Generated Node #0,0,0: 36:[36, 1] Operation: 27-26=1 Moving to Node #0,0,0 Current State: 36:[36, 1], Operations: ['70-34=36', '27-26=1'] Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[34, 26, 70, 27], Operations: [] Exploring Operation: 70-34=36, Resulting Numbers: [26, 27, 36] Generated Node #0,0: 36:[26, 27, 36] Operation: 70-34=36 Moving to Node #0,0 Current State: 36:[26, 27, 36], Operations: ['70-34=36'] Exploring Operation: 27-26=1, Resulting Numbers: [36, 1] Generated Node #0,0,0: 36:[36, 1] Operation: 27-26=1 Moving to Node #0,0,0 Current State: 36:[36, 1], Operations: ['70-34=36', '27-26=1'] Exploring Operation: 36*1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 94, 39, 3, 92 ]
73
[ "94-39=55", "3*55=165", "165-92=73" ]
Current State: 73:[94, 39, 3, 92], Operations: [] Exploring Operation: 94-39=55, Resulting Numbers: [3, 92, 55] Generated Node #2: [3, 92, 55] from Operation: 94-39=55 Current State: 73:[3, 92, 55], Operations: ['94-39=55'] Exploring Operation: 3*55=165, Resulting Numbers: [92, 165] Generated Node #3: [92, 165] from Operation: 3*55=165 Current State: 73:[92, 165], Operations: ['94-39=55', '3*55=165'] Exploring Operation: 165-92=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[94, 39, 3, 92], Operations: [] Exploring Operation: 39+3=42, Resulting Numbers: [94, 92, 42] Generated Node #0,0: 73:[94, 92, 42] Operation: 39+3=42 Exploring Operation: 92-3=89, Resulting Numbers: [94, 39, 89] Generated Node #0,1: 73:[94, 39, 89] Operation: 92-3=89 Exploring Operation: 94-3=91, Resulting Numbers: [39, 92, 91] Generated Node #0,2: 73:[39, 92, 91] Operation: 94-3=91 Moving to Node #0,0 Current State: 73:[94, 92, 42], Operations: ['39+3=42'] Exploring Operation: 94+42=136, Resulting Numbers: [92, 136] Generated Node #0,0,0: 73:[92, 136] Operation: 94+42=136 Exploring Operation: 94-42=52, Resulting Numbers: [92, 52] Generated Node #0,0,1: 73:[92, 52] Operation: 94-42=52 Exploring Operation: 92-42=50, Resulting Numbers: [94, 50] Generated Node #0,0,2: 73:[94, 50] Operation: 92-42=50 Moving to Node #0,1 Current State: 73:[94, 39, 89], Operations: ['92-3=89'] Exploring Operation: 94-39=55, Resulting Numbers: [89, 55] Generated Node #0,1,0: 73:[89, 55] Operation: 94-39=55 Exploring Operation: 89-39=50, Resulting Numbers: [94, 50] Generated Node #0,1,1: 73:[94, 50] Operation: 89-39=50 Exploring Operation: 94+39=133, Resulting Numbers: [89, 133] Generated Node #0,1,2: 73:[89, 133] Operation: 94+39=133 Moving to Node #0,2 Current State: 73:[39, 92, 91], Operations: ['94-3=91'] Exploring Operation: 92-39=53, Resulting Numbers: [91, 53] Generated Node #0,2,0: 73:[91, 53] Operation: 92-39=53 Exploring Operation: 91-39=52, Resulting Numbers: [92, 52] Generated Node #0,2,1: 73:[92, 52] Operation: 91-39=52 Exploring Operation: 39+92=131, Resulting Numbers: [91, 131] Generated Node #0,2,2: 73:[91, 131] Operation: 39+92=131 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 73:[91, 53], Operations: ['94-3=91', '92-39=53'] Exploring Operation: 91+53=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 91-53=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 91*53=4823, Resulting Numbers: [4823] 4823,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 73:[92, 52], Operations: ['94-3=91', '91-39=52'] Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,73 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 73:[91, 131], Operations: ['94-3=91', '39+92=131'] Exploring Operation: 131-91=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 91*131=11921, Resulting Numbers: [11921] 11921,73 unequal: No Solution Exploring Operation: 91+131=222, Resulting Numbers: [222] 222,73 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: 73:[89, 55], Operations: ['92-3=89', '94-39=55'] Exploring Operation: 89*55=4895, Resulting Numbers: [4895] 4895,73 unequal: No Solution Exploring Operation: 89-55=34, Resulting Numbers: [34] 34,73 unequal: No Solution Exploring Operation: 89+55=144, Resulting Numbers: [144] 144,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[92, 52], Operations: ['39+3=42', '94-42=52'] Exploring Operation: 92+52=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 92-52=40, Resulting Numbers: [40] 40,73 unequal: No Solution Exploring Operation: 92*52=4784, Resulting Numbers: [4784] 4784,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[94, 50], Operations: ['92-3=89', '89-39=50'] Exploring Operation: 94+50=144, Resulting Numbers: [144] 144,73 unequal: No Solution Exploring Operation: 94-50=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 94*50=4700, Resulting Numbers: [4700] 4700,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[94, 50], Operations: ['39+3=42', '92-42=50'] Exploring Operation: 94*50=4700, Resulting Numbers: [4700] 4700,73 unequal: No Solution Exploring Operation: 94-50=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 94+50=144, Resulting Numbers: [144] 144,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[89, 133], Operations: ['92-3=89', '94+39=133'] Exploring Operation: 89+133=222, Resulting Numbers: [222] 222,73 unequal: No Solution Exploring Operation: 133-89=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 89*133=11837, Resulting Numbers: [11837] 11837,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[92, 136], Operations: ['39+3=42', '94+42=136'] Exploring Operation: 92*136=12512, Resulting Numbers: [12512] 12512,73 unequal: No Solution Exploring Operation: 92+136=228, Resulting Numbers: [228] 228,73 unequal: No Solution Exploring Operation: 136-92=44, Resulting Numbers: [44] 44,73 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 44, 96, 16, 56 ]
68
[ "44+96=140", "16+56=72", "140-72=68" ]
Current State: 68:[44, 96, 16, 56], Operations: [] Exploring Operation: 44+96=140, Resulting Numbers: [16, 56, 140] Generated Node #2: [16, 56, 140] from Operation: 44+96=140 Current State: 68:[16, 56, 140], Operations: ['44+96=140'] Exploring Operation: 16+56=72, Resulting Numbers: [140, 72] Generated Node #3: [140, 72] from Operation: 16+56=72 Current State: 68:[140, 72], Operations: ['44+96=140', '16+56=72'] Exploring Operation: 140-72=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[44, 96, 16, 56], Operations: [] Exploring Operation: 96-56=40, Resulting Numbers: [44, 16, 40] Generated Node #0,0: 68:[44, 16, 40] Operation: 96-56=40 Exploring Operation: 96-44=52, Resulting Numbers: [16, 56, 52] Generated Node #0,1: 68:[16, 56, 52] Operation: 96-44=52 Exploring Operation: 96/16=6, Resulting Numbers: [44, 56, 6] Generated Node #0,2: 68:[44, 56, 6] Operation: 96/16=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[44, 16, 40], Operations: ['96-56=40'] Exploring Operation: 44+16=60, Resulting Numbers: [40, 60] Generated Node #0,0,0: 68:[40, 60] Operation: 44+16=60 Exploring Operation: 44-40=4, Resulting Numbers: [16, 4] Generated Node #0,0,1: 68:[16, 4] Operation: 44-40=4 Exploring Operation: 44-16=28, Resulting Numbers: [40, 28] Generated Node #0,0,2: 68:[40, 28] Operation: 44-16=28 Moving to Node #0,0,1 Current State: 68:[16, 4], Operations: ['96-56=40', '44-40=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,68 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[40, 28], Operations: ['96-56=40', '44-16=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[44, 96, 16, 56], Operations: [] Exploring Operation: 96-56=40, Resulting Numbers: [44, 16, 40] Generated Node #0,0: 68:[44, 16, 40] Operation: 96-56=40 Moving to Node #0,0 Current State: 68:[44, 16, 40], Operations: ['96-56=40'] Exploring Operation: 44-16=28, Resulting Numbers: [40, 28] Generated Node #0,0,2: 68:[40, 28] Operation: 44-16=28 Moving to Node #0,0,2 Current State: 68:[40, 28], Operations: ['96-56=40', '44-16=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 78, 4, 22, 20 ]
20
[ "78+22=100", "4*20=80", "100-80=20" ]
Current State: 20:[78, 4, 22, 20], Operations: [] Exploring Operation: 78+22=100, Resulting Numbers: [4, 20, 100] Generated Node #2: [4, 20, 100] from Operation: 78+22=100 Current State: 20:[4, 20, 100], Operations: ['78+22=100'] Exploring Operation: 4*20=80, Resulting Numbers: [100, 80] Generated Node #3: [100, 80] from Operation: 4*20=80 Current State: 20:[100, 80], Operations: ['78+22=100', '4*20=80'] Exploring Operation: 100-80=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[78, 4, 22, 20], Operations: [] Exploring Operation: 78-22=56, Resulting Numbers: [4, 20, 56] Generated Node #0,0: 20:[4, 20, 56] Operation: 78-22=56 Exploring Operation: 78-20=58, Resulting Numbers: [4, 22, 58] Generated Node #0,1: 20:[4, 22, 58] Operation: 78-20=58 Exploring Operation: 78-4=74, Resulting Numbers: [22, 20, 74] Generated Node #0,2: 20:[22, 20, 74] Operation: 78-4=74 Exploring Operation: 22-4=18, Resulting Numbers: [78, 20, 18] Generated Node #0,3: 20:[78, 20, 18] Operation: 22-4=18 Exploring Operation: 22-20=2, Resulting Numbers: [78, 4, 2] Generated Node #0,4: 20:[78, 4, 2] Operation: 22-20=2 Moving to Node #0,0 Current State: 20:[4, 20, 56], Operations: ['78-22=56'] Exploring Operation: 4+20=24, Resulting Numbers: [56, 24] Generated Node #0,0,0: 20:[56, 24] Operation: 4+20=24 Exploring Operation: 56/4=14, Resulting Numbers: [20, 14] Generated Node #0,0,1: 20:[20, 14] Operation: 56/4=14 Exploring Operation: 20/4=5, Resulting Numbers: [56, 5] Generated Node #0,0,2: 20:[56, 5] Operation: 20/4=5 Exploring Operation: 56-4=52, Resulting Numbers: [20, 52] Generated Node #0,0,3: 20:[20, 52] Operation: 56-4=52 Exploring Operation: 56-20=36, Resulting Numbers: [4, 36] Generated Node #0,0,4: 20:[4, 36] Operation: 56-20=36 Moving to Node #0,1 Current State: 20:[4, 22, 58], Operations: ['78-20=58'] Exploring Operation: 22-4=18, Resulting Numbers: [58, 18] Generated Node #0,1,0: 20:[58, 18] Operation: 22-4=18 Exploring Operation: 58-4=54, Resulting Numbers: [22, 54] Generated Node #0,1,1: 20:[22, 54] Operation: 58-4=54 Exploring Operation: 4+58=62, Resulting Numbers: [22, 62] Generated Node #0,1,2: 20:[22, 62] Operation: 4+58=62 Exploring Operation: 4+22=26, Resulting Numbers: [58, 26] Generated Node #0,1,3: 20:[58, 26] Operation: 4+22=26 Exploring Operation: 58-22=36, Resulting Numbers: [4, 36] Generated Node #0,1,4: 20:[4, 36] Operation: 58-22=36 Moving to Node #0,2 Current State: 20:[22, 20, 74], Operations: ['78-4=74'] Exploring Operation: 22+20=42, Resulting Numbers: [74, 42] Generated Node #0,2,0: 20:[74, 42] Operation: 22+20=42 Exploring Operation: 22-20=2, Resulting Numbers: [74, 2] Generated Node #0,2,1: 20:[74, 2] Operation: 22-20=2 Exploring Operation: 22+74=96, Resulting Numbers: [20, 96] Generated Node #0,2,2: 20:[20, 96] Operation: 22+74=96 Exploring Operation: 74-20=54, Resulting Numbers: [22, 54] Generated Node #0,2,3: 20:[22, 54] Operation: 74-20=54 Exploring Operation: 74-22=52, Resulting Numbers: [20, 52] Generated Node #0,2,4: 20:[20, 52] Operation: 74-22=52 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 20:[20, 52], Operations: ['78-4=74', '74-22=52'] Exploring Operation: 20*52=1040, Resulting Numbers: [1040] 1040,20 unequal: No Solution Exploring Operation: 52-20=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 20+52=72, Resulting Numbers: [72] 72,20 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 #0,2,3 Current State: 20:[22, 54], Operations: ['78-4=74', '74-20=54'] Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,20 unequal: No Solution Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,20 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 #0,2,1 Current State: 20:[74, 2], Operations: ['78-4=74', '22-20=2'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 74+2=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 74*2=148, Resulting Numbers: [148] 148,20 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 #0,2,0 Current State: 20:[74, 42], Operations: ['78-4=74', '22+20=42'] Exploring Operation: 74+42=116, Resulting Numbers: [116] 116,20 unequal: No Solution Exploring Operation: 74*42=3108, Resulting Numbers: [3108] 3108,20 unequal: No Solution Exploring Operation: 74-42=32, Resulting Numbers: [32] 32,20 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 #0,2,2 Current State: 20:[20, 96], Operations: ['78-4=74', '22+74=96'] Exploring Operation: 20+96=116, Resulting Numbers: [116] 116,20 unequal: No Solution Exploring Operation: 20*96=1920, Resulting Numbers: [1920] 1920,20 unequal: No Solution Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,20 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: 20:[78, 4, 