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
[ 14, 72, 98, 36 ]
35
[ "72/36=2", "98/2=49", "49-14=35" ]
Current State: 35:[14, 72, 98, 36], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [14, 98, 2] Generated Node #2: [14, 98, 2] from Operation: 72/36=2 Current State: 35:[14, 98, 2], Operations: ['72/36=2'] Exploring Operation: 98/2=49, Resulting Numbers: [14, 49] Generated Node #3: [14, 49] from Operation: 98/2=49 Current State: 35:[14, 49], Operations: ['72/36=2', '98/2=49'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[14, 72, 98, 36], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [72, 36, 7] Generated Node #0,0: 35:[72, 36, 7] Operation: 98/14=7 Exploring Operation: 98-72=26, Resulting Numbers: [14, 36, 26] Generated Node #0,1: 35:[14, 36, 26] Operation: 98-72=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[14, 36, 26], Operations: ['98-72=26'] Exploring Operation: 14+26=40, Resulting Numbers: [36, 40] Generated Node #0,1,0: 35:[36, 40] Operation: 14+26=40 Exploring Operation: 26-14=12, Resulting Numbers: [36, 12] Generated Node #0,1,1: 35:[36, 12] Operation: 26-14=12 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[36, 40], Operations: ['98-72=26', '14+26=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,35 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,35 unequal: No Solution No 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: 35:[36, 12], Operations: ['98-72=26', '26-14=12'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,35 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: 35:[72, 36, 7], Operations: ['98/14=7'] Exploring Operation: 72-36=36, Resulting Numbers: [7, 36] Generated Node #0,0,0: 35:[7, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [7, 2] Generated Node #0,0,1: 35:[7, 2] Operation: 72/36=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 35:[7, 36], Operations: ['98/14=7', '72-36=36'] Exploring Operation: 7+36=43, Resulting Numbers: [43] 43,35 unequal: No Solution Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,35 unequal: No Solution No 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: 35:[7, 2], Operations: ['98/14=7', '72/36=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,35 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
[ 92, 96, 22, 46 ]
88
[ "46-22=24", "96/24=4", "92-4=88" ]
Current State: 88:[92, 96, 22, 46], Operations: [] Exploring Operation: 46-22=24, Resulting Numbers: [92, 96, 24] Generated Node #2: [92, 96, 24] from Operation: 46-22=24 Current State: 88:[92, 96, 24], Operations: ['46-22=24'] Exploring Operation: 96/24=4, Resulting Numbers: [92, 4] Generated Node #3: [92, 4] from Operation: 96/24=4 Current State: 88:[92, 4], Operations: ['46-22=24', '96/24=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[92, 96, 22, 46], Operations: [] Exploring Operation: 46-22=24, Resulting Numbers: [92, 96, 24] Generated Node #0,0: 88:[92, 96, 24] Operation: 46-22=24 Exploring Operation: 96-46=50, Resulting Numbers: [92, 22, 50] Generated Node #0,1: 88:[92, 22, 50] Operation: 96-46=50 Exploring Operation: 92/46=2, Resulting Numbers: [96, 22, 2] Generated Node #0,2: 88:[96, 22, 2] Operation: 92/46=2 Exploring Operation: 92-46=46, Resulting Numbers: [96, 22, 46] Generated Node #0,3: 88:[96, 22, 46] Operation: 92-46=46 Exploring Operation: 96-92=4, Resulting Numbers: [22, 46, 4] Generated Node #0,4: 88:[22, 46, 4] Operation: 96-92=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 88:[22, 46, 4], Operations: ['96-92=4'] Exploring Operation: 22*4=88, Resulting Numbers: [46, 88] Generated Node #0,4,0: 88:[46, 88] Operation: 22*4=88 Exploring Operation: 22-4=18, Resulting Numbers: [46, 18] Generated Node #0,4,1: 88:[46, 18] Operation: 22-4=18 Exploring Operation: 22+4=26, Resulting Numbers: [46, 26] Generated Node #0,4,2: 88:[46, 26] Operation: 22+4=26 Exploring Operation: 46-22=24, Resulting Numbers: [4, 24] Generated Node #0,4,3: 88:[4, 24] Operation: 46-22=24 Exploring Operation: 46-4=42, Resulting Numbers: [22, 42] Generated Node #0,4,4: 88:[22, 42] Operation: 46-4=42 Moving to Node #0,4,0 Current State: 88:[46, 88], Operations: ['96-92=4', '22*4=88'] Exploring Operation: 46+88=134, Resulting Numbers: [134] 134,88 unequal: No Solution Exploring Operation: 88-46=42, Resulting Numbers: [42] 42,88 unequal: No Solution Exploring Operation: 46*88=4048, Resulting Numbers: [4048] 4048,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[22, 42], Operations: ['96-92=4', '46-4=42'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,88 unequal: No Solution Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[4, 24], Operations: ['96-92=4', '46-22=24'] Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[46, 18], Operations: ['96-92=4', '22-4=18'] Exploring Operation: 46*18=828, Resulting Numbers: [828] 828,88 unequal: No Solution Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[46, 26], Operations: ['96-92=4', '22+4=26'] Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,88 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,88 unequal: No Solution No 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: 88:[96, 22, 2], Operations: ['92/46=2'] Exploring Operation: 96-2=94, Resulting Numbers: [22, 94] Generated Node #0,2,0: 88:[22, 94] Operation: 96-2=94 Exploring Operation: 96+2=98, Resulting Numbers: [22, 98] Generated Node #0,2,1: 88:[22, 98] Operation: 96+2=98 Exploring Operation: 22/2=11, Resulting Numbers: [96, 11] Generated Node #0,2,2: 88:[96, 11] Operation: 22/2=11 Exploring Operation: 96/2=48, Resulting Numbers: [22, 48] Generated Node #0,2,3: 88:[22, 48] Operation: 96/2=48 Exploring Operation: 22*2=44, Resulting Numbers: [96, 44] Generated Node #0,2,4: 88:[96, 44] Operation: 22*2=44 Moving to Node #0,2,3 Current State: 88:[22, 48], Operations: ['92/46=2', '96/2=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 22*48=1056, Resulting Numbers: [1056] 1056,88 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[22, 94], Operations: ['92/46=2', '96-2=94'] Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 22+94=116, Resulting Numbers: [116] 116,88 unequal: No Solution Exploring Operation: 22*94=2068, Resulting Numbers: [2068] 2068,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[96, 11], Operations: ['92/46=2', '22/2=11'] Exploring Operation: 96*11=1056, Resulting Numbers: [1056] 1056,88 unequal: No Solution Exploring Operation: 96+11=107, Resulting Numbers: [107] 107,88 unequal: No Solution Exploring Operation: 96-11=85, Resulting Numbers: [85] 85,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[96, 44], Operations: ['92/46=2', '22*2=44'] Exploring Operation: 96*44=4224, Resulting Numbers: [4224] 4224,88 unequal: No Solution Exploring Operation: 96-44=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 96+44=140, Resulting Numbers: [140] 140,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[22, 98], Operations: ['92/46=2', '96+2=98'] Exploring Operation: 22+98=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 22*98=2156, Resulting Numbers: [2156] 2156,88 unequal: No Solution Exploring Operation: 98-22=76, Resulting Numbers: [76] 76,88 unequal: No Solution No 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: 88:[92, 22, 50], Operations: ['96-46=50'] Exploring Operation: 92+22=114, Resulting Numbers: [50, 114] Generated Node #0,1,0: 88:[50, 114] Operation: 92+22=114 Exploring Operation: 50-22=28, Resulting Numbers: [92, 28] Generated Node #0,1,1: 88:[92, 28] Operation: 50-22=28 Exploring Operation: 92-50=42, Resulting Numbers: [22, 42] Generated Node #0,1,2: 88:[22, 42] Operation: 92-50=42 Exploring Operation: 22+50=72, Resulting Numbers: [92, 72] Generated Node #0,1,3: 88:[92, 72] Operation: 22+50=72 Exploring Operation: 92-22=70, Resulting Numbers: [50, 70] Generated Node #0,1,4: 88:[50, 70] Operation: 92-22=70 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 88:[22, 42], Operations: ['96-46=50', '92-50=42'] Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 88:[92, 28], Operations: ['96-46=50', '50-22=28'] Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 92+28=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 92*28=2576, Resulting Numbers: [2576] 2576,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 88:[92, 72], Operations: ['96-46=50', '22+50=72'] Exploring Operation: 92+72=164, Resulting Numbers: [164] 164,88 unequal: No Solution Exploring Operation: 92-72=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 92*72=6624, Resulting Numbers: [6624] 6624,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 88:[50, 70], Operations: ['96-46=50', '92-22=70'] Exploring Operation: 70-50=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 50+70=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 50*70=3500, Resulting Numbers: [3500] 3500,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 88:[50, 114], Operations: ['96-46=50', '92+22=114'] Exploring Operation: 50+114=164, Resulting Numbers: [164] 164,88 unequal: No Solution Exploring Operation: 114-50=64, Resulting Numbers: [64] 64,88 unequal: No Solution Exploring Operation: 50*114=5700, Resulting Numbers: [5700] 5700,88 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: 88:[96, 22, 46], Operations: ['92-46=46'] Exploring Operation: 96-46=50, Resulting Numbers: [22, 50] Generated Node #0,3,0: 88:[22, 50] Operation: 96-46=50 Exploring Operation: 22+46=68, Resulting Numbers: [96, 68] Generated Node #0,3,1: 88:[96, 68] Operation: 22+46=68 Exploring Operation: 46-22=24, Resulting Numbers: [96, 24] Generated Node #0,3,2: 88:[96, 24] Operation: 46-22=24 Exploring Operation: 96+22=118, Resulting Numbers: [46, 118] Generated Node #0,3,3: 88:[46, 118] Operation: 96+22=118 Exploring Operation: 96-22=74, Resulting Numbers: [46, 74] Generated Node #0,3,4: 88:[46, 74] Operation: 96-22=74 Moving to Node #0,3,0 Current State: 88:[22, 50], Operations: ['92-46=46', '96-46=50'] Exploring Operation: 22+50=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 22*50=1100, Resulting Numbers: [1100] 1100,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[96, 24], Operations: ['92-46=46', '46-22=24'] Exploring Operation: 96*24=2304, Resulting Numbers: [2304] 2304,88 unequal: No Solution Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[46, 74], Operations: ['92-46=46', '96-22=74'] Exploring Operation: 46+74=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 74-46=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 46*74=3404, Resulting Numbers: [3404] 3404,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[96, 68], Operations: ['92-46=46', '22+46=68'] Exploring Operation: 96-68=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 96+68=164, Resulting Numbers: [164] 164,88 unequal: No Solution Exploring Operation: 96*68=6528, Resulting Numbers: [6528] 6528,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[46, 118], Operations: ['92-46=46', '96+22=118'] Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 46*118=5428, Resulting Numbers: [5428] 5428,88 unequal: No Solution Exploring Operation: 46+118=164, Resulting Numbers: [164] 164,88 unequal: No Solution No 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: 88:[92, 96, 24], Operations: ['46-22=24'] Exploring Operation: 96-92=4, Resulting Numbers: [24, 4] Generated Node #0,0,0: 88:[24, 4] Operation: 96-92=4 Exploring Operation: 96/24=4, Resulting Numbers: [92, 4] Generated Node #0,0,1: 88:[92, 4] Operation: 96/24=4 Exploring Operation: 96-24=72, Resulting Numbers: [92, 72] Generated Node #0,0,2: 88:[92, 72] Operation: 96-24=72 Exploring Operation: 92+24=116, Resulting Numbers: [96, 116] Generated Node #0,0,3: 88:[96, 116] Operation: 92+24=116 Exploring Operation: 92-24=68, Resulting Numbers: [96, 68] Generated Node #0,0,4: 88:[96, 68] Operation: 92-24=68 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[24, 4], Operations: ['46-22=24', '96-92=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,88 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[92, 4], Operations: ['46-22=24', '96/24=4'] Exploring Operation: 92*4=368, Resulting Numbers: [368] 368,88 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[92, 96, 22, 46], Operations: [] Exploring Operation: 46-22=24, Resulting Numbers: [92, 96, 24] Generated Node #0,0: 88:[92, 96, 24] Operation: 46-22=24 Moving to Node #0,0 Current State: 88:[92, 96, 24], Operations: ['46-22=24'] Exploring Operation: 96/24=4, Resulting Numbers: [92, 4] Generated Node #0,0,1: 88:[92, 4] Operation: 96/24=4 Moving to Node #0,0,1 Current State: 88:[92, 4], Operations: ['46-22=24', '96/24=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.911458
hs_5
mult_heuristic
[ 71, 11, 19, 56 ]
97
[ "71-11=60", "56-19=37", "60+37=97" ]
Current State: 97:[71, 11, 19, 56], Operations: [] Exploring Operation: 71-11=60, Resulting Numbers: [19, 56, 60] Generated Node #2: [19, 56, 60] from Operation: 71-11=60 Current State: 97:[19, 56, 60], Operations: ['71-11=60'] Exploring Operation: 56-19=37, Resulting Numbers: [60, 37] Generated Node #3: [60, 37] from Operation: 56-19=37 Current State: 97:[60, 37], Operations: ['71-11=60', '56-19=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[71, 11, 19, 56], Operations: [] Exploring Operation: 11+19=30, Resulting Numbers: [71, 56, 30] Generated Node #0,0: 97:[71, 56, 30] Operation: 11+19=30 Exploring Operation: 71+19=90, Resulting Numbers: [11, 56, 90] Generated Node #0,1: 97:[11, 56, 90] Operation: 71+19=90 Exploring Operation: 71+11=82, Resulting Numbers: [19, 56, 82] Generated Node #0,2: 97:[19, 56, 82] Operation: 71+11=82 Moving to Node #0,0 Current State: 97:[71, 56, 30], Operations: ['11+19=30'] Exploring Operation: 71+56=127, Resulting Numbers: [30, 127] Generated Node #0,0,0: 97:[30, 127] Operation: 71+56=127 Exploring Operation: 56+30=86, Resulting Numbers: [71, 86] Generated Node #0,0,1: 97:[71, 86] Operation: 56+30=86 Exploring Operation: 71+30=101, Resulting Numbers: [56, 101] Generated Node #0,0,2: 97:[56, 101] Operation: 71+30=101 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 97:[71, 86], Operations: ['11+19=30', '56+30=86'] Exploring Operation: 71+86=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 71*86=6106, Resulting Numbers: [6106] 6106,97 unequal: No Solution Exploring Operation: 86-71=15, Resulting Numbers: [15] 15,97 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:[56, 101], Operations: ['11+19=30', '71+30=101'] Exploring Operation: 101-56=45, Resulting Numbers: [45] 45,97 unequal: No Solution Exploring Operation: 56+101=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 56*101=5656, Resulting Numbers: [5656] 5656,97 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:[30, 127], Operations: ['11+19=30', '71+56=127'] Exploring Operation: 30+127=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 30*127=3810, Resulting Numbers: [3810] 3810,97 unequal: No Solution Exploring Operation: 127-30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[71, 11, 19, 56], Operations: [] Exploring Operation: 11+19=30, Resulting Numbers: [71, 56, 30] Generated Node #0,0: 97:[71, 56, 30] Operation: 11+19=30 Moving to Node #0,0 Current State: 97:[71, 56, 30], Operations: ['11+19=30'] Exploring Operation: 71+56=127, Resulting Numbers: [30, 127] Generated Node #0,0,0: 97:[30, 127] Operation: 71+56=127 Moving to Node #0,0,0 Current State: 97:[30, 127], Operations: ['11+19=30', '71+56=127'] Exploring Operation: 127-30=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 9, 25, 72, 60 ]
98
[ "9+25=34", "72+60=132", "132-34=98" ]
Current State: 98:[9, 25, 72, 60], Operations: [] Exploring Operation: 9+25=34, Resulting Numbers: [72, 60, 34] Generated Node #2: [72, 60, 34] from Operation: 9+25=34 Current State: 98:[72, 60, 34], Operations: ['9+25=34'] Exploring Operation: 72+60=132, Resulting Numbers: [34, 132] Generated Node #3: [34, 132] from Operation: 72+60=132 Current State: 98:[34, 132], Operations: ['9+25=34', '72+60=132'] Exploring Operation: 132-34=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[9, 25, 72, 60], Operations: [] Exploring Operation: 25-9=16, Resulting Numbers: [72, 60, 16] Generated Node #0,0: 98:[72, 60, 16] Operation: 25-9=16 Exploring Operation: 25+72=97, Resulting Numbers: [9, 60, 97] Generated Node #0,1: 98:[9, 60, 97] Operation: 25+72=97 Exploring Operation: 72-60=12, Resulting Numbers: [9, 25, 12] Generated Node #0,2: 98:[9, 25, 12] Operation: 72-60=12 Exploring Operation: 72-25=47, Resulting Numbers: [9, 60, 47] Generated Node #0,3: 98:[9, 60, 47] Operation: 72-25=47 Exploring Operation: 72/9=8, Resulting Numbers: [25, 60, 8] Generated Node #0,4: 98:[25, 60, 8] Operation: 72/9=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[9, 60, 97], Operations: ['25+72=97'] Exploring Operation: 9+97=106, Resulting Numbers: [60, 106] Generated Node #0,1,0: 98:[60, 106] Operation: 9+97=106 Exploring Operation: 97-9=88, Resulting Numbers: [60, 88] Generated Node #0,1,1: 98:[60, 88] Operation: 97-9=88 Exploring Operation: 60-9=51, Resulting Numbers: [97, 51] Generated Node #0,1,2: 98:[97, 51] Operation: 60-9=51 Exploring Operation: 97-60=37, Resulting Numbers: [9, 37] Generated Node #0,1,3: 98:[9, 37] Operation: 97-60=37 Exploring Operation: 9+60=69, Resulting Numbers: [97, 69] Generated Node #0,1,4: 98:[97, 69] Operation: 9+60=69 Moving to Node #0,1,2 Current State: 98:[97, 51], Operations: ['25+72=97', '60-9=51'] Exploring Operation: 97-51=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 97*51=4947, Resulting Numbers: [4947] 4947,98 unequal: No Solution Exploring Operation: 97+51=148, Resulting Numbers: [148] 148,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[9, 37], Operations: ['25+72=97', '97-60=37'] Exploring Operation: 9*37=333, Resulting Numbers: [333] 333,98 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,98 unequal: No Solution Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,98 unequal: No Solution Moving to Node #0,1,0 Current State: 98:[60, 106], Operations: ['25+72=97', '9+97=106'] Exploring Operation: 60+106=166, Resulting Numbers: [166] 166,98 unequal: No Solution Exploring Operation: 106-60=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 60*106=6360, Resulting Numbers: [6360] 6360,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[60, 88], Operations: ['25+72=97', '97-9=88'] Exploring Operation: 60*88=5280, Resulting Numbers: [5280] 5280,98 unequal: No Solution Exploring Operation: 88-60=28, Resulting Numbers: [28] 28,98 unequal: No Solution Exploring Operation: 60+88=148, Resulting Numbers: [148] 148,98 unequal: No Solution Moving to Node #0,1,4 Current State: 98:[97, 69], Operations: ['25+72=97', '9+60=69'] Exploring Operation: 97-69=28, Resulting Numbers: [28] 28,98 unequal: No Solution Exploring Operation: 97*69=6693, Resulting Numbers: [6693] 6693,98 unequal: No Solution Exploring Operation: 97+69=166, Resulting Numbers: [166] 166,98 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:[9, 25, 12], Operations: ['72-60=12'] Exploring Operation: 25-9=16, Resulting Numbers: [12, 16] Generated Node #0,2,0: 98:[12, 16] Operation: 25-9=16 Exploring Operation: 9+25=34, Resulting Numbers: [12, 34] Generated Node #0,2,1: 98:[12, 34] Operation: 9+25=34 Exploring Operation: 25-12=13, Resulting Numbers: [9, 13] Generated Node #0,2,2: 98:[9, 13] Operation: 25-12=13 Exploring Operation: 25+12=37, Resulting Numbers: [9, 37] Generated Node #0,2,3: 98:[9, 37] Operation: 25+12=37 Exploring Operation: 12-9=3, Resulting Numbers: [25, 3] Generated Node #0,2,4: 98:[25, 3] Operation: 12-9=3 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 98:[9, 13], Operations: ['72-60=12', '25-12=13'] Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,98 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[12, 16], Operations: ['72-60=12', '25-9=16'] Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,98 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,98 unequal: No Solution Exploring Operation: 12*16=192, Resulting Numbers: [192] 192,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 98:[25, 3], Operations: ['72-60=12', '12-9=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,98 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 98:[9, 37], Operations: ['72-60=12', '25+12=37'] Exploring Operation: 9+37=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 9*37=333, Resulting Numbers: [333] 333,98 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 98:[12, 34], Operations: ['72-60=12', '9+25=34'] Exploring Operation: 34-12=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 12+34=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 12*34=408, Resulting Numbers: [408] 408,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[9, 60, 47], Operations: ['72-25=47'] Exploring Operation: 60+47=107, Resulting Numbers: [9, 107] Generated Node #0,3,0: 98:[9, 107] Operation: 60+47=107 Exploring Operation: 9+47=56, Resulting Numbers: [60, 56] Generated Node #0,3,1: 98:[60, 56] Operation: 9+47=56 Exploring Operation: 60-9=51, Resulting Numbers: [47, 51] Generated Node #0,3,2: 98:[47, 51] Operation: 60-9=51 Exploring Operation: 9+60=69, Resulting Numbers: [47, 69] Generated Node #0,3,3: 98:[47, 69] Operation: 9+60=69 Exploring Operation: 60-47=13, Resulting Numbers: [9, 13] Generated Node #0,3,4: 98:[9, 13] Operation: 60-47=13 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 98:[9, 13], Operations: ['72-25=47', '60-47=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,98 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,98 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 98:[47, 51], Operations: ['72-25=47', '60-9=51'] Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[9, 25, 72, 60], Operations: [] Exploring Operation: 72-25=47, Resulting Numbers: [9, 60, 47] Generated Node #0,3: 98:[9, 60, 47] Operation: 72-25=47 Moving to Node #0,3 Current State: 98:[9, 60, 47], Operations: ['72-25=47'] Exploring Operation: 60-9=51, Resulting Numbers: [47, 51] Generated Node #0,3,2: 98:[47, 51] Operation: 60-9=51 Moving to Node #0,3,2 Current State: 98:[47, 51], Operations: ['72-25=47', '60-9=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
0.949653
hs_5
sum_heuristic
[ 40, 39, 37, 18 ]
44
[ "40-18=22", "39-37=2", "22*2=44" ]
Current State: 44:[40, 39, 37, 18], Operations: [] Exploring Operation: 40-18=22, Resulting Numbers: [39, 37, 22] Generated Node #2: [39, 37, 22] from Operation: 40-18=22 Current State: 44:[39, 37, 22], Operations: ['40-18=22'] Exploring Operation: 39-37=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 39-37=2 Current State: 44:[22, 2], Operations: ['40-18=22', '39-37=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[40, 39, 37, 18], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [40, 18, 2] Generated Node #0,0: 44:[40, 18, 2] Operation: 39-37=2 Exploring Operation: 40-37=3, Resulting Numbers: [39, 18, 3] Generated Node #0,1: 44:[39, 18, 3] Operation: 40-37=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[40, 18, 2], Operations: ['39-37=2'] Exploring Operation: 40+2=42, Resulting Numbers: [18, 42] Generated Node #0,0,0: 44:[18, 42] Operation: 40+2=42 Exploring Operation: 40-18=22, Resulting Numbers: [2, 22] Generated Node #0,0,1: 44:[2, 22] Operation: 40-18=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[2, 22], Operations: ['39-37=2', '40-18=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[40, 39, 37, 18], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [40, 18, 2] Generated Node #0,0: 44:[40, 18, 2] Operation: 39-37=2 Moving to Node #0,0 Current State: 44:[40, 18, 2], Operations: ['39-37=2'] Exploring Operation: 40-18=22, Resulting Numbers: [2, 22] Generated Node #0,0,1: 44:[2, 22] Operation: 40-18=22 Moving to Node #0,0,1 Current State: 44:[2, 22], Operations: ['39-37=2', '40-18=22'] Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 38, 72, 83, 91 ]
81
[ "91-72=19", "38/19=2", "83-2=81" ]
Current State: 81:[38, 72, 83, 91], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [38, 83, 19] Generated Node #2: [38, 83, 19] from Operation: 91-72=19 Current State: 81:[38, 83, 19], Operations: ['91-72=19'] Exploring Operation: 38/19=2, Resulting Numbers: [83, 2] Generated Node #3: [83, 2] from Operation: 38/19=2 Current State: 81:[83, 2], Operations: ['91-72=19', '38/19=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[38, 72, 83, 91], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [38, 83, 19] Generated Node #0,0: 81:[38, 83, 19] Operation: 91-72=19 Exploring Operation: 83-38=45, Resulting Numbers: [72, 91, 45] Generated Node #0,1: 81:[72, 91, 45] Operation: 83-38=45 Exploring Operation: 91-83=8, Resulting Numbers: [38, 72, 8] Generated Node #0,2: 81:[38, 72, 8] Operation: 91-83=8 Exploring Operation: 72-38=34, Resulting Numbers: [83, 91, 34] Generated Node #0,3: 81:[83, 91, 34] Operation: 72-38=34 Exploring Operation: 83-72=11, Resulting Numbers: [38, 91, 11] Generated Node #0,4: 81:[38, 91, 11] Operation: 83-72=11 Moving to Node #0,3 Current State: 81:[83, 91, 34], Operations: ['72-38=34'] Exploring Operation: 91+34=125, Resulting Numbers: [83, 125] Generated Node #0,3,0: 81:[83, 125] Operation: 91+34=125 Exploring Operation: 91-34=57, Resulting Numbers: [83, 57] Generated Node #0,3,1: 81:[83, 57] Operation: 91-34=57 Exploring Operation: 83-34=49, Resulting Numbers: [91, 49] Generated Node #0,3,2: 81:[91, 49] Operation: 83-34=49 Exploring Operation: 83+34=117, Resulting Numbers: [91, 117] Generated Node #0,3,3: 81:[91, 117] Operation: 83+34=117 Exploring Operation: 91-83=8, Resulting Numbers: [34, 8] Generated Node #0,3,4: 81:[34, 8] Operation: 91-83=8 Moving to Node #0,2 Current State: 81:[38, 72, 8], Operations: ['91-83=8'] Exploring Operation: 72+8=80, Resulting Numbers: [38, 80] Generated Node #0,2,0: 81:[38, 80] Operation: 72+8=80 Exploring Operation: 72/8=9, Resulting Numbers: [38, 9] Generated Node #0,2,1: 81:[38, 9] Operation: 72/8=9 Exploring Operation: 38+8=46, Resulting Numbers: [72, 46] Generated Node #0,2,2: 81:[72, 46] Operation: 38+8=46 Exploring Operation: 38-8=30, Resulting Numbers: [72, 30] Generated Node #0,2,3: 81:[72, 30] Operation: 38-8=30 Exploring Operation: 72-38=34, Resulting Numbers: [8, 34] Generated Node #0,2,4: 81:[8, 34] Operation: 72-38=34 Moving to Node #0,0 Current State: 81:[38, 83, 19], Operations: ['91-72=19'] Exploring Operation: 38+19=57, Resulting Numbers: [83, 57] Generated Node #0,0,0: 81:[83, 57] Operation: 38+19=57 Exploring Operation: 83-19=64, Resulting Numbers: [38, 64] Generated Node #0,0,1: 81:[38, 64] Operation: 83-19=64 Exploring Operation: 38-19=19, Resulting Numbers: [83, 19] Generated Node #0,0,2: 81:[83, 19] Operation: 38-19=19 Exploring Operation: 38/19=2, Resulting Numbers: [83, 2] Generated Node #0,0,3: 81:[83, 2] Operation: 38/19=2 Exploring Operation: 83-38=45, Resulting Numbers: [19, 45] Generated Node #0,0,4: 81:[19, 45] Operation: 83-38=45 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 81:[83, 2], Operations: ['91-72=19', '38/19=2'] Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,81 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[38, 72, 83, 91], Operations: [] Exploring Operation: 91-72=19, Resulting Numbers: [38, 83, 19] Generated Node #0,0: 81:[38, 83, 19] Operation: 91-72=19 Moving to Node #0,0 Current State: 81:[38, 83, 19], Operations: ['91-72=19'] Exploring Operation: 38/19=2, Resulting Numbers: [83, 2] Generated Node #0,0,3: 81:[83, 2] Operation: 38/19=2 Moving to Node #0,0,3 Current State: 81:[83, 2], Operations: ['91-72=19', '38/19=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 62, 16, 77, 8 ]
13
[ "77-62=15", "16/8=2", "15-2=13" ]
Current State: 13:[62, 16, 77, 8], Operations: [] Exploring Operation: 77-62=15, Resulting Numbers: [16, 8, 15] Generated Node #2: [16, 8, 15] from Operation: 77-62=15 Current State: 13:[16, 8, 15], Operations: ['77-62=15'] Exploring Operation: 16/8=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 16/8=2 Current State: 13:[15, 2], Operations: ['77-62=15', '16/8=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[62, 16, 77, 8], Operations: [] Exploring Operation: 62-8=54, Resulting Numbers: [16, 77, 54] Generated Node #0,0: 13:[16, 77, 54] Operation: 62-8=54 Exploring Operation: 77-62=15, Resulting Numbers: [16, 8, 15] Generated Node #0,1: 13:[16, 8, 15] Operation: 77-62=15 Exploring Operation: 62-16=46, Resulting Numbers: [77, 8, 46] Generated Node #0,2: 13:[77, 8, 46] Operation: 62-16=46 Exploring Operation: 77-16=61, Resulting Numbers: [62, 8, 61] Generated Node #0,3: 13:[62, 8, 61] Operation: 77-16=61 Exploring Operation: 77-8=69, Resulting Numbers: [62, 16, 69] Generated Node #0,4: 13:[62, 16, 69] Operation: 77-8=69 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[16, 8, 15], Operations: ['77-62=15'] Exploring Operation: 15-8=7, Resulting Numbers: [16, 7] Generated Node #0,1,0: 13:[16, 7] Operation: 15-8=7 Exploring Operation: 16+8=24, Resulting Numbers: [15, 24] Generated Node #0,1,1: 13:[15, 24] Operation: 16+8=24 Exploring Operation: 16-8=8, Resulting Numbers: [15, 8] Generated Node #0,1,2: 13:[15, 8] Operation: 16-8=8 Exploring Operation: 8+15=23, Resulting Numbers: [16, 23] Generated Node #0,1,3: 13:[16, 23] Operation: 8+15=23 Exploring Operation: 16/8=2, Resulting Numbers: [15, 2] Generated Node #0,1,4: 13:[15, 2] Operation: 16/8=2 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 13:[15, 8], Operations: ['77-62=15', '16-8=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,13 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 13:[16, 7], Operations: ['77-62=15', '15-8=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,13 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 13:[15, 24], Operations: ['77-62=15', '16+8=24'] Exploring Operation: 15+24=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,13 unequal: No Solution Exploring Operation: 15*24=360, Resulting Numbers: [360] 360,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 13:[16, 23], Operations: ['77-62=15', '8+15=23'] Exploring Operation: 16+23=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 16*23=368, Resulting Numbers: [368] 368,13 unequal: No Solution Exploring Operation: 23-16=7, Resulting Numbers: [7] 7,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 13:[15, 2], Operations: ['77-62=15', '16/8=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,13 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[62, 16, 77, 8], Operations: [] Exploring Operation: 77-62=15, Resulting Numbers: [16, 8, 15] Generated Node #0,1: 13:[16, 8, 15] Operation: 77-62=15 Moving to Node #0,1 Current State: 13:[16, 8, 15], Operations: ['77-62=15'] Exploring Operation: 16/8=2, Resulting Numbers: [15, 2] Generated Node #0,1,4: 13:[15, 2] Operation: 16/8=2 Moving to Node #0,1,4 Current State: 13:[15, 2], Operations: ['77-62=15', '16/8=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_5
mult_heuristic
[ 48, 75, 51, 66 ]
41
[ "51-48=3", "75/3=25", "66-25=41" ]
Current State: 41:[48, 75, 51, 66], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [75, 66, 3] Generated Node #2: [75, 66, 3] from Operation: 51-48=3 Current State: 41:[75, 66, 3], Operations: ['51-48=3'] Exploring Operation: 75/3=25, Resulting Numbers: [66, 25] Generated Node #3: [66, 25] from Operation: 75/3=25 Current State: 41:[66, 25], Operations: ['51-48=3', '75/3=25'] Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[48, 75, 51, 66], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [51, 66, 27] Generated Node #0,0: 41:[51, 66, 27] Operation: 75-48=27 Exploring Operation: 75-51=24, Resulting Numbers: [48, 66, 24] Generated Node #0,1: 41:[48, 66, 24] Operation: 75-51=24 Exploring Operation: 66-48=18, Resulting Numbers: [75, 51, 18] Generated Node #0,2: 41:[75, 51, 18] Operation: 66-48=18 Exploring Operation: 66-51=15, Resulting Numbers: [48, 75, 15] Generated Node #0,3: 41:[48, 75, 15] Operation: 66-51=15 Exploring Operation: 75-66=9, Resulting Numbers: [48, 51, 9] Generated Node #0,4: 41:[48, 51, 9] Operation: 75-66=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[51, 66, 27], Operations: ['75-48=27'] Exploring Operation: 66-51=15, Resulting Numbers: [27, 15] Generated Node #0,0,0: 41:[27, 15] Operation: 66-51=15 Exploring Operation: 51+27=78, Resulting Numbers: [66, 78] Generated Node #0,0,1: 41:[66, 78] Operation: 51+27=78 Exploring Operation: 66+27=93, Resulting Numbers: [51, 93] Generated Node #0,0,2: 41:[51, 93] Operation: 66+27=93 Exploring Operation: 51-27=24, Resulting Numbers: [66, 24] Generated Node #0,0,3: 41:[66, 24] Operation: 51-27=24 Exploring Operation: 66-27=39, Resulting Numbers: [51, 39] Generated Node #0,0,4: 41:[51, 39] Operation: 66-27=39 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 41:[51, 39], Operations: ['75-48=27', '66-27=39'] Exploring Operation: 51*39=1989, Resulting Numbers: [1989] 1989,41 unequal: No Solution Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 51+39=90, Resulting Numbers: [90] 90,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[27, 15], Operations: ['75-48=27', '66-51=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,41 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[66, 24], Operations: ['75-48=27', '51-27=24'] Exploring Operation: 66*24=1584, Resulting Numbers: [1584] 1584,41 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 66+24=90, Resulting Numbers: [90] 90,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[66, 78], Operations: ['75-48=27', '51+27=78'] Exploring Operation: 66+78=144, Resulting Numbers: [144] 144,41 unequal: No Solution Exploring Operation: 78-66=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 66*78=5148, Resulting Numbers: [5148] 5148,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[51, 93], Operations: ['75-48=27', '66+27=93'] Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,41 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[48, 66, 24], Operations: ['75-51=24'] Exploring Operation: 48+24=72, Resulting Numbers: [66, 72] Generated Node #0,1,0: 41:[66, 72] Operation: 48+24=72 Exploring Operation: 66+24=90, Resulting Numbers: [48, 90] Generated Node #0,1,1: 41:[48, 90] Operation: 66+24=90 Exploring Operation: 66-48=18, Resulting Numbers: [24, 18] Generated Node #0,1,2: 41:[24, 18] Operation: 66-48=18 Exploring Operation: 66-24=42, Resulting Numbers: [48, 42] Generated Node #0,1,3: 41:[48, 42] Operation: 66-24=42 Exploring Operation: 48-24=24, Resulting Numbers: [66, 24] Generated Node #0,1,4: 41:[66, 24] Operation: 48-24=24 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 41:[48, 42], Operations: ['75-51=24', '66-24=42'] Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,41 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[24, 18], Operations: ['75-51=24', '66-48=18'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 24+18=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 24*18=432, Resulting Numbers: [432] 432,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 41:[66, 24], Operations: ['75-51=24', '48-24=24'] Exploring Operation: 66*24=1584, Resulting Numbers: [1584] 1584,41 unequal: No Solution Exploring Operation: 66+24=90, Resulting Numbers: [90] 90,41 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[66, 72], Operations: ['75-51=24', '48+24=72'] Exploring Operation: 66*72=4752, Resulting Numbers: [4752] 4752,41 unequal: No Solution Exploring Operation: 72-66=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 66+72=138, Resulting Numbers: [138] 138,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[48, 90], Operations: ['75-51=24', '66+24=90'] Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,41 unequal: No Solution Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 41:[48, 51, 9], Operations: ['75-66=9'] Exploring Operation: 48+9=57, Resulting Numbers: [51, 57] Generated Node #0,4,0: 41:[51, 57] Operation: 48+9=57 Exploring Operation: 51+9=60, Resulting Numbers: [48, 60] Generated Node #0,4,1: 41:[48, 60] Operation: 51+9=60 Exploring Operation: 48-9=39, Resulting Numbers: [51, 39] Generated Node #0,4,2: 41:[51, 39] Operation: 48-9=39 Exploring Operation: 51-9=42, Resulting Numbers: [48, 42] Generated Node #0,4,3: 41:[48, 42] Operation: 51-9=42 Exploring Operation: 51-48=3, Resulting Numbers: [9, 3] Generated Node #0,4,4: 41:[9, 3] Operation: 51-48=3 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 41:[48, 42], Operations: ['75-66=9', '51-9=42'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 48*42=2016, Resulting Numbers: [2016] 2016,41 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 41:[51, 39], Operations: ['75-66=9', '48-9=39'] Exploring Operation: 51*39=1989, Resulting Numbers: [1989] 1989,41 unequal: No Solution Exploring Operation: 51-39=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 51+39=90, Resulting Numbers: [90] 90,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 41:[51, 57], Operations: ['75-66=9', '48+9=57'] Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 51+57=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 51*57=2907, Resulting Numbers: [2907] 2907,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 41:[48, 60], Operations: ['75-66=9', '51+9=60'] Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,41 unequal: No Solution Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 41:[9, 3], Operations: ['75-66=9', '51-48=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[75, 51, 18], Operations: ['66-48=18'] Exploring Operation: 51-18=33, Resulting Numbers: [75, 33] Generated Node #0,2,0: 41:[75, 33] Operation: 51-18=33 Exploring Operation: 75-18=57, Resulting Numbers: [51, 57] Generated Node #0,2,1: 41:[51, 57] Operation: 75-18=57 Exploring Operation: 51+18=69, Resulting Numbers: [75, 69] Generated Node #0,2,2: 41:[75, 69] Operation: 51+18=69 Exploring Operation: 75-51=24, Resulting Numbers: [18, 24] Generated Node #0,2,3: 41:[18, 24] Operation: 75-51=24 Exploring Operation: 75+18=93, Resulting Numbers: [51, 93] Generated Node #0,2,4: 41:[51, 93] Operation: 75+18=93 Moving to Node #0,2,1 Current State: 41:[51, 57], Operations: ['66-48=18', '75-18=57'] Exploring Operation: 51+57=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 51*57=2907, Resulting Numbers: [2907] 2907,41 unequal: No Solution Exploring Operation: 57-51=6, Resulting Numbers: [6] 6,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[18, 24], Operations: ['66-48=18', '75-51=24'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,41 unequal: No Solution Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[75, 33], Operations: ['66-48=18', '51-18=33'] Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,41 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[75, 69], Operations: ['66-48=18', '51+18=69'] Exploring Operation: 75*69=5175, Resulting Numbers: [5175] 5175,41 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,41 unequal: No Solution Moving to Node #0,2,4 Current State: 41:[51, 93], Operations: ['66-48=18', '75+18=93'] Exploring Operation: 51*93=4743, Resulting Numbers: [4743] 4743,41 unequal: No Solution Exploring Operation: 51+93=144, Resulting Numbers: [144] 144,41 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[48, 75, 15], Operations: ['66-51=15'] Exploring Operation: 75-48=27, Resulting Numbers: [15, 27] Generated Node #0,3,0: 41:[15, 27] Operation: 75-48=27 Exploring Operation: 48+15=63, Resulting Numbers: [75, 63] Generated Node #0,3,1: 41:[75, 63] Operation: 48+15=63 Exploring Operation: 75/15=5, Resulting Numbers: [48, 5] Generated Node #0,3,2: 41:[48, 5] Operation: 75/15=5 Exploring Operation: 48-15=33, Resulting Numbers: [75, 33] Generated Node #0,3,3: 41:[75, 33] Operation: 48-15=33 Exploring Operation: 75-15=60, Resulting Numbers: [48, 60] Generated Node #0,3,4: 41:[48, 60] Operation: 75-15=60 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 41:[48, 60], Operations: ['66-51=15', '75-15=60'] Exploring Operation: 48+60=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 48*60=2880, Resulting Numbers: [2880] 2880,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 41:[15, 27], Operations: ['66-51=15', '75-48=27'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 15*27=405, Resulting Numbers: [405] 405,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 41:[75, 33], Operations: ['66-51=15', '48-15=33'] Exploring Operation: 75+33=108, Resulting Numbers: [108] 108,41 unequal: No Solution Exploring Operation: 75*33=2475, Resulting Numbers: [2475] 2475,41 unequal: No Solution Exploring Operation: 75-33=42, Resulting Numbers: [42] 42,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 41:[48, 5], Operations: ['66-51=15', '75/15=5'] Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,41 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,41 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 41:[75, 63], Operations: ['66-51=15', '48+15=63'] Exploring Operation: 75*63=4725, Resulting Numbers: [4725] 4725,41 unequal: No Solution Exploring Operation: 75+63=138, Resulting Numbers: [138] 138,41 unequal: No Solution Exploring Operation: 75-63=12, Resulting Numbers: [12] 12,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 95, 11, 7, 82 ]
100
[ "95+82=177", "11*7=77", "177-77=100" ]