2], Operations: ['22-20=2'] Exploring Operation: 78-2=76, Resulting Numbers: [4, 76] Generated Node #0,4,0: 20:[4, 76] Operation: 78-2=76 Exploring Operation: 4/2=2, Resulting Numbers: [78, 2] Generated Node #0,4,1: 20:[78, 2] Operation: 4/2=2 Exploring Operation: 4-2=2, Resulting Numbers: [78, 2] Generated Node #0,4,2: 20:[78, 2] Operation: 4-2=2 Exploring Operation: 78-4=74, Resulting Numbers: [2, 74] Generated Node #0,4,3: 20:[2, 74] Operation: 78-4=74 Exploring Operation: 78/2=39, Resulting Numbers: [4, 39] Generated Node #0,4,4: 20:[4, 39] Operation: 78/2=39 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 20:[4, 39], Operations: ['22-20=2', '78/2=39'] Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,20 unequal: No Solution Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,20 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 #0,4,3 Current State: 20:[2, 74], Operations: ['22-20=2', '78-4=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,20 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,20 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 #0,4,0 Current State: 20:[4, 76], Operations: ['22-20=2', '78-2=76'] Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 4+76=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 4*76=304, Resulting Numbers: [304] 304,20 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 #0,4,1 Current State: 20:[78, 2], Operations: ['22-20=2', '4/2=2'] Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,20 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 #0,4,2 Current State: 20:[78, 2], Operations: ['22-20=2', '4-2=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,20 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,20 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: 20:[78, 20, 18], Operations: ['22-4=18'] Exploring Operation: 78+18=96, Resulting Numbers: [20, 96] Generated Node #0,3,0: 20:[20, 96] Operation: 78+18=96 Exploring Operation: 20+18=38, Resulting Numbers: [78, 38] Generated Node #0,3,1: 20:[78, 38] Operation: 20+18=38 Exploring Operation: 20-18=2, Resulting Numbers: [78, 2] Generated Node #0,3,2: 20:[78, 2] Operation: 20-18=2 Exploring Operation: 78-18=60, Resulting Numbers: [20, 60] Generated Node #0,3,3: 20:[20, 60] Operation: 78-18=60 Exploring Operation: 78-20=58, Resulting Numbers: [18, 58] Generated Node #0,3,4: 20:[18, 58] Operation: 78-20=58 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 20:[20, 60], Operations: ['22-4=18', '78-18=60'] Exploring Operation: 20*60=1200, Resulting Numbers: [1200] 1200,20 unequal: No Solution Exploring Operation: 60-20=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 60/20=3, Resulting Numbers: [3] 3,20 unequal: No Solution Exploring Operation: 20+60=80, Resulting Numbers: [80] 80,20 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 #0,3,4 Current State: 20:[18, 58], Operations: ['22-4=18', '78-20=58'] Exploring Operation: 18*58=1044, Resulting Numbers: [1044] 1044,20 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,20 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 #0,3,2 Current State: 20:[78, 2], Operations: ['22-4=18', '20-18=2'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,20 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,20 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,20 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 #0,3,0 Current State: 20:[20, 96], Operations: ['22-4=18', '78+18=96'] Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 20*96=1920, Resulting Numbers: [1920] 1920,20 unequal: No Solution Exploring Operation: 20+96=116, Resulting Numbers: [116] 116,20 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 #0,3,1 Current State: 20:[78, 38], Operations: ['22-4=18', '20+18=38'] Exploring Operation: 78+38=116, Resulting Numbers: [116] 116,20 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 78*38=2964, Resulting Numbers: [2964] 2964,20 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: 20:[20, 14], Operations: ['78-22=56', '56/4=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,20 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,20 unequal: No Solution Moving to Node #0,1,4 Current State: 20:[4, 36], Operations: ['78-20=58', '58-22=36'] Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,20 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,20 unequal: No Solution Moving to Node #0,0,4 Current State: 20:[4, 36], Operations: ['78-22=56', '56-20=36'] Exploring Operation: 4*36=144, Resulting Numbers: [144] 144,20 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,20 unequal: No Solution Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[20, 52], Operations: ['78-22=56', '56-4=52'] Exploring Operation: 52-20=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 20+52=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 20*52=1040, Resulting Numbers: [1040] 1040,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[22, 54], Operations: ['78-20=58', '58-4=54'] Exploring Operation: 22+54=76, Resulting Numbers: [76] 76,20 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 22*54=1188, Resulting Numbers: [1188] 1188,20 unequal: No Solution Moving to Node #0,0,2 Current State: 20:[56, 5], Operations: ['78-22=56', '20/4=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,20 unequal: No Solution Exploring Operation: 56*5=280, Resulting Numbers: [280] 280,20 unequal: No Solution Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[56, 24], Operations: ['78-22=56', '4+20=24'] Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 56*24=1344, Resulting Numbers: [1344] 1344,20 unequal: No Solution Exploring Operation: 56+24=80, Resulting Numbers: [80] 80,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[58, 18], Operations: ['78-20=58', '22-4=18'] Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,20 unequal: No Solution Exploring Operation: 58*18=1044, Resulting Numbers: [1044] 1044,20 unequal: No Solution Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,20 unequal: No Solution Moving to Node #0,1,2 Current State: 20:[22, 62], Operations: ['78-20=58', '4+58=62'] Exploring Operation: 22+62=84, Resulting Numbers: [84] 84,20 unequal: No Solution Exploring Operation: 22*62=1364, Resulting Numbers: [1364] 1364,20 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,20 unequal: No Solution Moving to Node #0,1,3 Current State: 20:[58, 26], Operations: ['78-20=58', '4+22=26'] Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,20 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,20 unequal: No Solution Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,20 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 51, 60, 23, 77 ]
11
[ "51+60=111", "23+77=100", "111-100=11" ]
Current State: 11:[51, 60, 23, 77], Operations: [] Exploring Operation: 51+60=111, Resulting Numbers: [23, 77, 111] Generated Node #2: [23, 77, 111] from Operation: 51+60=111 Current State: 11:[23, 77, 111], Operations: ['51+60=111'] Exploring Operation: 23+77=100, Resulting Numbers: [111, 100] Generated Node #3: [111, 100] from Operation: 23+77=100 Current State: 11:[111, 100], Operations: ['51+60=111', '23+77=100'] Exploring Operation: 111-100=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[51, 60, 23, 77], Operations: [] Exploring Operation: 77-60=17, Resulting Numbers: [51, 23, 17] Generated Node #0,0: 11:[51, 23, 17] Operation: 77-60=17 Exploring Operation: 77-51=26, Resulting Numbers: [60, 23, 26] Generated Node #0,1: 11:[60, 23, 26] Operation: 77-51=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[51, 23, 17], Operations: ['77-60=17'] Exploring Operation: 51-23=28, Resulting Numbers: [17, 28] Generated Node #0,0,0: 11:[17, 28] Operation: 51-23=28 Exploring Operation: 51/17=3, Resulting Numbers: [23, 3] Generated Node #0,0,1: 11:[23, 3] Operation: 51/17=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[23, 3], Operations: ['77-60=17', '51/17=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,11 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[17, 28], Operations: ['77-60=17', '51-23=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,11 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[51, 60, 23, 77], Operations: [] Exploring Operation: 77-60=17, Resulting Numbers: [51, 23, 17] Generated Node #0,0: 11:[51, 23, 17] Operation: 77-60=17 Moving to Node #0,0 Current State: 11:[51, 23, 17], Operations: ['77-60=17'] Exploring Operation: 51-23=28, Resulting Numbers: [17, 28] Generated Node #0,0,0: 11:[17, 28] Operation: 51-23=28 Moving to Node #0,0,0 Current State: 11:[17, 28], Operations: ['77-60=17', '51-23=28'] Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 74, 75, 81, 49 ]
82
[ "81-74=7", "49/7=7", "75+7=82" ]
Current State: 82:[74, 75, 81, 49], Operations: [] Exploring Operation: 81-74=7, Resulting Numbers: [75, 49, 7] Generated Node #2: [75, 49, 7] from Operation: 81-74=7 Current State: 82:[75, 49, 7], Operations: ['81-74=7'] Exploring Operation: 49/7=7, Resulting Numbers: [75, 7] Generated Node #3: [75, 7] from Operation: 49/7=7 Current State: 82:[75, 7], Operations: ['81-74=7', '49/7=7'] Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[74, 75, 81, 49], Operations: [] Exploring Operation: 75-49=26, Resulting Numbers: [74, 81, 26] Generated Node #0,0: 82:[74, 81, 26] Operation: 75-49=26 Exploring Operation: 81-75=6, Resulting Numbers: [74, 49, 6] Generated Node #0,1: 82:[74, 49, 6] Operation: 81-75=6 Exploring Operation: 81-74=7, Resulting Numbers: [75, 49, 7] Generated Node #0,2: 82:[75, 49, 7] Operation: 81-74=7 Exploring Operation: 75-74=1, Resulting Numbers: [81, 49, 1] Generated Node #0,3: 82:[81, 49, 1] Operation: 75-74=1 Exploring Operation: 74-49=25, Resulting Numbers: [75, 81, 25] Generated Node #0,4: 82:[75, 81, 25] Operation: 74-49=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[81, 49, 1], Operations: ['75-74=1'] Exploring Operation: 49-1=48, Resulting Numbers: [81, 48] Generated Node #0,3,0: 82:[81, 48] Operation: 49-1=48 Exploring Operation: 49*1=49, Resulting Numbers: [81, 49] Generated Node #0,3,1: 82:[81, 49] Operation: 49*1=49 Exploring Operation: 81/1=81, Resulting Numbers: [49, 81] Generated Node #0,3,2: 82:[49, 81] Operation: 81/1=81 Exploring Operation: 81*1=81, Resulting Numbers: [49, 81] Generated Node #0,3,3: 82:[49, 81] Operation: 81*1=81 Exploring Operation: 81+1=82, Resulting Numbers: [49, 82] Generated Node #0,3,4: 82:[49, 82] Operation: 81+1=82 Moving to Node #0,3,0 Current State: 82:[81, 48], Operations: ['75-74=1', '49-1=48'] Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 81+48=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 81*48=3888, Resulting Numbers: [3888] 3888,82 unequal: No Solution Moving to Node #0,3,4 Current State: 82:[49, 82], Operations: ['75-74=1', '81+1=82'] Exploring Operation: 49*82=4018, Resulting Numbers: [4018] 4018,82 unequal: No Solution Exploring Operation: 82-49=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 49+82=131, Resulting Numbers: [131] 131,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[81, 49], Operations: ['75-74=1', '49*1=49'] Exploring Operation: 81*49=3969, Resulting Numbers: [3969] 3969,82 unequal: No Solution Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 81+49=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[49, 81], Operations: ['75-74=1', '81/1=81'] Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,82 unequal: No Solution Exploring Operation: 49*81=3969, Resulting Numbers: [3969] 3969,82 unequal: No Solution Exploring Operation: 49+81=130, Resulting Numbers: [130] 130,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[49, 81], Operations: ['75-74=1', '81*1=81'] Exploring Operation: 49+81=130, Resulting Numbers: [130] 130,82 unequal: No Solution Exploring Operation: 49*81=3969, Resulting Numbers: [3969] 3969,82 unequal: No Solution Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[74, 49, 6], Operations: ['81-75=6'] Exploring Operation: 74-49=25, Resulting Numbers: [6, 25] Generated Node #0,1,0: 82:[6, 25] Operation: 74-49=25 Exploring Operation: 74+6=80, Resulting Numbers: [49, 80] Generated Node #0,1,1: 82:[49, 80] Operation: 74+6=80 Exploring Operation: 74-6=68, Resulting Numbers: [49, 68] Generated Node #0,1,2: 82:[49, 68] Operation: 74-6=68 Exploring Operation: 49-6=43, Resulting Numbers: [74, 43] Generated Node #0,1,3: 82:[74, 43] Operation: 49-6=43 Exploring Operation: 49+6=55, Resulting Numbers: [74, 55] Generated Node #0,1,4: 82:[74, 55] Operation: 49+6=55 