Current State: 100:[95, 11, 7, 82], Operations: [] Exploring Operation: 95+82=177, Resulting Numbers: [11, 7, 177] Generated Node #2: [11, 7, 177] from Operation: 95+82=177 Current State: 100:[11, 7, 177], Operations: ['95+82=177'] Exploring Operation: 11*7=77, Resulting Numbers: [177, 77] Generated Node #3: [177, 77] from Operation: 11*7=77 Current State: 100:[177, 77], Operations: ['95+82=177', '11*7=77'] Exploring Operation: 177-77=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[95, 11, 7, 82], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [95, 82, 4] Generated Node #0,0: 100:[95, 82, 4] Operation: 11-7=4 Exploring Operation: 7+82=89, Resulting Numbers: [95, 11, 89] Generated Node #0,1: 100:[95, 11, 89] Operation: 7+82=89 Exploring Operation: 11+82=93, Resulting Numbers: [95, 7, 93] Generated Node #0,2: 100:[95, 7, 93] Operation: 11+82=93 Exploring Operation: 95-82=13, Resulting Numbers: [11, 7, 13] Generated Node #0,3: 100:[11, 7, 13] Operation: 95-82=13 Exploring Operation: 95+7=102, Resulting Numbers: [11, 82, 102] Generated Node #0,4: 100:[11, 82, 102] Operation: 95+7=102 Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[11, 7, 13], Operations: ['95-82=13'] Exploring Operation: 7+13=20, Resulting Numbers: [11, 20] Generated Node #0,3,0: 100:[11, 20] Operation: 7+13=20 Exploring Operation: 13-11=2, Resulting Numbers: [7, 2] Generated Node #0,3,1: 100:[7, 2] Operation: 13-11=2 Exploring Operation: 13-7=6, Resulting Numbers: [11, 6] Generated Node #0,3,2: 100:[11, 6] Operation: 13-7=6 Exploring Operation: 11-7=4, Resulting Numbers: [13, 4] Generated Node #0,3,3: 100:[13, 4] Operation: 11-7=4 Exploring Operation: 11+13=24, Resulting Numbers: [7, 24] Generated Node #0,3,4: 100:[7, 24] Operation: 11+13=24 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 100:[11, 20], Operations: ['95-82=13', '7+13=20'] Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,100 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,100 unequal: No Solution No 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: 100:[7, 2], Operations: ['95-82=13', '13-11=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,100 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,100 unequal: No Solution No 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: 100:[11, 6], Operations: ['95-82=13', '13-7=6'] Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,100 unequal: No Solution No 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: 100:[13, 4], Operations: ['95-82=13', '11-7=4'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,100 unequal: No Solution No 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: 100:[7, 24], Operations: ['95-82=13', '11+13=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,100 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,100 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: 100:[95, 7, 93], Operations: ['11+82=93'] Exploring Operation: 95-93=2, Resulting Numbers: [7, 2] Generated Node #0,2,0: 100:[7, 2] Operation: 95-93=2 Exploring Operation: 95-7=88, Resulting Numbers: [93, 88] Generated Node #0,2,1: 100:[93, 88] Operation: 95-7=88 Exploring Operation: 7+93=100, Resulting Numbers: [95, 100] Generated Node #0,2,2: 100:[95, 100] Operation: 7+93=100 Exploring Operation: 93-7=86, Resulting Numbers: [95, 86] Generated Node #0,2,3: 100:[95, 86] Operation: 93-7=86 Exploring Operation: 95+7=102, Resulting Numbers: [93, 102] Generated Node #0,2,4: 100:[93, 102] Operation: 95+7=102 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 100:[7, 2], Operations: ['11+82=93', '95-93=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,100 unequal: No Solution No 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: 100:[95, 100], Operations: ['11+82=93', '7+93=100'] Exploring Operation: 100-95=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 95+100=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 95*100=9500, Resulting Numbers: [9500] 9500,100 unequal: No Solution No 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: 100:[93, 102], Operations: ['11+82=93', '95+7=102'] Exploring Operation: 93+102=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 93*102=9486, Resulting Numbers: [9486] 9486,100 unequal: No Solution Exploring Operation: 102-93=9, Resulting Numbers: [9] 9,100 unequal: No Solution No 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: 100:[93, 88], Operations: ['11+82=93', '95-7=88'] Exploring Operation: 93+88=181, Resulting Numbers: [181] 181,100 unequal: No Solution Exploring Operation: 93*88=8184, Resulting Numbers: [8184] 8184,100 unequal: No Solution Exploring Operation: 93-88=5, Resulting Numbers: [5] 5,100 unequal: No Solution No 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: 100:[95, 86], Operations: ['11+82=93', '93-7=86'] Exploring Operation: 95-86=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 95*86=8170, Resulting Numbers: [8170] 8170,100 unequal: No Solution Exploring Operation: 95+86=181, Resulting Numbers: [181] 181,100 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: 100:[95, 11, 89], Operations: ['7+82=89'] Exploring Operation: 95-89=6, Resulting Numbers: [11, 6] Generated Node #0,1,0: 100:[11, 6] Operation: 95-89=6 Exploring Operation: 89-11=78, Resulting Numbers: [95, 78] Generated Node #0,1,1: 100:[95, 78] Operation: 89-11=78 Exploring Operation: 95-11=84, Resulting Numbers: [89, 84] Generated Node #0,1,2: 100:[89, 84] Operation: 95-11=84 Exploring Operation: 95+11=106, Resulting Numbers: [89, 106] Generated Node #0,1,3: 100:[89, 106] Operation: 95+11=106 Exploring Operation: 11+89=100, Resulting Numbers: [95, 100] Generated Node #0,1,4: 100:[95, 100] Operation: 11+89=100 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[11, 6], Operations: ['7+82=89', '95-89=6'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,100 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,100 unequal: No Solution No 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: 100:[95, 100], Operations: ['7+82=89', '11+89=100'] Exploring Operation: 95*100=9500, Resulting Numbers: [9500] 9500,100 unequal: No Solution Exploring Operation: 95+100=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 100-95=5, Resulting Numbers: [5] 5,100 unequal: No Solution No 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: 100:[89, 106], Operations: ['7+82=89', '95+11=106'] Exploring Operation: 89*106=9434, Resulting Numbers: [9434] 9434,100 unequal: No Solution Exploring Operation: 89+106=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 106-89=17, Resulting Numbers: [17] 17,100 unequal: No Solution No 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: 100:[95, 78], Operations: ['7+82=89', '89-11=78'] Exploring Operation: 95+78=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 95-78=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 95*78=7410, Resulting Numbers: [7410] 7410,100 unequal: No Solution No 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: 100:[89, 84], Operations: ['7+82=89', '95-11=84'] Exploring Operation: 89+84=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 89*84=7476, Resulting Numbers: [7476] 7476,100 unequal: No Solution Exploring Operation: 89-84=5, Resulting Numbers: [5] 5,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 100:[11, 82, 102], Operations: ['95+7=102'] Exploring Operation: 102-11=91, Resulting Numbers: [82, 91] Generated Node #0,4,0: 100:[82, 91] Operation: 102-11=91 Exploring Operation: 82-11=71, Resulting Numbers: [102, 71] Generated Node #0,4,1: 100:[102, 71] Operation: 82-11=71 Exploring Operation: 11+82=93, Resulting Numbers: [102, 93] Generated Node #0,4,2: 100:[102, 93] Operation: 11+82=93 Exploring Operation: 102-82=20, Resulting Numbers: [11, 20] Generated Node #0,4,3: 100:[11, 20] Operation: 102-82=20 Exploring Operation: 11+102=113, Resulting Numbers: [82, 113] Generated Node #0,4,4: 100:[82, 113] Operation: 11+102=113 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 100:[11, 20], Operations: ['95+7=102', '102-82=20'] Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,100 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,100 unequal: No Solution No 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: 100:[102, 93], Operations: ['95+7=102', '11+82=93'] Exploring Operation: 102-93=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 102*93=9486, Resulting Numbers: [9486] 9486,100 unequal: No Solution Exploring Operation: 102+93=195, Resulting Numbers: [195] 195,100 unequal: No Solution No 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: 100:[102, 71], Operations: ['95+7=102', '82-11=71'] Exploring Operation: 102+71=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 102*71=7242, Resulting Numbers: [7242] 7242,100 unequal: No Solution Exploring Operation: 102-71=31, Resulting Numbers: [31] 31,100 unequal: No Solution No 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: 100:[82, 91], Operations: ['95+7=102', '102-11=91'] Exploring Operation: 82+91=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 91-82=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 82*91=7462, Resulting Numbers: [7462] 7462,100 unequal: No Solution No 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: 100:[82, 113], Operations: ['95+7=102', '11+102=113'] Exploring Operation: 82+113=195, Resulting Numbers: [195] 195,100 unequal: No Solution Exploring Operation: 82*113=9266, Resulting Numbers: [9266] 9266,100 unequal: No Solution Exploring Operation: 113-82=31, Resulting Numbers: [31] 31,100 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: 100:[95, 82, 4], Operations: ['11-7=4'] Exploring Operation: 82+4=86, Resulting Numbers: [95, 86] Generated Node #0,0,0: 100:[95, 86] Operation: 82+4=86 Exploring Operation: 95+4=99, Resulting Numbers: [82, 99] Generated Node #0,0,1: 100:[82, 99] Operation: 95+4=99 Exploring Operation: 95-82=13, Resulting Numbers: [4, 13] Generated Node #0,0,2: 100:[4, 13] Operation: 95-82=13 Exploring Operation: 82-4=78, Resulting Numbers: [95, 78] Generated Node #0,0,3: 100:[95, 78] Operation: 82-4=78 Exploring Operation: 95-4=91, Resulting Numbers: [82, 91] Generated Node #0,0,4: 100:[82, 91] Operation: 95-4=91 Moving to Node #0,0,2 Current State: 100:[4, 13], Operations: ['11-7=4', '95-82=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[82, 99], Operations: ['11-7=4', '95+4=99'] Exploring Operation: 82+99=181, Resulting Numbers: [181] 181,100 unequal: No Solution Exploring Operation: 82*99=8118, Resulting Numbers: [8118] 8118,100 unequal: No Solution Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[95, 86], Operations: ['11-7=4', '82+4=86'] Exploring Operation: 95-86=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 95+86=181, Resulting Numbers: [181] 181,100 unequal: No Solution Exploring Operation: 95*86=8170, Resulting Numbers: [8170] 8170,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[95, 78], Operations: ['11-7=4', '82-4=78'] Exploring Operation: 95+78=173, Resulting Numbers: [173] 173,100 unequal: No Solution Exploring Operation: 95*78=7410, Resulting Numbers: [7410] 7410,100 unequal: No Solution Exploring Operation: 95-78=17, Resulting Numbers: [17] 17,100 unequal: No Solution Moving to Node #0,0,4 Current State: 100:[82, 91], Operations: ['11-7=4', '95-4=91'] Exploring Operation: 82*91=7462, Resulting Numbers: [7462] 7462,100 unequal: No Solution Exploring Operation: 91-82=9, Resulting Numbers: [9] 9,100 unequal: No Solution Exploring Operation: 82+91=173, Resulting Numbers: [173] 173,100 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
[ 41, 31, 4, 15 ]
12
[ "41+31=72", "4*15=60", "72-60=12" ]
Current State: 12:[41, 31, 4, 15], Operations: [] Exploring Operation: 41+31=72, Resulting Numbers: [4, 15, 72] Generated Node #2: [4, 15, 72] from Operation: 41+31=72 Current State: 12:[4, 15, 72], Operations: ['41+31=72'] Exploring Operation: 4*15=60, Resulting Numbers: [72, 60] Generated Node #3: [72, 60] from Operation: 4*15=60 Current State: 12:[72, 60], Operations: ['41+31=72', '4*15=60'] Exploring Operation: 72-60=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[41, 31, 4, 15], Operations: [] Exploring Operation: 41-31=10, Resulting Numbers: [4, 15, 10] Generated Node #0,0: 12:[4, 15, 10] Operation: 41-31=10 Exploring Operation: 41-15=26, Resulting Numbers: [31, 4, 26] Generated Node #0,1: 12:[31, 4, 26] Operation: 41-15=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[4, 15, 10], Operations: ['41-31=10'] Exploring Operation: 15-4=11, Resulting Numbers: [10, 11] Generated Node #0,0,0: 12:[10, 11] Operation: 15-4=11 Exploring Operation: 15-10=5, Resulting Numbers: [4, 5] Generated Node #0,0,1: 12:[4, 5] Operation: 15-10=5 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[4, 5], Operations: ['41-31=10', '15-10=5'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[10, 11], Operations: ['41-31=10', '15-4=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[31, 4, 26], Operations: ['41-15=26'] Exploring Operation: 31-4=27, Resulting Numbers: [26, 27] Generated Node #0,1,0: 12:[26, 27] Operation: 31-4=27 Exploring Operation: 31-26=5, Resulting Numbers: [4, 5] Generated Node #0,1,1: 12:[4, 5] Operation: 31-26=5 Moving to Node #0,1,1 Current State: 12:[4, 5], Operations: ['41-15=26', '31-26=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[26, 27], Operations: ['41-15=26', '31-4=27'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 26+27=53, Resulting Numbers: [53] 53,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 41, 8, 43, 46 ]
83
[ "46-41=5", "8*5=40", "43+40=83" ]
Current State: 83:[41, 8, 43, 46], Operations: [] Exploring Operation: 46-41=5, Resulting Numbers: [8, 43, 5] Generated Node #2: [8, 43, 5] from Operation: 46-41=5 Current State: 83:[8, 43, 5], Operations: ['46-41=5'] Exploring Operation: 8*5=40, Resulting Numbers: [43, 40] Generated Node #3: [43, 40] from Operation: 8*5=40 Current State: 83:[43, 40], Operations: ['46-41=5', '8*5=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[41, 8, 43, 46], Operations: [] Exploring Operation: 41+43=84, Resulting Numbers: [8, 46, 84] Generated Node #0,0: 83:[8, 46, 84] Operation: 41+43=84 Exploring Operation: 41+8=49, Resulting Numbers: [43, 46, 49] Generated Node #0,1: 83:[43, 46, 49] Operation: 41+8=49 Exploring Operation: 8+43=51, Resulting Numbers: [41, 46, 51] Generated Node #0,2: 83:[41, 46, 51] Operation: 8+43=51 Exploring Operation: 8+46=54, Resulting Numbers: [41, 43, 54] Generated Node #0,3: 83:[41, 43, 54] Operation: 8+46=54 Exploring Operation: 41+46=87, Resulting Numbers: [8, 43, 87] Generated Node #0,4: 83:[8, 43, 87] Operation: 41+46=87 Moving to Node #0,1 Current State: 83:[43, 46, 49], Operations: ['41+8=49'] Exploring Operation: 49-43=6, Resulting Numbers: [46, 6] Generated Node #0,1,0: 83:[46, 6] Operation: 49-43=6 Exploring Operation: 46+49=95, Resulting Numbers: [43, 95] Generated Node #0,1,1: 83:[43, 95] Operation: 46+49=95 Exploring Operation: 43+49=92, Resulting Numbers: [46, 92] Generated Node #0,1,2: 83:[46, 92] Operation: 43+49=92 Exploring Operation: 43+46=89, Resulting Numbers: [49, 89] Generated Node #0,1,3: 83:[49, 89] Operation: 43+46=89 Exploring Operation: 46-43=3, Resulting Numbers: [49, 3] Generated Node #0,1,4: 83:[49, 3] Operation: 46-43=3 Moving to Node #0,3 Current State: 83:[41, 43, 54], Operations: ['8+46=54'] Exploring Operation: 54-41=13, Resulting Numbers: [43, 13] Generated Node #0,3,0: 83:[43, 13] Operation: 54-41=13 Exploring Operation: 43+54=97, Resulting Numbers: [41, 97] Generated Node #0,3,1: 83:[41, 97] Operation: 43+54=97 Exploring Operation: 43-41=2, Resulting Numbers: [54, 2] Generated Node #0,3,2: 83:[54, 2] Operation: 43-41=2 Exploring Operation: 41+54=95, Resulting Numbers: [43, 95] Generated Node #0,3,3: 83:[43, 95] Operation: 41+54=95 Exploring Operation: 41+43=84, Resulting Numbers: [54, 84] Generated Node #0,3,4: 83:[54, 84] Operation: 41+43=84 Moving to Node #0,2 Current State: 83:[41, 46, 51], Operations: ['8+43=51'] Exploring Operation: 46+51=97, Resulting Numbers: [41, 97] Generated Node #0,2,0: 83:[41, 97] Operation: 46+51=97 Exploring Operation: 41+51=92, Resulting Numbers: [46, 92] Generated Node #0,2,1: 83:[46, 92] Operation: 41+51=92 Exploring Operation: 41+46=87, Resulting Numbers: [51, 87] Generated Node #0,2,2: 83:[51, 87] Operation: 41+46=87 Exploring Operation: 51-41=10, Resulting Numbers: [46, 10] Generated Node #0,2,3: 83:[46, 10] Operation: 51-41=10 Exploring Operation: 46-41=5, Resulting Numbers: [51, 5] Generated Node #0,2,4: 83:[51, 5] Operation: 46-41=5 Moving to Node #0,0 Current State: 83:[8, 46, 84], Operations: ['41+43=84'] Exploring Operation: 84-8=76, Resulting Numbers: [46, 76] Generated Node #0,0,0: 83:[46, 76] Operation: 84-8=76 Exploring Operation: 84-46=38, Resulting Numbers: [8, 38] Generated Node #0,0,1: 83:[8, 38] Operation: 84-46=38 Exploring Operation: 8+84=92, Resulting Numbers: [46, 92] Generated Node #0,0,2: 83:[46, 92] Operation: 8+84=92 Exploring Operation: 46-8=38, Resulting Numbers: [84, 38] Generated Node #0,0,3: 83:[84, 38] Operation: 46-8=38 Exploring Operation: 8+46=54, Resulting Numbers: [84, 54] Generated Node #0,0,4: 83:[84, 54] Operation: 8+46=54 Moving to Node #0,4 Current State: 83:[8, 43, 87], Operations: ['41+46=87'] Exploring Operation: 8+43=51, Resulting Numbers: [87, 51] Generated Node #0,4,0: 83:[87, 51] Operation: 8+43=51 Exploring Operation: 87-43=44, Resulting Numbers: [8, 44] Generated Node #0,4,1: 83:[8, 44] Operation: 87-43=44 Exploring Operation: 8+87=95, Resulting Numbers: [43, 95] Generated Node #0,4,2: 83:[43, 95] Operation: 8+87=95 Exploring Operation: 43-8=35, Resulting Numbers: [87, 35] Generated Node #0,4,3: 83:[87, 35] Operation: 43-8=35 Exploring Operation: 87-8=79, Resulting Numbers: [43, 79] Generated Node #0,4,4: 83:[43, 79] Operation: 87-8=79 Moving to Node #0,3,4 Current State: 83:[54, 84], Operations: ['8+46=54', '41+43=84'] Exploring Operation: 54*84=4536, Resulting Numbers: [4536] 4536,83 unequal: No Solution Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 54+84=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[84, 54], Operations: ['41+43=84', '8+46=54'] Exploring Operation: 84+54=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 84-54=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 84*54=4536, Resulting Numbers: [4536] 4536,83 unequal: No Solution Moving to Node #0,4,0 Current State: 83:[87, 51], Operations: ['41+46=87', '8+43=51'] Exploring Operation: 87*51=4437, Resulting Numbers: [4437] 4437,83 unequal: No Solution Exploring Operation: 87+51=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[51, 87], Operations: ['8+43=51', '41+46=87'] Exploring Operation: 87-51=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 51*87=4437, Resulting Numbers: [4437] 4437,83 unequal: No Solution Exploring Operation: 51+87=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[49, 89], Operations: ['41+8=49', '43+46=89'] Exploring Operation: 49*89=4361, Resulting Numbers: [4361] 4361,83 unequal: No Solution Exploring Operation: 89-49=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 49+89=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[43, 79], Operations: ['41+46=87', '87-8=79'] Exploring Operation: 43+79=122, Resulting Numbers: [122] 122,83 unequal: No Solution Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 43*79=3397, Resulting Numbers: [3397] 3397,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[46, 76], Operations: ['41+43=84', '84-8=76'] Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 46*76=3496, Resulting Numbers: [3496] 3496,83 unequal: No Solution Exploring Operation: 46+76=122, Resulting Numbers: [122] 122,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[46, 92], Operations: ['8+43=51', '41+51=92'] Exploring Operation: 46+92=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 46*92=4232, Resulting Numbers: [4232] 4232,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[46, 92], Operations: ['41+8=49', '43+49=92'] Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 46*92=4232, Resulting Numbers: [4232] 4232,83 unequal: No Solution Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 46+92=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[46, 92], Operations: ['41+43=84', '8+84=92'] Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 46+92=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 46*92=4232, Resulting Numbers: [4232] 4232,83 unequal: No Solution Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[84, 38], Operations: ['41+43=84', '46-8=38'] Exploring Operation: 84*38=3192, Resulting Numbers: [3192] 3192,83 unequal: No Solution Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 84+38=122, Resulting Numbers: [122] 122,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[43, 95], Operations: ['8+46=54', '41+54=95'] Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 43*95=4085, Resulting Numbers: [4085] 4085,83 unequal: No Solution Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[43, 95], Operations: ['41+8=49', '46+49=95'] Exploring Operation: 43*95=4085, Resulting Numbers: [4085] 4085,83 unequal: No Solution Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,4,2 Current State: 83:[43, 95], Operations: ['41+46=87', '8+87=95'] Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 43*95=4085, Resulting Numbers: [4085] 4085,83 unequal: No Solution Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,4,3 Current State: 83:[87, 35], Operations: ['41+46=87', '43-8=35'] Exploring Operation: 87*35=3045, Resulting Numbers: [3045] 3045,83 unequal: No Solution Exploring Operation: 87+35=122, Resulting Numbers: [122] 122,83 unequal: No Solution Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[41, 97], Operations: ['8+43=51', '46+51=97'] Exploring Operation: 41*97=3977, Resulting Numbers: [3977] 3977,83 unequal: No Solution Exploring Operation: 97-41=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 41+97=138, Resulting Numbers: [138] 138,83 unequal: No Solution Moving to Node #0,3,1 Current State: 83:[41, 97], Operations: ['8+46=54', '43+54=97'] Exploring Operation: 41+97=138, Resulting Numbers: [138] 138,83 unequal: No Solution Exploring Operation: 41*97=3977, Resulting Numbers: [3977] 3977,83 unequal: No Solution Exploring Operation: 97-41=56, Resulting Numbers: [56] 56,83 unequal: No Solution Moving to Node #0,2,4 Current State: 83:[51, 5], Operations: ['8+43=51', '46-41=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[54, 2], Operations: ['8+46=54', '43-41=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[43, 13], Operations: ['8+46=54', '54-41=13'] Exploring Operation: 43+13=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 43*13=559, Resulting Numbers: [559] 559,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[46, 10], Operations: ['8+43=51', '51-41=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 46*10=460, Resulting Numbers: [460] 460,83 unequal: No Solution Exploring Operation: 46+10=56, Resulting Numbers: [56] 56,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[46, 6], Operations: ['41+8=49', '49-43=6'] Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,83 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,83 unequal: No Solution Moving to Node #0,4,1 Current State: 83:[8, 44], Operations: ['41+46=87', '87-43=44'] Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,83 unequal: No Solution Moving to Node #0,1,4 Current State: 83:[49, 3], Operations: ['41+8=49', '46-43=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,83 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[8, 38], Operations: ['41+43=84', '84-46=38'] Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,83 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 33, 54, 18, 84 ]
95
[ "33*18=594", "594/54=11", "84+11=95" ]
Current State: 95:[33, 54, 18, 84], Operations: [] Exploring Operation: 33*18=594, Resulting Numbers: [54, 84, 594] Generated Node #2: [54, 84, 594] from Operation: 33*18=594 Current State: 95:[54, 84, 594], Operations: ['33*18=594'] Exploring Operation: 594/54=11, Resulting Numbers: [84, 11] Generated Node #3: [84, 11] from Operation: 594/54=11 Current State: 95:[84, 11], Operations: ['33*18=594', '594/54=11'] Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[33, 54, 18, 84], Operations: [] Exploring Operation: 54-18=36, Resulting Numbers: [33, 84, 36] Generated Node #0,0: 95:[33, 84, 36] Operation: 54-18=36 Exploring Operation: 84-54=30, Resulting Numbers: [33, 18, 30] Generated Node #0,1: 95:[33, 18, 30] Operation: 84-54=30 Exploring Operation: 54/18=3, Resulting Numbers: [33, 84, 3] Generated Node #0,2: 95:[33, 84, 3] Operation: 54/18=3 Exploring Operation: 33+54=87, Resulting Numbers: [18, 84, 87] Generated Node #0,3: 95:[18, 84, 87] Operation: 33+54=87 Exploring Operation: 54-33=21, Resulting Numbers: [18, 84, 21] Generated Node #0,4: 95:[18, 84, 21] Operation: 54-33=21 Moving to Node #0,4 Current State: 95:[18, 84, 21], Operations: ['54-33=21'] Exploring Operation: 84-18=66, Resulting Numbers: [21, 66] Generated Node #0,4,0: 95:[21, 66] Operation: 84-18=66 Exploring Operation: 21-18=3, Resulting Numbers: [84, 3] Generated Node #0,4,1: 95:[84, 3] Operation: 21-18=3 Exploring Operation: 18+84=102, Resulting Numbers: [21, 102] Generated Node #0,4,2: 95:[21, 102] Operation: 18+84=102 Exploring Operation: 84/21=4, Resulting Numbers: [18, 4] Generated Node #0,4,3: 95:[18, 4] Operation: 84/21=4 Exploring Operation: 84+21=105, Resulting Numbers: [18, 105] Generated Node #0,4,4: 95:[18, 105] Operation: 84+21=105 Moving to Node #0,3 Current State: 95:[18, 84, 87], Operations: ['33+54=87'] Exploring Operation: 87-84=3, Resulting Numbers: [18, 3] Generated Node #0,3,0: 95:[18, 3] Operation: 87-84=3 Exploring Operation: 87-18=69, Resulting Numbers: [84, 69] Generated Node #0,3,1: 95:[84, 69] Operation: 87-18=69 Exploring Operation: 18+87=105, Resulting Numbers: [84, 105] Generated Node #0,3,2: 95:[84, 105] Operation: 18+87=105 Exploring Operation: 84-18=66, Resulting Numbers: [87, 66] Generated Node #0,3,3: 95:[87, 66] Operation: 84-18=66 Exploring Operation: 18+84=102, Resulting Numbers: [87, 102] Generated Node #0,3,4: 95:[87, 102] Operation: 18+84=102 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 95:[18, 3], Operations: ['33+54=87', '87-84=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,95 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 95:[87, 102], Operations: ['33+54=87', '18+84=102'] Exploring Operation: 87*102=8874, Resulting Numbers: [8874] 8874,95 unequal: No Solution Exploring Operation: 102-87=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 87+102=189, Resulting Numbers: [189] 189,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 95:[84, 105], Operations: ['33+54=87', '18+87=105'] Exploring Operation: 84*105=8820, Resulting Numbers: [8820] 8820,95 unequal: No Solution Exploring Operation: 84+105=189, Resulting Numbers: [189] 189,95 unequal: No Solution Exploring Operation: 105-84=21, Resulting Numbers: [21] 21,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 95:[84, 69], Operations: ['33+54=87', '87-18=69'] Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,95 unequal: No Solution Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 95:[87, 66], Operations: ['33+54=87', '84-18=66'] Exploring Operation: 87+66=153, Resulting Numbers: [153] 153,95 unequal: No Solution Exploring Operation: 87-66=21, Resulting Numbers: [21] 21,95 unequal: No Solution Exploring Operation: 87*66=5742, Resulting Numbers: [5742] 5742,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 95:[33, 18, 30], Operations: ['84-54=30'] Exploring Operation: 33+18=51, Resulting Numbers: [30, 51] Generated Node #0,1,0: 95:[30, 51] Operation: 33+18=51 Exploring Operation: 30-18=12, Resulting Numbers: [33, 12] Generated Node #0,1,1: 95:[33, 12] Operation: 30-18=12 Exploring Operation: 33-18=15, Resulting Numbers: [30, 15] Generated Node #0,1,2: 95:[30, 15] Operation: 33-18=15 Exploring Operation: 33+30=63, Resulting Numbers: [18, 63] Generated Node #0,1,3: 95:[18, 63] Operation: 33+30=63 Exploring Operation: 33-30=3, Resulting Numbers: [18, 3] Generated Node #0,1,4: 95:[18, 3] Operation: 33-30=3 Moving to Node #0,2 Current State: 95:[33, 84, 3], Operations: ['54/18=3'] Exploring Operation: 33-3=30, Resulting Numbers: [84, 30] Generated Node #0,2,0: 95:[84, 30] Operation: 33-3=30 Exploring Operation: 84+3=87, Resulting Numbers: [33, 87] Generated Node #0,2,1: 95:[33, 87] Operation: 84+3=87 Exploring Operation: 33/3=11, Resulting Numbers: [84, 11] Generated Node #0,2,2: 95:[84, 11] Operation: 33/3=11 Exploring Operation: 33*3=99, Resulting Numbers: [84, 99] Generated Node #0,2,3: 95:[84, 99] Operation: 33*3=99 Exploring Operation: 84/3=28, Resulting Numbers: [33, 28] Generated Node #0,2,4: 95:[33, 28] Operation: 84/3=28 Moving to Node #0,0 Current State: 95:[33, 84, 36], Operations: ['54-18=36'] Exploring Operation: 36-33=3, Resulting Numbers: [84, 3] Generated Node #0,0,0: 95:[84, 3] Operation: 36-33=3 Exploring Operation: 33+84=117, Resulting Numbers: [36, 117] Generated Node #0,0,1: 95:[36, 117] Operation: 33+84=117 Exploring Operation: 33+36=69, Resulting Numbers: [84, 69] Generated Node #0,0,2: 95:[84, 69] Operation: 33+36=69 Exploring Operation: 84-36=48, Resulting Numbers: [33, 48] Generated Node #0,0,3: 95:[33, 48] Operation: 84-36=48 Exploring Operation: 84+36=120, Resulting Numbers: [33, 120] Generated Node #0,0,4: 95:[33, 120] Operation: 84+36=120 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[84, 3], Operations: ['54-18=36', '36-33=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[84, 69], Operations: ['54-18=36', '33+36=69'] Exploring Operation: 84-69=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 84+69=153, Resulting Numbers: [153] 153,95 unequal: No Solution Exploring Operation: 84*69=5796, Resulting Numbers: [5796] 5796,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[36, 117], Operations: ['54-18=36', '33+84=117'] Exploring Operation: 117-36=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 36*117=4212, Resulting Numbers: [4212] 4212,95 unequal: No Solution Exploring Operation: 36+117=153, Resulting Numbers: [153] 153,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 95:[33, 120], Operations: ['54-18=36', '84+36=120'] Exploring Operation: 120-33=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 33+120=153, Resulting Numbers: [153] 153,95 unequal: No Solution Exploring Operation: 33*120=3960, Resulting Numbers: [3960] 3960,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 95:[33, 48], Operations: ['54-18=36', '84-36=48'] Exploring Operation: 48-33=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 33*48=1584, Resulting Numbers: [1584] 1584,95 unequal: No Solution Exploring Operation: 33+48=81, Resulting Numbers: [81] 81,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 95:[18, 4], Operations: ['54-33=21', '84/21=4'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,95 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,95 unequal: No Solution Moving to Node #0,1,4 Current State: 95:[18, 3], Operations: ['84-54=30', '33-30=3'] Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,95 unequal: No Solution Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,95 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,95 unequal: No Solution Moving to Node #0,4,2 Current State: 95:[21, 102], Operations: ['54-33=21', '18+84=102'] Exploring Operation: 21*102=2142, Resulting Numbers: [2142] 2142,95 unequal: No Solution Exploring Operation: 102-21=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 21+102=123, Resulting Numbers: [123] 123,95 unequal: No Solution Moving to Node #0,4,4 Current State: 95:[18, 105], Operations: ['54-33=21', '84+21=105'] Exploring Operation: 18*105=1890, Resulting Numbers: [1890] 1890,95 unequal: No Solution Exploring Operation: 18+105=123, Resulting Numbers: [123] 123,95 unequal: No Solution Exploring Operation: 105-18=87, Resulting Numbers: [87] 87,95 unequal: No Solution Moving to Node #0,4,1 Current State: 95:[84, 3], Operations: ['54-33=21', '21-18=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,95 unequal: No Solution Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[30, 15], Operations: ['84-54=30', '33-18=15'] Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,95 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,95 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,95 unequal: No Solution Moving to Node #0,2,3 Current State: 95:[84, 99], Operations: ['54/18=3', '33*3=99'] Exploring Operation: 84+99=183, Resulting Numbers: [183] 183,95 unequal: No Solution Exploring Operation: 99-84=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 84*99=8316, Resulting Numbers: [8316] 8316,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[84, 11], Operations: ['54/18=3', '33/3=11'] Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[33, 54, 18, 84], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [33, 84, 3] Generated Node #0,2: 95:[33, 84, 3] Operation: 54/18=3 Moving to Node #0,2 Current State: 95:[33, 84, 3], Operations: ['54/18=3'] Exploring Operation: 33/3=11, Resulting Numbers: [84, 11] Generated Node #0,2,2: 95:[84, 11] Operation: 33/3=11 Moving to Node #0,2,2 Current State: 95:[84, 11], Operations: ['54/18=3', '33/3=11'] Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.921007
hs_5
sum_heuristic
[ 11, 52, 90, 26 ]
53
[ "11+52=63", "90+26=116", "116-63=53" ]
Current State: 53:[11, 52, 90, 26], Operations: [] Exploring Operation: 11+52=63, Resulting Numbers: [90, 26, 63] Generated Node #2: [90, 26, 63] from Operation: 11+52=63 Current State: 53:[90, 26, 63], Operations: ['11+52=63'] Exploring Operation: 90+26=116, Resulting Numbers: [63, 116] Generated Node #3: [63, 116] from Operation: 90+26=116 Current State: 53:[63, 116], Operations: ['11+52=63', '90+26=116'] Exploring Operation: 116-63=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[11, 52, 90, 26], Operations: [] Exploring Operation: 90-26=64, Resulting Numbers: [11, 52, 64] Generated Node #0,0: 53:[11, 52, 64] Operation: 90-26=64 Exploring Operation: 11+52=63, Resulting Numbers: [90, 26, 63] Generated Node #0,1: 53:[90, 26, 63] Operation: 11+52=63 Exploring Operation: 11+26=37, Resulting Numbers: [52, 90, 37] Generated Node #0,2: 53:[52, 90, 37] Operation: 11+26=37 Exploring Operation: 90-11=79, Resulting Numbers: [52, 26, 79] Generated Node #0,3: 53:[52, 26, 79] Operation: 90-11=79 Moving to Node #0,0 Current State: 53:[11, 52, 64], Operations: ['90-26=64'] Exploring Operation: 11+64=75, Resulting Numbers: [52, 75] Generated Node #0,0,0: 53:[52, 75] Operation: 11+64=75 Exploring Operation: 52-11=41, Resulting Numbers: [64, 41] Generated Node #0,0,1: 53:[64, 41] Operation: 52-11=41 Exploring Operation: 11+52=63, Resulting Numbers: [64, 63] Generated Node #0,0,2: 53:[64, 63] Operation: 11+52=63 Exploring Operation: 64-11=53, Resulting Numbers: [52, 53] Generated Node #0,0,3: 53:[52, 53] Operation: 64-11=53 Moving to Node #0,3 Current State: 53:[52, 26, 79], Operations: ['90-11=79'] Exploring Operation: 52+26=78, Resulting Numbers: [79, 78] Generated Node #0,3,0: 53:[79, 78] Operation: 52+26=78 Exploring Operation: 52-26=26, Resulting Numbers: [79, 26] Generated Node #0,3,1: 53:[79, 26] Operation: 52-26=26 Exploring Operation: 79-26=53, Resulting Numbers: [52, 53] Generated Node #0,3,2: 53:[52, 53] Operation: 79-26=53 Exploring Operation: 79-52=27, Resulting Numbers: [26, 27] Generated Node #0,3,3: 53:[26, 27] Operation: 79-52=27 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[52, 53], Operations: ['90-11=79', '79-26=53'] Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[79, 78], Operations: ['90-11=79', '52+26=78'] Exploring Operation: 79*78=6162, Resulting Numbers: [6162] 6162,53 unequal: No Solution Exploring Operation: 79-78=1, Resulting Numbers: [1] 1,53 unequal: No Solution Exploring Operation: 79+78=157, Resulting Numbers: [157] 157,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[79, 26], Operations: ['90-11=79', '52-26=26'] Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[11, 52, 90, 26], Operations: [] Exploring Operation: 90-11=79, Resulting Numbers: [52, 26, 79] Generated Node #0,3: 53:[52, 26, 79] Operation: 90-11=79 Moving to Node #0,3 Current State: 53:[52, 26, 79], Operations: ['90-11=79'] Exploring Operation: 52-26=26, Resulting Numbers: [79, 26] Generated Node #0,3,1: 53:[79, 26] Operation: 52-26=26 Moving to Node #0,3,1 Current State: 53:[79, 26], Operations: ['90-11=79', '52-26=26'] Exploring Operation: 79-26=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 21, 50, 15, 55 ]
18
[ "55-50=5", "15/5=3", "21-3=18" ]
Current State: 18:[21, 50, 15, 55], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [21, 15, 5] Generated Node #2: [21, 15, 5] from Operation: 55-50=5 Current State: 18:[21, 15, 5], Operations: ['55-50=5'] Exploring Operation: 15/5=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 15/5=3 Current State: 18:[21, 3], Operations: ['55-50=5', '15/5=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[21, 50, 15, 55], Operations: [] Exploring Operation: 55-21=34, Resulting Numbers: [50, 15, 34] Generated Node #0,0: 18:[50, 15, 34] Operation: 55-21=34 Exploring Operation: 55-50=5, Resulting Numbers: [21, 15, 5] Generated Node #0,1: 18:[21, 15, 5] Operation: 55-50=5 Exploring Operation: 50-21=29, Resulting Numbers: [15, 55, 29] Generated Node #0,2: 18:[15, 55, 29] Operation: 50-21=29 Moving to Node #0,1 Current State: 18:[21, 15, 5], Operations: ['55-50=5'] Exploring Operation: 15/5=3, Resulting Numbers: [21, 3] Generated Node #0,1,0: 18:[21, 3] Operation: 15/5=3 Exploring Operation: 15-5=10, Resulting Numbers: [21, 10] Generated Node #0,1,1: 18:[21, 10] Operation: 15-5=10 Exploring Operation: 21-15=6, Resulting Numbers: [5, 6] Generated Node #0,1,2: 18:[5, 6] Operation: 21-15=6 Moving to Node #0,0 Current State: 18:[50, 15, 34], Operations: ['55-21=34'] Exploring Operation: 50-34=16, Resulting Numbers: [15, 16] Generated Node #0,0,0: 18:[15, 16] Operation: 50-34=16 Exploring Operation: 50-15=35, Resulting Numbers: [34, 35] Generated Node #0,0,1: 18:[34, 35] Operation: 50-15=35 Exploring Operation: 34-15=19, Resulting Numbers: [50, 19] Generated Node #0,0,2: 18:[50, 19] Operation: 34-15=19 Moving to Node #0,2 Current State: 18:[15, 55, 29], Operations: ['50-21=29'] Exploring Operation: 55-15=40, Resulting Numbers: [29, 40] Generated Node #0,2,0: 18:[29, 40] Operation: 55-15=40 Exploring Operation: 55-29=26, Resulting Numbers: [15, 26] Generated Node #0,2,1: 18:[15, 26] Operation: 55-29=26 Exploring Operation: 29-15=14, Resulting Numbers: [55, 14] Generated Node #0,2,2: 18:[55, 14] Operation: 29-15=14 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[15, 26], Operations: ['50-21=29', '55-29=26'] Exploring Operation: 15+26=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 15*26=390, Resulting Numbers: [390] 390,18 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[29, 40], Operations: ['50-21=29', '55-15=40'] Exploring Operation: 29*40=1160, Resulting Numbers: [1160] 1160,18 unequal: No Solution Exploring Operation: 29+40=69, Resulting Numbers: [69] 69,18 unequal: No Solution Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[55, 14], Operations: ['50-21=29', '29-15=14'] Exploring Operation: 55*14=770, Resulting Numbers: [770] 770,18 unequal: No Solution Exploring Operation: 55+14=69, Resulting Numbers: [69] 69,18 unequal: No Solution Exploring Operation: 55-14=41, Resulting Numbers: [41] 41,18 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: 18:[5, 6], Operations: ['55-50=5', '21-15=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[21, 3], Operations: ['55-50=5', '15/5=3'] Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[21, 50, 15, 55], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [21, 15, 5] Generated Node #0,1: 18:[21, 15, 5] Operation: 55-50=5 Moving to Node #0,1 Current State: 18:[21, 15, 5], Operations: ['55-50=5'] Exploring Operation: 15/5=3, Resulting Numbers: [21, 3] Generated Node #0,1,0: 18:[21, 3] Operation: 15/5=3 Moving to Node #0,1,0 Current State: 18:[21, 3], Operations: ['55-50=5', '15/5=3'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 3, 42, 74, 72 ]
90
[ "3+42=45", "74-72=2", "45*2=90" ]
Current State: 90:[3, 42, 74, 72], Operations: [] Exploring Operation: 3+42=45, Resulting Numbers: [74, 72, 45] Generated Node #2: [74, 72, 45] from Operation: 3+42=45 Current State: 90:[74, 72, 45], Operations: ['3+42=45'] Exploring Operation: 74-72=2, Resulting Numbers: [45, 2] Generated Node #3: [45, 2] from Operation: 74-72=2 Current State: 90:[45, 2], Operations: ['3+42=45', '74-72=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[3, 42, 74, 72], Operations: [] Exploring Operation: 72/3=24, Resulting Numbers: [42, 74, 24] Generated Node #0,0: 90:[42, 74, 24] Operation: 72/3=24 Exploring Operation: 3+42=45, Resulting Numbers: [74, 72, 45] Generated Node #0,1: 90:[74, 72, 45] Operation: 3+42=45 Exploring Operation: 72-42=30, Resulting Numbers: [3, 74, 30] Generated Node #0,2: 90:[3, 74, 30] Operation: 72-42=30 Exploring Operation: 74-72=2, Resulting Numbers: [3, 42, 2] Generated Node #0,3: 90:[3, 42, 2] Operation: 74-72=2 Exploring Operation: 74-42=32, Resulting Numbers: [3, 72, 32] Generated Node #0,4: 90:[3, 72, 32] Operation: 74-42=32 Moving to Node #0,3 Current State: 90:[3, 42, 2], Operations: ['74-72=2'] Exploring Operation: 3*2=6, Resulting Numbers: [42, 6] Generated Node #0,3,0: 90:[42, 6] Operation: 3*2=6 Exploring Operation: 3+2=5, Resulting Numbers: [42, 5] Generated Node #0,3,1: 90:[42, 5] Operation: 3+2=5 Exploring Operation: 42+2=44, Resulting Numbers: [3, 44] Generated Node #0,3,2: 90:[3, 44] Operation: 42+2=44 Exploring Operation: 3+42=45, Resulting Numbers: [2, 45] Generated Node #0,3,3: 90:[2, 45] Operation: 3+42=45 Exploring Operation: 42/3=14, Resulting Numbers: [2, 14] Generated Node #0,3,4: 90:[2, 14] Operation: 42/3=14 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 90:[2, 45], Operations: ['74-72=2', '3+42=45'] Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[3, 42, 74, 72], Operations: [] Exploring Operation: 74-72=2, Resulting Numbers: [3, 42, 2] Generated Node #0,3: 90:[3, 42, 2] Operation: 74-72=2 Moving to Node #0,3 Current State: 90:[3, 42, 2], Operations: ['74-72=2'] Exploring Operation: 3+42=45, Resulting Numbers: [2, 45] Generated Node #0,3,3: 90:[2, 45] Operation: 3+42=45 Moving to Node #0,3,3 Current State: 90:[2, 45], Operations: ['74-72=2', '3+42=45'] Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 73, 38, 7, 35 ]
40
[ "73-38=35", "35/7=5", "35+5=40" ]
Current State: 40:[73, 38, 7, 35], Operations: [] Exploring Operation: 73-38=35, Resulting Numbers: [7, 35, 35] Generated Node #2: [7, 35, 35] from Operation: 73-38=35 Current State: 40:[7, 35, 35], Operations: ['73-38=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,40 equal: Goal Reached Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[73, 38, 7, 35], Operations: [] Exploring Operation: 73-7=66, Resulting Numbers: [38, 35, 66] Generated Node #0,0: 40:[38, 35, 66] Operation: 73-7=66 Exploring Operation: 73-38=35, Resulting Numbers: [7, 35, 35] Generated Node #0,1: 40:[7, 35, 35] Operation: 73-38=35 Exploring Operation: 38-35=3, Resulting Numbers: [73, 7, 3] Generated Node #0,2: 40:[73, 7, 3] Operation: 38-35=3 Exploring Operation: 73-35=38, Resulting Numbers: [38, 7, 38] Generated Node #0,3: 40:[38, 7, 38] Operation: 73-35=38 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[38, 7, 38], Operations: ['73-35=38'] Exploring Operation: 38-38=0, Resulting Numbers: [7, 0] Generated Node #0,3,0: 40:[7, 0] Operation: 38-38=0 Exploring Operation: 7+38=45, Resulting Numbers: [38, 45] Generated Node #0,3,1: 40:[38, 45] Operation: 7+38=45 Exploring Operation: 38+7=45, Resulting Numbers: [38, 45] Generated Node #0,3,2: 40:[38, 45] Operation: 38+7=45 Exploring Operation: 38/38=1, Resulting Numbers: [7, 1] Generated Node #0,3,3: 40:[7, 1] Operation: 38/38=1 Moving to Node #0,3,3 Current State: 40:[7, 1], Operations: ['73-35=38', '38/38=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,40 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,3,0 Current State: 40:[7, 0], Operations: ['73-35=38', '38-38=0'] Exploring Operation: 7+0=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7-0=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7*0=0, Resulting Numbers: [0] 0,40 unequal: No Solution Moving to Node #0,3,2 Current State: 40:[38, 45], Operations: ['73-35=38', '38+7=45'] Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,40 unequal: No Solution Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,40 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,3,1 Current State: 40:[38, 45], Operations: ['73-35=38', '7+38=45'] Exploring Operation: 38+45=83, Resulting Numbers: [83] 83,40 unequal: No Solution Exploring Operation: 38*45=1710, Resulting Numbers: [1710] 1710,40 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[7, 35, 35], Operations: ['73-38=35'] Exploring Operation: 35-35=0, Resulting Numbers: [7, 0] Generated Node #0,1,0: 40:[7, 0] Operation: 35-35=0 Exploring Operation: 35/7=5, Resulting Numbers: [35, 5] Generated Node #0,1,1: 40:[35, 5] Operation: 35/7=5 Exploring Operation: 35/35=1, Resulting Numbers: [7, 1] Generated Node #0,1,2: 40:[7, 1] Operation: 35/35=1 Exploring Operation: 35/7=5, Resulting Numbers: [35, 5] Generated Node #0,1,3: 40:[35, 5] Operation: 35/7=5 Moving to Node #0,1,2 Current State: 40:[7, 1], Operations: ['73-38=35', '35/35=1'] Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,40 unequal: No Solution Moving to Node #0,1,0 Current State: 40:[7, 0], Operations: ['73-38=35', '35-35=0'] Exploring Operation: 7*0=0, Resulting Numbers: [0] 0,40 unequal: No Solution Exploring Operation: 7-0=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 7+0=7, Resulting Numbers: [7] 7,40 unequal: No Solution Moving to Node #0,1,3 Current State: 40:[35, 5], Operations: ['73-38=35', '35/7=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,40 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,40 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,40 unequal: No Solution Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[73, 38, 7, 35], Operations: [] Exploring Operation: 73-38=35, Resulting Numbers: [7, 35, 35] Generated Node #0,1: 40:[7, 35, 35] Operation: 73-38=35 Moving to Node #0,1 Current State: 40:[7, 35, 35], Operations: ['73-38=35'] Exploring Operation: 35/7=5, Resulting Numbers: [35, 5] Generated Node #0,1,3: 40:[35, 5] Operation: 35/7=5 Moving to Node #0,1,3 Current State: 40:[35, 5], Operations: ['73-38=35', '35/7=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 60, 2, 30, 40 ]
52
[ "60+2=62", "40-30=10", "62-10=52" ]
Current State: 52:[60, 2, 30, 40], Operations: [] Exploring Operation: 60+2=62, Resulting Numbers: [30, 40, 62] Generated Node #2: [30, 40, 62] from Operation: 60+2=62 Current State: 52:[30, 40, 62], Operations: ['60+2=62'] Exploring Operation: 40-30=10, Resulting Numbers: [62, 10] Generated Node #3: [62, 10] from Operation: 40-30=10 Current State: 52:[62, 10], Operations: ['60+2=62', '40-30=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[60, 2, 30, 40], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [2, 30, 20] Generated Node #0,0: 52:[2, 30, 20] Operation: 60-40=20 Moving to Node #0,0 Current State: 52:[2, 30, 20], Operations: ['60-40=20'] Exploring Operation: 30+20=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 52:[2, 50] Operation: 30+20=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[2, 50], Operations: ['60-40=20', '30+20=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[60, 2, 30, 40], Operations: [] Exploring Operation: 60-40=20, Resulting Numbers: [2, 30, 20] Generated Node #0,0: 52:[2, 30, 20] Operation: 60-40=20 Moving to Node #0,0 Current State: 52:[2, 30, 20], Operations: ['60-40=20'] Exploring Operation: 30+20=50, Resulting Numbers: [2, 50] Generated Node #0,0,0: 52:[2, 50] Operation: 30+20=50 Moving to Node #0,0,0 Current State: 52:[2, 50], Operations: ['60-40=20', '30+20=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 13, 18, 61, 84 ]
65
[ "18+61=79", "84-79=5", "13*5=65" ]
Current State: 65:[13, 18, 61, 84], Operations: [] Exploring Operation: 18+61=79, Resulting Numbers: [13, 84, 79] Generated Node #2: [13, 84, 79] from Operation: 18+61=79 Current State: 65:[13, 84, 79], Operations: ['18+61=79'] Exploring Operation: 84-79=5, Resulting Numbers: [13, 5] Generated Node #3: [13, 5] from Operation: 84-79=5 Current State: 65:[13, 5], Operations: ['18+61=79', '84-79=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[13, 18, 61, 84], Operations: [] Exploring Operation: 84-18=66, Resulting Numbers: [13, 61, 66] Generated Node #0,0: 65:[13, 61, 66] Operation: 84-18=66 Moving to Node #0,0 Current State: 65:[13, 61, 66], Operations: ['84-18=66'] Exploring Operation: 66-61=5, Resulting Numbers: [13, 5] Generated Node #0,0,0: 65:[13, 5] Operation: 66-61=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[13, 5], Operations: ['84-18=66', '66-61=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[13, 18, 61, 84], Operations: [] Exploring Operation: 84-18=66, Resulting Numbers: [13, 61, 66] Generated Node #0,0: 65:[13, 61, 66] Operation: 84-18=66 Moving to Node #0,0 Current State: 65:[13, 61, 66], Operations: ['84-18=66'] Exploring Operation: 66-61=5, Resulting Numbers: [13, 5] Generated Node #0,0,0: 65:[13, 5] Operation: 66-61=5 Moving to Node #0,0,0 Current State: 65:[13, 5], Operations: ['84-18=66', '66-61=5'] Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 11, 2, 62, 46 ]
89