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[49, 80], Operations: ['81-75=6', '74+6=80'] Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 82:[74, 43], Operations: ['81-75=6', '49-6=43'] Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,82 unequal: No Solution Exploring Operation: 74*43=3182, Resulting Numbers: [3182] 3182,82 unequal: No Solution Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[6, 25], Operations: ['81-75=6', '74-49=25'] Exploring Operation: 6+25=31, Resulting Numbers: [31] 31,82 unequal: No Solution Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,82 unequal: No Solution Exploring Operation: 6*25=150, Resulting Numbers: [150] 150,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[49, 68], Operations: ['81-75=6', '74-6=68'] Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,82 unequal: No Solution Exploring Operation: 49*68=3332, Resulting Numbers: [3332] 3332,82 unequal: No Solution Exploring Operation: 49+68=117, Resulting Numbers: [117] 117,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 82:[74, 55], Operations: ['81-75=6', '49+6=55'] Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,82 unequal: No Solution Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,82 unequal: No Solution Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[75, 49, 7], Operations: ['81-74=7'] Exploring Operation: 49/7=7, Resulting Numbers: [75, 7] Generated Node #0,2,0: 82:[75, 7] Operation: 49/7=7 Exploring Operation: 75-7=68, Resulting Numbers: [49, 68] Generated Node #0,2,1: 82:[49, 68] Operation: 75-7=68 Exploring Operation: 75-49=26, Resulting Numbers: [7, 26] Generated Node #0,2,2: 82:[7, 26] Operation: 75-49=26 Exploring Operation: 75+7=82, Resulting Numbers: [49, 82] Generated Node #0,2,3: 82:[49, 82] Operation: 75+7=82 Exploring Operation: 49-7=42, Resulting Numbers: [75, 42] Generated Node #0,2,4: 82:[75, 42] Operation: 49-7=42 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[49, 82], Operations: ['81-74=7', '75+7=82'] Exploring Operation: 49+82=131, Resulting Numbers: [131] 131,82 unequal: No Solution Exploring Operation: 82-49=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 49*82=4018, Resulting Numbers: [4018] 4018,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 82:[75, 42], Operations: ['81-74=7', '49-7=42'] Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,82 unequal: No Solution Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,82 unequal: No Solution Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[75, 7], Operations: ['81-74=7', '49/7=7'] Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,82 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,82 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[74, 75, 81, 49], Operations: [] Exploring Operation: 81-74=7, Resulting Numbers: [75, 49, 7] Generated Node #0,2: 82:[75, 49, 7] Operation: 81-74=7 Moving to Node #0,2 Current State: 82:[75, 49, 7], Operations: ['81-74=7'] Exploring Operation: 49/7=7, Resulting Numbers: [75, 7] Generated Node #0,2,0: 82:[75, 7] Operation: 49/7=7 Moving to Node #0,2,0 Current State: 82:[75, 7], Operations: ['81-74=7', '49/7=7'] Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.945313
hs_5
sum_heuristic
[ 69, 80, 60, 38 ]
33
[ "80-69=11", "60-38=22", "11+22=33" ]
Current State: 33:[69, 80, 60, 38], Operations: [] Exploring Operation: 80-69=11, Resulting Numbers: [60, 38, 11] Generated Node #2: [60, 38, 11] from Operation: 80-69=11 Current State: 33:[60, 38, 11], Operations: ['80-69=11'] Exploring Operation: 60-38=22, Resulting Numbers: [11, 22] Generated Node #3: [11, 22] from Operation: 60-38=22 Current State: 33:[11, 22], Operations: ['80-69=11', '60-38=22'] Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[69, 80, 60, 38], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [69, 60, 42] Generated Node #0,0: 33:[69, 60, 42] Operation: 80-38=42 Exploring Operation: 80-60=20, Resulting Numbers: [69, 38, 20] Generated Node #0,1: 33:[69, 38, 20] Operation: 80-60=20 Exploring Operation: 69-60=9, Resulting Numbers: [80, 38, 9] Generated Node #0,2: 33:[80, 38, 9] Operation: 69-60=9 Exploring Operation: 80-69=11, Resulting Numbers: [60, 38, 11] Generated Node #0,3: 33:[60, 38, 11] Operation: 80-69=11 Moving to Node #0,3 Current State: 33:[60, 38, 11], Operations: ['80-69=11'] Exploring Operation: 38-11=27, Resulting Numbers: [60, 27] Generated Node #0,3,0: 33:[60, 27] Operation: 38-11=27 Exploring Operation: 60-11=49, Resulting Numbers: [38, 49] Generated Node #0,3,1: 33:[38, 49] Operation: 60-11=49 Exploring Operation: 60-38=22, Resulting Numbers: [11, 22] Generated Node #0,3,2: 33:[11, 22] Operation: 60-38=22 Exploring Operation: 60+11=71, Resulting Numbers: [38, 71] Generated Node #0,3,3: 33:[38, 71] Operation: 60+11=71 Moving to Node #0,1 Current State: 33:[69, 38, 20], Operations: ['80-60=20'] Exploring Operation: 69-20=49, Resulting Numbers: [38, 49] Generated Node #0,1,0: 33:[38, 49] Operation: 69-20=49 Exploring Operation: 69-38=31, Resulting Numbers: [20, 31] Generated Node #0,1,1: 33:[20, 31] Operation: 69-38=31 Exploring Operation: 69+20=89, Resulting Numbers: [38, 89] Generated Node #0,1,2: 33:[38, 89] Operation: 69+20=89 Exploring Operation: 38-20=18, Resulting Numbers: [69, 18] Generated Node #0,1,3: 33:[69, 18] Operation: 38-20=18 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 33:[20, 31], Operations: ['80-60=20', '69-38=31'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,33 unequal: No Solution Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 33:[38, 49], Operations: ['80-60=20', '69-20=49'] Exploring Operation: 38*49=1862, Resulting Numbers: [1862] 1862,33 unequal: No Solution Exploring Operation: 38+49=87, Resulting Numbers: [87] 87,33 unequal: No Solution Exploring Operation: 49-38=11, Resulting Numbers: [11] 11,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 33:[69, 18], Operations: ['80-60=20', '38-20=18'] Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,33 unequal: No Solution Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 33:[38, 89], Operations: ['80-60=20', '69+20=89'] Exploring Operation: 89-38=51, Resulting Numbers: [51] 51,33 unequal: No Solution Exploring Operation: 38+89=127, Resulting Numbers: [127] 127,33 unequal: No Solution Exploring Operation: 38*89=3382, Resulting Numbers: [3382] 3382,33 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: 33:[80, 38, 9], Operations: ['69-60=9'] Exploring Operation: 80-9=71, Resulting Numbers: [38, 71] Generated Node #0,2,0: 33:[38, 71] Operation: 80-9=71 Exploring Operation: 38-9=29, Resulting Numbers: [80, 29] Generated Node #0,2,1: 33:[80, 29] Operation: 38-9=29 Exploring Operation: 80+9=89, Resulting Numbers: [38, 89] Generated Node #0,2,2: 33:[38, 89] Operation: 80+9=89 Exploring Operation: 80-38=42, Resulting Numbers: [9, 42] Generated Node #0,2,3: 33:[9, 42] Operation: 80-38=42 Moving to Node #0,0 Current State: 33:[69, 60, 42], Operations: ['80-38=42'] Exploring Operation: 69-60=9, Resulting Numbers: [42, 9] Generated Node #0,0,0: 33:[42, 9] Operation: 69-60=9 Exploring Operation: 69+60=129, Resulting Numbers: [42, 129] Generated Node #0,0,1: 33:[42, 129] Operation: 69+60=129 Exploring Operation: 69-42=27, Resulting Numbers: [60, 27] Generated Node #0,0,2: 33:[60, 27] Operation: 69-42=27 Exploring Operation: 60-42=18, Resulting Numbers: [69, 18] Generated Node #0,0,3: 33:[69, 18] Operation: 60-42=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[42, 9], Operations: ['80-38=42', '69-60=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[69, 80, 60, 38], Operations: [] Exploring Operation: 80-38=42, Resulting Numbers: [69, 60, 42] Generated Node #0,0: 33:[69, 60, 42] Operation: 80-38=42 Moving to Node #0,0 Current State: 33:[69, 60, 42], Operations: ['80-38=42'] Exploring Operation: 69-60=9, Resulting Numbers: [42, 9] Generated Node #0,0,0: 33:[42, 9] Operation: 69-60=9 Moving to Node #0,0,0 Current State: 33:[42, 9], Operations: ['80-38=42', '69-60=9'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 19, 3, 24, 45 ]
56
[ "19+45=64", "24/3=8", "64-8=56" ]
Current State: 56:[19, 3, 24, 45], Operations: [] Exploring Operation: 19+45=64, Resulting Numbers: [3, 24, 64] Generated Node #2: [3, 24, 64] from Operation: 19+45=64 Current State: 56:[3, 24, 64], Operations: ['19+45=64'] Exploring Operation: 24/3=8, Resulting Numbers: [64, 8] Generated Node #3: [64, 8] from Operation: 24/3=8 Current State: 56:[64, 8], Operations: ['19+45=64', '24/3=8'] Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[19, 3, 24, 45], Operations: [] Exploring Operation: 45-19=26, Resulting Numbers: [3, 24, 26] Generated Node #0,0: 56:[3, 24, 26] Operation: 45-19=26 Exploring Operation: 45/3=15, Resulting Numbers: [19, 24, 15] Generated Node #0,1: 56:[19, 24, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[3, 24, 26], Operations: ['45-19=26'] Exploring Operation: 26-24=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 56:[3, 2] Operation: 26-24=2 Exploring Operation: 24/3=8, Resulting Numbers: [26, 8] Generated Node #0,0,1: 56:[26, 8] Operation: 24/3=8 Moving to Node #0,0,0 Current State: 56:[3, 2], Operations: ['45-19=26', '26-24=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,56 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,56 unequal: No Solution Moving to Node #0,0,1 Current State: 56:[26, 8], Operations: ['45-19=26', '24/3=8'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,56 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[19, 24, 15], Operations: ['45/3=15'] Exploring Operation: 24-19=5, Resulting Numbers: [15, 5] Generated Node #0,1,0: 56:[15, 5] Operation: 24-19=5 Exploring Operation: 19-15=4, Resulting Numbers: [24, 4] Generated Node #0,1,1: 56:[24, 4] Operation: 19-15=4 Moving to Node #0,1,0 Current State: 56:[15, 5], Operations: ['45/3=15', '24-19=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[24, 4], Operations: ['45/3=15', '19-15=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,56 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,56 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
[ 82, 80, 16, 3 ]
70
[ "82+80=162", "162/3=54", "16+54=70" ]
Current State: 70:[82, 80, 16, 3], Operations: [] Exploring Operation: 82+80=162, Resulting Numbers: [16, 3, 162] Generated Node #2: [16, 3, 162] from Operation: 82+80=162 Current State: 70:[16, 3, 162], Operations: ['82+80=162'] Exploring Operation: 162/3=54, Resulting Numbers: [16, 54] Generated Node #3: [16, 54] from Operation: 162/3=54 Current State: 70:[16, 54], Operations: ['82+80=162', '162/3=54'] Exploring Operation: 16+54=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[82, 80, 16, 3], Operations: [] Exploring Operation: 80-16=64, Resulting Numbers: [82, 3, 64] Generated Node #0,0: 70:[82, 3, 64] Operation: 80-16=64 Exploring Operation: 82-16=66, Resulting Numbers: [80, 3, 66] Generated Node #0,1: 70:[80, 3, 66] Operation: 82-16=66 Exploring Operation: 82-80=2, Resulting Numbers: [16, 3, 2] Generated Node #0,2: 70:[16, 3, 2] Operation: 82-80=2 Exploring Operation: 80/16=5, Resulting Numbers: [82, 3, 5] Generated Node #0,3: 70:[82, 3, 5] Operation: 80/16=5 Moving to Node #0,2 Current State: 70:[16, 3, 2], Operations: ['82-80=2'] Exploring Operation: 16-2=14, Resulting Numbers: [3, 14] Generated Node #0,2,0: 70:[3, 14] Operation: 16-2=14 Exploring Operation: 3+2=5, Resulting Numbers: [16, 5] Generated Node #0,2,1: 70:[16, 5] Operation: 3+2=5 Exploring Operation: 16-3=13, Resulting Numbers: [2, 13] Generated Node #0,2,2: 70:[2, 13] Operation: 16-3=13 Exploring Operation: 16/2=8, Resulting Numbers: [3, 8] Generated Node #0,2,3: 70:[3, 8] Operation: 16/2=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 70:[3, 14], Operations: ['82-80=2', '16-2=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,70 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 70:[2, 13], Operations: ['82-80=2', '16-3=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,70 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[16, 5], Operations: ['82-80=2', '3+2=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 70:[3, 8], Operations: ['82-80=2', '16/2=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,70 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,70 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: 70:[82, 3, 5], Operations: ['80/16=5'] Exploring Operation: 82-3=79, Resulting Numbers: [5, 79] Generated Node #0,3,0: 70:[5, 79] Operation: 82-3=79 Exploring Operation: 