[ "46-11=35", "2*62=124", "124-35=89" ]
Current State: 89:[11, 2, 62, 46], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [2, 62, 35] Generated Node #2: [2, 62, 35] from Operation: 46-11=35 Current State: 89:[2, 62, 35], Operations: ['46-11=35'] Exploring Operation: 2*62=124, Resulting Numbers: [35, 124] Generated Node #3: [35, 124] from Operation: 2*62=124 Current State: 89:[35, 124], Operations: ['46-11=35', '2*62=124'] Exploring Operation: 124-35=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[11, 2, 62, 46], Operations: [] Exploring Operation: 2*46=92, Resulting Numbers: [11, 62, 92] Generated Node #0,0: 89:[11, 62, 92] Operation: 2*46=92 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[11, 62, 92], Operations: ['2*46=92'] Exploring Operation: 11+62=73, Resulting Numbers: [92, 73] Generated Node #0,0,0: 89:[92, 73] Operation: 11+62=73 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[92, 73], Operations: ['2*46=92', '11+62=73'] Exploring Operation: 92-73=19, Resulting Numbers: [19] 19,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 66, 90, 52, 26 ]
12
[ "90-66=24", "52/26=2", "24/2=12" ]
Current State: 12:[66, 90, 52, 26], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [52, 26, 24] Generated Node #2: [52, 26, 24] from Operation: 90-66=24 Current State: 12:[52, 26, 24], Operations: ['90-66=24'] Exploring Operation: 52/26=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 52/26=2 Current State: 12:[24, 2], Operations: ['90-66=24', '52/26=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[66, 90, 52, 26], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [52, 26, 24] Generated Node #0,0: 12:[52, 26, 24] Operation: 90-66=24 Exploring Operation: 66-52=14, Resulting Numbers: [90, 26, 14] Generated Node #0,1: 12:[90, 26, 14] Operation: 66-52=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[52, 26, 24], Operations: ['90-66=24'] Exploring Operation: 52/26=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 12:[24, 2] Operation: 52/26=2 Exploring Operation: 52-26=26, Resulting Numbers: [24, 26] Generated Node #0,0,1: 12:[24, 26] Operation: 52-26=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[24, 2], Operations: ['90-66=24', '52/26=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[66, 90, 52, 26], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [52, 26, 24] Generated Node #0,0: 12:[52, 26, 24] Operation: 90-66=24 Moving to Node #0,0 Current State: 12:[52, 26, 24], Operations: ['90-66=24'] Exploring Operation: 52/26=2, Resulting Numbers: [24, 2] Generated Node #0,0,0: 12:[24, 2] Operation: 52/26=2 Moving to Node #0,0,0 Current State: 12:[24, 2], Operations: ['90-66=24', '52/26=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 15, 39, 64, 17 ]
14
[ "17-15=2", "39*2=78", "78-64=14" ]
Current State: 14:[15, 39, 64, 17], Operations: [] Exploring Operation: 17-15=2, Resulting Numbers: [39, 64, 2] Generated Node #2: [39, 64, 2] from Operation: 17-15=2 Current State: 14:[39, 64, 2], Operations: ['17-15=2'] Exploring Operation: 39*2=78, Resulting Numbers: [64, 78] Generated Node #3: [64, 78] from Operation: 39*2=78 Current State: 14:[64, 78], Operations: ['17-15=2', '39*2=78'] Exploring Operation: 78-64=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[15, 39, 64, 17], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [15, 17, 25] Generated Node #0,0: 14:[15, 17, 25] Operation: 64-39=25 Exploring Operation: 39-15=24, Resulting Numbers: [64, 17, 24] Generated Node #0,1: 14:[64, 17, 24] Operation: 39-15=24 Exploring Operation: 64-15=49, Resulting Numbers: [39, 17, 49] Generated Node #0,2: 14:[39, 17, 49] Operation: 64-15=49 Exploring Operation: 64-17=47, Resulting Numbers: [15, 39, 47] Generated Node #0,3: 14:[15, 39, 47] Operation: 64-17=47 Exploring Operation: 39-17=22, Resulting Numbers: [15, 64, 22] Generated Node #0,4: 14:[15, 64, 22] Operation: 39-17=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[15, 17, 25], Operations: ['64-39=25'] Exploring Operation: 15+17=32, Resulting Numbers: [25, 32] Generated Node #0,0,0: 14:[25, 32] Operation: 15+17=32 Exploring Operation: 15+25=40, Resulting Numbers: [17, 40] Generated Node #0,0,1: 14:[17, 40] Operation: 15+25=40 Exploring Operation: 25-17=8, Resulting Numbers: [15, 8] Generated Node #0,0,2: 14:[15, 8] Operation: 25-17=8 Exploring Operation: 25-15=10, Resulting Numbers: [17, 10] Generated Node #0,0,3: 14:[17, 10] Operation: 25-15=10 Exploring Operation: 17-15=2, Resulting Numbers: [25, 2] Generated Node #0,0,4: 14:[25, 2] Operation: 17-15=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 14:[15, 8], Operations: ['64-39=25', '25-17=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 14:[17, 10], Operations: ['64-39=25', '25-15=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,14 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 14:[25, 2], Operations: ['64-39=25', '17-15=2'] Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 14:[25, 32], Operations: ['64-39=25', '15+17=32'] Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[17, 40], Operations: ['64-39=25', '15+25=40'] Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,14 unequal: No Solution Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[15, 39, 47], Operations: ['64-17=47'] Exploring Operation: 47-39=8, Resulting Numbers: [15, 8] Generated Node #0,3,0: 14:[15, 8] Operation: 47-39=8 Exploring Operation: 47-15=32, Resulting Numbers: [39, 32] Generated Node #0,3,1: 14:[39, 32] Operation: 47-15=32 Exploring Operation: 15+47=62, Resulting Numbers: [39, 62] Generated Node #0,3,2: 14:[39, 62] Operation: 15+47=62 Exploring Operation: 15+39=54, Resulting Numbers: [47, 54] Generated Node #0,3,3: 14:[47, 54] Operation: 15+39=54 Exploring Operation: 39-15=24, Resulting Numbers: [47, 24] Generated Node #0,3,4: 14:[47, 24] Operation: 39-15=24 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 14:[15, 8], Operations: ['64-17=47', '47-39=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 14:[39, 32], Operations: ['64-17=47', '47-15=32'] Exploring Operation: 39*32=1248, Resulting Numbers: [1248] 1248,14 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 14:[47, 24], Operations: ['64-17=47', '39-15=24'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 14:[39, 62], Operations: ['64-17=47', '15+47=62'] Exploring Operation: 39*62=2418, Resulting Numbers: [2418] 2418,14 unequal: No Solution Exploring Operation: 39+62=101, Resulting Numbers: [101] 101,14 unequal: No Solution Exploring Operation: 62-39=23, Resulting Numbers: [23] 23,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 14:[47, 54], Operations: ['64-17=47', '15+39=54'] Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,14 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 14:[15, 64, 22], Operations: ['39-17=22'] Exploring Operation: 64-22=42, Resulting Numbers: [15, 42] Generated Node #0,4,0: 14:[15, 42] Operation: 64-22=42 Exploring Operation: 15+22=37, Resulting Numbers: [64, 37] Generated Node #0,4,1: 14:[64, 37] Operation: 15+22=37 Exploring Operation: 64-15=49, Resulting Numbers: [22, 49] Generated Node #0,4,2: 14:[22, 49] Operation: 64-15=49 Exploring Operation: 22-15=7, Resulting Numbers: [64, 7] Generated Node #0,4,3: 14:[64, 7] Operation: 22-15=7 Exploring Operation: 15+64=79, Resulting Numbers: [22, 79] Generated Node #0,4,4: 14:[22, 79] Operation: 15+64=79 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 14:[15, 42], Operations: ['39-17=22', '64-22=42'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 14:[22, 49], Operations: ['39-17=22', '64-15=49'] Exploring Operation: 22+49=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 22*49=1078, Resulting Numbers: [1078] 1078,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 14:[64, 7], Operations: ['39-17=22', '22-15=7'] Exploring Operation: 64+7=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 64*7=448, Resulting Numbers: [448] 448,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 14:[64, 37], Operations: ['39-17=22', '15+22=37'] Exploring Operation: 64-37=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 64*37=2368, Resulting Numbers: [2368] 2368,14 unequal: No Solution Exploring Operation: 64+37=101, Resulting Numbers: [101] 101,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 14:[22, 79], Operations: ['39-17=22', '15+64=79'] Exploring Operation: 22*79=1738, Resulting Numbers: [1738] 1738,14 unequal: No Solution Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 22+79=101, Resulting Numbers: [101] 101,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[64, 17, 24], Operations: ['39-15=24'] Exploring Operation: 64-24=40, Resulting Numbers: [17, 40] Generated Node #0,1,0: 14:[17, 40] Operation: 64-24=40 Exploring Operation: 64+17=81, Resulting Numbers: [24, 81] Generated Node #0,1,1: 14:[24, 81] Operation: 64+17=81 Exploring Operation: 64-17=47, Resulting Numbers: [24, 47] Generated Node #0,1,2: 14:[24, 47] Operation: 64-17=47 Exploring Operation: 24-17=7, Resulting Numbers: [64, 7] Generated Node #0,1,3: 14:[64, 7] Operation: 24-17=7 Exploring Operation: 64+24=88, Resulting Numbers: [17, 88] Generated Node #0,1,4: 14:[17, 88] Operation: 64+24=88 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[17, 40], Operations: ['39-15=24', '64-24=40'] Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 14:[24, 47], Operations: ['39-15=24', '64-17=47'] Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 24+47=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 24*47=1128, Resulting Numbers: [1128] 1128,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 14:[64, 7], Operations: ['39-15=24', '24-17=7'] Exploring Operation: 64*7=448, Resulting Numbers: [448] 448,14 unequal: No Solution Exploring Operation: 64-7=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 64+7=71, Resulting Numbers: [71] 71,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[24, 81], Operations: ['39-15=24', '64+17=81'] Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,14 unequal: No Solution Exploring Operation: 24+81=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 24*81=1944, Resulting Numbers: [1944] 1944,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 14:[17, 88], Operations: ['39-15=24', '64+24=88'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 17*88=1496, Resulting Numbers: [1496] 1496,14 unequal: No Solution Exploring Operation: 17+88=105, Resulting Numbers: [105] 105,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[39, 17, 49], Operations: ['64-15=49'] Exploring Operation: 39-17=22, Resulting Numbers: [49, 22] Generated Node #0,2,0: 14:[49, 22] Operation: 39-17=22 Exploring Operation: 39+49=88, Resulting Numbers: [17, 88] Generated Node #0,2,1: 14:[17, 88] Operation: 39+49=88 Exploring Operation: 49-39=10, Resulting Numbers: [17, 10] Generated Node #0,2,2: 14:[17, 10] Operation: 49-39=10 Exploring Operation: 49-17=32, Resulting Numbers: [39, 32] Generated Node #0,2,3: 14:[39, 32] Operation: 49-17=32 Exploring Operation: 39+17=56, Resulting Numbers: [49, 56] Generated Node #0,2,4: 14:[49, 56] Operation: 39+17=56 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 14:[17, 10], Operations: ['64-15=49', '49-39=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 14:[49, 22], Operations: ['64-15=49', '39-17=22'] Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 49*22=1078, Resulting Numbers: [1078] 1078,14 unequal: No Solution Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 14:[39, 32], Operations: ['64-15=49', '49-17=32'] Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 39*32=1248, Resulting Numbers: [1248] 1248,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 14:[17, 88], Operations: ['64-15=49', '39+49=88'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,14 unequal: No Solution Exploring Operation: 17+88=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 17*88=1496, Resulting Numbers: [1496] 1496,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 14:[49, 56], Operations: ['64-15=49', '39+17=56'] Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 94, 87, 91, 79 ]
92
[ "94-87=7", "91/7=13", "79+13=92" ]
Current State: 92:[94, 87, 91, 79], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [91, 79, 7] Generated Node #2: [91, 79, 7] from Operation: 94-87=7 Current State: 92:[91, 79, 7], Operations: ['94-87=7'] Exploring Operation: 91/7=13, Resulting Numbers: [79, 13] Generated Node #3: [79, 13] from Operation: 91/7=13 Current State: 92:[79, 13], Operations: ['94-87=7', '91/7=13'] Exploring Operation: 79+13=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[94, 87, 91, 79], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [94, 91, 8] Generated Node #0,0: 92:[94, 91, 8] Operation: 87-79=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[94, 91, 8], Operations: ['87-79=8'] Exploring Operation: 94-91=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 92:[8, 3] Operation: 94-91=3 Moving to Node #0,0,0 Current State: 92:[8, 3], Operations: ['87-79=8', '94-91=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 33, 16, 26, 29 ]
51
[ "33-16=17", "29-26=3", "17*3=51" ]
Current State: 51:[33, 16, 26, 29], Operations: [] Exploring Operation: 33-16=17, Resulting Numbers: [26, 29, 17] Generated Node #2: [26, 29, 17] from Operation: 33-16=17 Current State: 51:[26, 29, 17], Operations: ['33-16=17'] Exploring Operation: 29-26=3, Resulting Numbers: [17, 3] Generated Node #3: [17, 3] from Operation: 29-26=3 Current State: 51:[17, 3], Operations: ['33-16=17', '29-26=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[33, 16, 26, 29], Operations: [] Exploring Operation: 33-29=4, Resulting Numbers: [16, 26, 4] Generated Node #0,0: 51:[16, 26, 4] Operation: 33-29=4 Moving to Node #0,0 Current State: 51:[16, 26, 4], Operations: ['33-29=4'] Exploring Operation: 26-4=22, Resulting Numbers: [16, 22] Generated Node #0,0,0: 51:[16, 22] Operation: 26-4=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[16, 22], Operations: ['33-29=4', '26-4=22'] Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,51 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
[ 86, 22, 24, 88 ]
45
[ "24-22=2", "86/2=43", "88-43=45" ]
Current State: 45:[86, 22, 24, 88], Operations: [] Exploring Operation: 24-22=2, Resulting Numbers: [86, 88, 2] Generated Node #2: [86, 88, 2] from Operation: 24-22=2 Current State: 45:[86, 88, 2], Operations: ['24-22=2'] Exploring Operation: 86/2=43, Resulting Numbers: [88, 43] Generated Node #3: [88, 43] from Operation: 86/2=43 Current State: 45:[88, 43], Operations: ['24-22=2', '86/2=43'] Exploring Operation: 88-43=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[86, 22, 24, 88], Operations: [] Exploring Operation: 88-24=64, Resulting Numbers: [86, 22, 64] Generated Node #0,0: 45:[86, 22, 64] Operation: 88-24=64 Exploring Operation: 88/22=4, Resulting Numbers: [86, 24, 4] Generated Node #0,1: 45:[86, 24, 4] Operation: 88/22=4 Exploring Operation: 88-86=2, Resulting Numbers: [22, 24, 2] Generated Node #0,2: 45:[22, 24, 2] Operation: 88-86=2 Exploring Operation: 86-24=62, Resulting Numbers: [22, 88, 62] Generated Node #0,3: 45:[22, 88, 62] Operation: 86-24=62 Moving to Node #0,2 Current State: 45:[22, 24, 2], Operations: ['88-86=2'] Exploring Operation: 22*2=44, Resulting Numbers: [24, 44] Generated Node #0,2,0: 45:[24, 44] Operation: 22*2=44 Exploring Operation: 22+24=46, Resulting Numbers: [2, 46] Generated Node #0,2,1: 45:[2, 46] Operation: 22+24=46 Exploring Operation: 24*2=48, Resulting Numbers: [22, 48] Generated Node #0,2,2: 45:[22, 48] Operation: 24*2=48 Exploring Operation: 24-22=2, Resulting Numbers: [2, 2] Generated Node #0,2,3: 45:[2, 2] Operation: 24-22=2 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 45:[2, 46], Operations: ['88-86=2', '22+24=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,45 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 45:[2, 2], Operations: ['88-86=2', '24-22=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[24, 44], Operations: ['88-86=2', '22*2=44'] Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 24*44=1056, Resulting Numbers: [1056] 1056,45 unequal: No Solution Exploring Operation: 24+44=68, Resulting Numbers: [68] 68,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 45:[22, 48], Operations: ['88-86=2', '24*2=48'] Exploring Operation: 48-22=26, Resulting Numbers: [26] 26,45 unequal: No Solution Exploring Operation: 22*48=1056, Resulting Numbers: [1056] 1056,45 unequal: No Solution Exploring Operation: 22+48=70, Resulting Numbers: [70] 70,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 45:[86, 24, 4], Operations: ['88/22=4'] Exploring Operation: 86-4=82, Resulting Numbers: [24, 82] Generated Node #0,1,0: 45:[24, 82] Operation: 86-4=82 Exploring Operation: 86-24=62, Resulting Numbers: [4, 62] Generated Node #0,1,1: 45:[4, 62] Operation: 86-24=62 Exploring Operation: 24/4=6, Resulting Numbers: [86, 6] Generated Node #0,1,2: 45:[86, 6] Operation: 24/4=6 Exploring Operation: 24-4=20, Resulting Numbers: [86, 20] Generated Node #0,1,3: 45:[86, 20] Operation: 24-4=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[4, 62], Operations: ['88/22=4', '86-24=62'] Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 4+62=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 4*62=248, Resulting Numbers: [248] 248,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[86, 6], Operations: ['88/22=4', '24/4=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,45 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[24, 82], Operations: ['88/22=4', '86-4=82'] Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 24*82=1968, Resulting Numbers: [1968] 1968,45 unequal: No Solution Exploring Operation: 24+82=106, Resulting Numbers: [106] 106,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[86, 20], Operations: ['88/22=4', '24-4=20'] Exploring Operation: 86*20=1720, Resulting Numbers: [1720] 1720,45 unequal: No Solution Exploring Operation: 86+20=106, Resulting Numbers: [106] 106,45 unequal: No Solution Exploring Operation: 86-20=66, Resulting Numbers: [66] 66,45 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: 45:[22, 88, 62], Operations: ['86-24=62'] Exploring Operation: 88/22=4, Resulting Numbers: [62, 4] Generated Node #0,3,0: 45:[62, 4] Operation: 88/22=4 Exploring Operation: 88-22=66, Resulting Numbers: [62, 66] Generated Node #0,3,1: 45:[62, 66] Operation: 88-22=66 Exploring Operation: 62-22=40, Resulting Numbers: [88, 40] Generated Node #0,3,2: 45:[88, 40] Operation: 62-22=40 Exploring Operation: 88-62=26, Resulting Numbers: [22, 26] Generated Node #0,3,3: 45:[22, 26] Operation: 88-62=26 Moving to Node #0,0 Current State: 45:[86, 22, 64], Operations: ['88-24=64'] Exploring Operation: 86-64=22, Resulting Numbers: [22, 22] Generated Node #0,0,0: 45:[22, 22] Operation: 86-64=22 Exploring Operation: 86-22=64, Resulting Numbers: [64, 64] Generated Node #0,0,1: 45:[64, 64] Operation: 86-22=64 Exploring Operation: 64-22=42, Resulting Numbers: [86, 42] Generated Node #0,0,2: 45:[86, 42] Operation: 64-22=42 Exploring Operation: 86+22=108, Resulting Numbers: [64, 108] Generated Node #0,0,3: 45:[64, 108] Operation: 86+22=108 Moving to Node #0,0,0 Current State: 45:[22, 22], Operations: ['88-24=64', '86-64=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[62, 4], Operations: ['86-24=62', '88/22=4'] Exploring Operation: 62*4=248, Resulting Numbers: [248] 248,45 unequal: No Solution Exploring Operation: 62+4=66, Resulting Numbers: [66] 66,45 unequal: No Solution Exploring Operation: 62-4=58, Resulting Numbers: [58] 58,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[22, 26], Operations: ['86-24=62', '88-62=26'] Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 22*26=572, Resulting Numbers: [572] 572,45 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[62, 66], Operations: ['86-24=62', '88-22=66'] Exploring Operation: 62*66=4092, Resulting Numbers: [4092] 4092,45 unequal: No Solution Exploring Operation: 62+66=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 66-62=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[64, 64], Operations: ['88-24=64', '86-22=64'] Exploring Operation: 64*64=4096, Resulting Numbers: [4096] 4096,45 unequal: No Solution Exploring Operation: 64/64=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 64+64=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 64-64=0, Resulting Numbers: [0] 0,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[86, 42], Operations: ['88-24=64', '64-22=42'] Exploring Operation: 86+42=128, Resulting Numbers: [128] 128,45 unequal: No Solution Exploring Operation: 86*42=3612, Resulting Numbers: [3612] 3612,45 unequal: No Solution Exploring Operation: 86-42=44, Resulting Numbers: [44] 44,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[88, 40], Operations: ['86-24=62', '62-22=40'] Exploring Operation: 88-40=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 88*40=3520, Resulting Numbers: [3520] 3520,45 unequal: No Solution Exploring Operation: 88+40=128, Resulting Numbers: [128] 128,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[64, 108], Operations: ['88-24=64', '86+22=108'] Exploring Operation: 64*108=6912, Resulting Numbers: [6912] 6912,45 unequal: No Solution Exploring Operation: 64+108=172, Resulting Numbers: [172] 172,45 unequal: No Solution Exploring Operation: 108-64=44, Resulting Numbers: [44] 44,45 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 53, 1, 73, 2 ]
60
[ "73-53=20", "1+2=3", "20*3=60" ]
Current State: 60:[53, 1, 73, 2], Operations: [] Exploring Operation: 73-53=20, Resulting Numbers: [1, 2, 20] Generated Node #2: [1, 2, 20] from Operation: 73-53=20 Current State: 60:[1, 2, 20], Operations: ['73-53=20'] Exploring Operation: 1+2=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 1+2=3 Current State: 60:[20, 3], Operations: ['73-53=20', '1+2=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[53, 1, 73, 2], Operations: [] Exploring Operation: 73-1=72, Resulting Numbers: [53, 2, 72] Generated Node #0,0: 60:[53, 2, 72] Operation: 73-1=72 Exploring Operation: 73-53=20, Resulting Numbers: [1, 2, 20] Generated Node #0,1: 60:[1, 2, 20] Operation: 73-53=20 Exploring Operation: 53+2=55, Resulting Numbers: [1, 73, 55] Generated Node #0,2: 60:[1, 73, 55] Operation: 53+2=55 Exploring Operation: 53+1=54, Resulting Numbers: [73, 2, 54] Generated Node #0,3: 60:[73, 2, 54] Operation: 53+1=54 Exploring Operation: 73-2=71, Resulting Numbers: [53, 1, 71] Generated Node #0,4: 60:[53, 1, 71] Operation: 73-2=71 Moving to Node #0,1 Current State: 60:[1, 2, 20], Operations: ['73-53=20'] Exploring Operation: 1*2=2, Resulting Numbers: [20, 2] Generated Node #0,1,0: 60:[20, 2] Operation: 1*2=2 Exploring Operation: 20/1=20, Resulting Numbers: [2, 20] Generated Node #0,1,1: 60:[2, 20] Operation: 20/1=20 Exploring Operation: 1*20=20, Resulting Numbers: [2, 20] Generated Node #0,1,2: 60:[2, 20] Operation: 1*20=20 Exploring Operation: 2/1=2, Resulting Numbers: [20, 2] Generated Node #0,1,3: 60:[20, 2] Operation: 2/1=2 Exploring Operation: 1+2=3, Resulting Numbers: [20, 3] Generated Node #0,1,4: 60:[20, 3] Operation: 1+2=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[20, 2], Operations: ['73-53=20', '1*2=2'] Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[2, 20], Operations: ['73-53=20', '20/1=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[2, 20], Operations: ['73-53=20', '1*20=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,60 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 60:[20, 2], Operations: ['73-53=20', '2/1=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,60 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,60 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 60:[20, 3], Operations: ['73-53=20', '1+2=3'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,60 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[53, 1, 73, 2], Operations: [] Exploring Operation: 73-53=20, Resulting Numbers: [1, 2, 20] Generated Node #0,1: 60:[1, 2, 20] Operation: 73-53=20 Moving to Node #0,1 Current State: 60:[1, 2, 20], Operations: ['73-53=20'] Exploring Operation: 1+2=3, Resulting Numbers: [20, 3] Generated Node #0,1,4: 60:[20, 3] Operation: 1+2=3 Moving to Node #0,1,4 Current State: 60:[20, 3], Operations: ['73-53=20', '1+2=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_5
mult_heuristic
[ 43, 24, 86, 5 ]
65
[ "24+86=110", "110/5=22", "43+22=65" ]
Current State: 65:[43, 24, 86, 5], Operations: [] Exploring Operation: 24+86=110, Resulting Numbers: [43, 5, 110] Generated Node #2: [43, 5, 110] from Operation: 24+86=110 Current State: 65:[43, 5, 110], Operations: ['24+86=110'] Exploring Operation: 110/5=22, Resulting Numbers: [43, 22] Generated Node #3: [43, 22] from Operation: 110/5=22 Current State: 65:[43, 22], Operations: ['24+86=110', '110/5=22'] Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[43, 24, 86, 5], Operations: [] Exploring Operation: 43+24=67, Resulting Numbers: [86, 5, 67] Generated Node #0,0: 65:[86, 5, 67] Operation: 43+24=67 Exploring Operation: 86-24=62, Resulting Numbers: [43, 5, 62] Generated Node #0,1: 65:[43, 5, 62] Operation: 86-24=62 Exploring Operation: 86/43=2, Resulting Numbers: [24, 5, 2] Generated Node #0,2: 65:[24, 5, 2] Operation: 86/43=2 Exploring Operation: 43-24=19, Resulting Numbers: [86, 5, 19] Generated Node #0,3: 65:[86, 5, 19] Operation: 43-24=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[24, 5, 2], Operations: ['86/43=2'] Exploring Operation: 24-5=19, Resulting Numbers: [2, 19] Generated Node #0,2,0: 65:[2, 19] Operation: 24-5=19 Exploring Operation: 24/2=12, Resulting Numbers: [5, 12] Generated Node #0,2,1: 65:[5, 12] Operation: 24/2=12 Exploring Operation: 24-2=22, Resulting Numbers: [5, 22] Generated Node #0,2,2: 65:[5, 22] Operation: 24-2=22 Exploring Operation: 24+2=26, Resulting Numbers: [5, 26] Generated Node #0,2,3: 65:[5, 26] Operation: 24+2=26 Moving to Node #0,2,1 Current State: 65:[5, 12], Operations: ['86/43=2', '24/2=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,65 unequal: No Solution Moving to Node #0,2,2 Current State: 65:[5, 22], Operations: ['86/43=2', '24-2=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,65 unequal: No Solution Moving to Node #0,2,0 Current State: 65:[2, 19], Operations: ['86/43=2', '24-5=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,65 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,65 unequal: No Solution Moving to Node #0,2,3 Current State: 65:[5, 26], Operations: ['86/43=2', '24+2=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,65 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,65 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[86, 5, 67], Operations: ['43+24=67'] Exploring Operation: 67-5=62, Resulting Numbers: [86, 62] Generated Node #0,0,0: 65:[86, 62] Operation: 67-5=62 Exploring Operation: 86-5=81, Resulting Numbers: [67, 81] Generated Node #0,0,1: 65:[67, 81] Operation: 86-5=81 Exploring Operation: 86+5=91, Resulting Numbers: [67, 91] Generated Node #0,0,2: 65:[67, 91] Operation: 86+5=91 Exploring Operation: 86-67=19, Resulting Numbers: [5, 19] Generated Node #0,0,3: 65:[5, 19] Operation: 86-67=19 Moving to Node #0,0,3 Current State: 65:[5, 19], Operations: ['43+24=67', '86-67=19'] Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,65 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[67, 81], Operations: ['43+24=67', '86-5=81'] Exploring Operation: 67*81=5427, Resulting Numbers: [5427] 5427,65 unequal: No Solution Exploring Operation: 81-67=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 67+81=148, Resulting Numbers: [148] 148,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[86, 62], Operations: ['43+24=67', '67-5=62'] Exploring Operation: 86+62=148, Resulting Numbers: [148] 148,65 unequal: No Solution Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 86*62=5332, Resulting Numbers: [5332] 5332,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[67, 91], Operations: ['43+24=67', '86+5=91'] Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 67+91=158, Resulting Numbers: [158] 158,65 unequal: No Solution Exploring Operation: 67*91=6097, Resulting Numbers: [6097] 6097,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[43, 5, 62], Operations: ['86-24=62'] Exploring Operation: 5+62=67, Resulting Numbers: [43, 67] Generated Node #0,1,0: 65:[43, 67] Operation: 5+62=67 Exploring Operation: 43+5=48, Resulting Numbers: [62, 48] Generated Node #0,1,1: 65:[62, 48] Operation: 43+5=48 Exploring Operation: 43-5=38, Resulting Numbers: [62, 38] Generated Node #0,1,2: 65:[62, 38] Operation: 43-5=38 Exploring Operation: 62-43=19, Resulting Numbers: [5, 19] Generated Node #0,1,3: 65:[5, 19] Operation: 62-43=19 Moving to Node #0,1,3 Current State: 65:[5, 19], Operations: ['86-24=62', '62-43=19'] Exploring Operation: 5*19=95, Resulting Numbers: [95] 95,65 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 5+19=24, Resulting Numbers: [24] 24,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[62, 48], Operations: ['86-24=62', '43+5=48'] Exploring Operation: 62*48=2976, Resulting Numbers: [2976] 2976,65 unequal: No Solution Exploring Operation: 62+48=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[43, 67], Operations: ['86-24=62', '5+62=67'] Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 43*67=2881, Resulting Numbers: [2881] 2881,65 unequal: No Solution Exploring Operation: 43+67=110, Resulting Numbers: [110] 110,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[62, 38], Operations: ['86-24=62', '43-5=38'] Exploring Operation: 62+38=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 62*38=2356, Resulting Numbers: [2356] 2356,65 unequal: No Solution Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[86, 5, 19], Operations: ['43-24=19'] Exploring Operation: 86+5=91, Resulting Numbers: [19, 91] Generated Node #0,3,0: 65:[19, 91] Operation: 86+5=91 Exploring Operation: 19-5=14, Resulting Numbers: [86, 14] Generated Node #0,3,1: 65:[86, 14] Operation: 19-5=14 Exploring Operation: 86-5=81, Resulting Numbers: [19, 81] Generated Node #0,3,2: 65:[19, 81] Operation: 86-5=81 Exploring Operation: 86-19=67, Resulting Numbers: [5, 67] Generated Node #0,3,3: 65:[5, 67] Operation: 86-19=67 Moving to Node #0,3,3 Current State: 65:[5, 67], Operations: ['43-24=19', '86-19=67'] Exploring Operation: 5+67=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[19, 81], Operations: ['43-24=19', '86-5=81'] Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 81-19=62, Resulting Numbers: [62] 62,65 unequal: No Solution Exploring Operation: 19*81=1539, Resulting Numbers: [1539] 1539,65 unequal: No Solution Moving to Node #0,3,1 Current State: 65:[86, 14], Operations: ['43-24=19', '19-5=14'] Exploring Operation: 86*14=1204, Resulting Numbers: [1204] 1204,65 unequal: No Solution Exploring Operation: 86+14=100, Resulting Numbers: [100] 100,65 unequal: No Solution Exploring Operation: 86-14=72, Resulting Numbers: [72] 72,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[19, 91], Operations: ['43-24=19', '86+5=91'] Exploring Operation: 19+91=110, Resulting Numbers: [110] 110,65 unequal: No Solution Exploring Operation: 19*91=1729, Resulting Numbers: [1729] 1729,65 unequal: No Solution Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,65 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
[ 42, 34, 74, 46 ]
10
[ "46-42=4", "74-34=40", "40/4=10" ]
Current State: 10:[42, 34, 74, 46], Operations: [] Exploring Operation: 46-42=4, Resulting Numbers: [34, 74, 4] Generated Node #2: [34, 74, 4] from Operation: 46-42=4 Current State: 10:[34, 74, 4], Operations: ['46-42=4'] Exploring Operation: 74-34=40, Resulting Numbers: [4, 40] Generated Node #3: [4, 40] from Operation: 74-34=40 Current State: 10:[4, 40], Operations: ['46-42=4', '74-34=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[42, 34, 74, 46], Operations: [] Exploring Operation: 74-46=28, Resulting Numbers: [42, 34, 28] Generated Node #0,0: 10:[42, 34, 28] Operation: 74-46=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[42, 34, 28], Operations: ['74-46=28'] Exploring Operation: 42-34=8, Resulting Numbers: [28, 8] Generated Node #0,0,0: 10:[28, 8] Operation: 42-34=8 Moving to Node #0,0,0 Current State: 10:[28, 8], Operations: ['74-46=28', '42-34=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,10 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, 36, 51, 68 ]
71
[ "52+36=88", "68-51=17", "88-17=71" ]
Current State: 71:[52, 36, 51, 68], Operations: [] Exploring Operation: 52+36=88, Resulting Numbers: [51, 68, 88] Generated Node #2: [51, 68, 88] from Operation: 52+36=88 Current State: 71:[51, 68, 88], Operations: ['52+36=88'] Exploring Operation: 68-51=17, Resulting Numbers: [88, 17] Generated Node #3: [88, 17] from Operation: 68-51=17 Current State: 71:[88, 17], Operations: ['52+36=88', '68-51=17'] Exploring Operation: 88-17=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[52, 36, 51, 68], Operations: [] Exploring Operation: 52-36=16, Resulting Numbers: [51, 68, 16] Generated Node #0,0: 71:[51, 68, 16] Operation: 52-36=16 Exploring Operation: 36+68=104, Resulting Numbers: [52, 51, 104] Generated Node #0,1: 71:[52, 51, 104] Operation: 36+68=104 Exploring Operation: 52+36=88, Resulting Numbers: [51, 68, 88] Generated Node #0,2: 71:[51, 68, 88] Operation: 52+36=88 Exploring Operation: 52+51=103, Resulting Numbers: [36, 68, 103] Generated Node #0,3: 71:[36, 68, 103] Operation: 52+51=103 Exploring Operation: 36+51=87, Resulting Numbers: [52, 68, 87] Generated Node #0,4: 71:[52, 68, 87] Operation: 36+51=87 Start Sub Search at level 1: Moving to Node #0,4 Current State: 71:[52, 68, 87], Operations: ['36+51=87'] Exploring Operation: 52+68=120, Resulting Numbers: [87, 120] Generated Node #0,4,0: 71:[87, 120] Operation: 52+68=120 Exploring Operation: 52+87=139, Resulting Numbers: [68, 139] Generated Node #0,4,1: 71:[68, 139] Operation: 52+87=139 Exploring Operation: 87-68=19, Resulting Numbers: [52, 19] Generated Node #0,4,2: 71:[52, 19] Operation: 87-68=19 Exploring Operation: 68-52=16, Resulting Numbers: [87, 16] Generated Node #0,4,3: 71:[87, 16] Operation: 68-52=16 Exploring Operation: 87-52=35, Resulting Numbers: [68, 35] Generated Node #0,4,4: 71:[68, 35] Operation: 87-52=35 Moving to Node #0,4,4 Current State: 71:[68, 35], Operations: ['36+51=87', '87-52=35'] Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,71 unequal: No Solution Exploring Operation: 68+35=103, Resulting Numbers: [103] 103,71 unequal: No Solution Exploring Operation: 68*35=2380, Resulting Numbers: [2380] 2380,71 unequal: No Solution Moving to Node #0,4,0 Current State: 71:[87, 120], Operations: ['36+51=87', '52+68=120'] Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,71 unequal: No Solution Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,71 unequal: No Solution Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,71 unequal: No Solution Moving to Node #0,4,1 Current State: 71:[68, 139], Operations: ['36+51=87', '52+87=139'] Exploring Operation: 68+139=207, Resulting Numbers: [207] 207,71 unequal: No Solution Exploring Operation: 139-68=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[52, 36, 51, 68], Operations: [] Exploring Operation: 36+51=87, Resulting Numbers: [52, 68, 87] Generated Node #0,4: 71:[52, 68, 87] Operation: 36+51=87 Moving to Node #0,4 Current State: 71:[52, 68, 87], Operations: ['36+51=87'] Exploring Operation: 52+87=139, Resulting Numbers: [68, 139] Generated Node #0,4,1: 71:[68, 139] Operation: 52+87=139 Moving to Node #0,4,1 Current State: 71:[68, 139], Operations: ['36+51=87', '52+87=139'] Exploring Operation: 139-68=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 40, 36, 45, 37 ]
63
[ "40-37=3", "36*3=108", "108-45=63" ]
Current State: 63:[40, 36, 45, 37], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [36, 45, 3] Generated Node #2: [36, 45, 3] from Operation: 40-37=3 Current State: 63:[36, 45, 3], Operations: ['40-37=3'] Exploring Operation: 36*3=108, Resulting Numbers: [45, 108] Generated Node #3: [45, 108] from Operation: 36*3=108 Current State: 63:[45, 108], Operations: ['40-37=3', '36*3=108'] Exploring Operation: 108-45=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[40, 36, 45, 37], Operations: [] Exploring Operation: 40-37=3, Resulting Numbers: [36, 45, 3] Generated Node #0,0: 63:[36, 45, 3] Operation: 40-37=3 Exploring Operation: 45-40=5, Resulting Numbers: [36, 37, 5] Generated Node #0,1: 63:[36, 37, 5] Operation: 45-40=5 Exploring Operation: 40-36=4, Resulting Numbers: [45, 37, 4] Generated Node #0,2: 63:[45, 37, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[36, 45, 3], Operations: ['40-37=3'] Exploring Operation: 36+45=81, Resulting Numbers: [3, 81] Generated Node #0,0,0: 63:[3, 81] Operation: 36+45=81 Exploring Operation: 45-36=9, Resulting Numbers: [3, 9] Generated Node #0,0,1: 63:[3, 9] Operation: 45-36=9 Exploring Operation: 36/3=12, Resulting Numbers: [45, 12] Generated Node #0,0,2: 63:[45, 12] Operation: 36/3=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[3, 9], Operations: ['40-37=3', '45-36=9'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[3, 81], Operations: ['40-37=3', '36+45=81'] Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,63 unequal: No Solution Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,63 unequal: No Solution Exploring Operation: 81/3=27, Resulting Numbers: [27] 27,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 63:[45, 12], Operations: ['40-37=3', '36/3=12'] Exploring Operation: 45+12=57, Resulting Numbers: [57] 57,63 unequal: No Solution Exploring Operation: 45*12=540, Resulting Numbers: [540] 540,63 unequal: No Solution Exploring Operation: 45-12=33, Resulting Numbers: [33] 33,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[36, 37, 5], Operations: ['45-40=5'] Exploring Operation: 36+37=73, Resulting Numbers: [5, 73] Generated Node #0,1,0: 63:[5, 73] Operation: 36+37=73 Exploring Operation: 36-5=31, Resulting Numbers: [37, 31] Generated Node #0,1,1: 63:[37, 31] Operation: 36-5=31 Exploring Operation: 37-36=1, Resulting Numbers: [5, 1] Generated Node #0,1,2: 63:[5, 1] Operation: 37-36=1 Moving to Node #0,1,2 Current State: 63:[5, 1], Operations: ['45-40=5', '37-36=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[5, 73], Operations: ['45-40=5', '36+37=73'] Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 5*73=365, Resulting Numbers: [365] 365,63 unequal: No Solution Exploring Operation: 5+73=78, Resulting Numbers: [78] 78,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[37, 31], Operations: ['45-40=5', '36-5=31'] Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,63 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,63 unequal: No Solution Exploring Operation: 37-31=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 #0,2 Current State: 63:[45, 37, 4], Operations: ['40-36=4'] Exploring Operation: 45-37=8, Resulting Numbers: [4, 8] Generated Node #0,2,0: 63:[4, 8] Operation: 45-37=8 Exploring Operation: 45+37=82, Resulting Numbers: [4, 82] Generated Node #0,2,1: 63:[4, 82] Operation: 45+37=82 Exploring Operation: 45+4=49, Resulting Numbers: [37, 49] Generated Node #0,2,2: 63:[37, 49] Operation: 45+4=49 Moving to Node #0,2,0 Current State: 63:[4, 8], Operations: ['40-36=4', '45-37=8'] Exploring Operation: 4+8=12, Resulting Numbers: [12] 12,63 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[4, 82], Operations: ['40-36=4', '45+37=82'] Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,63 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[37, 49], Operations: ['40-36=4', '45+4=49'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,63 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 37*49=1813, Resulting Numbers: [1813] 1813,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 59, 41, 52, 81 ]
11
[ "59-41=18", "81-52=29", "29-18=11" ]
Current State: 11:[59, 41, 52, 81], Operations: [] Exploring Operation: 59-41=18, Resulting Numbers: [52, 81, 18] Generated Node #2: [52, 81, 18] from Operation: 59-41=18 Current State: 11:[52, 81, 18], Operations: ['59-41=18'] Exploring Operation: 81-52=29, Resulting Numbers: [18, 29] Generated Node #3: [18, 29] from Operation: 81-52=29 Current State: 11:[18, 29], Operations: ['59-41=18', '81-52=29'] Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[59, 41, 52, 81], Operations: [] Exploring Operation: 59-52=7, Resulting Numbers: [41, 81, 7] Generated Node #0,0: 11:[41, 81, 7] Operation: 59-52=7 Exploring Operation: 81-59=22, Resulting Numbers: [41, 52, 22] Generated Node #0,1: 11:[41, 52, 22] Operation: 81-59=22 Exploring Operation: 81-52=29, Resulting Numbers: [59, 41, 29] Generated Node #0,2: 11:[59, 41, 29] Operation: 81-52=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[41, 52, 22], Operations: ['81-59=22'] Exploring Operation: 41-22=19, Resulting Numbers: [52, 19] Generated Node #0,1,0: 11:[52, 19] Operation: 41-22=19 Exploring Operation: 52-22=30, Resulting Numbers: [41, 30] Generated Node #0,1,1: 11:[41, 30] Operation: 52-22=30 Exploring Operation: 52-41=11, Resulting Numbers: [22, 11] Generated Node #0,1,2: 11:[22, 11] Operation: 52-41=11 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 11:[22, 11], Operations: ['81-59=22', '52-41=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,11 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[59, 41, 52, 81], Operations: [] Exploring Operation: 81-59=22, Resulting Numbers: [41, 52, 22] Generated Node #0,1: 11:[41, 52, 22] Operation: 81-59=22 Moving to Node #0,1 Current State: 11:[41, 52, 22], Operations: ['81-59=22'] Exploring Operation: 52-41=11, Resulting Numbers: [22, 11] Generated Node #0,1,2: 11:[22, 11] Operation: 52-41=11 Moving to Node #0,1,2 Current State: 11:[22, 11], Operations: ['81-59=22', '52-41=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 5, 4, 1, 5 ]
20
[ "5*5=25", "4+1=5", "25-5=20" ]
Current State: 20:[5, 4, 1, 5], Operations: [] Exploring Operation: 5*5=25, Resulting Numbers: [4, 1, 25] Generated Node #2: [4, 1, 25] from Operation: 5*5=25 Current State: 20:[4, 1, 25], Operations: ['5*5=25'] Exploring Operation: 4+1=5, Resulting Numbers: [25, 5] Generated Node #3: [25, 5] from Operation: 4+1=5 Current State: 20:[25, 5], Operations: ['5*5=25', '4+1=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[5, 4, 1, 5], Operations: [] Exploring Operation: 5*1=5, Resulting Numbers: [4, 5, 5] Generated Node #0,0: 20:[4, 5, 5] Operation: 5*1=5 Exploring Operation: 5-1=4, Resulting Numbers: [4, 5, 4] Generated Node #0,1: 20:[4, 5, 4] Operation: 5-1=4 Moving to Node #0,0 Current State: 20:[4, 5, 5], Operations: ['5*1=5'] Exploring Operation: 4*5=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 20:[5, 20] Operation: 4*5=20 Exploring Operation: 4*5=20, Resulting Numbers: [5, 20] Generated Node #0,0,1: 20:[5, 20] Operation: 4*5=20 Moving to Node #0,1 Current State: 20:[4, 5, 4], Operations: ['5-1=4'] Exploring Operation: 5*4=20, Resulting Numbers: [4, 20] Generated Node #0,1,0: 20:[4, 20] Operation: 5*4=20 Exploring Operation: 4*5=20, Resulting Numbers: [4, 20] Generated Node #0,1,1: 20:[4, 20] Operation: 4*5=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[4, 20], Operations: ['5-1=4', '5*4=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,20 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 #0,1,1 Current State: 20:[4, 20], Operations: ['5-1=4', '4*5=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,20 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: 20:[5, 20], Operations: ['5*1=5', '4*5=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,20 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,20 unequal: No Solution Moving to Node #0,0,1 Current State: 20:[5, 20], Operations: ['5*1=5', '4*5=20'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,20 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 12, 16, 77, 6 ]
80
[ "12*6=72", "77-72=5", "16*5=80" ]