82-5=77, Resulting Numbers: [3, 77] Generated Node #0,3,1: 70:[3, 77] Operation: 82-5=77 Exploring Operation: 3+5=8, Resulting Numbers: [82, 8] Generated Node #0,3,2: 70:[82, 8] Operation: 3+5=8 Exploring Operation: 5-3=2, Resulting Numbers: [82, 2] Generated Node #0,3,3: 70:[82, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 70:[3, 77], Operations: ['80/16=5', '82-5=77'] Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,70 unequal: No Solution Exploring Operation: 3*77=231, Resulting Numbers: [231] 231,70 unequal: No Solution Exploring Operation: 3+77=80, Resulting Numbers: [80] 80,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 70:[5, 79], Operations: ['80/16=5', '82-3=79'] Exploring Operation: 5+79=84, Resulting Numbers: [84] 84,70 unequal: No Solution Exploring Operation: 79-5=74, Resulting Numbers: [74] 74,70 unequal: No Solution Exploring Operation: 5*79=395, Resulting Numbers: [395] 395,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 70:[82, 2], Operations: ['80/16=5', '5-3=2'] Exploring Operation: 82*2=164, Resulting Numbers: [164] 164,70 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,70 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 70:[82, 8], Operations: ['80/16=5', '3+5=8'] Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,70 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,70 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,70 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: 70:[80, 3, 66], Operations: ['82-16=66'] Exploring Operation: 80+3=83, Resulting Numbers: [66, 83] Generated Node #0,1,0: 70:[66, 83] Operation: 80+3=83 Exploring Operation: 80-3=77, Resulting Numbers: [66, 77] Generated Node #0,1,1: 70:[66, 77] Operation: 80-3=77 Exploring Operation: 80-66=14, Resulting Numbers: [3, 14] Generated Node #0,1,2: 70:[3, 14] Operation: 80-66=14 Exploring Operation: 3+66=69, Resulting Numbers: [80, 69] Generated Node #0,1,3: 70:[80, 69] Operation: 3+66=69 Moving to Node #0,0 Current State: 70:[82, 3, 64], Operations: ['80-16=64'] Exploring Operation: 82-64=18, Resulting Numbers: [3, 18] Generated Node #0,0,0: 70:[3, 18] Operation: 82-64=18 Exploring Operation: 82-3=79, Resulting Numbers: [64, 79] Generated Node #0,0,1: 70:[64, 79] Operation: 82-3=79 Exploring Operation: 3+64=67, Resulting Numbers: [82, 67] Generated Node #0,0,2: 70:[82, 67] Operation: 3+64=67 Exploring Operation: 82+3=85, Resulting Numbers: [64, 85] Generated Node #0,0,3: 70:[64, 85] Operation: 82+3=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[3, 18], Operations: ['80-16=64', '82-64=18'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[64, 79], Operations: ['80-16=64', '82-3=79'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 64*79=5056, Resulting Numbers: [5056] 5056,70 unequal: No Solution Exploring Operation: 64+79=143, Resulting Numbers: [143] 143,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 70:[82, 67], Operations: ['80-16=64', '3+64=67'] Exploring Operation: 82+67=149, Resulting Numbers: [149] 149,70 unequal: No Solution Exploring Operation: 82*67=5494, Resulting Numbers: [5494] 5494,70 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 70:[64, 85], Operations: ['80-16=64', '82+3=85'] Exploring Operation: 64*85=5440, Resulting Numbers: [5440] 5440,70 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 64+85=149, Resulting Numbers: [149] 149,70 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: 70:[3, 14], Operations: ['82-16=66', '80-66=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[80, 69], Operations: ['82-16=66', '3+66=69'] Exploring Operation: 80+69=149, Resulting Numbers: [149] 149,70 unequal: No Solution Exploring Operation: 80*69=5520, Resulting Numbers: [5520] 5520,70 unequal: No Solution Exploring Operation: 80-69=11, Resulting Numbers: [11] 11,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[66, 77], Operations: ['82-16=66', '80-3=77'] Exploring Operation: 66+77=143, Resulting Numbers: [143] 143,70 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 66*77=5082, Resulting Numbers: [5082] 5082,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[66, 83], Operations: ['82-16=66', '80+3=83'] Exploring Operation: 83-66=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 66*83=5478, Resulting Numbers: [5478] 5478,70 unequal: No Solution Exploring Operation: 66+83=149, Resulting Numbers: [149] 149,70 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 1, 69, 58, 90 ]
36
[ "69-1=68", "90-58=32", "68-32=36" ]
Current State: 36:[1, 69, 58, 90], Operations: [] Exploring Operation: 69-1=68, Resulting Numbers: [58, 90, 68] Generated Node #2: [58, 90, 68] from Operation: 69-1=68 Current State: 36:[58, 90, 68], Operations: ['69-1=68'] Exploring Operation: 90-58=32, Resulting Numbers: [68, 32] Generated Node #3: [68, 32] from Operation: 90-58=32 Current State: 36:[68, 32], Operations: ['69-1=68', '90-58=32'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[1, 69, 58, 90], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [1, 58, 21] Generated Node #0,0: 36:[1, 58, 21] Operation: 90-69=21 Exploring Operation: 58-1=57, Resulting Numbers: [69, 90, 57] Generated Node #0,1: 36:[69, 90, 57] Operation: 58-1=57 Exploring Operation: 90-58=32, Resulting Numbers: [1, 69, 32] Generated Node #0,2: 36:[1, 69, 32] Operation: 90-58=32 Exploring Operation: 69-58=11, Resulting Numbers: [1, 90, 11] Generated Node #0,3: 36:[1, 90, 11] Operation: 69-58=11 Exploring Operation: 69-1=68, Resulting Numbers: [58, 90, 68] Generated Node #0,4: 36:[58, 90, 68] Operation: 69-1=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[1, 58, 21], Operations: ['90-69=21'] Exploring Operation: 1*58=58, Resulting Numbers: [21, 58] Generated Node #0,0,0: 36:[21, 58] Operation: 1*58=58 Exploring Operation: 58-1=57, Resulting Numbers: [21, 57] Generated Node #0,0,1: 36:[21, 57] Operation: 58-1=57 Exploring Operation: 58/1=58, Resulting Numbers: [21, 58] Generated Node #0,0,2: 36:[21, 58] Operation: 58/1=58 Exploring Operation: 21-1=20, Resulting Numbers: [58, 20] Generated Node #0,0,3: 36:[58, 20] Operation: 21-1=20 Exploring Operation: 58-21=37, Resulting Numbers: [1, 37] Generated Node #0,0,4: 36:[1, 37] Operation: 58-21=37 Moving to Node #0,0,4 Current State: 36:[1, 37], Operations: ['90-69=21', '58-21=37'] Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[1, 69, 58, 90], Operations: [] Exploring Operation: 90-69=21, Resulting Numbers: [1, 58, 21] Generated Node #0,0: 36:[1, 58, 21] Operation: 90-69=21 Moving to Node #0,0 Current State: 36:[1, 58, 21], Operations: ['90-69=21'] Exploring Operation: 58-21=37, Resulting Numbers: [1, 37] Generated Node #0,0,4: 36:[1, 37] Operation: 58-21=37 Moving to Node #0,0,4 Current State: 36:[1, 37], Operations: ['90-69=21', '58-21=37'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 7, 85, 47, 19 ]
89
[ "47-19=28", "28/7=4", "85+4=89" ]
Current State: 89:[7, 85, 47, 19], Operations: [] Exploring Operation: 47-19=28, Resulting Numbers: [7, 85, 28] Generated Node #2: [7, 85, 28] from Operation: 47-19=28 Current State: 89:[7, 85, 28], Operations: ['47-19=28'] Exploring Operation: 28/7=4, Resulting Numbers: [85, 4] Generated Node #3: [85, 4] from Operation: 28/7=4 Current State: 89:[85, 4], Operations: ['47-19=28', '28/7=4'] Exploring Operation: 85+4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[7, 85, 47, 19], Operations: [] Exploring Operation: 7*19=133, Resulting Numbers: [85, 47, 133] Generated Node #0,0: 89:[85, 47, 133] Operation: 7*19=133 Exploring Operation: 7+19=26, Resulting Numbers: [85, 47, 26] Generated Node #0,1: 89:[85, 47, 26] Operation: 7+19=26 Exploring Operation: 7+47=54, Resulting Numbers: [85, 19, 54] Generated Node #0,2: 89:[85, 19, 54] Operation: 7+47=54 Moving to Node #0,0 Current State: 89:[85, 47, 133], Operations: ['7*19=133'] Exploring Operation: 133-47=86, Resulting Numbers: [85, 86] Generated Node #0,0,0: 89:[85, 86] Operation: 133-47=86 Exploring Operation: 85+47=132, Resulting Numbers: [133, 132] Generated Node #0,0,1: 89:[133, 132] Operation: 85+47=132 Exploring Operation: 133-85=48, Resulting Numbers: [47, 48] Generated Node #0,0,2: 89:[47, 48] Operation: 133-85=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[85, 86], Operations: ['7*19=133', '133-47=86'] Exploring Operation: 85+86=171, Resulting Numbers: [171] 171,89 unequal: No Solution Exploring Operation: 85*86=7310, Resulting Numbers: [7310] 7310,89 unequal: No Solution Exploring Operation: 86-85=1, Resulting Numbers: [1] 1,89 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:[47, 48], Operations: ['7*19=133', '133-85=48'] Exploring Operation: 47*48=2256, Resulting Numbers: [2256] 2256,89 unequal: No Solution Exploring Operation: 48-47=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 47+48=95, Resulting Numbers: [95] 95,89 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:[133, 132], Operations: ['7*19=133', '85+47=132'] Exploring Operation: 133*132=17556, Resulting Numbers: [17556] 17556,89 unequal: No Solution Exploring Operation: 133-132=1, Resulting Numbers: [1] 1,89 unequal: No Solution Exploring Operation: 133+132=265, Resulting Numbers: [265] 265,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[85, 47, 26], Operations: ['7+19=26'] Exploring Operation: 85-26=59, Resulting Numbers: [47, 59] Generated Node #0,1,0: 89:[47, 59] Operation: 85-26=59 Exploring Operation: 47+26=73, Resulting Numbers: [85, 73] Generated Node #0,1,1: 89:[85, 73] Operation: 47+26=73 Exploring Operation: 85+26=111, Resulting Numbers: [47, 111] Generated Node #0,1,2: 89:[47, 111] Operation: 85+26=111 Moving to Node #0,2 Current State: 89:[85, 19, 54], Operations: ['7+47=54'] Exploring Operation: 85-19=66, Resulting Numbers: [54, 66] Generated Node #0,2,0: 89:[54, 66] Operation: 85-19=66 Exploring Operation: 19+54=73, Resulting Numbers: [85, 73] Generated Node #0,2,1: 89:[85, 73] Operation: 19+54=73 Exploring Operation: 85+19=104, Resulting Numbers: [54, 104] Generated Node #0,2,2: 89:[54, 104] Operation: 85+19=104 Moving to Node #0,1,1 Current State: 89:[85, 73], Operations: ['7+19=26', '47+26=73'] Exploring Operation: 85+73=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 85*73=6205, Resulting Numbers: [6205] 6205,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[85, 73], Operations: ['7+47=54', '19+54=73'] Exploring Operation: 85+73=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 85*73=6205, Resulting Numbers: [6205] 6205,89 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[54, 104], Operations: ['7+47=54', '85+19=104'] Exploring Operation: 54*104=5616, Resulting Numbers: [5616] 5616,89 unequal: No Solution Exploring Operation: 104-54=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 54+104=158, Resulting Numbers: [158] 158,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[54, 66], Operations: ['7+47=54', '85-19=66'] Exploring Operation: 54+66=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 66-54=12, Resulting Numbers: [12] 12,89 unequal: No Solution Exploring Operation: 54*66=3564, Resulting Numbers: [3564] 3564,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[47, 111], Operations: ['7+19=26', '85+26=111'] Exploring Operation: 111-47=64, Resulting Numbers: [64] 64,89 unequal: No Solution Exploring Operation: 47+111=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 47*111=5217, Resulting Numbers: [5217] 5217,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[47, 59], Operations: ['7+19=26', '85-26=59'] Exploring Operation: 47+59=106, Resulting Numbers: [106] 106,89 unequal: No Solution Exploring Operation: 47*59=2773, Resulting Numbers: [2773] 2773,89 unequal: No Solution Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,89 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 93, 83, 47, 34 ]
23
[ "93-83=10", "47-34=13", "10+13=23" ]