Current State: 80:[12, 16, 77, 6], Operations: [] Exploring Operation: 12*6=72, Resulting Numbers: [16, 77, 72] Generated Node #2: [16, 77, 72] from Operation: 12*6=72 Current State: 80:[16, 77, 72], Operations: ['12*6=72'] Exploring Operation: 77-72=5, Resulting Numbers: [16, 5] Generated Node #3: [16, 5] from Operation: 77-72=5 Current State: 80:[16, 5], Operations: ['12*6=72', '77-72=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[12, 16, 77, 6], Operations: [] Exploring Operation: 12/6=2, Resulting Numbers: [16, 77, 2] Generated Node #0,0: 80:[16, 77, 2] Operation: 12/6=2 Exploring Operation: 16-12=4, Resulting Numbers: [77, 6, 4] Generated Node #0,1: 80:[77, 6, 4] Operation: 16-12=4 Exploring Operation: 12-6=6, Resulting Numbers: [16, 77, 6] Generated Node #0,2: 80:[16, 77, 6] Operation: 12-6=6 Moving to Node #0,0 Current State: 80:[16, 77, 2], Operations: ['12/6=2'] Exploring Operation: 77+2=79, Resulting Numbers: [16, 79] Generated Node #0,0,0: 80:[16, 79] Operation: 77+2=79 Exploring Operation: 16+2=18, Resulting Numbers: [77, 18] Generated Node #0,0,1: 80:[77, 18] Operation: 16+2=18 Exploring Operation: 16/2=8, Resulting Numbers: [77, 8] Generated Node #0,0,2: 80:[77, 8] Operation: 16/2=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[16, 79], Operations: ['12/6=2', '77+2=79'] Exploring Operation: 16+79=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 16*79=1264, Resulting Numbers: [1264] 1264,80 unequal: No Solution Exploring Operation: 79-16=63, Resulting Numbers: [63] 63,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[77, 8], Operations: ['12/6=2', '16/2=8'] Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,80 unequal: No Solution Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,80 unequal: No Solution Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[77, 18], Operations: ['12/6=2', '16+2=18'] Exploring Operation: 77+18=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 77*18=1386, Resulting Numbers: [1386] 1386,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 80:[77, 6, 4], Operations: ['16-12=4'] Exploring Operation: 77+6=83, Resulting Numbers: [4, 83] Generated Node #0,1,0: 80:[4, 83] Operation: 77+6=83 Exploring Operation: 77+4=81, Resulting Numbers: [6, 81] Generated Node #0,1,1: 80:[6, 81] Operation: 77+4=81 Exploring Operation: 6+4=10, Resulting Numbers: [77, 10] Generated Node #0,1,2: 80:[77, 10] Operation: 6+4=10 Moving to Node #0,2 Current State: 80:[16, 77, 6], Operations: ['12-6=6'] Exploring Operation: 16-6=10, Resulting Numbers: [77, 10] Generated Node #0,2,0: 80:[77, 10] Operation: 16-6=10 Exploring Operation: 77+6=83, Resulting Numbers: [16, 83] Generated Node #0,2,1: 80:[16, 83] Operation: 77+6=83 Exploring Operation: 16+6=22, Resulting Numbers: [77, 22] Generated Node #0,2,2: 80:[77, 22] Operation: 16+6=22 Moving to Node #0,1,1 Current State: 80:[6, 81], Operations: ['16-12=4', '77+4=81'] Exploring Operation: 6+81=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 6*81=486, Resulting Numbers: [486] 486,80 unequal: No Solution Exploring Operation: 81-6=75, Resulting Numbers: [75] 75,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[77, 10], Operations: ['16-12=4', '6+4=10'] Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,80 unequal: No Solution Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[4, 83], Operations: ['16-12=4', '77+6=83'] Exploring Operation: 4+83=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 4*83=332, Resulting Numbers: [332] 332,80 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[77, 10], Operations: ['12-6=6', '16-6=10'] Exploring Operation: 77+10=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 77-10=67, Resulting Numbers: [67] 67,80 unequal: No Solution Exploring Operation: 77*10=770, Resulting Numbers: [770] 770,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[16, 83], Operations: ['12-6=6', '77+6=83'] Exploring Operation: 16*83=1328, Resulting Numbers: [1328] 1328,80 unequal: No Solution Exploring Operation: 16+83=99, Resulting Numbers: [99] 99,80 unequal: No Solution Exploring Operation: 83-16=67, Resulting Numbers: [67] 67,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[77, 22], Operations: ['12-6=6', '16+6=22'] Exploring Operation: 77-22=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 77*22=1694, Resulting Numbers: [1694] 1694,80 unequal: No Solution Exploring Operation: 77+22=99, Resulting Numbers: [99] 99,80 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 84, 7, 9, 47 ]
68
[ "84/7=12", "9+47=56", "12+56=68" ]
Current State: 68:[84, 7, 9, 47], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [9, 47, 12] Generated Node #2: [9, 47, 12] from Operation: 84/7=12 Current State: 68:[9, 47, 12], Operations: ['84/7=12'] Exploring Operation: 9+47=56, Resulting Numbers: [12, 56] Generated Node #3: [12, 56] from Operation: 9+47=56 Current State: 68:[12, 56], Operations: ['84/7=12', '9+47=56'] Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[84, 7, 9, 47], Operations: [] Exploring Operation: 84-47=37, Resulting Numbers: [7, 9, 37] Generated Node #0,0: 68:[7, 9, 37] Operation: 84-47=37 Moving to Node #0,0 Current State: 68:[7, 9, 37], Operations: ['84-47=37'] Exploring Operation: 9-7=2, Resulting Numbers: [37, 2] Generated Node #0,0,0: 68:[37, 2] Operation: 9-7=2 Moving to Node #0,0,0 Current State: 68:[37, 2], Operations: ['84-47=37', '9-7=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,68 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 85, 39, 14, 41 ]
69
[ "85+39=124", "14+41=55", "124-55=69" ]
Current State: 69:[85, 39, 14, 41], Operations: [] Exploring Operation: 85+39=124, Resulting Numbers: [14, 41, 124] Generated Node #2: [14, 41, 124] from Operation: 85+39=124 Current State: 69:[14, 41, 124], Operations: ['85+39=124'] Exploring Operation: 14+41=55, Resulting Numbers: [124, 55] Generated Node #3: [124, 55] from Operation: 14+41=55 Current State: 69:[124, 55], Operations: ['85+39=124', '14+41=55'] Exploring Operation: 124-55=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[85, 39, 14, 41], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [85, 14, 2] Generated Node #0,0: 69:[85, 14, 2] Operation: 41-39=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[85, 14, 2], Operations: ['41-39=2'] Exploring Operation: 85-14=71, Resulting Numbers: [2, 71] Generated Node #0,0,0: 69:[2, 71] Operation: 85-14=71 Moving to Node #0,0,0 Current State: 69:[2, 71], Operations: ['41-39=2', '85-14=71'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[85, 39, 14, 41], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [85, 14, 2] Generated Node #0,0: 69:[85, 14, 2] Operation: 41-39=2 Moving to Node #0,0 Current State: 69:[85, 14, 2], Operations: ['41-39=2'] Exploring Operation: 85-14=71, Resulting Numbers: [2, 71] Generated Node #0,0,0: 69:[2, 71] Operation: 85-14=71 Moving to Node #0,0,0 Current State: 69:[2, 71], Operations: ['41-39=2', '85-14=71'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 51, 2, 41, 88 ]
48
[ "51+41=92", "88/2=44", "92-44=48" ]
Current State: 48:[51, 2, 41, 88], Operations: [] Exploring Operation: 51+41=92, Resulting Numbers: [2, 88, 92] Generated Node #2: [2, 88, 92] from Operation: 51+41=92 Current State: 48:[2, 88, 92], Operations: ['51+41=92'] Exploring Operation: 88/2=44, Resulting Numbers: [92, 44] Generated Node #3: [92, 44] from Operation: 88/2=44 Current State: 48:[92, 44], Operations: ['51+41=92', '88/2=44'] Exploring Operation: 92-44=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[51, 2, 41, 88], Operations: [] Exploring Operation: 88-41=47, Resulting Numbers: [51, 2, 47] Generated Node #0,0: 48:[51, 2, 47] Operation: 88-41=47 Exploring Operation: 88-51=37, Resulting Numbers: [2, 41, 37] Generated Node #0,1: 48:[2, 41, 37] Operation: 88-51=37 Exploring Operation: 88/2=44, Resulting Numbers: [51, 41, 44] Generated Node #0,2: 48:[51, 41, 44] Operation: 88/2=44 Exploring Operation: 51-41=10, Resulting Numbers: [2, 88, 10] Generated Node #0,3: 48:[2, 88, 10] Operation: 51-41=10 Moving to Node #0,0 Current State: 48:[51, 2, 47], Operations: ['88-41=47'] Exploring Operation: 51+2=53, Resulting Numbers: [47, 53] Generated Node #0,0,0: 48:[47, 53] Operation: 51+2=53 Exploring Operation: 51-2=49, Resulting Numbers: [47, 49] Generated Node #0,0,1: 48:[47, 49] Operation: 51-2=49 Exploring Operation: 51-47=4, Resulting Numbers: [2, 4] Generated Node #0,0,2: 48:[2, 4] Operation: 51-47=4 Exploring Operation: 2+47=49, Resulting Numbers: [51, 49] Generated Node #0,0,3: 48:[51, 49] Operation: 2+47=49 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 48:[2, 4], Operations: ['88-41=47', '51-47=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[47, 49], Operations: ['88-41=47', '51-2=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,48 unequal: No Solution Exploring Operation: 47*49=2303, Resulting Numbers: [2303] 2303,48 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 48:[51, 49], Operations: ['88-41=47', '2+47=49'] Exploring Operation: 51*49=2499, Resulting Numbers: [2499] 2499,48 unequal: No Solution Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 51+49=100, Resulting Numbers: [100] 100,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[47, 53], Operations: ['88-41=47', '51+2=53'] Exploring Operation: 47+53=100, Resulting Numbers: [100] 100,48 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,48 unequal: No Solution Exploring Operation: 47*53=2491, Resulting Numbers: [2491] 2491,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 48:[51, 41, 44], Operations: ['88/2=44'] Exploring Operation: 51-41=10, Resulting Numbers: [44, 10] Generated Node #0,2,0: 48:[44, 10] Operation: 51-41=10 Exploring Operation: 41+44=85, Resulting Numbers: [51, 85] Generated Node #0,2,1: 48:[51, 85] Operation: 41+44=85 Exploring Operation: 51-44=7, Resulting Numbers: [41, 7] Generated Node #0,2,2: 48:[41, 7] Operation: 51-44=7 Exploring Operation: 44-41=3, Resulting Numbers: [51, 3] Generated Node #0,2,3: 48:[51, 3] Operation: 44-41=3 Moving to Node #0,1 Current State: 48:[2, 41, 37], Operations: ['88-51=37'] Exploring Operation: 41-37=4, Resulting Numbers: [2, 4] Generated Node #0,1,0: 48:[2, 4] Operation: 41-37=4 Exploring Operation: 2+37=39, Resulting Numbers: [41, 39] Generated Node #0,1,1: 48:[41, 39] Operation: 2+37=39 Exploring Operation: 2+41=43, Resulting Numbers: [37, 43] Generated Node #0,1,2: 48:[37, 43] Operation: 2+41=43 Exploring Operation: 37-2=35, Resulting Numbers: [41, 35] Generated Node #0,1,3: 48:[41, 35] Operation: 37-2=35 Moving to Node #0,3 Current State: 48:[2, 88, 10], Operations: ['51-41=10'] Exploring Operation: 88-2=86, Resulting Numbers: [10, 86] Generated Node #0,3,0: 48:[10, 86] Operation: 88-2=86 Exploring Operation: 2+10=12, Resulting Numbers: [88, 12] Generated Node #0,3,1: 48:[88, 12] Operation: 2+10=12 Exploring Operation: 88-10=78, Resulting Numbers: [2, 78] Generated Node #0,3,2: 48:[2, 78] Operation: 88-10=78 Exploring Operation: 88/2=44, Resulting Numbers: [10, 44] Generated Node #0,3,3: 48:[10, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 48:[10, 44], Operations: ['51-41=10', '88/2=44'] Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,48 unequal: No Solution Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 48:[2, 78], Operations: ['51-41=10', '88-10=78'] Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,48 unequal: No Solution Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,48 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 48:[10, 86], Operations: ['51-41=10', '88-2=86'] Exploring Operation: 10*86=860, Resulting Numbers: [860] 860,48 unequal: No Solution Exploring Operation: 10+86=96, Resulting Numbers: [96] 96,48 unequal: No Solution Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 48:[88, 12], Operations: ['51-41=10', '2+10=12'] Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,48 unequal: No Solution Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,48 unequal: No Solution Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,48 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: 48:[2, 4], Operations: ['88-51=37', '41-37=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,48 unequal: No Solution Moving to Node #0,2,3 Current State: 48:[51, 3], Operations: ['88/2=44', '44-41=3'] Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,48 unequal: No Solution Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,48 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[51, 2, 41, 88], Operations: [] Exploring Operation: 88/2=44, Resulting Numbers: [51, 41, 44] Generated Node #0,2: 48:[51, 41, 44] Operation: 88/2=44 Moving to Node #0,2 Current State: 48:[51, 41, 44], Operations: ['88/2=44'] Exploring Operation: 44-41=3, Resulting Numbers: [51, 3] Generated Node #0,2,3: 48:[51, 3] Operation: 44-41=3 Moving to Node #0,2,3 Current State: 48:[51, 3], Operations: ['88/2=44', '44-41=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.950521
hs_4
sum_heuristic
[ 31, 24, 26, 1 ]
80
[ "31+24=55", "26-1=25", "55+25=80" ]
Current State: 80:[31, 24, 26, 1], Operations: [] Exploring Operation: 31+24=55, Resulting Numbers: [26, 1, 55] Generated Node #2: [26, 1, 55] from Operation: 31+24=55 Current State: 80:[26, 1, 55], Operations: ['31+24=55'] Exploring Operation: 26-1=25, Resulting Numbers: [55, 25] Generated Node #3: [55, 25] from Operation: 26-1=25 Current State: 80:[55, 25], Operations: ['31+24=55', '26-1=25'] Exploring Operation: 55+25=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[31, 24, 26, 1], Operations: [] Exploring Operation: 31-26=5, Resulting Numbers: [24, 1, 5] Generated Node #0,0: 80:[24, 1, 5] Operation: 31-26=5 Exploring Operation: 31-24=7, Resulting Numbers: [26, 1, 7] Generated Node #0,1: 80:[26, 1, 7] Operation: 31-24=7 Exploring Operation: 31+1=32, Resulting Numbers: [24, 26, 32] Generated Node #0,2: 80:[24, 26, 32] Operation: 31+1=32 Exploring Operation: 26-24=2, Resulting Numbers: [31, 1, 2] Generated Node #0,3: 80:[31, 1, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[24, 1, 5], Operations: ['31-26=5'] Exploring Operation: 24-1=23, Resulting Numbers: [5, 23] Generated Node #0,0,0: 80:[5, 23] Operation: 24-1=23 Exploring Operation: 24-5=19, Resulting Numbers: [1, 19] Generated Node #0,0,1: 80:[1, 19] Operation: 24-5=19 Exploring Operation: 24/1=24, Resulting Numbers: [5, 24] Generated Node #0,0,2: 80:[5, 24] Operation: 24/1=24 Exploring Operation: 24*1=24, Resulting Numbers: [5, 24] Generated Node #0,0,3: 80:[5, 24] Operation: 24*1=24 Moving to Node #0,0,1 Current State: 80:[1, 19], Operations: ['31-26=5', '24-5=19'] Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[5, 23], Operations: ['31-26=5', '24-1=23'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 5*23=115, Resulting Numbers: [115] 115,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[5, 24], Operations: ['31-26=5', '24*1=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[5, 24], Operations: ['31-26=5', '24/1=24'] Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[26, 1, 7], Operations: ['31-24=7'] Exploring Operation: 1+7=8, Resulting Numbers: [26, 8] Generated Node #0,1,0: 80:[26, 8] Operation: 1+7=8 Exploring Operation: 26-7=19, Resulting Numbers: [1, 19] Generated Node #0,1,1: 80:[1, 19] Operation: 26-7=19 Exploring Operation: 26-1=25, Resulting Numbers: [7, 25] Generated Node #0,1,2: 80:[7, 25] Operation: 26-1=25 Exploring Operation: 26*1=26, Resulting Numbers: [7, 26] Generated Node #0,1,3: 80:[7, 26] Operation: 26*1=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[1, 19], Operations: ['31-24=7', '26-7=19'] Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,80 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,80 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 #0,1,0 Current State: 80:[26, 8], Operations: ['31-24=7', '1+7=8'] Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,80 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,80 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 #0,1,2 Current State: 80:[7, 25], Operations: ['31-24=7', '26-1=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,80 unequal: No Solution Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,80 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 #0,1,3 Current State: 80:[7, 26], Operations: ['31-24=7', '26*1=26'] Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,80 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 #0,3 Current State: 80:[31, 1, 2], Operations: ['26-24=2'] Exploring Operation: 31+2=33, Resulting Numbers: [1, 33] Generated Node #0,3,0: 80:[1, 33] Operation: 31+2=33 Exploring Operation: 31*1=31, Resulting Numbers: [2, 31] Generated Node #0,3,1: 80:[2, 31] Operation: 31*1=31 Exploring Operation: 31/1=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 80:[2, 31] Operation: 31/1=31 Exploring Operation: 31+1=32, Resulting Numbers: [2, 32] Generated Node #0,3,3: 80:[2, 32] Operation: 31+1=32 Moving to Node #0,3,0 Current State: 80:[1, 33], Operations: ['26-24=2', '31+2=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,80 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[2, 32], Operations: ['26-24=2', '31+1=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[2, 31], Operations: ['26-24=2', '31/1=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[2, 31], Operations: ['26-24=2', '31*1=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[24, 26, 32], Operations: ['31+1=32'] Exploring Operation: 32-26=6, Resulting Numbers: [24, 6] Generated Node #0,2,0: 80:[24, 6] Operation: 32-26=6 Exploring Operation: 32-24=8, Resulting Numbers: [26, 8] Generated Node #0,2,1: 80:[26, 8] Operation: 32-24=8 Exploring Operation: 26-24=2, Resulting Numbers: [32, 2] Generated Node #0,2,2: 80:[32, 2] Operation: 26-24=2 Exploring Operation: 24+26=50, Resulting Numbers: [32, 50] Generated Node #0,2,3: 80:[32, 50] Operation: 24+26=50 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[24, 6], Operations: ['31+1=32', '32-26=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 24*6=144, Resulting Numbers: [144] 144,80 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,80 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 #0,2,1 Current State: 80:[26, 8], Operations: ['31+1=32', '32-24=8'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,80 unequal: No Solution Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,80 unequal: No Solution Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,80 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 #0,2,2 Current State: 80:[32, 2], Operations: ['31+1=32', '26-24=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,80 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 #0,2,3 Current State: 80:[32, 50], Operations: ['31+1=32', '24+26=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 32*50=1600, Resulting Numbers: [1600] 1600,80 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 46, 92, 9, 49 ]
12
[ "92-46=46", "9+49=58", "58-46=12" ]
Current State: 12:[46, 92, 9, 49], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [9, 49, 46] Generated Node #2: [9, 49, 46] from Operation: 92-46=46 Current State: 12:[9, 49, 46], Operations: ['92-46=46'] Exploring Operation: 9+49=58, Resulting Numbers: [46, 58] Generated Node #3: [46, 58] from Operation: 9+49=58 Current State: 12:[46, 58], Operations: ['92-46=46', '9+49=58'] Exploring Operation: 58-46=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[46, 92, 9, 49], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [9, 49, 46] Generated Node #0,0: 12:[9, 49, 46] Operation: 92-46=46 Exploring Operation: 92-49=43, Resulting Numbers: [46, 9, 43] Generated Node #0,1: 12:[46, 9, 43] Operation: 92-49=43 Exploring Operation: 92/46=2, Resulting Numbers: [9, 49, 2] Generated Node #0,2: 12:[9, 49, 2] Operation: 92/46=2 Exploring Operation: 46-9=37, Resulting Numbers: [92, 49, 37] Generated Node #0,3: 12:[92, 49, 37] Operation: 46-9=37 Exploring Operation: 49-46=3, Resulting Numbers: [92, 9, 3] Generated Node #0,4: 12:[92, 9, 3] Operation: 49-46=3 Moving to Node #0,2 Current State: 12:[9, 49, 2], Operations: ['92/46=2'] Exploring Operation: 9+2=11, Resulting Numbers: [49, 11] Generated Node #0,2,0: 12:[49, 11] Operation: 9+2=11 Exploring Operation: 49-2=47, Resulting Numbers: [9, 47] Generated Node #0,2,1: 12:[9, 47] Operation: 49-2=47 Exploring Operation: 9-2=7, Resulting Numbers: [49, 7] Generated Node #0,2,2: 12:[49, 7] Operation: 9-2=7 Exploring Operation: 49+2=51, Resulting Numbers: [9, 51] Generated Node #0,2,3: 12:[9, 51] Operation: 49+2=51 Exploring Operation: 49-9=40, Resulting Numbers: [2, 40] Generated Node #0,2,4: 12:[2, 40] Operation: 49-9=40 Moving to Node #0,1 Current State: 12:[46, 9, 43], Operations: ['92-49=43'] Exploring Operation: 9+43=52, Resulting Numbers: [46, 52] Generated Node #0,1,0: 12:[46, 52] Operation: 9+43=52 Exploring Operation: 46-9=37, Resulting Numbers: [43, 37] Generated Node #0,1,1: 12:[43, 37] Operation: 46-9=37 Exploring Operation: 46+9=55, Resulting Numbers: [43, 55] Generated Node #0,1,2: 12:[43, 55] Operation: 46+9=55 Exploring Operation: 43-9=34, Resulting Numbers: [46, 34] Generated Node #0,1,3: 12:[46, 34] Operation: 43-9=34 Exploring Operation: 46-43=3, Resulting Numbers: [9, 3] Generated Node #0,1,4: 12:[9, 3] Operation: 46-43=3 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 12:[9, 3], Operations: ['92-49=43', '46-43=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[46, 92, 9, 49], Operations: [] Exploring Operation: 92-49=43, Resulting Numbers: [46, 9, 43] Generated Node #0,1: 12:[46, 9, 43] Operation: 92-49=43 Moving to Node #0,1 Current State: 12:[46, 9, 43], Operations: ['92-49=43'] Exploring Operation: 46-43=3, Resulting Numbers: [9, 3] Generated Node #0,1,4: 12:[9, 3] Operation: 46-43=3 Moving to Node #0,1,4 Current State: 12:[9, 3], Operations: ['92-49=43', '46-43=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 83, 67, 2, 38 ]
11
[ "83-67=16", "38-16=22", "22/2=11" ]
Current State: 11:[83, 67, 2, 38], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [2, 38, 16] Generated Node #2: [2, 38, 16] from Operation: 83-67=16 Current State: 11:[2, 38, 16], Operations: ['83-67=16'] Exploring Operation: 38-16=22, Resulting Numbers: [2, 22] Generated Node #3: [2, 22] from Operation: 38-16=22 Current State: 11:[2, 22], Operations: ['83-67=16', '38-16=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[83, 67, 2, 38], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [2, 38, 16] Generated Node #0,0: 11:[2, 38, 16] Operation: 83-67=16 Exploring Operation: 83-2=81, Resulting Numbers: [67, 38, 81] Generated Node #0,1: 11:[67, 38, 81] Operation: 83-2=81 Exploring Operation: 38/2=19, Resulting Numbers: [83, 67, 19] Generated Node #0,2: 11:[83, 67, 19] Operation: 38/2=19 Exploring Operation: 67-38=29, Resulting Numbers: [83, 2, 29] Generated Node #0,3: 11:[83, 2, 29] Operation: 67-38=29 Exploring Operation: 83-38=45, Resulting Numbers: [67, 2, 45] Generated Node #0,4: 11:[67, 2, 45] Operation: 83-38=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[2, 38, 16], Operations: ['83-67=16'] Exploring Operation: 38-2=36, Resulting Numbers: [16, 36] Generated Node #0,0,0: 11:[16, 36] Operation: 38-2=36 Exploring Operation: 38/2=19, Resulting Numbers: [16, 19] Generated Node #0,0,1: 11:[16, 19] Operation: 38/2=19 Exploring Operation: 38-16=22, Resulting Numbers: [2, 22] Generated Node #0,0,2: 11:[2, 22] Operation: 38-16=22 Exploring Operation: 16-2=14, Resulting Numbers: [38, 14] Generated Node #0,0,3: 11:[38, 14] Operation: 16-2=14 Exploring Operation: 16/2=8, Resulting Numbers: [38, 8] Generated Node #0,0,4: 11:[38, 8] Operation: 16/2=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[16, 19], Operations: ['83-67=16', '38/2=19'] Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,11 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,11 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 #0,0,2 Current State: 11:[2, 22], Operations: ['83-67=16', '38-16=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,11 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[83, 67, 2, 38], Operations: [] Exploring Operation: 83-67=16, Resulting Numbers: [2, 38, 16] Generated Node #0,0: 11:[2, 38, 16] Operation: 83-67=16 Moving to Node #0,0 Current State: 11:[2, 38, 16], Operations: ['83-67=16'] Exploring Operation: 38-16=22, Resulting Numbers: [2, 22] Generated Node #0,0,2: 11:[2, 22] Operation: 38-16=22 Moving to Node #0,0,2 Current State: 11:[2, 22], Operations: ['83-67=16', '38-16=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 40, 32, 56, 64 ]
14
[ "56-40=16", "64/32=2", "16-2=14" ]
Current State: 14:[40, 32, 56, 64], Operations: [] Exploring Operation: 56-40=16, Resulting Numbers: [32, 64, 16] Generated Node #2: [32, 64, 16] from Operation: 56-40=16 Current State: 14:[32, 64, 16], Operations: ['56-40=16'] Exploring Operation: 64/32=2, Resulting Numbers: [16, 2] Generated Node #3: [16, 2] from Operation: 64/32=2 Current State: 14:[16, 2], Operations: ['56-40=16', '64/32=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[40, 32, 56, 64], Operations: [] Exploring Operation: 64-56=8, Resulting Numbers: [40, 32, 8] Generated Node #0,0: 14:[40, 32, 8] Operation: 64-56=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[40, 32, 8], Operations: ['64-56=8'] Exploring Operation: 40-32=8, Resulting Numbers: [8, 8] Generated Node #0,0,0: 14:[8, 8] Operation: 40-32=8 Moving to Node #0,0,0 Current State: 14:[8, 8], Operations: ['64-56=8', '40-32=8'] Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,14 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
[ 80, 74, 18, 94 ]
78
[ "80+74=154", "94-18=76", "154-76=78" ]
Current State: 78:[80, 74, 18, 94], Operations: [] Exploring Operation: 80+74=154, Resulting Numbers: [18, 94, 154] Generated Node #2: [18, 94, 154] from Operation: 80+74=154 Current State: 78:[18, 94, 154], Operations: ['80+74=154'] Exploring Operation: 94-18=76, Resulting Numbers: [154, 76] Generated Node #3: [154, 76] from Operation: 94-18=76 Current State: 78:[154, 76], Operations: ['80+74=154', '94-18=76'] Exploring Operation: 154-76=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[80, 74, 18, 94], Operations: [] Exploring Operation: 94-18=76, Resulting Numbers: [80, 74, 76] Generated Node #0,0: 78:[80, 74, 76] Operation: 94-18=76 Moving to Node #0,0 Current State: 78:[80, 74, 76], Operations: ['94-18=76'] Exploring Operation: 80-74=6, Resulting Numbers: [76, 6] Generated Node #0,0,0: 78:[76, 6] Operation: 80-74=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[76, 6], Operations: ['94-18=76', '80-74=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 8, 58, 72, 60 ]
68
[ "60-58=2", "8/2=4", "72-4=68" ]
Current State: 68:[8, 58, 72, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [8, 72, 2] Generated Node #2: [8, 72, 2] from Operation: 60-58=2 Current State: 68:[8, 72, 2], Operations: ['60-58=2'] Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 8/2=4 Current State: 68:[72, 4], Operations: ['60-58=2', '8/2=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[8, 58, 72, 60], Operations: [] Exploring Operation: 72-60=12, Resulting Numbers: [8, 58, 12] Generated Node #0,0: 68:[8, 58, 12] Operation: 72-60=12 Exploring Operation: 72-58=14, Resulting Numbers: [8, 60, 14] Generated Node #0,1: 68:[8, 60, 14] Operation: 72-58=14 Exploring Operation: 8+60=68, Resulting Numbers: [58, 72, 68] Generated Node #0,2: 68:[58, 72, 68] Operation: 8+60=68 Exploring Operation: 60-58=2, Resulting Numbers: [8, 72, 2] Generated Node #0,3: 68:[8, 72, 2] Operation: 60-58=2 Exploring Operation: 8+58=66, Resulting Numbers: [72, 60, 66] Generated Node #0,4: 68:[72, 60, 66] Operation: 8+58=66 Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[8, 72, 2], Operations: ['60-58=2'] Exploring Operation: 72-8=64, Resulting Numbers: [2, 64] Generated Node #0,3,0: 68:[2, 64] Operation: 72-8=64 Exploring Operation: 8*2=16, Resulting Numbers: [72, 16] Generated Node #0,3,1: 68:[72, 16] Operation: 8*2=16 Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #0,3,2: 68:[72, 4] Operation: 8/2=4 Exploring Operation: 72/8=9, Resulting Numbers: [2, 9] Generated Node #0,3,3: 68:[2, 9] Operation: 72/8=9 Exploring Operation: 8-2=6, Resulting Numbers: [72, 6] Generated Node #0,3,4: 68:[72, 6] Operation: 8-2=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 68:[2, 64], Operations: ['60-58=2', '72-8=64'] Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,68 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,68 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 68:[72, 4], Operations: ['60-58=2', '8/2=4'] Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,68 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,68 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[8, 58, 72, 60], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [8, 72, 2] Generated Node #0,3: 68:[8, 72, 2] Operation: 60-58=2 Moving to Node #0,3 Current State: 68:[8, 72, 2], Operations: ['60-58=2'] Exploring Operation: 8/2=4, Resulting Numbers: [72, 4] Generated Node #0,3,2: 68:[72, 4] Operation: 8/2=4 Moving to Node #0,3,2 Current State: 68:[72, 4], Operations: ['60-58=2', '8/2=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 91, 2, 74, 40 ]
21
[ "91+2=93", "74+40=114", "114-93=21" ]
Current State: 21:[91, 2, 74, 40], Operations: [] Exploring Operation: 91+2=93, Resulting Numbers: [74, 40, 93] Generated Node #2: [74, 40, 93] from Operation: 91+2=93 Current State: 21:[74, 40, 93], Operations: ['91+2=93'] Exploring Operation: 74+40=114, Resulting Numbers: [93, 114] Generated Node #3: [93, 114] from Operation: 74+40=114 Current State: 21:[93, 114], Operations: ['91+2=93', '74+40=114'] Exploring Operation: 114-93=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[91, 2, 74, 40], Operations: [] Exploring Operation: 40/2=20, Resulting Numbers: [91, 74, 20] Generated Node #0,0: 21:[91, 74, 20] Operation: 40/2=20 Exploring Operation: 74-40=34, Resulting Numbers: [91, 2, 34] Generated Node #0,1: 21:[91, 2, 34] Operation: 74-40=34 Exploring Operation: 91-74=17, Resulting Numbers: [2, 40, 17] Generated Node #0,2: 21:[2, 40, 17] Operation: 91-74=17 Exploring Operation: 91-40=51, Resulting Numbers: [2, 74, 51] Generated Node #0,3: 21:[2, 74, 51] Operation: 91-40=51 Exploring Operation: 74/2=37, Resulting Numbers: [91, 40, 37] Generated Node #0,4: 21:[91, 40, 37] Operation: 74/2=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[2, 40, 17], Operations: ['91-74=17'] Exploring Operation: 40-17=23, Resulting Numbers: [2, 23] Generated Node #0,2,0: 21:[2, 23] Operation: 40-17=23 Exploring Operation: 2+40=42, Resulting Numbers: [17, 42] Generated Node #0,2,1: 21:[17, 42] Operation: 2+40=42 Exploring Operation: 40/2=20, Resulting Numbers: [17, 20] Generated Node #0,2,2: 21:[17, 20] Operation: 40/2=20 Exploring Operation: 40-2=38, Resulting Numbers: [17, 38] Generated Node #0,2,3: 21:[17, 38] Operation: 40-2=38 Exploring Operation: 2+17=19, Resulting Numbers: [40, 19] Generated Node #0,2,4: 21:[40, 19] Operation: 2+17=19 Moving to Node #0,2,0 Current State: 21:[2, 23], Operations: ['91-74=17', '40-17=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[91, 2, 74, 40], Operations: [] Exploring Operation: 91-74=17, Resulting Numbers: [2, 40, 17] Generated Node #0,2: 21:[2, 40, 17] Operation: 91-74=17 Moving to Node #0,2 Current State: 21:[2, 40, 17], Operations: ['91-74=17'] Exploring Operation: 40-17=23, Resulting Numbers: [2, 23] Generated Node #0,2,0: 21:[2, 23] Operation: 40-17=23 Moving to Node #0,2,0 Current State: 21:[2, 23], Operations: ['91-74=17', '40-17=23'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 87, 66, 35, 91 ]
77
[ "87-66=21", "91-35=56", "21+56=77" ]
Current State: 77:[87, 66, 35, 91], Operations: [] Exploring Operation: 87-66=21, Resulting Numbers: [35, 91, 21] Generated Node #2: [35, 91, 21] from Operation: 87-66=21 Current State: 77:[35, 91, 21], Operations: ['87-66=21'] Exploring Operation: 91-35=56, Resulting Numbers: [21, 56] Generated Node #3: [21, 56] from Operation: 91-35=56 Current State: 77:[21, 56], Operations: ['87-66=21', '91-35=56'] Exploring Operation: 21+56=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[87, 66, 35, 91], Operations: [] Exploring Operation: 91-87=4, Resulting Numbers: [66, 35, 4] Generated Node #0,0: 77:[66, 35, 4] Operation: 91-87=4 Exploring Operation: 66-35=31, Resulting Numbers: [87, 91, 31] Generated Node #0,1: 77:[87, 91, 31] Operation: 66-35=31 Exploring Operation: 91-35=56, Resulting Numbers: [87, 66, 56] Generated Node #0,2: 77:[87, 66, 56] Operation: 91-35=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[66, 35, 4], Operations: ['91-87=4'] Exploring Operation: 66-35=31, Resulting Numbers: [4, 31] Generated Node #0,0,0: 77:[4, 31] Operation: 66-35=31 Exploring Operation: 66+4=70, Resulting Numbers: [35, 70] Generated Node #0,0,1: 77:[35, 70] Operation: 66+4=70 Exploring Operation: 66+35=101, Resulting Numbers: [4, 101] Generated Node #0,0,2: 77:[4, 101] Operation: 66+35=101 Moving to Node #0,0,0 Current State: 77:[4, 31], Operations: ['91-87=4', '66-35=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,77 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[4, 101], Operations: ['91-87=4', '66+35=101'] Exploring Operation: 4+101=105, Resulting Numbers: [105] 105,77 unequal: No Solution Exploring Operation: 4*101=404, Resulting Numbers: [404] 404,77 unequal: No Solution Exploring Operation: 101-4=97, Resulting Numbers: [97] 97,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[35, 70], Operations: ['91-87=4', '66+4=70'] Exploring Operation: 35+70=105, Resulting Numbers: [105] 105,77 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[87, 66, 56], Operations: ['91-35=56'] Exploring Operation: 87-56=31, Resulting Numbers: [66, 31] Generated Node #0,2,0: 77:[66, 31] Operation: 87-56=31 Exploring Operation: 66-56=10, Resulting Numbers: [87, 10] Generated Node #0,2,1: 77:[87, 10] Operation: 66-56=10 Exploring Operation: 87-66=21, Resulting Numbers: [56, 21] Generated Node #0,2,2: 77:[56, 21] Operation: 87-66=21 Moving to Node #0,2,1 Current State: 77:[87, 10], Operations: ['91-35=56', '66-56=10'] Exploring Operation: 87*10=870, Resulting Numbers: [870] 870,77 unequal: No Solution Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[87, 66, 35, 91], Operations: [] Exploring Operation: 91-35=56, Resulting Numbers: [87, 66, 56] Generated Node #0,2: 77:[87, 66, 56] Operation: 91-35=56 Moving to Node #0,2 Current State: 77:[87, 66, 56], Operations: ['91-35=56'] Exploring Operation: 66-56=10, Resulting Numbers: [87, 10] Generated Node #0,2,1: 77:[87, 10] Operation: 66-56=10 Moving to Node #0,2,1 Current State: 77:[87, 10], Operations: ['91-35=56', '66-56=10'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 24, 53, 52, 95 ]
91
[ "95-53=42", "52*42=2184", "2184/24=91" ]
Current State: 91:[24, 53, 52, 95], Operations: [] Exploring Operation: 95-53=42, Resulting Numbers: [24, 52, 42] Generated Node #2: [24, 52, 42] from Operation: 95-53=42 Current State: 91:[24, 52, 42], Operations: ['95-53=42'] Exploring Operation: 52*42=2184, Resulting Numbers: [24, 2184] Generated Node #3: [24, 2184] from Operation: 52*42=2184 Current State: 91:[24, 2184], Operations: ['95-53=42', '52*42=2184'] Exploring Operation: 2184/24=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[24, 53, 52, 95], Operations: [] Exploring Operation: 53+52=105, Resulting Numbers: [24, 95, 105] Generated Node #0,0: 91:[24, 95, 105] Operation: 53+52=105 Exploring Operation: 53-52=1, Resulting Numbers: [24, 95, 1] Generated Node #0,1: 91:[24, 95, 1] Operation: 53-52=1 Moving to Node #0,1 Current State: 91:[24, 95, 1], Operations: ['53-52=1'] Exploring Operation: 95-1=94, Resulting Numbers: [24, 94] Generated Node #0,1,0: 91:[24, 94] Operation: 95-1=94 Exploring Operation: 24-1=23, Resulting Numbers: [95, 23] Generated Node #0,1,1: 91:[95, 23] Operation: 24-1=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[24, 94], Operations: ['53-52=1', '95-1=94'] Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,91 unequal: No Solution Exploring Operation: 24+94=118, Resulting Numbers: [118] 118,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[95, 23], Operations: ['53-52=1', '24-1=23'] Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,91 unequal: No Solution Exploring Operation: 95+23=118, Resulting Numbers: [118] 118,91 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: 91:[24, 95, 105], Operations: ['53+52=105'] Exploring Operation: 105-95=10, Resulting Numbers: [24, 10] Generated Node #0,0,0: 91:[24, 10] Operation: 105-95=10 Exploring Operation: 105-24=81, Resulting Numbers: [95, 81] Generated Node #0,0,1: 91:[95, 81] Operation: 105-24=81 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[24, 10], Operations: ['53+52=105', '105-95=10'] Exploring Operation: 24-10=14, Resulting Numbers: [14] 14,91 unequal: No Solution Exploring Operation: 24+10=34, Resulting Numbers: [34] 34,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[95, 81], Operations: ['53+52=105', '105-24=81'] Exploring Operation: 95+81=176, Resulting Numbers: [176] 176,91 unequal: No Solution Exploring Operation: 95-81=14, Resulting Numbers: [14] 14,91 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
[ 86, 65, 21, 46 ]
43
[ "65-21=44", "46-44=2", "86/2=43" ]
Current State: 43:[86, 65, 21, 46], Operations: [] Exploring Operation: 65-21=44, Resulting Numbers: [86, 46, 44] Generated Node #2: [86, 46, 44] from Operation: 65-21=44 Current State: 43:[86, 46, 44], Operations: ['65-21=44'] Exploring Operation: 46-44=2, Resulting Numbers: [86, 2] Generated Node #3: [86, 2] from Operation: 46-44=2 Current State: 43:[86, 2], Operations: ['65-21=44', '46-44=2'] Exploring Operation: 86/2=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[86, 65, 21, 46], Operations: [] Exploring Operation: 86-65=21, Resulting Numbers: [21, 46, 21] Generated Node #0,0: 43:[21, 46, 21] Operation: 86-65=21 Moving to Node #0,0 Current State: 43:[21, 46, 21], Operations: ['86-65=21'] Exploring Operation: 21+21=42, Resulting Numbers: [46, 42] Generated Node #0,0,0: 43:[46, 42] Operation: 21+21=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[46, 42], Operations: ['86-65=21', '21+21=42'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 65, 2, 57, 51 ]
100
[ "65-51=14", "2*57=114", "114-14=100" ]
Current State: 100:[65, 2, 57, 51], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [2, 57, 14] Generated Node #2: [2, 57, 14] from Operation: 65-51=14 Current State: 100:[2, 57, 14], Operations: ['65-51=14'] Exploring Operation: 2*57=114, Resulting Numbers: [14, 114] Generated Node #3: [14, 114] from Operation: 2*57=114 Current State: 100:[14, 114], Operations: ['65-51=14', '2*57=114'] Exploring Operation: 114-14=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[65, 2, 57, 51], Operations: [] Exploring Operation: 65-57=8, Resulting Numbers: [2, 51, 8] Generated Node #0,0: 100:[2, 51, 8] Operation: 65-57=8 Moving to Node #0,0 Current State: 100:[2, 51, 8], Operations: ['65-57=8'] Exploring Operation: 2+8=10, Resulting Numbers: [51, 10] Generated Node #0,0,0: 100:[51, 10] Operation: 2+8=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[51, 10], Operations: ['65-57=8', '2+8=10'] Exploring Operation: 51-10=41, Resulting Numbers: [41] 41,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 26, 92, 94, 36 ]
87
[ "94+36=130", "130/26=5", "92-5=87" ]
Current State: 87:[26, 92, 94, 36], Operations: [] Exploring Operation: 94+36=130, Resulting Numbers: [26, 92, 130] Generated Node #2: [26, 92, 130] from Operation: 94+36=130 Current State: 87:[26, 92, 130], Operations: ['94+36=130'] Exploring Operation: 130/26=5, Resulting Numbers: [92, 5] Generated Node #3: [92, 5] from Operation: 130/26=5 Current State: 87:[92, 5], Operations: ['94+36=130', '130/26=5'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[26, 92, 94, 36], Operations: [] Exploring Operation: 92-26=66, Resulting Numbers: [94, 36, 66] Generated Node #0,0: 87:[94, 36, 66] Operation: 92-26=66 Exploring Operation: 26+36=62, Resulting Numbers: [92, 94, 62] Generated Node #0,1: 87:[92, 94, 62] Operation: 26+36=62 Exploring Operation: 94-92=2, Resulting Numbers: [26, 36, 2] Generated Node #0,2: 87:[26, 36, 2] Operation: 94-92=2 Exploring Operation: 36-26=10, Resulting Numbers: [92, 94, 10] Generated Node #0,3: 87:[92, 94, 10] Operation: 36-26=10 Exploring Operation: 94-26=68, Resulting Numbers: [92, 36, 68] Generated Node #0,4: 87:[92, 36, 68] Operation: 94-26=68 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[26, 36, 2], Operations: ['94-92=2'] Exploring Operation: 26-2=24, Resulting Numbers: [36, 24] Generated Node #0,2,0: 87:[36, 24] Operation: 26-2=24 Exploring Operation: 26+2=28, Resulting Numbers: [36, 28] Generated Node #0,2,1: 87:[36, 28] Operation: 26+2=28 Exploring Operation: 36-26=10, Resulting Numbers: [2, 10] Generated Node #0,2,2: 87:[2, 10] Operation: 36-26=10 Exploring Operation: 36-2=34, Resulting Numbers: [26, 34] Generated Node #0,2,3: 87:[26, 34] Operation: 36-2=34 Exploring Operation: 36+2=38, Resulting Numbers: [26, 38] Generated Node #0,2,4: 87:[26, 38] Operation: 36+2=38 Moving to Node #0,2,1 Current State: 87:[36, 28], Operations: ['94-92=2', '26+2=28'] Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,87 unequal: No Solution Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,87 unequal: No Solution Moving to Node #0,2,3 Current State: 87:[26, 34], Operations: ['94-92=2', '36-2=34'] Exploring Operation: 26+34=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 34-26=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 26*34=884, Resulting Numbers: [884] 884,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[2, 10], Operations: ['94-92=2', '36-26=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[36, 24], Operations: ['94-92=2', '26-2=24'] Exploring Operation: 36*24=864, Resulting Numbers: [864] 864,87 unequal: No Solution Exploring Operation: 36+24=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,87 unequal: No Solution Moving to Node #0,2,4 Current State: 87:[26, 38], Operations: ['94-92=2', '36+2=38'] Exploring Operation: 26+38=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 26*38=988, Resulting Numbers: [988] 988,87 unequal: No Solution Exploring Operation: 38-26=12, Resulting Numbers: [12] 12,87 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 Current State: 87:[92, 94, 10], Operations: ['36-26=10'] Exploring Operation: 92-10=82, Resulting Numbers: [94, 82] Generated Node #0,3,0: 87:[94, 82] Operation: 92-10=82 Exploring Operation: 92+10=102, Resulting Numbers: [94, 102] Generated Node #0,3,1: 87:[94, 102] Operation: 92+10=102 Exploring Operation: 94-92=2, Resulting Numbers: [10, 2] Generated Node #0,3,2: 87:[10, 2] Operation: 94-92=2 Exploring Operation: 94-10=84, Resulting Numbers: [92, 84] Generated Node #0,3,3: 87:[92, 84] Operation: 94-10=84 Exploring Operation: 94+10=104, Resulting Numbers: [92, 104] Generated Node #0,3,4: 87:[92, 104] Operation: 94+10=104 Moving to Node #0,3,2 Current State: 87:[10, 2], Operations: ['36-26=10', '94-92=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[92, 84], Operations: ['36-26=10', '94-10=84'] Exploring Operation: 92+84=176, Resulting Numbers: [176] 176,87 unequal: No Solution Exploring Operation: 92*84=7728, Resulting Numbers: [7728] 7728,87 unequal: No Solution Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,87 unequal: No Solution Moving to Node #0,3,0 Current State: 87:[94, 82], Operations: ['36-26=10', '92-10=82'] Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,87 unequal: No Solution Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,87 unequal: No Solution Moving to Node #0,3,1 Current State: 87:[94, 102], Operations: ['36-26=10', '92+10=102'] Exploring Operation: 102-94=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 94+102=196, Resulting Numbers: [196] 196,87 unequal: No Solution Exploring Operation: 94*102=9588, Resulting Numbers: [9588] 9588,87 unequal: No Solution Moving to Node #0,3,4 Current State: 87:[92, 104], Operations: ['36-26=10', '94+10=104'] Exploring Operation: 104-92=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 92+104=196, Resulting Numbers: [196] 196,87 unequal: No Solution Exploring Operation: 92*104=9568, Resulting Numbers: [9568] 9568,87 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:[92, 36, 68], Operations: ['94-26=68'] Exploring Operation: 68-36=32, Resulting Numbers: [92, 32] Generated Node #0,4,0: 87:[92, 32] Operation: 68-36=32 Exploring Operation: 36+68=104, Resulting Numbers: [92, 104] Generated Node #0,4,1: 87:[92, 104] Operation: 36+68=104 Exploring Operation: 92-36=56, Resulting Numbers: [68, 56] Generated Node #0,4,2: 87:[68, 56] Operation: 92-36=56 Exploring Operation: 92-68=24, Resulting Numbers: [36, 24] Generated Node #0,4,3: 87:[36, 24] Operation: 92-68=24 Exploring Operation: 92+36=128, Resulting Numbers: [68, 128] Generated Node #0,4,4: 87:[68, 128] Operation: 92+36=128 Moving to Node #0,4,0 Current State: 87:[92, 32], Operations: ['94-26=68', '68-36=32'] Exploring Operation: 92*32=2944, Resulting Numbers: [2944] 2944,87 unequal: No Solution Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 92+32=124, Resulting Numbers: [124] 124,87 unequal: No Solution Moving to Node #0,4,3 Current State: 87:[36, 24], Operations: ['94-26=68', '92-68=24'] Exploring Operation: 36*24=864, Resulting Numbers: [864] 864,87 unequal: No Solution Exploring Operation: 36-24=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 36+24=60, Resulting Numbers: [60] 60,87 unequal: No Solution Moving to Node #0,4,1 Current State: 87:[92, 104], Operations: ['94-26=68', '36+68=104'] Exploring Operation: 92+104=196, Resulting Numbers: [196] 196,87 unequal: No Solution Exploring Operation: 104-92=12, Resulting Numbers: [12] 12,87 unequal: No Solution Exploring Operation: 92*104=9568, Resulting Numbers: [9568] 9568,87 unequal: No Solution Moving to Node #0,4,2 Current State: 87:[68, 56], Operations: ['94-26=68', '92-36=56'] Exploring Operation: 68*56=3808, Resulting Numbers: [3808] 3808,87 unequal: No Solution Exploring Operation: 68+56=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 68-56=12, Resulting Numbers: [12] 12,87 unequal: No Solution Moving to Node #0,4,4 Current State: 87:[68, 128], Operations: ['94-26=68', '92+36=128'] Exploring Operation: 68*128=8704, Resulting Numbers: [8704] 8704,87 unequal: No Solution Exploring Operation: 128-68=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 68+128=196, Resulting Numbers: [196] 196,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[94, 36, 66], Operations: ['92-26=66'] Exploring Operation: 66-36=30, Resulting Numbers: [94, 30] Generated Node #0,0,0: 87:[94, 30] Operation: 66-36=30 Exploring Operation: 36+66=102, Resulting Numbers: [94, 102] Generated Node #0,0,1: 87:[94, 102] Operation: 36+66=102 Exploring Operation: 94-66=28, Resulting Numbers: [36, 28] Generated Node #0,0,2: 87:[36, 28] Operation: 94-66=28 Exploring Operation: 94+36=130, Resulting Numbers: [66, 130] Generated Node #0,0,3: 87:[66, 130] Operation: 94+36=130 Exploring Operation: 94-36=58, Resulting Numbers: [66, 58] Generated Node #0,0,4: 87:[66, 58] Operation: 94-36=58 Moving to Node #0,0,0 Current State: 87:[94, 30], Operations: ['92-26=66', '66-36=30'] Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,87 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[36, 28], Operations: ['92-26=66', '94-66=28'] Exploring Operation: 36-28=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 36*28=1008, Resulting Numbers: [1008] 1008,87 unequal: No Solution Exploring Operation: 36+28=64, Resulting Numbers: [64] 64,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[94, 102], Operations: ['92-26=66', '36+66=102'] Exploring Operation: 94*102=9588, Resulting Numbers: [9588] 9588,87 unequal: No Solution Exploring Operation: 102-94=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 94+102=196, Resulting Numbers: [196] 196,87 unequal: No Solution Moving to Node #0,0,4 Current State: 87:[66, 58], Operations: ['92-26=66', '94-36=58'] Exploring Operation: 66-58=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 66+58=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 66*58=3828, Resulting Numbers: [3828] 3828,87 unequal: No Solution Moving to Node #0,0,3 Current State: 87:[66, 130], Operations: ['92-26=66', '94+36=130'] Exploring Operation: 66+130=196, Resulting Numbers: [196] 196,87 unequal: No Solution Exploring Operation: 130-66=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 66*130=8580, Resulting Numbers: [8580] 8580,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[92, 94, 62], Operations: ['26+36=62'] Exploring Operation: 92+62=154, Resulting Numbers: [94, 154] Generated Node #0,1,0: 87:[94, 154] Operation: 92+62=154 Exploring Operation: 92-62=30, Resulting Numbers: [94, 30] Generated Node #0,1,1: 87:[94, 30] Operation: 92-62=30 Exploring Operation: 94+62=156, Resulting Numbers: [92, 156] Generated Node #0,1,2: 87:[92, 156] Operation: 94+62=156 Exploring Operation: 94-62=32, Resulting Numbers: [92, 32] Generated Node #0,1,3: 87:[92, 32] Operation: 94-62=32 Exploring Operation: 94-92=2, Resulting Numbers: [62, 2] Generated Node #0,1,4: 87:[62, 2] Operation: 94-92=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[94, 30], Operations: ['26+36=62', '92-62=30'] Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,87 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 87:[92, 32], Operations: ['26+36=62', '94-62=32'] Exploring Operation: 92+32=124, Resulting Numbers: [124] 124,87 unequal: No Solution Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 92*32=2944, Resulting Numbers: [2944] 2944,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 87:[62, 2], Operations: ['26+36=62', '94-92=2'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,87 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 62*2=124, Resulting Numbers: [124] 124,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[94, 154], Operations: ['26+36=62', '92+62=154'] Exploring Operation: 94+154=248, Resulting Numbers: [248] 248,87 unequal: No Solution Exploring Operation: 154-94=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 94*154=14476, Resulting Numbers: [14476] 14476,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[92, 156], Operations: ['26+36=62', '94+62=156'] Exploring Operation: 156-92=64, Resulting Numbers: [64] 64,87 unequal: No Solution Exploring Operation: 92+156=248, Resulting Numbers: [248] 248,87 unequal: No Solution Exploring Operation: 92*156=14352, Resulting Numbers: [14352] 14352,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 16, 20, 7, 25 ]