Current State: 23:[93, 83, 47, 34], Operations: [] Exploring Operation: 93-83=10, Resulting Numbers: [47, 34, 10] Generated Node #2: [47, 34, 10] from Operation: 93-83=10 Current State: 23:[47, 34, 10], Operations: ['93-83=10'] Exploring Operation: 47-34=13, Resulting Numbers: [10, 13] Generated Node #3: [10, 13] from Operation: 47-34=13 Current State: 23:[10, 13], Operations: ['93-83=10', '47-34=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[93, 83, 47, 34], Operations: [] Exploring Operation: 93-83=10, Resulting Numbers: [47, 34, 10] Generated Node #0,0: 23:[47, 34, 10] Operation: 93-83=10 Moving to Node #0,0 Current State: 23:[47, 34, 10], Operations: ['93-83=10'] Exploring Operation: 47-34=13, Resulting Numbers: [10, 13] Generated Node #0,0,0: 23:[10, 13] Operation: 47-34=13 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[10, 13], Operations: ['93-83=10', '47-34=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[93, 83, 47, 34], Operations: [] Exploring Operation: 93-83=10, Resulting Numbers: [47, 34, 10] Generated Node #0,0: 23:[47, 34, 10] Operation: 93-83=10 Moving to Node #0,0 Current State: 23:[47, 34, 10], Operations: ['93-83=10'] Exploring Operation: 47-34=13, Resulting Numbers: [10, 13] Generated Node #0,0,0: 23:[10, 13] Operation: 47-34=13 Moving to Node #0,0,0 Current State: 23:[10, 13], Operations: ['93-83=10', '47-34=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 12, 69, 69, 30 ]
18
[ "12+69=81", "69+30=99", "99-81=18" ]
Current State: 18:[12, 69, 69, 30], Operations: [] Exploring Operation: 12+69=81, Resulting Numbers: [30, 81] Generated Node #2: [30, 81] from Operation: 12+69=81 Current State: 18:[30, 81], Operations: ['12+69=81'] Exploring Operation: 69+30=99, Resulting Numbers: [81, 99] Generated Node #3: [81, 99] from Operation: 69+30=99 Current State: 18:[81, 99], Operations: ['12+69=81', '69+30=99'] Exploring Operation: 99-81=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[12, 69, 69, 30], Operations: [] Exploring Operation: 69-69=0, Resulting Numbers: [12, 30, 0] Generated Node #0,0: 18:[12, 30, 0] Operation: 69-69=0 Exploring Operation: 69-30=39, Resulting Numbers: [12, 69, 39] Generated Node #0,1: 18:[12, 69, 39] Operation: 69-30=39 Exploring Operation: 69/69=1, Resulting Numbers: [12, 30, 1] Generated Node #0,2: 18:[12, 30, 1] Operation: 69/69=1 Exploring Operation: 69-30=39, Resulting Numbers: [12, 69, 39] Generated Node #0,3: 18:[12, 69, 39] Operation: 69-30=39 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[12, 30, 1], Operations: ['69/69=1'] Exploring Operation: 30-12=18, Resulting Numbers: [1, 18] Generated Node #0,2,0: 18:[1, 18] Operation: 30-12=18 Exploring Operation: 12*1=12, Resulting Numbers: [30, 12] Generated Node #0,2,1: 18:[30, 12] Operation: 12*1=12 Exploring Operation: 12-1=11, Resulting Numbers: [30, 11] Generated Node #0,2,2: 18:[30, 11] Operation: 12-1=11 Exploring Operation: 30-1=29, Resulting Numbers: [12, 29] Generated Node #0,2,3: 18:[12, 29] Operation: 30-1=29 Moving to Node #0,2,0 Current State: 18:[1, 18], Operations: ['69/69=1', '30-12=18'] Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[12, 69, 69, 30], Operations: [] Exploring Operation: 69/69=1, Resulting Numbers: [12, 30, 1] Generated Node #0,2: 18:[12, 30, 1] Operation: 69/69=1 Moving to Node #0,2 Current State: 18:[12, 30, 1], Operations: ['69/69=1'] Exploring Operation: 30-12=18, Resulting Numbers: [1, 18] Generated Node #0,2,0: 18:[1, 18] Operation: 30-12=18 Moving to Node #0,2,0 Current State: 18:[1, 18], Operations: ['69/69=1', '30-12=18'] Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 54, 67, 95, 40 ]
97
[ "67-40=27", "54/27=2", "95+2=97" ]
Current State: 97:[54, 67, 95, 40], Operations: [] Exploring Operation: 67-40=27, Resulting Numbers: [54, 95, 27] Generated Node #2: [54, 95, 27] from Operation: 67-40=27 Current State: 97:[54, 95, 27], Operations: ['67-40=27'] Exploring Operation: 54/27=2, Resulting Numbers: [95, 2] Generated Node #3: [95, 2] from Operation: 54/27=2 Current State: 97:[95, 2], Operations: ['67-40=27', '54/27=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[54, 67, 95, 40], Operations: [] Exploring Operation: 54+40=94, Resulting Numbers: [67, 95, 94] Generated Node #0,0: 97:[67, 95, 94] Operation: 54+40=94 Moving to Node #0,0 Current State: 97:[67, 95, 94], Operations: ['54+40=94'] Exploring Operation: 67+94=161, Resulting Numbers: [95, 161] Generated Node #0,0,0: 97:[95, 161] Operation: 67+94=161 Moving to Node #0,0,0 Current State: 97:[95, 161], Operations: ['54+40=94', '67+94=161'] Exploring Operation: 161-95=66, Resulting Numbers: [66] 66,97 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 33, 77, 7, 48 ]
70
[ "33+48=81", "77/7=11", "81-11=70" ]
Current State: 70:[33, 77, 7, 48], Operations: [] Exploring Operation: 33+48=81, Resulting Numbers: [77, 7, 81] Generated Node #2: [77, 7, 81] from Operation: 33+48=81 Current State: 70:[77, 7, 81], Operations: ['33+48=81'] Exploring Operation: 77/7=11, Resulting Numbers: [81, 11] Generated Node #3: [81, 11] from Operation: 77/7=11 Current State: 70:[81, 11], Operations: ['33+48=81', '77/7=11'] Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[33, 77, 7, 48], Operations: [] Exploring Operation: 77-48=29, Resulting Numbers: [33, 7, 29] Generated Node #0,0: 70:[33, 7, 29] Operation: 77-48=29 Exploring Operation: 48-33=15, Resulting Numbers: [77, 7, 15] Generated Node #0,1: 70:[77, 7, 15] Operation: 48-33=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[33, 7, 29], Operations: ['77-48=29'] Exploring Operation: 7+29=36, Resulting Numbers: [33, 36] Generated Node #0,0,0: 70:[33, 36] Operation: 7+29=36 Exploring Operation: 33-29=4, Resulting Numbers: [7, 4] Generated Node #0,0,1: 70:[7, 4] Operation: 33-29=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 70:[7, 4], Operations: ['77-48=29', '33-29=4'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[33, 36], Operations: ['77-48=29', '7+29=36'] Exploring Operation: 33+36=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[77, 7, 15], Operations: ['48-33=15'] Exploring Operation: 77-7=70, Resulting Numbers: [15, 70] Generated Node #0,1,0: 70:[15, 70] Operation: 77-7=70 Exploring Operation: 77/7=11, Resulting Numbers: [15, 11] Generated Node #0,1,1: 70:[15, 11] Operation: 77/7=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 70:[15, 70], Operations: ['48-33=15', '77-7=70'] Exploring Operation: 15+70=85, Resulting Numbers: [85] 85,70 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[15, 11], Operations: ['48-33=15', '77/7=11'] Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 91, 88, 88, 73 ]
73
[ "88-88=0", "91*0=0", "73+0=73" ]
Current State: 73:[91, 88, 88, 73], Operations: [] Exploring Operation: 88-88=0, Resulting Numbers: [91, 73, 0] Generated Node #2: [91, 73, 0] from Operation: 88-88=0 Current State: 73:[91, 73, 0], Operations: ['88-88=0'] Exploring Operation: 91*0=0, Resulting Numbers: [73, 0] Generated Node #3: [73, 0] from Operation: 91*0=0 Current State: 73:[73, 0], Operations: ['88-88=0', '91*0=0'] Exploring Operation: 73+0=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[91, 88, 88, 73], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [88, 73, 3] Generated Node #0,0: 73:[88, 73, 3] Operation: 91-88=3 Exploring Operation: 91-88=3, Resulting Numbers: [88, 73, 3] Generated Node #0,1: 73:[88, 73, 3] Operation: 91-88=3 Moving to Node #0,0 Current State: 73:[88, 73, 3], Operations: ['91-88=3'] Exploring Operation: 88+3=91, Resulting Numbers: [73, 91] Generated Node #0,0,0: 73:[73, 91] Operation: 88+3=91 Exploring Operation: 88-3=85, Resulting Numbers: [73, 85] Generated Node #0,0,1: 73:[73, 85] Operation: 88-3=85 Moving to Node #0,1 Current State: 73:[88, 73, 3], Operations: ['91-88=3'] Exploring Operation: 88-3=85, Resulting Numbers: [73, 85] Generated Node #0,1,0: 73:[73, 85] Operation: 88-3=85 Exploring Operation: 88+3=91, Resulting Numbers: [73, 91] Generated Node #0,1,1: 73:[73, 91] Operation: 88+3=91 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[73, 85], Operations: ['91-88=3', '88-3=85'] Exploring Operation: 73+85=158, Resulting Numbers: [158] 158,73 unequal: No Solution Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[73, 91], Operations: ['91-88=3', '88+3=91'] Exploring Operation: 73+91=164, Resulting Numbers: [164] 164,73 unequal: No Solution Exploring Operation: 91-73=18, Resulting Numbers: [18] 18,73 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: 73:[73, 85], Operations: ['91-88=3', '88-3=85'] Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,73 unequal: No Solution Exploring Operation: 73+85=158, Resulting Numbers: [158] 158,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[73, 91], Operations: ['91-88=3', '88+3=91'] Exploring Operation: 73+91=164, Resulting Numbers: [164] 164,73 unequal: No Solution Exploring Operation: 91-73=18, Resulting Numbers: [18] 18,73 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 32, 76, 34, 48 ]
58
[ "76-32=44", "48-34=14", "44+14=58" ]
Current State: 58:[32, 76, 34, 48], Operations: [] Exploring Operation: 76-32=44, Resulting Numbers: [34, 48, 44] Generated Node #2: [34, 48, 44] from Operation: 76-32=44 Current State: 58:[34, 48, 44], Operations: ['76-32=44'] Exploring Operation: 48-34=14, Resulting Numbers: [44, 14] Generated Node #3: [44, 14] from Operation: 48-34=14 Current State: 58:[44, 14], Operations: ['76-32=44', '48-34=14'] Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[32, 76, 34, 48], Operations: [] Exploring Operation: 76-34=42, Resulting Numbers: [32, 48, 42] Generated Node #0,0: 58:[32, 48, 42] Operation: 76-34=42 Exploring Operation: 76-48=28, Resulting Numbers: [32, 34, 28] Generated Node #0,1: 58:[32, 34, 28] Operation: 76-48=28 Exploring Operation: 34-32=2, Resulting Numbers: [76, 48, 2] Generated Node #0,2: 58:[76, 48, 2] Operation: 34-32=2 Moving to Node #0,1 Current State: 58:[32, 34, 28], Operations: ['76-48=28'] Exploring Operation: 32-28=4, Resulting Numbers: [34, 4] Generated Node #0,1,0: 58:[34, 4] Operation: 32-28=4 Exploring Operation: 32+28=60, Resulting Numbers: [34, 60] Generated Node #0,1,1: 58:[34, 60] Operation: 32+28=60 Exploring Operation: 34-32=2, Resulting Numbers: [28, 2] Generated Node #0,1,2: 58:[28, 2] Operation: 34-32=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 58:[28, 2], Operations: ['76-48=28', '34-32=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,58 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:[34, 4], Operations: ['76-48=28', '32-28=4'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,58 unequal: No Solution Exploring Operation: 34*4=136, Resulting Numbers: [136] 136,58 unequal: No Solution Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,58 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 #0,1,1 Current State: 58:[34, 60], Operations: ['76-48=28', '32+28=60'] Exploring Operation: 34*60=2040, Resulting Numbers: [2040] 2040,58 unequal: No Solution Exploring Operation: 60-34=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 34+60=94, Resulting Numbers: [94] 94,58 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:[32, 48, 42], Operations: ['76-34=42'] Exploring Operation: 42-32=10, Resulting Numbers: [48, 10] Generated Node #0,0,0: 58:[48, 10] Operation: 42-32=10 Exploring Operation: 48-42=6, Resulting Numbers: [32, 6] Generated Node #0,0,1: 58:[32, 6] Operation: 48-42=6 Exploring Operation: 48-32=16, Resulting Numbers: [42, 16] Generated Node #0,0,2: 58:[42, 16] Operation: 48-32=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[32, 6], Operations: ['76-34=42', '48-42=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,58 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[48, 10], Operations: ['76-34=42', '42-32=10'] Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,58 unequal: No Solution Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[32, 76, 34, 48], Operations: [] Exploring Operation: 76-34=42, Resulting Numbers: [32, 48, 42] Generated Node #0,0: 58:[32, 48, 42] Operation: 76-34=42 Moving to Node #0,0 Current State: 58:[32, 48, 42], Operations: ['76-34=42'] Exploring Operation: 42-32=10, Resulting Numbers: [48, 10] Generated Node #0,0,0: 58:[48, 10] Operation: 42-32=10 Moving to Node #0,0,0 Current State: 58:[48, 10], Operations: ['76-34=42', '42-32=10'] Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 94, 21, 32, 94 ]
10
[ "94/94=1", "32-21=11", "11-1=10" ]
Current State: 10:[94, 21, 32, 94], Operations: [] Exploring Operation: 94/94=1, Resulting Numbers: [21, 32, 1] Generated Node #2: [21, 32, 1] from Operation: 94/94=1 Current State: 10:[21, 32, 1], Operations: ['94/94=1'] Exploring Operation: 32-21=11, Resulting Numbers: [1, 11] Generated Node #3: [1, 11] from Operation: 32-21=11 Current State: 10:[1, 11], Operations: ['94/94=1', '32-21=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[94, 21, 32, 94], Operations: [] Exploring Operation: 94/94=1, Resulting Numbers: [21, 32, 1] Generated Node #0,0: 10:[21, 32, 1] Operation: 94/94=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[21, 32, 1], Operations: ['94/94=1'] Exploring Operation: 32-21=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 10:[1, 11] Operation: 32-21=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[1, 11], Operations: ['94/94=1', '32-21=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[94, 21, 32, 94], Operations: [] Exploring Operation: 94/94=1, Resulting Numbers: [21, 32, 1] Generated Node #0,0: 10:[21, 32, 1] Operation: 94/94=1 Moving to Node #0,0 Current State: 10:[21, 32, 1], Operations: ['94/94=1'] Exploring Operation: 32-21=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 10:[1, 11] Operation: 32-21=11 Moving to Node #0,0,0 Current State: 10:[1, 11], Operations: ['94/94=1', '32-21=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 81, 4, 92, 40 ]