27
[ "16*25=400", "400/20=20", "7+20=27" ]
Current State: 27:[16, 20, 7, 25], Operations: [] Exploring Operation: 16*25=400, Resulting Numbers: [20, 7, 400] Generated Node #2: [20, 7, 400] from Operation: 16*25=400 Current State: 27:[20, 7, 400], Operations: ['16*25=400'] Exploring Operation: 400/20=20, Resulting Numbers: [7, 20] Generated Node #3: [7, 20] from Operation: 400/20=20 Current State: 27:[7, 20], Operations: ['16*25=400', '400/20=20'] Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[16, 20, 7, 25], Operations: [] Exploring Operation: 25-16=9, Resulting Numbers: [20, 7, 9] Generated Node #0,0: 27:[20, 7, 9] Operation: 25-16=9 Exploring Operation: 25-20=5, Resulting Numbers: [16, 7, 5] Generated Node #0,1: 27:[16, 7, 5] Operation: 25-20=5 Exploring Operation: 16-7=9, Resulting Numbers: [20, 25, 9] Generated Node #0,2: 27:[20, 25, 9] Operation: 16-7=9 Exploring Operation: 20+7=27, Resulting Numbers: [16, 25, 27] Generated Node #0,3: 27:[16, 25, 27] Operation: 20+7=27 Exploring Operation: 20-16=4, Resulting Numbers: [7, 25, 4] Generated Node #0,4: 27:[7, 25, 4] Operation: 20-16=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[7, 25, 4], Operations: ['20-16=4'] Exploring Operation: 7+25=32, Resulting Numbers: [4, 32] Generated Node #0,4,0: 27:[4, 32] Operation: 7+25=32 Exploring Operation: 7-4=3, Resulting Numbers: [25, 3] Generated Node #0,4,1: 27:[25, 3] Operation: 7-4=3 Exploring Operation: 7*4=28, Resulting Numbers: [25, 28] Generated Node #0,4,2: 27:[25, 28] Operation: 7*4=28 Exploring Operation: 25+4=29, Resulting Numbers: [7, 29] Generated Node #0,4,3: 27:[7, 29] Operation: 25+4=29 Exploring Operation: 7+4=11, Resulting Numbers: [25, 11] Generated Node #0,4,4: 27:[25, 11] Operation: 7+4=11 Moving to Node #0,4,1 Current State: 27:[25, 3], Operations: ['20-16=4', '7-4=3'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,27 unequal: No Solution Moving to Node #0,4,2 Current State: 27:[25, 28], Operations: ['20-16=4', '7*4=28'] Exploring Operation: 25+28=53, Resulting Numbers: [53] 53,27 unequal: No Solution Exploring Operation: 25*28=700, Resulting Numbers: [700] 700,27 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,27 unequal: No Solution Moving to Node #0,4,3 Current State: 27:[7, 29], Operations: ['20-16=4', '25+4=29'] Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,27 unequal: No Solution Moving to Node #0,4,4 Current State: 27:[25, 11], Operations: ['20-16=4', '7+4=11'] Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,27 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,27 unequal: No Solution Moving to Node #0,4,0 Current State: 27:[4, 32], Operations: ['20-16=4', '7+25=32'] Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,27 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[20, 7, 9], Operations: ['25-16=9'] Exploring Operation: 20-7=13, Resulting Numbers: [9, 13] Generated Node #0,0,0: 27:[9, 13] Operation: 20-7=13 Exploring Operation: 9-7=2, Resulting Numbers: [20, 2] Generated Node #0,0,1: 27:[20, 2] Operation: 9-7=2 Exploring Operation: 20-9=11, Resulting Numbers: [7, 11] Generated Node #0,0,2: 27:[7, 11] Operation: 20-9=11 Exploring Operation: 20+7=27, Resulting Numbers: [9, 27] Generated Node #0,0,3: 27:[9, 27] Operation: 20+7=27 Exploring Operation: 20+9=29, Resulting Numbers: [7, 29] Generated Node #0,0,4: 27:[7, 29] Operation: 20+9=29 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 27:[9, 27], Operations: ['25-16=9', '20+7=27'] Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 9*27=243, Resulting Numbers: [243] 243,27 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 #0,0,0 Current State: 27:[9, 13], Operations: ['25-16=9', '20-7=13'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,27 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 #0,0,2 Current State: 27:[7, 11], Operations: ['25-16=9', '20-9=11'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,27 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 #0,0,4 Current State: 27:[7, 29], Operations: ['25-16=9', '20+9=29'] Exploring Operation: 7*29=203, Resulting Numbers: [203] 203,27 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 7+29=36, Resulting Numbers: [36] 36,27 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 #0,0,1 Current State: 27:[20, 2], Operations: ['25-16=9', '9-7=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,27 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 #0,2 Current State: 27:[20, 25, 9], Operations: ['16-7=9'] Exploring Operation: 25-9=16, Resulting Numbers: [20, 16] Generated Node #0,2,0: 27:[20, 16] Operation: 25-9=16 Exploring Operation: 20-9=11, Resulting Numbers: [25, 11] Generated Node #0,2,1: 27:[25, 11] Operation: 20-9=11 Exploring Operation: 25-20=5, Resulting Numbers: [9, 5] Generated Node #0,2,2: 27:[9, 5] Operation: 25-20=5 Exploring Operation: 25+9=34, Resulting Numbers: [20, 34] Generated Node #0,2,3: 27:[20, 34] Operation: 25+9=34 Exploring Operation: 20+9=29, Resulting Numbers: [25, 29] Generated Node #0,2,4: 27:[25, 29] Operation: 20+9=29 Moving to Node #0,2,2 Current State: 27:[9, 5], Operations: ['16-7=9', '25-20=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,27 unequal: No Solution Moving to Node #0,2,4 Current State: 27:[25, 29], Operations: ['16-7=9', '20+9=29'] Exploring Operation: 25+29=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 29-25=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 25*29=725, Resulting Numbers: [725] 725,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[25, 11], Operations: ['16-7=9', '20-9=11'] Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[20, 16], Operations: ['16-7=9', '25-9=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,27 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,27 unequal: No Solution Moving to Node #0,2,3 Current State: 27:[20, 34], Operations: ['16-7=9', '25+9=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,27 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[16, 25, 27], Operations: ['20+7=27'] Exploring Operation: 27-25=2, Resulting Numbers: [16, 2] Generated Node #0,3,0: 27:[16, 2] Operation: 27-25=2 Exploring Operation: 27-16=11, Resulting Numbers: [25, 11] Generated Node #0,3,1: 27:[25, 11] Operation: 27-16=11 Exploring Operation: 16+25=41, Resulting Numbers: [27, 41] Generated Node #0,3,2: 27:[27, 41] Operation: 16+25=41 Exploring Operation: 16+27=43, Resulting Numbers: [25, 43] Generated Node #0,3,3: 27:[25, 43] Operation: 16+27=43 Exploring Operation: 25-16=9, Resulting Numbers: [27, 9] Generated Node #0,3,4: 27:[27, 9] Operation: 25-16=9 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 27:[27, 9], Operations: ['20+7=27', '25-16=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,27 unequal: No Solution Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,27 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 27*9=243, Resulting Numbers: [243] 243,27 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 #0,3,1 Current State: 27:[25, 11], Operations: ['20+7=27', '27-16=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,27 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,27 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 #0,3,0 Current State: 27:[16, 2], Operations: ['20+7=27', '27-25=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,27 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,27 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 #0,3,2 Current State: 27:[27, 41], Operations: ['20+7=27', '16+25=41'] Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,27 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,27 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 #0,3,3 Current State: 27:[25, 43], Operations: ['20+7=27', '16+27=43'] Exploring Operation: 25*43=1075, Resulting Numbers: [1075] 1075,27 unequal: No Solution Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 25+43=68, Resulting Numbers: [68] 68,27 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 #0,1 Current State: 27:[16, 7, 5], Operations: ['25-20=5'] Exploring Operation: 16+7=23, Resulting Numbers: [5, 23] Generated Node #0,1,0: 27:[5, 23] Operation: 16+7=23 Exploring Operation: 16-7=9, Resulting Numbers: [5, 9] Generated Node #0,1,1: 27:[5, 9] Operation: 16-7=9 Exploring Operation: 16+5=21, Resulting Numbers: [7, 21] Generated Node #0,1,2: 27:[7, 21] Operation: 16+5=21 Exploring Operation: 16-5=11, Resulting Numbers: [7, 11] Generated Node #0,1,3: 27:[7, 11] Operation: 16-5=11 Exploring Operation: 7-5=2, Resulting Numbers: [16, 2] Generated Node #0,1,4: 27:[16, 2] Operation: 7-5=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[5, 9], Operations: ['25-20=5', '16-7=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,27 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,27 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 #0,1,3 Current State: 27:[7, 11], Operations: ['25-20=5', '16-5=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,27 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,27 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 #0,1,0 Current State: 27:[5, 23], Operations: ['25-20=5', '16+7=23'] Exploring Operation: 5+23=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 5*23=115, Resulting Numbers: [115] 115,27 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 #0,1,2 Current State: 27:[7, 21], Operations: ['25-20=5', '16+5=21'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,27 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,27 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 #0,1,4 Current State: 27:[16, 2], Operations: ['25-20=5', '7-5=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,27 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,27 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 44, 87, 2, 35 ]
83
[ "44+87=131", "35+131=166", "166/2=83" ]
Current State: 83:[44, 87, 2, 35], Operations: [] Exploring Operation: 44+87=131, Resulting Numbers: [2, 35, 131] Generated Node #2: [2, 35, 131] from Operation: 44+87=131 Current State: 83:[2, 35, 131], Operations: ['44+87=131'] Exploring Operation: 35+131=166, Resulting Numbers: [2, 166] Generated Node #3: [2, 166] from Operation: 35+131=166 Current State: 83:[2, 166], Operations: ['44+87=131', '35+131=166'] Exploring Operation: 166/2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[44, 87, 2, 35], Operations: [] Exploring Operation: 2*35=70, Resulting Numbers: [44, 87, 70] Generated Node #0,0: 83:[44, 87, 70] Operation: 2*35=70 Exploring Operation: 44+2=46, Resulting Numbers: [87, 35, 46] Generated Node #0,1: 83:[87, 35, 46] Operation: 44+2=46 Exploring Operation: 44*2=88, Resulting Numbers: [87, 35, 88] Generated Node #0,2: 83:[87, 35, 88] Operation: 44*2=88 Moving to Node #0,0 Current State: 83:[44, 87, 70], Operations: ['2*35=70'] Exploring Operation: 87-44=43, Resulting Numbers: [70, 43] Generated Node #0,0,0: 83:[70, 43] Operation: 87-44=43 Exploring Operation: 44+70=114, Resulting Numbers: [87, 114] Generated Node #0,0,1: 83:[87, 114] Operation: 44+70=114 Exploring Operation: 44+87=131, Resulting Numbers: [70, 131] Generated Node #0,0,2: 83:[70, 131] Operation: 44+87=131 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[87, 114], Operations: ['2*35=70', '44+70=114'] Exploring Operation: 87*114=9918, Resulting Numbers: [9918] 9918,83 unequal: No Solution Exploring Operation: 87+114=201, Resulting Numbers: [201] 201,83 unequal: No Solution Exploring Operation: 114-87=27, Resulting Numbers: [27] 27,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[70, 43], Operations: ['2*35=70', '87-44=43'] Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,83 unequal: No Solution Exploring Operation: 70+43=113, Resulting Numbers: [113] 113,83 unequal: No Solution Exploring Operation: 70*43=3010, Resulting Numbers: [3010] 3010,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 83:[70, 131], Operations: ['2*35=70', '44+87=131'] Exploring Operation: 131-70=61, Resulting Numbers: [61] 61,83 unequal: No Solution Exploring Operation: 70*131=9170, Resulting Numbers: [9170] 9170,83 unequal: No Solution Exploring Operation: 70+131=201, Resulting Numbers: [201] 201,83 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: 83:[87, 35, 88], Operations: ['44*2=88'] Exploring Operation: 88-35=53, Resulting Numbers: [87, 53] Generated Node #0,2,0: 83:[87, 53] Operation: 88-35=53 Exploring Operation: 87-35=52, Resulting Numbers: [88, 52] Generated Node #0,2,1: 83:[88, 52] Operation: 87-35=52 Exploring Operation: 87+35=122, Resulting Numbers: [88, 122] Generated Node #0,2,2: 83:[88, 122] Operation: 87+35=122 Moving to Node #0,1 Current State: 83:[87, 35, 46], Operations: ['44+2=46'] Exploring Operation: 35+46=81, Resulting Numbers: [87, 81] Generated Node #0,1,0: 83:[87, 81] Operation: 35+46=81 Exploring Operation: 87+35=122, Resulting Numbers: [46, 122] Generated Node #0,1,1: 83:[46, 122] Operation: 87+35=122 Exploring Operation: 87-35=52, Resulting Numbers: [46, 52] Generated Node #0,1,2: 83:[46, 52] Operation: 87-35=52 Moving to Node #0,1,0 Current State: 83:[87, 81], Operations: ['44+2=46', '35+46=81'] Exploring Operation: 87*81=7047, Resulting Numbers: [7047] 7047,83 unequal: No Solution Exploring Operation: 87-81=6, Resulting Numbers: [6] 6,83 unequal: No Solution Exploring Operation: 87+81=168, Resulting Numbers: [168] 168,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[87, 53], Operations: ['44*2=88', '88-35=53'] Exploring Operation: 87*53=4611, Resulting Numbers: [4611] 4611,83 unequal: No Solution Exploring Operation: 87+53=140, Resulting Numbers: [140] 140,83 unequal: No Solution Exploring Operation: 87-53=34, Resulting Numbers: [34] 34,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[88, 52], Operations: ['44*2=88', '87-35=52'] Exploring Operation: 88-52=36, Resulting Numbers: [36] 36,83 unequal: No Solution Exploring Operation: 88*52=4576, Resulting Numbers: [4576] 4576,83 unequal: No Solution Exploring Operation: 88+52=140, Resulting Numbers: [140] 140,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[88, 122], Operations: ['44*2=88', '87+35=122'] Exploring Operation: 88*122=10736, Resulting Numbers: [10736] 10736,83 unequal: No Solution Exploring Operation: 122-88=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 88+122=210, Resulting Numbers: [210] 210,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[46, 52], Operations: ['44+2=46', '87-35=52'] Exploring Operation: 46+52=98, Resulting Numbers: [98] 98,83 unequal: No Solution Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,83 unequal: No Solution Exploring Operation: 46*52=2392, Resulting Numbers: [2392] 2392,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[46, 122], Operations: ['44+2=46', '87+35=122'] Exploring Operation: 46+122=168, Resulting Numbers: [168] 168,83 unequal: No Solution Exploring Operation: 122-46=76, Resulting Numbers: [76] 76,83 unequal: No Solution Exploring Operation: 46*122=5612, Resulting Numbers: [5612] 5612,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 53, 75, 3, 90 ]
24
[ "75-53=22", "3*22=66", "90-66=24" ]
Current State: 24:[53, 75, 3, 90], Operations: [] Exploring Operation: 75-53=22, Resulting Numbers: [3, 90, 22] Generated Node #2: [3, 90, 22] from Operation: 75-53=22 Current State: 24:[3, 90, 22], Operations: ['75-53=22'] Exploring Operation: 3*22=66, Resulting Numbers: [90, 66] Generated Node #3: [90, 66] from Operation: 3*22=66 Current State: 24:[90, 66], Operations: ['75-53=22', '3*22=66'] Exploring Operation: 90-66=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[53, 75, 3, 90], Operations: [] Exploring Operation: 90-75=15, Resulting Numbers: [53, 3, 15] Generated Node #0,0: 24:[53, 3, 15] Operation: 90-75=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[53, 3, 15], Operations: ['90-75=15'] Exploring Operation: 53-15=38, Resulting Numbers: [3, 38] Generated Node #0,0,0: 24:[3, 38] Operation: 53-15=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[3, 38], Operations: ['90-75=15', '53-15=38'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,24 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_1
mult_heuristic
[ 11, 26, 33, 18 ]
88
[ "11+26=37", "33+18=51", "37+51=88" ]
Current State: 88:[11, 26, 33, 18], Operations: [] Exploring Operation: 11+26=37, Resulting Numbers: [33, 18, 37] Generated Node #2: [33, 18, 37] from Operation: 11+26=37 Current State: 88:[33, 18, 37], Operations: ['11+26=37'] Exploring Operation: 33+18=51, Resulting Numbers: [37, 51] Generated Node #3: [37, 51] from Operation: 33+18=51 Current State: 88:[37, 51], Operations: ['11+26=37', '33+18=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[11, 26, 33, 18], Operations: [] Exploring Operation: 33-26=7, Resulting Numbers: [11, 18, 7] Generated Node #0,0: 88:[11, 18, 7] Operation: 33-26=7 Moving to Node #0,0 Current State: 88:[11, 18, 7], Operations: ['33-26=7'] Exploring Operation: 18-7=11, Resulting Numbers: [11, 11] Generated Node #0,0,0: 88:[11, 11] Operation: 18-7=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[11, 11], Operations: ['33-26=7', '18-7=11'] Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,88 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
[ 61, 47, 80, 30 ]
58
[ "61+47=108", "80-30=50", "108-50=58" ]
Current State: 58:[61, 47, 80, 30], Operations: [] Exploring Operation: 61+47=108, Resulting Numbers: [80, 30, 108] Generated Node #2: [80, 30, 108] from Operation: 61+47=108 Current State: 58:[80, 30, 108], Operations: ['61+47=108'] Exploring Operation: 80-30=50, Resulting Numbers: [108, 50] Generated Node #3: [108, 50] from Operation: 80-30=50 Current State: 58:[108, 50], Operations: ['61+47=108', '80-30=50'] Exploring Operation: 108-50=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[61, 47, 80, 30], Operations: [] Exploring Operation: 61-47=14, Resulting Numbers: [80, 30, 14] Generated Node #0,0: 58:[80, 30, 14] Operation: 61-47=14 Exploring Operation: 80-30=50, Resulting Numbers: [61, 47, 50] Generated Node #0,1: 58:[61, 47, 50] Operation: 80-30=50 Exploring Operation: 80-47=33, Resulting Numbers: [61, 30, 33] Generated Node #0,2: 58:[61, 30, 33] Operation: 80-47=33 Exploring Operation: 80-61=19, Resulting Numbers: [47, 30, 19] Generated Node #0,3: 58:[47, 30, 19] Operation: 80-61=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[61, 30, 33], Operations: ['80-47=33'] Exploring Operation: 33-30=3, Resulting Numbers: [61, 3] Generated Node #0,2,0: 58:[61, 3] Operation: 33-30=3 Exploring Operation: 61-30=31, Resulting Numbers: [33, 31] Generated Node #0,2,1: 58:[33, 31] Operation: 61-30=31 Exploring Operation: 30+33=63, Resulting Numbers: [61, 63] Generated Node #0,2,2: 58:[61, 63] Operation: 30+33=63 Exploring Operation: 61-33=28, Resulting Numbers: [30, 28] Generated Node #0,2,3: 58:[30, 28] Operation: 61-33=28 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 58:[30, 28], Operations: ['80-47=33', '61-33=28'] Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,58 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[61, 47, 80, 30], Operations: [] Exploring Operation: 80-47=33, Resulting Numbers: [61, 30, 33] Generated Node #0,2: 58:[61, 30, 33] Operation: 80-47=33 Moving to Node #0,2 Current State: 58:[61, 30, 33], Operations: ['80-47=33'] Exploring Operation: 61-33=28, Resulting Numbers: [30, 28] Generated Node #0,2,3: 58:[30, 28] Operation: 61-33=28 Moving to Node #0,2,3 Current State: 58:[30, 28], Operations: ['80-47=33', '61-33=28'] Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 80, 62, 8, 26 ]
26
[ "80/8=10", "62-26=36", "36-10=26" ]
Current State: 26:[80, 62, 8, 26], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [62, 26, 10] Generated Node #2: [62, 26, 10] from Operation: 80/8=10 Current State: 26:[62, 26, 10], Operations: ['80/8=10'] Exploring Operation: 62-26=36, Resulting Numbers: [10, 36] Generated Node #3: [10, 36] from Operation: 62-26=36 Current State: 26:[10, 36], Operations: ['80/8=10', '62-26=36'] Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[80, 62, 8, 26], Operations: [] Exploring Operation: 62-26=36, Resulting Numbers: [80, 8, 36] Generated Node #0,0: 26:[80, 8, 36] Operation: 62-26=36 Exploring Operation: 80-8=72, Resulting Numbers: [62, 26, 72] Generated Node #0,1: 26:[62, 26, 72] Operation: 80-8=72 Exploring Operation: 80-62=18, Resulting Numbers: [8, 26, 18] Generated Node #0,2: 26:[8, 26, 18] Operation: 80-62=18 Exploring Operation: 80/8=10, Resulting Numbers: [62, 26, 10] Generated Node #0,3: 26:[62, 26, 10] Operation: 80/8=10 Exploring Operation: 80-26=54, Resulting Numbers: [62, 8, 54] Generated Node #0,4: 26:[62, 8, 54] Operation: 80-26=54 Start Sub Search at level 1: Moving to Node #0,2 Current State: 26:[8, 26, 18], Operations: ['80-62=18'] Exploring Operation: 18-8=10, Resulting Numbers: [26, 10] Generated Node #0,2,0: 26:[26, 10] Operation: 18-8=10 Exploring Operation: 8+26=34, Resulting Numbers: [18, 34] Generated Node #0,2,1: 26:[18, 34] Operation: 8+26=34 Exploring Operation: 26-18=8, Resulting Numbers: [8, 8] Generated Node #0,2,2: 26:[8, 8] Operation: 26-18=8 Exploring Operation: 26-8=18, Resulting Numbers: [18, 18] Generated Node #0,2,3: 26:[18, 18] Operation: 26-8=18 Exploring Operation: 8+18=26, Resulting Numbers: [26, 26] Generated Node #0,2,4: 26:[26, 26] Operation: 8+18=26 Moving to Node #0,2,4 Current State: 26:[26, 26], Operations: ['80-62=18', '8+18=26'] Exploring Operation: 26*26=676, Resulting Numbers: [676] 676,26 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,26 unequal: No Solution Exploring Operation: 26/26=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[26, 10], Operations: ['80-62=18', '18-8=10'] Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,26 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,26 unequal: No Solution Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[8, 8], Operations: ['80-62=18', '26-18=8'] Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,26 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,26 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,26 unequal: No Solution Moving to Node #0,2,3 Current State: 26:[18, 18], Operations: ['80-62=18', '26-8=18'] Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,26 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,26 unequal: No Solution Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,26 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[18, 34], Operations: ['80-62=18', '8+26=34'] Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,26 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,26 unequal: No Solution Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,26 unequal: No Solution No 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: 26:[62, 26, 10], Operations: ['80/8=10'] Exploring Operation: 62+10=72, Resulting Numbers: [26, 72] Generated Node #0,3,0: 26:[26, 72] Operation: 62+10=72 Exploring Operation: 62-26=36, Resulting Numbers: [10, 36] Generated Node #0,3,1: 26:[10, 36] Operation: 62-26=36 Exploring Operation: 26-10=16, Resulting Numbers: [62, 16] Generated Node #0,3,2: 26:[62, 16] Operation: 26-10=16 Exploring Operation: 62-10=52, Resulting Numbers: [26, 52] Generated Node #0,3,3: 26:[26, 52] Operation: 62-10=52 Exploring Operation: 26+10=36, Resulting Numbers: [62, 36] Generated Node #0,3,4: 26:[62, 36] Operation: 26+10=36 Moving to Node #0,3,1 Current State: 26:[10, 36], Operations: ['80/8=10', '62-26=36'] Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[80, 62, 8, 26], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [62, 26, 10] Generated Node #0,3: 26:[62, 26, 10] Operation: 80/8=10 Moving to Node #0,3 Current State: 26:[62, 26, 10], Operations: ['80/8=10'] Exploring Operation: 62-26=36, Resulting Numbers: [10, 36] Generated Node #0,3,1: 26:[10, 36] Operation: 62-26=36 Moving to Node #0,3,1 Current State: 26:[10, 36], Operations: ['80/8=10', '62-26=36'] Exploring Operation: 36-10=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 62, 7, 81, 3 ]
64
[ "81-62=19", "3*19=57", "7+57=64" ]
Current State: 64:[62, 7, 81, 3], Operations: [] Exploring Operation: 81-62=19, Resulting Numbers: [7, 3, 19] Generated Node #2: [7, 3, 19] from Operation: 81-62=19 Current State: 64:[7, 3, 19], Operations: ['81-62=19'] Exploring Operation: 3*19=57, Resulting Numbers: [7, 57] Generated Node #3: [7, 57] from Operation: 3*19=57 Current State: 64:[7, 57], Operations: ['81-62=19', '3*19=57'] Exploring Operation: 7+57=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[62, 7, 81, 3], Operations: [] Exploring Operation: 81/3=27, Resulting Numbers: [62, 7, 27] Generated Node #0,0: 64:[62, 7, 27] Operation: 81/3=27 Exploring Operation: 81-7=74, Resulting Numbers: [62, 3, 74] Generated Node #0,1: 64:[62, 3, 74] Operation: 81-7=74 Exploring Operation: 81-62=19, Resulting Numbers: [7, 3, 19] Generated Node #0,2: 64:[7, 3, 19] Operation: 81-62=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[7, 3, 19], Operations: ['81-62=19'] Exploring Operation: 7+3=10, Resulting Numbers: [19, 10] Generated Node #0,2,0: 64:[19, 10] Operation: 7+3=10 Exploring Operation: 19-3=16, Resulting Numbers: [7, 16] Generated Node #0,2,1: 64:[7, 16] Operation: 19-3=16 Exploring Operation: 7-3=4, Resulting Numbers: [19, 4] Generated Node #0,2,2: 64:[19, 4] Operation: 7-3=4 Moving to Node #0,2,1 Current State: 64:[7, 16], Operations: ['81-62=19', '19-3=16'] Exploring Operation: 7*16=112, Resulting Numbers: [112] 112,64 unequal: No Solution Exploring Operation: 7+16=23, Resulting Numbers: [23] 23,64 unequal: No Solution Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,64 unequal: No Solution Moving to Node #0,2,2 Current State: 64:[19, 4], Operations: ['81-62=19', '7-3=4'] Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,64 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,64 unequal: No Solution Moving to Node #0,2,0 Current State: 64:[19, 10], Operations: ['81-62=19', '7+3=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,64 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,64 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 Current State: 64:[62, 7, 27], Operations: ['81/3=27'] Exploring Operation: 27-7=20, Resulting Numbers: [62, 20] Generated Node #0,0,0: 64:[62, 20] Operation: 27-7=20 Exploring Operation: 62-27=35, Resulting Numbers: [7, 35] Generated Node #0,0,1: 64:[7, 35] Operation: 62-27=35 Exploring Operation: 7+27=34, Resulting Numbers: [62, 34] Generated Node #0,0,2: 64:[62, 34] Operation: 7+27=34 Moving to Node #0,0,1 Current State: 64:[7, 35], Operations: ['81/3=27', '62-27=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,64 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[62, 34], Operations: ['81/3=27', '7+27=34'] Exploring Operation: 62*34=2108, Resulting Numbers: [2108] 2108,64 unequal: No Solution Exploring Operation: 62+34=96, Resulting Numbers: [96] 96,64 unequal: No Solution Exploring Operation: 62-34=28, Resulting Numbers: [28] 28,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[62, 20], Operations: ['81/3=27', '27-7=20'] Exploring Operation: 62+20=82, Resulting Numbers: [82] 82,64 unequal: No Solution Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,64 unequal: No Solution Exploring Operation: 62*20=1240, Resulting Numbers: [1240] 1240,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[62, 3, 74], Operations: ['81-7=74'] Exploring Operation: 74-62=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 64:[3, 12] Operation: 74-62=12 Exploring Operation: 74-3=71, Resulting Numbers: [62, 71] Generated Node #0,1,1: 64:[62, 71] Operation: 74-3=71 Exploring Operation: 62+3=65, Resulting Numbers: [74, 65] Generated Node #0,1,2: 64:[74, 65] Operation: 62+3=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[3, 12], Operations: ['81-7=74', '74-62=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,64 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[62, 71], Operations: ['81-7=74', '74-3=71'] Exploring Operation: 62*71=4402, Resulting Numbers: [4402] 4402,64 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 62+71=133, Resulting Numbers: [133] 133,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 64:[74, 65], Operations: ['81-7=74', '62+3=65'] Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,64 unequal: No Solution Exploring Operation: 74*65=4810, Resulting Numbers: [4810] 4810,64 unequal: No Solution Exploring Operation: 74+65=139, Resulting Numbers: [139] 139,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 3, 69, 33, 73 ]
95
[ "3*33=99", "73-69=4", "99-4=95" ]
Current State: 95:[3, 69, 33, 73], Operations: [] Exploring Operation: 3*33=99, Resulting Numbers: [69, 73, 99] Generated Node #2: [69, 73, 99] from Operation: 3*33=99 Current State: 95:[69, 73, 99], Operations: ['3*33=99'] Exploring Operation: 73-69=4, Resulting Numbers: [99, 4] Generated Node #3: [99, 4] from Operation: 73-69=4 Current State: 95:[99, 4], Operations: ['3*33=99', '73-69=4'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[3, 69, 33, 73], Operations: [] Exploring Operation: 69+33=102, Resulting Numbers: [3, 73, 102] Generated Node #0,0: 95:[3, 73, 102] Operation: 69+33=102 Exploring Operation: 73-69=4, Resulting Numbers: [3, 33, 4] Generated Node #0,1: 95:[3, 33, 4] Operation: 73-69=4 Moving to Node #0,1 Current State: 95:[3, 33, 4], Operations: ['73-69=4'] Exploring Operation: 3*33=99, Resulting Numbers: [4, 99] Generated Node #0,1,0: 95:[4, 99] Operation: 3*33=99 Exploring Operation: 33/3=11, Resulting Numbers: [4, 11] Generated Node #0,1,1: 95:[4, 11] Operation: 33/3=11 Moving to Node #0,0 Current State: 95:[3, 73, 102], Operations: ['69+33=102'] Exploring Operation: 102-73=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 95:[3, 29] Operation: 102-73=29 Exploring Operation: 3+73=76, Resulting Numbers: [102, 76] Generated Node #0,0,1: 95:[102, 76] Operation: 3+73=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[3, 29], Operations: ['69+33=102', '102-73=29'] Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 95:[102, 76], Operations: ['69+33=102', '3+73=76'] Exploring Operation: 102+76=178, Resulting Numbers: [178] 178,95 unequal: No Solution Exploring Operation: 102-76=26, Resulting Numbers: [26] 26,95 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: 95:[4, 99], Operations: ['73-69=4', '3*33=99'] Exploring Operation: 4+99=103, Resulting Numbers: [103] 103,95 unequal: No Solution Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[3, 69, 33, 73], Operations: [] Exploring Operation: 73-69=4, Resulting Numbers: [3, 33, 4] Generated Node #0,1: 95:[3, 33, 4] Operation: 73-69=4 Moving to Node #0,1 Current State: 95:[3, 33, 4], Operations: ['73-69=4'] Exploring Operation: 3*33=99, Resulting Numbers: [4, 99] Generated Node #0,1,0: 95:[4, 99] Operation: 3*33=99 Moving to Node #0,1,0 Current State: 95:[4, 99], Operations: ['73-69=4', '3*33=99'] Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 46, 2, 16, 13 ]
10
[ "46+2=48", "48/16=3", "13-3=10" ]
Current State: 10:[46, 2, 16, 13], Operations: [] Exploring Operation: 46+2=48, Resulting Numbers: [16, 13, 48] Generated Node #2: [16, 13, 48] from Operation: 46+2=48 Current State: 10:[16, 13, 48], Operations: ['46+2=48'] Exploring Operation: 48/16=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 48/16=3 Current State: 10:[13, 3], Operations: ['46+2=48', '48/16=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[46, 2, 16, 13], Operations: [] Exploring Operation: 46/2=23, Resulting Numbers: [16, 13, 23] Generated Node #0,0: 10:[16, 13, 23] Operation: 46/2=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[16, 13, 23], Operations: ['46/2=23'] Exploring Operation: 23-16=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 10:[13, 7] Operation: 23-16=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[13, 7], Operations: ['46/2=23', '23-16=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 5, 78, 76, 79 ]
15
[ "78+76=154", "154-79=75", "75/5=15" ]
Current State: 15:[5, 78, 76, 79], Operations: [] Exploring Operation: 78+76=154, Resulting Numbers: [5, 79, 154] Generated Node #2: [5, 79, 154] from Operation: 78+76=154 Current State: 15:[5, 79, 154], Operations: ['78+76=154'] Exploring Operation: 154-79=75, Resulting Numbers: [5, 75] Generated Node #3: [5, 75] from Operation: 154-79=75 Current State: 15:[5, 75], Operations: ['78+76=154', '154-79=75'] Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[5, 78, 76, 79], Operations: [] Exploring Operation: 79-76=3, Resulting Numbers: [5, 78, 3] Generated Node #0,0: 15:[5, 78, 3] Operation: 79-76=3 Exploring Operation: 78-76=2, Resulting Numbers: [5, 79, 2] Generated Node #0,1: 15:[5, 79, 2] Operation: 78-76=2 Exploring Operation: 78-5=73, Resulting Numbers: [76, 79, 73] Generated Node #0,2: 15:[76, 79, 73] Operation: 78-5=73 Exploring Operation: 79-78=1, Resulting Numbers: [5, 76, 1] Generated Node #0,3: 15:[5, 76, 1] Operation: 79-78=1 Moving to Node #0,0 Current State: 15:[5, 78, 3], Operations: ['79-76=3'] Exploring Operation: 5*3=15, Resulting Numbers: [78, 15] Generated Node #0,0,0: 15:[78, 15] Operation: 5*3=15 Exploring Operation: 78-3=75, Resulting Numbers: [5, 75] Generated Node #0,0,1: 15:[5, 75] Operation: 78-3=75 Exploring Operation: 78/3=26, Resulting Numbers: [5, 26] Generated Node #0,0,2: 15:[5, 26] Operation: 78/3=26 Exploring Operation: 78-5=73, Resulting Numbers: [3, 73] Generated Node #0,0,3: 15:[3, 73] Operation: 78-5=73 Moving to Node #0,3 Current State: 15:[5, 76, 1], Operations: ['79-78=1'] Exploring Operation: 5/1=5, Resulting Numbers: [76, 5] Generated Node #0,3,0: 15:[76, 5] Operation: 5/1=5 Exploring Operation: 76-5=71, Resulting Numbers: [1, 71] Generated Node #0,3,1: 15:[1, 71] Operation: 76-5=71 Exploring Operation: 76-1=75, Resulting Numbers: [5, 75] Generated Node #0,3,2: 15:[5, 75] Operation: 76-1=75 Exploring Operation: 5*1=5, Resulting Numbers: [76, 5] Generated Node #0,3,3: 15:[76, 5] Operation: 5*1=5 Moving to Node #0,1 Current State: 15:[5, 79, 2], Operations: ['78-76=2'] Exploring Operation: 79-5=74, Resulting Numbers: [2, 74] Generated Node #0,1,0: 15:[2, 74] Operation: 79-5=74 Exploring Operation: 79-2=77, Resulting Numbers: [5, 77] Generated Node #0,1,1: 15:[5, 77] Operation: 79-2=77 Exploring Operation: 5-2=3, Resulting Numbers: [79, 3] Generated Node #0,1,2: 15:[79, 3] Operation: 5-2=3 Exploring Operation: 5+2=7, Resulting Numbers: [79, 7] Generated Node #0,1,3: 15:[79, 7] Operation: 5+2=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[2, 74], Operations: ['78-76=2', '79-5=74'] Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,15 unequal: No Solution Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,15 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,15 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[5, 77], Operations: ['78-76=2', '79-2=77'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 5+77=82, Resulting Numbers: [82] 82,15 unequal: No Solution Exploring Operation: 5*77=385, Resulting Numbers: [385] 385,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[79, 3], Operations: ['78-76=2', '5-2=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,15 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,15 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 15:[79, 7], Operations: ['78-76=2', '5+2=7'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,15 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 15:[76, 79, 73], Operations: ['78-5=73'] Exploring Operation: 76+79=155, Resulting Numbers: [73, 155] Generated Node #0,2,0: 15:[73, 155] Operation: 76+79=155 Exploring Operation: 76-73=3, Resulting Numbers: [79, 3] Generated Node #0,2,1: 15:[79, 3] Operation: 76-73=3 Exploring Operation: 79-73=6, Resulting Numbers: [76, 6] Generated Node #0,2,2: 15:[76, 6] Operation: 79-73=6 Exploring Operation: 79-76=3, Resulting Numbers: [73, 3] Generated Node #0,2,3: 15:[73, 3] Operation: 79-76=3 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[73, 3], Operations: ['78-5=73', '79-76=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,15 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,15 unequal: No Solution Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[76, 6], Operations: ['78-5=73', '79-73=6'] Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,15 unequal: No Solution Exploring Operation: 76*6=456, Resulting Numbers: [456] 456,15 unequal: No Solution Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[79, 3], Operations: ['78-5=73', '76-73=3'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,15 unequal: No Solution Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,15 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[73, 155], Operations: ['78-5=73', '76+79=155'] Exploring Operation: 73*155=11315, Resulting Numbers: [11315] 11315,15 unequal: No Solution Exploring Operation: 155-73=82, Resulting Numbers: [82] 82,15 unequal: No Solution Exploring Operation: 73+155=228, Resulting Numbers: [228] 228,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 15:[5, 26], Operations: ['79-76=3', '78/3=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,15 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,15 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[3, 73], Operations: ['79-76=3', '78-5=73'] Exploring Operation: 3*73=219, Resulting Numbers: [219] 219,15 unequal: No Solution Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,15 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[1, 71], Operations: ['79-78=1', '76-5=71'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,15 unequal: No Solution Exploring Operation: 71/1=71, Resulting Numbers: [71] 71,15 unequal: No Solution Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 1*71=71, Resulting Numbers: [71] 71,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[5, 75], Operations: ['79-76=3', '78-3=75'] Exploring Operation: 5*75=375, Resulting Numbers: [375] 375,15 unequal: No Solution Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,15 unequal: No Solution Exploring Operation: 5+75=80, Resulting Numbers: [80] 80,15 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[5, 78, 76, 79], Operations: [] Exploring Operation: 79-76=3, Resulting Numbers: [5, 78, 3] Generated Node #0,0: 15:[5, 78, 3] Operation: 79-76=3 Moving to Node #0,0 Current State: 15:[5, 78, 3], Operations: ['79-76=3'] Exploring Operation: 78-3=75, Resulting Numbers: [5, 75] Generated Node #0,0,1: 15:[5, 75] Operation: 78-3=75 Moving to Node #0,0,1 Current State: 15:[5, 75], Operations: ['79-76=3', '78-3=75'] Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.945313
hs_4
sum_heuristic
[ 38, 4, 3, 9 ]
59
[ "38+9=47", "4*3=12", "47+12=59" ]
Current State: 59:[38, 4, 3, 9], Operations: [] Exploring Operation: 38+9=47, Resulting Numbers: [4, 3, 47] Generated Node #2: [4, 3, 47] from Operation: 38+9=47 Current State: 59:[4, 3, 47], Operations: ['38+9=47'] Exploring Operation: 4*3=12, Resulting Numbers: [47, 12] Generated Node #3: [47, 12] from Operation: 4*3=12 Current State: 59:[47, 12], Operations: ['38+9=47', '4*3=12'] Exploring Operation: 47+12=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[38, 4, 3, 9], Operations: [] Exploring Operation: 3*9=27, Resulting Numbers: [38, 4, 27] Generated Node #0,0: 59:[38, 4, 27] Operation: 3*9=27 Exploring Operation: 4*9=36, Resulting Numbers: [38, 3, 36] Generated Node #0,1: 59:[38, 3, 36] Operation: 4*9=36 Moving to Node #0,1 Current State: 59:[38, 3, 36], Operations: ['4*9=36'] Exploring Operation: 3+36=39, Resulting Numbers: [38, 39] Generated Node #0,1,0: 59:[38, 39] Operation: 3+36=39 Exploring Operation: 38+3=41, Resulting Numbers: [36, 41] Generated Node #0,1,1: 59:[36, 41] Operation: 38+3=41 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[38, 39], Operations: ['4*9=36', '3+36=39'] Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,59 unequal: No Solution Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[36, 41], Operations: ['4*9=36', '38+3=41'] Exploring Operation: 36+41=77, Resulting Numbers: [77] 77,59 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 59:[38, 4, 27], Operations: ['3*9=27'] Exploring Operation: 4+27=31, Resulting Numbers: [38, 31] Generated Node #0,0,0: 59:[38, 31] Operation: 4+27=31 Exploring Operation: 38+4=42, Resulting Numbers: [27, 42] Generated Node #0,0,1: 59:[27, 42] Operation: 38+4=42 Moving to Node #0,0,0 Current State: 59:[38, 31], Operations: ['3*9=27', '4+27=31'] Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 38+31=69, Resulting Numbers: [69] 69,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[27, 42], Operations: ['3*9=27', '38+4=42'] Exploring Operation: 42-27=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 27+42=69, Resulting Numbers: [69] 69,59 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 39, 7, 42, 18 ]
33
[ "42-39=3", "18-7=11", "3*11=33" ]
Current State: 33:[39, 7, 42, 18], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [7, 18, 3] Generated Node #2: [7, 18, 3] from Operation: 42-39=3 Current State: 33:[7, 18, 3], Operations: ['42-39=3'] Exploring Operation: 18-7=11, Resulting Numbers: [3, 11] Generated Node #3: [3, 11] from Operation: 18-7=11 Current State: 33:[3, 11], Operations: ['42-39=3', '18-7=11'] Exploring Operation: 3*11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[39, 7, 42, 18], Operations: [] Exploring Operation: 39-7=32, Resulting Numbers: [42, 18, 32] Generated Node #0,0: 33:[42, 18, 32] Operation: 39-7=32 Exploring Operation: 42-39=3, Resulting Numbers: [7, 18, 3] Generated Node #0,1: 33:[7, 18, 3] Operation: 42-39=3 Exploring Operation: 42-7=35, Resulting Numbers: [39, 18, 35] Generated Node #0,2: 33:[39, 18, 35] Operation: 42-7=35 Exploring Operation: 42/7=6, Resulting Numbers: [39, 18, 6] Generated Node #0,3: 33:[39, 18, 6] Operation: 42/7=6 Exploring Operation: 18-7=11, Resulting Numbers: [39, 42, 11] Generated Node #0,4: 33:[39, 42, 11] Operation: 18-7=11 Moving to Node #0,1 Current State: 33:[7, 18, 3], Operations: ['42-39=3'] Exploring Operation: 7-3=4, Resulting Numbers: [18, 4] Generated Node #0,1,0: 33:[18, 4] Operation: 7-3=4 Exploring Operation: 7+18=25, Resulting Numbers: [3, 25] Generated Node #0,1,1: 33:[3, 25] Operation: 7+18=25 Exploring Operation: 7+3=10, Resulting Numbers: [18, 10] Generated Node #0,1,2: 33:[18, 10] Operation: 7+3=10 Exploring Operation: 18/3=6, Resulting Numbers: [7, 6] Generated Node #0,1,3: 33:[7, 6] Operation: 18/3=6 Exploring Operation: 18-7=11, Resulting Numbers: [3, 11] Generated Node #0,1,4: 33:[3, 11] Operation: 18-7=11 Moving to Node #0,4 Current State: 33:[39, 42, 11], Operations: ['18-7=11'] Exploring Operation: 42+11=53, Resulting Numbers: [39, 53] Generated Node #0,4,0: 33:[39, 53] Operation: 42+11=53 Exploring Operation: 42-39=3, Resulting Numbers: [11, 3] Generated Node #0,4,1: 33:[11, 3] Operation: 42-39=3 Exploring Operation: 42-11=31, Resulting Numbers: [39, 31] Generated Node #0,4,2: 33:[39, 31] Operation: 42-11=31 Exploring Operation: 39+11=50, Resulting Numbers: [42, 50] Generated Node #0,4,3: 33:[42, 50] Operation: 39+11=50 Exploring Operation: 39-11=28, Resulting Numbers: [42, 28] Generated Node #0,4,4: 33:[42, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 33:[11, 3], Operations: ['18-7=11', '42-39=3'] Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,33 unequal: No Solution Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[39, 7, 42, 18], Operations: [] Exploring Operation: 18-7=11, Resulting Numbers: [39, 42, 11] Generated Node #0,4: 33:[39, 42, 11] Operation: 18-7=11 Moving to Node #0,4 Current State: 33:[39, 42, 11], Operations: ['18-7=11'] Exploring Operation: 42-39=3, Resulting Numbers: [11, 3] Generated Node #0,4,1: 33:[11, 3] Operation: 42-39=3 Moving to Node #0,4,1 Current State: 33:[11, 3], Operations: ['18-7=11', '42-39=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 29, 61, 5, 48 ]
16
[ "61-29=32", "48+32=80", "80/5=16" ]
Current State: 16:[29, 61, 5, 48], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [5, 48, 32] Generated Node #2: [5, 48, 32] from Operation: 61-29=32 Current State: 16:[5, 48, 32], Operations: ['61-29=32'] Exploring Operation: 48+32=80, Resulting Numbers: [5, 80] Generated Node #3: [5, 80] from Operation: 48+32=80 Current State: 16:[5, 80], Operations: ['61-29=32', '48+32=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[29, 61, 5, 48], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [5, 48, 32] Generated Node #0,0: 16:[5, 48, 32] Operation: 61-29=32 Exploring Operation: 61-48=13, Resulting Numbers: [29, 5, 13] Generated Node #0,1: 16:[29, 5, 13] Operation: 61-48=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[29, 5, 13], Operations: ['61-48=13'] Exploring Operation: 29-13=16, Resulting Numbers: [5, 16] Generated Node #0,1,0: 16:[5, 16] Operation: 29-13=16 Exploring Operation: 29-5=24, Resulting Numbers: [13, 24] Generated Node #0,1,1: 16:[13, 24] Operation: 29-5=24 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[5, 16], Operations: ['61-48=13', '29-13=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[13, 24], Operations: ['61-48=13', '29-5=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,16 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[5, 48, 32], Operations: ['61-29=32'] Exploring Operation: 48-5=43, Resulting Numbers: [32, 43] Generated Node #0,0,0: 16:[32, 43] Operation: 48-5=43 Exploring Operation: 48-32=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 16:[5, 16] Operation: 48-32=16 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[5, 16], Operations: ['61-29=32', '48-32=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[32, 43], Operations: ['61-29=32', '48-5=43'] Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 70, 57, 86, 1 ]
98
[ "70-57=13", "86-1=85", "13+85=98" ]
Current State: 98:[70, 57, 86, 1], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [86, 1, 13] Generated Node #2: [86, 1, 13] from Operation: 70-57=13 Current State: 98:[86, 1, 13], Operations: ['70-57=13'] Exploring Operation: 86-1=85, Resulting Numbers: [13, 85] Generated Node #3: [13, 85] from Operation: 86-1=85 Current State: 98:[13, 85], Operations: ['70-57=13', '86-1=85'] Exploring Operation: 13+85=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[70, 57, 86, 1], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [57, 1, 16] Generated Node #0,0: 98:[57, 1, 16] Operation: 86-70=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[57, 1, 16], Operations: ['86-70=16'] Exploring Operation: 57-1=56, Resulting Numbers: [16, 56] Generated Node #0,0,0: 98:[16, 56] Operation: 57-1=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[16, 56], Operations: ['86-70=16', '57-1=56'] Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 78, 54, 16, 76 ]
86
[ "78-76=2", "16*2=32", "54+32=86" ]
Current State: 86:[78, 54, 16, 76], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [54, 16, 2] Generated Node #2: [54, 16, 2] from Operation: 78-76=2 Current State: 86:[54, 16, 2], Operations: ['78-76=2'] Exploring Operation: 16*2=32, Resulting Numbers: [54, 32] Generated Node #3: [54, 32] from Operation: 16*2=32 Current State: 86:[54, 32], Operations: ['78-76=2', '16*2=32'] Exploring Operation: 54+32=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[78, 54, 16, 76], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [54, 16, 2] Generated Node #0,0: 86:[54, 16, 2] Operation: 78-76=2 Exploring Operation: 54-16=38, Resulting Numbers: [78, 76, 38] Generated Node #0,1: 86:[78, 76, 38] Operation: 54-16=38 Exploring Operation: 16+76=92, Resulting Numbers: [78, 54, 92] Generated Node #0,2: 86:[78, 54, 92] Operation: 16+76=92 Moving to Node #0,1 Current State: 86:[78, 76, 38], Operations: ['54-16=38'] Exploring Operation: 78-38=40, Resulting Numbers: [76, 40] Generated Node #0,1,0: 86:[76, 40] Operation: 78-38=40 Exploring Operation: 78-76=2, Resulting Numbers: [38, 2] Generated Node #0,1,1: 86:[38, 2] Operation: 78-76=2 Exploring Operation: 76/38=2, Resulting Numbers: [78, 2] Generated Node #0,1,2: 86:[78, 2] Operation: 76/38=2 Moving to Node #0,0 Current State: 86:[54, 16, 2], Operations: ['78-76=2'] Exploring Operation: 54+16=70, Resulting Numbers: [2, 70] Generated Node #0,0,0: 86:[2, 70] Operation: 54+16=70 Exploring Operation: 54-16=38, Resulting Numbers: [2, 38] Generated Node #0,0,1: 86:[2, 38] Operation: 54-16=38 Exploring Operation: 16/2=8, Resulting Numbers: [54, 8] Generated Node #0,0,2: 86:[54, 8] Operation: 16/2=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[2, 38], Operations: ['78-76=2', '54-16=38'] Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,86 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[2, 70], Operations: ['78-76=2', '54+16=70'] Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,86 unequal: No Solution Exploring Operation: 2+70=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[54, 8], Operations: ['78-76=2', '16/2=8'] Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,86 unequal: No Solution Exploring Operation: 54*8=432, Resulting Numbers: [432] 432,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[78, 54, 92], Operations: ['16+76=92'] Exploring Operation: 78-54=24, Resulting Numbers: [92, 24] Generated Node #0,2,0: 86:[92, 24] Operation: 78-54=24 Exploring Operation: 92-78=14, Resulting Numbers: [54, 14] Generated Node #0,2,1: 86:[54, 14] Operation: 92-78=14 Exploring Operation: 92-54=38, Resulting Numbers: [78, 38] Generated Node #0,2,2: 86:[78, 38] Operation: 92-54=38 Moving to Node #0,1,1 Current State: 86:[38, 2], Operations: ['54-16=38', '78-76=2'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,86 unequal: No Solution Moving to Node #0,1,2 Current State: 86:[78, 2], Operations: ['54-16=38', '76/38=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,86 unequal: No Solution Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,86 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[76, 40], Operations: ['54-16=38', '78-38=40'] Exploring Operation: 76-40=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 76+40=116, Resulting Numbers: [116] 116,86 unequal: No Solution Exploring Operation: 76*40=3040, Resulting Numbers: [3040] 3040,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[78, 38], Operations: ['16+76=92', '92-54=38'] Exploring Operation: 78*38=2964, Resulting Numbers: [2964] 2964,86 unequal: No Solution Exploring Operation: 78-38=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 78+38=116, Resulting Numbers: [116] 116,86 unequal: No Solution Moving to Node #0,2,1 Current State: 86:[54, 14], Operations: ['16+76=92', '92-78=14'] Exploring Operation: 54*14=756, Resulting Numbers: [756] 756,86 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,86 unequal: No Solution Exploring Operation: 54+14=68, Resulting Numbers: [68] 68,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[92, 24], Operations: ['16+76=92', '78-54=24'] Exploring Operation: 92+24=116, Resulting Numbers: [116] 116,86 unequal: No Solution Exploring Operation: 92*24=2208, Resulting Numbers: [2208] 2208,86 unequal: No Solution Exploring Operation: 92-24=68, Resulting Numbers: [68] 68,86 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 41, 95, 54, 11 ]
93
[ "41+95=136", "54-11=43", "136-43=93" ]
Current State: 93:[41, 95, 54, 11], Operations: [] Exploring Operation: 41+95=136, Resulting Numbers: [54, 11, 136] Generated Node #2: [54, 11, 136] from Operation: 41+95=136 Current State: 93:[54, 11, 136], Operations: ['41+95=136'] Exploring Operation: 54-11=43, Resulting Numbers: [136, 43] Generated Node #3: [136, 43] from Operation: 54-11=43 Current State: 93:[136, 43], Operations: ['41+95=136', '54-11=43'] Exploring Operation: 136-43=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[41, 95, 54, 11], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [95, 11, 13] Generated Node #0,0: 93:[95, 11, 13] Operation: 54-41=13 Exploring Operation: 41+54=95, Resulting Numbers: [95, 11, 95] Generated Node #0,1: 93:[95, 11, 95] Operation: 41+54=95 Moving to Node #0,1 Current State: 93:[95, 11, 95], Operations: ['41+54=95'] Exploring Operation: 95/95=1, Resulting Numbers: [11, 1] Generated Node #0,1,0: 93:[11, 1] Operation: 95/95=1 Exploring Operation: 95-11=84, Resulting Numbers: [95, 84] Generated Node #0,1,1: 93:[95, 84] Operation: 95-11=84 Moving to Node #0,0 Current State: 93:[95, 11, 13], Operations: ['54-41=13'] Exploring Operation: 11+13=24, Resulting Numbers: [95, 24] Generated Node #0,0,0: 93:[95, 24] Operation: 11+13=24 Exploring Operation: 13-11=2, Resulting Numbers: [95, 2] Generated Node #0,0,1: 93:[95, 2] Operation: 13-11=2 Moving to Node #0,0,1 Current State: 93:[95, 2], Operations: ['54-41=13', '13-11=2'] Exploring Operation: 95+2=97, Resulting Numbers: [97] 97,93 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[41, 95, 54, 11], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [95, 11, 13] Generated Node #0,0: 93:[95, 11, 13] Operation: 54-41=13 Moving to Node #0,0 Current State: 93:[95, 11, 13], Operations: ['54-41=13'] Exploring Operation: 13-11=2, Resulting Numbers: [95, 2] Generated Node #0,0,1: 93:[95, 2] Operation: 13-11=2 Moving to Node #0,0,1 Current State: 93:[95, 2], Operations: ['54-41=13', '13-11=2'] Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 21, 7, 7, 33 ]
91
[ "33-21=12", "7*12=84", "7+84=91" ]
Current State: 91:[21, 7, 7, 33], Operations: [] Exploring Operation: 33-21=12, Resulting Numbers: [7, 7, 12] Generated Node #2: [7, 7, 12] from Operation: 33-21=12 Current State: 91:[7, 7, 12], Operations: ['33-21=12'] Exploring Operation: 7*12=84, Resulting Numbers: [84] 84,91 equal: Goal Reached Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[21, 7, 7, 33], Operations: [] Exploring Operation: 33-21=12, Resulting Numbers: [7, 7, 12] Generated Node #0,0: 91:[7, 7, 12] Operation: 33-21=12 Exploring Operation: 21-7=14, Resulting Numbers: [7, 33, 14] Generated Node #0,1: 91:[7, 33, 14] Operation: 21-7=14 Exploring Operation: 21-7=14, Resulting Numbers: [7, 33, 14] Generated Node #0,2: 91:[7, 33, 14] Operation: 21-7=14 Moving to Node #0,0 Current State: 91:[7, 7, 12], Operations: ['33-21=12'] Exploring Operation: 7+7=14, Resulting Numbers: [12, 14] Generated Node #0,0,0: 91:[12, 14] Operation: 7+7=14 Exploring Operation: 12-7=5, Resulting Numbers: [7, 5] Generated Node #0,0,1: 91:[7, 5] Operation: 12-7=5 Exploring Operation: 12-7=5, Resulting Numbers: [7, 5] Generated Node #0,0,2: 91:[7, 5] Operation: 12-7=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[12, 14], Operations: ['33-21=12', '7+7=14'] Exploring Operation: 12*14=168, Resulting Numbers: [168] 168,91 unequal: No Solution Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[7, 5], Operations: ['33-21=12', '12-7=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 91:[7, 5], Operations: ['33-21=12', '12-7=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,91 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: 91:[7, 33, 14], Operations: ['21-7=14'] Exploring Operation: 33-14=19, Resulting Numbers: [7, 19] Generated Node #0,1,0: 91:[7, 19] Operation: 33-14=19 Exploring Operation: 14-7=7, Resulting Numbers: [33, 7] Generated Node #0,1,1: 91:[33, 7] Operation: 14-7=7 Exploring Operation: 33-7=26, Resulting Numbers: [14, 26] Generated Node #0,1,2: 91:[14, 26] Operation: 33-7=26 Moving to Node #0,2 Current State: 91:[7, 33, 14], Operations: ['21-7=14'] Exploring Operation: 33-7=26, Resulting Numbers: [14, 26] Generated Node #0,2,0: 91:[14, 26] Operation: 33-7=26 Exploring Operation: 14-7=7, Resulting Numbers: [33, 7] Generated Node #0,2,1: 91:[33, 7] Operation: 14-7=7 Exploring Operation: 33-14=19, Resulting Numbers: [7, 19] Generated Node #0,2,2: 91:[7, 19] Operation: 33-14=19 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[7, 19], Operations: ['21-7=14', '33-14=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 91:[14, 26], Operations: ['21-7=14', '33-7=26'] Exploring Operation: 14*26=364, Resulting Numbers: [364] 364,91 unequal: No Solution Exploring Operation: 14+26=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 91:[33, 7], Operations: ['21-7=14', '14-7=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,91 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,91 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: 91:[7, 19], Operations: ['21-7=14', '33-14=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 7*19=133, Resulting Numbers: [133] 133,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[14, 26], Operations: ['21-7=14', '33-7=26'] Exploring Operation: 14+26=40, Resulting Numbers: [40] 40,91 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,91 unequal: No Solution Exploring Operation: 14*26=364, Resulting Numbers: [364] 364,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[33, 7], Operations: ['21-7=14', '14-7=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,91 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,91 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,91 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 18, 74, 71, 44 ]
65
[ "18+74=92", "71-44=27", "92-27=65" ]
Current State: 65:[18, 74, 71, 44], Operations: [] Exploring Operation: 18+74=92, Resulting Numbers: [71, 44, 92] Generated Node #2: [71, 44, 92] from Operation: 18+74=92 Current State: 65:[71, 44, 92], Operations: ['18+74=92'] Exploring Operation: 71-44=27, Resulting Numbers: [92, 27] Generated Node #3: [92, 27] from Operation: 71-44=27 Current State: 65:[92, 27], Operations: ['18+74=92', '71-44=27'] Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[18, 74, 71, 44], Operations: [] Exploring Operation: 74-44=30, Resulting Numbers: [18, 71, 30] Generated Node #0,0: 65:[18, 71, 30] Operation: 74-44=30 Exploring Operation: 71-44=27, Resulting Numbers: [18, 74, 27] Generated Node #0,1: 65:[18, 74, 27] Operation: 71-44=27 Exploring Operation: 18+44=62, Resulting Numbers: [74, 71, 62] Generated Node #0,2: 65:[74, 71, 62] Operation: 18+44=62 Exploring Operation: 74-71=3, Resulting Numbers: [18, 44, 3] Generated Node #0,3: 65:[18, 44, 3] Operation: 74-71=3 Exploring Operation: 44-18=26, Resulting Numbers: [74, 71, 26] Generated Node #0,4: 65:[74, 71, 26] Operation: 44-18=26 Moving to Node #0,2 Current State: 65:[74, 71, 62], Operations: ['18+44=62'] Exploring Operation: 74-71=3, Resulting Numbers: [62, 3] Generated Node #0,2,0: 65:[62, 3] Operation: 74-71=3 Exploring Operation: 71+62=133, Resulting Numbers: [74, 133] Generated Node #0,2,1: 65:[74, 133] Operation: 71+62=133 Exploring Operation: 74-62=12, Resulting Numbers: [71, 12] Generated Node #0,2,2: 65:[71, 12] Operation: 74-62=12 Exploring Operation: 74+62=136, Resulting Numbers: [71, 136] Generated Node #0,2,3: 65:[71, 136] Operation: 74+62=136 Exploring Operation: 71-62=9, Resulting Numbers: [74, 9] Generated Node #0,2,4: 65:[74, 9] Operation: 71-62=9 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[62, 3], Operations: ['18+44=62', '74-71=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[18, 74, 71, 44], Operations: [] Exploring Operation: 18+44=62, Resulting Numbers: [74, 71, 62] Generated Node #0,2: 65:[74, 71, 62] Operation: 18+44=62 Moving to Node #0,2 Current State: 65:[74, 71, 62], Operations: ['18+44=62'] Exploring Operation: 74-71=3, Resulting Numbers: [62, 3] Generated Node #0,2,0: 65:[62, 3] Operation: 74-71=3 Moving to Node #0,2,0 Current State: 65:[62, 3], Operations: ['18+44=62', '74-71=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 99, 92, 79, 59 ]
90
[ "99+59=158", "158/79=2", "92-2=90" ]
Current State: 90:[99, 92, 79, 59], Operations: [] Exploring Operation: 99+59=158, Resulting Numbers: [92, 79, 158] Generated Node #2: [92, 79, 158] from Operation: 99+59=158 Current State: 90:[92, 79, 158], Operations: ['99+59=158'] Exploring Operation: 158/79=2, Resulting Numbers: [92, 2] Generated Node #3: [92, 2] from Operation: 158/79=2 Current State: 90:[92, 2], Operations: ['99+59=158', '158/79=2'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[99, 92, 79, 59], Operations: [] Exploring Operation: 99-79=20, Resulting Numbers: [92, 59, 20] Generated Node #0,0: 90:[92, 59, 20] Operation: 99-79=20 Exploring Operation: 79-59=20, Resulting Numbers: [99, 92, 20] Generated Node #0,1: 90:[99, 92, 20] Operation: 79-59=20 Exploring Operation: 99-59=40, Resulting Numbers: [92, 79, 40] Generated Node #0,2: 90:[92, 79, 40] Operation: 99-59=40 Exploring Operation: 92-59=33, Resulting Numbers: [99, 79, 33] Generated Node #0,3: 90:[99, 79, 33] Operation: 92-59=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[99, 92, 20], Operations: ['79-59=20'] Exploring Operation: 92-20=72, Resulting Numbers: [99, 72] Generated Node #0,1,0: 90:[99, 72] Operation: 92-20=72 Exploring Operation: 99-92=7, Resulting Numbers: [20, 7] Generated Node #0,1,1: 90:[20, 7] Operation: 99-92=7 Exploring Operation: 99+20=119, Resulting Numbers: [92, 119] Generated Node #0,1,2: 90:[92, 119] Operation: 99+20=119 Exploring Operation: 99-20=79, Resulting Numbers: [92, 79] Generated Node #0,1,3: 90:[92, 79] Operation: 99-20=79 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[20, 7], Operations: ['79-59=20', '99-92=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,90 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,90 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 #0,1,3 Current State: 90:[92, 79], Operations: ['79-59=20', '99-20=79'] Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,90 unequal: No Solution Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 92*79=7268, Resulting Numbers: [7268] 7268,90 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 #0,1,0 Current State: 90:[99, 72], Operations: ['79-59=20', '92-20=72'] Exploring Operation: 99+72=171, Resulting Numbers: [171] 171,90 unequal: No Solution Exploring Operation: 99-72=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 99*72=7128, Resulting Numbers: [7128] 7128,90 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 #0,1,2 Current State: 90:[92, 119], Operations: ['79-59=20', '99+20=119'] Exploring Operation: 119-92=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 92*119=10948, Resulting Numbers: [10948] 10948,90 unequal: No Solution Exploring Operation: 92+119=211, Resulting Numbers: [211] 211,90 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[92, 59, 20], Operations: ['99-79=20'] Exploring Operation: 92-59=33, Resulting Numbers: [20, 33] Generated Node #0,0,0: 90:[20, 33] Operation: 92-59=33 Exploring Operation: 59-20=39, Resulting Numbers: [92, 39] Generated Node #0,0,1: 90:[92, 39] Operation: 59-20=39 Exploring Operation: 92-20=72, Resulting Numbers: [59, 72] Generated Node #0,0,2: 90:[59, 72] Operation: 92-20=72 Exploring Operation: 59+20=79, Resulting Numbers: [92, 79] Generated Node #0,0,3: 90:[92, 79] Operation: 59+20=79 Moving to Node #0,0,0 Current State: 90:[20, 33], Operations: ['99-79=20', '92-59=33'] Exploring Operation: 20*33=660, Resulting Numbers: [660] 660,90 unequal: No Solution Exploring Operation: 20+33=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[92, 39], Operations: ['99-79=20', '59-20=39'] Exploring Operation: 92-39=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 92+39=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 92*39=3588, Resulting Numbers: [3588] 3588,90 unequal: No Solution Moving to Node #0,0,3 Current State: 90:[92, 79], Operations: ['99-79=20', '59+20=79'] Exploring Operation: 92-79=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 92+79=171, Resulting Numbers: [171] 171,90 unequal: No Solution Exploring Operation: 92*79=7268, Resulting Numbers: [7268] 7268,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[59, 72], Operations: ['99-79=20', '92-20=72'] Exploring Operation: 72-59=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 59+72=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 59*72=4248, Resulting Numbers: [4248] 4248,90 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 #0,2 Current State: 90:[92, 79, 40], Operations: ['99-59=40'] Exploring Operation: 79-40=39, Resulting Numbers: [92, 39] Generated Node #0,2,0: 90:[92, 39] Operation: 79-40=39 Exploring Operation: 92-79=13, Resulting Numbers: [40, 13] Generated Node #0,2,1: 90:[40, 13] Operation: 92-79=13 Exploring Operation: 92-40=52, Resulting Numbers: [79, 52] Generated Node #0,2,2: 90:[79, 52] Operation: 92-40=52 Exploring Operation: 79+40=119, Resulting Numbers: [92, 119] Generated Node #0,2,3: 90:[92, 119] Operation: 79+40=119 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[40, 13], Operations: ['99-59=40', '92-79=13'] Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 40*13=520, Resulting Numbers: [520] 520,90 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 #0,2,0 Current State: 90:[92, 39], Operations: ['99-59=40', '79-40=39'] Exploring Operation: 92-39=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 92+39=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 92*39=3588, Resulting Numbers: [3588] 3588,90 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 #0,2,2 Current State: 90:[79, 52], Operations: ['99-59=40', '92-40=52'] Exploring Operation: 79+52=131, Resulting Numbers: [131] 131,90 unequal: No Solution Exploring Operation: 79*52=4108, Resulting Numbers: [4108] 4108,90 unequal: No Solution Exploring Operation: 79-52=27, Resulting Numbers: [27] 27,90 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 #0,2,3 Current State: 90:[92, 119], Operations: ['99-59=40', '79+40=119'] Exploring Operation: 92*119=10948, Resulting Numbers: [10948] 10948,90 unequal: No Solution Exploring Operation: 119-92=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 92+119=211, Resulting Numbers: [211] 211,90 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 Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[99, 79, 33], Operations: ['92-59=33'] Exploring Operation: 79+33=112, Resulting Numbers: [99, 112] Generated Node #0,3,0: 90:[99, 112] Operation: 79+33=112 Exploring Operation: 99/33=3, Resulting Numbers: [79, 3] Generated Node #0,3,1: 90:[79, 3] Operation: 99/33=3 Exploring Operation: 79-33=46, Resulting Numbers: [99, 46] Generated Node #0,3,2: 90:[99, 46] Operation: 79-33=46 Exploring Operation: 99-79=20, Resulting Numbers: [33, 20] Generated Node #0,3,3: 90:[33, 20] Operation: 99-79=20 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[33, 20], Operations: ['92-59=33', '99-79=20'] Exploring Operation: 33+20=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,90 unequal: No Solution Exploring Operation: 33*20=660, Resulting Numbers: [660] 660,90 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 #0,3,2 Current State: 90:[99, 46], Operations: ['92-59=33', '79-33=46'] Exploring Operation: 99-46=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 99+46=145, Resulting Numbers: [145] 145,90 unequal: No Solution Exploring Operation: 99*46=4554, Resulting Numbers: [4554] 4554,90 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 #0,3,1 Current State: 90:[79, 3], Operations: ['92-59=33', '99/33=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,90 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,90 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,90 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 #0,3,0 Current State: 90:[99, 112], Operations: ['92-59=33', '79+33=112'] Exploring Operation: 99+112=211, Resulting Numbers: [211] 211,90 unequal: No Solution Exploring Operation: 99*112=11088, Resulting Numbers: [11088] 11088,90 unequal: No Solution Exploring Operation: 112-99=13, Resulting Numbers: [13] 13,90 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_4
mult_heuristic
[ 9, 68, 4, 15 ]
65
[ "9-4=5", "15/5=3", "68-3=65" ]
Current State: 65:[9, 68, 4, 15], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [68, 15, 5] Generated Node #2: [68, 15, 5] from Operation: 9-4=5 Current State: 65:[68, 15, 5], Operations: ['9-4=5'] Exploring Operation: 15/5=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 15/5=3 Current State: 65:[68, 3], Operations: ['9-4=5', '15/5=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[9, 68, 4, 15], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [68, 15, 5] Generated Node #0,0: 65:[68, 15, 5] Operation: 9-4=5 Exploring Operation: 15-9=6, Resulting Numbers: [68, 4, 6] Generated Node #0,1: 65:[68, 4, 6] Operation: 15-9=6 Exploring Operation: 9+4=13, Resulting Numbers: [68, 15, 13] Generated Node #0,2: 65:[68, 15, 13] Operation: 9+4=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[68, 15, 5], Operations: ['9-4=5'] Exploring Operation: 15/5=3, Resulting Numbers: [68, 3] Generated Node #0,0,0: 65:[68, 3] Operation: 15/5=3 Exploring Operation: 68-5=63, Resulting Numbers: [15, 63] Generated Node #0,0,1: 65:[15, 63] Operation: 68-5=63 Exploring Operation: 15-5=10, Resulting Numbers: [68, 10] Generated Node #0,0,2: 65:[68, 10] Operation: 15-5=10 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 65:[15, 63], Operations: ['9-4=5', '68-5=63'] Exploring Operation: 15+63=78, Resulting Numbers: [78] 78,65 unequal: No Solution Exploring Operation: 15*63=945, Resulting Numbers: [945] 945,65 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,65 unequal: No Solution No 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: 65:[68, 3], Operations: ['9-4=5', '15/5=3'] Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,65 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[9, 68, 4, 15], Operations: [] Exploring Operation: 9-4=5, Resulting Numbers: [68, 15, 5] Generated Node #0,0: 65:[68, 15, 5] Operation: 9-4=5 Moving to Node #0,0 Current State: 65:[68, 15, 5], Operations: ['9-4=5'] Exploring Operation: 15/5=3, Resulting Numbers: [68, 3] Generated Node #0,0,0: 65:[68, 3] Operation: 15/5=3 Moving to Node #0,0,0 Current State: 65:[68, 3], Operations: ['9-4=5', '15/5=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 3, 41, 31, 6 ]
19
[ "3+41=44", "31-6=25", "44-25=19" ]
Current State: 19:[3, 41, 31, 6], Operations: [] Exploring Operation: 3+41=44, Resulting Numbers: [31, 6, 44] Generated Node #2: [31, 6, 44] from Operation: 3+41=44 Current State: 19:[31, 6, 44], Operations: ['3+41=44'] Exploring Operation: 31-6=25, Resulting Numbers: [44, 25] Generated Node #3: [44, 25] from Operation: 31-6=25 Current State: 19:[44, 25], Operations: ['3+41=44', '31-6=25'] Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[3, 41, 31, 6], Operations: [] Exploring Operation: 41-3=38, Resulting Numbers: [31, 6, 38] Generated Node #0,0: 19:[31, 6, 38] Operation: 41-3=38 Exploring Operation: 41-31=10, Resulting Numbers: [3, 6, 10] Generated Node #0,1: 19:[3, 6, 10] Operation: 41-31=10 Exploring Operation: 3*6=18, Resulting Numbers: [41, 31, 18] Generated Node #0,2: 19:[41, 31, 18] Operation: 3*6=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 19:[41, 31, 18], Operations: ['3*6=18'] Exploring Operation: 41-18=23, Resulting Numbers: [31, 23] Generated Node #0,2,0: 19:[31, 23] Operation: 41-18=23 Exploring Operation: 31-18=13, Resulting Numbers: [41, 13] Generated Node #0,2,1: 19:[41, 13] Operation: 31-18=13 Exploring Operation: 41-31=10, Resulting Numbers: [18, 10] Generated Node #0,2,2: 19:[18, 10] Operation: 41-31=10 Moving to Node #0,2,2 Current State: 19:[18, 10], Operations: ['3*6=18', '41-31=10'] Exploring Operation: 18*10=180, Resulting Numbers: [180] 180,19 unequal: No Solution Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,2,0 Current State: 19:[31, 23], Operations: ['3*6=18', '41-18=23'] Exploring Operation: 31*23=713, Resulting Numbers: [713] 713,19 unequal: No Solution Exploring Operation: 31+23=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,19 unequal: No Solution Moving to Node #0,2,1 Current State: 19:[41, 13], Operations: ['3*6=18', '31-18=13'] Exploring Operation: 41-13=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 41+13=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 41*13=533, Resulting Numbers: [533] 533,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[3, 6, 10], Operations: ['41-31=10'] Exploring Operation: 3*6=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 19:[10, 18] Operation: 3*6=18 Exploring Operation: 3+10=13, Resulting Numbers: [6, 13] Generated Node #0,1,1: 19:[6, 13] Operation: 3+10=13 Exploring Operation: 3+6=9, Resulting Numbers: [10, 9] Generated Node #0,1,2: 19:[10, 9] Operation: 3+6=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[10, 18], Operations: ['41-31=10', '3*6=18'] Exploring Operation: 10*18=180, Resulting Numbers: [180] 180,19 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,19 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,19 unequal: No Solution No 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: 19:[6, 13], Operations: ['41-31=10', '3+10=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,19 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[3, 41, 31, 6], Operations: [] Exploring Operation: 41-31=10, Resulting Numbers: [3, 6, 10] Generated Node #0,1: 19:[3, 6, 10] Operation: 41-31=10 Moving to Node #0,1 Current State: 19:[3, 6, 10], Operations: ['41-31=10'] Exploring Operation: 3+10=13, Resulting Numbers: [6, 13] Generated Node #0,1,1: 19:[6, 13] Operation: 3+10=13 Moving to Node #0,1,1 Current State: 19:[6, 13], Operations: ['41-31=10', '3+10=13'] Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
mult_heuristic
[ 19, 38, 2, 68 ]
79
[ "19+38=57", "2*68=136", "136-57=79" ]
Current State: 79:[19, 38, 2, 68], Operations: [] Exploring Operation: 19+38=57, Resulting Numbers: [2, 68, 57] Generated Node #2: [2, 68, 57] from Operation: 19+38=57 Current State: 79:[2, 68, 57], Operations: ['19+38=57'] Exploring Operation: 2*68=136, Resulting Numbers: [57, 136] Generated Node #3: [57, 136] from Operation: 2*68=136 Current State: 79:[57, 136], Operations: ['19+38=57', '2*68=136'] Exploring Operation: 136-57=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[19, 38, 2, 68], Operations: [] Exploring Operation: 19*2=38, Resulting Numbers: [38, 68, 38] Generated Node #0,0: 79:[38, 68, 38] Operation: 19*2=38 Exploring Operation: 19+38=57, Resulting Numbers: [2, 68, 57] Generated Node #0,1: 79:[2, 68, 57] Operation: 19+38=57 Exploring Operation: 38*2=76, Resulting Numbers: [19, 68, 76] Generated Node #0,2: 79:[19, 68, 76] Operation: 38*2=76 Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[19, 68, 76], Operations: ['38*2=76'] Exploring Operation: 19+68=87, Resulting Numbers: [76, 87] Generated Node #0,2,0: 79:[76, 87] Operation: 19+68=87 Exploring Operation: 68-19=49, Resulting Numbers: [76, 49] Generated Node #0,2,1: 79:[76, 49] Operation: 68-19=49 Exploring Operation: 19+76=95, Resulting Numbers: [68, 95] Generated Node #0,2,2: 79:[68, 95] Operation: 19+76=95 Moving to Node #0,2,0 Current State: 79:[76, 87], Operations: ['38*2=76', '19+68=87'] Exploring Operation: 76+87=163, Resulting Numbers: [163] 163,79 unequal: No Solution Exploring Operation: 76*87=6612, Resulting Numbers: [6612] 6612,79 unequal: No Solution Exploring Operation: 87-76=11, Resulting Numbers: [11] 11,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[68, 95], Operations: ['38*2=76', '19+76=95'] Exploring Operation: 95-68=27, Resulting Numbers: [27] 27,79 unequal: No Solution Exploring Operation: 68*95=6460, Resulting Numbers: [6460] 6460,79 unequal: No Solution Exploring Operation: 68+95=163, Resulting Numbers: [163] 163,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[76, 49], Operations: ['38*2=76', '68-19=49'] Exploring Operation: 76+49=125, Resulting Numbers: [125] 125,79 unequal: No Solution Exploring Operation: 76*49=3724, Resulting Numbers: [3724] 3724,79 unequal: No Solution Exploring Operation: 76-49=27, Resulting Numbers: [27] 27,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[38, 68, 38], Operations: ['19*2=38'] Exploring Operation: 68+38=106, Resulting Numbers: [38, 106] Generated Node #0,0,0: 79:[38, 106] Operation: 68+38=106 Exploring Operation: 38+68=106, Resulting Numbers: [38, 106] Generated Node #0,0,1: 79:[38, 106] Operation: 38+68=106 Exploring Operation: 38+38=76, Resulting Numbers: [68, 76] Generated Node #0,0,2: 79:[68, 76] Operation: 38+38=76 Moving to Node #0,0,2 Current State: 79:[68, 76], Operations: ['19*2=38', '38+38=76'] Exploring Operation: 68+76=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 76-68=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 68*76=5168, Resulting Numbers: [5168] 5168,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[38, 106], Operations: ['19*2=38', '68+38=106'] Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,79 unequal: No Solution Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[38, 106], Operations: ['19*2=38', '38+68=106'] Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,79 unequal: No Solution Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,79 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[2, 68, 57], Operations: ['19+38=57'] Exploring Operation: 2+57=59, Resulting Numbers: [68, 59] Generated Node #0,1,0: 79:[68, 59] Operation: 2+57=59 Exploring Operation: 68-2=66, Resulting Numbers: [57, 66] Generated Node #0,1,1: 79:[57, 66] Operation: 68-2=66 Exploring Operation: 2+68=70, Resulting Numbers: [57, 70] Generated Node #0,1,2: 79:[57, 70] Operation: 2+68=70 Moving to Node #0,1,0 Current State: 79:[68, 59], Operations: ['19+38=57', '2+57=59'] Exploring Operation: 68*59=4012, Resulting Numbers: [4012] 4012,79 unequal: No Solution Exploring Operation: 68+59=127, Resulting Numbers: [127] 127,79 unequal: No Solution Exploring Operation: 68-59=9, Resulting Numbers: [9] 9,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[57, 70], Operations: ['19+38=57', '2+68=70'] Exploring Operation: 57*70=3990, Resulting Numbers: [3990] 3990,79 unequal: No Solution Exploring Operation: 70-57=13, Resulting Numbers: [13] 13,79 unequal: No Solution Exploring Operation: 57+70=127, Resulting Numbers: [127] 127,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[57, 66], Operations: ['19+38=57', '68-2=66'] Exploring Operation: 57*66=3762, Resulting Numbers: [3762] 3762,79 unequal: No Solution Exploring Operation: 57+66=123, Resulting Numbers: [123] 123,79 unequal: No Solution Exploring Operation: 66-57=9, Resulting Numbers: [9] 9,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 37, 72, 7, 89 ]
61
[ "72-37=35", "7+89=96", "96-35=61" ]
Current State: 61:[37, 72, 7, 89], Operations: [] Exploring Operation: 72-37=35, Resulting Numbers: [7, 89, 35] Generated Node #2: [7, 89, 35] from Operation: 72-37=35 Current State: 61:[7, 89, 35], Operations: ['72-37=35'] Exploring Operation: 7+89=96, Resulting Numbers: [35, 96] Generated Node #3: [35, 96] from Operation: 7+89=96 Current State: 61:[35, 96], Operations: ['72-37=35', '7+89=96'] Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[37, 72, 7, 89], Operations: [] Exploring Operation: 72-7=65, Resulting Numbers: [37, 89, 65] Generated Node #0,0: 61:[37, 89, 65] Operation: 72-7=65 Exploring Operation: 37-7=30, Resulting Numbers: [72, 89, 30] Generated Node #0,1: 61:[72, 89, 30] Operation: 37-7=30 Exploring Operation: 89-7=82, Resulting Numbers: [37, 72, 82] Generated Node #0,2: 61:[37, 72, 82] Operation: 89-7=82 Exploring Operation: 37+7=44, Resulting Numbers: [72, 89, 44] Generated Node #0,3: 61:[72, 89, 44] Operation: 37+7=44 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[37, 89, 65], Operations: ['72-7=65'] Exploring Operation: 37+89=126, Resulting Numbers: [65, 126] Generated Node #0,0,0: 61:[65, 126] Operation: 37+89=126 Exploring Operation: 89-37=52, Resulting Numbers: [65, 52] Generated Node #0,0,1: 61:[65, 52] Operation: 89-37=52 Exploring Operation: 65-37=28, Resulting Numbers: [89, 28] Generated Node #0,0,2: 61:[89, 28] Operation: 65-37=28 Exploring Operation: 89-65=24, Resulting Numbers: [37, 24] Generated Node #0,0,3: 61:[37, 24] Operation: 89-65=24 Moving to Node #0,0,1 Current State: 61:[65, 52], Operations: ['72-7=65', '89-37=52'] Exploring Operation: 65+52=117, Resulting Numbers: [117] 117,61 unequal: No Solution Exploring Operation: 65-52=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 65*52=3380, Resulting Numbers: [3380] 3380,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[37, 24], Operations: ['72-7=65', '89-65=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[37, 72, 7, 89], Operations: [] Exploring Operation: 72-7=65, Resulting Numbers: [37, 89, 65] Generated Node #0,0: 61:[37, 89, 65] Operation: 72-7=65 Moving to Node #0,0 Current State: 61:[37, 89, 65], Operations: ['72-7=65'] Exploring Operation: 89-65=24, Resulting Numbers: [37, 24] Generated Node #0,0,3: 61:[37, 24] Operation: 89-65=24 Moving to Node #0,0,3 Current State: 61:[37, 24], Operations: ['72-7=65', '89-65=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 12, 45, 22, 95 ]
40
[ "45-12=33", "95-22=73", "73-33=40" ]
Current State: 40:[12, 45, 22, 95], Operations: [] Exploring Operation: 45-12=33, Resulting Numbers: [22, 95, 33] Generated Node #2: [22, 95, 33] from Operation: 45-12=33 Current State: 40:[22, 95, 33], Operations: ['45-12=33'] Exploring Operation: 95-22=73, Resulting Numbers: [33, 73] Generated Node #3: [33, 73] from Operation: 95-22=73 Current State: 40:[33, 73], Operations: ['45-12=33', '95-22=73'] Exploring Operation: 73-33=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[12, 45, 22, 95], Operations: [] Exploring Operation: 95-22=73, Resulting Numbers: [12, 45, 73] Generated Node #0,0: 40:[12, 45, 73] Operation: 95-22=73 Exploring Operation: 95-45=50, Resulting Numbers: [12, 22, 50] Generated Node #0,1: 40:[12, 22, 50] Operation: 95-45=50 Moving to Node #0,1 Current State: 40:[12, 22, 50], Operations: ['95-45=50'] Exploring Operation: 50-12=38, Resulting Numbers: [22, 38] Generated Node #0,1,0: 40:[22, 38] Operation: 50-12=38 Exploring Operation: 22-12=10, Resulting Numbers: [50, 10] Generated Node #0,1,1: 40:[50, 10] Operation: 22-12=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 40:[22, 38], Operations: ['95-45=50', '50-12=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,40 unequal: No Solution Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[50, 10], Operations: ['95-45=50', '22-12=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[12, 45, 22, 95], Operations: [] Exploring Operation: 95-45=50, Resulting Numbers: [12, 22, 50] Generated Node #0,1: 40:[12, 22, 50] Operation: 95-45=50 Moving to Node #0,1 Current State: 40:[12, 22, 50], Operations: ['95-45=50'] Exploring Operation: 22-12=10, Resulting Numbers: [50, 10] Generated Node #0,1,1: 40:[50, 10] Operation: 22-12=10 Moving to Node #0,1,1 Current State: 40:[50, 10], Operations: ['95-45=50', '22-12=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 10, 58, 20, 40 ]
60
[ "40-20=20", "20/10=2", "58+2=60" ]
Current State: 60:[10, 58, 20, 40], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [10, 58, 20] Generated Node #2: [10, 58, 20] from Operation: 40-20=20 Current State: 60:[10, 58, 20], Operations: ['40-20=20'] Exploring Operation: 20/10=2, Resulting Numbers: [58, 2] Generated Node #3: [58, 2] from Operation: 20/10=2 Current State: 60:[58, 2], Operations: ['40-20=20', '20/10=2'] Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[10, 58, 20, 40], Operations: [] Exploring Operation: 40/10=4, Resulting Numbers: [58, 20, 4] Generated Node #0,0: 60:[58, 20, 4] Operation: 40/10=4 Exploring Operation: 40-10=30, Resulting Numbers: [58, 20, 30] Generated Node #0,1: 60:[58, 20, 30] Operation: 40-10=30 Moving to Node #0,0 Current State: 60:[58, 20, 4], Operations: ['40/10=4'] Exploring Operation: 20/4=5, Resulting Numbers: [58, 5] Generated Node #0,0,0: 60:[58, 5] Operation: 20/4=5 Exploring Operation: 58+4=62, Resulting Numbers: [20, 62] Generated Node #0,0,1: 60:[20, 62] Operation: 58+4=62 Moving to Node #0,1 Current State: 60:[58, 20, 30], Operations: ['40-10=30'] Exploring Operation: 58-30=28, Resulting Numbers: [20, 28] Generated Node #0,1,0: 60:[20, 28] Operation: 58-30=28 Exploring Operation: 30-20=10, Resulting Numbers: [58, 10] Generated Node #0,1,1: 60:[58, 10] Operation: 30-20=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[20, 28], Operations: ['40-10=30', '58-30=28'] Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,60 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[58, 10], Operations: ['40-10=30', '30-20=10'] Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,60 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,60 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: 60:[58, 5], Operations: ['40/10=4', '20/4=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,60 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[20, 62], Operations: ['40/10=4', '58+4=62'] Exploring Operation: 62-20=42, Resulting Numbers: [42] 42,60 unequal: No Solution Exploring Operation: 20+62=82, Resulting Numbers: [82] 82,60 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 41, 4, 73, 98 ]
12
[ "41-4=37", "98-73=25", "37-25=12" ]
Current State: 12:[41, 4, 73, 98], Operations: [] Exploring Operation: 41-4=37, Resulting Numbers: [73, 98, 37] Generated Node #2: [73, 98, 37] from Operation: 41-4=37 Current State: 12:[73, 98, 37], Operations: ['41-4=37'] Exploring Operation: 98-73=25, Resulting Numbers: [37, 25] Generated Node #3: [37, 25] from Operation: 98-73=25 Current State: 12:[37, 25], Operations: ['41-4=37', '98-73=25'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[41, 4, 73, 98], Operations: [] Exploring Operation: 98-73=25, Resulting Numbers: [41, 4, 25] Generated Node #0,0: 12:[41, 4, 25] Operation: 98-73=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[41, 4, 25], Operations: ['98-73=25'] Exploring Operation: 41-25=16, Resulting Numbers: [4, 16] Generated Node #0,0,0: 12:[4, 16] Operation: 41-25=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[4, 16], Operations: ['98-73=25', '41-25=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[41, 4, 73, 98], Operations: [] Exploring Operation: 98-73=25, Resulting Numbers: [41, 4, 25] Generated Node #0,0: 12:[41, 4, 25] Operation: 98-73=25 Moving to Node #0,0 Current State: 12:[41, 4, 25], Operations: ['98-73=25'] Exploring Operation: 41-25=16, Resulting Numbers: [4, 16] Generated Node #0,0,0: 12:[4, 16] Operation: 41-25=16 Moving to Node #0,0,0 Current State: 12:[4, 16], Operations: ['98-73=25', '41-25=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 32, 78, 56, 79 ]
69
[ "78-32=46", "79-56=23", "46+23=69" ]