84
[ "92-81=11", "4*11=44", "40+44=84" ]
Current State: 84:[81, 4, 92, 40], Operations: [] Exploring Operation: 92-81=11, Resulting Numbers: [4, 40, 11] Generated Node #2: [4, 40, 11] from Operation: 92-81=11 Current State: 84:[4, 40, 11], Operations: ['92-81=11'] Exploring Operation: 4*11=44, Resulting Numbers: [40, 44] Generated Node #3: [40, 44] from Operation: 4*11=44 Current State: 84:[40, 44], Operations: ['92-81=11', '4*11=44'] Exploring Operation: 40+44=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[81, 4, 92, 40], Operations: [] Exploring Operation: 92-4=88, Resulting Numbers: [81, 40, 88] Generated Node #0,0: 84:[81, 40, 88] Operation: 92-4=88 Exploring Operation: 92-81=11, Resulting Numbers: [4, 40, 11] Generated Node #0,1: 84:[4, 40, 11] Operation: 92-81=11 Exploring Operation: 81-40=41, Resulting Numbers: [4, 92, 41] Generated Node #0,2: 84:[4, 92, 41] Operation: 81-40=41 Exploring Operation: 92/4=23, Resulting Numbers: [81, 40, 23] Generated Node #0,3: 84:[81, 40, 23] Operation: 92/4=23 Moving to Node #0,1 Current State: 84:[4, 40, 11], Operations: ['92-81=11'] Exploring Operation: 11-4=7, Resulting Numbers: [40, 7] Generated Node #0,1,0: 84:[40, 7] Operation: 11-4=7 Exploring Operation: 40-11=29, Resulting Numbers: [4, 29] Generated Node #0,1,1: 84:[4, 29] Operation: 40-11=29 Exploring Operation: 40/4=10, Resulting Numbers: [11, 10] Generated Node #0,1,2: 84:[11, 10] Operation: 40/4=10 Exploring Operation: 4+40=44, Resulting Numbers: [11, 44] Generated Node #0,1,3: 84:[11, 44] Operation: 4+40=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[4, 29], Operations: ['92-81=11', '40-11=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,84 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[40, 7], Operations: ['92-81=11', '11-4=7'] Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,84 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[11, 10], Operations: ['92-81=11', '40/4=10'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 11*10=110, Resulting Numbers: [110] 110,84 unequal: No Solution Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[11, 44], Operations: ['92-81=11', '4+40=44'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,84 unequal: No Solution Exploring Operation: 11*44=484, Resulting Numbers: [484] 484,84 unequal: No Solution Exploring Operation: 11+44=55, Resulting Numbers: [55] 55,84 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: 84:[81, 40, 23], Operations: ['92/4=23'] Exploring Operation: 81-23=58, Resulting Numbers: [40, 58] Generated Node #0,3,0: 84:[40, 58] Operation: 81-23=58 Exploring Operation: 81+23=104, Resulting Numbers: [40, 104] Generated Node #0,3,1: 84:[40, 104] Operation: 81+23=104 Exploring Operation: 81-40=41, Resulting Numbers: [23, 41] Generated Node #0,3,2: 84:[23, 41] Operation: 81-40=41 Exploring Operation: 40-23=17, Resulting Numbers: [81, 17] Generated Node #0,3,3: 84:[81, 17] Operation: 40-23=17 Moving to Node #0,2 Current State: 84:[4, 92, 41], Operations: ['81-40=41'] Exploring Operation: 92-41=51, Resulting Numbers: [4, 51] Generated Node #0,2,0: 84:[4, 51] Operation: 92-41=51 Exploring Operation: 92/4=23, Resulting Numbers: [41, 23] Generated Node #0,2,1: 84:[41, 23] Operation: 92/4=23 Exploring Operation: 4+41=45, Resulting Numbers: [92, 45] Generated Node #0,2,2: 84:[92, 45] Operation: 4+41=45 Exploring Operation: 92-4=88, Resulting Numbers: [41, 88] Generated Node #0,2,3: 84:[41, 88] Operation: 92-4=88 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[41, 23], Operations: ['81-40=41', '92/4=23'] Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,84 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[41, 88], Operations: ['81-40=41', '92-4=88'] Exploring Operation: 41+88=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 41*88=3608, Resulting Numbers: [3608] 3608,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[4, 51], Operations: ['81-40=41', '92-41=51'] Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,84 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[92, 45], Operations: ['81-40=41', '4+41=45'] Exploring Operation: 92*45=4140, Resulting Numbers: [4140] 4140,84 unequal: No Solution Exploring Operation: 92+45=137, Resulting Numbers: [137] 137,84 unequal: No Solution Exploring Operation: 92-45=47, Resulting Numbers: [47] 47,84 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: 84:[81, 40, 88], Operations: ['92-4=88'] Exploring Operation: 81-40=41, Resulting Numbers: [88, 41] Generated Node #0,0,0: 84:[88, 41] Operation: 81-40=41 Exploring Operation: 88-40=48, Resulting Numbers: [81, 48] Generated Node #0,0,1: 84:[81, 48] Operation: 88-40=48 Exploring Operation: 88-81=7, Resulting Numbers: [40, 7] Generated Node #0,0,2: 84:[40, 7] Operation: 88-81=7 Exploring Operation: 81+40=121, Resulting Numbers: [88, 121] Generated Node #0,0,3: 84:[88, 121] Operation: 81+40=121 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[40, 7], Operations: ['92-4=88', '88-81=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,84 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[88, 41], Operations: ['92-4=88', '81-40=41'] Exploring Operation: 88-41=47, Resulting Numbers: [47] 47,84 unequal: No Solution Exploring Operation: 88*41=3608, Resulting Numbers: [3608] 3608,84 unequal: No Solution Exploring Operation: 88+41=129, Resulting Numbers: [129] 129,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[81, 48], Operations: ['92-4=88', '88-40=48'] Exploring Operation: 81-48=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 81+48=129, Resulting Numbers: [129] 129,84 unequal: No Solution Exploring Operation: 81*48=3888, Resulting Numbers: [3888] 3888,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[88, 121], Operations: ['92-4=88', '81+40=121'] Exploring Operation: 88+121=209, Resulting Numbers: [209] 209,84 unequal: No Solution Exploring Operation: 88*121=10648, Resulting Numbers: [10648] 10648,84 unequal: No Solution Exploring Operation: 121-88=33, Resulting Numbers: [33] 33,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 84:[23, 41], Operations: ['92/4=23', '81-40=41'] Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 23*41=943, Resulting Numbers: [943] 943,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[81, 17], Operations: ['92/4=23', '40-23=17'] Exploring Operation: 81-17=64, Resulting Numbers: [64] 64,84 unequal: No Solution Exploring Operation: 81+17=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 81*17=1377, Resulting Numbers: [1377] 1377,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[40, 58], Operations: ['92/4=23', '81-23=58'] Exploring Operation: 40*58=2320, Resulting Numbers: [2320] 2320,84 unequal: No Solution Exploring Operation: 40+58=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[40, 104], Operations: ['92/4=23', '81+23=104'] Exploring Operation: 40*104=4160, Resulting Numbers: [4160] 4160,84 unequal: No Solution Exploring Operation: 40+104=144, Resulting Numbers: [144] 144,84 unequal: No Solution Exploring Operation: 104-40=64, Resulting Numbers: [64] 64,84 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 3, 22, 20, 94 ]
100
[ "22-20=2", "3*2=6", "94+6=100" ]
Current State: 100:[3, 22, 20, 94], Operations: [] Exploring Operation: 22-20=2, Resulting Numbers: [3, 94, 2] Generated Node #2: [3, 94, 2] from Operation: 22-20=2 Current State: 100:[3, 94, 2], Operations: ['22-20=2'] Exploring Operation: 3*2=6, Resulting Numbers: [94, 6] Generated Node #3: [94, 6] from Operation: 3*2=6 Current State: 100:[94, 6], Operations: ['22-20=2', '3*2=6'] Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[3, 22, 20, 94], Operations: [] Exploring Operation: 22-3=19, Resulting Numbers: [20, 94, 19] Generated Node #0,0: 100:[20, 94, 19] Operation: 22-3=19 Exploring Operation: 3+22=25, Resulting Numbers: [20, 94, 25] Generated Node #0,1: 100:[20, 94, 25] Operation: 3+22=25 Exploring Operation: 3+94=97, Resulting Numbers: [22, 20, 97] Generated Node #0,2: 100:[22, 20, 97] Operation: 3+94=97 Exploring Operation: 22-20=2, Resulting Numbers: [3, 94, 2] Generated Node #0,3: 100:[3, 94, 2] Operation: 22-20=2 Moving to Node #0,2 Current State: 100:[22, 20, 97], Operations: ['3+94=97'] Exploring Operation: 20+97=117, Resulting Numbers: [22, 117] Generated Node #0,2,0: 100:[22, 117] Operation: 20+97=117 Exploring Operation: 22+97=119, Resulting Numbers: [20, 119] Generated Node #0,2,1: 100:[20, 119] Operation: 22+97=119 Exploring Operation: 22+20=42, Resulting Numbers: [97, 42] Generated Node #0,2,2: 100:[97, 42] Operation: 22+20=42 Exploring Operation: 22-20=2, Resulting Numbers: [97, 2] Generated Node #0,2,3: 100:[97, 2] Operation: 22-20=2 Moving to Node #0,1 Current State: 100:[20, 94, 25], Operations: ['3+22=25'] Exploring Operation: 20+94=114, Resulting Numbers: [25, 114] Generated Node #0,1,0: 100:[25, 114] Operation: 20+94=114 Exploring Operation: 94+25=119, Resulting Numbers: [20, 119] Generated Node #0,1,1: 100:[20, 119] Operation: 94+25=119 Exploring Operation: 20+25=45, Resulting Numbers: [94, 45] Generated Node #0,1,2: 100:[94, 45] Operation: 20+25=45 Exploring Operation: 25-20=5, Resulting Numbers: [94, 5] Generated Node #0,1,3: 100:[94, 5] Operation: 25-20=5 Moving to Node #0,3 Current State: 100:[3, 94, 2], Operations: ['22-20=2'] Exploring Operation: 3+2=5, Resulting Numbers: [94, 5] Generated Node #0,3,0: 100:[94, 5] Operation: 3+2=5 Exploring Operation: 94/2=47, Resulting Numbers: [3, 47] Generated Node #0,3,1: 100:[3, 47] Operation: 94/2=47 Exploring Operation: 94+2=96, Resulting Numbers: [3, 96] Generated Node #0,3,2: 100:[3, 96] Operation: 94+2=96 Exploring Operation: 3+94=97, Resulting Numbers: [2, 97] Generated Node #0,3,3: 100:[2, 97] Operation: 3+94=97 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 100:[2, 97], Operations: ['22-20=2', '3+94=97'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,100 unequal: No Solution Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 2*97=194, Resulting Numbers: [194] 194,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 100:[3, 47], Operations: ['22-20=2', '94/2=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,100 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[3, 96], Operations: ['22-20=2', '94+2=96'] Exploring Operation: 3*96=288, Resulting Numbers: [288] 288,100 unequal: No Solution Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,100 unequal: No Solution Exploring Operation: 3+96=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 100:[94, 5], Operations: ['22-20=2', '3+2=5'] Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,100 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,100 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: 100:[20, 94, 19], Operations: ['22-3=19'] Exploring Operation: 94+19=113, Resulting Numbers: [20, 113] Generated Node #0,0,0: 100:[20, 113] Operation: 94+19=113 Exploring Operation: 20+19=39, Resulting Numbers: [94, 39] Generated Node #0,0,1: 100:[94, 39] Operation: 20+19=39 Exploring Operation: 20+94=114, Resulting Numbers: [19, 114] Generated Node #0,0,2: 100:[19, 114] Operation: 20+94=114 Exploring Operation: 20-19=1, Resulting Numbers: [94, 1] Generated Node #0,0,3: 100:[94, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 100:[94, 1], Operations: ['22-3=19', '20-19=1'] Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,100 unequal: No Solution Exploring Operation: 94+1=95, Resulting Numbers: [95] 95,100 unequal: No Solution Exploring Operation: 94-1=93, Resulting Numbers: [93] 93,100 unequal: No Solution Exploring Operation: 94/1=94, Resulting Numbers: [94] 94,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[20, 113], Operations: ['22-3=19', '94+19=113'] Exploring Operation: 113-20=93, Resulting Numbers: [93] 93,100 unequal: No Solution Exploring Operation: 