Current State: 69:[32, 78, 56, 79], Operations: [] Exploring Operation: 78-32=46, Resulting Numbers: [56, 79, 46] Generated Node #2: [56, 79, 46] from Operation: 78-32=46 Current State: 69:[56, 79, 46], Operations: ['78-32=46'] Exploring Operation: 79-56=23, Resulting Numbers: [46, 23] Generated Node #3: [46, 23] from Operation: 79-56=23 Current State: 69:[46, 23], Operations: ['78-32=46', '79-56=23'] Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[32, 78, 56, 79], Operations: [] Exploring Operation: 56-32=24, Resulting Numbers: [78, 79, 24] Generated Node #0,0: 69:[78, 79, 24] Operation: 56-32=24 Exploring Operation: 79-56=23, Resulting Numbers: [32, 78, 23] Generated Node #0,1: 69:[32, 78, 23] Operation: 79-56=23 Moving to Node #0,1 Current State: 69:[32, 78, 23], Operations: ['79-56=23'] Exploring Operation: 32-23=9, Resulting Numbers: [78, 9] Generated Node #0,1,0: 69:[78, 9] Operation: 32-23=9 Exploring Operation: 78-32=46, Resulting Numbers: [23, 46] Generated Node #0,1,1: 69:[23, 46] Operation: 78-32=46 Moving to Node #0,0 Current State: 69:[78, 79, 24], Operations: ['56-32=24'] Exploring Operation: 79-24=55, Resulting Numbers: [78, 55] Generated Node #0,0,0: 69:[78, 55] Operation: 79-24=55 Exploring Operation: 79-78=1, Resulting Numbers: [24, 1] Generated Node #0,0,1: 69:[24, 1] Operation: 79-78=1 Moving to Node #0,0,1 Current State: 69:[24, 1], Operations: ['56-32=24', '79-78=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[78, 9], Operations: ['79-56=23', '32-23=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[32, 78, 56, 79], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [32, 78, 23] Generated Node #0,1: 69:[32, 78, 23] Operation: 79-56=23 Moving to Node #0,1 Current State: 69:[32, 78, 23], Operations: ['79-56=23'] Exploring Operation: 32-23=9, Resulting Numbers: [78, 9] Generated Node #0,1,0: 69:[78, 9] Operation: 32-23=9 Moving to Node #0,1,0 Current State: 69:[78, 9], Operations: ['79-56=23', '32-23=9'] Exploring Operation: 78-9=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.988715
hs_2
mult_heuristic
[ 86, 96, 43, 94 ]
92
[ "86/43=2", "94*2=188", "188-96=92" ]
Current State: 92:[86, 96, 43, 94], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [96, 94, 2] Generated Node #2: [96, 94, 2] from Operation: 86/43=2 Current State: 92:[96, 94, 2], Operations: ['86/43=2'] Exploring Operation: 94*2=188, Resulting Numbers: [96, 188] Generated Node #3: [96, 188] from Operation: 94*2=188 Current State: 92:[96, 188], Operations: ['86/43=2', '94*2=188'] Exploring Operation: 188-96=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[86, 96, 43, 94], Operations: [] Exploring Operation: 96-94=2, Resulting Numbers: [86, 43, 2] Generated Node #0,0: 92:[86, 43, 2] Operation: 96-94=2 Exploring Operation: 86/43=2, Resulting Numbers: [96, 94, 2] Generated Node #0,1: 92:[96, 94, 2] Operation: 86/43=2 Exploring Operation: 86-43=43, Resulting Numbers: [96, 94, 43] Generated Node #0,2: 92:[96, 94, 43] Operation: 86-43=43 Moving to Node #0,1 Current State: 92:[96, 94, 2], Operations: ['86/43=2'] Exploring Operation: 96-94=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 92:[2, 2] Operation: 96-94=2 Exploring Operation: 96/2=48, Resulting Numbers: [94, 48] Generated Node #0,1,1: 92:[94, 48] Operation: 96/2=48 Exploring Operation: 96-2=94, Resulting Numbers: [94, 94] Generated Node #0,1,2: 92:[94, 94] Operation: 96-2=94 Moving to Node #0,0 Current State: 92:[86, 43, 2], Operations: ['96-94=2'] Exploring Operation: 86-43=43, Resulting Numbers: [2, 43] Generated Node #0,0,0: 92:[2, 43] Operation: 86-43=43 Exploring Operation: 86/2=43, Resulting Numbers: [43, 43] Generated Node #0,0,1: 92:[43, 43] Operation: 86/2=43 Exploring Operation: 86/43=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 92:[2, 2] Operation: 86/43=2 Moving to Node #0,2 Current State: 92:[96, 94, 43], Operations: ['86-43=43'] Exploring Operation: 96-94=2, Resulting Numbers: [43, 2] Generated Node #0,2,0: 92:[43, 2] Operation: 96-94=2 Exploring Operation: 96-43=53, Resulting Numbers: [94, 53] Generated Node #0,2,1: 92:[94, 53] Operation: 96-43=53 Exploring Operation: 94-43=51, Resulting Numbers: [96, 51] Generated Node #0,2,2: 92:[96, 51] Operation: 94-43=51 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 92:[43, 2], Operations: ['86-43=43', '96-94=2'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 43+2=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 43*2=86, Resulting Numbers: [86] 86,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 92:[94, 53], Operations: ['86-43=43', '96-43=53'] Exploring Operation: 94*53=4982, Resulting Numbers: [4982] 4982,92 unequal: No Solution Exploring Operation: 94+53=147, Resulting Numbers: [147] 147,92 unequal: No Solution Exploring Operation: 94-53=41, Resulting Numbers: [41] 41,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 92:[96, 51], Operations: ['86-43=43', '94-43=51'] Exploring Operation: 96-51=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 96*51=4896, Resulting Numbers: [4896] 4896,92 unequal: No Solution Exploring Operation: 96+51=147, Resulting Numbers: [147] 147,92 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: 92:[2, 2], Operations: ['86/43=2', '96-94=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[2, 2], Operations: ['96-94=2', '86/43=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[2, 43], Operations: ['96-94=2', '86-43=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,92 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[94, 94], Operations: ['86/43=2', '96-2=94'] Exploring Operation: 94/94=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 94-94=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 94+94=188, Resulting Numbers: [188] 188,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[94, 48], Operations: ['86/43=2', '96/2=48'] Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,92 unequal: No Solution Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[43, 43], Operations: ['96-94=2', '86/2=43'] Exploring Operation: 43-43=0, Resulting Numbers: [0] 0,92 unequal: No Solution Exploring Operation: 43+43=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 43/43=1, Resulting Numbers: [1] 1,92 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 28, 95, 91, 13 ]
91
[ "28*13=364", "95-91=4", "364/4=91" ]
Current State: 91:[28, 95, 91, 13], Operations: [] Exploring Operation: 28*13=364, Resulting Numbers: [95, 91, 364] Generated Node #2: [95, 91, 364] from Operation: 28*13=364 Current State: 91:[95, 91, 364], Operations: ['28*13=364'] Exploring Operation: 95-91=4, Resulting Numbers: [364, 4] Generated Node #3: [364, 4] from Operation: 95-91=4 Current State: 91:[364, 4], Operations: ['28*13=364', '95-91=4'] Exploring Operation: 364/4=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[28, 95, 91, 13], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [28, 13, 4] Generated Node #0,0: 91:[28, 13, 4] Operation: 95-91=4 Exploring Operation: 28-13=15, Resulting Numbers: [95, 91, 15] Generated Node #0,1: 91:[95, 91, 15] Operation: 28-13=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[95, 91, 15], Operations: ['28-13=15'] Exploring Operation: 95-91=4, Resulting Numbers: [15, 4] Generated Node #0,1,0: 91:[15, 4] Operation: 95-91=4 Exploring Operation: 95-15=80, Resulting Numbers: [91, 80] Generated Node #0,1,1: 91:[91, 80] Operation: 95-15=80 Moving to Node #0,1,0 Current State: 91:[15, 4], Operations: ['28-13=15', '95-91=4'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[91, 80], Operations: ['28-13=15', '95-15=80'] Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 91+80=171, Resulting Numbers: [171] 171,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[28, 13, 4], Operations: ['95-91=4'] Exploring Operation: 28/4=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 91:[13, 7] Operation: 28/4=7 Exploring Operation: 28-13=15, Resulting Numbers: [4, 15] Generated Node #0,0,1: 91:[4, 15] Operation: 28-13=15 Moving to Node #0,0,0 Current State: 91:[13, 7], Operations: ['95-91=4', '28/4=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[28, 95, 91, 13], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [28, 13, 4] Generated Node #0,0: 91:[28, 13, 4] Operation: 95-91=4 Moving to Node #0,0 Current State: 91:[28, 13, 4], Operations: ['95-91=4'] Exploring Operation: 28/4=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 91:[13, 7] Operation: 28/4=7 Moving to Node #0,0,0 Current State: 91:[13, 7], Operations: ['95-91=4', '28/4=7'] Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 36, 40, 50, 75 ]
29
[ "40-36=4", "75-50=25", "4+25=29" ]
Current State: 29:[36, 40, 50, 75], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [50, 75, 4] Generated Node #2: [50, 75, 4] from Operation: 40-36=4 Current State: 29:[50, 75, 4], Operations: ['40-36=4'] Exploring Operation: 75-50=25, Resulting Numbers: [4, 25] Generated Node #3: [4, 25] from Operation: 75-50=25 Current State: 29:[4, 25], Operations: ['40-36=4', '75-50=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[36, 40, 50, 75], Operations: [] Exploring Operation: 75-36=39, Resulting Numbers: [40, 50, 39] Generated Node #0,0: 29:[40, 50, 39] Operation: 75-36=39 Exploring Operation: 50-36=14, Resulting Numbers: [40, 75, 14] Generated Node #0,1: 29:[40, 75, 14] Operation: 50-36=14 Exploring Operation: 50-40=10, Resulting Numbers: [36, 75, 10] Generated Node #0,2: 29:[36, 75, 10] Operation: 50-40=10 Exploring Operation: 75-40=35, Resulting Numbers: [36, 50, 35] Generated Node #0,3: 29:[36, 50, 35] Operation: 75-40=35 Exploring Operation: 75-50=25, Resulting Numbers: [36, 40, 25] Generated Node #0,4: 29:[36, 40, 25] Operation: 75-50=25 Moving to Node #0,4 Current State: 29:[36, 40, 25], Operations: ['75-50=25'] Exploring Operation: 36-25=11, Resulting Numbers: [40, 11] Generated Node #0,4,0: 29:[40, 11] Operation: 36-25=11 Exploring Operation: 36+25=61, Resulting Numbers: [40, 61] Generated Node #0,4,1: 29:[40, 61] Operation: 36+25=61 Exploring Operation: 40-25=15, Resulting Numbers: [36, 15] Generated Node #0,4,2: 29:[36, 15] Operation: 40-25=15 Exploring Operation: 40+25=65, Resulting Numbers: [36, 65] Generated Node #0,4,3: 29:[36, 65] Operation: 40+25=65 Exploring Operation: 40-36=4, Resulting Numbers: [25, 4] Generated Node #0,4,4: 29:[25, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 29:[36, 15], Operations: ['75-50=25', '40-25=15'] Exploring Operation: 36-15=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 36+15=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 36*15=540, Resulting Numbers: [540] 540,29 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 #0,4,0 Current State: 29:[40, 11], Operations: ['75-50=25', '36-25=11'] Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,29 unequal: No Solution Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,29 unequal: No Solution Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[36, 40, 50, 75], Operations: [] Exploring Operation: 75-50=25, Resulting Numbers: [36, 40, 25] Generated Node #0,4: 29:[36, 40, 25] Operation: 75-50=25 Moving to Node #0,4 Current State: 29:[36, 40, 25], Operations: ['75-50=25'] Exploring Operation: 36-25=11, Resulting Numbers: [40, 11] Generated Node #0,4,0: 29:[40, 11] Operation: 36-25=11 Moving to Node #0,4,0 Current State: 29:[40, 11], Operations: ['75-50=25', '36-25=11'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 24, 7, 50, 60 ]
72
[ "7+50=57", "60-57=3", "24*3=72" ]
Current State: 72:[24, 7, 50, 60], Operations: [] Exploring Operation: 7+50=57, Resulting Numbers: [24, 60, 57] Generated Node #2: [24, 60, 57] from Operation: 7+50=57 Current State: 72:[24, 60, 57], Operations: ['7+50=57'] Exploring Operation: 60-57=3, Resulting Numbers: [24, 3] Generated Node #3: [24, 3] from Operation: 60-57=3 Current State: 72:[24, 3], Operations: ['7+50=57', '60-57=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[24, 7, 50, 60], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [24, 7, 10] Generated Node #0,0: 72:[24, 7, 10] Operation: 60-50=10 Exploring Operation: 24+50=74, Resulting Numbers: [7, 60, 74] Generated Node #0,1: 72:[7, 60, 74] Operation: 24+50=74 Exploring Operation: 50-24=26, Resulting Numbers: [7, 60, 26] Generated Node #0,2: 72:[7, 60, 26] Operation: 50-24=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[24, 7, 10], Operations: ['60-50=10'] Exploring Operation: 7+10=17, Resulting Numbers: [24, 17] Generated Node #0,0,0: 72:[24, 17] Operation: 7+10=17 Exploring Operation: 24-7=17, Resulting Numbers: [10, 17] Generated Node #0,0,1: 72:[10, 17] Operation: 24-7=17 Exploring Operation: 10-7=3, Resulting Numbers: [24, 3] Generated Node #0,0,2: 72:[24, 3] Operation: 10-7=3 Moving to Node #0,0,2 Current State: 72:[24, 3], Operations: ['60-50=10', '10-7=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,72 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[24, 7, 50, 60], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [24, 7, 10] Generated Node #0,0: 72:[24, 7, 10] Operation: 60-50=10 Moving to Node #0,0 Current State: 72:[24, 7, 10], Operations: ['60-50=10'] Exploring Operation: 10-7=3, Resulting Numbers: [24, 3] Generated Node #0,0,2: 72:[24, 3] Operation: 10-7=3 Moving to Node #0,0,2 Current State: 72:[24, 3], Operations: ['60-50=10', '10-7=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 36, 41, 38, 82 ]
39
[ "41-36=5", "82-38=44", "44-5=39" ]
Current State: 39:[36, 41, 38, 82], Operations: [] Exploring Operation: 41-36=5, Resulting Numbers: [38, 82, 5] Generated Node #2: [38, 82, 5] from Operation: 41-36=5 Current State: 39:[38, 82, 5], Operations: ['41-36=5'] Exploring Operation: 82-38=44, Resulting Numbers: [5, 44] Generated Node #3: [5, 44] from Operation: 82-38=44 Current State: 39:[5, 44], Operations: ['41-36=5', '82-38=44'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[36, 41, 38, 82], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [36, 38, 2] Generated Node #0,0: 39:[36, 38, 2] Operation: 82/41=2 Moving to Node #0,0 Current State: 39:[36, 38, 2], Operations: ['82/41=2'] Exploring Operation: 38-36=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 39:[2, 2] Operation: 38-36=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[2, 2], Operations: ['82/41=2', '38-36=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,39 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
[ 4, 64, 23, 27 ]
15
[ "64-4=60", "27-23=4", "60/4=15" ]
Current State: 15:[4, 64, 23, 27], Operations: [] Exploring Operation: 64-4=60, Resulting Numbers: [23, 27, 60] Generated Node #2: [23, 27, 60] from Operation: 64-4=60 Current State: 15:[23, 27, 60], Operations: ['64-4=60'] Exploring Operation: 27-23=4, Resulting Numbers: [60, 4] Generated Node #3: [60, 4] from Operation: 27-23=4 Current State: 15:[60, 4], Operations: ['64-4=60', '27-23=4'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[4, 64, 23, 27], Operations: [] Exploring Operation: 64-23=41, Resulting Numbers: [4, 27, 41] Generated Node #0,0: 15:[4, 27, 41] Operation: 64-23=41 Exploring Operation: 27-23=4, Resulting Numbers: [4, 64, 4] Generated Node #0,1: 15:[4, 64, 4] Operation: 27-23=4 Exploring Operation: 64-27=37, Resulting Numbers: [4, 23, 37] Generated Node #0,2: 15:[4, 23, 37] Operation: 64-27=37 Exploring Operation: 64-4=60, Resulting Numbers: [23, 27, 60] Generated Node #0,3: 15:[23, 27, 60] Operation: 64-4=60 Exploring Operation: 64/4=16, Resulting Numbers: [23, 27, 16] Generated Node #0,4: 15:[23, 27, 16] Operation: 64/4=16 Start Sub Search at level 1: Moving to Node #0,4 Current State: 15:[23, 27, 16], Operations: ['64/4=16'] Exploring Operation: 23+27=50, Resulting Numbers: [16, 50] Generated Node #0,4,0: 15:[16, 50] Operation: 23+27=50 Exploring Operation: 23+16=39, Resulting Numbers: [27, 39] Generated Node #0,4,1: 15:[27, 39] Operation: 23+16=39 Exploring Operation: 27-16=11, Resulting Numbers: [23, 11] Generated Node #0,4,2: 15:[23, 11] Operation: 27-16=11 Exploring Operation: 23-16=7, Resulting Numbers: [27, 7] Generated Node #0,4,3: 15:[27, 7] Operation: 23-16=7 Exploring Operation: 27-23=4, Resulting Numbers: [16, 4] Generated Node #0,4,4: 15:[16, 4] Operation: 27-23=4 Moving to Node #0,4,4 Current State: 15:[16, 4], Operations: ['64/4=16', '27-23=4'] Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,15 unequal: No Solution Moving to Node #0,4,2 Current State: 15:[23, 11], Operations: ['64/4=16', '27-16=11'] Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,15 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,15 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,15 unequal: No Solution Moving to Node #0,4,3 Current State: 15:[27, 7], Operations: ['64/4=16', '23-16=7'] Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,15 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,15 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,4,0 Current State: 15:[16, 50], Operations: ['64/4=16', '23+27=50'] Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,15 unequal: No Solution Exploring Operation: 16*50=800, Resulting Numbers: [800] 800,15 unequal: No Solution Exploring Operation: 16+50=66, Resulting Numbers: [66] 66,15 unequal: No Solution Moving to Node #0,4,1 Current State: 15:[27, 39], Operations: ['64/4=16', '23+16=39'] Exploring Operation: 27*39=1053, Resulting Numbers: [1053] 1053,15 unequal: No Solution Exploring Operation: 27+39=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 39-27=12, Resulting Numbers: [12] 12,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[4, 23, 37], Operations: ['64-27=37'] Exploring Operation: 4+23=27, Resulting Numbers: [37, 27] Generated Node #0,2,0: 15:[37, 27] Operation: 4+23=27 Exploring Operation: 37-4=33, Resulting Numbers: [23, 33] Generated Node #0,2,1: 15:[23, 33] Operation: 37-4=33 Exploring Operation: 37-23=14, Resulting Numbers: [4, 14] Generated Node #0,2,2: 15:[4, 14] Operation: 37-23=14 Exploring Operation: 4+37=41, Resulting Numbers: [23, 41] Generated Node #0,2,3: 15:[23, 41] Operation: 4+37=41 Exploring Operation: 23-4=19, Resulting Numbers: [37, 19] Generated Node #0,2,4: 15:[37, 19] Operation: 23-4=19 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 15:[4, 14], Operations: ['64-27=37', '37-23=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,15 unequal: No Solution No 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: 15:[23, 33], Operations: ['64-27=37', '37-4=33'] Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 23*33=759, Resulting Numbers: [759] 759,15 unequal: No Solution Exploring Operation: 23+33=56, Resulting Numbers: [56] 56,15 unequal: No Solution No 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: 15:[37, 19], Operations: ['64-27=37', '23-4=19'] Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,15 unequal: No Solution Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,15 unequal: No Solution No 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: 15:[37, 27], Operations: ['64-27=37', '4+23=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,15 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,15 unequal: No Solution No 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: 15:[23, 41], Operations: ['64-27=37', '4+37=41'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 23*41=943, Resulting Numbers: [943] 943,15 unequal: No Solution Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,15 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: 15:[4, 27, 41], Operations: ['64-23=41'] Exploring Operation: 41-27=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 15:[4, 14] Operation: 41-27=14 Exploring Operation: 4+41=45, Resulting Numbers: [27, 45] Generated Node #0,0,1: 15:[27, 45] Operation: 4+41=45 Exploring Operation: 4+27=31, Resulting Numbers: [41, 31] Generated Node #0,0,2: 15:[41, 31] Operation: 4+27=31 Exploring Operation: 27-4=23, Resulting Numbers: [41, 23] Generated Node #0,0,3: 15:[41, 23] Operation: 27-4=23 Exploring Operation: 41-4=37, Resulting Numbers: [27, 37] Generated Node #0,0,4: 15:[27, 37] Operation: 41-4=37 Moving to Node #0,0,0 Current State: 15:[4, 14], Operations: ['64-23=41', '41-27=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[27, 37], Operations: ['64-23=41', '41-4=37'] Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 27*37=999, Resulting Numbers: [999] 999,15 unequal: No Solution Exploring Operation: 27+37=64, Resulting Numbers: [64] 64,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[41, 23], Operations: ['64-23=41', '27-4=23'] Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,15 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[27, 45], Operations: ['64-23=41', '4+41=45'] Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 27*45=1215, Resulting Numbers: [1215] 1215,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[41, 31], Operations: ['64-23=41', '4+27=31'] Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,15 unequal: No Solution Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,15 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[4, 64, 4], Operations: ['27-23=4'] Exploring Operation: 4*4=16, Resulting Numbers: [64, 16] Generated Node #0,1,0: 15:[64, 16] Operation: 4*4=16 Exploring Operation: 64/4=16, Resulting Numbers: [4, 16] Generated Node #0,1,1: 15:[4, 16] Operation: 64/4=16 Exploring Operation: 64-4=60, Resulting Numbers: [4, 60] Generated Node #0,1,2: 15:[4, 60] Operation: 64-4=60 Exploring Operation: 64-4=60, Resulting Numbers: [4, 60] Generated Node #0,1,3: 15:[4, 60] Operation: 64-4=60 Exploring Operation: 64/4=16, Resulting Numbers: [4, 16] Generated Node #0,1,4: 15:[4, 16] Operation: 64/4=16 Moving to Node #0,1,1 Current State: 15:[4, 16], Operations: ['27-23=4', '64/4=16'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[4, 16], Operations: ['27-23=4', '64/4=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,15 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[4, 60], Operations: ['27-23=4', '64-4=60'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[4, 64, 23, 27], Operations: [] Exploring Operation: 27-23=4, Resulting Numbers: [4, 64, 4] Generated Node #0,1: 15:[4, 64, 4] Operation: 27-23=4 Moving to Node #0,1 Current State: 15:[4, 64, 4], Operations: ['27-23=4'] Exploring Operation: 64-4=60, Resulting Numbers: [4, 60] Generated Node #0,1,2: 15:[4, 60] Operation: 64-4=60 Moving to Node #0,1,2 Current State: 15:[4, 60], Operations: ['27-23=4', '64-4=60'] Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.927083
hs_5
sum_heuristic
[ 58, 96, 39, 43 ]
44
[ "96-58=38", "39+43=82", "82-38=44" ]
Current State: 44:[58, 96, 39, 43], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [39, 43, 38] Generated Node #2: [39, 43, 38] from Operation: 96-58=38 Current State: 44:[39, 43, 38], Operations: ['96-58=38'] Exploring Operation: 39+43=82, Resulting Numbers: [38, 82] Generated Node #3: [38, 82] from Operation: 39+43=82 Current State: 44:[38, 82], Operations: ['96-58=38', '39+43=82'] Exploring Operation: 82-38=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[58, 96, 39, 43], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [39, 43, 38] Generated Node #0,0: 44:[39, 43, 38] Operation: 96-58=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[39, 43, 38], Operations: ['96-58=38'] Exploring Operation: 39-38=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 44:[43, 1] Operation: 39-38=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[43, 1], Operations: ['96-58=38', '39-38=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[58, 96, 39, 43], Operations: [] Exploring Operation: 96-58=38, Resulting Numbers: [39, 43, 38] Generated Node #0,0: 44:[39, 43, 38] Operation: 96-58=38 Moving to Node #0,0 Current State: 44:[39, 43, 38], Operations: ['96-58=38'] Exploring Operation: 39-38=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 44:[43, 1] Operation: 39-38=1 Moving to Node #0,0,0 Current State: 44:[43, 1], Operations: ['96-58=38', '39-38=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 35, 41, 68, 98 ]
24
[ "41-35=6", "98-68=30", "30-6=24" ]
Current State: 24:[35, 41, 68, 98], Operations: [] Exploring Operation: 41-35=6, Resulting Numbers: [68, 98, 6] Generated Node #2: [68, 98, 6] from Operation: 41-35=6 Current State: 24:[68, 98, 6], Operations: ['41-35=6'] Exploring Operation: 98-68=30, Resulting Numbers: [6, 30] Generated Node #3: [6, 30] from Operation: 98-68=30 Current State: 24:[6, 30], Operations: ['41-35=6', '98-68=30'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[35, 41, 68, 98], Operations: [] Exploring Operation: 98-68=30, Resulting Numbers: [35, 41, 30] Generated Node #0,0: 24:[35, 41, 30] Operation: 98-68=30 Moving to Node #0,0 Current State: 24:[35, 41, 30], Operations: ['98-68=30'] Exploring Operation: 41-35=6, Resulting Numbers: [30, 6] Generated Node #0,0,0: 24:[30, 6] Operation: 41-35=6 Moving to Node #0,0,0 Current State: 24:[30, 6], Operations: ['98-68=30', '41-35=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[35, 41, 68, 98], Operations: [] Exploring Operation: 98-68=30, Resulting Numbers: [35, 41, 30] Generated Node #0,0: 24:[35, 41, 30] Operation: 98-68=30 Moving to Node #0,0 Current State: 24:[35, 41, 30], Operations: ['98-68=30'] Exploring Operation: 41-35=6, Resulting Numbers: [30, 6] Generated Node #0,0,0: 24:[30, 6] Operation: 41-35=6 Moving to Node #0,0,0 Current State: 24:[30, 6], Operations: ['98-68=30', '41-35=6'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 75, 53, 78, 96 ]
32
[ "78-53=25", "75/25=3", "96/3=32" ]
Current State: 32:[75, 53, 78, 96], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [75, 96, 25] Generated Node #2: [75, 96, 25] from Operation: 78-53=25 Current State: 32:[75, 96, 25], Operations: ['78-53=25'] Exploring Operation: 75/25=3, Resulting Numbers: [96, 3] Generated Node #3: [96, 3] from Operation: 75/25=3 Current State: 32:[96, 3], Operations: ['78-53=25', '75/25=3'] Exploring Operation: 96/3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[75, 53, 78, 96], Operations: [] Exploring Operation: 96-78=18, Resulting Numbers: [75, 53, 18] Generated Node #0,0: 32:[75, 53, 18] Operation: 96-78=18 Moving to Node #0,0 Current State: 32:[75, 53, 18], Operations: ['96-78=18'] Exploring Operation: 75-53=22, Resulting Numbers: [18, 22] Generated Node #0,0,0: 32:[18, 22] Operation: 75-53=22 Moving to Node #0,0,0 Current State: 32:[18, 22], Operations: ['96-78=18', '75-53=22'] Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,32 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 19, 84, 66, 44 ]
43
[ "84-19=65", "66-44=22", "65-22=43" ]
Current State: 43:[19, 84, 66, 44], Operations: [] Exploring Operation: 84-19=65, Resulting Numbers: [66, 44, 65] Generated Node #2: [66, 44, 65] from Operation: 84-19=65 Current State: 43:[66, 44, 65], Operations: ['84-19=65'] Exploring Operation: 66-44=22, Resulting Numbers: [65, 22] Generated Node #3: [65, 22] from Operation: 66-44=22 Current State: 43:[65, 22], Operations: ['84-19=65', '66-44=22'] Exploring Operation: 65-22=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[19, 84, 66, 44], Operations: [] Exploring Operation: 66-19=47, Resulting Numbers: [84, 44, 47] Generated Node #0,0: 43:[84, 44, 47] Operation: 66-19=47 Exploring Operation: 84-19=65, Resulting Numbers: [66, 44, 65] Generated Node #0,1: 43:[66, 44, 65] Operation: 84-19=65 Exploring Operation: 84-66=18, Resulting Numbers: [19, 44, 18] Generated Node #0,2: 43:[19, 44, 18] Operation: 84-66=18 Exploring Operation: 84-44=40, Resulting Numbers: [19, 66, 40] Generated Node #0,3: 43:[19, 66, 40] Operation: 84-44=40 Exploring Operation: 44-19=25, Resulting Numbers: [84, 66, 25] Generated Node #0,4: 43:[84, 66, 25] Operation: 44-19=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[84, 44, 47], Operations: ['66-19=47'] Exploring Operation: 84-44=40, Resulting Numbers: [47, 40] Generated Node #0,0,0: 43:[47, 40] Operation: 84-44=40 Exploring Operation: 47-44=3, Resulting Numbers: [84, 3] Generated Node #0,0,1: 43:[84, 3] Operation: 47-44=3 Exploring Operation: 84+44=128, Resulting Numbers: [47, 128] Generated Node #0,0,2: 43:[47, 128] Operation: 84+44=128 Exploring Operation: 84-47=37, Resulting Numbers: [44, 37] Generated Node #0,0,3: 43:[44, 37] Operation: 84-47=37 Exploring Operation: 84+47=131, Resulting Numbers: [44, 131] Generated Node #0,0,4: 43:[44, 131] Operation: 84+47=131 Moving to Node #0,0,0 Current State: 43:[47, 40], Operations: ['66-19=47', '84-44=40'] Exploring Operation: 47+40=87, Resulting Numbers: [87] 87,43 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 47*40=1880, Resulting Numbers: [1880] 1880,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[44, 37], Operations: ['66-19=47', '84-47=37'] Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,43 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[84, 3], Operations: ['66-19=47', '47-44=3'] Exploring Operation: 84*3=252, Resulting Numbers: [252] 252,43 unequal: No Solution Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,43 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[47, 128], Operations: ['66-19=47', '84+44=128'] Exploring Operation: 128-47=81, Resulting Numbers: [81] 81,43 unequal: No Solution Exploring Operation: 47+128=175, Resulting Numbers: [175] 175,43 unequal: No Solution Exploring Operation: 47*128=6016, Resulting Numbers: [6016] 6016,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[44, 131], Operations: ['66-19=47', '84+47=131'] Exploring Operation: 131-44=87, Resulting Numbers: [87] 87,43 unequal: No Solution Exploring Operation: 44*131=5764, Resulting Numbers: [5764] 5764,43 unequal: No Solution Exploring Operation: 44+131=175, Resulting Numbers: [175] 175,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[66, 44, 65], Operations: ['84-19=65'] Exploring Operation: 66-65=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 66-65=1 Exploring Operation: 65-44=21, Resulting Numbers: [66, 21] Generated Node #0,1,1: 43:[66, 21] Operation: 65-44=21 Exploring Operation: 66-44=22, Resulting Numbers: [65, 22] Generated Node #0,1,2: 43:[65, 22] Operation: 66-44=22 Exploring Operation: 66+65=131, Resulting Numbers: [44, 131] Generated Node #0,1,3: 43:[44, 131] Operation: 66+65=131 Exploring Operation: 66+44=110, Resulting Numbers: [65, 110] Generated Node #0,1,4: 43:[65, 110] Operation: 66+44=110 Moving to Node #0,1,0 Current State: 43:[44, 1], Operations: ['84-19=65', '66-65=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,43 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[19, 84, 66, 44], Operations: [] Exploring Operation: 84-19=65, Resulting Numbers: [66, 44, 65] Generated Node #0,1: 43:[66, 44, 65] Operation: 84-19=65 Moving to Node #0,1 Current State: 43:[66, 44, 65], Operations: ['84-19=65'] Exploring Operation: 66-65=1, Resulting Numbers: [44, 1] Generated Node #0,1,0: 43:[44, 1] Operation: 66-65=1 Moving to Node #0,1,0 Current State: 43:[44, 1], Operations: ['84-19=65', '66-65=1'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 63, 2, 78, 39 ]
67
[ "63+2=65", "78/39=2", "65+2=67" ]
Current State: 67:[63, 2, 78, 39], Operations: [] Exploring Operation: 63+2=65, Resulting Numbers: [78, 39, 65] Generated Node #2: [78, 39, 65] from Operation: 63+2=65 Current State: 67:[78, 39, 65], Operations: ['63+2=65'] Exploring Operation: 78/39=2, Resulting Numbers: [65, 2] Generated Node #3: [65, 2] from Operation: 78/39=2 Current State: 67:[65, 2], Operations: ['63+2=65', '78/39=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[63, 2, 78, 39], Operations: [] Exploring Operation: 78-2=76, Resulting Numbers: [63, 39, 76] Generated Node #0,0: 67:[63, 39, 76] Operation: 78-2=76 Exploring Operation: 63-2=61, Resulting Numbers: [78, 39, 61] Generated Node #0,1: 67:[78, 39, 61] Operation: 63-2=61 Exploring Operation: 2*39=78, Resulting Numbers: [63, 78, 78] Generated Node #0,2: 67:[63, 78, 78] Operation: 2*39=78 Exploring Operation: 63+2=65, Resulting Numbers: [78, 39, 65] Generated Node #0,3: 67:[78, 39, 65] Operation: 63+2=65 Exploring Operation: 2+39=41, Resulting Numbers: [63, 78, 41] Generated Node #0,4: 67:[63, 78, 41] Operation: 2+39=41 Moving to Node #0,2 Current State: 67:[63, 78, 78], Operations: ['2*39=78'] Exploring Operation: 78-63=15, Resulting Numbers: [78, 15] Generated Node #0,2,0: 67:[78, 15] Operation: 78-63=15 Exploring Operation: 78-78=0, Resulting Numbers: [63, 0] Generated Node #0,2,1: 67:[63, 0] Operation: 78-78=0 Exploring Operation: 63+78=141, Resulting Numbers: [78, 141] Generated Node #0,2,2: 67:[78, 141] Operation: 63+78=141 Exploring Operation: 78-63=15, Resulting Numbers: [78, 15] Generated Node #0,2,3: 67:[78, 15] Operation: 78-63=15 Exploring Operation: 78/78=1, Resulting Numbers: [63, 1] Generated Node #0,2,4: 67:[63, 1] Operation: 78/78=1 Moving to Node #0,3 Current State: 67:[78, 39, 65], Operations: ['63+2=65'] Exploring Operation: 65-39=26, Resulting Numbers: [78, 26] Generated Node #0,3,0: 67:[78, 26] Operation: 65-39=26 Exploring Operation: 39+65=104, Resulting Numbers: [78, 104] Generated Node #0,3,1: 67:[78, 104] Operation: 39+65=104 Exploring Operation: 78/39=2, Resulting Numbers: [65, 2] Generated Node #0,3,2: 67:[65, 2] Operation: 78/39=2 Exploring Operation: 78+39=117, Resulting Numbers: [65, 117] Generated Node #0,3,3: 67:[65, 117] Operation: 78+39=117 Exploring Operation: 78-39=39, Resulting Numbers: [65, 39] Generated Node #0,3,4: 67:[65, 39] Operation: 78-39=39 Moving to Node #0,0 Current State: 67:[63, 39, 76], Operations: ['78-2=76'] Exploring Operation: 63+39=102, Resulting Numbers: [76, 102] Generated Node #0,0,0: 67:[76, 102] Operation: 63+39=102 Exploring Operation: 76-63=13, Resulting Numbers: [39, 13] Generated Node #0,0,1: 67:[39, 13] Operation: 76-63=13 Exploring Operation: 39+76=115, Resulting Numbers: [63, 115] Generated Node #0,0,2: 67:[63, 115] Operation: 39+76=115 Exploring Operation: 76-39=37, Resulting Numbers: [63, 37] Generated Node #0,0,3: 67:[63, 37] Operation: 76-39=37 Exploring Operation: 63-39=24, Resulting Numbers: [76, 24] Generated Node #0,0,4: 67:[76, 24] Operation: 63-39=24 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[63, 37], Operations: ['78-2=76', '76-39=37'] Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 63+37=100, Resulting Numbers: [100] 100,67 unequal: No Solution Exploring Operation: 63*37=2331, Resulting Numbers: [2331] 2331,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[76, 102], Operations: ['78-2=76', '63+39=102'] Exploring Operation: 102-76=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 76+102=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 76*102=7752, Resulting Numbers: [7752] 7752,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[63, 115], Operations: ['78-2=76', '39+76=115'] Exploring Operation: 63+115=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 63*115=7245, Resulting Numbers: [7245] 7245,67 unequal: No Solution Exploring Operation: 115-63=52, Resulting Numbers: [52] 52,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 67:[76, 24], Operations: ['78-2=76', '63-39=24'] Exploring Operation: 76-24=52, Resulting Numbers: [52] 52,67 unequal: No Solution Exploring Operation: 76*24=1824, Resulting Numbers: [1824] 1824,67 unequal: No Solution Exploring Operation: 76+24=100, Resulting Numbers: [100] 100,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[39, 13], Operations: ['78-2=76', '76-63=13'] Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,67 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,67 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: 67:[63, 78, 41], Operations: ['2+39=41'] Exploring Operation: 63+41=104, Resulting Numbers: [78, 104] Generated Node #0,4,0: 67:[78, 104] Operation: 63+41=104 Exploring Operation: 78-41=37, Resulting Numbers: [63, 37] Generated Node #0,4,1: 67:[63, 37] Operation: 78-41=37 Exploring Operation: 78+41=119, Resulting Numbers: [63, 119] Generated Node #0,4,2: 67:[63, 119] Operation: 78+41=119 Exploring Operation: 78-63=15, Resulting Numbers: [41, 15] Generated Node #0,4,3: 67:[41, 15] Operation: 78-63=15 Exploring Operation: 63-41=22, Resulting Numbers: [78, 22] Generated Node #0,4,4: 67:[78, 22] Operation: 63-41=22 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 67:[63, 37], Operations: ['2+39=41', '78-41=37'] Exploring Operation: 63*37=2331, Resulting Numbers: [2331] 2331,67 unequal: No Solution Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 63+37=100, Resulting Numbers: [100] 100,67 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 #0,4,0 Current State: 67:[78, 104], Operations: ['2+39=41', '63+41=104'] Exploring Operation: 104-78=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 78*104=8112, Resulting Numbers: [8112] 8112,67 unequal: No Solution Exploring Operation: 78+104=182, Resulting Numbers: [182] 182,67 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 #0,4,2 Current State: 67:[63, 119], Operations: ['2+39=41', '78+41=119'] Exploring Operation: 63*119=7497, Resulting Numbers: [7497] 7497,67 unequal: No Solution Exploring Operation: 119-63=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 63+119=182, Resulting Numbers: [182] 182,67 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 #0,4,4 Current State: 67:[78, 22], Operations: ['2+39=41', '63-41=22'] Exploring Operation: 78+22=100, Resulting Numbers: [100] 100,67 unequal: No Solution Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 78*22=1716, Resulting Numbers: [1716] 1716,67 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 #0,4,3 Current State: 67:[41, 15], Operations: ['2+39=41', '78-63=15'] Exploring Operation: 41+15=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,67 unequal: No Solution Exploring Operation: 41*15=615, Resulting Numbers: [615] 615,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 67:[78, 39, 61], Operations: ['63-2=61'] Exploring Operation: 78-39=39, Resulting Numbers: [61, 39] Generated Node #0,1,0: 67:[61, 39] Operation: 78-39=39 Exploring Operation: 78/39=2, Resulting Numbers: [61, 2] Generated Node #0,1,1: 67:[61, 2] Operation: 78/39=2 Exploring Operation: 78+39=117, Resulting Numbers: [61, 117] Generated Node #0,1,2: 67:[61, 117] Operation: 78+39=117 Exploring Operation: 61-39=22, Resulting Numbers: [78, 22] Generated Node #0,1,3: 67:[78, 22] Operation: 61-39=22 Exploring Operation: 39+61=100, Resulting Numbers: [78, 100] Generated Node #0,1,4: 67:[78, 100] Operation: 39+61=100 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[61, 39], Operations: ['63-2=61', '78-39=39'] Exploring Operation: 61-39=22, Resulting Numbers: [22] 22,67 unequal: No Solution Exploring Operation: 61*39=2379, Resulting Numbers: [2379] 2379,67 unequal: No Solution Exploring Operation: 61+39=100, Resulting Numbers: [100] 100,67 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 #0,1,4 Current State: 67:[78, 100], Operations: ['63-2=61', '39+61=100'] Exploring Operation: 78+100=178, Resulting Numbers: [178] 178,67 unequal: No Solution Exploring Operation: 78*100=7800, Resulting Numbers: [7800] 7800,67 unequal: No Solution Exploring Operation: 100-78=22, Resulting Numbers: [22] 22,67 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 #0,1,2 Current State: 67:[61, 117], Operations: ['63-2=61', '78+39=117'] Exploring Operation: 117-61=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 61*117=7137, Resulting Numbers: [7137] 7137,67 unequal: No Solution Exploring Operation: 61+117=178, Resulting Numbers: [178] 178,67 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 #0,1,3 Current State: 67:[78, 22], Operations: ['63-2=61', '61-39=22'] Exploring Operation: 78+22=100, Resulting Numbers: [100] 100,67 unequal: No Solution Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,67 unequal: No Solution Exploring Operation: 78*22=1716, Resulting Numbers: [1716] 1716,67 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:[61, 2], Operations: ['63-2=61', '78/39=2'] Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,67 unequal: No Solution Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,67 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,4 Current State: 67:[65, 39], Operations: ['63+2=65', '78-39=39'] Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,67 unequal: No Solution Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[78, 104], Operations: ['63+2=65', '39+65=104'] Exploring Operation: 78*104=8112, Resulting Numbers: [8112] 8112,67 unequal: No Solution Exploring Operation: 78+104=182, Resulting Numbers: [182] 182,67 unequal: No Solution Exploring Operation: 104-78=26, Resulting Numbers: [26] 26,67 unequal: No Solution Moving to Node #0,3,0 Current State: 67:[78, 26], Operations: ['63+2=65', '65-39=26'] Exploring Operation: 78*26=2028, Resulting Numbers: [2028] 2028,67 unequal: No Solution Exploring Operation: 78+26=104, Resulting Numbers: [104] 104,67 unequal: No Solution Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,67 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,67 unequal: No Solution Moving to Node #0,3,3 Current State: 67:[65, 117], Operations: ['63+2=65', '78+39=117'] Exploring Operation: 117-65=52, Resulting Numbers: [52] 52,67 unequal: No Solution Exploring Operation: 65+117=182, Resulting Numbers: [182] 182,67 unequal: No Solution Exploring Operation: 65*117=7605, Resulting Numbers: [7605] 7605,67 unequal: No Solution Moving to Node #0,2,0 Current State: 67:[78, 15], Operations: ['2*39=78', '78-63=15'] Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,67 unequal: No Solution Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,67 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,67 unequal: No Solution Moving to Node #0,2,3 Current State: 67:[78, 15], Operations: ['2*39=78', '78-63=15'] Exploring Operation: 78+15=93, Resulting Numbers: [93] 93,67 unequal: No Solution Exploring Operation: 78-15=63, Resulting Numbers: [63] 63,67 unequal: No Solution Exploring Operation: 78*15=1170, Resulting Numbers: [1170] 1170,67 unequal: No Solution Moving to Node #0,3,2 Current State: 67:[65, 2], Operations: ['63+2=65', '78/39=2'] Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,67 unequal: No Solution Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[63, 2, 78, 39], Operations: [] Exploring Operation: 63+2=65, Resulting Numbers: [78, 39, 65] Generated Node #0,3: 67:[78, 39, 65] Operation: 63+2=65 Moving to Node #0,3 Current State: 67:[78, 39, 65], Operations: ['63+2=65'] Exploring Operation: 78/39=2, Resulting Numbers: [65, 2] Generated Node #0,3,2: 67:[65, 2] Operation: 78/39=2 Moving to Node #0,3,2 Current State: 67:[65, 2], Operations: ['63+2=65', '78/39=2'] Exploring Operation: 65+2=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
0.912326
hs_5
sum_heuristic
[ 28, 77, 82, 2 ]
61
[ "28*2=56", "82-77=5", "56+5=61" ]
Current State: 61:[28, 77, 82, 2], Operations: [] Exploring Operation: 28*2=56, Resulting Numbers: [77, 82, 56] Generated Node #2: [77, 82, 56] from Operation: 28*2=56 Current State: 61:[77, 82, 56], Operations: ['28*2=56'] Exploring Operation: 82-77=5, Resulting Numbers: [56, 5] Generated Node #3: [56, 5] from Operation: 82-77=5 Current State: 61:[56, 5], Operations: ['28*2=56', '82-77=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[28, 77, 82, 2], Operations: [] Exploring Operation: 77-2=75, Resulting Numbers: [28, 82, 75] Generated Node #0,0: 61:[28, 82, 75] Operation: 77-2=75 Exploring Operation: 28+2=30, Resulting Numbers: [77, 82, 30] Generated Node #0,1: 61:[77, 82, 30] Operation: 28+2=30 Exploring Operation: 28*2=56, Resulting Numbers: [77, 82, 56] Generated Node #0,2: 61:[77, 82, 56] Operation: 28*2=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[77, 82, 56], Operations: ['28*2=56'] Exploring Operation: 82-56=26, Resulting Numbers: [77, 26] Generated Node #0,2,0: 61:[77, 26] Operation: 82-56=26 Exploring Operation: 82-77=5, Resulting Numbers: [56, 5] Generated Node #0,2,1: 61:[56, 5] Operation: 82-77=5 Exploring Operation: 77-56=21, Resulting Numbers: [82, 21] Generated Node #0,2,2: 61:[82, 21] Operation: 77-56=21 Moving to Node #0,2,0 Current State: 61:[77, 26], Operations: ['28*2=56', '82-56=26'] Exploring Operation: 77*26=2002, Resulting Numbers: [2002] 2002,61 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,61 unequal: No Solution Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[56, 5], Operations: ['28*2=56', '82-77=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[28, 77, 82, 2], Operations: [] Exploring Operation: 28*2=56, Resulting Numbers: [77, 82, 56] Generated Node #0,2: 61:[77, 82, 56] Operation: 28*2=56 Moving to Node #0,2 Current State: 61:[77, 82, 56], Operations: ['28*2=56'] Exploring Operation: 82-77=5, Resulting Numbers: [56, 5] Generated Node #0,2,1: 61:[56, 5] Operation: 82-77=5 Moving to Node #0,2,1 Current State: 61:[56, 5], Operations: ['28*2=56', '82-77=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 18, 63, 82, 96 ]
54
[ "63*82=5166", "18+5166=5184", "5184/96=54" ]
Current State: 54:[18, 63, 82, 96], Operations: [] Exploring Operation: 63*82=5166, Resulting Numbers: [18, 96, 5166] Generated Node #2: [18, 96, 5166] from Operation: 63*82=5166 Current State: 54:[18, 96, 5166], Operations: ['63*82=5166'] Exploring Operation: 18+5166=5184, Resulting Numbers: [96, 5184] Generated Node #3: [96, 5184] from Operation: 18+5166=5184 Current State: 54:[96, 5184], Operations: ['63*82=5166', '18+5166=5184'] Exploring Operation: 5184/96=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[18, 63, 82, 96], Operations: [] Exploring Operation: 96-63=33, Resulting Numbers: [18, 82, 33] Generated Node #0,0: 54:[18, 82, 33] Operation: 96-63=33 Exploring Operation: 82-63=19, Resulting Numbers: [18, 96, 19] Generated Node #0,1: 54:[18, 96, 19] Operation: 82-63=19 Exploring Operation: 96-82=14, Resulting Numbers: [18, 63, 14] Generated Node #0,2: 54:[18, 63, 14] Operation: 96-82=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[18, 63, 14], Operations: ['96-82=14'] Exploring Operation: 18-14=4, Resulting Numbers: [63, 4] Generated Node #0,2,0: 54:[63, 4] Operation: 18-14=4 Exploring Operation: 63-14=49, Resulting Numbers: [18, 49] Generated Node #0,2,1: 54:[18, 49] Operation: 63-14=49 Exploring Operation: 63-18=45, Resulting Numbers: [14, 45] Generated Node #0,2,2: 54:[14, 45] Operation: 63-18=45 Moving to Node #0,2,1 Current State: 54:[18, 49], Operations: ['96-82=14', '63-14=49'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,54 unequal: No Solution Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[63, 4], Operations: ['96-82=14', '18-14=4'] Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,54 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[14, 45], Operations: ['96-82=14', '63-18=45'] Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,54 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[18, 82, 33], Operations: ['96-63=33'] Exploring Operation: 18+33=51, Resulting Numbers: [82, 51] Generated Node #0,0,0: 54:[82, 51] Operation: 18+33=51 Exploring Operation: 82-33=49, Resulting Numbers: [18, 49] Generated Node #0,0,1: 54:[18, 49] Operation: 82-33=49 Exploring Operation: 82-18=64, Resulting Numbers: [33, 64] Generated Node #0,0,2: 54:[33, 64] Operation: 82-18=64 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[18, 49], Operations: ['96-63=33', '82-33=49'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,54 unequal: No Solution Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 54:[33, 64], Operations: ['96-63=33', '82-18=64'] Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,54 unequal: No Solution Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,54 unequal: No Solution Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[82, 51], Operations: ['96-63=33', '18+33=51'] Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,54 unequal: No Solution Exploring Operation: 82+51=133, Resulting Numbers: [133] 133,54 unequal: No Solution Exploring Operation: 82*51=4182, Resulting Numbers: [4182] 4182,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[18, 96, 19], Operations: ['82-63=19'] Exploring Operation: 19-18=1, Resulting Numbers: [96, 1] Generated Node #0,1,0: 54:[96, 1] Operation: 19-18=1 Exploring Operation: 96-19=77, Resulting Numbers: [18, 77] Generated Node #0,1,1: 54:[18, 77] Operation: 96-19=77 Exploring Operation: 96-18=78, Resulting Numbers: [19, 78] Generated Node #0,1,2: 54:[19, 78] Operation: 96-18=78 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[18, 77], Operations: ['82-63=19', '96-19=77'] Exploring Operation: 18+77=95, Resulting Numbers: [95] 95,54 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 18*77=1386, Resulting Numbers: [1386] 1386,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 54:[19, 78], Operations: ['82-63=19', '96-18=78'] Exploring Operation: 19+78=97, Resulting Numbers: [97] 97,54 unequal: No Solution Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 19*78=1482, Resulting Numbers: [1482] 1482,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 54:[96, 1], Operations: ['82-63=19', '19-18=1'] Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 63, 37, 8, 19 ]
73
[ "63+37=100", "8+19=27", "100-27=73" ]
Current State: 73:[63, 37, 8, 19], Operations: [] Exploring Operation: 63+37=100, Resulting Numbers: [8, 19, 100] Generated Node #2: [8, 19, 100] from Operation: 63+37=100 Current State: 73:[8, 19, 100], Operations: ['63+37=100'] Exploring Operation: 8+19=27, Resulting Numbers: [100, 27] Generated Node #3: [100, 27] from Operation: 8+19=27 Current State: 73:[100, 27], Operations: ['63+37=100', '8+19=27'] Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[63, 37, 8, 19], Operations: [] Exploring Operation: 37+19=56, Resulting Numbers: [63, 8, 56] Generated Node #0,0: 73:[63, 8, 56] Operation: 37+19=56 Exploring Operation: 37+8=45, Resulting Numbers: [63, 19, 45] Generated Node #0,1: 73:[63, 19, 45] Operation: 37+8=45 Exploring Operation: 63+8=71, Resulting Numbers: [37, 19, 71] Generated Node #0,2: 73:[37, 19, 71] Operation: 63+8=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[63, 8, 56], Operations: ['37+19=56'] Exploring Operation: 63+8=71, Resulting Numbers: [56, 71] Generated Node #0,0,0: 73:[56, 71] Operation: 63+8=71 Exploring Operation: 8+56=64, Resulting Numbers: [63, 64] Generated Node #0,0,1: 73:[63, 64] Operation: 8+56=64 Exploring Operation: 63-8=55, Resulting Numbers: [56, 55] Generated Node #0,0,2: 73:[56, 55] Operation: 63-8=55 Moving to Node #0,0,0 Current State: 73:[56, 71], Operations: ['37+19=56', '63+8=71'] Exploring Operation: 56+71=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 56*71=3976, Resulting Numbers: [3976] 3976,73 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[63, 64], Operations: ['37+19=56', '8+56=64'] Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,73 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[56, 55], Operations: ['37+19=56', '63-8=55'] Exploring Operation: 56*55=3080, Resulting Numbers: [3080] 3080,73 unequal: No Solution Exploring Operation: 56+55=111, Resulting Numbers: [111] 111,73 unequal: No Solution Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,73 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 Current State: 73:[63, 19, 45], Operations: ['37+8=45'] Exploring Operation: 19+45=64, Resulting Numbers: [63, 64] Generated Node #0,1,0: 73:[63, 64] Operation: 19+45=64 Exploring Operation: 63-19=44, Resulting Numbers: [45, 44] Generated Node #0,1,1: 73:[45, 44] Operation: 63-19=44 Exploring Operation: 63+19=82, Resulting Numbers: [45, 82] Generated Node #0,1,2: 73:[45, 82] Operation: 63+19=82 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[63, 64], Operations: ['37+8=45', '19+45=64'] Exploring Operation: 63*64=4032, Resulting Numbers: [4032] 4032,73 unequal: No Solution Exploring Operation: 63+64=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 64-63=1, Resulting Numbers: [1] 1,73 unequal: No Solution No 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: 73:[45, 82], Operations: ['37+8=45', '63+19=82'] Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,73 unequal: No Solution No 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: 73:[45, 44], Operations: ['37+8=45', '63-19=44'] Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,73 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,73 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: 73:[37, 19, 71], Operations: ['63+8=71'] Exploring Operation: 37+19=56, Resulting Numbers: [71, 56] Generated Node #0,2,0: 73:[71, 56] Operation: 37+19=56 Exploring Operation: 19+71=90, Resulting Numbers: [37, 90] Generated Node #0,2,1: 73:[37, 90] Operation: 19+71=90 Exploring Operation: 37-19=18, Resulting Numbers: [71, 18] Generated Node #0,2,2: 73:[71, 18] Operation: 37-19=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[71, 56], Operations: ['63+8=71', '37+19=56'] Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,73 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,73 unequal: No Solution No 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: 73:[37, 90], Operations: ['63+8=71', '19+71=90'] Exploring Operation: 37*90=3330, Resulting Numbers: [3330] 3330,73 unequal: No Solution Exploring Operation: 37+90=127, Resulting Numbers: [127] 127,73 unequal: No Solution Exploring Operation: 90-37=53, Resulting Numbers: [53] 53,73 unequal: No Solution No 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: 73:[71, 18], Operations: ['63+8=71', '37-19=18'] Exploring Operation: 71*18=1278, Resulting Numbers: [1278] 1278,73 unequal: No Solution Exploring Operation: 71+18=89, Resulting Numbers: [89] 89,73 unequal: No Solution Exploring Operation: 71-18=53, Resulting Numbers: [53] 53,73 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
[ 85, 11, 66, 55 ]
47
[ "85-11=74", "66+55=121", "121-74=47" ]
Current State: 47:[85, 11, 66, 55], Operations: [] Exploring Operation: 85-11=74, Resulting Numbers: [66, 55, 74] Generated Node #2: [66, 55, 74] from Operation: 85-11=74 Current State: 47:[66, 55, 74], Operations: ['85-11=74'] Exploring Operation: 66+55=121, Resulting Numbers: [74, 121] Generated Node #3: [74, 121] from Operation: 66+55=121 Current State: 47:[74, 121], Operations: ['85-11=74', '66+55=121'] Exploring Operation: 121-74=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[85, 11, 66, 55], Operations: [] Exploring Operation: 85-11=74, Resulting Numbers: [66, 55, 74] Generated Node #0,0: 47:[66, 55, 74] Operation: 85-11=74 Exploring Operation: 55-11=44, Resulting Numbers: [85, 66, 44] Generated Node #0,1: 47:[85, 66, 44] Operation: 55-11=44 Exploring Operation: 66-11=55, Resulting Numbers: [85, 55, 55] Generated Node #0,2: 47:[85, 55, 55] Operation: 66-11=55 Moving to Node #0,0 Current State: 47:[66, 55, 74], Operations: ['85-11=74'] Exploring Operation: 74-66=8, Resulting Numbers: [55, 8] Generated Node #0,0,0: 47:[55, 8] Operation: 74-66=8 Exploring Operation: 74-55=19, Resulting Numbers: [66, 19] Generated Node #0,0,1: 47:[66, 19] Operation: 74-55=19 Exploring Operation: 66-55=11, Resulting Numbers: [74, 11] Generated Node #0,0,2: 47:[74, 11] Operation: 66-55=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[55, 8], Operations: ['85-11=74', '74-66=8'] Exploring Operation: 55+8=63, Resulting Numbers: [63] 63,47 unequal: No Solution Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[85, 11, 66, 55], Operations: [] Exploring Operation: 85-11=74, Resulting Numbers: [66, 55, 74] Generated Node #0,0: 47:[66, 55, 74] Operation: 85-11=74 Moving to Node #0,0 Current State: 47:[66, 55, 74], Operations: ['85-11=74'] Exploring Operation: 74-66=8, Resulting Numbers: [55, 8] Generated Node #0,0,0: 47:[55, 8] Operation: 74-66=8 Moving to Node #0,0,0 Current State: 47:[55, 8], Operations: ['85-11=74', '74-66=8'] Exploring Operation: 55-8=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 18, 27, 46, 4 ]
80
[ "46-18=28", "27*4=108", "108-28=80" ]
Current State: 80:[18, 27, 46, 4], Operations: [] Exploring Operation: 46-18=28, Resulting Numbers: [27, 4, 28] Generated Node #2: [27, 4, 28] from Operation: 46-18=28 Current State: 80:[27, 4, 28], Operations: ['46-18=28'] Exploring Operation: 27*4=108, Resulting Numbers: [28, 108] Generated Node #3: [28, 108] from Operation: 27*4=108 Current State: 80:[28, 108], Operations: ['46-18=28', '27*4=108'] Exploring Operation: 108-28=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[18, 27, 46, 4], Operations: [] Exploring Operation: 27-18=9, Resulting Numbers: [46, 4, 9] Generated Node #0,0: 80:[46, 4, 9] Operation: 27-18=9 Exploring Operation: 46-27=19, Resulting Numbers: [18, 4, 19] Generated Node #0,1: 80:[18, 4, 19] Operation: 46-27=19 Moving to Node #0,1 Current State: 80:[18, 4, 19], Operations: ['46-27=19'] Exploring Operation: 18+4=22, Resulting Numbers: [19, 22] Generated Node #0,1,0: 80:[19, 22] Operation: 18+4=22 Exploring Operation: 19-18=1, Resulting Numbers: [4, 1] Generated Node #0,1,1: 80:[4, 1] Operation: 19-18=1 Moving to Node #0,0 Current State: 80:[46, 4, 9], Operations: ['27-18=9'] Exploring Operation: 46-9=37, Resulting Numbers: [4, 37] Generated Node #0,0,0: 80:[4, 37] Operation: 46-9=37 Exploring Operation: 46-4=42, Resulting Numbers: [9, 42] Generated Node #0,0,1: 80:[9, 42] Operation: 46-4=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[4, 37], Operations: ['27-18=9', '46-9=37'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[9, 42], Operations: ['27-18=9', '46-4=42'] Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,80 unequal: No Solution Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 80:[4, 1], Operations: ['46-27=19', '19-18=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[19, 22], Operations: ['46-27=19', '18+4=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,80 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 80, 37, 25, 21 ]
71
[ "80+37=117", "25+21=46", "117-46=71" ]
Current State: 71:[80, 37, 25, 21], Operations: [] Exploring Operation: 80+37=117, Resulting Numbers: [25, 21, 117] Generated Node #2: [25, 21, 117] from Operation: 80+37=117 Current State: 71:[25, 21, 117], Operations: ['80+37=117'] Exploring Operation: 25+21=46, Resulting Numbers: [117, 46] Generated Node #3: [117, 46] from Operation: 25+21=46 Current State: 71:[117, 46], Operations: ['80+37=117', '25+21=46'] Exploring Operation: 117-46=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[80, 37, 25, 21], Operations: [] Exploring Operation: 37+25=62, Resulting Numbers: [80, 21, 62] Generated Node #0,0: 71:[80, 21, 62] Operation: 37+25=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[80, 21, 62], Operations: ['37+25=62'] Exploring Operation: 80-21=59, Resulting Numbers: [62, 59] Generated Node #0,0,0: 71:[62, 59] Operation: 80-21=59 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 71:[62, 59], Operations: ['37+25=62', '80-21=59'] Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,71 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 12, 36, 37, 26 ]
59
[ "12+36=48", "37-26=11", "48+11=59" ]
Current State: 59:[12, 36, 37, 26], Operations: [] Exploring Operation: 12+36=48, Resulting Numbers: [37, 26, 48] Generated Node #2: [37, 26, 48] from Operation: 12+36=48 Current State: 59:[37, 26, 48], Operations: ['12+36=48'] Exploring Operation: 37-26=11, Resulting Numbers: [48, 11] Generated Node #3: [48, 11] from Operation: 37-26=11 Current State: 59:[48, 11], Operations: ['12+36=48', '37-26=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[12, 36, 37, 26], Operations: [] Exploring Operation: 12+36=48, Resulting Numbers: [37, 26, 48] Generated Node #0,0: 59:[37, 26, 48] Operation: 12+36=48 Exploring Operation: 12+37=49, Resulting Numbers: [36, 26, 49] Generated Node #0,1: 59:[36, 26, 49] Operation: 12+37=49 Exploring Operation: 12+26=38, Resulting Numbers: [36, 37, 38] Generated Node #0,2: 59:[36, 37, 38] Operation: 12+26=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[37, 26, 48], Operations: ['12+36=48'] Exploring Operation: 37+26=63, Resulting Numbers: [48, 63] Generated Node #0,0,0: 59:[48, 63] Operation: 37+26=63 Exploring Operation: 37-26=11, Resulting Numbers: [48, 11] Generated Node #0,0,1: 59:[48, 11] Operation: 37-26=11 Exploring Operation: 26+48=74, Resulting Numbers: [37, 74] Generated Node #0,0,2: 59:[37, 74] Operation: 26+48=74 Moving to Node #0,0,0 Current State: 59:[48, 63], Operations: ['12+36=48', '37+26=63'] Exploring Operation: 48+63=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 63-48=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 48*63=3024, Resulting Numbers: [3024] 3024,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[37, 74], Operations: ['12+36=48', '26+48=74'] Exploring Operation: 74-37=37, Resulting Numbers: [37] 37,59 unequal: No Solution Exploring Operation: 37+74=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 74/37=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[48, 11], Operations: ['12+36=48', '37-26=11'] Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,59 unequal: No Solution Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[12, 36, 37, 26], Operations: [] Exploring Operation: 12+36=48, Resulting Numbers: [37, 26, 48] Generated Node #0,0: 59:[37, 26, 48] Operation: 12+36=48 Moving to Node #0,0 Current State: 59:[37, 26, 48], Operations: ['12+36=48'] Exploring Operation: 37-26=11, Resulting Numbers: [48, 11] Generated Node #0,0,1: 59:[48, 11] Operation: 37-26=11 Moving to Node #0,0,1 Current State: 59:[48, 11], Operations: ['12+36=48', '37-26=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 6, 72, 63, 15 ]
85
[ "63+15=78", "78/6=13", "72+13=85" ]
Current State: 85:[6, 72, 63, 15], Operations: [] Exploring Operation: 63+15=78, Resulting Numbers: [6, 72, 78] Generated Node #2: [6, 72, 78] from Operation: 63+15=78 Current State: 85:[6, 72, 78], Operations: ['63+15=78'] Exploring Operation: 78/6=13, Resulting Numbers: [72, 13] Generated Node #3: [72, 13] from Operation: 78/6=13 Current State: 85:[72, 13], Operations: ['63+15=78', '78/6=13'] Exploring Operation: 72+13=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[6, 72, 63, 15], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [6, 15, 9] Generated Node #0,0: 85:[6, 15, 9] Operation: 72-63=9 Exploring Operation: 63+15=78, Resulting Numbers: [6, 72, 78] Generated Node #0,1: 85:[6, 72, 78] Operation: 63+15=78 Exploring Operation: 72+15=87, Resulting Numbers: [6, 63, 87] Generated Node #0,2: 85:[6, 63, 87] Operation: 72+15=87 Moving to Node #0,0 Current State: 85:[6, 15, 9], Operations: ['72-63=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15, 15] Generated Node #0,0,0: 85:[15, 15] Operation: 6+9=15 Exploring Operation: 9-6=3, Resulting Numbers: [15, 3] Generated Node #0,0,1: 85:[15, 3] Operation: 9-6=3 Exploring Operation: 15-9=6, Resulting Numbers: [6, 6] Generated Node #0,0,2: 85:[6, 6] Operation: 15-9=6 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 85:[6, 6], Operations: ['72-63=9', '15-9=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,85 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 #0,0,0 Current State: 85:[15, 15], Operations: ['72-63=9', '6+9=15'] Exploring Operation: 15-15=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 15/15=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 15+15=30, Resulting Numbers: [30] 30,85 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:[15, 3], Operations: ['72-63=9', '9-6=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,85 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:[6, 72, 78], Operations: ['63+15=78'] Exploring Operation: 78-72=6, Resulting Numbers: [6, 6] Generated Node #0,1,0: 85:[6, 6] Operation: 78-72=6 Exploring Operation: 6+72=78, Resulting Numbers: [78, 78] Generated Node #0,1,1: 85:[78, 78] Operation: 6+72=78 Exploring Operation: 72/6=12, Resulting Numbers: [78, 12] Generated Node #0,1,2: 85:[78, 12] Operation: 72/6=12 Moving to Node #0,2 Current State: 85:[6, 63, 87], Operations: ['72+15=87'] Exploring Operation: 87-63=24, Resulting Numbers: [6, 24] Generated Node #0,2,0: 85:[6, 24] Operation: 87-63=24 Exploring Operation: 6+63=69, Resulting Numbers: [87, 69] Generated Node #0,2,1: 85:[87, 69] Operation: 6+63=69 Exploring Operation: 87-6=81, Resulting Numbers: [63, 81] Generated Node #0,2,2: 85:[63, 81] Operation: 87-6=81 Moving to Node #0,1,0 Current State: 85:[6, 6], Operations: ['63+15=78', '78-72=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,85 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[6, 24], Operations: ['72+15=87', '87-63=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,85 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[78, 12], Operations: ['63+15=78', '72/6=12'] Exploring Operation: 78-12=66, Resulting Numbers: [66] 66,85 unequal: No Solution Exploring Operation: 78+12=90, Resulting Numbers: [90] 90,85 unequal: No Solution Exploring Operation: 78*12=936, Resulting Numbers: [936] 936,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[78, 78], Operations: ['63+15=78', '6+72=78'] Exploring Operation: 78+78=156, Resulting Numbers: [156] 156,85 unequal: No Solution Exploring Operation: 78/78=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 78-78=0, Resulting Numbers: [0] 0,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[87, 69], Operations: ['72+15=87', '6+63=69'] Exploring Operation: 87-69=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 87*69=6003, Resulting Numbers: [6003] 6003,85 unequal: No Solution Exploring Operation: 87+69=156, Resulting Numbers: [156] 156,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[63, 81], Operations: ['72+15=87', '87-6=81'] Exploring Operation: 81-63=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 63+81=144, Resulting Numbers: [144] 144,85 unequal: No Solution Exploring Operation: 63*81=5103, Resulting Numbers: [5103] 5103,85 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 14, 52, 3, 82 ]
47
[ "52-14=38", "3+82=85", "85-38=47" ]
Current State: 47:[14, 52, 3, 82], Operations: [] Exploring Operation: 52-14=38, Resulting Numbers: [3, 82, 38] Generated Node #2: [3, 82, 38] from Operation: 52-14=38 Current State: 47:[3, 82, 38], Operations: ['52-14=38'] Exploring Operation: 3+82=85, Resulting Numbers: [38, 85] Generated Node #3: [38, 85] from Operation: 3+82=85 Current State: 47:[38, 85], Operations: ['52-14=38', '3+82=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[14, 52, 3, 82], Operations: [] Exploring Operation: 14*3=42, Resulting Numbers: [52, 82, 42] Generated Node #0,0: 47:[52, 82, 42] Operation: 14*3=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[52, 82, 42], Operations: ['14*3=42'] Exploring Operation: 82-42=40, Resulting Numbers: [52, 40] Generated Node #0,0,0: 47:[52, 40] Operation: 82-42=40 Moving to Node #0,0,0 Current State: 47:[52, 40], Operations: ['14*3=42', '82-42=40'] Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 65, 60, 8, 43 ]
83
[ "65-60=5", "8*5=40", "43+40=83" ]
Current State: 83:[65, 60, 8, 43], Operations: [] Exploring Operation: 65-60=5, Resulting Numbers: [8, 43, 5] Generated Node #2: [8, 43, 5] from Operation: 65-60=5 Current State: 83:[8, 43, 5], Operations: ['65-60=5'] Exploring Operation: 8*5=40, Resulting Numbers: [43, 40] Generated Node #3: [43, 40] from Operation: 8*5=40 Current State: 83:[43, 40], Operations: ['65-60=5', '8*5=40'] Exploring Operation: 43+40=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[65, 60, 8, 43], Operations: [] Exploring Operation: 60+8=68, Resulting Numbers: [65, 43, 68] Generated Node #0,0: 83:[65, 43, 68] Operation: 60+8=68 Exploring Operation: 65+8=73, Resulting Numbers: [60, 43, 73] Generated Node #0,1: 83:[60, 43, 73] Operation: 65+8=73 Exploring Operation: 8+43=51, Resulting Numbers: [65, 60, 51] Generated Node #0,2: 83:[65, 60, 51] Operation: 8+43=51 Exploring Operation: 65-8=57, Resulting Numbers: [60, 43, 57] Generated Node #0,3: 83:[60, 43, 57] Operation: 65-8=57 Exploring Operation: 60-8=52, Resulting Numbers: [65, 43, 52] Generated Node #0,4: 83:[65, 43, 52] Operation: 60-8=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[65, 43, 68], Operations: ['60+8=68'] Exploring Operation: 65-43=22, Resulting Numbers: [68, 22] Generated Node #0,0,0: 83:[68, 22] Operation: 65-43=22 Exploring Operation: 68-43=25, Resulting Numbers: [65, 25] Generated Node #0,0,1: 83:[65, 25] Operation: 68-43=25 Exploring Operation: 43+68=111, Resulting Numbers: [65, 111] Generated Node #0,0,2: 83:[65, 111] Operation: 43+68=111 Exploring Operation: 65+43=108, Resulting Numbers: [68, 108] Generated Node #0,0,3: 83:[68, 108] Operation: 65+43=108 Exploring Operation: 65+68=133, Resulting Numbers: [43, 133] Generated Node #0,0,4: 83:[43, 133] Operation: 65+68=133 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 83:[68, 108], Operations: ['60+8=68', '65+43=108'] Exploring Operation: 68+108=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 108-68=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 68*108=7344, Resulting Numbers: [7344] 7344,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 83:[65, 111], Operations: ['60+8=68', '43+68=111'] Exploring Operation: 65*111=7215, Resulting Numbers: [7215] 7215,83 unequal: No Solution Exploring Operation: 111-65=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 65+111=176, Resulting Numbers: [176] 176,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[68, 22], Operations: ['60+8=68', '65-43=22'] Exploring Operation: 68+22=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 68-22=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 68*22=1496, Resulting Numbers: [1496] 1496,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[65, 25], Operations: ['60+8=68', '68-43=25'] Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 83:[43, 133], Operations: ['60+8=68', '65+68=133'] Exploring Operation: 43+133=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 133-43=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 43*133=5719, Resulting Numbers: [5719] 5719,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[60, 43, 73], Operations: ['65+8=73'] Exploring Operation: 60+73=133, Resulting Numbers: [43, 133] Generated Node #0,1,0: 83:[43, 133] Operation: 60+73=133 Exploring Operation: 73-43=30, Resulting Numbers: [60, 30] Generated Node #0,1,1: 83:[60, 30] Operation: 73-43=30 Exploring Operation: 60+43=103, Resulting Numbers: [73, 103] Generated Node #0,1,2: 83:[73, 103] Operation: 60+43=103 Exploring Operation: 60-43=17, Resulting Numbers: [73, 17] Generated Node #0,1,3: 83:[73, 17] Operation: 60-43=17 Exploring Operation: 43+73=116, Resulting Numbers: [60, 116] Generated Node #0,1,4: 83:[60, 116] Operation: 43+73=116 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[73, 103], Operations: ['65+8=73', '60+43=103'] Exploring Operation: 73+103=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 103-73=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 73*103=7519, Resulting Numbers: [7519] 7519,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 83:[60, 116], Operations: ['65+8=73', '43+73=116'] Exploring Operation: 60+116=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 116-60=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 60*116=6960, Resulting Numbers: [6960] 6960,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[60, 30], Operations: ['65+8=73', '73-43=30'] Exploring Operation: 60/30=2, Resulting Numbers: [2] 2,83 unequal: No Solution Exploring Operation: 60+30=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 60-30=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 60*30=1800, Resulting Numbers: [1800] 1800,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 83:[73, 17], Operations: ['65+8=73', '60-43=17'] Exploring Operation: 73+17=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 73*17=1241, Resulting Numbers: [1241] 1241,83 unequal: No Solution Exploring Operation: 73-17=56, Resulting Numbers: [56] 56,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[43, 133], Operations: ['65+8=73', '60+73=133'] Exploring Operation: 43+133=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 133-43=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 43*133=5719, Resulting Numbers: [5719] 5719,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[65, 60, 51], Operations: ['8+43=51'] Exploring Operation: 60+51=111, Resulting Numbers: [65, 111] Generated Node #0,2,0: 83:[65, 111] Operation: 60+51=111 Exploring Operation: 65-51=14, Resulting Numbers: [60, 14] Generated Node #0,2,1: 83:[60, 14] Operation: 65-51=14 Exploring Operation: 60-51=9, Resulting Numbers: [65, 9] Generated Node #0,2,2: 83:[65, 9] Operation: 60-51=9 Exploring Operation: 65+60=125, Resulting Numbers: [51, 125] Generated Node #0,2,3: 83:[51, 125] Operation: 65+60=125 Exploring Operation: 65+51=116, Resulting Numbers: [60, 116] Generated Node #0,2,4: 83:[60, 116] Operation: 65+51=116 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[65, 111], Operations: ['8+43=51', '60+51=111'] Exploring Operation: 65*111=7215, Resulting Numbers: [7215] 7215,83 unequal: No Solution Exploring Operation: 111-65=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 65+111=176, Resulting Numbers: [176] 176,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 83:[60, 116], Operations: ['8+43=51', '65+51=116'] Exploring Operation: 60*116=6960, Resulting Numbers: [6960] 6960,83 unequal: No Solution Exploring Operation: 60+116=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 116-60=56, Resulting Numbers: [56] 56,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[51, 125], Operations: ['8+43=51', '65+60=125'] Exploring Operation: 51+125=176, Resulting Numbers: [176] 176,83 unequal: No Solution Exploring Operation: 51*125=6375, Resulting Numbers: [6375] 6375,83 unequal: No Solution Exploring Operation: 125-51=74, Resulting Numbers: [74] 74,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[60, 14], Operations: ['8+43=51', '65-51=14'] Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,83 unequal: No Solution Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[65, 9], Operations: ['8+43=51', '60-51=9'] Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 83:[60, 43, 57], Operations: ['65-8=57'] Exploring Operation: 60+43=103, Resulting Numbers: [57, 103] Generated Node #0,3,0: 83:[57, 103] Operation: 60+43=103 Exploring Operation: 43+57=100, Resulting Numbers: [60, 100] Generated Node #0,3,1: 83:[60, 100] Operation: 43+57=100 Exploring Operation: 60-43=17, Resulting Numbers: [57, 17] Generated Node #0,3,2: 83:[57, 17] Operation: 60-43=17 Exploring Operation: 60+57=117, Resulting Numbers: [43, 117] Generated Node #0,3,3: 83:[43, 117] Operation: 60+57=117 Exploring Operation: 57-43=14, Resulting Numbers: [60, 14] Generated Node #0,3,4: 83:[60, 14] Operation: 57-43=14 Moving to Node #0,3,1 Current State: 83:[60, 100], Operations: ['65-8=57', '43+57=100'] Exploring Operation: 100-60=40, Resulting Numbers: [40] 40,83 unequal: No Solution Exploring Operation: 60+100=160, Resulting Numbers: [160] 160,83 unequal: No Solution Exploring Operation: 60*100=6000, Resulting Numbers: [6000] 6000,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[57, 103], Operations: ['65-8=57', '60+43=103'] Exploring Operation: 57*103=5871, Resulting Numbers: [5871] 5871,83 unequal: No Solution Exploring Operation: 103-57=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 57+103=160, Resulting Numbers: [160] 160,83 unequal: No Solution Moving to Node #0,3,3 Current State: 83:[43, 117], Operations: ['65-8=57', '60+57=117'] Exploring Operation: 117-43=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 43*117=5031, Resulting Numbers: [5031] 5031,83 unequal: No Solution Exploring Operation: 43+117=160, Resulting Numbers: [160] 160,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[57, 17], Operations: ['65-8=57', '60-43=17'] Exploring Operation: 57*17=969, Resulting Numbers: [969] 969,83 unequal: No Solution Exploring Operation: 57+17=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 57-17=40, Resulting Numbers: [40] 40,83 unequal: No Solution Moving to Node #0,3,4 Current State: 83:[60, 14], Operations: ['65-8=57', '57-43=14'] Exploring Operation: 60*14=840, Resulting Numbers: [840] 840,83 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 60+14=74, Resulting Numbers: [74] 74,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 83:[65, 43, 52], Operations: ['60-8=52'] Exploring Operation: 65-43=22, Resulting Numbers: [52, 22] Generated Node #0,4,0: 83:[52, 22] Operation: 65-43=22 Exploring Operation: 52-43=9, Resulting Numbers: [65, 9] Generated Node #0,4,1: 83:[65, 9] Operation: 52-43=9 Exploring Operation: 43+52=95, Resulting Numbers: [65, 95] Generated Node #0,4,2: 83:[65, 95] Operation: 43+52=95 Exploring Operation: 65+43=108, Resulting Numbers: [52, 108] Generated Node #0,4,3: 83:[52, 108] Operation: 65+43=108 Exploring Operation: 65+52=117, Resulting Numbers: [43, 117] Generated Node #0,4,4: 83:[43, 117] Operation: 65+52=117 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 83:[65, 95], Operations: ['60-8=52', '43+52=95'] Exploring Operation: 65*95=6175, Resulting Numbers: [6175] 6175,83 unequal: No Solution Exploring Operation: 95-65=30, Resulting Numbers: [30] 30,83 unequal: No Solution Exploring Operation: 65+95=160, Resulting Numbers: [160] 160,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 83:[52, 108], Operations: ['60-8=52', '65+43=108'] Exploring Operation: 52*108=5616, Resulting Numbers: [5616] 5616,83 unequal: No Solution Exploring Operation: 108-52=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 52+108=160, Resulting Numbers: [160] 160,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 83:[43, 117], Operations: ['60-8=52', '65+52=117'] Exploring Operation: 117-43=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 43+117=160, Resulting Numbers: [160] 160,83 unequal: No Solution Exploring Operation: 43*117=5031, Resulting Numbers: [5031] 5031,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 83:[52, 22], Operations: ['60-8=52', '65-43=22'] Exploring Operation: 52*22=1144, Resulting Numbers: [1144] 1144,83 unequal: No Solution Exploring Operation: 52+22=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 52-22=30, Resulting Numbers: [30] 30,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 83:[65, 9], Operations: ['60-8=52', '52-43=9'] Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,83 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,83 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 4, 84, 43, 23 ]
41
[ "84/4=21", "43-23=20", "21+20=41" ]
Current State: 41:[4, 84, 43, 23], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [43, 23, 21] Generated Node #2: [43, 23, 21] from Operation: 84/4=21 Current State: 41:[43, 23, 21], Operations: ['84/4=21'] Exploring Operation: 43-23=20, Resulting Numbers: [21, 20] Generated Node #3: [21, 20] from Operation: 43-23=20 Current State: 41:[21, 20], Operations: ['84/4=21', '43-23=20'] Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[4, 84, 43, 23], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [84, 43, 27] Generated Node #0,0: 41:[84, 43, 27] Operation: 4+23=27 Exploring Operation: 84-43=41, Resulting Numbers: [4, 23, 41] Generated Node #0,1: 41:[4, 23, 41] Operation: 84-43=41 Exploring Operation: 84-4=80, Resulting Numbers: [43, 23, 80] Generated Node #0,2: 41:[43, 23, 80] Operation: 84-4=80 Exploring Operation: 84/4=21, Resulting Numbers: [43, 23, 21] Generated Node #0,3: 41:[43, 23, 21] Operation: 84/4=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[43, 23, 21], Operations: ['84/4=21'] Exploring Operation: 43+21=64, Resulting Numbers: [23, 64] Generated Node #0,3,0: 41:[23, 64] Operation: 43+21=64 Exploring Operation: 43-23=20, Resulting Numbers: [21, 20] Generated Node #0,3,1: 41:[21, 20] Operation: 43-23=20 Exploring Operation: 43-21=22, Resulting Numbers: [23, 22] Generated Node #0,3,2: 41:[23, 22] Operation: 43-21=22 Exploring Operation: 23+21=44, Resulting Numbers: [43, 44] Generated Node #0,3,3: 41:[43, 44] Operation: 23+21=44 Moving to Node #0,3,3 Current State: 41:[43, 44], Operations: ['84/4=21', '23+21=44'] Exploring Operation: 43*44=1892, Resulting Numbers: [1892] 1892,41 unequal: No Solution Exploring Operation: 43+44=87, Resulting Numbers: [87] 87,41 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[23, 22], Operations: ['84/4=21', '43-21=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,41 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[21, 20], Operations: ['84/4=21', '43-23=20'] Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[4, 84, 43, 23], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [43, 23, 21] Generated Node #0,3: 41:[43, 23, 21] Operation: 84/4=21 Moving to Node #0,3 Current State: 41:[43, 23, 21], Operations: ['84/4=21'] Exploring Operation: 43-23=20, Resulting Numbers: [21, 20] Generated Node #0,3,1: 41:[21, 20] Operation: 43-23=20 Moving to Node #0,3,1 Current State: 41:[21, 20], Operations: ['84/4=21', '43-23=20'] Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 51, 98, 92, 43 ]
100
[ "51+98=149", "92-43=49", "149-49=100" ]
Current State: 100:[51, 98, 92, 43], Operations: [] Exploring Operation: 51+98=149, Resulting Numbers: [92, 43, 149] Generated Node #2: [92, 43, 149] from Operation: 51+98=149 Current State: 100:[92, 43, 149], Operations: ['51+98=149'] Exploring Operation: 92-43=49, Resulting Numbers: [149, 49] Generated Node #3: [149, 49] from Operation: 92-43=49 Current State: 100:[149, 49], Operations: ['51+98=149', '92-43=49'] Exploring Operation: 149-49=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[51, 98, 92, 43], Operations: [] Exploring Operation: 92-43=49, Resulting Numbers: [51, 98, 49] Generated Node #0,0: 100:[51, 98, 49] Operation: 92-43=49 Exploring Operation: 98-92=6, Resulting Numbers: [51, 43, 6] Generated Node #0,1: 100:[51, 43, 6] Operation: 98-92=6 Exploring Operation: 51-43=8, Resulting Numbers: [98, 92, 8] Generated Node #0,2: 100:[98, 92, 8] Operation: 51-43=8 Moving to Node #0,0 Current State: 100:[51, 98, 49], Operations: ['92-43=49'] Exploring Operation: 98/49=2, Resulting Numbers: [51, 2] Generated Node #0,0,0: 100:[51, 2] Operation: 98/49=2 Exploring Operation: 51+49=100, Resulting Numbers: [98, 100] Generated Node #0,0,1: 100:[98, 100] Operation: 51+49=100 Exploring Operation: 51-49=2, Resulting Numbers: [98, 2] Generated Node #0,0,2: 100:[98, 2] Operation: 51-49=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[51, 2], Operations: ['92-43=49', '98/49=2'] Exploring Operation: 51*2=102, Resulting Numbers: [102] 102,100 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,100 unequal: No Solution Exploring Operation: 51+2=53, Resulting Numbers: [53] 53,100 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:[98, 100], Operations: ['92-43=49', '51+49=100'] Exploring Operation: 98*100=9800, Resulting Numbers: [9800] 9800,100 unequal: No Solution Exploring Operation: 100-98=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 98+100=198, Resulting Numbers: [198] 198,100 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:[98, 2], Operations: ['92-43=49', '51-49=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[51, 98, 92, 43], Operations: [] Exploring Operation: 92-43=49, Resulting Numbers: [51, 98, 49] Generated Node #0,0: 100:[51, 98, 49] Operation: 92-43=49 Moving to Node #0,0 Current State: 100:[51, 98, 49], Operations: ['92-43=49'] Exploring Operation: 51-49=2, Resulting Numbers: [98, 2] Generated Node #0,0,2: 100:[98, 2] Operation: 51-49=2 Moving to Node #0,0,2 Current State: 100:[98, 2], Operations: ['92-43=49', '51-49=2'] Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 42, 94, 85, 57 ]
17
[ "94-42=52", "57-52=5", "85/5=17" ]
Current State: 17:[42, 94, 85, 57], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [85, 57, 52] Generated Node #2: [85, 57, 52] from Operation: 94-42=52 Current State: 17:[85, 57, 52], Operations: ['94-42=52'] Exploring Operation: 57-52=5, Resulting Numbers: [85, 5] Generated Node #3: [85, 5] from Operation: 57-52=5 Current State: 17:[85, 5], Operations: ['94-42=52', '57-52=5'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[42, 94, 85, 57], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [42, 57, 9] Generated Node #0,0: 17:[42, 57, 9] Operation: 94-85=9 Exploring Operation: 85-57=28, Resulting Numbers: [42, 94, 28] Generated Node #0,1: 17:[42, 94, 28] Operation: 85-57=28 Exploring Operation: 94-57=37, Resulting Numbers: [42, 85, 37] Generated Node #0,2: 17:[42, 85, 37] Operation: 94-57=37 Moving to Node #0,0 Current State: 17:[42, 57, 9], Operations: ['94-85=9'] Exploring Operation: 57-9=48, Resulting Numbers: [42, 48] Generated Node #0,0,0: 17:[42, 48] Operation: 57-9=48 Exploring Operation: 57-42=15, Resulting Numbers: [9, 15] Generated Node #0,0,1: 17:[9, 15] Operation: 57-42=15 Exploring Operation: 42-9=33, Resulting Numbers: [57, 33] Generated Node #0,0,2: 17:[57, 33] Operation: 42-9=33 Moving to Node #0,1 Current State: 17:[42, 94, 28], Operations: ['85-57=28'] Exploring Operation: 94-28=66, Resulting Numbers: [42, 66] Generated Node #0,1,0: 17:[42, 66] Operation: 94-28=66 Exploring Operation: 42-28=14, Resulting Numbers: [94, 14] Generated Node #0,1,1: 17:[94, 14] Operation: 42-28=14 Exploring Operation: 94-42=52, Resulting Numbers: [28, 52] Generated Node #0,1,2: 17:[28, 52] Operation: 94-42=52 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 17:[28, 52], Operations: ['85-57=28', '94-42=52'] Exploring Operation: 28+52=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 28*52=1456, Resulting Numbers: [1456] 1456,17 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[42, 66], Operations: ['85-57=28', '94-28=66'] Exploring Operation: 66-42=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 42*66=2772, Resulting Numbers: [2772] 2772,17 unequal: No Solution Exploring Operation: 42+66=108, Resulting Numbers: [108] 108,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[94, 14], Operations: ['85-57=28', '42-28=14'] Exploring Operation: 94+14=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 94*14=1316, Resulting Numbers: [1316] 1316,17 unequal: No Solution Exploring Operation: 94-14=80, Resulting Numbers: [80] 80,17 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: 17:[42, 85, 37], Operations: ['94-57=37'] Exploring Operation: 42-37=5, Resulting Numbers: [85, 5] Generated Node #0,2,0: 17:[85, 5] Operation: 42-37=5 Exploring Operation: 85-42=43, Resulting Numbers: [37, 43] Generated Node #0,2,1: 17:[37, 43] Operation: 85-42=43 Exploring Operation: 85-37=48, Resulting Numbers: [42, 48] Generated Node #0,2,2: 17:[42, 48] Operation: 85-37=48 Moving to Node #0,0,1 Current State: 17:[9, 15], Operations: ['94-85=9', '57-42=15'] Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,17 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[37, 43], Operations: ['94-57=37', '85-42=43'] Exploring Operation: 37*43=1591, Resulting Numbers: [1591] 1591,17 unequal: No Solution Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[57, 33], Operations: ['94-85=9', '42-9=33'] Exploring Operation: 57-33=24, Resulting Numbers: [24] 24,17 unequal: No Solution Exploring Operation: 57*33=1881, Resulting Numbers: [1881] 1881,17 unequal: No Solution Exploring Operation: 57+33=90, Resulting Numbers: [90] 90,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[42, 48], Operations: ['94-57=37', '85-37=48'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,17 unequal: No Solution Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[42, 48], Operations: ['94-85=9', '57-9=48'] Exploring Operation: 42*48=2016, Resulting Numbers: [2016] 2016,17 unequal: No Solution Exploring Operation: 42+48=90, Resulting Numbers: [90] 90,17 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[85, 5], Operations: ['94-57=37', '42-37=5'] Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,17 unequal: No Solution Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,17 unequal: No Solution Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[42, 94, 85, 57], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [42, 85, 37] Generated Node #0,2: 17:[42, 85, 37] Operation: 94-57=37 Moving to Node #0,2 Current State: 17:[42, 85, 37], Operations: ['94-57=37'] Exploring Operation: 42-37=5, Resulting Numbers: [85, 5] Generated Node #0,2,0: 17:[85, 5] Operation: 42-37=5 Moving to Node #0,2,0 Current State: 17:[85, 5], Operations: ['94-57=37', '42-37=5'] Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.962674
hs_3
sum_heuristic
[ 34, 6, 9, 64 ]
86
[ "34-9=25", "6*25=150", "150-64=86" ]
Current State: 86:[34, 6, 9, 64], Operations: [] Exploring Operation: 34-9=25, Resulting Numbers: [6, 64, 25] Generated Node #2: [6, 64, 25] from Operation: 34-9=25 Current State: 86:[6, 64, 25], Operations: ['34-9=25'] Exploring Operation: 6*25=150, Resulting Numbers: [64, 150] Generated Node #3: [64, 150] from Operation: 6*25=150 Current State: 86:[64, 150], Operations: ['34-9=25', '6*25=150'] Exploring Operation: 150-64=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[34, 6, 9, 64], Operations: [] Exploring Operation: 34+64=98, Resulting Numbers: [6, 9, 98] Generated Node #0,0: 86:[6, 9, 98] Operation: 34+64=98 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[6, 9, 98], Operations: ['34+64=98'] Exploring Operation: 98-9=89, Resulting Numbers: [6, 89] Generated Node #0,0,0: 86:[6, 89] Operation: 98-9=89 Moving to Node #0,0,0 Current State: 86:[6, 89], Operations: ['34+64=98', '98-9=89'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,86 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
[ 2, 44, 47, 26 ]
56
[ "44-26=18", "18/2=9", "47+9=56" ]
Current State: 56:[2, 44, 47, 26], Operations: [] Exploring Operation: 44-26=18, Resulting Numbers: [2, 47, 18] Generated Node #2: [2, 47, 18] from Operation: 44-26=18 Current State: 56:[2, 47, 18], Operations: ['44-26=18'] Exploring Operation: 18/2=9, Resulting Numbers: [47, 9] Generated Node #3: [47, 9] from Operation: 18/2=9 Current State: 56:[47, 9], Operations: ['44-26=18', '18/2=9'] Exploring Operation: 47+9=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[2, 44, 47, 26], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [2, 26, 3] Generated Node #0,0: 56:[2, 26, 3] Operation: 47-44=3 Exploring Operation: 44-26=18, Resulting Numbers: [2, 47, 18] Generated Node #0,1: 56:[2, 47, 18] Operation: 44-26=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[2, 26, 3], Operations: ['47-44=3'] Exploring Operation: 2+26=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 56:[3, 28] Operation: 2+26=28 Exploring Operation: 26+3=29, Resulting Numbers: [2, 29] Generated Node #0,0,1: 56:[2, 29] Operation: 26+3=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[3, 28], Operations: ['47-44=3', '2+26=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,56 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 56:[2, 29], Operations: ['47-44=3', '26+3=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,56 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:[2, 47, 18], Operations: ['44-26=18'] Exploring Operation: 47+18=65, Resulting Numbers: [2, 65] Generated Node #0,1,0: 56:[2, 65] Operation: 47+18=65 Exploring Operation: 47-18=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 56:[2, 29] Operation: 47-18=29 Moving to Node #0,1,1 Current State: 56:[2, 29], Operations: ['44-26=18', '47-18=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,56 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,56 unequal: No Solution Moving to Node #0,1,0 Current State: 56:[2, 65], Operations: ['44-26=18', '47+18=65'] Exploring Operation: 2+65=67, Resulting Numbers: [67] 67,56 unequal: No Solution Exploring Operation: 65-2=63, Resulting Numbers: [63] 63,56 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