20*113=2260, Resulting Numbers: [2260] 2260,100 unequal: No Solution Exploring Operation: 20+113=133, Resulting Numbers: [133] 133,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 100:[19, 114], Operations: ['22-3=19', '20+94=114'] Exploring Operation: 19+114=133, Resulting Numbers: [133] 133,100 unequal: No Solution Exploring Operation: 114-19=95, Resulting Numbers: [95] 95,100 unequal: No Solution Exploring Operation: 114/19=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 19*114=2166, Resulting Numbers: [2166] 2166,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 100:[94, 39], Operations: ['22-3=19', '20+19=39'] Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,100 unequal: No Solution Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,100 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: 100:[97, 2], Operations: ['3+94=97', '22-20=2'] Exploring Operation: 97*2=194, Resulting Numbers: [194] 194,100 unequal: No Solution Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,100 unequal: No Solution Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[94, 5], Operations: ['3+22=25', '25-20=5'] Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,100 unequal: No Solution Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,100 unequal: No Solution Moving to Node #0,1,2 Current State: 100:[94, 45], Operations: ['3+22=25', '20+25=45'] Exploring Operation: 94*45=4230, Resulting Numbers: [4230] 4230,100 unequal: No Solution Exploring Operation: 94+45=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 94-45=49, Resulting Numbers: [49] 49,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[97, 42], Operations: ['3+94=97', '22+20=42'] Exploring Operation: 97+42=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 97*42=4074, Resulting Numbers: [4074] 4074,100 unequal: No Solution Exploring Operation: 97-42=55, Resulting Numbers: [55] 55,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[25, 114], Operations: ['3+22=25', '20+94=114'] Exploring Operation: 114-25=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 25+114=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 25*114=2850, Resulting Numbers: [2850] 2850,100 unequal: No Solution Moving to Node #0,2,0 Current State: 100:[22, 117], Operations: ['3+94=97', '20+97=117'] Exploring Operation: 117-22=95, Resulting Numbers: [95] 95,100 unequal: No Solution Exploring Operation: 22*117=2574, Resulting Numbers: [2574] 2574,100 unequal: No Solution Exploring Operation: 22+117=139, Resulting Numbers: [139] 139,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[20, 119], Operations: ['3+22=25', '94+25=119'] Exploring Operation: 20+119=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 20*119=2380, Resulting Numbers: [2380] 2380,100 unequal: No Solution Exploring Operation: 119-20=99, Resulting Numbers: [99] 99,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[20, 119], Operations: ['3+94=97', '22+97=119'] Exploring Operation: 20+119=139, Resulting Numbers: [139] 139,100 unequal: No Solution Exploring Operation: 119-20=99, Resulting Numbers: [99] 99,100 unequal: No Solution Exploring Operation: 20*119=2380, Resulting Numbers: [2380] 2380,100 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 63, 8, 15, 57 ]
51
[ "63-15=48", "48/8=6", "57-6=51" ]
Current State: 51:[63, 8, 15, 57], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [8, 57, 48] Generated Node #2: [8, 57, 48] from Operation: 63-15=48 Current State: 51:[8, 57, 48], Operations: ['63-15=48'] Exploring Operation: 48/8=6, Resulting Numbers: [57, 6] Generated Node #3: [57, 6] from Operation: 48/8=6 Current State: 51:[57, 6], Operations: ['63-15=48', '48/8=6'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[63, 8, 15, 57], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [8, 57, 48] Generated Node #0,0: 51:[8, 57, 48] Operation: 63-15=48 Exploring Operation: 63-8=55, Resulting Numbers: [15, 57, 55] Generated Node #0,1: 51:[15, 57, 55] Operation: 63-8=55 Exploring Operation: 63-57=6, Resulting Numbers: [8, 15, 6] Generated Node #0,2: 51:[8, 15, 6] Operation: 63-57=6 Moving to Node #0,2 Current State: 51:[8, 15, 6], Operations: ['63-57=6'] Exploring Operation: 8*6=48, Resulting Numbers: [15, 48] Generated Node #0,2,0: 51:[15, 48] Operation: 8*6=48 Exploring Operation: 8-6=2, Resulting Numbers: [15, 2] Generated Node #0,2,1: 51:[15, 2] Operation: 8-6=2 Exploring Operation: 8+6=14, Resulting Numbers: [15, 14] Generated Node #0,2,2: 51:[15, 14] Operation: 8+6=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 51:[15, 2], Operations: ['63-57=6', '8-6=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,51 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,51 unequal: No Solution No 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: 51:[15, 48], Operations: ['63-57=6', '8*6=48'] Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,51 unequal: No Solution Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,51 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,51 unequal: No Solution No 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: 51:[15, 14], Operations: ['63-57=6', '8+6=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,51 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,51 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: 51:[15, 57, 55], Operations: ['63-8=55'] Exploring Operation: 57-55=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 51:[15, 2] Operation: 57-55=2 Exploring Operation: 55-15=40, Resulting Numbers: [57, 40] Generated Node #0,1,1: 51:[57, 40] Operation: 55-15=40 Exploring Operation: 57-15=42, Resulting Numbers: [55, 42] Generated Node #0,1,2: 51:[55, 42] Operation: 57-15=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 51:[15, 2], Operations: ['63-8=55', '57-55=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,51 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,51 unequal: No Solution No 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: 51:[55, 42], Operations: ['63-8=55', '57-15=42'] Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,51 unequal: No Solution Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,51 unequal: No Solution No 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: 51:[57, 40], Operations: ['63-8=55', '55-15=40'] Exploring Operation: 57+40=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 57-40=17, Resulting Numbers: [17] 17,51 unequal: No Solution Exploring Operation: 57*40=2280, Resulting Numbers: [2280] 2280,51 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: 51:[8, 57, 48], Operations: ['63-15=48'] Exploring Operation: 48/8=6, Resulting Numbers: [57, 6] Generated Node #0,0,0: 51:[57, 6] Operation: 48/8=6 Exploring Operation: 8+48=56, Resulting Numbers: [57, 56] Generated Node #0,0,1: 51:[57, 56] Operation: 8+48=56 Exploring Operation: 57-8=49, Resulting Numbers: [48, 49] Generated Node #0,0,2: 51:[48, 49] Operation: 57-8=49 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 51:[48, 49], Operations: ['63-15=48', '57-8=49'] Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,51 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,51 unequal: No Solution Exploring Operation: 48*49=2352, Resulting Numbers: [2352] 2352,51 unequal: No Solution No 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: 51:[57, 6], Operations: ['63-15=48', '48/8=6'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[63, 8, 15, 57], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [8, 57, 48] Generated Node #0,0: 51:[8, 57, 48] Operation: 63-15=48 Moving to Node #0,0 Current State: 51:[8, 57, 48], Operations: ['63-15=48'] Exploring Operation: 48/8=6, Resulting Numbers: [57, 6] Generated Node #0,0,0: 51:[57, 6] Operation: 48/8=6 Moving to Node #0,0,0 Current State: 51:[57, 6], Operations: ['63-15=48', '48/8=6'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_3
sum_heuristic
[ 28, 56, 96, 78 ]
36
[ "56/28=2", "96-78=18", "2*18=36" ]
Current State: 36:[28, 56, 96, 78], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [96, 78, 2] Generated Node #2: [96, 78, 2] from Operation: 56/28=2 Current State: 36:[96, 78, 2], Operations: ['56/28=2'] Exploring Operation: 96-78=18, Resulting Numbers: [2, 18] Generated Node #3: [2, 18] from Operation: 96-78=18 Current State: 36:[2, 18], Operations: ['56/28=2', '96-78=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[28, 56, 96, 78], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [28, 56, 18] Generated Node #0,0: 36:[28, 56, 18] Operation: 96-78=18 Exploring Operation: 96-56=40, Resulting Numbers: [28, 78, 40] Generated Node #0,1: 36:[28, 78, 40] Operation: 96-56=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[28, 56, 18], Operations: ['96-78=18'] Exploring Operation: 56-28=28, Resulting Numbers: [18, 28] Generated Node #0,0,0: 36:[18, 28] Operation: 56-28=28 Exploring Operation: 56/28=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 36:[18, 2] Operation: 56/28=2 Moving to Node #0,0,1 Current State: 36:[18, 2], Operations: ['96-78=18', '56/28=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,36 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[28, 56, 96, 78], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [28, 56, 18] Generated Node #0,0: 36:[28, 56, 18] Operation: 96-78=18 Moving to Node #0,0 Current State: 36:[28, 56, 18], Operations: ['96-78=18'] Exploring Operation: 56/28=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 36:[18, 2] Operation: 56/28=2 Moving to Node #0,0,1 Current State: 36:[18, 2], Operations: ['96-78=18', '56/28=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 22, 66, 21, 80 ]
15
[ "66-22=44", "80-21=59", "59-44=15" ]
Current State: 15:[22, 66, 21, 80], Operations: [] Exploring Operation: 66-22=44, Resulting Numbers: [21, 80, 44] Generated Node #2: [21, 80, 44] from Operation: 66-22=44 Current State: 15:[21, 80, 44], Operations: ['66-22=44'] Exploring Operation: 80-21=59, Resulting Numbers: [44, 59] Generated Node #3: [44, 59] from Operation: 80-21=59 Current State: 15:[44, 59], Operations: ['66-22=44', '80-21=59'] Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[22, 66, 21, 80], Operations: [] Exploring Operation: 80-66=14, Resulting Numbers: [22, 21, 14] Generated Node #0,0: 15:[22, 21, 14] Operation: 80-66=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[22, 21, 14], Operations: ['80-66=14'] Exploring Operation: 22-21=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 15:[14, 1] Operation: 22-21=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[14, 1], Operations: ['80-66=14', '22-21=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[22, 66, 21, 80], Operations: [] Exploring Operation: 80-66=14, Resulting Numbers: [22, 21, 14] Generated Node #0,0: 15:[22, 21, 14] Operation: 80-66=14 Moving to Node #0,0 Current State: 15:[22, 21, 14], Operations: ['80-66=14'] Exploring Operation: 22-21=1, Resulting Numbers: [14, 1] Generated Node #0,0,0: 15:[14, 1] Operation: 22-21=1 Moving to Node #0,0,0 Current State: 15:[14, 1], Operations: ['80-66=14', '22-21=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 98, 85, 3, 29 ]
32
[ "98+85=183", "183/3=61", "61-29=32" ]
Current State: 32:[98, 85, 3, 29], Operations: [] Exploring Operation: 98+85=183, Resulting Numbers: [3, 29, 183] Generated Node #2: [3, 29, 183] from Operation: 98+85=183 Current State: 32:[3, 29, 183], Operations: ['98+85=183'] Exploring Operation: 183/3=61, Resulting Numbers: [29, 61] Generated Node #3: [29, 61] from Operation: 183/3=61 Current State: 32:[29, 61], Operations: ['98+85=183', '183/3=61'] Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[98, 85, 3, 29], Operations: [] Exploring Operation: 98-85=13, Resulting Numbers: [3, 29, 13] Generated Node #0,0: 32:[3, 29, 13] Operation: 98-85=13 Exploring Operation: 85-29=56, Resulting Numbers: [98, 3, 56] Generated Node #0,1: 32:[98, 3, 56] Operation: 85-29=56 Exploring Operation: 98-3=95, Resulting Numbers: [85, 29, 95] Generated Node #0,2: 32:[85, 29, 95] Operation: 98-3=95 Exploring Operation: 98-29=69, Resulting Numbers: [85, 3, 69] Generated Node #0,3: 32:[85, 3, 69] Operation: 98-29=69 Moving to Node #0,0 Current State: 32:[3, 29, 13], Operations: ['98-85=13'] Exploring Operation: 29-13=16, Resulting Numbers: [3, 16] Generated Node #0,0,0: 32:[3, 16] Operation: 29-13=16 Exploring Operation: 13-3=10, Resulting Numbers: [29, 10] Generated Node #0,0,1: 32:[29, 10] Operation: 13-3=10 Exploring Operation: 3+29=32, Resulting Numbers: [13, 32] Generated Node #0,0,2: 32:[13, 32] Operation: 3+29=32 Exploring Operation: 3+13=16, Resulting Numbers: [29, 16] Generated Node #0,0,3: 32:[29, 16] Operation: 3+13=16 Moving to Node #0,3 Current State: 32:[85, 3, 69], Operations: ['98-29=69'] Exploring Operation: 69/3=23, Resulting Numbers: [85, 23] Generated Node #0,3,0: 32:[85, 23] Operation: 69/3=23 Exploring Operation: 69-3=66, Resulting Numbers: [85, 66] Generated Node #0,3,1: 32:[85, 66] Operation: 69-3=66 Exploring Operation: 85-3=82, Resulting Numbers: [69, 82] Generated Node #0,3,2: 32:[69, 82] Operation: 85-3=82 Exploring Operation: 85-69=16, Resulting Numbers: [3, 16] Generated Node #0,3,3: 32:[3, 16] Operation: 85-69=16 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 32:[3, 16], Operations: ['98-29=69', '85-69=16'] Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,32 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 32:[85, 23], Operations: ['98-29=69', '69/3=23'] Exploring Operation: 85-23=62, Resulting Numbers: [62] 62,32 unequal: No Solution Exploring Operation: 85*23=1955, Resulting Numbers: [1955] 1955,32 unequal: No Solution Exploring Operation: 85+23=108, Resulting Numbers: [108] 108,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 32:[85, 66], Operations: ['98-29=69', '69-3=66'] Exploring Operation: 85-66=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 85*66=5610, Resulting Numbers: [5610] 5610,32 unequal: No Solution Exploring Operation: 85+66=151, Resulting Numbers: [151] 151,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 32:[69, 82], Operations: ['98-29=69', '85-3=82'] Exploring Operation: 69+82=151, Resulting Numbers: [151] 151,32 unequal: No Solution Exploring Operation: 82-69=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 69*82=5658, Resulting Numbers: [5658] 5658,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 32:[98, 3, 56], Operations: ['85-29=56'] Exploring Operation: 98-3=95, Resulting Numbers: [56, 95] Generated Node #0,1,0: 32:[56, 95] Operation: 98-3=95 Exploring Operation: 56-3=53, Resulting Numbers: [98, 53] Generated Node #0,1,1: 32:[98, 53] Operation: 56-3=53 Exploring Operation: 98-56=42, Resulting Numbers: [3, 42] Generated Node #0,1,2: 32:[3, 42] Operation: 98-56=42 Exploring Operation: 98+3=101, Resulting Numbers: [56, 101] Generated Node #0,1,3: 32:[56, 101] Operation: 98+3=101 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 32:[3, 42], Operations: ['85-29=56', '98-56=42'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,32 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,32 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 32:[56, 95], Operations: ['85-29=56', '98-3=95'] Exploring Operation: 56+95=151, Resulting Numbers: [151] 151,32 unequal: No Solution Exploring Operation: 95-56=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 56*95=5320, Resulting Numbers: [5320] 5320,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[98, 53], Operations: ['85-29=56', '56-3=53'] Exploring Operation: 98+53=151, Resulting Numbers: [151] 151,32 unequal: No Solution Exploring Operation: 98-53=45, Resulting Numbers: [45] 45,32 unequal: No Solution Exploring Operation: 98*53=5194, Resulting Numbers: [5194] 5194,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[56, 101], Operations: ['85-29=56', '98+3=101'] Exploring Operation: 56*101=5656, Resulting Numbers: [5656] 5656,32 unequal: No Solution Exploring Operation: 101-56=45, Resulting Numbers: [45] 45,32 unequal: No Solution Exploring Operation: 56+101=157, Resulting Numbers: [157] 157,32 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: 32:[85, 29, 95], Operations: ['98-3=95'] Exploring Operation: 85-29=56, Resulting Numbers: [95, 56] Generated Node #0,2,0: 32:[95, 56] Operation: 85-29=56 Exploring Operation: 85+29=114, Resulting Numbers: [95, 114] Generated Node #0,2,1: 32:[95, 114] Operation: 85+29=114 Exploring Operation: 95-29=66, Resulting Numbers: [85, 66] Generated Node #0,2,2: 32:[85, 66] Operation: 95-29=66 Exploring Operation: 95-85=10, Resulting Numbers: [29, 10] Generated Node #0,2,3: 32:[29, 10] Operation: 95-85=10 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 32:[29, 10], Operations: ['98-3=95', '95-85=10'] Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,32 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[95, 56], Operations: ['98-3=95', '85-29=56'] Exploring Operation: 95-56=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 95+56=151, Resulting Numbers: [151] 151,32 unequal: No Solution Exploring Operation: 95*56=5320, Resulting Numbers: [5320] 5320,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 32:[85, 66], Operations: ['98-3=95', '95-29=66'] Exploring Operation: 85*66=5610, Resulting Numbers: [5610] 5610,32 unequal: No Solution Exploring Operation: 85+66=151, Resulting Numbers: [151] 151,32 unequal: No Solution Exploring Operation: 85-66=19, Resulting Numbers: [19] 19,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[95, 114], Operations: ['98-3=95', '85+29=114'] Exploring Operation: 95+114=209, Resulting Numbers: [209] 209,32 unequal: No Solution Exploring Operation: 114-95=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 95*114=10830, Resulting Numbers: [10830] 10830,32 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: 32:[3, 16], Operations: ['98-85=13', '29-13=16'] Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[29, 16], Operations: ['98-85=13', '3+13=16'] Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,32 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,32 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[13, 32], Operations: ['98-85=13', '3+29=32'] Exploring Operation: 13+32=45, Resulting Numbers: [45] 45,32 unequal: No Solution Exploring Operation: 13*32=416, Resulting Numbers: [416] 416,32 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[29, 10], Operations: ['98-85=13', '13-3=10'] Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,32 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,32 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 19, 4, 11, 28 ]
49
[ "28-11=17", "4*17=68", "68-19=49" ]
Current State: 49:[19, 4, 11, 28], Operations: [] Exploring Operation: 28-11=17, Resulting Numbers: [19, 4, 17] Generated Node #2: [19, 4, 17] from Operation: 28-11=17 Current State: 49:[19, 4, 17], Operations: ['28-11=17'] Exploring Operation: 4*17=68, Resulting Numbers: [19, 68] Generated Node #3: [19, 68] from Operation: 4*17=68 Current State: 49:[19, 68], Operations: ['28-11=17', '4*17=68'] Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[19, 4, 11, 28], Operations: [] Exploring Operation: 19+28=47, Resulting Numbers: [4, 11, 47] Generated Node #0,0: 49:[4, 11, 47] Operation: 19+28=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[4, 11, 47], Operations: ['19+28=47'] Exploring Operation: 11-4=7, Resulting Numbers: [47, 7] Generated Node #0,0,0: 49:[47, 7] Operation: 11-4=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[47, 7], Operations: ['19+28=47', '11-4=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 24, 52, 82, 51 ]
45
[ "24+52=76", "82-51=31", "76-31=45" ]
Current State: 45:[24, 52, 82, 51], Operations: [] Exploring Operation: 24+52=76, Resulting Numbers: [82, 51, 76] Generated Node #2: [82, 51, 76] from Operation: 24+52=76 Current State: 45:[82, 51, 76], Operations: ['24+52=76'] Exploring Operation: 82-51=31, Resulting Numbers: [76, 31] Generated Node #3: [76, 31] from Operation: 82-51=31 Current State: 45:[76, 31], Operations: ['24+52=76', '82-51=31'] Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[24, 52, 82, 51], Operations: [] Exploring Operation: 82-52=30, Resulting Numbers: [24, 51, 30] Generated Node #0,0: 45:[24, 51, 30] Operation: 82-52=30 Exploring Operation: 82-24=58, Resulting Numbers: [52, 51, 58] Generated Node #0,1: 45:[52, 51, 58] Operation: 82-24=58 Moving to Node #0,1 Current State: 45:[52, 51, 58], Operations: ['82-24=58'] Exploring Operation: 58-52=6, Resulting Numbers: [51, 6] Generated Node #0,1,0: 45:[51, 6] Operation: 58-52=6 Exploring Operation: 58-51=7, Resulting Numbers: [52, 7] Generated Node #0,1,1: 45:[52, 7] Operation: 58-51=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[51, 6], Operations: ['82-24=58', '58-52=6'] Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[24, 52, 82, 51], Operations: [] Exploring Operation: 82-24=58, Resulting Numbers: [52, 51, 58] Generated Node #0,1: 45:[52, 51, 58] Operation: 82-24=58 Moving to Node #0,1 Current State: 45:[52, 51, 58], Operations: ['82-24=58'] Exploring Operation: 58-52=6, Resulting Numbers: [51, 6] Generated Node #0,1,0: 45:[51, 6] Operation: 58-52=6 Moving to Node #0,1,0 Current State: 45:[51, 6], Operations: ['82-24=58', '58-52=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 19, 26, 80, 42 ]
28
[ "80-42=38", "38/19=2", "26+2=28" ]
Current State: 28:[19, 26, 80, 42], Operations: [] Exploring Operation: 80-42=38, Resulting Numbers: [19, 26, 38] Generated Node #2: [19, 26, 38] from Operation: 80-42=38 Current State: 28:[19, 26, 38], Operations: ['80-42=38'] Exploring Operation: 38/19=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 38/19=2 Current State: 28:[26, 2], Operations: ['80-42=38', '38/19=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[19, 26, 80, 42], Operations: [] Exploring Operation: 80-26=54, Resulting Numbers: [19, 42, 54] Generated Node #0,0: 28:[19, 42, 54] Operation: 80-26=54 Exploring Operation: 80-42=38, Resulting Numbers: [19, 26, 38] Generated Node #0,1: 28:[19, 26, 38] Operation: 80-42=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[19, 26, 38], Operations: ['80-42=38'] Exploring Operation: 38/19=2, Resulting Numbers: [26, 2] Generated Node #0,1,0: 28:[26, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [26, 19] Generated Node #0,1,1: 28:[26, 19] Operation: 38-19=19 Moving to Node #0,1,0 Current State: 28:[26, 2], Operations: ['80-42=38', '38/19=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[19, 26, 80, 42], Operations: [] Exploring Operation: 80-42=38, Resulting Numbers: [19, 26, 38] Generated Node #0,1: 28:[19, 26, 38] Operation: 80-42=38 Moving to Node #0,1 Current State: 28:[19, 26, 38], Operations: ['80-42=38'] Exploring Operation: 38/19=2, Resulting Numbers: [26, 2] Generated Node #0,1,0: 28:[26, 2] Operation: 38/19=2 Moving to Node #0,1,0 Current State: 28:[26, 2], Operations: ['80-42=38', '38/19=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 29, 66, 40, 9 ]
64
[ "29+66=95", "40-9=31", "95-31=64" ]
Current State: 64:[29, 66, 40, 9], Operations: [] Exploring Operation: 29+66=95, Resulting Numbers: [40, 9, 95] Generated Node #2: [40, 9, 95] from Operation: 29+66=95 Current State: 64:[40, 9, 95], Operations: ['29+66=95'] Exploring Operation: 40-9=31, Resulting Numbers: [95, 31] Generated Node #3: [95, 31] from Operation: 40-9=31 Current State: 64:[95, 31], Operations: ['29+66=95', '40-9=31'] Exploring Operation: 95-31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[29, 66, 40, 9], Operations: [] Exploring Operation: 29+40=69, Resulting Numbers: [66, 9, 69] Generated Node #0,0: 64:[66, 9, 69] Operation: 29+40=69 Exploring Operation: 40-29=11, Resulting Numbers: [66, 9, 11] Generated Node #0,1: 64:[66, 9, 11] Operation: 40-29=11 Exploring Operation: 40-9=31, Resulting Numbers: [29, 66, 31] Generated Node #0,2: 64:[29, 66, 31] Operation: 40-9=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[66, 9, 11], Operations: ['40-29=11'] Exploring Operation: 11-9=2, Resulting Numbers: [66, 2] Generated Node #0,1,0: 64:[66, 2] Operation: 11-9=2 Exploring Operation: 9+11=20, Resulting Numbers: [66, 20] Generated Node #0,1,1: 64:[66, 20] Operation: 9+11=20 Exploring Operation: 66/11=6, Resulting Numbers: [9, 6] Generated Node #0,1,2: 64:[9, 6] Operation: 66/11=6 Moving to Node #0,1,0 Current State: 64:[66, 2], Operations: ['40-29=11', '11-9=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,64 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,64 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[29, 66, 40, 9], Operations: [] Exploring Operation: 40-29=11, Resulting Numbers: [66, 9, 11] Generated Node #0,1: 64:[66, 9, 11] Operation: 40-29=11 Moving to Node #0,1 Current State: 64:[66, 9, 11], Operations: ['40-29=11'] Exploring Operation: 11-9=2, Resulting Numbers: [66, 2] Generated Node #0,1,0: 64:[66, 2] Operation: 11-9=2 Moving to Node #0,1,0 Current State: 64:[66, 2], Operations: ['40-29=11', '11-9=2'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic