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
[ 18, 22, 12, 96 ]
41
[ "18*22=396", "96+396=492", "492/12=41" ]
Current State: 41:[18, 22, 12, 96], Operations: [] Exploring Operation: 18*22=396, Resulting Numbers: [12, 96, 396] Generated Node #2: [12, 96, 396] from Operation: 18*22=396 Current State: 41:[12, 96, 396], Operations: ['18*22=396'] Exploring Operation: 96+396=492, Resulting Numbers: [12, 492] Generated Node #3: [12, 492] from Operation: 96+396=492 Current State: 41:[12, 492], Operations: ['18*22=396', '96+396=492'] Exploring Operation: 492/12=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[18, 22, 12, 96], Operations: [] Exploring Operation: 96/12=8, Resulting Numbers: [18, 22, 8] Generated Node #0,0: 41:[18, 22, 8] Operation: 96/12=8 Exploring Operation: 96-18=78, Resulting Numbers: [22, 12, 78] Generated Node #0,1: 41:[22, 12, 78] Operation: 96-18=78 Exploring Operation: 18+22=40, Resulting Numbers: [12, 96, 40] Generated Node #0,2: 41:[12, 96, 40] Operation: 18+22=40 Exploring Operation: 18+12=30, Resulting Numbers: [22, 96, 30] Generated Node #0,3: 41:[22, 96, 30] Operation: 18+12=30 Exploring Operation: 22+12=34, Resulting Numbers: [18, 96, 34] Generated Node #0,4: 41:[18, 96, 34] Operation: 22+12=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[18, 22, 8], Operations: ['96/12=8'] Exploring Operation: 22-8=14, Resulting Numbers: [18, 14] Generated Node #0,0,0: 41:[18, 14] Operation: 22-8=14 Exploring Operation: 18-8=10, Resulting Numbers: [22, 10] Generated Node #0,0,1: 41:[22, 10] Operation: 18-8=10 Exploring Operation: 22+8=30, Resulting Numbers: [18, 30] Generated Node #0,0,2: 41:[18, 30] Operation: 22+8=30 Exploring Operation: 18+8=26, Resulting Numbers: [22, 26] Generated Node #0,0,3: 41:[22, 26] Operation: 18+8=26 Exploring Operation: 18+22=40, Resulting Numbers: [8, 40] Generated Node #0,0,4: 41:[8, 40] Operation: 18+22=40 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[18, 30], Operations: ['96/12=8', '22+8=30'] Exploring Operation: 18*30=540, Resulting Numbers: [540] 540,41 unequal: No Solution Exploring Operation: 18+30=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 30-18=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:[22, 26], Operations: ['96/12=8', '18+8=26'] Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 22*26=572, Resulting Numbers: [572] 572,41 unequal: No Solution Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,41 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 #0,0,4 Current State: 41:[8, 40], Operations: ['96/12=8', '18+22=40'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,41 unequal: No Solution Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,41 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,41 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:[18, 14], Operations: ['96/12=8', '22-8=14'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,41 unequal: No Solution Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,41 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:[22, 10], Operations: ['96/12=8', '18-8=10'] Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,41 unequal: No Solution Exploring Operation: 22+10=32, Resulting Numbers: [32] 32,41 unequal: No Solution Exploring Operation: 22*10=220, Resulting Numbers: [220] 220,41 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:[22, 12, 78], Operations: ['96-18=78'] Exploring Operation: 22+12=34, Resulting Numbers: [78, 34] Generated Node #0,1,0: 41:[78, 34] Operation: 22+12=34 Exploring Operation: 22-12=10, Resulting Numbers: [78, 10] Generated Node #0,1,1: 41:[78, 10] Operation: 22-12=10 Exploring Operation: 78-22=56, Resulting Numbers: [12, 56] Generated Node #0,1,2: 41:[12, 56] Operation: 78-22=56 Exploring Operation: 78-12=66, Resulting Numbers: [22, 66] Generated Node #0,1,3: 41:[22, 66] Operation: 78-12=66 Exploring Operation: 12+78=90, Resulting Numbers: [22, 90] Generated Node #0,1,4: 41:[22, 90] Operation: 12+78=90 Moving to Node #0,1,0 Current State: 41:[78, 34], Operations: ['96-18=78', '22+12=34'] Exploring Operation: 78-34=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 78+34=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 78*34=2652, Resulting Numbers: [2652] 2652,41 unequal: No Solution Moving to Node #0,1,3 Current State: 41:[22, 66], Operations: ['96-18=78', '78-12=66'] Exploring Operation: 22*66=1452, Resulting Numbers: [1452] 1452,41 unequal: No Solution Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 22+66=88, Resulting Numbers: [88] 88,41 unequal: No Solution Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[12, 56], Operations: ['96-18=78', '78-22=56'] Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 12*56=672, Resulting Numbers: [672] 672,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[78, 10], Operations: ['96-18=78', '22-12=10'] Exploring Operation: 78*10=780, Resulting Numbers: [780] 780,41 unequal: No Solution Exploring Operation: 78+10=88, Resulting Numbers: [88] 88,41 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,41 unequal: No Solution Moving to Node #0,1,4 Current State: 41:[22, 90], Operations: ['96-18=78', '12+78=90'] Exploring Operation: 22*90=1980, Resulting Numbers: [1980] 1980,41 unequal: No Solution Exploring Operation: 90-22=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 22+90=112, Resulting Numbers: [112] 112,41 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 #0,2 Current State: 41:[12, 96, 40], Operations: ['18+22=40'] Exploring Operation: 96-40=56, Resulting Numbers: [12, 56] Generated Node #0,2,0: 41:[12, 56] Operation: 96-40=56 Exploring Operation: 12+40=52, Resulting Numbers: [96, 52] Generated Node #0,2,1: 41:[96, 52] Operation: 12+40=52 Exploring Operation: 96/12=8, Resulting Numbers: [40, 8] Generated Node #0,2,2: 41:[40, 8] Operation: 96/12=8 Exploring Operation: 12+96=108, Resulting Numbers: [40, 108] Generated Node #0,2,3: 41:[40, 108] Operation: 12+96=108 Exploring Operation: 96-12=84, Resulting Numbers: [40, 84] Generated Node #0,2,4: 41:[40, 84] Operation: 96-12=84 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[40, 8], Operations: ['18+22=40', '96/12=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,41 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,41 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 41:[12, 56], Operations: ['18+22=40', '96-40=56'] Exploring Operation: 12+56=68, Resulting Numbers: [68] 68,41 unequal: No Solution Exploring Operation: 56-12=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 12*56=672, Resulting Numbers: [672] 672,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 41:[40, 84], Operations: ['18+22=40', '96-12=84'] Exploring Operation: 84-40=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 40+84=124, Resulting Numbers: [124] 124,41 unequal: No Solution Exploring Operation: 40*84=3360, Resulting Numbers: [3360] 3360,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 41:[96, 52], Operations: ['18+22=40', '12+40=52'] Exploring Operation: 96+52=148, Resulting Numbers: [148] 148,41 unequal: No Solution Exploring Operation: 96*52=4992, Resulting Numbers: [4992] 4992,41 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 41:[40, 108], Operations: ['18+22=40', '12+96=108'] Exploring Operation: 40*108=4320, Resulting Numbers: [4320] 4320,41 unequal: No Solution Exploring Operation: 40+108=148, Resulting Numbers: [148] 148,41 unequal: No Solution Exploring Operation: 108-40=68, Resulting Numbers: [68] 68,41 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 #0,3 Current State: 41:[22, 96, 30], Operations: ['18+12=30'] Exploring Operation: 30-22=8, Resulting Numbers: [96, 8] Generated Node #0,3,0: 41:[96, 8] Operation: 30-22=8 Exploring Operation: 96-22=74, Resulting Numbers: [30, 74] Generated Node #0,3,1: 41:[30, 74] Operation: 96-22=74 Exploring Operation: 96-30=66, Resulting Numbers: [22, 66] Generated Node #0,3,2: 41:[22, 66] Operation: 96-30=66 Exploring Operation: 22+96=118, Resulting Numbers: [30, 118] Generated Node #0,3,3: 41:[30, 118] Operation: 22+96=118 Exploring Operation: 22+30=52, Resulting Numbers: [96, 52] Generated Node #0,3,4: 41:[96, 52] Operation: 22+30=52 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 41:[30, 74], Operations: ['18+12=30', '96-22=74'] Exploring Operation: 30*74=2220, Resulting Numbers: [2220] 2220,41 unequal: No Solution Exploring Operation: 74-30=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 30+74=104, Resulting Numbers: [104] 104,41 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:[22, 66], Operations: ['18+12=30', '96-30=66'] Exploring Operation: 66/22=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 22+66=88, Resulting Numbers: [88] 88,41 unequal: No Solution Exploring Operation: 22*66=1452, Resulting Numbers: [1452] 1452,41 unequal: No Solution Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,41 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 #0,3,4 Current State: 41:[96, 52], Operations: ['18+12=30', '22+30=52'] Exploring Operation: 96*52=4992, Resulting Numbers: [4992] 4992,41 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 96+52=148, Resulting Numbers: [148] 148,41 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:[96, 8], Operations: ['18+12=30', '30-22=8'] Exploring Operation: 96-8=88, Resulting Numbers: [88] 88,41 unequal: No Solution Exploring Operation: 96+8=104, Resulting Numbers: [104] 104,41 unequal: No Solution Exploring Operation: 96*8=768, Resulting Numbers: [768] 768,41 unequal: No Solution Exploring Operation: 96/8=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 #0,3,3 Current State: 41:[30, 118], Operations: ['18+12=30', '22+96=118'] Exploring Operation: 30*118=3540, Resulting Numbers: [3540] 3540,41 unequal: No Solution Exploring Operation: 118-30=88, Resulting Numbers: [88] 88,41 unequal: No Solution Exploring Operation: 30+118=148, Resulting Numbers: [148] 148,41 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:[18, 96, 34], Operations: ['22+12=34'] Exploring Operation: 34-18=16, Resulting Numbers: [96, 16] Generated Node #0,4,0: 41:[96, 16] Operation: 34-18=16 Exploring Operation: 96-18=78, Resulting Numbers: [34, 78] Generated Node #0,4,1: 41:[34, 78] Operation: 96-18=78 Exploring Operation: 96-34=62, Resulting Numbers: [18, 62] Generated Node #0,4,2: 41:[18, 62] Operation: 96-34=62 Exploring Operation: 18+34=52, Resulting Numbers: [96, 52] Generated Node #0,4,3: 41:[96, 52] Operation: 18+34=52 Exploring Operation: 18+96=114, Resulting Numbers: [34, 114] Generated Node #0,4,4: 41:[34, 114] Operation: 18+96=114 Moving to Node #0,4,1 Current State: 41:[34, 78], Operations: ['22+12=34', '96-18=78'] Exploring Operation: 78-34=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 34+78=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 34*78=2652, Resulting Numbers: [2652] 2652,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[18, 62], Operations: ['22+12=34', '96-34=62'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,41 unequal: No Solution Exploring Operation: 18+62=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 18*62=1116, Resulting Numbers: [1116] 1116,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[96, 52], Operations: ['22+12=34', '18+34=52'] Exploring Operation: 96+52=148, Resulting Numbers: [148] 148,41 unequal: No Solution Exploring Operation: 96*52=4992, Resulting Numbers: [4992] 4992,41 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,41 unequal: No Solution Moving to Node #0,4,0 Current State: 41:[96, 16], Operations: ['22+12=34', '34-18=16'] Exploring Operation: 96*16=1536, Resulting Numbers: [1536] 1536,41 unequal: No Solution Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 96/16=6, Resulting Numbers: [6] 6,41 unequal: No Solution Exploring Operation: 96+16=112, Resulting Numbers: [112] 112,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[34, 114], Operations: ['22+12=34', '18+96=114'] Exploring Operation: 114-34=80, Resulting Numbers: [80] 80,41 unequal: No Solution Exploring Operation: 34*114=3876, Resulting Numbers: [3876] 3876,41 unequal: No Solution Exploring Operation: 34+114=148, Resulting Numbers: [148] 148,41 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
[ 24, 41, 1, 49 ]
33
[ "41-24=17", "1+49=50", "50-17=33" ]
Current State: 33:[24, 41, 1, 49], Operations: [] Exploring Operation: 41-24=17, Resulting Numbers: [1, 49, 17] Generated Node #2: [1, 49, 17] from Operation: 41-24=17 Current State: 33:[1, 49, 17], Operations: ['41-24=17'] Exploring Operation: 1+49=50, Resulting Numbers: [17, 50] Generated Node #3: [17, 50] from Operation: 1+49=50 Current State: 33:[17, 50], Operations: ['41-24=17', '1+49=50'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[24, 41, 1, 49], Operations: [] Exploring Operation: 49-24=25, Resulting Numbers: [41, 1, 25] Generated Node #0,0: 33:[41, 1, 25] Operation: 49-24=25 Exploring Operation: 49-41=8, Resulting Numbers: [24, 1, 8] Generated Node #0,1: 33:[24, 1, 8] Operation: 49-41=8 Exploring Operation: 41-24=17, Resulting Numbers: [1, 49, 17] Generated Node #0,2: 33:[1, 49, 17] Operation: 41-24=17 Moving to Node #0,1 Current State: 33:[24, 1, 8], Operations: ['49-41=8'] Exploring Operation: 24-8=16, Resulting Numbers: [1, 16] Generated Node #0,1,0: 33:[1, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [1, 3] Generated Node #0,1,1: 33:[1, 3] Operation: 24/8=3 Exploring Operation: 24+8=32, Resulting Numbers: [1, 32] Generated Node #0,1,2: 33:[1, 32] Operation: 24+8=32 Moving to Node #0,0 Current State: 33:[41, 1, 25], Operations: ['49-24=25'] Exploring Operation: 41-1=40, Resulting Numbers: [25, 40] Generated Node #0,0,0: 33:[25, 40] Operation: 41-1=40 Exploring Operation: 1+25=26, Resulting Numbers: [41, 26] Generated Node #0,0,1: 33:[41, 26] Operation: 1+25=26 Exploring Operation: 41-25=16, Resulting Numbers: [1, 16] Generated Node #0,0,2: 33:[1, 16] Operation: 41-25=16 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 33:[1, 16], Operations: ['49-24=25', '41-25=16'] Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,33 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[25, 40], Operations: ['49-24=25', '41-1=40'] Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,33 unequal: No Solution Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[41, 26], Operations: ['49-24=25', '1+25=26'] Exploring Operation: 41*26=1066, Resulting Numbers: [1066] 1066,33 unequal: No Solution Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,33 unequal: No Solution Exploring Operation: 41+26=67, Resulting Numbers: [67] 67,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 33:[1, 49, 17], Operations: ['41-24=17'] Exploring Operation: 49-1=48, Resulting Numbers: [17, 48] Generated Node #0,2,0: 33:[17, 48] Operation: 49-1=48 Exploring Operation: 17-1=16, Resulting Numbers: [49, 16] Generated Node #0,2,1: 33:[49, 16] Operation: 17-1=16 Exploring Operation: 49-17=32, Resulting Numbers: [1, 32] Generated Node #0,2,2: 33:[1, 32] Operation: 49-17=32 Moving to Node #0,1,1 Current State: 33:[1, 3], Operations: ['49-41=8', '24/8=3'] Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,33 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,33 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[1, 32], Operations: ['49-41=8', '24+8=32'] Exploring Operation: 1*32=32, Resulting Numbers: [32] 32,33 unequal: No Solution Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[24, 41, 1, 49], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [24, 1, 8] Generated Node #0,1: 33:[24, 1, 8] Operation: 49-41=8 Moving to Node #0,1 Current State: 33:[24, 1, 8], Operations: ['49-41=8'] Exploring Operation: 24+8=32, Resulting Numbers: [1, 32] Generated Node #0,1,2: 33:[1, 32] Operation: 24+8=32 Moving to Node #0,1,2 Current State: 33:[1, 32], Operations: ['49-41=8', '24+8=32'] Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.973958
hs_3
sum_heuristic
[ 83, 38, 19, 55 ]
57
[ "83*38=3154", "3154-19=3135", "3135/55=57" ]
Current State: 57:[83, 38, 19, 55], Operations: [] Exploring Operation: 83*38=3154, Resulting Numbers: [19, 55, 3154] Generated Node #2: [19, 55, 3154] from Operation: 83*38=3154 Current State: 57:[19, 55, 3154], Operations: ['83*38=3154'] Exploring Operation: 3154-19=3135, Resulting Numbers: [55, 3135] Generated Node #3: [55, 3135] from Operation: 3154-19=3135 Current State: 57:[55, 3135], Operations: ['83*38=3154', '3154-19=3135'] Exploring Operation: 3135/55=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[83, 38, 19, 55], Operations: [] Exploring Operation: 83-38=45, Resulting Numbers: [19, 55, 45] Generated Node #0,0: 57:[19, 55, 45] Operation: 83-38=45 Exploring Operation: 83-55=28, Resulting Numbers: [38, 19, 28] Generated Node #0,1: 57:[38, 19, 28] Operation: 83-55=28 Exploring Operation: 83-19=64, Resulting Numbers: [38, 55, 64] Generated Node #0,2: 57:[38, 55, 64] Operation: 83-19=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[19, 55, 45], Operations: ['83-38=45'] Exploring Operation: 45-19=26, Resulting Numbers: [55, 26] Generated Node #0,0,0: 57:[55, 26] Operation: 45-19=26 Exploring Operation: 55-45=10, Resulting Numbers: [19, 10] Generated Node #0,0,1: 57:[19, 10] Operation: 55-45=10 Exploring Operation: 19+45=64, Resulting Numbers: [55, 64] Generated Node #0,0,2: 57:[55, 64] Operation: 19+45=64 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[19, 10], Operations: ['83-38=45', '55-45=10'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,57 unequal: No Solution No 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: 57:[55, 26], Operations: ['83-38=45', '45-19=26'] Exploring Operation: 55*26=1430, Resulting Numbers: [1430] 1430,57 unequal: No Solution Exploring Operation: 55+26=81, Resulting Numbers: [81] 81,57 unequal: No Solution Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,57 unequal: No Solution No 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: 57:[55, 64], Operations: ['83-38=45', '19+45=64'] Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,57 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,57 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[38, 19, 28], Operations: ['83-55=28'] Exploring Operation: 38-19=19, Resulting Numbers: [28, 19] Generated Node #0,1,0: 57:[28, 19] Operation: 38-19=19 Exploring Operation: 38+19=57, Resulting Numbers: [28, 57] Generated Node #0,1,1: 57:[28, 57] Operation: 38+19=57 Exploring Operation: 38-28=10, Resulting Numbers: [19, 10] Generated Node #0,1,2: 57:[19, 10] Operation: 38-28=10 Moving to Node #0,1,2 Current State: 57:[19, 10], Operations: ['83-55=28', '38-28=10'] Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[28, 19], Operations: ['83-55=28', '38-19=19'] Exploring Operation: 28+19=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,57 unequal: No Solution Exploring Operation: 28*19=532, Resulting Numbers: [532] 532,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[28, 57], Operations: ['83-55=28', '38+19=57'] Exploring Operation: 28+57=85, Resulting Numbers: [85] 85,57 unequal: No Solution Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 28*57=1596, Resulting Numbers: [1596] 1596,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[38, 55, 64], Operations: ['83-19=64'] Exploring Operation: 64-38=26, Resulting Numbers: [55, 26] Generated Node #0,2,0: 57:[55, 26] Operation: 64-38=26 Exploring Operation: 55-38=17, Resulting Numbers: [64, 17] Generated Node #0,2,1: 57:[64, 17] Operation: 55-38=17 Exploring Operation: 64-55=9, Resulting Numbers: [38, 9] Generated Node #0,2,2: 57:[38, 9] Operation: 64-55=9 Moving to Node #0,2,0 Current State: 57:[55, 26], Operations: ['83-19=64', '64-38=26'] Exploring Operation: 55-26=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 55*26=1430, Resulting Numbers: [1430] 1430,57 unequal: No Solution Exploring Operation: 55+26=81, Resulting Numbers: [81] 81,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[64, 17], Operations: ['83-19=64', '55-38=17'] Exploring Operation: 64*17=1088, Resulting Numbers: [1088] 1088,57 unequal: No Solution Exploring Operation: 64-17=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[38, 9], Operations: ['83-19=64', '64-55=9'] Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,57 unequal: No Solution Exploring Operation: 38*9=342, Resulting Numbers: [342] 342,57 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
[ 51, 11, 31, 44 ]
24
[ "51-31=20", "44/11=4", "20+4=24" ]
Current State: 24:[51, 11, 31, 44], Operations: [] Exploring Operation: 51-31=20, Resulting Numbers: [11, 44, 20] Generated Node #2: [11, 44, 20] from Operation: 51-31=20 Current State: 24:[11, 44, 20], Operations: ['51-31=20'] Exploring Operation: 44/11=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 44/11=4 Current State: 24:[20, 4], Operations: ['51-31=20', '44/11=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[51, 11, 31, 44], Operations: [] Exploring Operation: 51-44=7, Resulting Numbers: [11, 31, 7] Generated Node #0,0: 24:[11, 31, 7] Operation: 51-44=7 Moving to Node #0,0 Current State: 24:[11, 31, 7], Operations: ['51-44=7'] Exploring Operation: 31-7=24, Resulting Numbers: [11, 24] Generated Node #0,0,0: 24:[11, 24] Operation: 31-7=24 Moving to Node #0,0,0 Current State: 24:[11, 24], Operations: ['51-44=7', '31-7=24'] Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,24 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 72, 41, 52, 12 ]
87
[ "72/12=6", "41+52=93", "93-6=87" ]
Current State: 87:[72, 41, 52, 12], Operations: [] Exploring Operation: 72/12=6, Resulting Numbers: [41, 52, 6] Generated Node #2: [41, 52, 6] from Operation: 72/12=6 Current State: 87:[41, 52, 6], Operations: ['72/12=6'] Exploring Operation: 41+52=93, Resulting Numbers: [6, 93] Generated Node #3: [6, 93] from Operation: 41+52=93 Current State: 87:[6, 93], Operations: ['72/12=6', '41+52=93'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[72, 41, 52, 12], Operations: [] Exploring Operation: 41+52=93, Resulting Numbers: [72, 12, 93] Generated Node #0,0: 87:[72, 12, 93] Operation: 41+52=93 Exploring Operation: 72-52=20, Resulting Numbers: [41, 12, 20] Generated Node #0,1: 87:[41, 12, 20] Operation: 72-52=20 Exploring Operation: 52-41=11, Resulting Numbers: [72, 12, 11] Generated Node #0,2: 87:[72, 12, 11] Operation: 52-41=11 Exploring Operation: 72-41=31, Resulting Numbers: [52, 12, 31] Generated Node #0,3: 87:[52, 12, 31] Operation: 72-41=31 Moving to Node #0,0 Current State: 87:[72, 12, 93], Operations: ['41+52=93'] Exploring Operation: 93-12=81, Resulting Numbers: [72, 81] Generated Node #0,0,0: 87:[72, 81] Operation: 93-12=81 Exploring Operation: 72/12=6, Resulting Numbers: [93, 6] Generated Node #0,0,1: 87:[93, 6] Operation: 72/12=6 Exploring Operation: 93-72=21, Resulting Numbers: [12, 21] Generated Node #0,0,2: 87:[12, 21] Operation: 93-72=21 Exploring Operation: 72+12=84, Resulting Numbers: [93, 84] Generated Node #0,0,3: 87:[93, 84] Operation: 72+12=84 Moving to Node #0,1 Current State: 87:[41, 12, 20], Operations: ['72-52=20'] Exploring Operation: 20-12=8, Resulting Numbers: [41, 8] Generated Node #0,1,0: 87:[41, 8] Operation: 20-12=8 Exploring Operation: 12+20=32, Resulting Numbers: [41, 32] Generated Node #0,1,1: 87:[41, 32] Operation: 12+20=32 Exploring Operation: 41-20=21, Resulting Numbers: [12, 21] Generated Node #0,1,2: 87:[12, 21] Operation: 41-20=21 Exploring Operation: 41-12=29, Resulting Numbers: [20, 29] Generated Node #0,1,3: 87:[20, 29] Operation: 41-12=29 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 87:[20, 29], Operations: ['72-52=20', '41-12=29'] Exploring Operation: 29-20=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 20+29=49, Resulting Numbers: [49] 49,87 unequal: No Solution Exploring Operation: 20*29=580, Resulting Numbers: [580] 580,87 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 #0,1,1 Current State: 87:[41, 32], Operations: ['72-52=20', '12+20=32'] Exploring Operation: 41*32=1312, Resulting Numbers: [1312] 1312,87 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 41+32=73, Resulting Numbers: [73] 73,87 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 #0,1,0 Current State: 87:[41, 8], Operations: ['72-52=20', '20-12=8'] Exploring Operation: 41*8=328, Resulting Numbers: [328] 328,87 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 41+8=49, Resulting Numbers: [49] 49,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[12, 21], Operations: ['72-52=20', '41-20=21'] Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,87 unequal: No Solution Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,87 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: 87:[72, 12, 11], Operations: ['52-41=11'] Exploring Operation: 12-11=1, Resulting Numbers: [72, 1] Generated Node #0,2,0: 87:[72, 1] Operation: 12-11=1 Exploring Operation: 72+12=84, Resulting Numbers: [11, 84] Generated Node #0,2,1: 87:[11, 84] Operation: 72+12=84 Exploring Operation: 72/12=6, Resulting Numbers: [11, 6] Generated Node #0,2,2: 87:[11, 6] Operation: 72/12=6 Exploring Operation: 72+11=83, Resulting Numbers: [12, 83] Generated Node #0,2,3: 87:[12, 83] Operation: 72+11=83 Moving to Node #0,3 Current State: 87:[52, 12, 31], Operations: ['72-41=31'] Exploring Operation: 52-12=40, Resulting Numbers: [31, 40] Generated Node #0,3,0: 87:[31, 40] Operation: 52-12=40 Exploring Operation: 52-31=21, Resulting Numbers: [12, 21] Generated Node #0,3,1: 87:[12, 21] Operation: 52-31=21 Exploring Operation: 52+31=83, Resulting Numbers: [12, 83] Generated Node #0,3,2: 87:[12, 83] Operation: 52+31=83 Exploring Operation: 52+12=64, Resulting Numbers: [31, 64] Generated Node #0,3,3: 87:[31, 64] Operation: 52+12=64 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 87:[31, 40], Operations: ['72-41=31', '52-12=40'] Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,87 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,87 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 #0,3,2 Current State: 87:[12, 83], Operations: ['72-41=31', '52+31=83'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 87:[12, 21], Operations: ['72-41=31', '52-31=21'] Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,87 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,87 unequal: No Solution Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 87:[31, 64], Operations: ['72-41=31', '52+12=64'] Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,87 unequal: No Solution Exploring Operation: 31+64=95, Resulting Numbers: [95] 95,87 unequal: No Solution Exploring Operation: 31*64=1984, Resulting Numbers: [1984] 1984,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 87:[93, 6], Operations: ['41+52=93', '72/12=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[72, 41, 52, 12], Operations: [] Exploring Operation: 41+52=93, Resulting Numbers: [72, 12, 93] Generated Node #0,0: 87:[72, 12, 93] Operation: 41+52=93 Moving to Node #0,0 Current State: 87:[72, 12, 93], Operations: ['41+52=93'] Exploring Operation: 72/12=6, Resulting Numbers: [93, 6] Generated Node #0,0,1: 87:[93, 6] Operation: 72/12=6 Moving to Node #0,0,1 Current State: 87:[93, 6], Operations: ['41+52=93', '72/12=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.957465
hs_4
mult_heuristic
[ 69, 28, 83, 56 ]
42
[ "69+28=97", "83+56=139", "139-97=42" ]
Current State: 42:[69, 28, 83, 56], Operations: [] Exploring Operation: 69+28=97, Resulting Numbers: [83, 56, 97] Generated Node #2: [83, 56, 97] from Operation: 69+28=97 Current State: 42:[83, 56, 97], Operations: ['69+28=97'] Exploring Operation: 83+56=139, Resulting Numbers: [97, 139] Generated Node #3: [97, 139] from Operation: 83+56=139 Current State: 42:[97, 139], Operations: ['69+28=97', '83+56=139'] Exploring Operation: 139-97=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[69, 28, 83, 56], Operations: [] Exploring Operation: 83-28=55, Resulting Numbers: [69, 56, 55] Generated Node #0,0: 42:[69, 56, 55] Operation: 83-28=55 Exploring Operation: 83-69=14, Resulting Numbers: [28, 56, 14] Generated Node #0,1: 42:[28, 56, 14] Operation: 83-69=14 Exploring Operation: 69-56=13, Resulting Numbers: [28, 83, 13] Generated Node #0,2: 42:[28, 83, 13] Operation: 69-56=13 Exploring Operation: 83-56=27, Resulting Numbers: [69, 28, 27] Generated Node #0,3: 42:[69, 28, 27] Operation: 83-56=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[28, 56, 14], Operations: ['83-69=14'] Exploring Operation: 56/28=2, Resulting Numbers: [14, 2] Generated Node #0,1,0: 42:[14, 2] Operation: 56/28=2 Exploring Operation: 56-28=28, Resulting Numbers: [14, 28] Generated Node #0,1,1: 42:[14, 28] Operation: 56-28=28 Exploring Operation: 56/14=4, Resulting Numbers: [28, 4] Generated Node #0,1,2: 42:[28, 4] Operation: 56/14=4 Exploring Operation: 56-14=42, Resulting Numbers: [28, 42] Generated Node #0,1,3: 42:[28, 42] Operation: 56-14=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 42:[14, 2], Operations: ['83-69=14', '56/28=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,42 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,42 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 42:[14, 28], Operations: ['83-69=14', '56-28=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,42 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,42 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[69, 28, 83, 56], Operations: [] Exploring Operation: 83-69=14, Resulting Numbers: [28, 56, 14] Generated Node #0,1: 42:[28, 56, 14] Operation: 83-69=14 Moving to Node #0,1 Current State: 42:[28, 56, 14], Operations: ['83-69=14'] Exploring Operation: 56-28=28, Resulting Numbers: [14, 28] Generated Node #0,1,1: 42:[14, 28] Operation: 56-28=28 Moving to Node #0,1,1 Current State: 42:[14, 28], Operations: ['83-69=14', '56-28=28'] Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 5, 18, 37, 86 ]
33
[ "5*18=90", "37+86=123", "123-90=33" ]
Current State: 33:[5, 18, 37, 86], Operations: [] Exploring Operation: 5*18=90, Resulting Numbers: [37, 86, 90] Generated Node #2: [37, 86, 90] from Operation: 5*18=90 Current State: 33:[37, 86, 90], Operations: ['5*18=90'] Exploring Operation: 37+86=123, Resulting Numbers: [90, 123] Generated Node #3: [90, 123] from Operation: 37+86=123 Current State: 33:[90, 123], Operations: ['5*18=90', '37+86=123'] Exploring Operation: 123-90=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[5, 18, 37, 86], Operations: [] Exploring Operation: 18-5=13, Resulting Numbers: [37, 86, 13] Generated Node #0,0: 33:[37, 86, 13] Operation: 18-5=13 Exploring Operation: 86-18=68, Resulting Numbers: [5, 37, 68] Generated Node #0,1: 33:[5, 37, 68] Operation: 86-18=68 Exploring Operation: 86-37=49, Resulting Numbers: [5, 18, 49] Generated Node #0,2: 33:[5, 18, 49] Operation: 86-37=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[5, 18, 49], Operations: ['86-37=49'] Exploring Operation: 49-18=31, Resulting Numbers: [5, 31] Generated Node #0,2,0: 33:[5, 31] Operation: 49-18=31 Exploring Operation: 49-5=44, Resulting Numbers: [18, 44] Generated Node #0,2,1: 33:[18, 44] Operation: 49-5=44 Exploring Operation: 18-5=13, Resulting Numbers: [49, 13] Generated Node #0,2,2: 33:[49, 13] Operation: 18-5=13 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 33:[5, 31], Operations: ['86-37=49', '49-18=31'] Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,33 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 33:[18, 44], Operations: ['86-37=49', '49-5=44'] Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 18+44=62, Resulting Numbers: [62] 62,33 unequal: No Solution Exploring Operation: 18*44=792, Resulting Numbers: [792] 792,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 33:[49, 13], Operations: ['86-37=49', '18-5=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,33 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[5, 37, 68], Operations: ['86-18=68'] Exploring Operation: 68-37=31, Resulting Numbers: [5, 31] Generated Node #0,1,0: 33:[5, 31] Operation: 68-37=31 Exploring Operation: 37-5=32, Resulting Numbers: [68, 32] Generated Node #0,1,1: 33:[68, 32] Operation: 37-5=32 Exploring Operation: 68-5=63, Resulting Numbers: [37, 63] Generated Node #0,1,2: 33:[37, 63] Operation: 68-5=63 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 33:[5, 31], Operations: ['86-18=68', '68-37=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,33 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 33:[37, 63], Operations: ['86-18=68', '68-5=63'] Exploring Operation: 37*63=2331, Resulting Numbers: [2331] 2331,33 unequal: No Solution Exploring Operation: 37+63=100, Resulting Numbers: [100] 100,33 unequal: No Solution Exploring Operation: 63-37=26, Resulting Numbers: [26] 26,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 33:[68, 32], Operations: ['86-18=68', '37-5=32'] Exploring Operation: 68*32=2176, Resulting Numbers: [2176] 2176,33 unequal: No Solution Exploring Operation: 68+32=100, Resulting Numbers: [100] 100,33 unequal: No Solution Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[37, 86, 13], Operations: ['18-5=13'] Exploring Operation: 86-37=49, Resulting Numbers: [13, 49] Generated Node #0,0,0: 33:[13, 49] Operation: 86-37=49 Exploring Operation: 37-13=24, Resulting Numbers: [86, 24] Generated Node #0,0,1: 33:[86, 24] Operation: 37-13=24 Exploring Operation: 86-13=73, Resulting Numbers: [37, 73] Generated Node #0,0,2: 33:[37, 73] Operation: 86-13=73 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[13, 49], Operations: ['18-5=13', '86-37=49'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 13+49=62, Resulting Numbers: [62] 62,33 unequal: No Solution Exploring Operation: 13*49=637, Resulting Numbers: [637] 637,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 33:[37, 73], Operations: ['18-5=13', '86-13=73'] Exploring Operation: 37+73=110, Resulting Numbers: [110] 110,33 unequal: No Solution Exploring Operation: 73-37=36, Resulting Numbers: [36] 36,33 unequal: No Solution Exploring Operation: 37*73=2701, Resulting Numbers: [2701] 2701,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[86, 24], Operations: ['18-5=13', '37-13=24'] Exploring Operation: 86*24=2064, Resulting Numbers: [2064] 2064,33 unequal: No Solution Exploring Operation: 86-24=62, Resulting Numbers: [62] 62,33 unequal: No Solution Exploring Operation: 86+24=110, Resulting Numbers: [110] 110,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 85, 28, 80, 44 ]
90
[ "44-28=16", "80/16=5", "85+5=90" ]
Current State: 90:[85, 28, 80, 44], Operations: [] Exploring Operation: 44-28=16, Resulting Numbers: [85, 80, 16] Generated Node #2: [85, 80, 16] from Operation: 44-28=16 Current State: 90:[85, 80, 16], Operations: ['44-28=16'] Exploring Operation: 80/16=5, Resulting Numbers: [85, 5] Generated Node #3: [85, 5] from Operation: 80/16=5 Current State: 90:[85, 5], Operations: ['44-28=16', '80/16=5'] Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[85, 28, 80, 44], Operations: [] Exploring Operation: 80-28=52, Resulting Numbers: [85, 44, 52] Generated Node #0,0: 90:[85, 44, 52] Operation: 80-28=52 Exploring Operation: 85-80=5, Resulting Numbers: [28, 44, 5] Generated Node #0,1: 90:[28, 44, 5] Operation: 85-80=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[28, 44, 5], Operations: ['85-80=5'] Exploring Operation: 44-28=16, Resulting Numbers: [5, 16] Generated Node #0,1,0: 90:[5, 16] Operation: 44-28=16 Exploring Operation: 28+5=33, Resulting Numbers: [44, 33] Generated Node #0,1,1: 90:[44, 33] Operation: 28+5=33 Moving to Node #0,1,0 Current State: 90:[5, 16], Operations: ['85-80=5', '44-28=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[44, 33], Operations: ['85-80=5', '28+5=33'] Exploring Operation: 44+33=77, Resulting Numbers: [77] 77,90 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[85, 44, 52], Operations: ['80-28=52'] Exploring Operation: 52-44=8, Resulting Numbers: [85, 8] Generated Node #0,0,0: 90:[85, 8] Operation: 52-44=8 Exploring Operation: 85-52=33, Resulting Numbers: [44, 33] Generated Node #0,0,1: 90:[44, 33] Operation: 85-52=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[44, 33], Operations: ['80-28=52', '85-52=33'] Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 44+33=77, Resulting Numbers: [77] 77,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[85, 8], Operations: ['80-28=52', '52-44=8'] Exploring Operation: 85+8=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 85-8=77, Resulting Numbers: [77] 77,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 98, 99, 18, 79 ]
99
[ "98-18=80", "80-79=1", "99*1=99" ]
Current State: 99:[98, 99, 18, 79], Operations: [] Exploring Operation: 98-18=80, Resulting Numbers: [99, 79, 80] Generated Node #2: [99, 79, 80] from Operation: 98-18=80 Current State: 99:[99, 79, 80], Operations: ['98-18=80'] Exploring Operation: 80-79=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 80-79=1 Current State: 99:[99, 1], Operations: ['98-18=80', '80-79=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[98, 99, 18, 79], Operations: [] Exploring Operation: 99-79=20, Resulting Numbers: [98, 18, 20] Generated Node #0,0: 99:[98, 18, 20] Operation: 99-79=20 Exploring Operation: 18+79=97, Resulting Numbers: [98, 99, 97] Generated Node #0,1: 99:[98, 99, 97] Operation: 18+79=97 Exploring Operation: 98-79=19, Resulting Numbers: [99, 18, 19] Generated Node #0,2: 99:[99, 18, 19] Operation: 98-79=19 Moving to Node #0,1 Current State: 99:[98, 99, 97], Operations: ['18+79=97'] Exploring Operation: 99-97=2, Resulting Numbers: [98, 2] Generated Node #0,1,0: 99:[98, 2] Operation: 99-97=2 Exploring Operation: 98-97=1, Resulting Numbers: [99, 1] Generated Node #0,1,1: 99:[99, 1] Operation: 98-97=1 Exploring Operation: 99-98=1, Resulting Numbers: [97, 1] Generated Node #0,1,2: 99:[97, 1] Operation: 99-98=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[98, 2], Operations: ['18+79=97', '99-97=2'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,99 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,99 unequal: No Solution Exploring Operation: 98+2=100, Resulting Numbers: [100] 100,99 unequal: No Solution No 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: 99:[99, 1], Operations: ['18+79=97', '98-97=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[98, 99, 18, 79], Operations: [] Exploring Operation: 18+79=97, Resulting Numbers: [98, 99, 97] Generated Node #0,1: 99:[98, 99, 97] Operation: 18+79=97 Moving to Node #0,1 Current State: 99:[98, 99, 97], Operations: ['18+79=97'] Exploring Operation: 98-97=1, Resulting Numbers: [99, 1] Generated Node #0,1,1: 99:[99, 1] Operation: 98-97=1 Moving to Node #0,1,1 Current State: 99:[99, 1], Operations: ['18+79=97', '98-97=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 2, 84, 25, 91 ]
27
[ "84-25=59", "2*59=118", "118-91=27" ]
Current State: 27:[2, 84, 25, 91], Operations: [] Exploring Operation: 84-25=59, Resulting Numbers: [2, 91, 59] Generated Node #2: [2, 91, 59] from Operation: 84-25=59 Current State: 27:[2, 91, 59], Operations: ['84-25=59'] Exploring Operation: 2*59=118, Resulting Numbers: [91, 118] Generated Node #3: [91, 118] from Operation: 2*59=118 Current State: 27:[91, 118], Operations: ['84-25=59', '2*59=118'] Exploring Operation: 118-91=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[2, 84, 25, 91], Operations: [] Exploring Operation: 91-25=66, Resulting Numbers: [2, 84, 66] Generated Node #0,0: 27:[2, 84, 66] Operation: 91-25=66 Exploring Operation: 91-84=7, Resulting Numbers: [2, 25, 7] Generated Node #0,1: 27:[2, 25, 7] Operation: 91-84=7 Exploring Operation: 84-25=59, Resulting Numbers: [2, 91, 59] Generated Node #0,2: 27:[2, 91, 59] Operation: 84-25=59 Exploring Operation: 84/2=42, Resulting Numbers: [25, 91, 42] Generated Node #0,3: 27:[25, 91, 42] Operation: 84/2=42 Moving to Node #0,1 Current State: 27:[2, 25, 7], Operations: ['91-84=7'] Exploring Operation: 2+25=27, Resulting Numbers: [7, 27] Generated Node #0,1,0: 27:[7, 27] Operation: 2+25=27 Exploring Operation: 2+7=9, Resulting Numbers: [25, 9] Generated Node #0,1,1: 27:[25, 9] Operation: 2+7=9 Exploring Operation: 25-2=23, Resulting Numbers: [7, 23] Generated Node #0,1,2: 27:[7, 23] Operation: 25-2=23 Exploring Operation: 7-2=5, Resulting Numbers: [25, 5] Generated Node #0,1,3: 27:[25, 5] Operation: 7-2=5 Moving to Node #0,3 Current State: 27:[25, 91, 42], Operations: ['84/2=42'] Exploring Operation: 91-42=49, Resulting Numbers: [25, 49] Generated Node #0,3,0: 27:[25, 49] Operation: 91-42=49 Exploring Operation: 25+91=116, Resulting Numbers: [42, 116] Generated Node #0,3,1: 27:[42, 116] Operation: 25+91=116 Exploring Operation: 42-25=17, Resulting Numbers: [91, 17] Generated Node #0,3,2: 27:[91, 17] Operation: 42-25=17 Exploring Operation: 91-25=66, Resulting Numbers: [42, 66] Generated Node #0,3,3: 27:[42, 66] Operation: 91-25=66 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 27:[25, 49], Operations: ['84/2=42', '91-42=49'] Exploring Operation: 25*49=1225, Resulting Numbers: [1225] 1225,27 unequal: No Solution Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 25+49=74, Resulting Numbers: [74] 74,27 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 #0,3,3 Current State: 27:[42, 66], Operations: ['84/2=42', '91-25=66'] Exploring Operation: 66-42=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 42*66=2772, Resulting Numbers: [2772] 2772,27 unequal: No Solution Exploring Operation: 42+66=108, Resulting Numbers: [108] 108,27 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 #0,3,2 Current State: 27:[91, 17], Operations: ['84/2=42', '42-25=17'] Exploring Operation: 91*17=1547, Resulting Numbers: [1547] 1547,27 unequal: No Solution Exploring Operation: 91-17=74, Resulting Numbers: [74] 74,27 unequal: No Solution Exploring Operation: 91+17=108, Resulting Numbers: [108] 108,27 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 #0,3,1 Current State: 27:[42, 116], Operations: ['84/2=42', '25+91=116'] Exploring Operation: 42+116=158, Resulting Numbers: [158] 158,27 unequal: No Solution Exploring Operation: 42*116=4872, Resulting Numbers: [4872] 4872,27 unequal: No Solution Exploring Operation: 116-42=74, Resulting Numbers: [74] 74,27 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: 27:[2, 91, 59], Operations: ['84-25=59'] Exploring Operation: 91-2=89, Resulting Numbers: [59, 89] Generated Node #0,2,0: 27:[59, 89] Operation: 91-2=89 Exploring Operation: 59-2=57, Resulting Numbers: [91, 57] Generated Node #0,2,1: 27:[91, 57] Operation: 59-2=57 Exploring Operation: 91-59=32, Resulting Numbers: [2, 32] Generated Node #0,2,2: 27:[2, 32] Operation: 91-59=32 Exploring Operation: 2+91=93, Resulting Numbers: [59, 93] Generated Node #0,2,3: 27:[59, 93] Operation: 2+91=93 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[2, 32], Operations: ['84-25=59', '91-59=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,27 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,27 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 #0,2,0 Current State: 27:[59, 89], Operations: ['84-25=59', '91-2=89'] Exploring Operation: 59+89=148, Resulting Numbers: [148] 148,27 unequal: No Solution Exploring Operation: 59*89=5251, Resulting Numbers: [5251] 5251,27 unequal: No Solution Exploring Operation: 89-59=30, Resulting Numbers: [30] 30,27 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 #0,2,1 Current State: 27:[91, 57], Operations: ['84-25=59', '59-2=57'] Exploring Operation: 91+57=148, Resulting Numbers: [148] 148,27 unequal: No Solution Exploring Operation: 91-57=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 91*57=5187, Resulting Numbers: [5187] 5187,27 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 #0,2,3 Current State: 27:[59, 93], Operations: ['84-25=59', '2+91=93'] Exploring Operation: 93-59=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 59+93=152, Resulting Numbers: [152] 152,27 unequal: No Solution Exploring Operation: 59*93=5487, Resulting Numbers: [5487] 5487,27 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: 27:[2, 84, 66], Operations: ['91-25=66'] Exploring Operation: 84-66=18, Resulting Numbers: [2, 18] Generated Node #0,0,0: 27:[2, 18] Operation: 84-66=18 Exploring Operation: 84-2=82, Resulting Numbers: [66, 82] Generated Node #0,0,1: 27:[66, 82] Operation: 84-2=82 Exploring Operation: 66/2=33, Resulting Numbers: [84, 33] Generated Node #0,0,2: 27:[84, 33] Operation: 66/2=33 Exploring Operation: 84/2=42, Resulting Numbers: [66, 42] Generated Node #0,0,3: 27:[66, 42] Operation: 84/2=42 Moving to Node #0,1,0 Current State: 27:[7, 27], Operations: ['91-84=7', '2+25=27'] Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,27 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[25, 9], Operations: ['91-84=7', '2+7=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,27 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[25, 5], Operations: ['91-84=7', '7-2=5'] Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,27 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,27 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[7, 23], Operations: ['91-84=7', '25-2=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,27 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[2, 18], Operations: ['91-25=66', '84-66=18'] Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,27 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,27 unequal: No Solution Moving to Node #0,0,3 Current State: 27:[66, 42], Operations: ['91-25=66', '84/2=42'] Exploring Operation: 66-42=24, Resulting Numbers: [24] 24,27 unequal: No Solution Exploring Operation: 66+42=108, Resulting Numbers: [108] 108,27 unequal: No Solution Exploring Operation: 66*42=2772, Resulting Numbers: [2772] 2772,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[84, 33], Operations: ['91-25=66', '66/2=33'] Exploring Operation: 84-33=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 84+33=117, Resulting Numbers: [117] 117,27 unequal: No Solution Exploring Operation: 84*33=2772, Resulting Numbers: [2772] 2772,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[66, 82], Operations: ['91-25=66', '84-2=82'] Exploring Operation: 66*82=5412, Resulting Numbers: [5412] 5412,27 unequal: No Solution Exploring Operation: 66+82=148, Resulting Numbers: [148] 148,27 unequal: No Solution Exploring Operation: 82-66=16, Resulting Numbers: [16] 16,27 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 81, 29, 2, 15 ]
93
[ "81+29=110", "2+15=17", "110-17=93" ]
Current State: 93:[81, 29, 2, 15], Operations: [] Exploring Operation: 81+29=110, Resulting Numbers: [2, 15, 110] Generated Node #2: [2, 15, 110] from Operation: 81+29=110 Current State: 93:[2, 15, 110], Operations: ['81+29=110'] Exploring Operation: 2+15=17, Resulting Numbers: [110, 17] Generated Node #3: [110, 17] from Operation: 2+15=17 Current State: 93:[110, 17], Operations: ['81+29=110', '2+15=17'] Exploring Operation: 110-17=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[81, 29, 2, 15], Operations: [] Exploring Operation: 81+2=83, Resulting Numbers: [29, 15, 83] Generated Node #0,0: 93:[29, 15, 83] Operation: 81+2=83 Exploring Operation: 2*15=30, Resulting Numbers: [81, 29, 30] Generated Node #0,1: 93:[81, 29, 30] Operation: 2*15=30 Exploring Operation: 81+15=96, Resulting Numbers: [29, 2, 96] Generated Node #0,2: 93:[29, 2, 96] Operation: 81+15=96 Moving to Node #0,2 Current State: 93:[29, 2, 96], Operations: ['81+15=96'] Exploring Operation: 29+2=31, Resulting Numbers: [96, 31] Generated Node #0,2,0: 93:[96, 31] Operation: 29+2=31 Exploring Operation: 29-2=27, Resulting Numbers: [96, 27] Generated Node #0,2,1: 93:[96, 27] Operation: 29-2=27 Exploring Operation: 96-2=94, Resulting Numbers: [29, 94] Generated Node #0,2,2: 93:[29, 94] Operation: 96-2=94 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[96, 31], Operations: ['81+15=96', '29+2=31'] Exploring Operation: 96+31=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 96*31=2976, Resulting Numbers: [2976] 2976,93 unequal: No Solution Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[29, 94], Operations: ['81+15=96', '96-2=94'] Exploring Operation: 29+94=123, Resulting Numbers: [123] 123,93 unequal: No Solution Exploring Operation: 94-29=65, Resulting Numbers: [65] 65,93 unequal: No Solution Exploring Operation: 29*94=2726, Resulting Numbers: [2726] 2726,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[96, 27], Operations: ['81+15=96', '29-2=27'] Exploring Operation: 96*27=2592, Resulting Numbers: [2592] 2592,93 unequal: No Solution Exploring Operation: 96+27=123, Resulting Numbers: [123] 123,93 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 93:[81, 29, 30], Operations: ['2*15=30'] Exploring Operation: 30-29=1, Resulting Numbers: [81, 1] Generated Node #0,1,0: 93:[81, 1] Operation: 30-29=1 Exploring Operation: 81+30=111, Resulting Numbers: [29, 111] Generated Node #0,1,1: 93:[29, 111] Operation: 81+30=111 Exploring Operation: 81+29=110, Resulting Numbers: [30, 110] Generated Node #0,1,2: 93:[30, 110] Operation: 81+29=110 Moving to Node #0,0 Current State: 93:[29, 15, 83], Operations: ['81+2=83'] Exploring Operation: 29+15=44, Resulting Numbers: [83, 44] Generated Node #0,0,0: 93:[83, 44] Operation: 29+15=44 Exploring Operation: 29-15=14, Resulting Numbers: [83, 14] Generated Node #0,0,1: 93:[83, 14] Operation: 29-15=14 Exploring Operation: 15+83=98, Resulting Numbers: [29, 98] Generated Node #0,0,2: 93:[29, 98] Operation: 15+83=98 Moving to Node #0,0,2 Current State: 93:[29, 98], Operations: ['81+2=83', '15+83=98'] Exploring Operation: 29+98=127, Resulting Numbers: [127] 127,93 unequal: No Solution Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,93 unequal: No Solution Exploring Operation: 29*98=2842, Resulting Numbers: [2842] 2842,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[81, 1], Operations: ['2*15=30', '30-29=1'] Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,93 unequal: No Solution Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,93 unequal: No Solution Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,93 unequal: No Solution Moving to Node #0,1,2 Current State: 93:[30, 110], Operations: ['2*15=30', '81+29=110'] Exploring Operation: 30+110=140, Resulting Numbers: [140] 140,93 unequal: No Solution Exploring Operation: 110-30=80, Resulting Numbers: [80] 80,93 unequal: No Solution Exploring Operation: 30*110=3300, Resulting Numbers: [3300] 3300,93 unequal: No Solution Moving to Node #0,1,1 Current State: 93:[29, 111], Operations: ['2*15=30', '81+30=111'] Exploring Operation: 29*111=3219, Resulting Numbers: [3219] 3219,93 unequal: No Solution Exploring Operation: 29+111=140, Resulting Numbers: [140] 140,93 unequal: No Solution Exploring Operation: 111-29=82, Resulting Numbers: [82] 82,93 unequal: No Solution Moving to Node #0,0,1 Current State: 93:[83, 14], Operations: ['81+2=83', '29-15=14'] Exploring Operation: 83+14=97, Resulting Numbers: [97] 97,93 unequal: No Solution Exploring Operation: 83*14=1162, Resulting Numbers: [1162] 1162,93 unequal: No Solution Exploring Operation: 83-14=69, Resulting Numbers: [69] 69,93 unequal: No Solution Moving to Node #0,0,0 Current State: 93:[83, 44], Operations: ['81+2=83', '29+15=44'] Exploring Operation: 83*44=3652, Resulting Numbers: [3652] 3652,93 unequal: No Solution Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,93 unequal: No Solution Exploring Operation: 83+44=127, Resulting Numbers: [127] 127,93 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 55, 16, 69, 51 ]
57
[ "55-16=39", "69-51=18", "39+18=57" ]
Current State: 57:[55, 16, 69, 51], Operations: [] Exploring Operation: 55-16=39, Resulting Numbers: [69, 51, 39] Generated Node #2: [69, 51, 39] from Operation: 55-16=39 Current State: 57:[69, 51, 39], Operations: ['55-16=39'] Exploring Operation: 69-51=18, Resulting Numbers: [39, 18] Generated Node #3: [39, 18] from Operation: 69-51=18 Current State: 57:[39, 18], Operations: ['55-16=39', '69-51=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[55, 16, 69, 51], Operations: [] Exploring Operation: 69-51=18, Resulting Numbers: [55, 16, 18] Generated Node #0,0: 57:[55, 16, 18] Operation: 69-51=18 Exploring Operation: 69-16=53, Resulting Numbers: [55, 51, 53] Generated Node #0,1: 57:[55, 51, 53] Operation: 69-16=53 Moving to Node #0,0 Current State: 57:[55, 16, 18], Operations: ['69-51=18'] Exploring Operation: 55+16=71, Resulting Numbers: [18, 71] Generated Node #0,0,0: 57:[18, 71] Operation: 55+16=71 Exploring Operation: 18-16=2, Resulting Numbers: [55, 2] Generated Node #0,0,1: 57:[55, 2] Operation: 18-16=2 Moving to Node #0,1 Current State: 57:[55, 51, 53], Operations: ['69-16=53'] Exploring Operation: 55-51=4, Resulting Numbers: [53, 4] Generated Node #0,1,0: 57:[53, 4] Operation: 55-51=4 Exploring Operation: 53-51=2, Resulting Numbers: [55, 2] Generated Node #0,1,1: 57:[55, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[55, 2], Operations: ['69-16=53', '53-51=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[55, 16, 69, 51], Operations: [] Exploring Operation: 69-16=53, Resulting Numbers: [55, 51, 53] Generated Node #0,1: 57:[55, 51, 53] Operation: 69-16=53 Moving to Node #0,1 Current State: 57:[55, 51, 53], Operations: ['69-16=53'] Exploring Operation: 53-51=2, Resulting Numbers: [55, 2] Generated Node #0,1,1: 57:[55, 2] Operation: 53-51=2 Moving to Node #0,1,1 Current State: 57:[55, 2], Operations: ['69-16=53', '53-51=2'] Exploring Operation: 55+2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 49, 40, 91, 54 ]
83
[ "54-49=5", "40/5=8", "91-8=83" ]
Current State: 83:[49, 40, 91, 54], Operations: [] Exploring Operation: 54-49=5, Resulting Numbers: [40, 91, 5] Generated Node #2: [40, 91, 5] from Operation: 54-49=5 Current State: 83:[40, 91, 5], Operations: ['54-49=5'] Exploring Operation: 40/5=8, Resulting Numbers: [91, 8] Generated Node #3: [91, 8] from Operation: 40/5=8 Current State: 83:[91, 8], Operations: ['54-49=5', '40/5=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[49, 40, 91, 54], Operations: [] Exploring Operation: 40+54=94, Resulting Numbers: [49, 91, 94] Generated Node #0,0: 83:[49, 91, 94] Operation: 40+54=94 Exploring Operation: 49+54=103, Resulting Numbers: [40, 91, 103] Generated Node #0,1: 83:[40, 91, 103] Operation: 49+54=103 Exploring Operation: 49+40=89, Resulting Numbers: [91, 54, 89] Generated Node #0,2: 83:[91, 54, 89] Operation: 49+40=89 Exploring Operation: 91-40=51, Resulting Numbers: [49, 54, 51] Generated Node #0,3: 83:[49, 54, 51] Operation: 91-40=51 Moving to Node #0,2 Current State: 83:[91, 54, 89], Operations: ['49+40=89'] Exploring Operation: 54+89=143, Resulting Numbers: [91, 143] Generated Node #0,2,0: 83:[91, 143] Operation: 54+89=143 Exploring Operation: 89-54=35, Resulting Numbers: [91, 35] Generated Node #0,2,1: 83:[91, 35] Operation: 89-54=35 Exploring Operation: 91-54=37, Resulting Numbers: [89, 37] Generated Node #0,2,2: 83:[89, 37] Operation: 91-54=37 Exploring Operation: 91+54=145, Resulting Numbers: [89, 145] Generated Node #0,2,3: 83:[89, 145] Operation: 91+54=145 Moving to Node #0,0 Current State: 83:[49, 91, 94], Operations: ['40+54=94'] Exploring Operation: 49+94=143, Resulting Numbers: [91, 143] Generated Node #0,0,0: 83:[91, 143] Operation: 49+94=143 Exploring Operation: 91-49=42, Resulting Numbers: [94, 42] Generated Node #0,0,1: 83:[94, 42] Operation: 91-49=42 Exploring Operation: 49+91=140, Resulting Numbers: [94, 140] Generated Node #0,0,2: 83:[94, 140] Operation: 49+91=140 Exploring Operation: 94-49=45, Resulting Numbers: [91, 45] Generated Node #0,0,3: 83:[91, 45] Operation: 94-49=45 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 83:[91, 45], Operations: ['40+54=94', '94-49=45'] Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,83 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 91*45=4095, Resulting Numbers: [4095] 4095,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[94, 42], Operations: ['40+54=94', '91-49=42'] Exploring Operation: 94*42=3948, Resulting Numbers: [3948] 3948,83 unequal: No Solution Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 94+42=136, Resulting Numbers: [136] 136,83 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:[91, 143], Operations: ['40+54=94', '49+94=143'] Exploring Operation: 91+143=234, Resulting Numbers: [234] 234,83 unequal: No Solution Exploring Operation: 91*143=13013, Resulting Numbers: [13013] 13013,83 unequal: No Solution Exploring Operation: 143-91=52, Resulting Numbers: [52] 52,83 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:[94, 140], Operations: ['40+54=94', '49+91=140'] Exploring Operation: 140-94=46, Resulting Numbers: [46] 46,83 unequal: No Solution Exploring Operation: 94*140=13160, Resulting Numbers: [13160] 13160,83 unequal: No Solution Exploring Operation: 94+140=234, Resulting Numbers: [234] 234,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[40, 91, 103], Operations: ['49+54=103'] Exploring Operation: 103-40=63, Resulting Numbers: [91, 63] Generated Node #0,1,0: 83:[91, 63] Operation: 103-40=63 Exploring Operation: 91-40=51, Resulting Numbers: [103, 51] Generated Node #0,1,1: 83:[103, 51] Operation: 91-40=51 Exploring Operation: 40+91=131, Resulting Numbers: [103, 131] Generated Node #0,1,2: 83:[103, 131] Operation: 40+91=131 Exploring Operation: 40+103=143, Resulting Numbers: [91, 143] Generated Node #0,1,3: 83:[91, 143] Operation: 40+103=143 Moving to Node #0,3 Current State: 83:[49, 54, 51], Operations: ['91-40=51'] Exploring Operation: 49+54=103, Resulting Numbers: [51, 103] Generated Node #0,3,0: 83:[51, 103] Operation: 49+54=103 Exploring Operation: 54-49=5, Resulting Numbers: [51, 5] Generated Node #0,3,1: 83:[51, 5] Operation: 54-49=5 Exploring Operation: 49+51=100, Resulting Numbers: [54, 100] Generated Node #0,3,2: 83:[54, 100] Operation: 49+51=100 Exploring Operation: 54+51=105, Resulting Numbers: [49, 105] Generated Node #0,3,3: 83:[49, 105] Operation: 54+51=105 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 83:[54, 100], Operations: ['91-40=51', '49+51=100'] Exploring Operation: 54*100=5400, Resulting Numbers: [5400] 5400,83 unequal: No Solution Exploring Operation: 54+100=154, Resulting Numbers: [154] 154,83 unequal: No Solution Exploring Operation: 100-54=46, Resulting Numbers: [46] 46,83 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 #0,3,0 Current State: 83:[51, 103], Operations: ['91-40=51', '49+54=103'] Exploring Operation: 103-51=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 51+103=154, Resulting Numbers: [154] 154,83 unequal: No Solution Exploring Operation: 51*103=5253, Resulting Numbers: [5253] 5253,83 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 #0,3,3 Current State: 83:[49, 105], Operations: ['91-40=51', '54+51=105'] Exploring Operation: 49*105=5145, Resulting Numbers: [5145] 5145,83 unequal: No Solution Exploring Operation: 105-49=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 49+105=154, Resulting Numbers: [154] 154,83 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 #0,3,1 Current State: 83:[51, 5], Operations: ['91-40=51', '54-49=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,83 unequal: No Solution 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 No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 83:[91, 63], Operations: ['49+54=103', '103-40=63'] Exploring Operation: 91*63=5733, Resulting Numbers: [5733] 5733,83 unequal: No Solution Exploring Operation: 91+63=154, Resulting Numbers: [154] 154,83 unequal: No Solution Exploring Operation: 91-63=28, Resulting Numbers: [28] 28,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[103, 51], Operations: ['49+54=103', '91-40=51'] Exploring Operation: 103*51=5253, Resulting Numbers: [5253] 5253,83 unequal: No Solution Exploring Operation: 103-51=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 103+51=154, Resulting Numbers: [154] 154,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[89, 37], Operations: ['49+40=89', '91-54=37'] Exploring Operation: 89-37=52, Resulting Numbers: [52] 52,83 unequal: No Solution Exploring Operation: 89+37=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 89*37=3293, Resulting Numbers: [3293] 3293,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[91, 35], Operations: ['49+40=89', '89-54=35'] Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,83 unequal: No Solution Exploring Operation: 91*35=3185, Resulting Numbers: [3185] 3185,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[103, 131], Operations: ['49+54=103', '40+91=131'] Exploring Operation: 131-103=28, Resulting Numbers: [28] 28,83 unequal: No Solution Exploring Operation: 103+131=234, Resulting Numbers: [234] 234,83 unequal: No Solution Exploring Operation: 103*131=13493, Resulting Numbers: [13493] 13493,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[91, 143], Operations: ['49+40=89', '54+89=143'] Exploring Operation: 91+143=234, Resulting Numbers: [234] 234,83 unequal: No Solution Exploring Operation: 91*143=13013, Resulting Numbers: [13013] 13013,83 unequal: No Solution Exploring Operation: 143-91=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,1,3 Current State: 83:[91, 143], Operations: ['49+54=103', '40+103=143'] Exploring Operation: 91*143=13013, Resulting Numbers: [13013] 13013,83 unequal: No Solution Exploring Operation: 91+143=234, Resulting Numbers: [234] 234,83 unequal: No Solution Exploring Operation: 143-91=52, Resulting Numbers: [52] 52,83 unequal: No Solution Moving to Node #0,2,3 Current State: 83:[89, 145], Operations: ['49+40=89', '91+54=145'] Exploring Operation: 145-89=56, Resulting Numbers: [56] 56,83 unequal: No Solution Exploring Operation: 89+145=234, Resulting Numbers: [234] 234,83 unequal: No Solution Exploring Operation: 89*145=12905, Resulting Numbers: [12905] 12905,83 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 61, 35, 5, 13 ]
44
[ "61-35=26", "5+13=18", "26+18=44" ]
Current State: 44:[61, 35, 5, 13], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [5, 13, 26] Generated Node #2: [5, 13, 26] from Operation: 61-35=26 Current State: 44:[5, 13, 26], Operations: ['61-35=26'] Exploring Operation: 5+13=18, Resulting Numbers: [26, 18] Generated Node #3: [26, 18] from Operation: 5+13=18 Current State: 44:[26, 18], Operations: ['61-35=26', '5+13=18'] Exploring Operation: 26+18=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[61, 35, 5, 13], Operations: [] Exploring Operation: 61-13=48, Resulting Numbers: [35, 5, 48] Generated Node #0,0: 44:[35, 5, 48] Operation: 61-13=48 Exploring Operation: 35/5=7, Resulting Numbers: [61, 13, 7] Generated Node #0,1: 44:[61, 13, 7] Operation: 35/5=7 Exploring Operation: 61-35=26, Resulting Numbers: [5, 13, 26] Generated Node #0,2: 44:[5, 13, 26] Operation: 61-35=26 Exploring Operation: 35-13=22, Resulting Numbers: [61, 5, 22] Generated Node #0,3: 44:[61, 5, 22] Operation: 35-13=22 Moving to Node #0,2 Current State: 44:[5, 13, 26], Operations: ['61-35=26'] Exploring Operation: 26-13=13, Resulting Numbers: [5, 13] Generated Node #0,2,0: 44:[5, 13] Operation: 26-13=13 Exploring Operation: 26/13=2, Resulting Numbers: [5, 2] Generated Node #0,2,1: 44:[5, 2] Operation: 26/13=2 Exploring Operation: 13+26=39, Resulting Numbers: [5, 39] Generated Node #0,2,2: 44:[5, 39] Operation: 13+26=39 Exploring Operation: 26-5=21, Resulting Numbers: [13, 21] Generated Node #0,2,3: 44:[13, 21] Operation: 26-5=21 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 44:[5, 2], Operations: ['61-35=26', '26/13=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 44:[5, 13], Operations: ['61-35=26', '26-13=13'] Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,44 unequal: No Solution Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 44:[13, 21], Operations: ['61-35=26', '26-5=21'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,44 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 44:[5, 39], Operations: ['61-35=26', '13+26=39'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,44 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,44 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[61, 35, 5, 13], Operations: [] Exploring Operation: 61-35=26, Resulting Numbers: [5, 13, 26] Generated Node #0,2: 44:[5, 13, 26] Operation: 61-35=26 Moving to Node #0,2 Current State: 44:[5, 13, 26], Operations: ['61-35=26'] Exploring Operation: 13+26=39, Resulting Numbers: [5, 39] Generated Node #0,2,2: 44:[5, 39] Operation: 13+26=39 Moving to Node #0,2,2 Current State: 44:[5, 39], Operations: ['61-35=26', '13+26=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 6, 52, 48, 49 ]
18
[ "6+48=54", "52-49=3", "54/3=18" ]
Current State: 18:[6, 52, 48, 49], Operations: [] Exploring Operation: 6+48=54, Resulting Numbers: [52, 49, 54] Generated Node #2: [52, 49, 54] from Operation: 6+48=54 Current State: 18:[52, 49, 54], Operations: ['6+48=54'] Exploring Operation: 52-49=3, Resulting Numbers: [54, 3] Generated Node #3: [54, 3] from Operation: 52-49=3 Current State: 18:[54, 3], Operations: ['6+48=54', '52-49=3'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[6, 52, 48, 49], Operations: [] Exploring Operation: 52-6=46, Resulting Numbers: [48, 49, 46] Generated Node #0,0: 18:[48, 49, 46] Operation: 52-6=46 Exploring Operation: 49-48=1, Resulting Numbers: [6, 52, 1] Generated Node #0,1: 18:[6, 52, 1] Operation: 49-48=1 Exploring Operation: 48/6=8, Resulting Numbers: [52, 49, 8] Generated Node #0,2: 18:[52, 49, 8] Operation: 48/6=8 Exploring Operation: 52-48=4, Resulting Numbers: [6, 49, 4] Generated Node #0,3: 18:[6, 49, 4] Operation: 52-48=4 Exploring Operation: 52-49=3, Resulting Numbers: [6, 48, 3] Generated Node #0,4: 18:[6, 48, 3] Operation: 52-49=3 Moving to Node #0,4 Current State: 18:[6, 48, 3], Operations: ['52-49=3'] Exploring Operation: 48-6=42, Resulting Numbers: [3, 42] Generated Node #0,4,0: 18:[3, 42] Operation: 48-6=42 Exploring Operation: 48-3=45, Resulting Numbers: [6, 45] Generated Node #0,4,1: 18:[6, 45] Operation: 48-3=45 Exploring Operation: 48/6=8, Resulting Numbers: [3, 8] Generated Node #0,4,2: 18:[3, 8] Operation: 48/6=8 Exploring Operation: 48/3=16, Resulting Numbers: [6, 16] Generated Node #0,4,3: 18:[6, 16] Operation: 48/3=16 Exploring Operation: 6+3=9, Resulting Numbers: [48, 9] Generated Node #0,4,4: 18:[48, 9] Operation: 6+3=9 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 18:[3, 8], Operations: ['52-49=3', '48/6=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,18 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 #0,4,3 Current State: 18:[6, 16], Operations: ['52-49=3', '48/3=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,18 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 #0,4,0 Current State: 18:[3, 42], Operations: ['52-49=3', '48-6=42'] Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,18 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,18 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 #0,4,1 Current State: 18:[6, 45], Operations: ['52-49=3', '48-3=45'] Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,18 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,18 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 #0,4,4 Current State: 18:[48, 9], Operations: ['52-49=3', '6+3=9'] Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,18 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,18 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: 18:[6, 49, 4], Operations: ['52-48=4'] Exploring Operation: 6-4=2, Resulting Numbers: [49, 2] Generated Node #0,3,0: 18:[49, 2] Operation: 6-4=2 Exploring Operation: 49-6=43, Resulting Numbers: [4, 43] Generated Node #0,3,1: 18:[4, 43] Operation: 49-6=43 Exploring Operation: 49+4=53, Resulting Numbers: [6, 53] Generated Node #0,3,2: 18:[6, 53] Operation: 49+4=53 Exploring Operation: 49-4=45, Resulting Numbers: [6, 45] Generated Node #0,3,3: 18:[6, 45] Operation: 49-4=45 Exploring Operation: 6+4=10, Resulting Numbers: [49, 10] Generated Node #0,3,4: 18:[49, 10] Operation: 6+4=10 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[4, 43], Operations: ['52-48=4', '49-6=43'] Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,18 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,18 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 #0,3,3 Current State: 18:[6, 45], Operations: ['52-48=4', '49-4=45'] Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,18 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,18 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 #0,3,0 Current State: 18:[49, 2], Operations: ['52-48=4', '6-4=2'] Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,18 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,18 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 #0,3,4 Current State: 18:[49, 10], Operations: ['52-48=4', '6+4=10'] Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,18 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 49*10=490, Resulting Numbers: [490] 490,18 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 #0,3,2 Current State: 18:[6, 53], Operations: ['52-48=4', '49+4=53'] Exploring Operation: 6*53=318, Resulting Numbers: [318] 318,18 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 6+53=59, Resulting Numbers: [59] 59,18 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: 18:[6, 52, 1], Operations: ['49-48=1'] Exploring Operation: 52*1=52, Resulting Numbers: [6, 52] Generated Node #0,1,0: 18:[6, 52] Operation: 52*1=52 Exploring Operation: 6*1=6, Resulting Numbers: [52, 6] Generated Node #0,1,1: 18:[52, 6] Operation: 6*1=6 Exploring Operation: 52-6=46, Resulting Numbers: [1, 46] Generated Node #0,1,2: 18:[1, 46] Operation: 52-6=46 Exploring Operation: 6/1=6, Resulting Numbers: [52, 6] Generated Node #0,1,3: 18:[52, 6] Operation: 6/1=6 Exploring Operation: 52-1=51, Resulting Numbers: [6, 51] Generated Node #0,1,4: 18:[6, 51] Operation: 52-1=51 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[1, 46], Operations: ['49-48=1', '52-6=46'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 1*46=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 1+46=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 18:[6, 51], Operations: ['49-48=1', '52-1=51'] Exploring Operation: 6*51=306, Resulting Numbers: [306] 306,18 unequal: No Solution Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,18 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[6, 52], Operations: ['49-48=1', '52*1=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,18 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[52, 6], Operations: ['49-48=1', '6*1=6'] Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[52, 6], Operations: ['49-48=1', '6/1=6'] Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,18 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,18 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: 18:[52, 49, 8], Operations: ['48/6=8'] Exploring Operation: 52+8=60, Resulting Numbers: [49, 60] Generated Node #0,2,0: 18:[49, 60] Operation: 52+8=60 Exploring Operation: 49-8=41, Resulting Numbers: [52, 41] Generated Node #0,2,1: 18:[52, 41] Operation: 49-8=41 Exploring Operation: 52-49=3, Resulting Numbers: [8, 3] Generated Node #0,2,2: 18:[8, 3] Operation: 52-49=3 Exploring Operation: 52-8=44, Resulting Numbers: [49, 44] Generated Node #0,2,3: 18:[49, 44] Operation: 52-8=44 Exploring Operation: 49+8=57, Resulting Numbers: [52, 57] Generated Node #0,2,4: 18:[52, 57] Operation: 49+8=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[8, 3], Operations: ['48/6=8', '52-49=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 8+3=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 #0,2,1 Current State: 18:[52, 41], Operations: ['48/6=8', '49-8=41'] Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 52*41=2132, Resulting Numbers: [2132] 2132,18 unequal: No Solution Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,18 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 #0,2,3 Current State: 18:[49, 44], Operations: ['48/6=8', '52-8=44'] Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,18 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,18 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:[49, 60], Operations: ['48/6=8', '52+8=60'] Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,18 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 #0,2,4 Current State: 18:[52, 57], Operations: ['48/6=8', '49+8=57'] Exploring Operation: 52+57=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 52*57=2964, Resulting Numbers: [2964] 2964,18 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,18 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: 18:[48, 49, 46], Operations: ['52-6=46'] Exploring Operation: 49-48=1, Resulting Numbers: [46, 1] Generated Node #0,0,0: 18:[46, 1] Operation: 49-48=1 Exploring Operation: 48+46=94, Resulting Numbers: [49, 94] Generated Node #0,0,1: 18:[49, 94] Operation: 48+46=94 Exploring Operation: 48+49=97, Resulting Numbers: [46, 97] Generated Node #0,0,2: 18:[46, 97] Operation: 48+49=97 Exploring Operation: 49-46=3, Resulting Numbers: [48, 3] Generated Node #0,0,3: 18:[48, 3] Operation: 49-46=3 Exploring Operation: 48-46=2, Resulting Numbers: [49, 2] Generated Node #0,0,4: 18:[49, 2] Operation: 48-46=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[46, 1], Operations: ['52-6=46', '49-48=1'] Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,18 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 #0,0,3 Current State: 18:[48, 3], Operations: ['52-6=46', '49-46=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,18 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,18 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 #0,0,4 Current State: 18:[49, 2], Operations: ['52-6=46', '48-46=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,18 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,18 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,18 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 #0,0,1 Current State: 18:[49, 94], Operations: ['52-6=46', '48+46=94'] Exploring Operation: 94-49=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 49+94=143, Resulting Numbers: [143] 143,18 unequal: No Solution Exploring Operation: 49*94=4606, Resulting Numbers: [4606] 4606,18 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 #0,0,2 Current State: 18:[46, 97], Operations: ['52-6=46', '48+49=97'] Exploring Operation: 46+97=143, Resulting Numbers: [143] 143,18 unequal: No Solution Exploring Operation: 97-46=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 46*97=4462, Resulting Numbers: [4462] 4462,18 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
[ 9, 2, 2, 60 ]
76
[ "9*2=18", "60-2=58", "18+58=76" ]
Current State: 76:[9, 2, 2, 60], Operations: [] Exploring Operation: 9*2=18, Resulting Numbers: [60, 18] Generated Node #2: [60, 18] from Operation: 9*2=18 Current State: 76:[60, 18], Operations: ['9*2=18'] Exploring Operation: 60-2=58, Resulting Numbers: [18, 58] Generated Node #3: [18, 58] from Operation: 60-2=58 Current State: 76:[18, 58], Operations: ['9*2=18', '60-2=58'] Exploring Operation: 18+58=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[9, 2, 2, 60], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [9, 2, 30] Generated Node #0,0: 76:[9, 2, 30] Operation: 60/2=30 Exploring Operation: 60/2=30, Resulting Numbers: [9, 2, 30] Generated Node #0,1: 76:[9, 2, 30] Operation: 60/2=30 Exploring Operation: 9+60=69, Resulting Numbers: [2, 2, 69] Generated Node #0,2: 76:[2, 2, 69] Operation: 9+60=69 Exploring Operation: 60-9=51, Resulting Numbers: [2, 2, 51] Generated Node #0,3: 76:[2, 2, 51] Operation: 60-9=51 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[2, 2, 69], Operations: ['9+60=69'] Exploring Operation: 2+2=4, Resulting Numbers: [69, 4] Generated Node #0,2,0: 76:[69, 4] Operation: 2+2=4 Exploring Operation: 2*2=4, Resulting Numbers: [69, 4] Generated Node #0,2,1: 76:[69, 4] Operation: 2*2=4 Exploring Operation: 2+69=71, Resulting Numbers: [2, 71] Generated Node #0,2,2: 76:[2, 71] Operation: 2+69=71 Exploring Operation: 2+69=71, Resulting Numbers: [2, 71] Generated Node #0,2,3: 76:[2, 71] Operation: 2+69=71 Moving to Node #0,2,2 Current State: 76:[2, 71], Operations: ['9+60=69', '2+69=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,76 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[2, 71], Operations: ['9+60=69', '2+69=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,76 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[69, 4], Operations: ['9+60=69', '2*2=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,76 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,76 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[69, 4], Operations: ['9+60=69', '2+2=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,76 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,76 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[9, 2, 30], Operations: ['60/2=30'] Exploring Operation: 30/2=15, Resulting Numbers: [9, 15] Generated Node #0,0,0: 76:[9, 15] Operation: 30/2=15 Exploring Operation: 9*2=18, Resulting Numbers: [30, 18] Generated Node #0,0,1: 76:[30, 18] Operation: 9*2=18 Exploring Operation: 9+30=39, Resulting Numbers: [2, 39] Generated Node #0,0,2: 76:[2, 39] Operation: 9+30=39 Exploring Operation: 30-9=21, Resulting Numbers: [2, 21] Generated Node #0,0,3: 76:[2, 21] Operation: 30-9=21 Moving to Node #0,0,2 Current State: 76:[2, 39], Operations: ['60/2=30', '9+30=39'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,76 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[2, 21], Operations: ['60/2=30', '30-9=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,76 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[30, 18], Operations: ['60/2=30', '9*2=18'] Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,76 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,76 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[9, 15], Operations: ['60/2=30', '30/2=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,76 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[9, 2, 30], Operations: ['60/2=30'] Exploring Operation: 30-9=21, Resulting Numbers: [2, 21] Generated Node #0,1,0: 76:[2, 21] Operation: 30-9=21 Exploring Operation: 30/2=15, Resulting Numbers: [9, 15] Generated Node #0,1,1: 76:[9, 15] Operation: 30/2=15 Exploring Operation: 9+30=39, Resulting Numbers: [2, 39] Generated Node #0,1,2: 76:[2, 39] Operation: 9+30=39 Exploring Operation: 9*2=18, Resulting Numbers: [30, 18] Generated Node #0,1,3: 76:[30, 18] Operation: 9*2=18 Moving to Node #0,1,2 Current State: 76:[2, 39], Operations: ['60/2=30', '9+30=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,76 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,76 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[2, 21], Operations: ['60/2=30', '30-9=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,76 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,76 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[30, 18], Operations: ['60/2=30', '9*2=18'] Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,76 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,76 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[9, 15], Operations: ['60/2=30', '30/2=15'] Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,76 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,76 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[2, 2, 51], Operations: ['60-9=51'] Exploring Operation: 2*2=4, Resulting Numbers: [51, 4] Generated Node #0,3,0: 76:[51, 4] Operation: 2*2=4 Exploring Operation: 51-2=49, Resulting Numbers: [2, 49] Generated Node #0,3,1: 76:[2, 49] Operation: 51-2=49 Exploring Operation: 2+2=4, Resulting Numbers: [51, 4] Generated Node #0,3,2: 76:[51, 4] Operation: 2+2=4 Exploring Operation: 51-2=49, Resulting Numbers: [2, 49] Generated Node #0,3,3: 76:[2, 49] Operation: 51-2=49 Moving to Node #0,3,1 Current State: 76:[2, 49], Operations: ['60-9=51', '51-2=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,76 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,76 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[2, 49], Operations: ['60-9=51', '51-2=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,76 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,76 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[51, 4], Operations: ['60-9=51', '2+2=4'] Exploring Operation: 51+4=55, Resulting Numbers: [55] 55,76 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,76 unequal: No Solution Exploring Operation: 51*4=204, Resulting Numbers: [204] 204,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[51, 4], Operations: ['60-9=51', '2*2=4'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,76 unequal: No Solution Exploring Operation: 51*4=204, Resulting Numbers: [204] 204,76 unequal: No Solution Exploring Operation: 51+4=55, Resulting Numbers: [55] 55,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 46, 89, 71, 85 ]
21
[ "46+89=135", "71+85=156", "156-135=21" ]
Current State: 21:[46, 89, 71, 85], Operations: [] Exploring Operation: 46+89=135, Resulting Numbers: [71, 85, 135] Generated Node #2: [71, 85, 135] from Operation: 46+89=135 Current State: 21:[71, 85, 135], Operations: ['46+89=135'] Exploring Operation: 71+85=156, Resulting Numbers: [135, 156] Generated Node #3: [135, 156] from Operation: 71+85=156 Current State: 21:[135, 156], Operations: ['46+89=135', '71+85=156'] Exploring Operation: 156-135=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[46, 89, 71, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [46, 71, 4] Generated Node #0,0: 21:[46, 71, 4] Operation: 89-85=4 Exploring Operation: 89-71=18, Resulting Numbers: [46, 85, 18] Generated Node #0,1: 21:[46, 85, 18] Operation: 89-71=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[46, 71, 4], Operations: ['89-85=4'] Exploring Operation: 71-46=25, Resulting Numbers: [4, 25] Generated Node #0,0,0: 21:[4, 25] Operation: 71-46=25 Exploring Operation: 46-4=42, Resulting Numbers: [71, 42] Generated Node #0,0,1: 21:[71, 42] Operation: 46-4=42 Moving to Node #0,0,0 Current State: 21:[4, 25], Operations: ['89-85=4', '71-46=25'] Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[46, 89, 71, 85], Operations: [] Exploring Operation: 89-85=4, Resulting Numbers: [46, 71, 4] Generated Node #0,0: 21:[46, 71, 4] Operation: 89-85=4 Moving to Node #0,0 Current State: 21:[46, 71, 4], Operations: ['89-85=4'] Exploring Operation: 71-46=25, Resulting Numbers: [4, 25] Generated Node #0,0,0: 21:[4, 25] Operation: 71-46=25 Moving to Node #0,0,0 Current State: 21:[4, 25], Operations: ['89-85=4', '71-46=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 49, 37, 42, 10 ]
35
[ "49-37=12", "42*10=420", "420/12=35" ]
Current State: 35:[49, 37, 42, 10], Operations: [] Exploring Operation: 49-37=12, Resulting Numbers: [42, 10, 12] Generated Node #2: [42, 10, 12] from Operation: 49-37=12 Current State: 35:[42, 10, 12], Operations: ['49-37=12'] Exploring Operation: 42*10=420, Resulting Numbers: [12, 420] Generated Node #3: [12, 420] from Operation: 42*10=420 Current State: 35:[12, 420], Operations: ['49-37=12', '42*10=420'] Exploring Operation: 420/12=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[49, 37, 42, 10], Operations: [] Exploring Operation: 49-10=39, Resulting Numbers: [37, 42, 39] Generated Node #0,0: 35:[37, 42, 39] Operation: 49-10=39 Exploring Operation: 42-37=5, Resulting Numbers: [49, 10, 5] Generated Node #0,1: 35:[49, 10, 5] Operation: 42-37=5 Exploring Operation: 49-37=12, Resulting Numbers: [42, 10, 12] Generated Node #0,2: 35:[42, 10, 12] Operation: 49-37=12 Exploring Operation: 49-42=7, Resulting Numbers: [37, 10, 7] Generated Node #0,3: 35:[37, 10, 7] Operation: 49-42=7 Moving to Node #0,3 Current State: 35:[37, 10, 7], Operations: ['49-42=7'] Exploring Operation: 37-7=30, Resulting Numbers: [10, 30] Generated Node #0,3,0: 35:[10, 30] Operation: 37-7=30 Exploring Operation: 37-10=27, Resulting Numbers: [7, 27] Generated Node #0,3,1: 35:[7, 27] Operation: 37-10=27 Exploring Operation: 10-7=3, Resulting Numbers: [37, 3] Generated Node #0,3,2: 35:[37, 3] Operation: 10-7=3 Exploring Operation: 37+10=47, Resulting Numbers: [7, 47] Generated Node #0,3,3: 35:[7, 47] Operation: 37+10=47 Moving to Node #0,0 Current State: 35:[37, 42, 39], Operations: ['49-10=39'] Exploring Operation: 42-39=3, Resulting Numbers: [37, 3] Generated Node #0,0,0: 35:[37, 3] Operation: 42-39=3 Exploring Operation: 42-37=5, Resulting Numbers: [39, 5] Generated Node #0,0,1: 35:[39, 5] Operation: 42-37=5 Exploring Operation: 39-37=2, Resulting Numbers: [42, 2] Generated Node #0,0,2: 35:[42, 2] Operation: 39-37=2 Exploring Operation: 37+42=79, Resulting Numbers: [39, 79] Generated Node #0,0,3: 35:[39, 79] Operation: 37+42=79 Moving to Node #0,2 Current State: 35:[42, 10, 12], Operations: ['49-37=12'] Exploring Operation: 42-10=32, Resulting Numbers: [12, 32] Generated Node #0,2,0: 35:[12, 32] Operation: 42-10=32 Exploring Operation: 10+12=22, Resulting Numbers: [42, 22] Generated Node #0,2,1: 35:[42, 22] Operation: 10+12=22 Exploring Operation: 12-10=2, Resulting Numbers: [42, 2] Generated Node #0,2,2: 35:[42, 2] Operation: 12-10=2 Exploring Operation: 42-12=30, Resulting Numbers: [10, 30] Generated Node #0,2,3: 35:[10, 30] Operation: 42-12=30 Moving to Node #0,1 Current State: 35:[49, 10, 5], Operations: ['42-37=5'] Exploring Operation: 10-5=5, Resulting Numbers: [49, 5] Generated Node #0,1,0: 35:[49, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [49, 2] Generated Node #0,1,1: 35:[49, 2] Operation: 10/5=2 Exploring Operation: 49-5=44, Resulting Numbers: [10, 44] Generated Node #0,1,2: 35:[10, 44] Operation: 49-5=44 Exploring Operation: 49-10=39, Resulting Numbers: [5, 39] Generated Node #0,1,3: 35:[5, 39] Operation: 49-10=39 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 35:[5, 39], Operations: ['42-37=5', '49-10=39'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,35 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[10, 44], Operations: ['42-37=5', '49-5=44'] Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,35 unequal: No Solution Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,35 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[49, 5], Operations: ['42-37=5', '10-5=5'] Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 49*5=245, Resulting Numbers: [245] 245,35 unequal: No Solution Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[49, 2], Operations: ['42-37=5', '10/5=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,35 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 35:[37, 3], Operations: ['49-42=7', '10-7=3'] Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,35 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,35 unequal: No Solution Moving to Node #0,0,1 Current State: 35:[39, 5], Operations: ['49-10=39', '42-37=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,35 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,35 unequal: No Solution Moving to Node #0,0,0 Current State: 35:[37, 3], Operations: ['49-10=39', '42-39=3'] Exploring Operation: 37*3=111, Resulting Numbers: [111] 111,35 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 37+3=40, Resulting Numbers: [40] 40,35 unequal: No Solution Moving to Node #0,3,1 Current State: 35:[7, 27], Operations: ['49-42=7', '37-10=27'] Exploring Operation: 7*27=189, Resulting Numbers: [189] 189,35 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,35 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,35 unequal: No Solution Moving to Node #0,3,0 Current State: 35:[10, 30], Operations: ['49-42=7', '37-7=30'] Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,35 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[10, 30], Operations: ['49-37=12', '42-12=30'] Exploring Operation: 30/10=3, Resulting Numbers: [3] 3,35 unequal: No Solution Exploring Operation: 10+30=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 10*30=300, Resulting Numbers: [300] 300,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[12, 32], Operations: ['49-37=12', '42-10=32'] Exploring Operation: 12+32=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 12*32=384, Resulting Numbers: [384] 384,35 unequal: No Solution Moving to Node #0,0,2 Current State: 35:[42, 2], Operations: ['49-10=39', '39-37=2'] Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[42, 2], Operations: ['49-37=12', '12-10=2'] Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,35 unequal: No Solution Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 42/2=21, Resulting Numbers: [21] 21,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[7, 47], Operations: ['49-42=7', '37+10=47'] Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,35 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 7*47=329, Resulting Numbers: [329] 329,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[42, 22], Operations: ['49-37=12', '10+12=22'] Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,35 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,35 unequal: No Solution Exploring Operation: 42*22=924, Resulting Numbers: [924] 924,35 unequal: No Solution Moving to Node #0,0,3 Current State: 35:[39, 79], Operations: ['49-10=39', '37+42=79'] Exploring Operation: 39+79=118, Resulting Numbers: [118] 118,35 unequal: No Solution Exploring Operation: 39*79=3081, Resulting Numbers: [3081] 3081,35 unequal: No Solution Exploring Operation: 79-39=40, Resulting Numbers: [40] 40,35 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 96, 66, 44, 76 ]
63
[ "76-44=32", "96/32=3", "66-3=63" ]
Current State: 63:[96, 66, 44, 76], Operations: [] Exploring Operation: 76-44=32, Resulting Numbers: [96, 66, 32] Generated Node #2: [96, 66, 32] from Operation: 76-44=32 Current State: 63:[96, 66, 32], Operations: ['76-44=32'] Exploring Operation: 96/32=3, Resulting Numbers: [66, 3] Generated Node #3: [66, 3] from Operation: 96/32=3 Current State: 63:[66, 3], Operations: ['76-44=32', '96/32=3'] Exploring Operation: 66-3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[96, 66, 44, 76], Operations: [] Exploring Operation: 96-44=52, Resulting Numbers: [66, 76, 52] Generated Node #0,0: 63:[66, 76, 52] Operation: 96-44=52 Exploring Operation: 96-76=20, Resulting Numbers: [66, 44, 20] Generated Node #0,1: 63:[66, 44, 20] Operation: 96-76=20 Exploring Operation: 96-66=30, Resulting Numbers: [44, 76, 30] Generated Node #0,2: 63:[44, 76, 30] Operation: 96-66=30 Moving to Node #0,1 Current State: 63:[66, 44, 20], Operations: ['96-76=20'] Exploring Operation: 66-44=22, Resulting Numbers: [20, 22] Generated Node #0,1,0: 63:[20, 22] Operation: 66-44=22 Exploring Operation: 44+20=64, Resulting Numbers: [66, 64] Generated Node #0,1,1: 63:[66, 64] Operation: 44+20=64 Exploring Operation: 44-20=24, Resulting Numbers: [66, 24] Generated Node #0,1,2: 63:[66, 24] Operation: 44-20=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[20, 22], Operations: ['96-76=20', '66-44=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[66, 64], Operations: ['96-76=20', '44+20=64'] Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 66+64=130, Resulting Numbers: [130] 130,63 unequal: No Solution Exploring Operation: 66*64=4224, Resulting Numbers: [4224] 4224,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 63:[66, 24], Operations: ['96-76=20', '44-20=24'] Exploring Operation: 66+24=90, Resulting Numbers: [90] 90,63 unequal: No Solution Exploring Operation: 66*24=1584, Resulting Numbers: [1584] 1584,63 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 63:[66, 76, 52], Operations: ['96-44=52'] Exploring Operation: 76-66=10, Resulting Numbers: [52, 10] Generated Node #0,0,0: 63:[52, 10] Operation: 76-66=10 Exploring Operation: 66-52=14, Resulting Numbers: [76, 14] Generated Node #0,0,1: 63:[76, 14] Operation: 66-52=14 Exploring Operation: 76-52=24, Resulting Numbers: [66, 24] Generated Node #0,0,2: 63:[66, 24] Operation: 76-52=24 Moving to Node #0,2 Current State: 63:[44, 76, 30], Operations: ['96-66=30'] Exploring Operation: 44+30=74, Resulting Numbers: [76, 74] Generated Node #0,2,0: 63:[76, 74] Operation: 44+30=74 Exploring Operation: 44-30=14, Resulting Numbers: [76, 14] Generated Node #0,2,1: 63:[76, 14] Operation: 44-30=14 Exploring Operation: 76-44=32, Resulting Numbers: [30, 32] Generated Node #0,2,2: 63:[30, 32] Operation: 76-44=32 Moving to Node #0,0,2 Current State: 63:[66, 24], Operations: ['96-44=52', '76-52=24'] Exploring Operation: 66+24=90, Resulting Numbers: [90] 90,63 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 66*24=1584, Resulting Numbers: [1584] 1584,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[52, 10], Operations: ['96-44=52', '76-66=10'] Exploring Operation: 52+10=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,63 unequal: No Solution Exploring Operation: 52*10=520, Resulting Numbers: [520] 520,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[76, 14], Operations: ['96-44=52', '66-52=14'] Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,63 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[76, 14], Operations: ['96-66=30', '44-30=14'] Exploring Operation: 76*14=1064, Resulting Numbers: [1064] 1064,63 unequal: No Solution Exploring Operation: 76-14=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 76+14=90, Resulting Numbers: [90] 90,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[30, 32], Operations: ['96-66=30', '76-44=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[76, 74], Operations: ['96-66=30', '44+30=74'] Exploring Operation: 76+74=150, Resulting Numbers: [150] 150,63 unequal: No Solution Exploring Operation: 76*74=5624, Resulting Numbers: [5624] 5624,63 unequal: No Solution Exploring Operation: 76-74=2, Resulting Numbers: [2] 2,63 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 68, 80, 13, 36 ]
16
[ "80-68=12", "36/12=3", "13+3=16" ]
Current State: 16:[68, 80, 13, 36], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [13, 36, 12] Generated Node #2: [13, 36, 12] from Operation: 80-68=12 Current State: 16:[13, 36, 12], Operations: ['80-68=12'] Exploring Operation: 36/12=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 36/12=3 Current State: 16:[13, 3], Operations: ['80-68=12', '36/12=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[68, 80, 13, 36], Operations: [] Exploring Operation: 80-13=67, Resulting Numbers: [68, 36, 67] Generated Node #0,0: 16:[68, 36, 67] Operation: 80-13=67 Exploring Operation: 80-36=44, Resulting Numbers: [68, 13, 44] Generated Node #0,1: 16:[68, 13, 44] Operation: 80-36=44 Exploring Operation: 68-36=32, Resulting Numbers: [80, 13, 32] Generated Node #0,2: 16:[80, 13, 32] Operation: 68-36=32 Exploring Operation: 68-13=55, Resulting Numbers: [80, 36, 55] Generated Node #0,3: 16:[80, 36, 55] Operation: 68-13=55 Exploring Operation: 80-68=12, Resulting Numbers: [13, 36, 12] Generated Node #0,4: 16:[13, 36, 12] Operation: 80-68=12 Moving to Node #0,4 Current State: 16:[13, 36, 12], Operations: ['80-68=12'] Exploring Operation: 36/12=3, Resulting Numbers: [13, 3] Generated Node #0,4,0: 16:[13, 3] Operation: 36/12=3 Exploring Operation: 36-12=24, Resulting Numbers: [13, 24] Generated Node #0,4,1: 16:[13, 24] Operation: 36-12=24 Exploring Operation: 13-12=1, Resulting Numbers: [36, 1] Generated Node #0,4,2: 16:[36, 1] Operation: 13-12=1 Exploring Operation: 13+12=25, Resulting Numbers: [36, 25] Generated Node #0,4,3: 16:[36, 25] Operation: 13+12=25 Exploring Operation: 36-13=23, Resulting Numbers: [12, 23] Generated Node #0,4,4: 16:[12, 23] Operation: 36-13=23 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 16:[13, 3], Operations: ['80-68=12', '36/12=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,16 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[68, 80, 13, 36], Operations: [] Exploring Operation: 80-68=12, Resulting Numbers: [13, 36, 12] Generated Node #0,4: 16:[13, 36, 12] Operation: 80-68=12 Moving to Node #0,4 Current State: 16:[13, 36, 12], Operations: ['80-68=12'] Exploring Operation: 36/12=3, Resulting Numbers: [13, 3] Generated Node #0,4,0: 16:[13, 3] Operation: 36/12=3 Moving to Node #0,4,0 Current State: 16:[13, 3], Operations: ['80-68=12', '36/12=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 15, 9, 18, 11 ]
78
[ "18-11=7", "9*7=63", "15+63=78" ]
Current State: 78:[15, 9, 18, 11], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [15, 9, 7] Generated Node #2: [15, 9, 7] from Operation: 18-11=7 Current State: 78:[15, 9, 7], Operations: ['18-11=7'] Exploring Operation: 9*7=63, Resulting Numbers: [15, 63] Generated Node #3: [15, 63] from Operation: 9*7=63 Current State: 78:[15, 63], Operations: ['18-11=7', '9*7=63'] Exploring Operation: 15+63=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[15, 9, 18, 11], Operations: [] Exploring Operation: 18-15=3, Resulting Numbers: [9, 11, 3] Generated Node #0,0: 78:[9, 11, 3] Operation: 18-15=3 Exploring Operation: 18/9=2, Resulting Numbers: [15, 11, 2] Generated Node #0,1: 78:[15, 11, 2] Operation: 18/9=2 Moving to Node #0,1 Current State: 78:[15, 11, 2], Operations: ['18/9=2'] Exploring Operation: 15+11=26, Resulting Numbers: [2, 26] Generated Node #0,1,0: 78:[2, 26] Operation: 15+11=26 Exploring Operation: 15-11=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 78:[2, 4] Operation: 15-11=4 Moving to Node #0,0 Current State: 78:[9, 11, 3], Operations: ['18-15=3'] Exploring Operation: 9-3=6, Resulting Numbers: [11, 6] Generated Node #0,0,0: 78:[11, 6] Operation: 9-3=6 Exploring Operation: 11-9=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 78:[3, 2] Operation: 11-9=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[3, 2], Operations: ['18-15=3', '11-9=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[11, 6], Operations: ['18-15=3', '9-3=6'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,78 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: 78:[2, 26], Operations: ['18/9=2', '15+11=26'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,78 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[2, 4], Operations: ['18/9=2', '15-11=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 38, 69, 78, 66 ]
37
[ "38+69=107", "78+66=144", "144-107=37" ]
Current State: 37:[38, 69, 78, 66], Operations: [] Exploring Operation: 38+69=107, Resulting Numbers: [78, 66, 107] Generated Node #2: [78, 66, 107] from Operation: 38+69=107 Current State: 37:[78, 66, 107], Operations: ['38+69=107'] Exploring Operation: 78+66=144, Resulting Numbers: [107, 144] Generated Node #3: [107, 144] from Operation: 78+66=144 Current State: 37:[107, 144], Operations: ['38+69=107', '78+66=144'] Exploring Operation: 144-107=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[38, 69, 78, 66], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [38, 66, 9] Generated Node #0,0: 37:[38, 66, 9] Operation: 78-69=9 Exploring Operation: 78-66=12, Resulting Numbers: [38, 69, 12] Generated Node #0,1: 37:[38, 69, 12] Operation: 78-66=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[38, 66, 9], Operations: ['78-69=9'] Exploring Operation: 66-38=28, Resulting Numbers: [9, 28] Generated Node #0,0,0: 37:[9, 28] Operation: 66-38=28 Exploring Operation: 66-9=57, Resulting Numbers: [38, 57] Generated Node #0,0,1: 37:[38, 57] Operation: 66-9=57 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[38, 57], Operations: ['78-69=9', '66-9=57'] Exploring Operation: 57-38=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 38+57=95, Resulting Numbers: [95] 95,37 unequal: No Solution No 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: 37:[9, 28], Operations: ['78-69=9', '66-38=28'] Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[38, 69, 78, 66], Operations: [] Exploring Operation: 78-69=9, Resulting Numbers: [38, 66, 9] Generated Node #0,0: 37:[38, 66, 9] Operation: 78-69=9 Moving to Node #0,0 Current State: 37:[38, 66, 9], Operations: ['78-69=9'] Exploring Operation: 66-38=28, Resulting Numbers: [9, 28] Generated Node #0,0,0: 37:[9, 28] Operation: 66-38=28 Moving to Node #0,0,0 Current State: 37:[9, 28], Operations: ['78-69=9', '66-38=28'] Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 96, 36, 56, 6 ]
36
[ "96/6=16", "56-36=20", "16+20=36" ]
Current State: 36:[96, 36, 56, 6], Operations: [] Exploring Operation: 96/6=16, Resulting Numbers: [36, 56, 16] Generated Node #2: [36, 56, 16] from Operation: 96/6=16 Current State: 36:[36, 56, 16], Operations: ['96/6=16'] Exploring Operation: 56-36=20, Resulting Numbers: [16, 20] Generated Node #3: [16, 20] from Operation: 56-36=20 Current State: 36:[16, 20], Operations: ['96/6=16', '56-36=20'] Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[96, 36, 56, 6], Operations: [] Exploring Operation: 96-6=90, Resulting Numbers: [36, 56, 90] Generated Node #0,0: 36:[36, 56, 90] Operation: 96-6=90 Exploring Operation: 96-36=60, Resulting Numbers: [56, 6, 60] Generated Node #0,1: 36:[56, 6, 60] Operation: 96-36=60 Exploring Operation: 96-56=40, Resulting Numbers: [36, 6, 40] Generated Node #0,2: 36:[36, 6, 40] Operation: 96-56=40 Exploring Operation: 56-36=20, Resulting Numbers: [96, 6, 20] Generated Node #0,3: 36:[96, 6, 20] Operation: 56-36=20 Exploring Operation: 96/6=16, Resulting Numbers: [36, 56, 16] Generated Node #0,4: 36:[36, 56, 16] Operation: 96/6=16 Moving to Node #0,2 Current State: 36:[36, 6, 40], Operations: ['96-56=40'] Exploring Operation: 36+6=42, Resulting Numbers: [40, 42] Generated Node #0,2,0: 36:[40, 42] Operation: 36+6=42 Exploring Operation: 36/6=6, Resulting Numbers: [40, 6] Generated Node #0,2,1: 36:[40, 6] Operation: 36/6=6 Exploring Operation: 40-6=34, Resulting Numbers: [36, 34] Generated Node #0,2,2: 36:[36, 34] Operation: 40-6=34 Exploring Operation: 36-6=30, Resulting Numbers: [40, 30] Generated Node #0,2,3: 36:[40, 30] Operation: 36-6=30 Exploring Operation: 40-36=4, Resulting Numbers: [6, 4] Generated Node #0,2,4: 36:[6, 4] Operation: 40-36=4 Moving to Node #0,4 Current State: 36:[36, 56, 16], Operations: ['96/6=16'] Exploring Operation: 56+16=72, Resulting Numbers: [36, 72] Generated Node #0,4,0: 36:[36, 72] Operation: 56+16=72 Exploring Operation: 56-16=40, Resulting Numbers: [36, 40] Generated Node #0,4,1: 36:[36, 40] Operation: 56-16=40 Exploring Operation: 36+16=52, Resulting Numbers: [56, 52] Generated Node #0,4,2: 36:[56, 52] Operation: 36+16=52 Exploring Operation: 36-16=20, Resulting Numbers: [56, 20] Generated Node #0,4,3: 36:[56, 20] Operation: 36-16=20 Exploring Operation: 56-36=20, Resulting Numbers: [16, 20] Generated Node #0,4,4: 36:[16, 20] Operation: 56-36=20 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 36:[36, 40], Operations: ['96/6=16', '56-16=40'] Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,36 unequal: No Solution Exploring Operation: 36*40=1440, Resulting Numbers: [1440] 1440,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 36:[16, 20], Operations: ['96/6=16', '56-36=20'] Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[96, 36, 56, 6], Operations: [] Exploring Operation: 96/6=16, Resulting Numbers: [36, 56, 16] Generated Node #0,4: 36:[36, 56, 16] Operation: 96/6=16 Moving to Node #0,4 Current State: 36:[36, 56, 16], Operations: ['96/6=16'] Exploring Operation: 56-36=20, Resulting Numbers: [16, 20] Generated Node #0,4,4: 36:[16, 20] Operation: 56-36=20 Moving to Node #0,4,4 Current State: 36:[16, 20], Operations: ['96/6=16', '56-36=20'] Exploring Operation: 16+20=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 25, 30, 84, 66 ]
20
[ "25*66=1650", "30+1650=1680", "1680/84=20" ]
Current State: 20:[25, 30, 84, 66], Operations: [] Exploring Operation: 25*66=1650, Resulting Numbers: [30, 84, 1650] Generated Node #2: [30, 84, 1650] from Operation: 25*66=1650 Current State: 20:[30, 84, 1650], Operations: ['25*66=1650'] Exploring Operation: 30+1650=1680, Resulting Numbers: [84, 1680] Generated Node #3: [84, 1680] from Operation: 30+1650=1680 Current State: 20:[84, 1680], Operations: ['25*66=1650', '30+1650=1680'] Exploring Operation: 1680/84=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[25, 30, 84, 66], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [25, 30, 18] Generated Node #0,0: 20:[25, 30, 18] Operation: 84-66=18 Exploring Operation: 84-30=54, Resulting Numbers: [25, 66, 54] Generated Node #0,1: 20:[25, 66, 54] Operation: 84-30=54 Moving to Node #0,0 Current State: 20:[25, 30, 18], Operations: ['84-66=18'] Exploring Operation: 30-18=12, Resulting Numbers: [25, 12] Generated Node #0,0,0: 20:[25, 12] Operation: 30-18=12 Exploring Operation: 30-25=5, Resulting Numbers: [18, 5] Generated Node #0,0,1: 20:[18, 5] Operation: 30-25=5 Moving to Node #0,1 Current State: 20:[25, 66, 54], Operations: ['84-30=54'] Exploring Operation: 66-25=41, Resulting Numbers: [54, 41] Generated Node #0,1,0: 20:[54, 41] Operation: 66-25=41 Exploring Operation: 66-54=12, Resulting Numbers: [25, 12] Generated Node #0,1,1: 20:[25, 12] Operation: 66-54=12 Moving to Node #0,0,1 Current State: 20:[18, 5], Operations: ['84-66=18', '30-25=5'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,20 unequal: No Solution Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[25, 12], Operations: ['84-30=54', '66-54=12'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,20 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[25, 12], Operations: ['84-66=18', '30-18=12'] Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,20 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[54, 41], Operations: ['84-30=54', '66-25=41'] Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,20 unequal: No Solution Exploring Operation: 54+41=95, Resulting Numbers: [95] 95,20 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 72, 24, 33, 18 ]
87
[ "72/24=3", "18*3=54", "33+54=87" ]
Current State: 87:[72, 24, 33, 18], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [33, 18, 3] Generated Node #2: [33, 18, 3] from Operation: 72/24=3 Current State: 87:[33, 18, 3], Operations: ['72/24=3'] Exploring Operation: 18*3=54, Resulting Numbers: [33, 54] Generated Node #3: [33, 54] from Operation: 18*3=54 Current State: 87:[33, 54], Operations: ['72/24=3', '18*3=54'] Exploring Operation: 33+54=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[72, 24, 33, 18], Operations: [] Exploring Operation: 72/18=4, Resulting Numbers: [24, 33, 4] Generated Node #0,0: 87:[24, 33, 4] Operation: 72/18=4 Exploring Operation: 72+18=90, Resulting Numbers: [24, 33, 90] Generated Node #0,1: 87:[24, 33, 90] Operation: 72+18=90 Moving to Node #0,0 Current State: 87:[24, 33, 4], Operations: ['72/18=4'] Exploring Operation: 24+4=28, Resulting Numbers: [33, 28] Generated Node #0,0,0: 87:[33, 28] Operation: 24+4=28 Exploring Operation: 33-4=29, Resulting Numbers: [24, 29] Generated Node #0,0,1: 87:[24, 29] Operation: 33-4=29 Moving to Node #0,1 Current State: 87:[24, 33, 90], Operations: ['72+18=90'] Exploring Operation: 90-24=66, Resulting Numbers: [33, 66] Generated Node #0,1,0: 87:[33, 66] Operation: 90-24=66 Exploring Operation: 33-24=9, Resulting Numbers: [90, 9] Generated Node #0,1,1: 87:[90, 9] Operation: 33-24=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[90, 9], Operations: ['72+18=90', '33-24=9'] Exploring Operation: 90-9=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 90/9=10, Resulting Numbers: [10] 10,87 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 #0,1,0 Current State: 87:[33, 66], Operations: ['72+18=90', '90-24=66'] Exploring Operation: 66/33=2, Resulting Numbers: [2] 2,87 unequal: No Solution Exploring Operation: 66-33=33, Resulting Numbers: [33] 33,87 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: 87:[33, 28], Operations: ['72/18=4', '24+4=28'] Exploring Operation: 33+28=61, Resulting Numbers: [61] 61,87 unequal: No Solution Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[24, 29], Operations: ['72/18=4', '33-4=29'] Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,87 unequal: No Solution Exploring Operation: 24+29=53, Resulting Numbers: [53] 53,87 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 3, 83, 70, 89 ]
38
[ "3*70=210", "83+89=172", "210-172=38" ]
Current State: 38:[3, 83, 70, 89], Operations: [] Exploring Operation: 3*70=210, Resulting Numbers: [83, 89, 210] Generated Node #2: [83, 89, 210] from Operation: 3*70=210 Current State: 38:[83, 89, 210], Operations: ['3*70=210'] Exploring Operation: 83+89=172, Resulting Numbers: [210, 172] Generated Node #3: [210, 172] from Operation: 83+89=172 Current State: 38:[210, 172], Operations: ['3*70=210', '83+89=172'] Exploring Operation: 210-172=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[3, 83, 70, 89], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [3, 83, 19] Generated Node #0,0: 38:[3, 83, 19] Operation: 89-70=19 Exploring Operation: 89-83=6, Resulting Numbers: [3, 70, 6] Generated Node #0,1: 38:[3, 70, 6] Operation: 89-83=6 Exploring Operation: 83-70=13, Resulting Numbers: [3, 89, 13] Generated Node #0,2: 38:[3, 89, 13] Operation: 83-70=13 Exploring Operation: 83-3=80, Resulting Numbers: [70, 89, 80] Generated Node #0,3: 38:[70, 89, 80] Operation: 83-3=80 Moving to Node #0,1 Current State: 38:[3, 70, 6], Operations: ['89-83=6'] Exploring Operation: 3*6=18, Resulting Numbers: [70, 18] Generated Node #0,1,0: 38:[70, 18] Operation: 3*6=18 Exploring Operation: 70-3=67, Resulting Numbers: [6, 67] Generated Node #0,1,1: 38:[6, 67] Operation: 70-3=67 Exploring Operation: 6/3=2, Resulting Numbers: [70, 2] Generated Node #0,1,2: 38:[70, 2] Operation: 6/3=2 Exploring Operation: 70-6=64, Resulting Numbers: [3, 64] Generated Node #0,1,3: 38:[3, 64] Operation: 70-6=64 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 38:[3, 64], Operations: ['89-83=6', '70-6=64'] Exploring Operation: 3+64=67, Resulting Numbers: [67] 67,38 unequal: No Solution Exploring Operation: 3*64=192, Resulting Numbers: [192] 192,38 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 38:[70, 2], Operations: ['89-83=6', '6/3=2'] Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,38 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,38 unequal: No Solution Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[70, 18], Operations: ['89-83=6', '3*6=18'] Exploring Operation: 70*18=1260, Resulting Numbers: [1260] 1260,38 unequal: No Solution Exploring Operation: 70+18=88, Resulting Numbers: [88] 88,38 unequal: No Solution Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 38:[6, 67], Operations: ['89-83=6', '70-3=67'] Exploring Operation: 6+67=73, Resulting Numbers: [73] 73,38 unequal: No Solution Exploring Operation: 67-6=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 6*67=402, Resulting Numbers: [402] 402,38 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: 38:[3, 83, 19], Operations: ['89-70=19'] Exploring Operation: 83-19=64, Resulting Numbers: [3, 64] Generated Node #0,0,0: 38:[3, 64] Operation: 83-19=64 Exploring Operation: 3+83=86, Resulting Numbers: [19, 86] Generated Node #0,0,1: 38:[19, 86] Operation: 3+83=86 Exploring Operation: 3+19=22, Resulting Numbers: [83, 22] Generated Node #0,0,2: 38:[83, 22] Operation: 3+19=22 Exploring Operation: 83-3=80, Resulting Numbers: [19, 80] Generated Node #0,0,3: 38:[19, 80] Operation: 83-3=80 Moving to Node #0,2 Current State: 38:[3, 89, 13], Operations: ['83-70=13'] Exploring Operation: 3*13=39, Resulting Numbers: [89, 39] Generated Node #0,2,0: 38:[89, 39] Operation: 3*13=39 Exploring Operation: 89-3=86, Resulting Numbers: [13, 86] Generated Node #0,2,1: 38:[13, 86] Operation: 89-3=86 Exploring Operation: 89-13=76, Resulting Numbers: [3, 76] Generated Node #0,2,2: 38:[3, 76] Operation: 89-13=76 Exploring Operation: 3+13=16, Resulting Numbers: [89, 16] Generated Node #0,2,3: 38:[89, 16] Operation: 3+13=16 Moving to Node #0,3 Current State: 38:[70, 89, 80], Operations: ['83-3=80'] Exploring Operation: 80-70=10, Resulting Numbers: [89, 10] Generated Node #0,3,0: 38:[89, 10] Operation: 80-70=10 Exploring Operation: 70+89=159, Resulting Numbers: [80, 159] Generated Node #0,3,1: 38:[80, 159] Operation: 70+89=159 Exploring Operation: 89-70=19, Resulting Numbers: [80, 19] Generated Node #0,3,2: 38:[80, 19] Operation: 89-70=19 Exploring Operation: 89-80=9, Resulting Numbers: [70, 9] Generated Node #0,3,3: 38:[70, 9] Operation: 89-80=9 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[70, 9], Operations: ['83-3=80', '89-80=9'] Exploring Operation: 70+9=79, Resulting Numbers: [79] 79,38 unequal: No Solution Exploring Operation: 70-9=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 70*9=630, Resulting Numbers: [630] 630,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[80, 19], Operations: ['83-3=80', '89-70=19'] Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,38 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[89, 10], Operations: ['83-3=80', '80-70=10'] Exploring Operation: 89*10=890, Resulting Numbers: [890] 890,38 unequal: No Solution Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,38 unequal: No Solution Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[80, 159], Operations: ['83-3=80', '70+89=159'] Exploring Operation: 80+159=239, Resulting Numbers: [239] 239,38 unequal: No Solution Exploring Operation: 80*159=12720, Resulting Numbers: [12720] 12720,38 unequal: No Solution Exploring Operation: 159-80=79, Resulting Numbers: [79] 79,38 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: 38:[3, 64], Operations: ['89-70=19', '83-19=64'] Exploring Operation: 3+64=67, Resulting Numbers: [67] 67,38 unequal: No Solution Exploring Operation: 3*64=192, Resulting Numbers: [192] 192,38 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[3, 76], Operations: ['83-70=13', '89-13=76'] Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,38 unequal: No Solution Exploring Operation: 3*76=228, Resulting Numbers: [228] 228,38 unequal: No Solution Exploring Operation: 3+76=79, Resulting Numbers: [79] 79,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[19, 80], Operations: ['89-70=19', '83-3=80'] Exploring Operation: 19*80=1520, Resulting Numbers: [1520] 1520,38 unequal: No Solution Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,38 unequal: No Solution Exploring Operation: 19+80=99, Resulting Numbers: [99] 99,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[19, 86], Operations: ['89-70=19', '3+83=86'] Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,38 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,38 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[83, 22], Operations: ['89-70=19', '3+19=22'] Exploring Operation: 83+22=105, Resulting Numbers: [105] 105,38 unequal: No Solution Exploring Operation: 83*22=1826, Resulting Numbers: [1826] 1826,38 unequal: No Solution Exploring Operation: 83-22=61, Resulting Numbers: [61] 61,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[89, 39], Operations: ['83-70=13', '3*13=39'] Exploring Operation: 89-39=50, Resulting Numbers: [50] 50,38 unequal: No Solution Exploring Operation: 89*39=3471, Resulting Numbers: [3471] 3471,38 unequal: No Solution Exploring Operation: 89+39=128, Resulting Numbers: [128] 128,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[13, 86], Operations: ['83-70=13', '89-3=86'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,38 unequal: No Solution Exploring Operation: 13*86=1118, Resulting Numbers: [1118] 1118,38 unequal: No Solution Exploring Operation: 13+86=99, Resulting Numbers: [99] 99,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[89, 16], Operations: ['83-70=13', '3+13=16'] Exploring Operation: 89+16=105, Resulting Numbers: [105] 105,38 unequal: No Solution Exploring Operation: 89*16=1424, Resulting Numbers: [1424] 1424,38 unequal: No Solution Exploring Operation: 89-16=73, Resulting Numbers: [73] 73,38 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 19, 23, 51, 27 ]
74
[ "23-19=4", "51+27=78", "78-4=74" ]
Current State: 74:[19, 23, 51, 27], Operations: [] Exploring Operation: 23-19=4, Resulting Numbers: [51, 27, 4] Generated Node #2: [51, 27, 4] from Operation: 23-19=4 Current State: 74:[51, 27, 4], Operations: ['23-19=4'] Exploring Operation: 51+27=78, Resulting Numbers: [4, 78] Generated Node #3: [4, 78] from Operation: 51+27=78 Current State: 74:[4, 78], Operations: ['23-19=4', '51+27=78'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[19, 23, 51, 27], Operations: [] Exploring Operation: 23+51=74, Resulting Numbers: [19, 27, 74] Generated Node #0,0: 74:[19, 27, 74] Operation: 23+51=74 Exploring Operation: 19+51=70, Resulting Numbers: [23, 27, 70] Generated Node #0,1: 74:[23, 27, 70] Operation: 19+51=70 Exploring Operation: 23-19=4, Resulting Numbers: [51, 27, 4] Generated Node #0,2: 74:[51, 27, 4] Operation: 23-19=4 Exploring Operation: 19+23=42, Resulting Numbers: [51, 27, 42] Generated Node #0,3: 74:[51, 27, 42] Operation: 19+23=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[51, 27, 4], Operations: ['23-19=4'] Exploring Operation: 51+27=78, Resulting Numbers: [4, 78] Generated Node #0,2,0: 74:[4, 78] Operation: 51+27=78 Exploring Operation: 51-27=24, Resulting Numbers: [4, 24] Generated Node #0,2,1: 74:[4, 24] Operation: 51-27=24 Exploring Operation: 27+4=31, Resulting Numbers: [51, 31] Generated Node #0,2,2: 74:[51, 31] Operation: 27+4=31 Exploring Operation: 51-4=47, Resulting Numbers: [27, 47] Generated Node #0,2,3: 74:[27, 47] Operation: 51-4=47 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[4, 78], Operations: ['23-19=4', '51+27=78'] Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,74 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[19, 23, 51, 27], Operations: [] Exploring Operation: 23-19=4, Resulting Numbers: [51, 27, 4] Generated Node #0,2: 74:[51, 27, 4] Operation: 23-19=4 Moving to Node #0,2 Current State: 74:[51, 27, 4], Operations: ['23-19=4'] Exploring Operation: 51+27=78, Resulting Numbers: [4, 78] Generated Node #0,2,0: 74:[4, 78] Operation: 51+27=78 Moving to Node #0,2,0 Current State: 74:[4, 78], Operations: ['23-19=4', '51+27=78'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 36, 77, 32, 8 ]
18
[ "77*8=616", "32+616=648", "648/36=18" ]
Current State: 18:[36, 77, 32, 8], Operations: [] Exploring Operation: 77*8=616, Resulting Numbers: [36, 32, 616] Generated Node #2: [36, 32, 616] from Operation: 77*8=616 Current State: 18:[36, 32, 616], Operations: ['77*8=616'] Exploring Operation: 32+616=648, Resulting Numbers: [36, 648] Generated Node #3: [36, 648] from Operation: 32+616=648 Current State: 18:[36, 648], Operations: ['77*8=616', '32+616=648'] Exploring Operation: 648/36=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[36, 77, 32, 8], Operations: [] Exploring Operation: 77-32=45, Resulting Numbers: [36, 8, 45] Generated Node #0,0: 18:[36, 8, 45] Operation: 77-32=45 Exploring Operation: 77-36=41, Resulting Numbers: [32, 8, 41] Generated Node #0,1: 18:[32, 8, 41] Operation: 77-36=41 Exploring Operation: 32/8=4, Resulting Numbers: [36, 77, 4] Generated Node #0,2: 18:[36, 77, 4] Operation: 32/8=4 Exploring Operation: 36-8=28, Resulting Numbers: [77, 32, 28] Generated Node #0,3: 18:[77, 32, 28] Operation: 36-8=28 Exploring Operation: 36-32=4, Resulting Numbers: [77, 8, 4] Generated Node #0,4: 18:[77, 8, 4] Operation: 36-32=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[32, 8, 41], Operations: ['77-36=41'] Exploring Operation: 41-32=9, Resulting Numbers: [8, 9] Generated Node #0,1,0: 18:[8, 9] Operation: 41-32=9 Exploring Operation: 32/8=4, Resulting Numbers: [41, 4] Generated Node #0,1,1: 18:[41, 4] Operation: 32/8=4 Exploring Operation: 32-8=24, Resulting Numbers: [41, 24] Generated Node #0,1,2: 18:[41, 24] Operation: 32-8=24 Exploring Operation: 41-8=33, Resulting Numbers: [32, 33] Generated Node #0,1,3: 18:[32, 33] Operation: 41-8=33 Exploring Operation: 32+8=40, Resulting Numbers: [41, 40] Generated Node #0,1,4: 18:[41, 40] Operation: 32+8=40 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[8, 9], Operations: ['77-36=41', '41-32=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,18 unequal: No Solution No 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: 18:[41, 4], Operations: ['77-36=41', '32/8=4'] Exploring Operation: 41*4=164, Resulting Numbers: [164] 164,18 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 41+4=45, Resulting Numbers: [45] 45,18 unequal: No Solution No 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: 18:[41, 24], Operations: ['77-36=41', '32-8=24'] Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,18 unequal: No Solution Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,18 unequal: No Solution No 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: 18:[32, 33], Operations: ['77-36=41', '41-8=33'] Exploring Operation: 32+33=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 32*33=1056, Resulting Numbers: [1056] 1056,18 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,18 unequal: No Solution No 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: 18:[41, 40], Operations: ['77-36=41', '32+8=40'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,18 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,18 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: 18:[36, 8, 45], Operations: ['77-32=45'] Exploring Operation: 36-8=28, Resulting Numbers: [45, 28] Generated Node #0,0,0: 18:[45, 28] Operation: 36-8=28 Exploring Operation: 45-36=9, Resulting Numbers: [8, 9] Generated Node #0,0,1: 18:[8, 9] Operation: 45-36=9 Exploring Operation: 36+8=44, Resulting Numbers: [45, 44] Generated Node #0,0,2: 18:[45, 44] Operation: 36+8=44 Exploring Operation: 45-8=37, Resulting Numbers: [36, 37] Generated Node #0,0,3: 18:[36, 37] Operation: 45-8=37 Exploring Operation: 8+45=53, Resulting Numbers: [36, 53] Generated Node #0,0,4: 18:[36, 53] Operation: 8+45=53 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[8, 9], Operations: ['77-32=45', '45-36=9'] Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,18 unequal: No Solution No 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: 18:[45, 28], Operations: ['77-32=45', '36-8=28'] Exploring Operation: 45*28=1260, Resulting Numbers: [1260] 1260,18 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,18 unequal: No Solution No 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: 18:[36, 37], Operations: ['77-32=45', '45-8=37'] Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 36*37=1332, Resulting Numbers: [1332] 1332,18 unequal: No Solution No 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: 18:[45, 44], Operations: ['77-32=45', '36+8=44'] Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,18 unequal: No Solution Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,18 unequal: No Solution No 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: 18:[36, 53], Operations: ['77-32=45', '8+45=53'] Exploring Operation: 36*53=1908, Resulting Numbers: [1908] 1908,18 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,18 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: 18:[77, 8, 4], Operations: ['36-32=4'] Exploring Operation: 8+4=12, Resulting Numbers: [77, 12] Generated Node #0,4,0: 18:[77, 12] Operation: 8+4=12 Exploring Operation: 77-8=69, Resulting Numbers: [4, 69] Generated Node #0,4,1: 18:[4, 69] Operation: 77-8=69 Exploring Operation: 8-4=4, Resulting Numbers: [77, 4] Generated Node #0,4,2: 18:[77, 4] Operation: 8-4=4 Exploring Operation: 77-4=73, Resulting Numbers: [8, 73] Generated Node #0,4,3: 18:[8, 73] Operation: 77-4=73 Exploring Operation: 8/4=2, Resulting Numbers: [77, 2] Generated Node #0,4,4: 18:[77, 2] Operation: 8/4=2 Moving to Node #0,4,1 Current State: 18:[4, 69], Operations: ['36-32=4', '77-8=69'] Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 4*69=276, Resulting Numbers: [276] 276,18 unequal: No Solution Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[8, 73], Operations: ['36-32=4', '77-4=73'] Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,18 unequal: No Solution Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[77, 2], Operations: ['36-32=4', '8/4=2'] Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,18 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,18 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,18 unequal: No Solution Moving to Node #0,4,2 Current State: 18:[77, 4], Operations: ['36-32=4', '8-4=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[77, 12], Operations: ['36-32=4', '8+4=12'] Exploring Operation: 77*12=924, Resulting Numbers: [924] 924,18 unequal: No Solution Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,18 unequal: No Solution Exploring Operation: 77+12=89, Resulting Numbers: [89] 89,18 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 Current State: 18:[36, 77, 4], Operations: ['32/8=4'] Exploring Operation: 36+4=40, Resulting Numbers: [77, 40] Generated Node #0,2,0: 18:[77, 40] Operation: 36+4=40 Exploring Operation: 36/4=9, Resulting Numbers: [77, 9] Generated Node #0,2,1: 18:[77, 9] Operation: 36/4=9 Exploring Operation: 77-36=41, Resulting Numbers: [4, 41] Generated Node #0,2,2: 18:[4, 41] Operation: 77-36=41 Exploring Operation: 36-4=32, Resulting Numbers: [77, 32] Generated Node #0,2,3: 18:[77, 32] Operation: 36-4=32 Exploring Operation: 77-4=73, Resulting Numbers: [36, 73] Generated Node #0,2,4: 18:[36, 73] Operation: 77-4=73 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 18:[4, 41], Operations: ['32/8=4', '77-36=41'] Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,18 unequal: No Solution No 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: 18:[77, 9], Operations: ['32/8=4', '36/4=9'] Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,18 unequal: No Solution Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,18 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,18 unequal: No Solution No 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: 18:[77, 32], Operations: ['32/8=4', '36-4=32'] Exploring Operation: 77-32=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 77*32=2464, Resulting Numbers: [2464] 2464,18 unequal: No Solution Exploring Operation: 77+32=109, Resulting Numbers: [109] 109,18 unequal: No Solution No 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: 18:[36, 73], Operations: ['32/8=4', '77-4=73'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,18 unequal: No Solution No 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: 18:[77, 40], Operations: ['32/8=4', '36+4=40'] Exploring Operation: 77-40=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 77+40=117, Resulting Numbers: [117] 117,18 unequal: No Solution Exploring Operation: 77*40=3080, Resulting Numbers: [3080] 3080,18 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: 18:[77, 32, 28], Operations: ['36-8=28'] Exploring Operation: 32-28=4, Resulting Numbers: [77, 4] Generated Node #0,3,0: 18:[77, 4] Operation: 32-28=4 Exploring Operation: 77-28=49, Resulting Numbers: [32, 49] Generated Node #0,3,1: 18:[32, 49] Operation: 77-28=49 Exploring Operation: 77-32=45, Resulting Numbers: [28, 45] Generated Node #0,3,2: 18:[28, 45] Operation: 77-32=45 Exploring Operation: 77+32=109, Resulting Numbers: [28, 109] Generated Node #0,3,3: 18:[28, 109] Operation: 77+32=109 Exploring Operation: 77+28=105, Resulting Numbers: [32, 105] Generated Node #0,3,4: 18:[32, 105] Operation: 77+28=105 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 18:[28, 45], Operations: ['36-8=28', '77-32=45'] Exploring Operation: 28+45=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 28*45=1260, Resulting Numbers: [1260] 1260,18 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,18 unequal: No Solution No 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: 18:[32, 49], Operations: ['36-8=28', '77-28=49'] Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,18 unequal: No Solution No 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: 18:[77, 4], Operations: ['36-8=28', '32-28=4'] Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,18 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,18 unequal: No Solution No 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: 18:[28, 109], Operations: ['36-8=28', '77+32=109'] Exploring Operation: 28*109=3052, Resulting Numbers: [3052] 3052,18 unequal: No Solution Exploring Operation: 109-28=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 28+109=137, Resulting Numbers: [137] 137,18 unequal: No Solution No 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: 18:[32, 105], Operations: ['36-8=28', '77+28=105'] Exploring Operation: 105-32=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 32*105=3360, Resulting Numbers: [3360] 3360,18 unequal: No Solution Exploring Operation: 32+105=137, Resulting Numbers: [137] 137,18 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
[ 24, 54, 40, 42 ]
20
[ "54-42=12", "24/12=2", "40/2=20" ]
Current State: 20:[24, 54, 40, 42], Operations: [] Exploring Operation: 54-42=12, Resulting Numbers: [24, 40, 12] Generated Node #2: [24, 40, 12] from Operation: 54-42=12 Current State: 20:[24, 40, 12], Operations: ['54-42=12'] Exploring Operation: 24/12=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 24/12=2 Current State: 20:[40, 2], Operations: ['54-42=12', '24/12=2'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[24, 54, 40, 42], Operations: [] Exploring Operation: 54-40=14, Resulting Numbers: [24, 42, 14] Generated Node #0,0: 20:[24, 42, 14] Operation: 54-40=14 Exploring Operation: 54-42=12, Resulting Numbers: [24, 40, 12] Generated Node #0,1: 20:[24, 40, 12] Operation: 54-42=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[24, 40, 12], Operations: ['54-42=12'] Exploring Operation: 40-12=28, Resulting Numbers: [24, 28] Generated Node #0,1,0: 20:[24, 28] Operation: 40-12=28 Exploring Operation: 40-24=16, Resulting Numbers: [12, 16] Generated Node #0,1,1: 20:[12, 16] Operation: 40-24=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 20:[12, 16], Operations: ['54-42=12', '40-24=16'] Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 20:[24, 28], Operations: ['54-42=12', '40-12=28'] Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[24, 42, 14], Operations: ['54-40=14'] Exploring Operation: 42-24=18, Resulting Numbers: [14, 18] Generated Node #0,0,0: 20:[14, 18] Operation: 42-24=18 Exploring Operation: 42/14=3, Resulting Numbers: [24, 3] Generated Node #0,0,1: 20:[24, 3] Operation: 42/14=3 Moving to Node #0,0,1 Current State: 20:[24, 3], Operations: ['54-40=14', '42/14=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,20 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,20 unequal: No Solution Moving to Node #0,0,0 Current State: 20:[14, 18], Operations: ['54-40=14', '42-24=18'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,20 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
[ 56, 37, 74, 82 ]
85
[ "56+37=93", "82-74=8", "93-8=85" ]
Current State: 85:[56, 37, 74, 82], Operations: [] Exploring Operation: 56+37=93, Resulting Numbers: [74, 82, 93] Generated Node #2: [74, 82, 93] from Operation: 56+37=93 Current State: 85:[74, 82, 93], Operations: ['56+37=93'] Exploring Operation: 82-74=8, Resulting Numbers: [93, 8] Generated Node #3: [93, 8] from Operation: 82-74=8 Current State: 85:[93, 8], Operations: ['56+37=93', '82-74=8'] Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[56, 37, 74, 82], Operations: [] Exploring Operation: 56+37=93, Resulting Numbers: [74, 82, 93] Generated Node #0,0: 85:[74, 82, 93] Operation: 56+37=93 Exploring Operation: 56-37=19, Resulting Numbers: [74, 82, 19] Generated Node #0,1: 85:[74, 82, 19] Operation: 56-37=19 Moving to Node #0,1 Current State: 85:[74, 82, 19], Operations: ['56-37=19'] Exploring Operation: 82-74=8, Resulting Numbers: [19, 8] Generated Node #0,1,0: 85:[19, 8] Operation: 82-74=8 Exploring Operation: 74+19=93, Resulting Numbers: [82, 93] Generated Node #0,1,1: 85:[82, 93] Operation: 74+19=93 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[19, 8], Operations: ['56-37=19', '82-74=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[82, 93], Operations: ['56-37=19', '74+19=93'] Exploring Operation: 82+93=175, Resulting Numbers: [175] 175,85 unequal: No Solution Exploring Operation: 93-82=11, Resulting Numbers: [11] 11,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 85:[74, 82, 93], Operations: ['56+37=93'] Exploring Operation: 93-74=19, Resulting Numbers: [82, 19] Generated Node #0,0,0: 85:[82, 19] Operation: 93-74=19 Exploring Operation: 82-74=8, Resulting Numbers: [93, 8] Generated Node #0,0,1: 85:[93, 8] Operation: 82-74=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[82, 19], Operations: ['56+37=93', '93-74=19'] Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,85 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:[93, 8], Operations: ['56+37=93', '82-74=8'] Exploring Operation: 93+8=101, Resulting Numbers: [101] 101,85 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[56, 37, 74, 82], Operations: [] Exploring Operation: 56+37=93, Resulting Numbers: [74, 82, 93] Generated Node #0,0: 85:[74, 82, 93] Operation: 56+37=93 Moving to Node #0,0 Current State: 85:[74, 82, 93], Operations: ['56+37=93'] Exploring Operation: 82-74=8, Resulting Numbers: [93, 8] Generated Node #0,0,1: 85:[93, 8] Operation: 82-74=8 Moving to Node #0,0,1 Current State: 85:[93, 8], Operations: ['56+37=93', '82-74=8'] Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 38, 84, 65, 47 ]
45
[ "84-65=19", "38/19=2", "47-2=45" ]
Current State: 45:[38, 84, 65, 47], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [38, 47, 19] Generated Node #2: [38, 47, 19] from Operation: 84-65=19 Current State: 45:[38, 47, 19], Operations: ['84-65=19'] Exploring Operation: 38/19=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 38/19=2 Current State: 45:[47, 2], Operations: ['84-65=19', '38/19=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[38, 84, 65, 47], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [38, 47, 19] Generated Node #0,0: 45:[38, 47, 19] Operation: 84-65=19 Exploring Operation: 84-38=46, Resulting Numbers: [65, 47, 46] Generated Node #0,1: 45:[65, 47, 46] Operation: 84-38=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[38, 47, 19], Operations: ['84-65=19'] Exploring Operation: 38/19=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 45:[47, 2] Operation: 38/19=2 Exploring Operation: 47-38=9, Resulting Numbers: [19, 9] Generated Node #0,0,1: 45:[19, 9] Operation: 47-38=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[47, 2], Operations: ['84-65=19', '38/19=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[38, 84, 65, 47], Operations: [] Exploring Operation: 84-65=19, Resulting Numbers: [38, 47, 19] Generated Node #0,0: 45:[38, 47, 19] Operation: 84-65=19 Moving to Node #0,0 Current State: 45:[38, 47, 19], Operations: ['84-65=19'] Exploring Operation: 38/19=2, Resulting Numbers: [47, 2] Generated Node #0,0,0: 45:[47, 2] Operation: 38/19=2 Moving to Node #0,0,0 Current State: 45:[47, 2], Operations: ['84-65=19', '38/19=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 33, 84, 27, 96 ]
82
[ "33-27=6", "84/6=14", "96-14=82" ]
Current State: 82:[33, 84, 27, 96], Operations: [] Exploring Operation: 33-27=6, Resulting Numbers: [84, 96, 6] Generated Node #2: [84, 96, 6] from Operation: 33-27=6 Current State: 82:[84, 96, 6], Operations: ['33-27=6'] Exploring Operation: 84/6=14, Resulting Numbers: [96, 14] Generated Node #3: [96, 14] from Operation: 84/6=14 Current State: 82:[96, 14], Operations: ['33-27=6', '84/6=14'] Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[33, 84, 27, 96], Operations: [] Exploring Operation: 33-27=6, Resulting Numbers: [84, 96, 6] Generated Node #0,0: 82:[84, 96, 6] Operation: 33-27=6 Exploring Operation: 33+27=60, Resulting Numbers: [84, 96, 60] Generated Node #0,1: 82:[84, 96, 60] Operation: 33+27=60 Exploring Operation: 96-27=69, Resulting Numbers: [33, 84, 69] Generated Node #0,2: 82:[33, 84, 69] Operation: 96-27=69 Exploring Operation: 96-84=12, Resulting Numbers: [33, 27, 12] Generated Node #0,3: 82:[33, 27, 12] Operation: 96-84=12 Exploring Operation: 96-33=63, Resulting Numbers: [84, 27, 63] Generated Node #0,4: 82:[84, 27, 63] Operation: 96-33=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[84, 96, 6], Operations: ['33-27=6'] Exploring Operation: 84+6=90, Resulting Numbers: [96, 90] Generated Node #0,0,0: 82:[96, 90] Operation: 84+6=90 Exploring Operation: 84-6=78, Resulting Numbers: [96, 78] Generated Node #0,0,1: 82:[96, 78] Operation: 84-6=78 Exploring Operation: 96-84=12, Resulting Numbers: [6, 12] Generated Node #0,0,2: 82:[6, 12] Operation: 96-84=12 Exploring Operation: 96-6=90, Resulting Numbers: [84, 90] Generated Node #0,0,3: 82:[84, 90] Operation: 96-6=90 Exploring Operation: 96/6=16, Resulting Numbers: [84, 16] Generated Node #0,0,4: 82:[84, 16] Operation: 96/6=16 Moving to Node #0,0,3 Current State: 82:[84, 90], Operations: ['33-27=6', '96-6=90'] Exploring Operation: 84+90=174, Resulting Numbers: [174] 174,82 unequal: No Solution Exploring Operation: 84*90=7560, Resulting Numbers: [7560] 7560,82 unequal: No Solution Exploring Operation: 90-84=6, Resulting Numbers: [6] 6,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[6, 12], Operations: ['33-27=6', '96-84=12'] Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,0,4 Current State: 82:[84, 16], Operations: ['33-27=6', '96/6=16'] Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,82 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,82 unequal: No Solution Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[96, 78], Operations: ['33-27=6', '84-6=78'] Exploring Operation: 96-78=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 96*78=7488, Resulting Numbers: [7488] 7488,82 unequal: No Solution Exploring Operation: 96+78=174, Resulting Numbers: [174] 174,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[96, 90], Operations: ['33-27=6', '84+6=90'] Exploring Operation: 96*90=8640, Resulting Numbers: [8640] 8640,82 unequal: No Solution Exploring Operation: 96-90=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 96+90=186, Resulting Numbers: [186] 186,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[33, 84, 69], Operations: ['96-27=69'] Exploring Operation: 69-33=36, Resulting Numbers: [84, 36] Generated Node #0,2,0: 82:[84, 36] Operation: 69-33=36 Exploring Operation: 33+69=102, Resulting Numbers: [84, 102] Generated Node #0,2,1: 82:[84, 102] Operation: 33+69=102 Exploring Operation: 84-69=15, Resulting Numbers: [33, 15] Generated Node #0,2,2: 82:[33, 15] Operation: 84-69=15 Exploring Operation: 33+84=117, Resulting Numbers: [69, 117] Generated Node #0,2,3: 82:[69, 117] Operation: 33+84=117 Exploring Operation: 84-33=51, Resulting Numbers: [69, 51] Generated Node #0,2,4: 82:[69, 51] Operation: 84-33=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[84, 36], Operations: ['96-27=69', '69-33=36'] Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,82 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[33, 15], Operations: ['96-27=69', '84-69=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[84, 102], Operations: ['96-27=69', '33+69=102'] Exploring Operation: 84*102=8568, Resulting Numbers: [8568] 8568,82 unequal: No Solution Exploring Operation: 84+102=186, Resulting Numbers: [186] 186,82 unequal: No Solution Exploring Operation: 102-84=18, Resulting Numbers: [18] 18,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 82:[69, 51], Operations: ['96-27=69', '84-33=51'] Exploring Operation: 69*51=3519, Resulting Numbers: [3519] 3519,82 unequal: No Solution Exploring Operation: 69+51=120, Resulting Numbers: [120] 120,82 unequal: No Solution Exploring Operation: 69-51=18, Resulting Numbers: [18] 18,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[69, 117], Operations: ['96-27=69', '33+84=117'] Exploring Operation: 117-69=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 69+117=186, Resulting Numbers: [186] 186,82 unequal: No Solution Exploring Operation: 69*117=8073, Resulting Numbers: [8073] 8073,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[33, 27, 12], Operations: ['96-84=12'] Exploring Operation: 33-27=6, Resulting Numbers: [12, 6] Generated Node #0,3,0: 82:[12, 6] Operation: 33-27=6 Exploring Operation: 33+12=45, Resulting Numbers: [27, 45] Generated Node #0,3,1: 82:[27, 45] Operation: 33+12=45 Exploring Operation: 33+27=60, Resulting Numbers: [12, 60] Generated Node #0,3,2: 82:[12, 60] Operation: 33+27=60 Exploring Operation: 27-12=15, Resulting Numbers: [33, 15] Generated Node #0,3,3: 82:[33, 15] Operation: 27-12=15 Exploring Operation: 27+12=39, Resulting Numbers: [33, 39] Generated Node #0,3,4: 82:[33, 39] Operation: 27+12=39 Moving to Node #0,3,4 Current State: 82:[33, 39], Operations: ['96-84=12', '27+12=39'] Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,82 unequal: No Solution Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[12, 6], Operations: ['96-84=12', '33-27=6'] Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,82 unequal: No Solution Moving to Node #0,3,1 Current State: 82:[27, 45], Operations: ['96-84=12', '33+12=45'] Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 27*45=1215, Resulting Numbers: [1215] 1215,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[33, 15], Operations: ['96-84=12', '27-12=15'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,82 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,82 unequal: No Solution Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[12, 60], Operations: ['96-84=12', '33+27=60'] Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 12*60=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 12+60=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[84, 96, 60], Operations: ['33+27=60'] Exploring Operation: 84-60=24, Resulting Numbers: [96, 24] Generated Node #0,1,0: 82:[96, 24] Operation: 84-60=24 Exploring Operation: 96-60=36, Resulting Numbers: [84, 36] Generated Node #0,1,1: 82:[84, 36] Operation: 96-60=36 Exploring Operation: 96-84=12, Resulting Numbers: [60, 12] Generated Node #0,1,2: 82:[60, 12] Operation: 96-84=12 Exploring Operation: 96+60=156, Resulting Numbers: [84, 156] Generated Node #0,1,3: 82:[84, 156] Operation: 96+60=156 Exploring Operation: 84+60=144, Resulting Numbers: [96, 144] Generated Node #0,1,4: 82:[96, 144] Operation: 84+60=144 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[84, 36], Operations: ['33+27=60', '96-60=36'] Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,82 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[60, 12], Operations: ['33+27=60', '96-84=12'] Exploring Operation: 60*12=720, Resulting Numbers: [720] 720,82 unequal: No Solution Exploring Operation: 60/12=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 60+12=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 60-12=48, Resulting Numbers: [48] 48,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[96, 24], Operations: ['33+27=60', '84-60=24'] Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 96*24=2304, Resulting Numbers: [2304] 2304,82 unequal: No Solution Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,82 unequal: No Solution Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 82:[84, 156], Operations: ['33+27=60', '96+60=156'] Exploring Operation: 156-84=72, Resulting Numbers: [72] 72,82 unequal: No Solution Exploring Operation: 84*156=13104, Resulting Numbers: [13104] 13104,82 unequal: No Solution Exploring Operation: 84+156=240, Resulting Numbers: [240] 240,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 82:[96, 144], Operations: ['33+27=60', '84+60=144'] Exploring Operation: 96*144=13824, Resulting Numbers: [13824] 13824,82 unequal: No Solution Exploring Operation: 96+144=240, Resulting Numbers: [240] 240,82 unequal: No Solution Exploring Operation: 144-96=48, Resulting Numbers: [48] 48,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 82:[84, 27, 63], Operations: ['96-33=63'] Exploring Operation: 84+27=111, Resulting Numbers: [63, 111] Generated Node #0,4,0: 82:[63, 111] Operation: 84+27=111 Exploring Operation: 27+63=90, Resulting Numbers: [84, 90] Generated Node #0,4,1: 82:[84, 90] Operation: 27+63=90 Exploring Operation: 63-27=36, Resulting Numbers: [84, 36] Generated Node #0,4,2: 82:[84, 36] Operation: 63-27=36 Exploring Operation: 84-27=57, Resulting Numbers: [63, 57] Generated Node #0,4,3: 82:[63, 57] Operation: 84-27=57 Exploring Operation: 84-63=21, Resulting Numbers: [27, 21] Generated Node #0,4,4: 82:[27, 21] Operation: 84-63=21 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 82:[84, 36], Operations: ['96-33=63', '63-27=36'] Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,82 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 82:[84, 90], Operations: ['96-33=63', '27+63=90'] Exploring Operation: 84+90=174, Resulting Numbers: [174] 174,82 unequal: No Solution Exploring Operation: 90-84=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 84*90=7560, Resulting Numbers: [7560] 7560,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 82:[27, 21], Operations: ['96-33=63', '84-63=21'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,82 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 82:[63, 57], Operations: ['96-33=63', '84-27=57'] Exploring Operation: 63+57=120, Resulting Numbers: [120] 120,82 unequal: No Solution Exploring Operation: 63*57=3591, Resulting Numbers: [3591] 3591,82 unequal: No Solution Exploring Operation: 63-57=6, Resulting Numbers: [6] 6,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 82:[63, 111], Operations: ['96-33=63', '84+27=111'] Exploring Operation: 111-63=48, Resulting Numbers: [48] 48,82 unequal: No Solution Exploring Operation: 63*111=6993, Resulting Numbers: [6993] 6993,82 unequal: No Solution Exploring Operation: 63+111=174, Resulting Numbers: [174] 174,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 75, 40, 80, 14 ]
32
[ "75-40=35", "80*14=1120", "1120/35=32" ]
Current State: 32:[75, 40, 80, 14], Operations: [] Exploring Operation: 75-40=35, Resulting Numbers: [80, 14, 35] Generated Node #2: [80, 14, 35] from Operation: 75-40=35 Current State: 32:[80, 14, 35], Operations: ['75-40=35'] Exploring Operation: 80*14=1120, Resulting Numbers: [35, 1120] Generated Node #3: [35, 1120] from Operation: 80*14=1120 Current State: 32:[35, 1120], Operations: ['75-40=35', '80*14=1120'] Exploring Operation: 1120/35=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[75, 40, 80, 14], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [75, 14, 2] Generated Node #0,0: 32:[75, 14, 2] Operation: 80/40=2 Exploring Operation: 80-40=40, Resulting Numbers: [75, 14, 40] Generated Node #0,1: 32:[75, 14, 40] Operation: 80-40=40 Exploring Operation: 75-40=35, Resulting Numbers: [80, 14, 35] Generated Node #0,2: 32:[80, 14, 35] Operation: 75-40=35 Exploring Operation: 80-75=5, Resulting Numbers: [40, 14, 5] Generated Node #0,3: 32:[40, 14, 5] Operation: 80-75=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[40, 14, 5], Operations: ['80-75=5'] Exploring Operation: 14-5=9, Resulting Numbers: [40, 9] Generated Node #0,3,0: 32:[40, 9] Operation: 14-5=9 Exploring Operation: 40/5=8, Resulting Numbers: [14, 8] Generated Node #0,3,1: 32:[14, 8] Operation: 40/5=8 Exploring Operation: 40-14=26, Resulting Numbers: [5, 26] Generated Node #0,3,2: 32:[5, 26] Operation: 40-14=26 Exploring Operation: 40-5=35, Resulting Numbers: [14, 35] Generated Node #0,3,3: 32:[14, 35] Operation: 40-5=35 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 32:[14, 8], Operations: ['80-75=5', '40/5=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,32 unequal: No Solution No 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: 32:[14, 35], Operations: ['80-75=5', '40-5=35'] Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,32 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,32 unequal: No Solution No 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: 32:[5, 26], Operations: ['80-75=5', '40-14=26'] Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,32 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,32 unequal: No Solution No 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: 32:[40, 9], Operations: ['80-75=5', '14-5=9'] Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 40*9=360, Resulting Numbers: [360] 360,32 unequal: No Solution Exploring Operation: 40+9=49, Resulting Numbers: [49] 49,32 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: 32:[75, 14, 2], Operations: ['80/40=2'] Exploring Operation: 14+2=16, Resulting Numbers: [75, 16] Generated Node #0,0,0: 32:[75, 16] Operation: 14+2=16 Exploring Operation: 75-14=61, Resulting Numbers: [2, 61] Generated Node #0,0,1: 32:[2, 61] Operation: 75-14=61 Exploring Operation: 14/2=7, Resulting Numbers: [75, 7] Generated Node #0,0,2: 32:[75, 7] Operation: 14/2=7 Exploring Operation: 75-2=73, Resulting Numbers: [14, 73] Generated Node #0,0,3: 32:[14, 73] Operation: 75-2=73 Moving to Node #0,0,1 Current State: 32:[2, 61], Operations: ['80/40=2', '75-14=61'] Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 2*61=122, Resulting Numbers: [122] 122,32 unequal: No Solution Exploring Operation: 2+61=63, Resulting Numbers: [63] 63,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[14, 73], Operations: ['80/40=2', '75-2=73'] Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 14*73=1022, Resulting Numbers: [1022] 1022,32 unequal: No Solution Exploring Operation: 14+73=87, Resulting Numbers: [87] 87,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[75, 16], Operations: ['80/40=2', '14+2=16'] Exploring Operation: 75-16=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 75*16=1200, Resulting Numbers: [1200] 1200,32 unequal: No Solution Exploring Operation: 75+16=91, Resulting Numbers: [91] 91,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[75, 7], Operations: ['80/40=2', '14/2=7'] Exploring Operation: 75*7=525, Resulting Numbers: [525] 525,32 unequal: No Solution Exploring Operation: 75-7=68, Resulting Numbers: [68] 68,32 unequal: No Solution Exploring Operation: 75+7=82, Resulting Numbers: [82] 82,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[75, 14, 40], Operations: ['80-40=40'] Exploring Operation: 75-14=61, Resulting Numbers: [40, 61] Generated Node #0,1,0: 32:[40, 61] Operation: 75-14=61 Exploring Operation: 75+14=89, Resulting Numbers: [40, 89] Generated Node #0,1,1: 32:[40, 89] Operation: 75+14=89 Exploring Operation: 40-14=26, Resulting Numbers: [75, 26] Generated Node #0,1,2: 32:[75, 26] Operation: 40-14=26 Exploring Operation: 75-40=35, Resulting Numbers: [14, 35] Generated Node #0,1,3: 32:[14, 35] Operation: 75-40=35 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 32:[14, 35], Operations: ['80-40=40', '75-40=35'] Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,32 unequal: No Solution No 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: 32:[40, 61], Operations: ['80-40=40', '75-14=61'] Exploring Operation: 40+61=101, Resulting Numbers: [101] 101,32 unequal: No Solution Exploring Operation: 40*61=2440, Resulting Numbers: [2440] 2440,32 unequal: No Solution Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,32 unequal: No Solution No 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: 32:[75, 26], Operations: ['80-40=40', '40-14=26'] Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 75*26=1950, Resulting Numbers: [1950] 1950,32 unequal: No Solution Exploring Operation: 75+26=101, Resulting Numbers: [101] 101,32 unequal: No Solution No 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: 32:[40, 89], Operations: ['80-40=40', '75+14=89'] Exploring Operation: 40*89=3560, Resulting Numbers: [3560] 3560,32 unequal: No Solution Exploring Operation: 89-40=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 40+89=129, Resulting Numbers: [129] 129,32 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: 32:[80, 14, 35], Operations: ['75-40=35'] Exploring Operation: 80-35=45, Resulting Numbers: [14, 45] Generated Node #0,2,0: 32:[14, 45] Operation: 80-35=45 Exploring Operation: 80-14=66, Resulting Numbers: [35, 66] Generated Node #0,2,1: 32:[35, 66] Operation: 80-14=66 Exploring Operation: 35-14=21, Resulting Numbers: [80, 21] Generated Node #0,2,2: 32:[80, 21] Operation: 35-14=21 Exploring Operation: 80+14=94, Resulting Numbers: [35, 94] Generated Node #0,2,3: 32:[35, 94] Operation: 80+14=94 Moving to Node #0,2,0 Current State: 32:[14, 45], Operations: ['75-40=35', '80-35=45'] Exploring Operation: 14*45=630, Resulting Numbers: [630] 630,32 unequal: No Solution Exploring Operation: 14+45=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[35, 66], Operations: ['75-40=35', '80-14=66'] Exploring Operation: 35+66=101, Resulting Numbers: [101] 101,32 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 35*66=2310, Resulting Numbers: [2310] 2310,32 unequal: No Solution Moving to Node #0,2,2 Current State: 32:[80, 21], Operations: ['75-40=35', '35-14=21'] Exploring Operation: 80+21=101, Resulting Numbers: [101] 101,32 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 80*21=1680, Resulting Numbers: [1680] 1680,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[35, 94], Operations: ['75-40=35', '80+14=94'] Exploring Operation: 35+94=129, Resulting Numbers: [129] 129,32 unequal: No Solution Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 35*94=3290, Resulting Numbers: [3290] 3290,32 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
[ 38, 47, 11, 90 ]
45
[ "47-38=9", "11-9=2", "90/2=45" ]
Current State: 45:[38, 47, 11, 90], Operations: [] Exploring Operation: 47-38=9, Resulting Numbers: [11, 90, 9] Generated Node #2: [11, 90, 9] from Operation: 47-38=9 Current State: 45:[11, 90, 9], Operations: ['47-38=9'] Exploring Operation: 11-9=2, Resulting Numbers: [90, 2] Generated Node #3: [90, 2] from Operation: 11-9=2 Current State: 45:[90, 2], Operations: ['47-38=9', '11-9=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[38, 47, 11, 90], Operations: [] Exploring Operation: 90-47=43, Resulting Numbers: [38, 11, 43] Generated Node #0,0: 45:[38, 11, 43] Operation: 90-47=43 Exploring Operation: 47-38=9, Resulting Numbers: [11, 90, 9] Generated Node #0,1: 45:[11, 90, 9] Operation: 47-38=9 Exploring Operation: 38+11=49, Resulting Numbers: [47, 90, 49] Generated Node #0,2: 45:[47, 90, 49] Operation: 38+11=49 Exploring Operation: 90-38=52, Resulting Numbers: [47, 11, 52] Generated Node #0,3: 45:[47, 11, 52] Operation: 90-38=52 Exploring Operation: 90-11=79, Resulting Numbers: [38, 47, 79] Generated Node #0,4: 45:[38, 47, 79] Operation: 90-11=79 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[38, 11, 43], Operations: ['90-47=43'] Exploring Operation: 38+11=49, Resulting Numbers: [43, 49] Generated Node #0,0,0: 45:[43, 49] Operation: 38+11=49 Exploring Operation: 43-38=5, Resulting Numbers: [11, 5] Generated Node #0,0,1: 45:[11, 5] Operation: 43-38=5 Exploring Operation: 43-11=32, Resulting Numbers: [38, 32] Generated Node #0,0,2: 45:[38, 32] Operation: 43-11=32 Exploring Operation: 38-11=27, Resulting Numbers: [43, 27] Generated Node #0,0,3: 45:[43, 27] Operation: 38-11=27 Exploring Operation: 11+43=54, Resulting Numbers: [38, 54] Generated Node #0,0,4: 45:[38, 54] Operation: 11+43=54 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 45:[11, 5], Operations: ['90-47=43', '43-38=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,45 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[43, 49], Operations: ['90-47=43', '38+11=49'] Exploring Operation: 43*49=2107, Resulting Numbers: [2107] 2107,45 unequal: No Solution Exploring Operation: 43+49=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 49-43=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 45:[43, 27], Operations: ['90-47=43', '38-11=27'] Exploring Operation: 43*27=1161, Resulting Numbers: [1161] 1161,45 unequal: No Solution Exploring Operation: 43+27=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 43-27=16, Resulting Numbers: [16] 16,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 45:[38, 54], Operations: ['90-47=43', '11+43=54'] Exploring Operation: 38+54=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 38*54=2052, Resulting Numbers: [2052] 2052,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[38, 32], Operations: ['90-47=43', '43-11=32'] Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,45 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[47, 11, 52], Operations: ['90-38=52'] Exploring Operation: 47-11=36, Resulting Numbers: [52, 36] Generated Node #0,3,0: 45:[52, 36] Operation: 47-11=36 Exploring Operation: 52-11=41, Resulting Numbers: [47, 41] Generated Node #0,3,1: 45:[47, 41] Operation: 52-11=41 Exploring Operation: 52-47=5, Resulting Numbers: [11, 5] Generated Node #0,3,2: 45:[11, 5] Operation: 52-47=5 Exploring Operation: 47+11=58, Resulting Numbers: [52, 58] Generated Node #0,3,3: 45:[52, 58] Operation: 47+11=58 Exploring Operation: 11+52=63, Resulting Numbers: [47, 63] Generated Node #0,3,4: 45:[47, 63] Operation: 11+52=63 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 45:[11, 5], Operations: ['90-38=52', '52-47=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,45 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 45:[47, 41], Operations: ['90-38=52', '52-11=41'] Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 45:[52, 36], Operations: ['90-38=52', '47-11=36'] Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 52*36=1872, Resulting Numbers: [1872] 1872,45 unequal: No Solution Exploring Operation: 52+36=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 45:[52, 58], Operations: ['90-38=52', '47+11=58'] Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 52*58=3016, Resulting Numbers: [3016] 3016,45 unequal: No Solution Exploring Operation: 52+58=110, Resulting Numbers: [110] 110,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 45:[47, 63], Operations: ['90-38=52', '11+52=63'] Exploring Operation: 47*63=2961, Resulting Numbers: [2961] 2961,45 unequal: No Solution Exploring Operation: 47+63=110, Resulting Numbers: [110] 110,45 unequal: No Solution Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 45:[38, 47, 79], Operations: ['90-11=79'] Exploring Operation: 47-38=9, Resulting Numbers: [79, 9] Generated Node #0,4,0: 45:[79, 9] Operation: 47-38=9 Exploring Operation: 38+47=85, Resulting Numbers: [79, 85] Generated Node #0,4,1: 45:[79, 85] Operation: 38+47=85 Exploring Operation: 79-38=41, Resulting Numbers: [47, 41] Generated Node #0,4,2: 45:[47, 41] Operation: 79-38=41 Exploring Operation: 79-47=32, Resulting Numbers: [38, 32] Generated Node #0,4,3: 45:[38, 32] Operation: 79-47=32 Exploring Operation: 38+79=117, Resulting Numbers: [47, 117] Generated Node #0,4,4: 45:[47, 117] Operation: 38+79=117 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 45:[47, 41], Operations: ['90-11=79', '79-38=41'] Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,45 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 45:[38, 32], Operations: ['90-11=79', '79-47=32'] Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,45 unequal: No Solution Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 45:[79, 9], Operations: ['90-11=79', '47-38=9'] Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,45 unequal: No Solution Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 45:[79, 85], Operations: ['90-11=79', '38+47=85'] Exploring Operation: 79+85=164, Resulting Numbers: [164] 164,45 unequal: No Solution Exploring Operation: 85-79=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 79*85=6715, Resulting Numbers: [6715] 6715,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 45:[47, 117], Operations: ['90-11=79', '38+79=117'] Exploring Operation: 47+117=164, Resulting Numbers: [164] 164,45 unequal: No Solution Exploring Operation: 117-47=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 47*117=5499, Resulting Numbers: [5499] 5499,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[11, 90, 9], Operations: ['47-38=9'] Exploring Operation: 90-11=79, Resulting Numbers: [9, 79] Generated Node #0,1,0: 45:[9, 79] Operation: 90-11=79 Exploring Operation: 90-9=81, Resulting Numbers: [11, 81] Generated Node #0,1,1: 45:[11, 81] Operation: 90-9=81 Exploring Operation: 90/9=10, Resulting Numbers: [11, 10] Generated Node #0,1,2: 45:[11, 10] Operation: 90/9=10 Exploring Operation: 11+9=20, Resulting Numbers: [90, 20] Generated Node #0,1,3: 45:[90, 20] Operation: 11+9=20 Exploring Operation: 11-9=2, Resulting Numbers: [90, 2] Generated Node #0,1,4: 45:[90, 2] Operation: 11-9=2 Moving to Node #0,1,2 Current State: 45:[11, 10], Operations: ['47-38=9', '90/9=10'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 11*10=110, Resulting Numbers: [110] 110,45 unequal: No Solution Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[9, 79], Operations: ['47-38=9', '90-11=79'] Exploring Operation: 9*79=711, Resulting Numbers: [711] 711,45 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,45 unequal: No Solution Exploring Operation: 9+79=88, Resulting Numbers: [88] 88,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[11, 81], Operations: ['47-38=9', '90-9=81'] Exploring Operation: 11*81=891, Resulting Numbers: [891] 891,45 unequal: No Solution Exploring Operation: 11+81=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,45 unequal: No Solution Moving to Node #0,1,4 Current State: 45:[90, 2], Operations: ['47-38=9', '11-9=2'] Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,45 unequal: No Solution Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,45 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[38, 47, 11, 90], Operations: [] Exploring Operation: 47-38=9, Resulting Numbers: [11, 90, 9] Generated Node #0,1: 45:[11, 90, 9] Operation: 47-38=9 Moving to Node #0,1 Current State: 45:[11, 90, 9], Operations: ['47-38=9'] Exploring Operation: 11-9=2, Resulting Numbers: [90, 2] Generated Node #0,1,4: 45:[90, 2] Operation: 11-9=2 Moving to Node #0,1,4 Current State: 45:[90, 2], Operations: ['47-38=9', '11-9=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.925347
hs_5
mult_heuristic
[ 21, 48, 8, 51 ]
71
[ "51-48=3", "21*3=63", "8+63=71" ]
Current State: 71:[21, 48, 8, 51], Operations: [] Exploring Operation: 51-48=3, Resulting Numbers: [21, 8, 3] Generated Node #2: [21, 8, 3] from Operation: 51-48=3 Current State: 71:[21, 8, 3], Operations: ['51-48=3'] Exploring Operation: 21*3=63, Resulting Numbers: [8, 63] Generated Node #3: [8, 63] from Operation: 21*3=63 Current State: 71:[8, 63], Operations: ['51-48=3', '21*3=63'] Exploring Operation: 8+63=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[21, 48, 8, 51], Operations: [] Exploring Operation: 21+8=29, Resulting Numbers: [48, 51, 29] Generated Node #0,0: 71:[48, 51, 29] Operation: 21+8=29 Exploring Operation: 21+48=69, Resulting Numbers: [8, 51, 69] Generated Node #0,1: 71:[8, 51, 69] Operation: 21+48=69 Moving to Node #0,0 Current State: 71:[48, 51, 29], Operations: ['21+8=29'] Exploring Operation: 51+29=80, Resulting Numbers: [48, 80] Generated Node #0,0,0: 71:[48, 80] Operation: 51+29=80 Exploring Operation: 48+29=77, Resulting Numbers: [51, 77] Generated Node #0,0,1: 71:[51, 77] Operation: 48+29=77 Moving to Node #0,1 Current State: 71:[8, 51, 69], Operations: ['21+48=69'] Exploring Operation: 8+69=77, Resulting Numbers: [51, 77] Generated Node #0,1,0: 71:[51, 77] Operation: 8+69=77 Exploring Operation: 8+51=59, Resulting Numbers: [69, 59] Generated Node #0,1,1: 71:[69, 59] Operation: 8+51=59 Moving to Node #0,1,1 Current State: 71:[69, 59], Operations: ['21+48=69', '8+51=59'] Exploring Operation: 69-59=10, Resulting Numbers: [10] 10,71 unequal: No Solution Exploring Operation: 69+59=128, Resulting Numbers: [128] 128,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[51, 77], Operations: ['21+8=29', '48+29=77'] Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[51, 77], Operations: ['21+48=69', '8+69=77'] Exploring Operation: 51+77=128, Resulting Numbers: [128] 128,71 unequal: No Solution Exploring Operation: 77-51=26, Resulting Numbers: [26] 26,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[48, 80], Operations: ['21+8=29', '51+29=80'] Exploring Operation: 80-48=32, Resulting Numbers: [32] 32,71 unequal: No Solution Exploring Operation: 48+80=128, Resulting Numbers: [128] 128,71 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 95, 94, 93, 28 ]
68
[ "95+94=189", "93+28=121", "189-121=68" ]
Current State: 68:[95, 94, 93, 28], Operations: [] Exploring Operation: 95+94=189, Resulting Numbers: [93, 28, 189] Generated Node #2: [93, 28, 189] from Operation: 95+94=189 Current State: 68:[93, 28, 189], Operations: ['95+94=189'] Exploring Operation: 93+28=121, Resulting Numbers: [189, 121] Generated Node #3: [189, 121] from Operation: 93+28=121 Current State: 68:[189, 121], Operations: ['95+94=189', '93+28=121'] Exploring Operation: 189-121=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[95, 94, 93, 28], Operations: [] Exploring Operation: 94-28=66, Resulting Numbers: [95, 93, 66] Generated Node #0,0: 68:[95, 93, 66] Operation: 94-28=66 Exploring Operation: 95-93=2, Resulting Numbers: [94, 28, 2] Generated Node #0,1: 68:[94, 28, 2] Operation: 95-93=2 Exploring Operation: 94-93=1, Resulting Numbers: [95, 28, 1] Generated Node #0,2: 68:[95, 28, 1] Operation: 94-93=1 Exploring Operation: 95-94=1, Resulting Numbers: [93, 28, 1] Generated Node #0,3: 68:[93, 28, 1] Operation: 95-94=1 Exploring Operation: 95-28=67, Resulting Numbers: [94, 93, 67] Generated Node #0,4: 68:[94, 93, 67] Operation: 95-28=67 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[94, 28, 2], Operations: ['95-93=2'] Exploring Operation: 94-28=66, Resulting Numbers: [2, 66] Generated Node #0,1,0: 68:[2, 66] Operation: 94-28=66 Exploring Operation: 94-2=92, Resulting Numbers: [28, 92] Generated Node #0,1,1: 68:[28, 92] Operation: 94-2=92 Exploring Operation: 28+2=30, Resulting Numbers: [94, 30] Generated Node #0,1,2: 68:[94, 30] Operation: 28+2=30 Exploring Operation: 28/2=14, Resulting Numbers: [94, 14] Generated Node #0,1,3: 68:[94, 14] Operation: 28/2=14 Exploring Operation: 94/2=47, Resulting Numbers: [28, 47] Generated Node #0,1,4: 68:[28, 47] Operation: 94/2=47 Moving to Node #0,1,0 Current State: 68:[2, 66], Operations: ['95-93=2', '94-28=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,68 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[95, 94, 93, 28], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [94, 28, 2] Generated Node #0,1: 68:[94, 28, 2] Operation: 95-93=2 Moving to Node #0,1 Current State: 68:[94, 28, 2], Operations: ['95-93=2'] Exploring Operation: 94-28=66, Resulting Numbers: [2, 66] Generated Node #0,1,0: 68:[2, 66] Operation: 94-28=66 Moving to Node #0,1,0 Current State: 68:[2, 66], Operations: ['95-93=2', '94-28=66'] Exploring Operation: 2+66=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 24, 5, 32, 34 ]
52
[ "5+34=39", "32*39=1248", "1248/24=52" ]
Current State: 52:[24, 5, 32, 34], Operations: [] Exploring Operation: 5+34=39, Resulting Numbers: [24, 32, 39] Generated Node #2: [24, 32, 39] from Operation: 5+34=39 Current State: 52:[24, 32, 39], Operations: ['5+34=39'] Exploring Operation: 32*39=1248, Resulting Numbers: [24, 1248] Generated Node #3: [24, 1248] from Operation: 32*39=1248 Current State: 52:[24, 1248], Operations: ['5+34=39', '32*39=1248'] Exploring Operation: 1248/24=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[24, 5, 32, 34], Operations: [] Exploring Operation: 34-24=10, Resulting Numbers: [5, 32, 10] Generated Node #0,0: 52:[5, 32, 10] Operation: 34-24=10 Exploring Operation: 32-5=27, Resulting Numbers: [24, 34, 27] Generated Node #0,1: 52:[24, 34, 27] Operation: 32-5=27 Exploring Operation: 24+32=56, Resulting Numbers: [5, 34, 56] Generated Node #0,2: 52:[5, 34, 56] Operation: 24+32=56 Exploring Operation: 34-32=2, Resulting Numbers: [24, 5, 2] Generated Node #0,3: 52:[24, 5, 2] Operation: 34-32=2 Exploring Operation: 34-5=29, Resulting Numbers: [24, 32, 29] Generated Node #0,4: 52:[24, 32, 29] Operation: 34-5=29 Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[24, 5, 2], Operations: ['34-32=2'] Exploring Operation: 24+5=29, Resulting Numbers: [2, 29] Generated Node #0,3,0: 52:[2, 29] Operation: 24+5=29 Exploring Operation: 24+2=26, Resulting Numbers: [5, 26] Generated Node #0,3,1: 52:[5, 26] Operation: 24+2=26 Exploring Operation: 24/2=12, Resulting Numbers: [5, 12] Generated Node #0,3,2: 52:[5, 12] Operation: 24/2=12 Exploring Operation: 5-2=3, Resulting Numbers: [24, 3] Generated Node #0,3,3: 52:[24, 3] Operation: 5-2=3 Exploring Operation: 24*2=48, Resulting Numbers: [5, 48] Generated Node #0,3,4: 52:[5, 48] Operation: 24*2=48 Moving to Node #0,3,1 Current State: 52:[5, 26], Operations: ['34-32=2', '24+2=26'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[5, 12], Operations: ['34-32=2', '24/2=12'] Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,52 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[2, 29], Operations: ['34-32=2', '24+5=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[24, 3], Operations: ['34-32=2', '5-2=3'] Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,52 unequal: No Solution Moving to Node #0,3,4 Current State: 52:[5, 48], Operations: ['34-32=2', '24*2=48'] Exploring Operation: 5*48=240, Resulting Numbers: [240] 240,52 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 5+48=53, Resulting Numbers: [53] 53,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[5, 32, 10], Operations: ['34-24=10'] Exploring Operation: 10/5=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 52:[32, 2] Operation: 10/5=2 Exploring Operation: 32-10=22, Resulting Numbers: [5, 22] Generated Node #0,0,1: 52:[5, 22] Operation: 32-10=22 Exploring Operation: 10-5=5, Resulting Numbers: [32, 5] Generated Node #0,0,2: 52:[32, 5] Operation: 10-5=5 Exploring Operation: 32-5=27, Resulting Numbers: [10, 27] Generated Node #0,0,3: 52:[10, 27] Operation: 32-5=27 Exploring Operation: 5+10=15, Resulting Numbers: [32, 15] Generated Node #0,0,4: 52:[32, 15] Operation: 5+10=15 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 52:[10, 27], Operations: ['34-24=10', '32-5=27'] Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,52 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,52 unequal: No Solution No 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: 52:[5, 22], Operations: ['34-24=10', '32-10=22'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,52 unequal: No Solution No 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: 52:[32, 2], Operations: ['34-24=10', '10/5=2'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,52 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,52 unequal: No Solution No 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: 52:[32, 5], Operations: ['34-24=10', '10-5=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,52 unequal: No Solution No 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: 52:[32, 15], Operations: ['34-24=10', '5+10=15'] Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,52 unequal: No Solution Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,52 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: 52:[24, 34, 27], Operations: ['32-5=27'] Exploring Operation: 27-24=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 52:[34, 3] Operation: 27-24=3 Exploring Operation: 34-24=10, Resulting Numbers: [27, 10] Generated Node #0,1,1: 52:[27, 10] Operation: 34-24=10 Exploring Operation: 34-27=7, Resulting Numbers: [24, 7] Generated Node #0,1,2: 52:[24, 7] Operation: 34-27=7 Exploring Operation: 24+27=51, Resulting Numbers: [34, 51] Generated Node #0,1,3: 52:[34, 51] Operation: 24+27=51 Exploring Operation: 24+34=58, Resulting Numbers: [27, 58] Generated Node #0,1,4: 52:[27, 58] Operation: 24+34=58 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[27, 10], Operations: ['32-5=27', '34-24=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,52 unequal: No Solution No 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: 52:[24, 7], Operations: ['32-5=27', '34-27=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,52 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,52 unequal: No Solution No 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: 52:[27, 58], Operations: ['32-5=27', '24+34=58'] Exploring Operation: 27*58=1566, Resulting Numbers: [1566] 1566,52 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,52 unequal: No Solution No 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: 52:[34, 3], Operations: ['32-5=27', '27-24=3'] Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,52 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,52 unequal: No Solution No 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: 52:[34, 51], Operations: ['32-5=27', '24+27=51'] Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,52 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,52 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: 52:[24, 32, 29], Operations: ['34-5=29'] Exploring Operation: 24+29=53, Resulting Numbers: [32, 53] Generated Node #0,4,0: 52:[32, 53] Operation: 24+29=53 Exploring Operation: 32-29=3, Resulting Numbers: [24, 3] Generated Node #0,4,1: 52:[24, 3] Operation: 32-29=3 Exploring Operation: 32-24=8, Resulting Numbers: [29, 8] Generated Node #0,4,2: 52:[29, 8] Operation: 32-24=8 Exploring Operation: 24+32=56, Resulting Numbers: [29, 56] Generated Node #0,4,3: 52:[29, 56] Operation: 24+32=56 Exploring Operation: 29-24=5, Resulting Numbers: [32, 5] Generated Node #0,4,4: 52:[32, 5] Operation: 29-24=5 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 52:[24, 3], Operations: ['34-5=29', '32-29=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,52 unequal: No Solution No 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: 52:[32, 53], Operations: ['34-5=29', '24+29=53'] Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,52 unequal: No Solution Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,52 unequal: No Solution No 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: 52:[29, 8], Operations: ['34-5=29', '32-24=8'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,52 unequal: No Solution Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,52 unequal: No Solution No 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: 52:[29, 56], Operations: ['34-5=29', '24+32=56'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 29+56=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 29*56=1624, Resulting Numbers: [1624] 1624,52 unequal: No Solution No 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: 52:[32, 5], Operations: ['34-5=29', '29-24=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,52 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,52 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: 52:[5, 34, 56], Operations: ['24+32=56'] Exploring Operation: 34-5=29, Resulting Numbers: [56, 29] Generated Node #0,2,0: 52:[56, 29] Operation: 34-5=29 Exploring Operation: 56-5=51, Resulting Numbers: [34, 51] Generated Node #0,2,1: 52:[34, 51] Operation: 56-5=51 Exploring Operation: 56-34=22, Resulting Numbers: [5, 22] Generated Node #0,2,2: 52:[5, 22] Operation: 56-34=22 Exploring Operation: 5+34=39, Resulting Numbers: [56, 39] Generated Node #0,2,3: 52:[56, 39] Operation: 5+34=39 Exploring Operation: 5+56=61, Resulting Numbers: [34, 61] Generated Node #0,2,4: 52:[34, 61] Operation: 5+56=61 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[5, 22], Operations: ['24+32=56', '56-34=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,52 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,52 unequal: No Solution No 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: 52:[56, 29], Operations: ['24+32=56', '34-5=29'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 56*29=1624, Resulting Numbers: [1624] 1624,52 unequal: No Solution No 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: 52:[34, 51], Operations: ['24+32=56', '56-5=51'] Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,52 unequal: No Solution No 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: 52:[56, 39], Operations: ['24+32=56', '5+34=39'] Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,52 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,52 unequal: No Solution No 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: 52:[34, 61], Operations: ['24+32=56', '5+56=61'] Exploring Operation: 61-34=27, Resulting Numbers: [27] 27,52 unequal: No Solution Exploring Operation: 34*61=2074, Resulting Numbers: [2074] 2074,52 unequal: No Solution Exploring Operation: 34+61=95, Resulting Numbers: [95] 95,52 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, 1, 49, 3 ]
81
[ "3-1=2", "16*2=32", "49+32=81" ]
Current State: 81:[16, 1, 49, 3], Operations: [] Exploring Operation: 3-1=2, Resulting Numbers: [16, 49, 2] Generated Node #2: [16, 49, 2] from Operation: 3-1=2 Current State: 81:[16, 49, 2], Operations: ['3-1=2'] Exploring Operation: 16*2=32, Resulting Numbers: [49, 32] Generated Node #3: [49, 32] from Operation: 16*2=32 Current State: 81:[49, 32], Operations: ['3-1=2', '16*2=32'] Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[16, 1, 49, 3], Operations: [] Exploring Operation: 49-16=33, Resulting Numbers: [1, 3, 33] Generated Node #0,0: 81:[1, 3, 33] Operation: 49-16=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[1, 3, 33], Operations: ['49-16=33'] Exploring Operation: 33/3=11, Resulting Numbers: [1, 11] Generated Node #0,0,0: 81:[1, 11] Operation: 33/3=11 Moving to Node #0,0,0 Current State: 81:[1, 11], Operations: ['49-16=33', '33/3=11'] Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,81 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, 7, 78, 6 ]
24
[ "78/26=3", "7-3=4", "6*4=24" ]
Current State: 24:[26, 7, 78, 6], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [7, 6, 3] Generated Node #2: [7, 6, 3] from Operation: 78/26=3 Current State: 24:[7, 6, 3], Operations: ['78/26=3'] Exploring Operation: 7-3=4, Resulting Numbers: [6, 4] Generated Node #3: [6, 4] from Operation: 7-3=4 Current State: 24:[6, 4], Operations: ['78/26=3', '7-3=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[26, 7, 78, 6], Operations: [] Exploring Operation: 78-7=71, Resulting Numbers: [26, 6, 71] Generated Node #0,0: 24:[26, 6, 71] Operation: 78-7=71 Exploring Operation: 78-26=52, Resulting Numbers: [7, 6, 52] Generated Node #0,1: 24:[7, 6, 52] Operation: 78-26=52 Exploring Operation: 78/26=3, Resulting Numbers: [7, 6, 3] Generated Node #0,2: 24:[7, 6, 3] Operation: 78/26=3 Exploring Operation: 78/6=13, Resulting Numbers: [26, 7, 13] Generated Node #0,3: 24:[26, 7, 13] Operation: 78/6=13 Moving to Node #0,2 Current State: 24:[7, 6, 3], Operations: ['78/26=3'] Exploring Operation: 6-3=3, Resulting Numbers: [7, 3] Generated Node #0,2,0: 24:[7, 3] Operation: 6-3=3 Exploring Operation: 7-3=4, Resulting Numbers: [6, 4] Generated Node #0,2,1: 24:[6, 4] Operation: 7-3=4 Exploring Operation: 7+6=13, Resulting Numbers: [3, 13] Generated Node #0,2,2: 24:[3, 13] Operation: 7+6=13 Exploring Operation: 7-6=1, Resulting Numbers: [3, 1] Generated Node #0,2,3: 24:[3, 1] Operation: 7-6=1 Moving to Node #0,3 Current State: 24:[26, 7, 13], Operations: ['78/6=13'] Exploring Operation: 26-7=19, Resulting Numbers: [13, 19] Generated Node #0,3,0: 24:[13, 19] Operation: 26-7=19 Exploring Operation: 26/13=2, Resulting Numbers: [7, 2] Generated Node #0,3,1: 24:[7, 2] Operation: 26/13=2 Exploring Operation: 26-13=13, Resulting Numbers: [7, 13] Generated Node #0,3,2: 24:[7, 13] Operation: 26-13=13 Exploring Operation: 13-7=6, Resulting Numbers: [26, 6] Generated Node #0,3,3: 24:[26, 6] Operation: 13-7=6 Moving to Node #0,1 Current State: 24:[7, 6, 52], Operations: ['78-26=52'] Exploring Operation: 7+6=13, Resulting Numbers: [52, 13] Generated Node #0,1,0: 24:[52, 13] Operation: 7+6=13 Exploring Operation: 7-6=1, Resulting Numbers: [52, 1] Generated Node #0,1,1: 24:[52, 1] Operation: 7-6=1 Exploring Operation: 52-7=45, Resulting Numbers: [6, 45] Generated Node #0,1,2: 24:[6, 45] Operation: 52-7=45 Exploring Operation: 52-6=46, Resulting Numbers: [7, 46] Generated Node #0,1,3: 24:[7, 46] Operation: 52-6=46 Moving to Node #0,0 Current State: 24:[26, 6, 71], Operations: ['78-7=71'] Exploring Operation: 71-26=45, Resulting Numbers: [6, 45] Generated Node #0,0,0: 24:[6, 45] Operation: 71-26=45 Exploring Operation: 26+6=32, Resulting Numbers: [71, 32] Generated Node #0,0,1: 24:[71, 32] Operation: 26+6=32 Exploring Operation: 26-6=20, Resulting Numbers: [71, 20] Generated Node #0,0,2: 24:[71, 20] Operation: 26-6=20 Exploring Operation: 71-6=65, Resulting Numbers: [26, 65] Generated Node #0,0,3: 24:[26, 65] Operation: 71-6=65 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[6, 45], Operations: ['78-7=71', '71-26=45'] Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,24 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 24:[26, 65], Operations: ['78-7=71', '71-6=65'] Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 26+65=91, Resulting Numbers: [91] 91,24 unequal: No Solution Exploring Operation: 26*65=1690, Resulting Numbers: [1690] 1690,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[71, 20], Operations: ['78-7=71', '26-6=20'] Exploring Operation: 71+20=91, Resulting Numbers: [91] 91,24 unequal: No Solution Exploring Operation: 71*20=1420, Resulting Numbers: [1420] 1420,24 unequal: No Solution Exploring Operation: 71-20=51, Resulting Numbers: [51] 51,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[71, 32], Operations: ['78-7=71', '26+6=32'] Exploring Operation: 71+32=103, Resulting Numbers: [103] 103,24 unequal: No Solution Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,24 unequal: No Solution Exploring Operation: 71*32=2272, Resulting Numbers: [2272] 2272,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 24:[6, 4], Operations: ['78/26=3', '7-3=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[26, 7, 78, 6], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [7, 6, 3] Generated Node #0,2: 24:[7, 6, 3] Operation: 78/26=3 Moving to Node #0,2 Current State: 24:[7, 6, 3], Operations: ['78/26=3'] Exploring Operation: 7-3=4, Resulting Numbers: [6, 4] Generated Node #0,2,1: 24:[6, 4] Operation: 7-3=4 Moving to Node #0,2,1 Current State: 24:[6, 4], Operations: ['78/26=3', '7-3=4'] Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.967882
hs_4
sum_heuristic
[ 87, 2, 37, 20 ]
40
[ "87-37=50", "20/2=10", "50-10=40" ]
Current State: 40:[87, 2, 37, 20], Operations: [] Exploring Operation: 87-37=50, Resulting Numbers: [2, 20, 50] Generated Node #2: [2, 20, 50] from Operation: 87-37=50 Current State: 40:[2, 20, 50], Operations: ['87-37=50'] Exploring Operation: 20/2=10, Resulting Numbers: [50, 10] Generated Node #3: [50, 10] from Operation: 20/2=10 Current State: 40:[50, 10], Operations: ['87-37=50', '20/2=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[87, 2, 37, 20], Operations: [] Exploring Operation: 87-20=67, Resulting Numbers: [2, 37, 67] Generated Node #0,0: 40:[2, 37, 67] Operation: 87-20=67 Exploring Operation: 2*20=40, Resulting Numbers: [87, 37, 40] Generated Node #0,1: 40:[87, 37, 40] Operation: 2*20=40 Exploring Operation: 2+37=39, Resulting Numbers: [87, 20, 39] Generated Node #0,2: 40:[87, 20, 39] Operation: 2+37=39 Exploring Operation: 87-2=85, Resulting Numbers: [37, 20, 85] Generated Node #0,3: 40:[37, 20, 85] Operation: 87-2=85 Exploring Operation: 87-37=50, Resulting Numbers: [2, 20, 50] Generated Node #0,4: 40:[2, 20, 50] Operation: 87-37=50 Moving to Node #0,4 Current State: 40:[2, 20, 50], Operations: ['87-37=50'] Exploring Operation: 50-20=30, Resulting Numbers: [2, 30] Generated Node #0,4,0: 40:[2, 30] Operation: 50-20=30 Exploring Operation: 20/2=10, Resulting Numbers: [50, 10] Generated Node #0,4,1: 40:[50, 10] Operation: 20/2=10 Exploring Operation: 50/2=25, Resulting Numbers: [20, 25] Generated Node #0,4,2: 40:[20, 25] Operation: 50/2=25 Exploring Operation: 2*20=40, Resulting Numbers: [50, 40] Generated Node #0,4,3: 40:[50, 40] Operation: 2*20=40 Exploring Operation: 50-2=48, Resulting Numbers: [20, 48] Generated Node #0,4,4: 40:[20, 48] Operation: 50-2=48 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 40:[20, 25], Operations: ['87-37=50', '50/2=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,40 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,40 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,40 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 #0,4,4 Current State: 40:[20, 48], Operations: ['87-37=50', '50-2=48'] Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,40 unequal: No Solution Exploring Operation: 20*48=960, Resulting Numbers: [960] 960,40 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,40 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 #0,4,0 Current State: 40:[2, 30], Operations: ['87-37=50', '50-20=30'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,40 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,40 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,40 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 #0,4,1 Current State: 40:[50, 10], Operations: ['87-37=50', '20/2=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[87, 2, 37, 20], Operations: [] Exploring Operation: 87-37=50, Resulting Numbers: [2, 20, 50] Generated Node #0,4: 40:[2, 20, 50] Operation: 87-37=50 Moving to Node #0,4 Current State: 40:[2, 20, 50], Operations: ['87-37=50'] Exploring Operation: 20/2=10, Resulting Numbers: [50, 10] Generated Node #0,4,1: 40:[50, 10] Operation: 20/2=10 Moving to Node #0,4,1 Current State: 40:[50, 10], Operations: ['87-37=50', '20/2=10'] Exploring Operation: 50-10=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
sum_heuristic
[ 56, 61, 34, 84 ]
18
[ "61-34=27", "56*27=1512", "1512/84=18" ]
Current State: 18:[56, 61, 34, 84], Operations: [] Exploring Operation: 61-34=27, Resulting Numbers: [56, 84, 27] Generated Node #2: [56, 84, 27] from Operation: 61-34=27 Current State: 18:[56, 84, 27], Operations: ['61-34=27'] Exploring Operation: 56*27=1512, Resulting Numbers: [84, 1512] Generated Node #3: [84, 1512] from Operation: 56*27=1512 Current State: 18:[84, 1512], Operations: ['61-34=27', '56*27=1512'] Exploring Operation: 1512/84=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[56, 61, 34, 84], Operations: [] Exploring Operation: 84-61=23, Resulting Numbers: [56, 34, 23] Generated Node #0,0: 18:[56, 34, 23] Operation: 84-61=23 Moving to Node #0,0 Current State: 18:[56, 34, 23], Operations: ['84-61=23'] Exploring Operation: 56-34=22, Resulting Numbers: [23, 22] Generated Node #0,0,0: 18:[23, 22] Operation: 56-34=22 Moving to Node #0,0,0 Current State: 18:[23, 22], Operations: ['84-61=23', '56-34=22'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,18 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 11, 51, 71, 9 ]
79
[ "11*9=99", "71-51=20", "99-20=79" ]
Current State: 79:[11, 51, 71, 9], Operations: [] Exploring Operation: 11*9=99, Resulting Numbers: [51, 71, 99] Generated Node #2: [51, 71, 99] from Operation: 11*9=99 Current State: 79:[51, 71, 99], Operations: ['11*9=99'] Exploring Operation: 71-51=20, Resulting Numbers: [99, 20] Generated Node #3: [99, 20] from Operation: 71-51=20 Current State: 79:[99, 20], Operations: ['11*9=99', '71-51=20'] Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[11, 51, 71, 9], Operations: [] Exploring Operation: 11+51=62, Resulting Numbers: [71, 9, 62] Generated Node #0,0: 79:[71, 9, 62] Operation: 11+51=62 Exploring Operation: 11*9=99, Resulting Numbers: [51, 71, 99] Generated Node #0,1: 79:[51, 71, 99] Operation: 11*9=99 Moving to Node #0,1 Current State: 79:[51, 71, 99], Operations: ['11*9=99'] Exploring Operation: 99-51=48, Resulting Numbers: [71, 48] Generated Node #0,1,0: 79:[71, 48] Operation: 99-51=48 Exploring Operation: 51+71=122, Resulting Numbers: [99, 122] Generated Node #0,1,1: 79:[99, 122] Operation: 51+71=122 Moving to Node #0,0 Current State: 79:[71, 9, 62], Operations: ['11+51=62'] Exploring Operation: 71+9=80, Resulting Numbers: [62, 80] Generated Node #0,0,0: 79:[62, 80] Operation: 71+9=80 Exploring Operation: 9+62=71, Resulting Numbers: [71, 71] Generated Node #0,0,1: 79:[71, 71] Operation: 9+62=71 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[71, 71], Operations: ['11+51=62', '9+62=71'] Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,79 unequal: No Solution Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,79 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 #0,0,0 Current State: 79:[62, 80], Operations: ['11+51=62', '71+9=80'] Exploring Operation: 62+80=142, Resulting Numbers: [142] 142,79 unequal: No Solution Exploring Operation: 80-62=18, Resulting Numbers: [18] 18,79 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: 79:[71, 48], Operations: ['11*9=99', '99-51=48'] Exploring Operation: 71+48=119, Resulting Numbers: [119] 119,79 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[99, 122], Operations: ['11*9=99', '51+71=122'] Exploring Operation: 99+122=221, Resulting Numbers: [221] 221,79 unequal: No Solution Exploring Operation: 122-99=23, Resulting Numbers: [23] 23,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 14, 22, 11, 35 ]
16
[ "22-14=8", "35-11=24", "24-8=16" ]
Current State: 16:[14, 22, 11, 35], Operations: [] Exploring Operation: 22-14=8, Resulting Numbers: [11, 35, 8] Generated Node #2: [11, 35, 8] from Operation: 22-14=8 Current State: 16:[11, 35, 8], Operations: ['22-14=8'] Exploring Operation: 35-11=24, Resulting Numbers: [8, 24] Generated Node #3: [8, 24] from Operation: 35-11=24 Current State: 16:[8, 24], Operations: ['22-14=8', '35-11=24'] Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[14, 22, 11, 35], Operations: [] Exploring Operation: 35-22=13, Resulting Numbers: [14, 11, 13] Generated Node #0,0: 16:[14, 11, 13] Operation: 35-22=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[14, 11, 13], Operations: ['35-22=13'] Exploring Operation: 13-11=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 16:[14, 2] Operation: 13-11=2 Moving to Node #0,0,0 Current State: 16:[14, 2], Operations: ['35-22=13', '13-11=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[14, 22, 11, 35], Operations: [] Exploring Operation: 35-22=13, Resulting Numbers: [14, 11, 13] Generated Node #0,0: 16:[14, 11, 13] Operation: 35-22=13 Moving to Node #0,0 Current State: 16:[14, 11, 13], Operations: ['35-22=13'] Exploring Operation: 13-11=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 16:[14, 2] Operation: 13-11=2 Moving to Node #0,0,0 Current State: 16:[14, 2], Operations: ['35-22=13', '13-11=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 25, 23, 70, 3 ]
74
[ "25+23=48", "3*48=144", "144-70=74" ]
Current State: 74:[25, 23, 70, 3], Operations: [] Exploring Operation: 25+23=48, Resulting Numbers: [70, 3, 48] Generated Node #2: [70, 3, 48] from Operation: 25+23=48 Current State: 74:[70, 3, 48], Operations: ['25+23=48'] Exploring Operation: 3*48=144, Resulting Numbers: [70, 144] Generated Node #3: [70, 144] from Operation: 3*48=144 Current State: 74:[70, 144], Operations: ['25+23=48', '3*48=144'] Exploring Operation: 144-70=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[25, 23, 70, 3], Operations: [] Exploring Operation: 25+23=48, Resulting Numbers: [70, 3, 48] Generated Node #0,0: 74:[70, 3, 48] Operation: 25+23=48 Exploring Operation: 70-25=45, Resulting Numbers: [23, 3, 45] Generated Node #0,1: 74:[23, 3, 45] Operation: 70-25=45 Exploring Operation: 23*3=69, Resulting Numbers: [25, 70, 69] Generated Node #0,2: 74:[25, 70, 69] Operation: 23*3=69 Exploring Operation: 25-23=2, Resulting Numbers: [70, 3, 2] Generated Node #0,3: 74:[70, 3, 2] Operation: 25-23=2 Exploring Operation: 25*3=75, Resulting Numbers: [23, 70, 75] Generated Node #0,4: 74:[23, 70, 75] Operation: 25*3=75 Moving to Node #0,3 Current State: 74:[70, 3, 2], Operations: ['25-23=2'] Exploring Operation: 3-2=1, Resulting Numbers: [70, 1] Generated Node #0,3,0: 74:[70, 1] Operation: 3-2=1 Exploring Operation: 70/2=35, Resulting Numbers: [3, 35] Generated Node #0,3,1: 74:[3, 35] Operation: 70/2=35 Exploring Operation: 70-3=67, Resulting Numbers: [2, 67] Generated Node #0,3,2: 74:[2, 67] Operation: 70-3=67 Exploring Operation: 70+3=73, Resulting Numbers: [2, 73] Generated Node #0,3,3: 74:[2, 73] Operation: 70+3=73 Exploring Operation: 70+2=72, Resulting Numbers: [3, 72] Generated Node #0,3,4: 74:[3, 72] Operation: 70+2=72 Moving to Node #0,0 Current State: 74:[70, 3, 48], Operations: ['25+23=48'] Exploring Operation: 70-3=67, Resulting Numbers: [48, 67] Generated Node #0,0,0: 74:[48, 67] Operation: 70-3=67 Exploring Operation: 48-3=45, Resulting Numbers: [70, 45] Generated Node #0,0,1: 74:[70, 45] Operation: 48-3=45 Exploring Operation: 70+3=73, Resulting Numbers: [48, 73] Generated Node #0,0,2: 74:[48, 73] Operation: 70+3=73 Exploring Operation: 70-48=22, Resulting Numbers: [3, 22] Generated Node #0,0,3: 74:[3, 22] Operation: 70-48=22 Exploring Operation: 3+48=51, Resulting Numbers: [70, 51] Generated Node #0,0,4: 74:[70, 51] Operation: 3+48=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[70, 45], Operations: ['25+23=48', '48-3=45'] Exploring Operation: 70+45=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 70-45=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 70*45=3150, Resulting Numbers: [3150] 3150,74 unequal: No Solution No 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: 74:[48, 73], Operations: ['25+23=48', '70+3=73'] Exploring Operation: 73-48=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 48+73=121, Resulting Numbers: [121] 121,74 unequal: No Solution Exploring Operation: 48*73=3504, Resulting Numbers: [3504] 3504,74 unequal: No Solution No 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: 74:[3, 22], Operations: ['25+23=48', '70-48=22'] Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,74 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,74 unequal: No Solution No 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: 74:[48, 67], Operations: ['25+23=48', '70-3=67'] Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,74 unequal: No Solution Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,74 unequal: No Solution No 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: 74:[70, 51], Operations: ['25+23=48', '3+48=51'] Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,74 unequal: No Solution Exploring Operation: 70*51=3570, Resulting Numbers: [3570] 3570,74 unequal: No Solution Exploring Operation: 70+51=121, Resulting Numbers: [121] 121,74 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: 74:[23, 70, 75], Operations: ['25*3=75'] Exploring Operation: 70-23=47, Resulting Numbers: [75, 47] Generated Node #0,4,0: 74:[75, 47] Operation: 70-23=47 Exploring Operation: 75-70=5, Resulting Numbers: [23, 5] Generated Node #0,4,1: 74:[23, 5] Operation: 75-70=5 Exploring Operation: 75-23=52, Resulting Numbers: [70, 52] Generated Node #0,4,2: 74:[70, 52] Operation: 75-23=52 Exploring Operation: 23+70=93, Resulting Numbers: [75, 93] Generated Node #0,4,3: 74:[75, 93] Operation: 23+70=93 Exploring Operation: 23+75=98, Resulting Numbers: [70, 98] Generated Node #0,4,4: 74:[70, 98] Operation: 23+75=98 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 74:[75, 47], Operations: ['25*3=75', '70-23=47'] Exploring Operation: 75-47=28, Resulting Numbers: [28] 28,74 unequal: No Solution Exploring Operation: 75+47=122, Resulting Numbers: [122] 122,74 unequal: No Solution Exploring Operation: 75*47=3525, Resulting Numbers: [3525] 3525,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 74:[23, 5], Operations: ['25*3=75', '75-70=5'] Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,74 unequal: No Solution Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,74 unequal: No Solution No 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: 74:[70, 52], Operations: ['25*3=75', '75-23=52'] Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 70+52=122, Resulting Numbers: [122] 122,74 unequal: No Solution Exploring Operation: 70*52=3640, Resulting Numbers: [3640] 3640,74 unequal: No Solution No 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: 74:[75, 93], Operations: ['25*3=75', '23+70=93'] Exploring Operation: 75*93=6975, Resulting Numbers: [6975] 6975,74 unequal: No Solution Exploring Operation: 93-75=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 75+93=168, Resulting Numbers: [168] 168,74 unequal: No Solution No 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: 74:[70, 98], Operations: ['25*3=75', '23+75=98'] Exploring Operation: 70+98=168, Resulting Numbers: [168] 168,74 unequal: No Solution Exploring Operation: 70*98=6860, Resulting Numbers: [6860] 6860,74 unequal: No Solution Exploring Operation: 98-70=28, Resulting Numbers: [28] 28,74 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: 74:[25, 70, 69], Operations: ['23*3=69'] Exploring Operation: 69-25=44, Resulting Numbers: [70, 44] Generated Node #0,2,0: 74:[70, 44] Operation: 69-25=44 Exploring Operation: 25+70=95, Resulting Numbers: [69, 95] Generated Node #0,2,1: 74:[69, 95] Operation: 25+70=95 Exploring Operation: 70-69=1, Resulting Numbers: [25, 1] Generated Node #0,2,2: 74:[25, 1] Operation: 70-69=1 Exploring Operation: 70-25=45, Resulting Numbers: [69, 45] Generated Node #0,2,3: 74:[69, 45] Operation: 70-25=45 Exploring Operation: 25+69=94, Resulting Numbers: [70, 94] Generated Node #0,2,4: 74:[70, 94] Operation: 25+69=94 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 74:[70, 44], Operations: ['23*3=69', '69-25=44'] Exploring Operation: 70*44=3080, Resulting Numbers: [3080] 3080,74 unequal: No Solution Exploring Operation: 70-44=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 70+44=114, Resulting Numbers: [114] 114,74 unequal: No Solution No 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: 74:[25, 1], Operations: ['23*3=69', '70-69=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,74 unequal: No Solution No 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: 74:[69, 45], Operations: ['23*3=69', '70-25=45'] Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 69+45=114, Resulting Numbers: [114] 114,74 unequal: No Solution Exploring Operation: 69*45=3105, Resulting Numbers: [3105] 3105,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 74:[70, 94], Operations: ['23*3=69', '25+69=94'] Exploring Operation: 70*94=6580, Resulting Numbers: [6580] 6580,74 unequal: No Solution Exploring Operation: 70+94=164, Resulting Numbers: [164] 164,74 unequal: No Solution Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,74 unequal: No Solution No 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: 74:[69, 95], Operations: ['23*3=69', '25+70=95'] Exploring Operation: 69*95=6555, Resulting Numbers: [6555] 6555,74 unequal: No Solution Exploring Operation: 69+95=164, Resulting Numbers: [164] 164,74 unequal: No Solution Exploring Operation: 95-69=26, Resulting Numbers: [26] 26,74 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: 74:[23, 3, 45], Operations: ['70-25=45'] Exploring Operation: 45-3=42, Resulting Numbers: [23, 42] Generated Node #0,1,0: 74:[23, 42] Operation: 45-3=42 Exploring Operation: 23+45=68, Resulting Numbers: [3, 68] Generated Node #0,1,1: 74:[3, 68] Operation: 23+45=68 Exploring Operation: 23*3=69, Resulting Numbers: [45, 69] Generated Node #0,1,2: 74:[45, 69] Operation: 23*3=69 Exploring Operation: 23+3=26, Resulting Numbers: [45, 26] Generated Node #0,1,3: 74:[45, 26] Operation: 23+3=26 Exploring Operation: 45-23=22, Resulting Numbers: [3, 22] Generated Node #0,1,4: 74:[3, 22] Operation: 45-23=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[3, 68], Operations: ['70-25=45', '23+45=68'] Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,74 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,74 unequal: No Solution No 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: 74:[45, 69], Operations: ['70-25=45', '23*3=69'] Exploring Operation: 69-45=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 45+69=114, Resulting Numbers: [114] 114,74 unequal: No Solution Exploring Operation: 45*69=3105, Resulting Numbers: [3105] 3105,74 unequal: No Solution No 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: 74:[3, 22], Operations: ['70-25=45', '45-23=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,74 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,74 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,74 unequal: No Solution No 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: 74:[23, 42], Operations: ['70-25=45', '45-3=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,74 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,74 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,74 unequal: No Solution No 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: 74:[45, 26], Operations: ['70-25=45', '23+3=26'] Exploring Operation: 45*26=1170, Resulting Numbers: [1170] 1170,74 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,74 unequal: No Solution Exploring Operation: 45+26=71, Resulting Numbers: [71] 71,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 74:[2, 73], Operations: ['25-23=2', '70+3=73'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,74 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,74 unequal: No Solution Moving to Node #0,3,4 Current State: 74:[3, 72], Operations: ['25-23=2', '70+2=72'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,74 unequal: No Solution Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 3*72=216, Resulting Numbers: [216] 216,74 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,74 unequal: No Solution Moving to Node #0,3,1 Current State: 74:[3, 35], Operations: ['25-23=2', '70/2=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,74 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,74 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,74 unequal: No Solution Moving to Node #0,3,0 Current State: 74:[70, 1], Operations: ['25-23=2', '3-2=1'] Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 70*1=70, Resulting Numbers: [70] 70,74 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,74 unequal: No Solution Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,74 unequal: No Solution Moving to Node #0,3,2 Current State: 74:[2, 67], Operations: ['25-23=2', '70-3=67'] Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,74 unequal: No Solution Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,74 unequal: No Solution Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,74 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 5, 65, 48, 65 ]
54
[ "5+48=53", "65/65=1", "53+1=54" ]
Current State: 54:[5, 65, 48, 65], Operations: [] Exploring Operation: 5+48=53, Resulting Numbers: [65, 65, 53] Generated Node #2: [65, 65, 53] from Operation: 5+48=53 Current State: 54:[65, 65, 53], Operations: ['5+48=53'] Exploring Operation: 65/65=1, Resulting Numbers: [53, 1] Generated Node #3: [53, 1] from Operation: 65/65=1 Current State: 54:[53, 1], Operations: ['5+48=53', '65/65=1'] Exploring Operation: 53+1=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[5, 65, 48, 65], Operations: [] Exploring Operation: 65-48=17, Resulting Numbers: [5, 65, 17] Generated Node #0,0: 54:[5, 65, 17] Operation: 65-48=17 Exploring Operation: 65/65=1, Resulting Numbers: [5, 48, 1] Generated Node #0,1: 54:[5, 48, 1] Operation: 65/65=1 Exploring Operation: 65-65=0, Resulting Numbers: [5, 48, 0] Generated Node #0,2: 54:[5, 48, 0] Operation: 65-65=0 Moving to Node #0,1 Current State: 54:[5, 48, 1], Operations: ['65/65=1'] Exploring Operation: 5+1=6, Resulting Numbers: [48, 6] Generated Node #0,1,0: 54:[48, 6] Operation: 5+1=6 Exploring Operation: 48+1=49, Resulting Numbers: [5, 49] Generated Node #0,1,1: 54:[5, 49] Operation: 48+1=49 Exploring Operation: 5+48=53, Resulting Numbers: [1, 53] Generated Node #0,1,2: 54:[1, 53] Operation: 5+48=53 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 54:[1, 53], Operations: ['65/65=1', '5+48=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[5, 65, 48, 65], Operations: [] Exploring Operation: 65/65=1, Resulting Numbers: [5, 48, 1] Generated Node #0,1: 54:[5, 48, 1] Operation: 65/65=1 Moving to Node #0,1 Current State: 54:[5, 48, 1], Operations: ['65/65=1'] Exploring Operation: 5+48=53, Resulting Numbers: [1, 53] Generated Node #0,1,2: 54:[1, 53] Operation: 5+48=53 Moving to Node #0,1,2 Current State: 54:[1, 53], Operations: ['65/65=1', '5+48=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 13, 16, 11, 31 ]
46
[ "13-11=2", "31*2=62", "62-16=46" ]
Current State: 46:[13, 16, 11, 31], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [16, 31, 2] Generated Node #2: [16, 31, 2] from Operation: 13-11=2 Current State: 46:[16, 31, 2], Operations: ['13-11=2'] Exploring Operation: 31*2=62, Resulting Numbers: [16, 62] Generated Node #3: [16, 62] from Operation: 31*2=62 Current State: 46:[16, 62], Operations: ['13-11=2', '31*2=62'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[13, 16, 11, 31], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [16, 31, 2] Generated Node #0,0: 46:[16, 31, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[16, 31, 2], Operations: ['13-11=2'] Exploring Operation: 16+31=47, Resulting Numbers: [2, 47] Generated Node #0,0,0: 46:[2, 47] Operation: 16+31=47 Moving to Node #0,0,0 Current State: 46:[2, 47], Operations: ['13-11=2', '16+31=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 99, 84, 14, 35 ]
34
[ "99-84=15", "14+35=49", "49-15=34" ]
Current State: 34:[99, 84, 14, 35], Operations: [] Exploring Operation: 99-84=15, Resulting Numbers: [14, 35, 15] Generated Node #2: [14, 35, 15] from Operation: 99-84=15 Current State: 34:[14, 35, 15], Operations: ['99-84=15'] Exploring Operation: 14+35=49, Resulting Numbers: [15, 49] Generated Node #3: [15, 49] from Operation: 14+35=49 Current State: 34:[15, 49], Operations: ['99-84=15', '14+35=49'] Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[99, 84, 14, 35], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [99, 35, 6] Generated Node #0,0: 34:[99, 35, 6] Operation: 84/14=6 Exploring Operation: 99-35=64, Resulting Numbers: [84, 14, 64] Generated Node #0,1: 34:[84, 14, 64] Operation: 99-35=64 Exploring Operation: 84-35=49, Resulting Numbers: [99, 14, 49] Generated Node #0,2: 34:[99, 14, 49] Operation: 84-35=49 Exploring Operation: 99-84=15, Resulting Numbers: [14, 35, 15] Generated Node #0,3: 34:[14, 35, 15] Operation: 99-84=15 Moving to Node #0,3 Current State: 34:[14, 35, 15], Operations: ['99-84=15'] Exploring Operation: 35-14=21, Resulting Numbers: [15, 21] Generated Node #0,3,0: 34:[15, 21] Operation: 35-14=21 Exploring Operation: 15-14=1, Resulting Numbers: [35, 1] Generated Node #0,3,1: 34:[35, 1] Operation: 15-14=1 Exploring Operation: 14+15=29, Resulting Numbers: [35, 29] Generated Node #0,3,2: 34:[35, 29] Operation: 14+15=29 Exploring Operation: 35-15=20, Resulting Numbers: [14, 20] Generated Node #0,3,3: 34:[14, 20] Operation: 35-15=20 Moving to Node #0,0 Current State: 34:[99, 35, 6], Operations: ['84/14=6'] Exploring Operation: 99-35=64, Resulting Numbers: [6, 64] Generated Node #0,0,0: 34:[6, 64] Operation: 99-35=64 Exploring Operation: 99+6=105, Resulting Numbers: [35, 105] Generated Node #0,0,1: 34:[35, 105] Operation: 99+6=105 Exploring Operation: 99-6=93, Resulting Numbers: [35, 93] Generated Node #0,0,2: 34:[35, 93] Operation: 99-6=93 Exploring Operation: 35-6=29, Resulting Numbers: [99, 29] Generated Node #0,0,3: 34:[99, 29] Operation: 35-6=29 Moving to Node #0,2 Current State: 34:[99, 14, 49], Operations: ['84-35=49'] Exploring Operation: 99-49=50, Resulting Numbers: [14, 50] Generated Node #0,2,0: 34:[14, 50] Operation: 99-49=50 Exploring Operation: 99-14=85, Resulting Numbers: [49, 85] Generated Node #0,2,1: 34:[49, 85] Operation: 99-14=85 Exploring Operation: 49-14=35, Resulting Numbers: [99, 35] Generated Node #0,2,2: 34:[99, 35] Operation: 49-14=35 Exploring Operation: 99+14=113, Resulting Numbers: [49, 113] Generated Node #0,2,3: 34:[49, 113] Operation: 99+14=113 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 34:[14, 50], Operations: ['84-35=49', '99-49=50'] Exploring Operation: 14*50=700, Resulting Numbers: [700] 700,34 unequal: No Solution Exploring Operation: 50-14=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 14+50=64, Resulting Numbers: [64] 64,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 34:[49, 85], Operations: ['84-35=49', '99-14=85'] Exploring Operation: 49*85=4165, Resulting Numbers: [4165] 4165,34 unequal: No Solution Exploring Operation: 49+85=134, Resulting Numbers: [134] 134,34 unequal: No Solution Exploring Operation: 85-49=36, Resulting Numbers: [36] 36,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 34:[99, 35], Operations: ['84-35=49', '49-14=35'] Exploring Operation: 99+35=134, Resulting Numbers: [134] 134,34 unequal: No Solution Exploring Operation: 99*35=3465, Resulting Numbers: [3465] 3465,34 unequal: No Solution Exploring Operation: 99-35=64, Resulting Numbers: [64] 64,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 34:[49, 113], Operations: ['84-35=49', '99+14=113'] Exploring Operation: 49+113=162, Resulting Numbers: [162] 162,34 unequal: No Solution Exploring Operation: 113-49=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 49*113=5537, Resulting Numbers: [5537] 5537,34 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: 34:[84, 14, 64], Operations: ['99-35=64'] Exploring Operation: 84-14=70, Resulting Numbers: [64, 70] Generated Node #0,1,0: 34:[64, 70] Operation: 84-14=70 Exploring Operation: 64-14=50, Resulting Numbers: [84, 50] Generated Node #0,1,1: 34:[84, 50] Operation: 64-14=50 Exploring Operation: 84/14=6, Resulting Numbers: [64, 6] Generated Node #0,1,2: 34:[64, 6] Operation: 84/14=6 Exploring Operation: 84-64=20, Resulting Numbers: [14, 20] Generated Node #0,1,3: 34:[14, 20] Operation: 84-64=20 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 34:[14, 20], Operations: ['99-35=64', '84-64=20'] Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[99, 84, 14, 35], Operations: [] Exploring Operation: 99-35=64, Resulting Numbers: [84, 14, 64] Generated Node #0,1: 34:[84, 14, 64] Operation: 99-35=64 Moving to Node #0,1 Current State: 34:[84, 14, 64], Operations: ['99-35=64'] Exploring Operation: 84-64=20, Resulting Numbers: [14, 20] Generated Node #0,1,3: 34:[14, 20] Operation: 84-64=20 Moving to Node #0,1,3 Current State: 34:[14, 20], Operations: ['99-35=64', '84-64=20'] Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 56, 51, 13, 40 ]
54
[ "56+51=107", "13+40=53", "107-53=54" ]
Current State: 54:[56, 51, 13, 40], Operations: [] Exploring Operation: 56+51=107, Resulting Numbers: [13, 40, 107] Generated Node #2: [13, 40, 107] from Operation: 56+51=107 Current State: 54:[13, 40, 107], Operations: ['56+51=107'] Exploring Operation: 13+40=53, Resulting Numbers: [107, 53] Generated Node #3: [107, 53] from Operation: 13+40=53 Current State: 54:[107, 53], Operations: ['56+51=107', '13+40=53'] Exploring Operation: 107-53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[56, 51, 13, 40], Operations: [] Exploring Operation: 13+40=53, Resulting Numbers: [56, 51, 53] Generated Node #0,0: 54:[56, 51, 53] Operation: 13+40=53 Exploring Operation: 40-13=27, Resulting Numbers: [56, 51, 27] Generated Node #0,1: 54:[56, 51, 27] Operation: 40-13=27 Moving to Node #0,1 Current State: 54:[56, 51, 27], Operations: ['40-13=27'] Exploring Operation: 56-27=29, Resulting Numbers: [51, 29] Generated Node #0,1,0: 54:[51, 29] Operation: 56-27=29 Exploring Operation: 56-51=5, Resulting Numbers: [27, 5] Generated Node #0,1,1: 54:[27, 5] Operation: 56-51=5 Moving to Node #0,0 Current State: 54:[56, 51, 53], Operations: ['13+40=53'] Exploring Operation: 56-51=5, Resulting Numbers: [53, 5] Generated Node #0,0,0: 54:[53, 5] Operation: 56-51=5 Exploring Operation: 53-51=2, Resulting Numbers: [56, 2] Generated Node #0,0,1: 54:[56, 2] Operation: 53-51=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[53, 5], Operations: ['13+40=53', '56-51=5'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,54 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 #0,0,1 Current State: 54:[56, 2], Operations: ['13+40=53', '53-51=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[56, 51, 13, 40], Operations: [] Exploring Operation: 13+40=53, Resulting Numbers: [56, 51, 53] Generated Node #0,0: 54:[56, 51, 53] Operation: 13+40=53 Moving to Node #0,0 Current State: 54:[56, 51, 53], Operations: ['13+40=53'] Exploring Operation: 53-51=2, Resulting Numbers: [56, 2] Generated Node #0,0,1: 54:[56, 2] Operation: 53-51=2 Moving to Node #0,0,1 Current State: 54:[56, 2], Operations: ['13+40=53', '53-51=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
sum_heuristic
[ 48, 34, 4, 21 ]
99
[ "48+34=82", "21-4=17", "82+17=99" ]
Current State: 99:[48, 34, 4, 21], Operations: [] Exploring Operation: 48+34=82, Resulting Numbers: [4, 21, 82] Generated Node #2: [4, 21, 82] from Operation: 48+34=82 Current State: 99:[4, 21, 82], Operations: ['48+34=82'] Exploring Operation: 21-4=17, Resulting Numbers: [82, 17] Generated Node #3: [82, 17] from Operation: 21-4=17 Current State: 99:[82, 17], Operations: ['48+34=82', '21-4=17'] Exploring Operation: 82+17=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[48, 34, 4, 21], Operations: [] Exploring Operation: 48/4=12, Resulting Numbers: [34, 21, 12] Generated Node #0,0: 99:[34, 21, 12] Operation: 48/4=12 Exploring Operation: 48-21=27, Resulting Numbers: [34, 4, 27] Generated Node #0,1: 99:[34, 4, 27] Operation: 48-21=27 Moving to Node #0,1 Current State: 99:[34, 4, 27], Operations: ['48-21=27'] Exploring Operation: 34-27=7, Resulting Numbers: [4, 7] Generated Node #0,1,0: 99:[4, 7] Operation: 34-27=7 Exploring Operation: 4+27=31, Resulting Numbers: [34, 31] Generated Node #0,1,1: 99:[34, 31] Operation: 4+27=31 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[4, 7], Operations: ['48-21=27', '34-27=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,99 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,99 unequal: No Solution No 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: 99:[34, 31], Operations: ['48-21=27', '4+27=31'] Exploring Operation: 34+31=65, Resulting Numbers: [65] 65,99 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,99 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: 99:[34, 21, 12], Operations: ['48/4=12'] Exploring Operation: 21-12=9, Resulting Numbers: [34, 9] Generated Node #0,0,0: 99:[34, 9] Operation: 21-12=9 Exploring Operation: 21+12=33, Resulting Numbers: [34, 33] Generated Node #0,0,1: 99:[34, 33] Operation: 21+12=33 Moving to Node #0,0,0 Current State: 99:[34, 9], Operations: ['48/4=12', '21-12=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,99 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[34, 33], Operations: ['48/4=12', '21+12=33'] Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,99 unequal: No Solution Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 4, 72, 68, 36 ]
95
[ "72+36=108", "108/4=27", "68+27=95" ]
Current State: 95:[4, 72, 68, 36], Operations: [] Exploring Operation: 72+36=108, Resulting Numbers: [4, 68, 108] Generated Node #2: [4, 68, 108] from Operation: 72+36=108 Current State: 95:[4, 68, 108], Operations: ['72+36=108'] Exploring Operation: 108/4=27, Resulting Numbers: [68, 27] Generated Node #3: [68, 27] from Operation: 108/4=27 Current State: 95:[68, 27], Operations: ['72+36=108', '108/4=27'] Exploring Operation: 68+27=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[4, 72, 68, 36], Operations: [] Exploring Operation: 68+36=104, Resulting Numbers: [4, 72, 104] Generated Node #0,0: 95:[4, 72, 104] Operation: 68+36=104 Exploring Operation: 72/36=2, Resulting Numbers: [4, 68, 2] Generated Node #0,1: 95:[4, 68, 2] Operation: 72/36=2 Exploring Operation: 72-68=4, Resulting Numbers: [4, 36, 4] Generated Node #0,2: 95:[4, 36, 4] Operation: 72-68=4 Exploring Operation: 68-36=32, Resulting Numbers: [4, 72, 32] Generated Node #0,3: 95:[4, 72, 32] Operation: 68-36=32 Moving to Node #0,2 Current State: 95:[4, 36, 4], Operations: ['72-68=4'] Exploring Operation: 36-4=32, Resulting Numbers: [4, 32] Generated Node #0,2,0: 95:[4, 32] Operation: 36-4=32 Exploring Operation: 36/4=9, Resulting Numbers: [4, 9] Generated Node #0,2,1: 95:[4, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [4, 32] Generated Node #0,2,2: 95:[4, 32] Operation: 36-4=32 Exploring Operation: 36/4=9, Resulting Numbers: [4, 9] Generated Node #0,2,3: 95:[4, 9] Operation: 36/4=9 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 95:[4, 9], Operations: ['72-68=4', '36/4=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,95 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 95:[4, 9], Operations: ['72-68=4', '36/4=9'] Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 95:[4, 32], Operations: ['72-68=4', '36-4=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,95 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 95:[4, 32], Operations: ['72-68=4', '36-4=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,95 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:[4, 68, 2], Operations: ['72/36=2'] Exploring Operation: 4+68=72, Resulting Numbers: [2, 72] Generated Node #0,1,0: 95:[2, 72] Operation: 4+68=72 Exploring Operation: 68/2=34, Resulting Numbers: [4, 34] Generated Node #0,1,1: 95:[4, 34] Operation: 68/2=34 Exploring Operation: 68/4=17, Resulting Numbers: [2, 17] Generated Node #0,1,2: 95:[2, 17] Operation: 68/4=17 Exploring Operation: 68+2=70, Resulting Numbers: [4, 70] Generated Node #0,1,3: 95:[4, 70] Operation: 68+2=70 Moving to Node #0,0 Current State: 95:[4, 72, 104], Operations: ['68+36=104'] Exploring Operation: 104-4=100, Resulting Numbers: [72, 100] Generated Node #0,0,0: 95:[72, 100] Operation: 104-4=100 Exploring Operation: 104-72=32, Resulting Numbers: [4, 32] Generated Node #0,0,1: 95:[4, 32] Operation: 104-72=32 Exploring Operation: 72/4=18, Resulting Numbers: [104, 18] Generated Node #0,0,2: 95:[104, 18] Operation: 72/4=18 Exploring Operation: 4+72=76, Resulting Numbers: [104, 76] Generated Node #0,0,3: 95:[104, 76] Operation: 4+72=76 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 95:[104, 18], Operations: ['68+36=104', '72/4=18'] Exploring Operation: 104*18=1872, Resulting Numbers: [1872] 1872,95 unequal: No Solution Exploring Operation: 104-18=86, Resulting Numbers: [86] 86,95 unequal: No Solution Exploring Operation: 104+18=122, Resulting Numbers: [122] 122,95 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:[4, 32], Operations: ['68+36=104', '104-72=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,95 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,95 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 95:[72, 100], Operations: ['68+36=104', '104-4=100'] Exploring Operation: 72*100=7200, Resulting Numbers: [7200] 7200,95 unequal: No Solution Exploring Operation: 72+100=172, Resulting Numbers: [172] 172,95 unequal: No Solution Exploring Operation: 100-72=28, Resulting Numbers: [28] 28,95 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:[104, 76], Operations: ['68+36=104', '4+72=76'] Exploring Operation: 104*76=7904, Resulting Numbers: [7904] 7904,95 unequal: No Solution Exploring Operation: 104-76=28, Resulting Numbers: [28] 28,95 unequal: No Solution Exploring Operation: 104+76=180, Resulting Numbers: [180] 180,95 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: 95:[4, 72, 32], Operations: ['68-36=32'] Exploring Operation: 32/4=8, Resulting Numbers: [72, 8] Generated Node #0,3,0: 95:[72, 8] Operation: 32/4=8 Exploring Operation: 72+32=104, Resulting Numbers: [4, 104] Generated Node #0,3,1: 95:[4, 104] Operation: 72+32=104 Exploring Operation: 72/4=18, Resulting Numbers: [32, 18] Generated Node #0,3,2: 95:[32, 18] Operation: 72/4=18 Exploring Operation: 72-32=40, Resulting Numbers: [4, 40] Generated Node #0,3,3: 95:[4, 40] Operation: 72-32=40 Moving to Node #0,1,2 Current State: 95:[2, 17], Operations: ['72/36=2', '68/4=17'] Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,95 unequal: No Solution Moving to Node #0,3,1 Current State: 95:[4, 104], Operations: ['68-36=32', '72+32=104'] Exploring Operation: 4+104=108, Resulting Numbers: [108] 108,95 unequal: No Solution Exploring Operation: 104/4=26, Resulting Numbers: [26] 26,95 unequal: No Solution Exploring Operation: 104-4=100, Resulting Numbers: [100] 100,95 unequal: No Solution Exploring Operation: 4*104=416, Resulting Numbers: [416] 416,95 unequal: No Solution Moving to Node #0,3,2 Current State: 95:[32, 18], Operations: ['68-36=32', '72/4=18'] Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,95 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,95 unequal: No Solution Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[4, 34], Operations: ['72/36=2', '68/2=34'] Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,95 unequal: No Solution Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[4, 40], Operations: ['68-36=32', '72-32=40'] Exploring Operation: 40/4=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 4*40=160, Resulting Numbers: [160] 160,95 unequal: No Solution Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,95 unequal: No Solution Exploring Operation: 4+40=44, Resulting Numbers: [44] 44,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[2, 72], Operations: ['72/36=2', '4+68=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,95 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,95 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,95 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,95 unequal: No Solution Moving to Node #0,3,0 Current State: 95:[72, 8], Operations: ['68-36=32', '32/4=8'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,95 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,95 unequal: No Solution Exploring Operation: 72*8=576, Resulting Numbers: [576] 576,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[4, 70], Operations: ['72/36=2', '68+2=70'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,95 unequal: No Solution Exploring Operation: 4*70=280, Resulting Numbers: [280] 280,95 unequal: No Solution Exploring Operation: 4+70=74, Resulting Numbers: [74] 74,95 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 28, 24, 1, 73 ]
70
[ "28-24=4", "1+73=74", "74-4=70" ]
Current State: 70:[28, 24, 1, 73], Operations: [] Exploring Operation: 28-24=4, Resulting Numbers: [1, 73, 4] Generated Node #2: [1, 73, 4] from Operation: 28-24=4 Current State: 70:[1, 73, 4], Operations: ['28-24=4'] Exploring Operation: 1+73=74, Resulting Numbers: [4, 74] Generated Node #3: [4, 74] from Operation: 1+73=74 Current State: 70:[4, 74], Operations: ['28-24=4', '1+73=74'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[28, 24, 1, 73], Operations: [] Exploring Operation: 28-24=4, Resulting Numbers: [1, 73, 4] Generated Node #0,0: 70:[1, 73, 4] Operation: 28-24=4 Exploring Operation: 24-1=23, Resulting Numbers: [28, 73, 23] Generated Node #0,1: 70:[28, 73, 23] Operation: 24-1=23 Exploring Operation: 28+1=29, Resulting Numbers: [24, 73, 29] Generated Node #0,2: 70:[24, 73, 29] Operation: 28+1=29 Moving to Node #0,0 Current State: 70:[1, 73, 4], Operations: ['28-24=4'] Exploring Operation: 73-1=72, Resulting Numbers: [4, 72] Generated Node #0,0,0: 70:[4, 72] Operation: 73-1=72 Exploring Operation: 73-4=69, Resulting Numbers: [1, 69] Generated Node #0,0,1: 70:[1, 69] Operation: 73-4=69 Exploring Operation: 1+4=5, Resulting Numbers: [73, 5] Generated Node #0,0,2: 70:[73, 5] Operation: 1+4=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[1, 69], Operations: ['28-24=4', '73-4=69'] Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 1+69=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[28, 24, 1, 73], Operations: [] Exploring Operation: 28-24=4, Resulting Numbers: [1, 73, 4] Generated Node #0,0: 70:[1, 73, 4] Operation: 28-24=4 Moving to Node #0,0 Current State: 70:[1, 73, 4], Operations: ['28-24=4'] Exploring Operation: 73-4=69, Resulting Numbers: [1, 69] Generated Node #0,0,1: 70:[1, 69] Operation: 73-4=69 Moving to Node #0,0,1 Current State: 70:[1, 69], Operations: ['28-24=4', '73-4=69'] Exploring Operation: 1+69=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 32, 64, 90, 97 ]
83
[ "64/32=2", "90*2=180", "180-97=83" ]
Current State: 83:[32, 64, 90, 97], Operations: [] Exploring Operation: 64/32=2, Resulting Numbers: [90, 97, 2] Generated Node #2: [90, 97, 2] from Operation: 64/32=2 Current State: 83:[90, 97, 2], Operations: ['64/32=2'] Exploring Operation: 90*2=180, Resulting Numbers: [97, 180] Generated Node #3: [97, 180] from Operation: 90*2=180 Current State: 83:[97, 180], Operations: ['64/32=2', '90*2=180'] Exploring Operation: 180-97=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[32, 64, 90, 97], Operations: [] Exploring Operation: 90-32=58, Resulting Numbers: [64, 97, 58] Generated Node #0,0: 83:[64, 97, 58] Operation: 90-32=58 Exploring Operation: 97-32=65, Resulting Numbers: [64, 90, 65] Generated Node #0,1: 83:[64, 90, 65] Operation: 97-32=65 Exploring Operation: 32+64=96, Resulting Numbers: [90, 97, 96] Generated Node #0,2: 83:[90, 97, 96] Operation: 32+64=96 Moving to Node #0,2 Current State: 83:[90, 97, 96], Operations: ['32+64=96'] Exploring Operation: 97-96=1, Resulting Numbers: [90, 1] Generated Node #0,2,0: 83:[90, 1] Operation: 97-96=1 Exploring Operation: 97-90=7, Resulting Numbers: [96, 7] Generated Node #0,2,1: 83:[96, 7] Operation: 97-90=7 Exploring Operation: 96-90=6, Resulting Numbers: [97, 6] Generated Node #0,2,2: 83:[97, 6] Operation: 96-90=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[90, 1], Operations: ['32+64=96', '97-96=1'] Exploring Operation: 90/1=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,83 unequal: No Solution Exploring Operation: 90-1=89, Resulting Numbers: [89] 89,83 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 #0,2,1 Current State: 83:[96, 7], Operations: ['32+64=96', '97-90=7'] Exploring Operation: 96*7=672, Resulting Numbers: [672] 672,83 unequal: No Solution Exploring Operation: 96-7=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 96+7=103, Resulting Numbers: [103] 103,83 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 #0,2,2 Current State: 83:[97, 6], Operations: ['32+64=96', '96-90=6'] Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,83 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,83 unequal: No Solution Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[64, 90, 65], Operations: ['97-32=65'] Exploring Operation: 90-65=25, Resulting Numbers: [64, 25] Generated Node #0,1,0: 83:[64, 25] Operation: 90-65=25 Exploring Operation: 64+65=129, Resulting Numbers: [90, 129] Generated Node #0,1,1: 83:[90, 129] Operation: 64+65=129 Exploring Operation: 90-64=26, Resulting Numbers: [65, 26] Generated Node #0,1,2: 83:[65, 26] Operation: 90-64=26 Moving to Node #0,0 Current State: 83:[64, 97, 58], Operations: ['90-32=58'] Exploring Operation: 64+58=122, Resulting Numbers: [97, 122] Generated Node #0,0,0: 83:[97, 122] Operation: 64+58=122 Exploring Operation: 97-64=33, Resulting Numbers: [58, 33] Generated Node #0,0,1: 83:[58, 33] Operation: 97-64=33 Exploring Operation: 97-58=39, Resulting Numbers: [64, 39] Generated Node #0,0,2: 83:[64, 39] Operation: 97-58=39 Moving to Node #0,1,1 Current State: 83:[90, 129], Operations: ['97-32=65', '64+65=129'] Exploring Operation: 90*129=11610, Resulting Numbers: [11610] 11610,83 unequal: No Solution Exploring Operation: 129-90=39, Resulting Numbers: [39] 39,83 unequal: No Solution Exploring Operation: 90+129=219, Resulting Numbers: [219] 219,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[97, 122], Operations: ['90-32=58', '64+58=122'] Exploring Operation: 97*122=11834, Resulting Numbers: [11834] 11834,83 unequal: No Solution Exploring Operation: 122-97=25, Resulting Numbers: [25] 25,83 unequal: No Solution Exploring Operation: 97+122=219, Resulting Numbers: [219] 219,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[64, 39], Operations: ['90-32=58', '97-58=39'] Exploring Operation: 64+39=103, Resulting Numbers: [103] 103,83 unequal: No Solution Exploring Operation: 64*39=2496, Resulting Numbers: [2496] 2496,83 unequal: No Solution Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[58, 33], Operations: ['90-32=58', '97-64=33'] Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,83 unequal: No Solution Exploring Operation: 58*33=1914, Resulting Numbers: [1914] 1914,83 unequal: No Solution Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[65, 26], Operations: ['97-32=65', '90-64=26'] Exploring Operation: 65+26=91, Resulting Numbers: [91] 91,83 unequal: No Solution Exploring Operation: 65*26=1690, Resulting Numbers: [1690] 1690,83 unequal: No Solution Exploring Operation: 65-26=39, Resulting Numbers: [39] 39,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[64, 25], Operations: ['97-32=65', '90-65=25'] Exploring Operation: 64*25=1600, Resulting Numbers: [1600] 1600,83 unequal: No Solution Exploring Operation: 64+25=89, Resulting Numbers: [89] 89,83 unequal: No Solution Exploring Operation: 64-25=39, Resulting Numbers: [39] 39,83 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 65, 36, 27, 13 ]
52
[ "36-27=9", "13*9=117", "117-65=52" ]
Current State: 52:[65, 36, 27, 13], Operations: [] Exploring Operation: 36-27=9, Resulting Numbers: [65, 13, 9] Generated Node #2: [65, 13, 9] from Operation: 36-27=9 Current State: 52:[65, 13, 9], Operations: ['36-27=9'] Exploring Operation: 13*9=117, Resulting Numbers: [65, 117] Generated Node #3: [65, 117] from Operation: 13*9=117 Current State: 52:[65, 117], Operations: ['36-27=9', '13*9=117'] Exploring Operation: 117-65=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[65, 36, 27, 13], Operations: [] Exploring Operation: 65-13=52, Resulting Numbers: [36, 27, 52] Generated Node #0,0: 52:[36, 27, 52] Operation: 65-13=52 Exploring Operation: 65-36=29, Resulting Numbers: [27, 13, 29] Generated Node #0,1: 52:[27, 13, 29] Operation: 65-36=29 Moving to Node #0,1 Current State: 52:[27, 13, 29], Operations: ['65-36=29'] Exploring Operation: 29-27=2, Resulting Numbers: [13, 2] Generated Node #0,1,0: 52:[13, 2] Operation: 29-27=2 Exploring Operation: 27-13=14, Resulting Numbers: [29, 14] Generated Node #0,1,1: 52:[29, 14] Operation: 27-13=14 Moving to Node #0,0 Current State: 52:[36, 27, 52], Operations: ['65-13=52'] Exploring Operation: 36-27=9, Resulting Numbers: [52, 9] Generated Node #0,0,0: 52:[52, 9] Operation: 36-27=9 Exploring Operation: 52-36=16, Resulting Numbers: [27, 16] Generated Node #0,0,1: 52:[27, 16] Operation: 52-36=16 Moving to Node #0,1,0 Current State: 52:[13, 2], Operations: ['65-36=29', '29-27=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[52, 9], Operations: ['65-13=52', '36-27=9'] Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[29, 14], Operations: ['65-36=29', '27-13=14'] Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[27, 16], Operations: ['65-13=52', '52-36=16'] Exploring Operation: 27+16=43, Resulting Numbers: [43] 43,52 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,52 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 2, 65, 87, 5 ]
99
[ "87-5=82", "2*82=164", "164-65=99" ]
Current State: 99:[2, 65, 87, 5], Operations: [] Exploring Operation: 87-5=82, Resulting Numbers: [2, 65, 82] Generated Node #2: [2, 65, 82] from Operation: 87-5=82 Current State: 99:[2, 65, 82], Operations: ['87-5=82'] Exploring Operation: 2*82=164, Resulting Numbers: [65, 164] Generated Node #3: [65, 164] from Operation: 2*82=164 Current State: 99:[65, 164], Operations: ['87-5=82', '2*82=164'] Exploring Operation: 164-65=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[2, 65, 87, 5], Operations: [] Exploring Operation: 65/5=13, Resulting Numbers: [2, 87, 13] Generated Node #0,0: 99:[2, 87, 13] Operation: 65/5=13 Exploring Operation: 87+5=92, Resulting Numbers: [2, 65, 92] Generated Node #0,1: 99:[2, 65, 92] Operation: 87+5=92 Exploring Operation: 87-65=22, Resulting Numbers: [2, 5, 22] Generated Node #0,2: 99:[2, 5, 22] Operation: 87-65=22 Exploring Operation: 65-5=60, Resulting Numbers: [2, 87, 60] Generated Node #0,3: 99:[2, 87, 60] Operation: 65-5=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[2, 5, 22], Operations: ['87-65=22'] Exploring Operation: 22/2=11, Resulting Numbers: [5, 11] Generated Node #0,2,0: 99:[5, 11] Operation: 22/2=11 Exploring Operation: 5+22=27, Resulting Numbers: [2, 27] Generated Node #0,2,1: 99:[2, 27] Operation: 5+22=27 Exploring Operation: 5-2=3, Resulting Numbers: [22, 3] Generated Node #0,2,2: 99:[22, 3] Operation: 5-2=3 Exploring Operation: 22-5=17, Resulting Numbers: [2, 17] Generated Node #0,2,3: 99:[2, 17] Operation: 22-5=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[5, 11], Operations: ['87-65=22', '22/2=11'] Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,99 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[2, 27], Operations: ['87-65=22', '5+22=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[2, 17], Operations: ['87-65=22', '22-5=17'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,99 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,99 unequal: No Solution Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[22, 3], Operations: ['87-65=22', '5-2=3'] Exploring Operation: 22+3=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,99 unequal: No Solution Exploring Operation: 22*3=66, Resulting Numbers: [66] 66,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[2, 87, 13], Operations: ['65/5=13'] Exploring Operation: 13-2=11, Resulting Numbers: [87, 11] Generated Node #0,0,0: 99:[87, 11] Operation: 13-2=11 Exploring Operation: 87+13=100, Resulting Numbers: [2, 100] Generated Node #0,0,1: 99:[2, 100] Operation: 87+13=100 Exploring Operation: 87-2=85, Resulting Numbers: [13, 85] Generated Node #0,0,2: 99:[13, 85] Operation: 87-2=85 Exploring Operation: 2+87=89, Resulting Numbers: [13, 89] Generated Node #0,0,3: 99:[13, 89] Operation: 2+87=89 Moving to Node #0,0,1 Current State: 99:[2, 100], Operations: ['65/5=13', '87+13=100'] Exploring Operation: 2*100=200, Resulting Numbers: [200] 200,99 unequal: No Solution Exploring Operation: 2+100=102, Resulting Numbers: [102] 102,99 unequal: No Solution Exploring Operation: 100/2=50, Resulting Numbers: [50] 50,99 unequal: No Solution Exploring Operation: 100-2=98, Resulting Numbers: [98] 98,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[13, 89], Operations: ['65/5=13', '2+87=89'] Exploring Operation: 13*89=1157, Resulting Numbers: [1157] 1157,99 unequal: No Solution Exploring Operation: 13+89=102, Resulting Numbers: [102] 102,99 unequal: No Solution Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[87, 11], Operations: ['65/5=13', '13-2=11'] Exploring Operation: 87+11=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 87*11=957, Resulting Numbers: [957] 957,99 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[13, 85], Operations: ['65/5=13', '87-2=85'] Exploring Operation: 13+85=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 85-13=72, Resulting Numbers: [72] 72,99 unequal: No Solution Exploring Operation: 13*85=1105, Resulting Numbers: [1105] 1105,99 unequal: No Solution No 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: 99:[2, 65, 92], Operations: ['87+5=92'] Exploring Operation: 2*65=130, Resulting Numbers: [92, 130] Generated Node #0,1,0: 99:[92, 130] Operation: 2*65=130 Exploring Operation: 65-2=63, Resulting Numbers: [92, 63] Generated Node #0,1,1: 99:[92, 63] Operation: 65-2=63 Exploring Operation: 92-65=27, Resulting Numbers: [2, 27] Generated Node #0,1,2: 99:[2, 27] Operation: 92-65=27 Exploring Operation: 2+92=94, Resulting Numbers: [65, 94] Generated Node #0,1,3: 99:[65, 94] Operation: 2+92=94 Moving to Node #0,1,2 Current State: 99:[2, 27], Operations: ['87+5=92', '92-65=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,99 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[65, 94], Operations: ['87+5=92', '2+92=94'] Exploring Operation: 65+94=159, Resulting Numbers: [159] 159,99 unequal: No Solution Exploring Operation: 65*94=6110, Resulting Numbers: [6110] 6110,99 unequal: No Solution Exploring Operation: 94-65=29, Resulting Numbers: [29] 29,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[92, 63], Operations: ['87+5=92', '65-2=63'] Exploring Operation: 92+63=155, Resulting Numbers: [155] 155,99 unequal: No Solution Exploring Operation: 92-63=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 92*63=5796, Resulting Numbers: [5796] 5796,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[92, 130], Operations: ['87+5=92', '2*65=130'] Exploring Operation: 130-92=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 92+130=222, Resulting Numbers: [222] 222,99 unequal: No Solution Exploring Operation: 92*130=11960, Resulting Numbers: [11960] 11960,99 unequal: No Solution No 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: 99:[2, 87, 60], Operations: ['65-5=60'] Exploring Operation: 2*60=120, Resulting Numbers: [87, 120] Generated Node #0,3,0: 99:[87, 120] Operation: 2*60=120 Exploring Operation: 60/2=30, Resulting Numbers: [87, 30] Generated Node #0,3,1: 99:[87, 30] Operation: 60/2=30 Exploring Operation: 2+87=89, Resulting Numbers: [60, 89] Generated Node #0,3,2: 99:[60, 89] Operation: 2+87=89 Exploring Operation: 87-60=27, Resulting Numbers: [2, 27] Generated Node #0,3,3: 99:[2, 27] Operation: 87-60=27 Moving to Node #0,3,3 Current State: 99:[2, 27], Operations: ['65-5=60', '87-60=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[87, 30], Operations: ['65-5=60', '60/2=30'] Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,99 unequal: No Solution Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[87, 120], Operations: ['65-5=60', '2*60=120'] Exploring Operation: 87*120=10440, Resulting Numbers: [10440] 10440,99 unequal: No Solution Exploring Operation: 87+120=207, Resulting Numbers: [207] 207,99 unequal: No Solution Exploring Operation: 120-87=33, Resulting Numbers: [33] 33,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[60, 89], Operations: ['65-5=60', '2+87=89'] Exploring Operation: 60+89=149, Resulting Numbers: [149] 149,99 unequal: No Solution Exploring Operation: 89-60=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 60*89=5340, Resulting Numbers: [5340] 5340,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 29, 20, 5, 5 ]
10
[ "29-20=9", "5/5=1", "9+1=10" ]
Current State: 10:[29, 20, 5, 5], Operations: [] Exploring Operation: 29-20=9, Resulting Numbers: [5, 5, 9] Generated Node #2: [5, 5, 9] from Operation: 29-20=9 Current State: 10:[5, 5, 9], Operations: ['29-20=9'] Exploring Operation: 5/5=1, Resulting Numbers: [9, 1] Generated Node #3: [9, 1] from Operation: 5/5=1 Current State: 10:[9, 1], Operations: ['29-20=9', '5/5=1'] Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[29, 20, 5, 5], Operations: [] Exploring Operation: 20/5=4, Resulting Numbers: [29, 5, 4] Generated Node #0,0: 10:[29, 5, 4] Operation: 20/5=4 Exploring Operation: 29-20=9, Resulting Numbers: [5, 5, 9] Generated Node #0,1: 10:[5, 5, 9] Operation: 29-20=9 Exploring Operation: 20/5=4, Resulting Numbers: [29, 5, 4] Generated Node #0,2: 10:[29, 5, 4] Operation: 20/5=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[5, 5, 9], Operations: ['29-20=9'] Exploring Operation: 9-5=4, Resulting Numbers: [5, 4] Generated Node #0,1,0: 10:[5, 4] Operation: 9-5=4 Exploring Operation: 5+5=10, Resulting Numbers: [9, 10] Generated Node #0,1,1: 10:[9, 10] Operation: 5+5=10 Exploring Operation: 9-5=4, Resulting Numbers: [5, 4] Generated Node #0,1,2: 10:[5, 4] Operation: 9-5=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[5, 4], Operations: ['29-20=9', '9-5=4'] Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[9, 10], Operations: ['29-20=9', '5+5=10'] Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,10 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 10:[5, 4], Operations: ['29-20=9', '9-5=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,10 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[29, 5, 4], Operations: ['20/5=4'] Exploring Operation: 29-5=24, Resulting Numbers: [4, 24] Generated Node #0,0,0: 10:[4, 24] Operation: 29-5=24 Exploring Operation: 29-4=25, Resulting Numbers: [5, 25] Generated Node #0,0,1: 10:[5, 25] Operation: 29-4=25 Exploring Operation: 5+4=9, Resulting Numbers: [29, 9] Generated Node #0,0,2: 10:[29, 9] Operation: 5+4=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[4, 24], Operations: ['20/5=4', '29-5=24'] Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,10 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[5, 25], Operations: ['20/5=4', '29-4=25'] Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,10 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 10:[29, 9], Operations: ['20/5=4', '5+4=9'] Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,10 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[29, 5, 4], Operations: ['20/5=4'] Exploring Operation: 29-4=25, Resulting Numbers: [5, 25] Generated Node #0,2,0: 10:[5, 25] Operation: 29-4=25 Exploring Operation: 29-5=24, Resulting Numbers: [4, 24] Generated Node #0,2,1: 10:[4, 24] Operation: 29-5=24 Exploring Operation: 5+4=9, Resulting Numbers: [29, 9] Generated Node #0,2,2: 10:[29, 9] Operation: 5+4=9 Moving to Node #0,2,0 Current State: 10:[5, 25], Operations: ['20/5=4', '29-4=25'] Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,10 unequal: No Solution Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,10 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[4, 24], Operations: ['20/5=4', '29-5=24'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,10 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Moving to Node #0,2,2 Current State: 10:[29, 9], Operations: ['20/5=4', '5+4=9'] Exploring Operation: 29+9=38, Resulting Numbers: [38] 38,10 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 29*9=261, Resulting Numbers: [261] 261,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 14, 43, 91, 42 ]
51
[ "42/14=3", "91-43=48", "3+48=51" ]
Current State: 51:[14, 43, 91, 42], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [43, 91, 3] Generated Node #2: [43, 91, 3] from Operation: 42/14=3 Current State: 51:[43, 91, 3], Operations: ['42/14=3'] Exploring Operation: 91-43=48, Resulting Numbers: [3, 48] Generated Node #3: [3, 48] from Operation: 91-43=48 Current State: 51:[3, 48], Operations: ['42/14=3', '91-43=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[14, 43, 91, 42], Operations: [] Exploring Operation: 91-42=49, Resulting Numbers: [14, 43, 49] Generated Node #0,0: 51:[14, 43, 49] Operation: 91-42=49 Exploring Operation: 91-43=48, Resulting Numbers: [14, 42, 48] Generated Node #0,1: 51:[14, 42, 48] Operation: 91-43=48 Exploring Operation: 42/14=3, Resulting Numbers: [43, 91, 3] Generated Node #0,2: 51:[43, 91, 3] Operation: 42/14=3 Exploring Operation: 43-42=1, Resulting Numbers: [14, 91, 1] Generated Node #0,3: 51:[14, 91, 1] Operation: 43-42=1 Exploring Operation: 91-14=77, Resulting Numbers: [43, 42, 77] Generated Node #0,4: 51:[43, 42, 77] Operation: 91-14=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[14, 43, 49], Operations: ['91-42=49'] Exploring Operation: 43-14=29, Resulting Numbers: [49, 29] Generated Node #0,0,0: 51:[49, 29] Operation: 43-14=29 Exploring Operation: 49-43=6, Resulting Numbers: [14, 6] Generated Node #0,0,1: 51:[14, 6] Operation: 49-43=6 Exploring Operation: 14+49=63, Resulting Numbers: [43, 63] Generated Node #0,0,2: 51:[43, 63] Operation: 14+49=63 Exploring Operation: 14+43=57, Resulting Numbers: [49, 57] Generated Node #0,0,3: 51:[49, 57] Operation: 14+43=57 Exploring Operation: 49-14=35, Resulting Numbers: [43, 35] Generated Node #0,0,4: 51:[43, 35] Operation: 49-14=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[14, 6], Operations: ['91-42=49', '49-43=6'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,51 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,51 unequal: No Solution No 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: 51:[49, 57], Operations: ['91-42=49', '14+43=57'] Exploring Operation: 49+57=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 49*57=2793, Resulting Numbers: [2793] 2793,51 unequal: No Solution Exploring Operation: 57-49=8, Resulting Numbers: [8] 8,51 unequal: No Solution No 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: 51:[49, 29], Operations: ['91-42=49', '43-14=29'] Exploring Operation: 49+29=78, Resulting Numbers: [78] 78,51 unequal: No Solution Exploring Operation: 49*29=1421, Resulting Numbers: [1421] 1421,51 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,51 unequal: No Solution No 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: 51:[43, 63], Operations: ['91-42=49', '14+49=63'] Exploring Operation: 43+63=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 43*63=2709, Resulting Numbers: [2709] 2709,51 unequal: No Solution Exploring Operation: 63-43=20, Resulting Numbers: [20] 20,51 unequal: No Solution No 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: 51:[43, 35], Operations: ['91-42=49', '49-14=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,51 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,51 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,51 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: 51:[14, 42, 48], Operations: ['91-43=48'] Exploring Operation: 42-14=28, Resulting Numbers: [48, 28] Generated Node #0,1,0: 51:[48, 28] Operation: 42-14=28 Exploring Operation: 42/14=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 51:[48, 3] Operation: 42/14=3 Exploring Operation: 14+48=62, Resulting Numbers: [42, 62] Generated Node #0,1,2: 51:[42, 62] Operation: 14+48=62 Exploring Operation: 14+42=56, Resulting Numbers: [48, 56] Generated Node #0,1,3: 51:[48, 56] Operation: 14+42=56 Exploring Operation: 48-42=6, Resulting Numbers: [14, 6] Generated Node #0,1,4: 51:[14, 6] Operation: 48-42=6 Moving to Node #0,1,1 Current State: 51:[48, 3], Operations: ['91-43=48', '42/14=3'] Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,51 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[14, 43, 91, 42], Operations: [] Exploring Operation: 91-43=48, Resulting Numbers: [14, 42, 48] Generated Node #0,1: 51:[14, 42, 48] Operation: 91-43=48 Moving to Node #0,1 Current State: 51:[14, 42, 48], Operations: ['91-43=48'] Exploring Operation: 42/14=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 51:[48, 3] Operation: 42/14=3 Moving to Node #0,1,1 Current State: 51:[48, 3], Operations: ['91-43=48', '42/14=3'] Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 7, 13, 63, 3 ]
16
[ "63/7=9", "9/3=3", "13+3=16" ]
Current State: 16:[7, 13, 63, 3], Operations: [] Exploring Operation: 63/7=9, Resulting Numbers: [13, 3, 9] Generated Node #2: [13, 3, 9] from Operation: 63/7=9 Current State: 16:[13, 3, 9], Operations: ['63/7=9'] Exploring Operation: 9/3=3, Resulting Numbers: [13, 3] Generated Node #3: [13, 3] from Operation: 9/3=3 Current State: 16:[13, 3], Operations: ['63/7=9', '9/3=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[7, 13, 63, 3], Operations: [] Exploring Operation: 63/3=21, Resulting Numbers: [7, 13, 21] Generated Node #0,0: 16:[7, 13, 21] Operation: 63/3=21 Exploring Operation: 63/7=9, Resulting Numbers: [13, 3, 9] Generated Node #0,1: 16:[13, 3, 9] Operation: 63/7=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[13, 3, 9], Operations: ['63/7=9'] Exploring Operation: 13+3=16, Resulting Numbers: [9, 16] Generated Node #0,1,0: 16:[9, 16] Operation: 13+3=16 Exploring Operation: 13-9=4, Resulting Numbers: [3, 4] Generated Node #0,1,1: 16:[3, 4] Operation: 13-9=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[9, 16], Operations: ['63/7=9', '13+3=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,16 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,16 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:[3, 4], Operations: ['63/7=9', '13-9=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,16 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:[7, 13, 21], Operations: ['63/3=21'] Exploring Operation: 21/7=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 16:[13, 3] Operation: 21/7=3 Exploring Operation: 21-13=8, Resulting Numbers: [7, 8] Generated Node #0,0,1: 16:[7, 8] Operation: 21-13=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[7, 8], Operations: ['63/3=21', '21-13=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,16 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:[13, 3], Operations: ['63/3=21', '21/7=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[7, 13, 63, 3], Operations: [] Exploring Operation: 63/3=21, Resulting Numbers: [7, 13, 21] Generated Node #0,0: 16:[7, 13, 21] Operation: 63/3=21 Moving to Node #0,0 Current State: 16:[7, 13, 21], Operations: ['63/3=21'] Exploring Operation: 21/7=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 16:[13, 3] Operation: 21/7=3 Moving to Node #0,0,0 Current State: 16:[13, 3], Operations: ['63/3=21', '21/7=3'] Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 33, 38, 69, 9 ]
18
[ "33+38=71", "71-69=2", "9*2=18" ]
Current State: 18:[33, 38, 69, 9], Operations: [] Exploring Operation: 33+38=71, Resulting Numbers: [69, 9, 71] Generated Node #2: [69, 9, 71] from Operation: 33+38=71 Current State: 18:[69, 9, 71], Operations: ['33+38=71'] Exploring Operation: 71-69=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 71-69=2 Current State: 18:[9, 2], Operations: ['33+38=71', '71-69=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[33, 38, 69, 9], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [69, 9, 5] Generated Node #0,0: 18:[69, 9, 5] Operation: 38-33=5 Exploring Operation: 33-9=24, Resulting Numbers: [38, 69, 24] Generated Node #0,1: 18:[38, 69, 24] Operation: 33-9=24 Exploring Operation: 69-33=36, Resulting Numbers: [38, 9, 36] Generated Node #0,2: 18:[38, 9, 36] Operation: 69-33=36 Exploring Operation: 38-9=29, Resulting Numbers: [33, 69, 29] Generated Node #0,3: 18:[33, 69, 29] Operation: 38-9=29 Exploring Operation: 69-38=31, Resulting Numbers: [33, 9, 31] Generated Node #0,4: 18:[33, 9, 31] Operation: 69-38=31 Moving to Node #0,4 Current State: 18:[33, 9, 31], Operations: ['69-38=31'] Exploring Operation: 33+9=42, Resulting Numbers: [31, 42] Generated Node #0,4,0: 18:[31, 42] Operation: 33+9=42 Exploring Operation: 33-9=24, Resulting Numbers: [31, 24] Generated Node #0,4,1: 18:[31, 24] Operation: 33-9=24 Exploring Operation: 31-9=22, Resulting Numbers: [33, 22] Generated Node #0,4,2: 18:[33, 22] Operation: 31-9=22 Exploring Operation: 9+31=40, Resulting Numbers: [33, 40] Generated Node #0,4,3: 18:[33, 40] Operation: 9+31=40 Exploring Operation: 33-31=2, Resulting Numbers: [9, 2] Generated Node #0,4,4: 18:[9, 2] Operation: 33-31=2 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 18:[9, 2], Operations: ['69-38=31', '33-31=2'] Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[33, 38, 69, 9], Operations: [] Exploring Operation: 69-38=31, Resulting Numbers: [33, 9, 31] Generated Node #0,4: 18:[33, 9, 31] Operation: 69-38=31 Moving to Node #0,4 Current State: 18:[33, 9, 31], Operations: ['69-38=31'] Exploring Operation: 33-31=2, Resulting Numbers: [9, 2] Generated Node #0,4,4: 18:[9, 2] Operation: 33-31=2 Moving to Node #0,4,4 Current State: 18:[9, 2], Operations: ['69-38=31', '33-31=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 54, 62, 23, 59 ]
20
[ "54*23=1242", "1242-62=1180", "1180/59=20" ]
Current State: 20:[54, 62, 23, 59], Operations: [] Exploring Operation: 54*23=1242, Resulting Numbers: [62, 59, 1242] Generated Node #2: [62, 59, 1242] from Operation: 54*23=1242 Current State: 20:[62, 59, 1242], Operations: ['54*23=1242'] Exploring Operation: 1242-62=1180, Resulting Numbers: [59, 1180] Generated Node #3: [59, 1180] from Operation: 1242-62=1180 Current State: 20:[59, 1180], Operations: ['54*23=1242', '1242-62=1180'] Exploring Operation: 1180/59=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[54, 62, 23, 59], Operations: [] Exploring Operation: 59-54=5, Resulting Numbers: [62, 23, 5] Generated Node #0,0: 20:[62, 23, 5] Operation: 59-54=5 Exploring Operation: 62-54=8, Resulting Numbers: [23, 59, 8] Generated Node #0,1: 20:[23, 59, 8] Operation: 62-54=8 Exploring Operation: 62-59=3, Resulting Numbers: [54, 23, 3] Generated Node #0,2: 20:[54, 23, 3] Operation: 62-59=3 Moving to Node #0,2 Current State: 20:[54, 23, 3], Operations: ['62-59=3'] Exploring Operation: 54-23=31, Resulting Numbers: [3, 31] Generated Node #0,2,0: 20:[3, 31] Operation: 54-23=31 Exploring Operation: 54/3=18, Resulting Numbers: [23, 18] Generated Node #0,2,1: 20:[23, 18] Operation: 54/3=18 Exploring Operation: 54-3=51, Resulting Numbers: [23, 51] Generated Node #0,2,2: 20:[23, 51] Operation: 54-3=51 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[23, 18], Operations: ['62-59=3', '54/3=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,20 unequal: No Solution Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[3, 31], Operations: ['62-59=3', '54-23=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 20:[23, 51], Operations: ['62-59=3', '54-3=51'] Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,20 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,20 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,20 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: 20:[23, 59, 8], Operations: ['62-54=8'] Exploring Operation: 23-8=15, Resulting Numbers: [59, 15] Generated Node #0,1,0: 20:[59, 15] Operation: 23-8=15 Exploring Operation: 59-8=51, Resulting Numbers: [23, 51] Generated Node #0,1,1: 20:[23, 51] Operation: 59-8=51 Exploring Operation: 59-23=36, Resulting Numbers: [8, 36] Generated Node #0,1,2: 20:[8, 36] Operation: 59-23=36 Moving to Node #0,0 Current State: 20:[62, 23, 5], Operations: ['59-54=5'] Exploring Operation: 23-5=18, Resulting Numbers: [62, 18] Generated Node #0,0,0: 20:[62, 18] Operation: 23-5=18 Exploring Operation: 62-23=39, Resulting Numbers: [5, 39] Generated Node #0,0,1: 20:[5, 39] Operation: 62-23=39 Exploring Operation: 62-5=57, Resulting Numbers: [23, 57] Generated Node #0,0,2: 20:[23, 57] Operation: 62-5=57 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[5, 39], Operations: ['59-54=5', '62-23=39'] Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,20 unequal: No Solution Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 20:[23, 57], Operations: ['59-54=5', '62-5=57'] Exploring Operation: 57-23=34, Resulting Numbers: [34] 34,20 unequal: No Solution Exploring Operation: 23+57=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 23*57=1311, Resulting Numbers: [1311] 1311,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[62, 18], Operations: ['59-54=5', '23-5=18'] Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,20 unequal: No Solution Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,20 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: 20:[8, 36], Operations: ['62-54=8', '59-23=36'] Exploring Operation: 8+36=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 8*36=288, Resulting Numbers: [288] 288,20 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[23, 51], Operations: ['62-54=8', '59-8=51'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,20 unequal: No Solution Exploring Operation: 23*51=1173, Resulting Numbers: [1173] 1173,20 unequal: No Solution Exploring Operation: 23+51=74, Resulting Numbers: [74] 74,20 unequal: No Solution Moving to Node #0,1,0 Current State: 20:[59, 15], Operations: ['62-54=8', '23-8=15'] Exploring Operation: 59+15=74, Resulting Numbers: [74] 74,20 unequal: No Solution Exploring Operation: 59-15=44, Resulting Numbers: [44] 44,20 unequal: No Solution Exploring Operation: 59*15=885, Resulting Numbers: [885] 885,20 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 32, 76, 79, 35 ]
61
[ "79-76=3", "32*3=96", "96-35=61" ]
Current State: 61:[32, 76, 79, 35], Operations: [] Exploring Operation: 79-76=3, Resulting Numbers: [32, 35, 3] Generated Node #2: [32, 35, 3] from Operation: 79-76=3 Current State: 61:[32, 35, 3], Operations: ['79-76=3'] Exploring Operation: 32*3=96, Resulting Numbers: [35, 96] Generated Node #3: [35, 96] from Operation: 32*3=96 Current State: 61:[35, 96], Operations: ['79-76=3', '32*3=96'] Exploring Operation: 96-35=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[32, 76, 79, 35], Operations: [] Exploring Operation: 79-32=47, Resulting Numbers: [76, 35, 47] Generated Node #0,0: 61:[76, 35, 47] Operation: 79-32=47 Exploring Operation: 32+35=67, Resulting Numbers: [76, 79, 67] Generated Node #0,1: 61:[76, 79, 67] Operation: 32+35=67 Exploring Operation: 76-32=44, Resulting Numbers: [79, 35, 44] Generated Node #0,2: 61:[79, 35, 44] Operation: 76-32=44 Exploring Operation: 79-35=44, Resulting Numbers: [32, 76, 44] Generated Node #0,3: 61:[32, 76, 44] Operation: 79-35=44 Moving to Node #0,1 Current State: 61:[76, 79, 67], Operations: ['32+35=67'] Exploring Operation: 79-67=12, Resulting Numbers: [76, 12] Generated Node #0,1,0: 61:[76, 12] Operation: 79-67=12 Exploring Operation: 76-67=9, Resulting Numbers: [79, 9] Generated Node #0,1,1: 61:[79, 9] Operation: 76-67=9 Exploring Operation: 76+79=155, Resulting Numbers: [67, 155] Generated Node #0,1,2: 61:[67, 155] Operation: 76+79=155 Exploring Operation: 79-76=3, Resulting Numbers: [67, 3] Generated Node #0,1,3: 61:[67, 3] Operation: 79-76=3 Moving to Node #0,0 Current State: 61:[76, 35, 47], Operations: ['79-32=47'] Exploring Operation: 76-35=41, Resulting Numbers: [47, 41] Generated Node #0,0,0: 61:[47, 41] Operation: 76-35=41 Exploring Operation: 76+35=111, Resulting Numbers: [47, 111] Generated Node #0,0,1: 61:[47, 111] Operation: 76+35=111 Exploring Operation: 35+47=82, Resulting Numbers: [76, 82] Generated Node #0,0,2: 61:[76, 82] Operation: 35+47=82 Exploring Operation: 76-47=29, Resulting Numbers: [35, 29] Generated Node #0,0,3: 61:[35, 29] Operation: 76-47=29 Moving to Node #0,3 Current State: 61:[32, 76, 44], Operations: ['79-35=44'] Exploring Operation: 76-32=44, Resulting Numbers: [44, 44] Generated Node #0,3,0: 61:[44, 44] Operation: 76-32=44 Exploring Operation: 32+44=76, Resulting Numbers: [76, 76] Generated Node #0,3,1: 61:[76, 76] Operation: 32+44=76 Exploring Operation: 32+76=108, Resulting Numbers: [44, 108] Generated Node #0,3,2: 61:[44, 108] Operation: 32+76=108 Exploring Operation: 76-44=32, Resulting Numbers: [32, 32] Generated Node #0,3,3: 61:[32, 32] Operation: 76-44=32 Moving to Node #0,2 Current State: 61:[79, 35, 44], Operations: ['76-32=44'] Exploring Operation: 79-44=35, Resulting Numbers: [35, 35] Generated Node #0,2,0: 61:[35, 35] Operation: 79-44=35 Exploring Operation: 79+35=114, Resulting Numbers: [44, 114] Generated Node #0,2,1: 61:[44, 114] Operation: 79+35=114 Exploring Operation: 79-35=44, Resulting Numbers: [44, 44] Generated Node #0,2,2: 61:[44, 44] Operation: 79-35=44 Exploring Operation: 35+44=79, Resulting Numbers: [79, 79] Generated Node #0,2,3: 61:[79, 79] Operation: 35+44=79 Moving to Node #0,3,1 Current State: 61:[76, 76], Operations: ['79-35=44', '32+44=76'] Exploring Operation: 76*76=5776, Resulting Numbers: [5776] 5776,61 unequal: No Solution Exploring Operation: 76+76=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 76/76=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 76-76=0, Resulting Numbers: [0] 0,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[44, 44], Operations: ['76-32=44', '79-35=44'] Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,61 unequal: No Solution Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[47, 41], Operations: ['79-32=47', '76-35=41'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,61 unequal: No Solution Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[44, 44], Operations: ['79-35=44', '76-32=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,61 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[79, 79], Operations: ['76-32=44', '35+44=79'] Exploring Operation: 79+79=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 79-79=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 79/79=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 79*79=6241, Resulting Numbers: [6241] 6241,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[76, 82], Operations: ['79-32=47', '35+47=82'] Exploring Operation: 76*82=6232, Resulting Numbers: [6232] 6232,61 unequal: No Solution Exploring Operation: 76+82=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 82-76=6, Resulting Numbers: [6] 6,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[35, 35], Operations: ['76-32=44', '79-44=35'] Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 35*35=1225, Resulting Numbers: [1225] 1225,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[32, 32], Operations: ['79-35=44', '76-44=32'] Exploring Operation: 32/32=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 32-32=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 32+32=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 32*32=1024, Resulting Numbers: [1024] 1024,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[35, 29], Operations: ['79-32=47', '76-47=29'] Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,61 unequal: No Solution Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[44, 108], Operations: ['79-35=44', '32+76=108'] Exploring Operation: 44*108=4752, Resulting Numbers: [4752] 4752,61 unequal: No Solution Exploring Operation: 44+108=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 108-44=64, Resulting Numbers: [64] 64,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[67, 3], Operations: ['32+35=67', '79-76=3'] Exploring Operation: 67+3=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 67*3=201, Resulting Numbers: [201] 201,61 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[47, 111], Operations: ['79-32=47', '76+35=111'] Exploring Operation: 111-47=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 47+111=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 47*111=5217, Resulting Numbers: [5217] 5217,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[76, 12], Operations: ['32+35=67', '79-67=12'] Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,61 unequal: No Solution Exploring Operation: 76-12=64, Resulting Numbers: [64] 64,61 unequal: No Solution Exploring Operation: 76*12=912, Resulting Numbers: [912] 912,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[79, 9], Operations: ['32+35=67', '76-67=9'] Exploring Operation: 79*9=711, Resulting Numbers: [711] 711,61 unequal: No Solution Exploring Operation: 79-9=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 79+9=88, Resulting Numbers: [88] 88,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[44, 114], Operations: ['76-32=44', '79+35=114'] Exploring Operation: 44+114=158, Resulting Numbers: [158] 158,61 unequal: No Solution Exploring Operation: 114-44=70, Resulting Numbers: [70] 70,61 unequal: No Solution Exploring Operation: 44*114=5016, Resulting Numbers: [5016] 5016,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[67, 155], Operations: ['32+35=67', '76+79=155'] Exploring Operation: 67*155=10385, Resulting Numbers: [10385] 10385,61 unequal: No Solution Exploring Operation: 67+155=222, Resulting Numbers: [222] 222,61 unequal: No Solution Exploring Operation: 155-67=88, Resulting Numbers: [88] 88,61 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 13, 5, 43, 76 ]
70
[ "43-13=30", "30/5=6", "76-6=70" ]
Current State: 70:[13, 5, 43, 76], Operations: [] Exploring Operation: 43-13=30, Resulting Numbers: [5, 76, 30] Generated Node #2: [5, 76, 30] from Operation: 43-13=30 Current State: 70:[5, 76, 30], Operations: ['43-13=30'] Exploring Operation: 30/5=6, Resulting Numbers: [76, 6] Generated Node #3: [76, 6] from Operation: 30/5=6 Current State: 70:[76, 6], Operations: ['43-13=30', '30/5=6'] Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[13, 5, 43, 76], Operations: [] Exploring Operation: 76-43=33, Resulting Numbers: [13, 5, 33] Generated Node #0,0: 70:[13, 5, 33] Operation: 76-43=33 Moving to Node #0,0 Current State: 70:[13, 5, 33], Operations: ['76-43=33'] Exploring Operation: 13-5=8, Resulting Numbers: [33, 8] Generated Node #0,0,0: 70:[33, 8] Operation: 13-5=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[33, 8], Operations: ['76-43=33', '13-5=8'] Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,70 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
[ 21, 57, 1, 64 ]
100
[ "57-21=36", "1*64=64", "36+64=100" ]
Current State: 100:[21, 57, 1, 64], Operations: [] Exploring Operation: 57-21=36, Resulting Numbers: [1, 64, 36] Generated Node #2: [1, 64, 36] from Operation: 57-21=36 Current State: 100:[1, 64, 36], Operations: ['57-21=36'] Exploring Operation: 1*64=64, Resulting Numbers: [36, 64] Generated Node #3: [36, 64] from Operation: 1*64=64 Current State: 100:[36, 64], Operations: ['57-21=36', '1*64=64'] Exploring Operation: 36+64=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[21, 57, 1, 64], Operations: [] Exploring Operation: 64-21=43, Resulting Numbers: [57, 1, 43] Generated Node #0,0: 100:[57, 1, 43] Operation: 64-21=43 Exploring Operation: 21-1=20, Resulting Numbers: [57, 64, 20] Generated Node #0,1: 100:[57, 64, 20] Operation: 21-1=20 Exploring Operation: 64-57=7, Resulting Numbers: [21, 1, 7] Generated Node #0,2: 100:[21, 1, 7] Operation: 64-57=7 Moving to Node #0,2 Current State: 100:[21, 1, 7], Operations: ['64-57=7'] Exploring Operation: 21-1=20, Resulting Numbers: [7, 20] Generated Node #0,2,0: 100:[7, 20] Operation: 21-1=20 Exploring Operation: 21/7=3, Resulting Numbers: [1, 3] Generated Node #0,2,1: 100:[1, 3] Operation: 21/7=3 Exploring Operation: 7-1=6, Resulting Numbers: [21, 6] Generated Node #0,2,2: 100:[21, 6] Operation: 7-1=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[7, 20], Operations: ['64-57=7', '21-1=20'] Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,100 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,100 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,100 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 #0,2,1 Current State: 100:[1, 3], Operations: ['64-57=7', '21/7=3'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,100 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 #0,2,2 Current State: 100:[21, 6], Operations: ['64-57=7', '7-1=6'] Exploring Operation: 21+6=27, Resulting Numbers: [27] 27,100 unequal: No Solution Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,100 unequal: No Solution Exploring Operation: 21*6=126, Resulting Numbers: [126] 126,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 100:[57, 1, 43], Operations: ['64-21=43'] Exploring Operation: 57-1=56, Resulting Numbers: [43, 56] Generated Node #0,0,0: 100:[43, 56] Operation: 57-1=56 Exploring Operation: 57+43=100, Resulting Numbers: [1, 100] Generated Node #0,0,1: 100:[1, 100] Operation: 57+43=100 Exploring Operation: 57-43=14, Resulting Numbers: [1, 14] Generated Node #0,0,2: 100:[1, 14] Operation: 57-43=14 Moving to Node #0,1 Current State: 100:[57, 64, 20], Operations: ['21-1=20'] Exploring Operation: 57+64=121, Resulting Numbers: [20, 121] Generated Node #0,1,0: 100:[20, 121] Operation: 57+64=121 Exploring Operation: 64-57=7, Resulting Numbers: [20, 7] Generated Node #0,1,1: 100:[20, 7] Operation: 64-57=7 Exploring Operation: 64-20=44, Resulting Numbers: [57, 44] Generated Node #0,1,2: 100:[57, 44] Operation: 64-20=44 Moving to Node #0,0,1 Current State: 100:[1, 100], Operations: ['64-21=43', '57+43=100'] Exploring Operation: 1+100=101, Resulting Numbers: [101] 101,100 unequal: No Solution Exploring Operation: 1*100=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[21, 57, 1, 64], Operations: [] Exploring Operation: 64-21=43, Resulting Numbers: [57, 1, 43] Generated Node #0,0: 100:[57, 1, 43] Operation: 64-21=43 Moving to Node #0,0 Current State: 100:[57, 1, 43], Operations: ['64-21=43'] Exploring Operation: 57+43=100, Resulting Numbers: [1, 100] Generated Node #0,0,1: 100:[1, 100] Operation: 57+43=100 Moving to Node #0,0,1 Current State: 100:[1, 100], Operations: ['64-21=43', '57+43=100'] Exploring Operation: 1*100=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 62, 86, 16, 36 ]
54
[ "86-62=24", "36*24=864", "864/16=54" ]
Current State: 54:[62, 86, 16, 36], Operations: [] Exploring Operation: 86-62=24, Resulting Numbers: [16, 36, 24] Generated Node #2: [16, 36, 24] from Operation: 86-62=24 Current State: 54:[16, 36, 24], Operations: ['86-62=24'] Exploring Operation: 36*24=864, Resulting Numbers: [16, 864] Generated Node #3: [16, 864] from Operation: 36*24=864 Current State: 54:[16, 864], Operations: ['86-62=24', '36*24=864'] Exploring Operation: 864/16=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[62, 86, 16, 36], Operations: [] Exploring Operation: 86-36=50, Resulting Numbers: [62, 16, 50] Generated Node #0,0: 54:[62, 16, 50] Operation: 86-36=50 Exploring Operation: 62-36=26, Resulting Numbers: [86, 16, 26] Generated Node #0,1: 54:[86, 16, 26] Operation: 62-36=26 Exploring Operation: 16+36=52, Resulting Numbers: [62, 86, 52] Generated Node #0,2: 54:[62, 86, 52] Operation: 16+36=52 Exploring Operation: 86-16=70, Resulting Numbers: [62, 36, 70] Generated Node #0,3: 54:[62, 36, 70] Operation: 86-16=70 Exploring Operation: 86-62=24, Resulting Numbers: [16, 36, 24] Generated Node #0,4: 54:[16, 36, 24] Operation: 86-62=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[62, 16, 50], Operations: ['86-36=50'] Exploring Operation: 62+16=78, Resulting Numbers: [50, 78] Generated Node #0,0,0: 54:[50, 78] Operation: 62+16=78 Exploring Operation: 62-16=46, Resulting Numbers: [50, 46] Generated Node #0,0,1: 54:[50, 46] Operation: 62-16=46 Exploring Operation: 62-50=12, Resulting Numbers: [16, 12] Generated Node #0,0,2: 54:[16, 12] Operation: 62-50=12 Exploring Operation: 50-16=34, Resulting Numbers: [62, 34] Generated Node #0,0,3: 54:[62, 34] Operation: 50-16=34 Exploring Operation: 16+50=66, Resulting Numbers: [62, 66] Generated Node #0,0,4: 54:[62, 66] Operation: 16+50=66 Moving to Node #0,0,2 Current State: 54:[16, 12], Operations: ['86-36=50', '62-50=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,54 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[50, 46], Operations: ['86-36=50', '62-16=46'] Exploring Operation: 50*46=2300, Resulting Numbers: [2300] 2300,54 unequal: No Solution Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 50-46=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[62, 34], Operations: ['86-36=50', '50-16=34'] Exploring Operation: 62+34=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 62-34=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 62*34=2108, Resulting Numbers: [2108] 2108,54 unequal: No Solution Moving to Node #0,0,4 Current State: 54:[62, 66], Operations: ['86-36=50', '16+50=66'] Exploring Operation: 66-62=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 62+66=128, Resulting Numbers: [128] 128,54 unequal: No Solution Exploring Operation: 62*66=4092, Resulting Numbers: [4092] 4092,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[50, 78], Operations: ['86-36=50', '62+16=78'] Exploring Operation: 78-50=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 50*78=3900, Resulting Numbers: [3900] 3900,54 unequal: No Solution Exploring Operation: 50+78=128, Resulting Numbers: [128] 128,54 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 #0,4 Current State: 54:[16, 36, 24], Operations: ['86-62=24'] Exploring Operation: 36+24=60, Resulting Numbers: [16, 60] Generated Node #0,4,0: 54:[16, 60] Operation: 36+24=60 Exploring Operation: 36-16=20, Resulting Numbers: [24, 20] Generated Node #0,4,1: 54:[24, 20] Operation: 36-16=20 Exploring Operation: 36-24=12, Resulting Numbers: [16, 12] Generated Node #0,4,2: 54:[16, 12] Operation: 36-24=12 Exploring Operation: 16+36=52, Resulting Numbers: [24, 52] Generated Node #0,4,3: 54:[24, 52] Operation: 16+36=52 Exploring Operation: 24-16=8, Resulting Numbers: [36, 8] Generated Node #0,4,4: 54:[36, 8] Operation: 24-16=8 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 54:[24, 20], Operations: ['86-62=24', '36-16=20'] Exploring Operation: 24*20=480, Resulting Numbers: [480] 480,54 unequal: No Solution Exploring Operation: 24+20=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,54 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 #0,4,2 Current State: 54:[16, 12], Operations: ['86-62=24', '36-24=12'] Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,54 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 #0,4,3 Current State: 54:[24, 52], Operations: ['86-62=24', '16+36=52'] Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 24*52=1248, Resulting Numbers: [1248] 1248,54 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 #0,4,0 Current State: 54:[16, 60], Operations: ['86-62=24', '36+24=60'] Exploring Operation: 16*60=960, Resulting Numbers: [960] 960,54 unequal: No Solution Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 16+60=76, Resulting Numbers: [76] 76,54 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 #0,4,4 Current State: 54:[36, 8], Operations: ['86-62=24', '24-16=8'] Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,54 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 #0,3 Current State: 54:[62, 36, 70], Operations: ['86-16=70'] Exploring Operation: 62+36=98, Resulting Numbers: [70, 98] Generated Node #0,3,0: 54:[70, 98] Operation: 62+36=98 Exploring Operation: 62-36=26, Resulting Numbers: [70, 26] Generated Node #0,3,1: 54:[70, 26] Operation: 62-36=26 Exploring Operation: 70-36=34, Resulting Numbers: [62, 34] Generated Node #0,3,2: 54:[62, 34] Operation: 70-36=34 Exploring Operation: 70-62=8, Resulting Numbers: [36, 8] Generated Node #0,3,3: 54:[36, 8] Operation: 70-62=8 Exploring Operation: 36+70=106, Resulting Numbers: [62, 106] Generated Node #0,3,4: 54:[62, 106] Operation: 36+70=106 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 54:[36, 8], Operations: ['86-16=70', '70-62=8'] Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,54 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 #0,3,2 Current State: 54:[62, 34], Operations: ['86-16=70', '70-36=34'] Exploring Operation: 62+34=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 62*34=2108, Resulting Numbers: [2108] 2108,54 unequal: No Solution Exploring Operation: 62-34=28, Resulting Numbers: [28] 28,54 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 #0,3,1 Current State: 54:[70, 26], Operations: ['86-16=70', '62-36=26'] Exploring Operation: 70*26=1820, Resulting Numbers: [1820] 1820,54 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 70+26=96, Resulting Numbers: [96] 96,54 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 #0,3,0 Current State: 54:[70, 98], Operations: ['86-16=70', '62+36=98'] Exploring Operation: 98-70=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 70+98=168, Resulting Numbers: [168] 168,54 unequal: No Solution Exploring Operation: 70*98=6860, Resulting Numbers: [6860] 6860,54 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 #0,3,4 Current State: 54:[62, 106], Operations: ['86-16=70', '36+70=106'] Exploring Operation: 62+106=168, Resulting Numbers: [168] 168,54 unequal: No Solution Exploring Operation: 62*106=6572, Resulting Numbers: [6572] 6572,54 unequal: No Solution Exploring Operation: 106-62=44, Resulting Numbers: [44] 44,54 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:[86, 16, 26], Operations: ['62-36=26'] Exploring Operation: 16+26=42, Resulting Numbers: [86, 42] Generated Node #0,1,0: 54:[86, 42] Operation: 16+26=42 Exploring Operation: 26-16=10, Resulting Numbers: [86, 10] Generated Node #0,1,1: 54:[86, 10] Operation: 26-16=10 Exploring Operation: 86-26=60, Resulting Numbers: [16, 60] Generated Node #0,1,2: 54:[16, 60] Operation: 86-26=60 Exploring Operation: 86+16=102, Resulting Numbers: [26, 102] Generated Node #0,1,3: 54:[26, 102] Operation: 86+16=102 Exploring Operation: 86-16=70, Resulting Numbers: [26, 70] Generated Node #0,1,4: 54:[26, 70] Operation: 86-16=70 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 54:[16, 60], Operations: ['62-36=26', '86-26=60'] Exploring Operation: 16+60=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 16*60=960, Resulting Numbers: [960] 960,54 unequal: No Solution Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,54 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 #0,1,4 Current State: 54:[26, 70], Operations: ['62-36=26', '86-16=70'] Exploring Operation: 26*70=1820, Resulting Numbers: [1820] 1820,54 unequal: No Solution Exploring Operation: 26+70=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 70-26=44, Resulting Numbers: [44] 44,54 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 #0,1,1 Current State: 54:[86, 10], Operations: ['62-36=26', '26-16=10'] Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,54 unequal: No Solution Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,54 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:[86, 42], Operations: ['62-36=26', '16+26=42'] Exploring Operation: 86*42=3612, Resulting Numbers: [3612] 3612,54 unequal: No Solution Exploring Operation: 86-42=44, Resulting Numbers: [44] 44,54 unequal: No Solution Exploring Operation: 86+42=128, Resulting Numbers: [128] 128,54 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 #0,1,3 Current State: 54:[26, 102], Operations: ['62-36=26', '86+16=102'] Exploring Operation: 26+102=128, Resulting Numbers: [128] 128,54 unequal: No Solution Exploring Operation: 102-26=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 26*102=2652, Resulting Numbers: [2652] 2652,54 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 #0,2 Current State: 54:[62, 86, 52], Operations: ['16+36=52'] Exploring Operation: 62+52=114, Resulting Numbers: [86, 114] Generated Node #0,2,0: 54:[86, 114] Operation: 62+52=114 Exploring Operation: 86-52=34, Resulting Numbers: [62, 34] Generated Node #0,2,1: 54:[62, 34] Operation: 86-52=34 Exploring Operation: 86-62=24, Resulting Numbers: [52, 24] Generated Node #0,2,2: 54:[52, 24] Operation: 86-62=24 Exploring Operation: 62-52=10, Resulting Numbers: [86, 10] Generated Node #0,2,3: 54:[86, 10] Operation: 62-52=10 Exploring Operation: 86+52=138, Resulting Numbers: [62, 138] Generated Node #0,2,4: 54:[62, 138] Operation: 86+52=138 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 54:[52, 24], Operations: ['16+36=52', '86-62=24'] Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,54 unequal: No Solution Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,54 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 #0,2,1 Current State: 54:[62, 34], Operations: ['16+36=52', '86-52=34'] Exploring Operation: 62-34=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 62+34=96, Resulting Numbers: [96] 96,54 unequal: No Solution Exploring Operation: 62*34=2108, Resulting Numbers: [2108] 2108,54 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 #0,2,3 Current State: 54:[86, 10], Operations: ['16+36=52', '62-52=10'] Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,54 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,54 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 #0,2,0 Current State: 54:[86, 114], Operations: ['16+36=52', '62+52=114'] Exploring Operation: 86*114=9804, Resulting Numbers: [9804] 9804,54 unequal: No Solution Exploring Operation: 86+114=200, Resulting Numbers: [200] 200,54 unequal: No Solution Exploring Operation: 114-86=28, Resulting Numbers: [28] 28,54 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 #0,2,4 Current State: 54:[62, 138], Operations: ['16+36=52', '86+52=138'] Exploring Operation: 62*138=8556, Resulting Numbers: [8556] 8556,54 unequal: No Solution Exploring Operation: 62+138=200, Resulting Numbers: [200] 200,54 unequal: No Solution Exploring Operation: 138-62=76, Resulting Numbers: [76] 76,54 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_5
mult_heuristic
[ 61, 51, 56, 25 ]
50
[ "61+51=112", "112/56=2", "25*2=50" ]
Current State: 50:[61, 51, 56, 25], Operations: [] Exploring Operation: 61+51=112, Resulting Numbers: [56, 25, 112] Generated Node #2: [56, 25, 112] from Operation: 61+51=112 Current State: 50:[56, 25, 112], Operations: ['61+51=112'] Exploring Operation: 112/56=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 112/56=2 Current State: 50:[25, 2], Operations: ['61+51=112', '112/56=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[61, 51, 56, 25], Operations: [] Exploring Operation: 51-25=26, Resulting Numbers: [61, 56, 26] Generated Node #0,0: 50:[61, 56, 26] Operation: 51-25=26 Exploring Operation: 61-51=10, Resulting Numbers: [56, 25, 10] Generated Node #0,1: 50:[56, 25, 10] Operation: 61-51=10 Exploring Operation: 61-25=36, Resulting Numbers: [51, 56, 36] Generated Node #0,2: 50:[51, 56, 36] Operation: 61-25=36 Exploring Operation: 56-51=5, Resulting Numbers: [61, 25, 5] Generated Node #0,3: 50:[61, 25, 5] Operation: 56-51=5 Exploring Operation: 61-56=5, Resulting Numbers: [51, 25, 5] Generated Node #0,4: 50:[51, 25, 5] Operation: 61-56=5 Moving to Node #0,4 Current State: 50:[51, 25, 5], Operations: ['61-56=5'] Exploring Operation: 25+5=30, Resulting Numbers: [51, 30] Generated Node #0,4,0: 50:[51, 30] Operation: 25+5=30 Exploring Operation: 51+5=56, Resulting Numbers: [25, 56] Generated Node #0,4,1: 50:[25, 56] Operation: 51+5=56 Exploring Operation: 51-5=46, Resulting Numbers: [25, 46] Generated Node #0,4,2: 50:[25, 46] Operation: 51-5=46 Exploring Operation: 25/5=5, Resulting Numbers: [51, 5] Generated Node #0,4,3: 50:[51, 5] Operation: 25/5=5 Exploring Operation: 51-25=26, Resulting Numbers: [5, 26] Generated Node #0,4,4: 50:[5, 26] Operation: 51-25=26 Moving to Node #0,1 Current State: 50:[56, 25, 10], Operations: ['61-51=10'] Exploring Operation: 25+10=35, Resulting Numbers: [56, 35] Generated Node #0,1,0: 50:[56, 35] Operation: 25+10=35 Exploring Operation: 25-10=15, Resulting Numbers: [56, 15] Generated Node #0,1,1: 50:[56, 15] Operation: 25-10=15 Exploring Operation: 56-10=46, Resulting Numbers: [25, 46] Generated Node #0,1,2: 50:[25, 46] Operation: 56-10=46 Exploring Operation: 56-25=31, Resulting Numbers: [10, 31] Generated Node #0,1,3: 50:[10, 31] Operation: 56-25=31 Exploring Operation: 56+10=66, Resulting Numbers: [25, 66] Generated Node #0,1,4: 50:[25, 66] Operation: 56+10=66 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 50:[25, 46], Operations: ['61-51=10', '56-10=46'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,50 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 50:[10, 31], Operations: ['61-51=10', '56-25=31'] Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[56, 15], Operations: ['61-51=10', '25-10=15'] Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,50 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 50:[56, 35], Operations: ['61-51=10', '25+10=35'] Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,50 unequal: No Solution Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 50:[25, 66], Operations: ['61-51=10', '56+10=66'] Exploring Operation: 25*66=1650, Resulting Numbers: [1650] 1650,50 unequal: No Solution Exploring Operation: 25+66=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 50:[61, 25, 5], Operations: ['56-51=5'] Exploring Operation: 61-25=36, Resulting Numbers: [5, 36] Generated Node #0,3,0: 50:[5, 36] Operation: 61-25=36 Exploring Operation: 61-5=56, Resulting Numbers: [25, 56] Generated Node #0,3,1: 50:[25, 56] Operation: 61-5=56 Exploring Operation: 25+5=30, Resulting Numbers: [61, 30] Generated Node #0,3,2: 50:[61, 30] Operation: 25+5=30 Exploring Operation: 25/5=5, Resulting Numbers: [61, 5] Generated Node #0,3,3: 50:[61, 5] Operation: 25/5=5 Exploring Operation: 61+5=66, Resulting Numbers: [25, 66] Generated Node #0,3,4: 50:[25, 66] Operation: 61+5=66 Moving to Node #0,0 Current State: 50:[61, 56, 26], Operations: ['51-25=26'] Exploring Operation: 56-26=30, Resulting Numbers: [61, 30] Generated Node #0,0,0: 50:[61, 30] Operation: 56-26=30 Exploring Operation: 61+26=87, Resulting Numbers: [56, 87] Generated Node #0,0,1: 50:[56, 87] Operation: 61+26=87 Exploring Operation: 61-56=5, Resulting Numbers: [26, 5] Generated Node #0,0,2: 50:[26, 5] Operation: 61-56=5 Exploring Operation: 61-26=35, Resulting Numbers: [56, 35] Generated Node #0,0,3: 50:[56, 35] Operation: 61-26=35 Exploring Operation: 56+26=82, Resulting Numbers: [61, 82] Generated Node #0,0,4: 50:[61, 82] Operation: 56+26=82 Moving to Node #0,2 Current State: 50:[51, 56, 36], Operations: ['61-25=36'] Exploring Operation: 56-36=20, Resulting Numbers: [51, 20] Generated Node #0,2,0: 50:[51, 20] Operation: 56-36=20 Exploring Operation: 56-51=5, Resulting Numbers: [36, 5] Generated Node #0,2,1: 50:[36, 5] Operation: 56-51=5 Exploring Operation: 51-36=15, Resulting Numbers: [56, 15] Generated Node #0,2,2: 50:[56, 15] Operation: 51-36=15 Exploring Operation: 56+36=92, Resulting Numbers: [51, 92] Generated Node #0,2,3: 50:[51, 92] Operation: 56+36=92 Exploring Operation: 51+36=87, Resulting Numbers: [56, 87] Generated Node #0,2,4: 50:[56, 87] Operation: 51+36=87 Moving to Node #0,4,3 Current State: 50:[51, 5], Operations: ['61-56=5', '25/5=5'] Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,50 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,50 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,50 unequal: No Solution Moving to Node #0,4,4 Current State: 50:[5, 26], Operations: ['61-56=5', '51-25=26'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[26, 5], Operations: ['51-25=26', '61-56=5'] Exploring Operation: 26*5=130, Resulting Numbers: [130] 130,50 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,50 unequal: No Solution Moving to Node #0,4,2 Current State: 50:[25, 46], Operations: ['61-56=5', '51-5=46'] Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,50 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,50 unequal: No Solution Moving to Node #0,3,1 Current State: 50:[25, 56], Operations: ['56-51=5', '61-5=56'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,50 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,50 unequal: No Solution Moving to Node #0,4,1 Current State: 50:[25, 56], Operations: ['61-56=5', '51+5=56'] Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,50 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,50 unequal: No Solution Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,4,0 Current State: 50:[51, 30], Operations: ['61-56=5', '25+5=30'] Exploring Operation: 51*30=1530, Resulting Numbers: [1530] 1530,50 unequal: No Solution Exploring Operation: 51+30=81, Resulting Numbers: [81] 81,50 unequal: No Solution Exploring Operation: 51-30=21, Resulting Numbers: [21] 21,50 unequal: No Solution Moving to Node #0,2,0 Current State: 50:[51, 20], Operations: ['61-25=36', '56-36=20'] Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,50 unequal: No Solution Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,3,0 Current State: 50:[5, 36], Operations: ['56-51=5', '61-25=36'] Exploring Operation: 5*36=180, Resulting Numbers: [180] 180,50 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 5+36=41, Resulting Numbers: [41] 41,50 unequal: No Solution Moving to Node #0,2,1 Current State: 50:[36, 5], Operations: ['61-25=36', '56-51=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,50 unequal: No Solution Moving to Node #0,2,2 Current State: 50:[56, 15], Operations: ['61-25=36', '51-36=15'] Exploring Operation: 56*15=840, Resulting Numbers: [840] 840,50 unequal: No Solution Exploring Operation: 56+15=71, Resulting Numbers: [71] 71,50 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,50 unequal: No Solution Moving to Node #0,3,3 Current State: 50:[61, 5], Operations: ['56-51=5', '25/5=5'] Exploring Operation: 61+5=66, Resulting Numbers: [66] 66,50 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,50 unequal: No Solution Exploring Operation: 61*5=305, Resulting Numbers: [305] 305,50 unequal: No Solution Moving to Node #0,3,2 Current State: 50:[61, 30], Operations: ['56-51=5', '25+5=30'] Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 61*30=1830, Resulting Numbers: [1830] 1830,50 unequal: No Solution Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[61, 30], Operations: ['51-25=26', '56-26=30'] Exploring Operation: 61*30=1830, Resulting Numbers: [1830] 1830,50 unequal: No Solution Exploring Operation: 61+30=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 61-30=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,0,3 Current State: 50:[56, 35], Operations: ['51-25=26', '61-26=35'] Exploring Operation: 56+35=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 56*35=1960, Resulting Numbers: [1960] 1960,50 unequal: No Solution Exploring Operation: 56-35=21, Resulting Numbers: [21] 21,50 unequal: No Solution Moving to Node #0,3,4 Current State: 50:[25, 66], Operations: ['56-51=5', '61+5=66'] Exploring Operation: 25+66=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 25*66=1650, Resulting Numbers: [1650] 1650,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[56, 87], Operations: ['51-25=26', '61+26=87'] Exploring Operation: 56+87=143, Resulting Numbers: [143] 143,50 unequal: No Solution Exploring Operation: 56*87=4872, Resulting Numbers: [4872] 4872,50 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,2,4 Current State: 50:[56, 87], Operations: ['61-25=36', '51+36=87'] Exploring Operation: 56+87=143, Resulting Numbers: [143] 143,50 unequal: No Solution Exploring Operation: 56*87=4872, Resulting Numbers: [4872] 4872,50 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,50 unequal: No Solution Moving to Node #0,2,3 Current State: 50:[51, 92], Operations: ['61-25=36', '56+36=92'] Exploring Operation: 51*92=4692, Resulting Numbers: [4692] 4692,50 unequal: No Solution Exploring Operation: 92-51=41, Resulting Numbers: [41] 41,50 unequal: No Solution Exploring Operation: 51+92=143, Resulting Numbers: [143] 143,50 unequal: No Solution Moving to Node #0,0,4 Current State: 50:[61, 82], Operations: ['51-25=26', '56+26=82'] Exploring Operation: 61+82=143, Resulting Numbers: [143] 143,50 unequal: No Solution Exploring Operation: 82-61=21, Resulting Numbers: [21] 21,50 unequal: No Solution Exploring Operation: 61*82=5002, Resulting Numbers: [5002] 5002,50 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 52, 80, 91, 79 ]
39
[ "91-52=39", "80-79=1", "39*1=39" ]
Current State: 39:[52, 80, 91, 79], Operations: [] Exploring Operation: 91-52=39, Resulting Numbers: [80, 79, 39] Generated Node #2: [80, 79, 39] from Operation: 91-52=39 Current State: 39:[80, 79, 39], Operations: ['91-52=39'] Exploring Operation: 80-79=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 80-79=1 Current State: 39:[39, 1], Operations: ['91-52=39', '80-79=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[52, 80, 91, 79], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [52, 79, 11] Generated Node #0,0: 39:[52, 79, 11] Operation: 91-80=11 Moving to Node #0,0 Current State: 39:[52, 79, 11], Operations: ['91-80=11'] Exploring Operation: 79-52=27, Resulting Numbers: [11, 27] Generated Node #0,0,0: 39:[11, 27] Operation: 79-52=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[11, 27], Operations: ['91-80=11', '79-52=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,39 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
[ 76, 51, 8, 63 ]
20
[ "63-51=12", "8*12=96", "96-76=20" ]
Current State: 20:[76, 51, 8, 63], Operations: [] Exploring Operation: 63-51=12, Resulting Numbers: [76, 8, 12] Generated Node #2: [76, 8, 12] from Operation: 63-51=12 Current State: 20:[76, 8, 12], Operations: ['63-51=12'] Exploring Operation: 8*12=96, Resulting Numbers: [76, 96] Generated Node #3: [76, 96] from Operation: 8*12=96 Current State: 20:[76, 96], Operations: ['63-51=12', '8*12=96'] Exploring Operation: 96-76=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[76, 51, 8, 63], Operations: [] Exploring Operation: 76-63=13, Resulting Numbers: [51, 8, 13] Generated Node #0,0: 20:[51, 8, 13] Operation: 76-63=13 Exploring Operation: 76-8=68, Resulting Numbers: [51, 63, 68] Generated Node #0,1: 20:[51, 63, 68] Operation: 76-8=68 Exploring Operation: 63-51=12, Resulting Numbers: [76, 8, 12] Generated Node #0,2: 20:[76, 8, 12] Operation: 63-51=12 Exploring Operation: 76-51=25, Resulting Numbers: [8, 63, 25] Generated Node #0,3: 20:[8, 63, 25] Operation: 76-51=25 Moving to Node #0,0 Current State: 20:[51, 8, 13], Operations: ['76-63=13'] Exploring Operation: 51-13=38, Resulting Numbers: [8, 38] Generated Node #0,0,0: 20:[8, 38] Operation: 51-13=38 Exploring Operation: 13-8=5, Resulting Numbers: [51, 5] Generated Node #0,0,1: 20:[51, 5] Operation: 13-8=5 Exploring Operation: 8+13=21, Resulting Numbers: [51, 21] Generated Node #0,0,2: 20:[51, 21] Operation: 8+13=21 Exploring Operation: 51-8=43, Resulting Numbers: [13, 43] Generated Node #0,0,3: 20:[13, 43] Operation: 51-8=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[8, 38], Operations: ['76-63=13', '51-13=38'] Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,20 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 20:[13, 43], Operations: ['76-63=13', '51-8=43'] Exploring Operation: 13*43=559, Resulting Numbers: [559] 559,20 unequal: No Solution Exploring Operation: 43-13=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 13+43=56, Resulting Numbers: [56] 56,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 20:[51, 5], Operations: ['76-63=13', '13-8=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 20:[51, 21], Operations: ['76-63=13', '8+13=21'] Exploring Operation: 51*21=1071, Resulting Numbers: [1071] 1071,20 unequal: No Solution Exploring Operation: 51+21=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 20:[8, 63, 25], Operations: ['76-51=25'] Exploring Operation: 63-25=38, Resulting Numbers: [8, 38] Generated Node #0,3,0: 20:[8, 38] Operation: 63-25=38 Exploring Operation: 8+63=71, Resulting Numbers: [25, 71] Generated Node #0,3,1: 20:[25, 71] Operation: 8+63=71 Exploring Operation: 25-8=17, Resulting Numbers: [63, 17] Generated Node #0,3,2: 20:[63, 17] Operation: 25-8=17 Exploring Operation: 63-8=55, Resulting Numbers: [25, 55] Generated Node #0,3,3: 20:[25, 55] Operation: 63-8=55 Moving to Node #0,2 Current State: 20:[76, 8, 12], Operations: ['63-51=12'] Exploring Operation: 8+12=20, Resulting Numbers: [76, 20] Generated Node #0,2,0: 20:[76, 20] Operation: 8+12=20 Exploring Operation: 76-8=68, Resulting Numbers: [12, 68] Generated Node #0,2,1: 20:[12, 68] Operation: 76-8=68 Exploring Operation: 12-8=4, Resulting Numbers: [76, 4] Generated Node #0,2,2: 20:[76, 4] Operation: 12-8=4 Exploring Operation: 76-12=64, Resulting Numbers: [8, 64] Generated Node #0,2,3: 20:[8, 64] Operation: 76-12=64 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 20:[8, 64], Operations: ['63-51=12', '76-12=64'] Exploring Operation: 8*64=512, Resulting Numbers: [512] 512,20 unequal: No Solution Exploring Operation: 64/8=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 8+64=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 20:[12, 68], Operations: ['63-51=12', '76-8=68'] Exploring Operation: 12+68=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 12*68=816, Resulting Numbers: [816] 816,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[76, 20], Operations: ['63-51=12', '8+12=20'] Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,20 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 20:[76, 4], Operations: ['63-51=12', '12-8=4'] Exploring Operation: 76*4=304, Resulting Numbers: [304] 304,20 unequal: No Solution Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,20 unequal: No Solution Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,20 unequal: No Solution Exploring Operation: 76+4=80, Resulting Numbers: [80] 80,20 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: 20:[51, 63, 68], Operations: ['76-8=68'] Exploring Operation: 51+63=114, Resulting Numbers: [68, 114] Generated Node #0,1,0: 20:[68, 114] Operation: 51+63=114 Exploring Operation: 68-63=5, Resulting Numbers: [51, 5] Generated Node #0,1,1: 20:[51, 5] Operation: 68-63=5 Exploring Operation: 68-51=17, Resulting Numbers: [63, 17] Generated Node #0,1,2: 20:[63, 17] Operation: 68-51=17 Exploring Operation: 63-51=12, Resulting Numbers: [68, 12] Generated Node #0,1,3: 20:[68, 12] Operation: 63-51=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[51, 5], Operations: ['76-8=68', '68-63=5'] Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 51*5=255, Resulting Numbers: [255] 255,20 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 #0,1,2 Current State: 20:[63, 17], Operations: ['76-8=68', '68-51=17'] Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 63+17=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 63*17=1071, Resulting Numbers: [1071] 1071,20 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 #0,1,3 Current State: 20:[68, 12], Operations: ['76-8=68', '63-51=12'] Exploring Operation: 68-12=56, Resulting Numbers: [56] 56,20 unequal: No Solution Exploring Operation: 68+12=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 68*12=816, Resulting Numbers: [816] 816,20 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 #0,1,0 Current State: 20:[68, 114], Operations: ['76-8=68', '51+63=114'] Exploring Operation: 68+114=182, Resulting Numbers: [182] 182,20 unequal: No Solution Exploring Operation: 68*114=7752, Resulting Numbers: [7752] 7752,20 unequal: No Solution Exploring Operation: 114-68=46, Resulting Numbers: [46] 46,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 20:[8, 38], Operations: ['76-51=25', '63-25=38'] Exploring Operation: 8*38=304, Resulting Numbers: [304] 304,20 unequal: No Solution Exploring Operation: 8+38=46, Resulting Numbers: [46] 46,20 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,20 unequal: No Solution Moving to Node #0,3,3 Current State: 20:[25, 55], Operations: ['76-51=25', '63-8=55'] Exploring Operation: 25*55=1375, Resulting Numbers: [1375] 1375,20 unequal: No Solution Exploring Operation: 55-25=30, Resulting Numbers: [30] 30,20 unequal: No Solution Exploring Operation: 25+55=80, Resulting Numbers: [80] 80,20 unequal: No Solution Moving to Node #0,3,2 Current State: 20:[63, 17], Operations: ['76-51=25', '25-8=17'] Exploring Operation: 63+17=80, Resulting Numbers: [80] 80,20 unequal: No Solution Exploring Operation: 63*17=1071, Resulting Numbers: [1071] 1071,20 unequal: No Solution Exploring Operation: 63-17=46, Resulting Numbers: [46] 46,20 unequal: No Solution Moving to Node #0,3,1 Current State: 20:[25, 71], Operations: ['76-51=25', '8+63=71'] Exploring Operation: 25+71=96, Resulting Numbers: [96] 96,20 unequal: No Solution Exploring Operation: 25*71=1775, Resulting Numbers: [1775] 1775,20 unequal: No Solution Exploring Operation: 71-25=46, Resulting Numbers: [46] 46,20 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 23, 52, 49, 27 ]
52
[ "49-23=26", "27-26=1", "52*1=52" ]
Current State: 52:[23, 52, 49, 27], Operations: [] Exploring Operation: 49-23=26, Resulting Numbers: [52, 27, 26] Generated Node #2: [52, 27, 26] from Operation: 49-23=26 Current State: 52:[52, 27, 26], Operations: ['49-23=26'] Exploring Operation: 27-26=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 27-26=1 Current State: 52:[52, 1], Operations: ['49-23=26', '27-26=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[23, 52, 49, 27], Operations: [] Exploring Operation: 49-23=26, Resulting Numbers: [52, 27, 26] Generated Node #0,0: 52:[52, 27, 26] Operation: 49-23=26 Exploring Operation: 27-23=4, Resulting Numbers: [52, 49, 4] Generated Node #0,1: 52:[52, 49, 4] Operation: 27-23=4 Exploring Operation: 52-23=29, Resulting Numbers: [49, 27, 29] Generated Node #0,2: 52:[49, 27, 29] Operation: 52-23=29 Exploring Operation: 52-49=3, Resulting Numbers: [23, 27, 3] Generated Node #0,3: 52:[23, 27, 3] Operation: 52-49=3 Exploring Operation: 23+27=50, Resulting Numbers: [52, 49, 50] Generated Node #0,4: 52:[52, 49, 50] Operation: 23+27=50 Moving to Node #0,0 Current State: 52:[52, 27, 26], Operations: ['49-23=26'] Exploring Operation: 52-26=26, Resulting Numbers: [27, 26] Generated Node #0,0,0: 52:[27, 26] Operation: 52-26=26 Exploring Operation: 27+26=53, Resulting Numbers: [52, 53] Generated Node #0,0,1: 52:[52, 53] Operation: 27+26=53 Exploring Operation: 52-27=25, Resulting Numbers: [26, 25] Generated Node #0,0,2: 52:[26, 25] Operation: 52-27=25 Exploring Operation: 52/26=2, Resulting Numbers: [27, 2] Generated Node #0,0,3: 52:[27, 2] Operation: 52/26=2 Exploring Operation: 27-26=1, Resulting Numbers: [52, 1] Generated Node #0,0,4: 52:[52, 1] Operation: 27-26=1 Moving to Node #0,1 Current State: 52:[52, 49, 4], Operations: ['27-23=4'] Exploring Operation: 49+4=53, Resulting Numbers: [52, 53] Generated Node #0,1,0: 52:[52, 53] Operation: 49+4=53 Exploring Operation: 52/4=13, Resulting Numbers: [49, 13] Generated Node #0,1,1: 52:[49, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [49, 48] Generated Node #0,1,2: 52:[49, 48] Operation: 52-4=48 Exploring Operation: 52+4=56, Resulting Numbers: [49, 56] Generated Node #0,1,3: 52:[49, 56] Operation: 52+4=56 Exploring Operation: 52-49=3, Resulting Numbers: [4, 3] Generated Node #0,1,4: 52:[4, 3] Operation: 52-49=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 52:[52, 53], Operations: ['27-23=4', '49+4=53'] Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,52 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 52:[4, 3], Operations: ['27-23=4', '52-49=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 52:[49, 13], Operations: ['27-23=4', '52/4=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,52 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 52:[49, 48], Operations: ['27-23=4', '52-4=48'] Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,52 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 52:[49, 56], Operations: ['27-23=4', '52+4=56'] Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,52 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,52 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,52 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: 52:[23, 27, 3], Operations: ['52-49=3'] Exploring Operation: 23+3=26, Resulting Numbers: [27, 26] Generated Node #0,3,0: 52:[27, 26] Operation: 23+3=26 Exploring Operation: 27-23=4, Resulting Numbers: [3, 4] Generated Node #0,3,1: 52:[3, 4] Operation: 27-23=4 Exploring Operation: 27-3=24, Resulting Numbers: [23, 24] Generated Node #0,3,2: 52:[23, 24] Operation: 27-3=24 Exploring Operation: 23-3=20, Resulting Numbers: [27, 20] Generated Node #0,3,3: 52:[27, 20] Operation: 23-3=20 Exploring Operation: 23+27=50, Resulting Numbers: [3, 50] Generated Node #0,3,4: 52:[3, 50] Operation: 23+27=50 Moving to Node #0,4 Current State: 52:[52, 49, 50], Operations: ['23+27=50'] Exploring Operation: 52-50=2, Resulting Numbers: [49, 2] Generated Node #0,4,0: 52:[49, 2] Operation: 52-50=2 Exploring Operation: 50-49=1, Resulting Numbers: [52, 1] Generated Node #0,4,1: 52:[52, 1] Operation: 50-49=1 Exploring Operation: 52+49=101, Resulting Numbers: [50, 101] Generated Node #0,4,2: 52:[50, 101] Operation: 52+49=101 Exploring Operation: 52-49=3, Resulting Numbers: [50, 3] Generated Node #0,4,3: 52:[50, 3] Operation: 52-49=3 Exploring Operation: 49+50=99, Resulting Numbers: [52, 99] Generated Node #0,4,4: 52:[52, 99] Operation: 49+50=99 Moving to Node #0,2 Current State: 52:[49, 27, 29], Operations: ['52-23=29'] Exploring Operation: 29-27=2, Resulting Numbers: [49, 2] Generated Node #0,2,0: 52:[49, 2] Operation: 29-27=2 Exploring Operation: 49-29=20, Resulting Numbers: [27, 20] Generated Node #0,2,1: 52:[27, 20] Operation: 49-29=20 Exploring Operation: 49-27=22, Resulting Numbers: [29, 22] Generated Node #0,2,2: 52:[29, 22] Operation: 49-27=22 Exploring Operation: 27+29=56, Resulting Numbers: [49, 56] Generated Node #0,2,3: 52:[49, 56] Operation: 27+29=56 Exploring Operation: 49+27=76, Resulting Numbers: [29, 76] Generated Node #0,2,4: 52:[29, 76] Operation: 49+27=76 Moving to Node #0,0,0 Current State: 52:[27, 26], Operations: ['49-23=26', '52-26=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,52 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[26, 25], Operations: ['49-23=26', '52-27=25'] Exploring Operation: 26*25=650, Resulting Numbers: [650] 650,52 unequal: No Solution Exploring Operation: 26+25=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[3, 4], Operations: ['52-49=3', '27-23=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,52 unequal: No Solution Moving to Node #0,3,0 Current State: 52:[27, 26], Operations: ['52-49=3', '23+3=26'] Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[52, 53], Operations: ['49-23=26', '27+26=53'] Exploring Operation: 52*53=2756, Resulting Numbers: [2756] 2756,52 unequal: No Solution Exploring Operation: 52+53=105, Resulting Numbers: [105] 105,52 unequal: No Solution Exploring Operation: 53-52=1, Resulting Numbers: [1] 1,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[52, 1], Operations: ['49-23=26', '27-26=1'] Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,52 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,52 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[23, 52, 49, 27], Operations: [] Exploring Operation: 49-23=26, Resulting Numbers: [52, 27, 26] Generated Node #0,0: 52:[52, 27, 26] Operation: 49-23=26 Moving to Node #0,0 Current State: 52:[52, 27, 26], Operations: ['49-23=26'] Exploring Operation: 27-26=1, Resulting Numbers: [52, 1] Generated Node #0,0,4: 52:[52, 1] Operation: 27-26=1 Moving to Node #0,0,4 Current State: 52:[52, 1], Operations: ['49-23=26', '27-26=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
0.94184
hs_5
sum_heuristic
[ 62, 86, 28, 57 ]
61
[ "86-62=24", "28+57=85", "85-24=61" ]
Current State: 61:[62, 86, 28, 57], Operations: [] Exploring Operation: 86-62=24, Resulting Numbers: [28, 57, 24] Generated Node #2: [28, 57, 24] from Operation: 86-62=24 Current State: 61:[28, 57, 24], Operations: ['86-62=24'] Exploring Operation: 28+57=85, Resulting Numbers: [24, 85] Generated Node #3: [24, 85] from Operation: 28+57=85 Current State: 61:[24, 85], Operations: ['86-62=24', '28+57=85'] Exploring Operation: 85-24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[62, 86, 28, 57], Operations: [] Exploring Operation: 86-28=58, Resulting Numbers: [62, 57, 58] Generated Node #0,0: 61:[62, 57, 58] Operation: 86-28=58 Exploring Operation: 62-28=34, Resulting Numbers: [86, 57, 34] Generated Node #0,1: 61:[86, 57, 34] Operation: 62-28=34 Exploring Operation: 28+57=85, Resulting Numbers: [62, 86, 85] Generated Node #0,2: 61:[62, 86, 85] Operation: 28+57=85 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[62, 57, 58], Operations: ['86-28=58'] Exploring Operation: 57+58=115, Resulting Numbers: [62, 115] Generated Node #0,0,0: 61:[62, 115] Operation: 57+58=115 Exploring Operation: 62+57=119, Resulting Numbers: [58, 119] Generated Node #0,0,1: 61:[58, 119] Operation: 62+57=119 Exploring Operation: 62-57=5, Resulting Numbers: [58, 5] Generated Node #0,0,2: 61:[58, 5] Operation: 62-57=5 Moving to Node #0,0,0 Current State: 61:[62, 115], Operations: ['86-28=58', '57+58=115'] Exploring Operation: 115-62=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 62*115=7130, Resulting Numbers: [7130] 7130,61 unequal: No Solution Exploring Operation: 62+115=177, Resulting Numbers: [177] 177,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[58, 5], Operations: ['86-28=58', '62-57=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,61 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,61 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[58, 119], Operations: ['86-28=58', '62+57=119'] Exploring Operation: 58*119=6902, Resulting Numbers: [6902] 6902,61 unequal: No Solution Exploring Operation: 58+119=177, Resulting Numbers: [177] 177,61 unequal: No Solution Exploring Operation: 119-58=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[62, 86, 28, 57], Operations: [] Exploring Operation: 86-28=58, Resulting Numbers: [62, 57, 58] Generated Node #0,0: 61:[62, 57, 58] Operation: 86-28=58 Moving to Node #0,0 Current State: 61:[62, 57, 58], Operations: ['86-28=58'] Exploring Operation: 62+57=119, Resulting Numbers: [58, 119] Generated Node #0,0,1: 61:[58, 119] Operation: 62+57=119 Moving to Node #0,0,1 Current State: 61:[58, 119], Operations: ['86-28=58', '62+57=119'] Exploring Operation: 119-58=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 87, 46, 93, 22 ]
86
[ "93-87=6", "22*6=132", "132-46=86" ]
Current State: 86:[87, 46, 93, 22], Operations: [] Exploring Operation: 93-87=6, Resulting Numbers: [46, 22, 6] Generated Node #2: [46, 22, 6] from Operation: 93-87=6 Current State: 86:[46, 22, 6], Operations: ['93-87=6'] Exploring Operation: 22*6=132, Resulting Numbers: [46, 132] Generated Node #3: [46, 132] from Operation: 22*6=132 Current State: 86:[46, 132], Operations: ['93-87=6', '22*6=132'] Exploring Operation: 132-46=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[87, 46, 93, 22], Operations: [] Exploring Operation: 93-46=47, Resulting Numbers: [87, 22, 47] Generated Node #0,0: 86:[87, 22, 47] Operation: 93-46=47 Exploring Operation: 46+22=68, Resulting Numbers: [87, 93, 68] Generated Node #0,1: 86:[87, 93, 68] Operation: 46+22=68 Exploring Operation: 93-87=6, Resulting Numbers: [46, 22, 6] Generated Node #0,2: 86:[46, 22, 6] Operation: 93-87=6 Exploring Operation: 93-22=71, Resulting Numbers: [87, 46, 71] Generated Node #0,3: 86:[87, 46, 71] Operation: 93-22=71 Moving to Node #0,3 Current State: 86:[87, 46, 71], Operations: ['93-22=71'] Exploring Operation: 46+71=117, Resulting Numbers: [87, 117] Generated Node #0,3,0: 86:[87, 117] Operation: 46+71=117 Exploring Operation: 87-71=16, Resulting Numbers: [46, 16] Generated Node #0,3,1: 86:[46, 16] Operation: 87-71=16 Exploring Operation: 71-46=25, Resulting Numbers: [87, 25] Generated Node #0,3,2: 86:[87, 25] Operation: 71-46=25 Exploring Operation: 87-46=41, Resulting Numbers: [71, 41] Generated Node #0,3,3: 86:[71, 41] Operation: 87-46=41 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 86:[46, 16], Operations: ['93-22=71', '87-71=16'] Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,86 unequal: No Solution Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,86 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 #0,3,3 Current State: 86:[71, 41], Operations: ['93-22=71', '87-46=41'] Exploring Operation: 71-41=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 71+41=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 71*41=2911, Resulting Numbers: [2911] 2911,86 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 #0,3,2 Current State: 86:[87, 25], Operations: ['93-22=71', '71-46=25'] Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 87*25=2175, Resulting Numbers: [2175] 2175,86 unequal: No Solution Exploring Operation: 87+25=112, Resulting Numbers: [112] 112,86 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 #0,3,0 Current State: 86:[87, 117], Operations: ['93-22=71', '46+71=117'] Exploring Operation: 117-87=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 87+117=204, Resulting Numbers: [204] 204,86 unequal: No Solution Exploring Operation: 87*117=10179, Resulting Numbers: [10179] 10179,86 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: 86:[87, 22, 47], Operations: ['93-46=47'] Exploring Operation: 87-47=40, Resulting Numbers: [22, 40] Generated Node #0,0,0: 86:[22, 40] Operation: 87-47=40 Exploring Operation: 47-22=25, Resulting Numbers: [87, 25] Generated Node #0,0,1: 86:[87, 25] Operation: 47-22=25 Exploring Operation: 87-22=65, Resulting Numbers: [47, 65] Generated Node #0,0,2: 86:[47, 65] Operation: 87-22=65 Exploring Operation: 22+47=69, Resulting Numbers: [87, 69] Generated Node #0,0,3: 86:[87, 69] Operation: 22+47=69 Moving to Node #0,1 Current State: 86:[87, 93, 68], Operations: ['46+22=68'] Exploring Operation: 93-87=6, Resulting Numbers: [68, 6] Generated Node #0,1,0: 86:[68, 6] Operation: 93-87=6 Exploring Operation: 87+68=155, Resulting Numbers: [93, 155] Generated Node #0,1,1: 86:[93, 155] Operation: 87+68=155 Exploring Operation: 87-68=19, Resulting Numbers: [93, 19] Generated Node #0,1,2: 86:[93, 19] Operation: 87-68=19 Exploring Operation: 93-68=25, Resulting Numbers: [87, 25] Generated Node #0,1,3: 86:[87, 25] Operation: 93-68=25 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[87, 25], Operations: ['46+22=68', '93-68=25'] Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 87+25=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 87*25=2175, Resulting Numbers: [2175] 2175,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[68, 6], Operations: ['46+22=68', '93-87=6'] Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,86 unequal: No Solution Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[93, 19], Operations: ['46+22=68', '87-68=19'] Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 93+19=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 93*19=1767, Resulting Numbers: [1767] 1767,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[93, 155], Operations: ['46+22=68', '87+68=155'] Exploring Operation: 93*155=14415, Resulting Numbers: [14415] 14415,86 unequal: No Solution Exploring Operation: 93+155=248, Resulting Numbers: [248] 248,86 unequal: No Solution Exploring Operation: 155-93=62, Resulting Numbers: [62] 62,86 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:[46, 22, 6], Operations: ['93-87=6'] Exploring Operation: 46+22=68, Resulting Numbers: [6, 68] Generated Node #0,2,0: 86:[6, 68] Operation: 46+22=68 Exploring Operation: 22-6=16, Resulting Numbers: [46, 16] Generated Node #0,2,1: 86:[46, 16] Operation: 22-6=16 Exploring Operation: 22+6=28, Resulting Numbers: [46, 28] Generated Node #0,2,2: 86:[46, 28] Operation: 22+6=28 Exploring Operation: 46-22=24, Resulting Numbers: [6, 24] Generated Node #0,2,3: 86:[6, 24] Operation: 46-22=24 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 86:[46, 16], Operations: ['93-87=6', '22-6=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,86 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 86:[46, 28], Operations: ['93-87=6', '22+6=28'] Exploring Operation: 46+28=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 46*28=1288, Resulting Numbers: [1288] 1288,86 unequal: No Solution Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 86:[6, 68], Operations: ['93-87=6', '46+22=68'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 86:[6, 24], Operations: ['93-87=6', '46-22=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,86 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,86 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 86:[87, 69], Operations: ['93-46=47', '22+47=69'] Exploring Operation: 87+69=156, Resulting Numbers: [156] 156,86 unequal: No Solution Exploring Operation: 87*69=6003, Resulting Numbers: [6003] 6003,86 unequal: No Solution Exploring Operation: 87-69=18, Resulting Numbers: [18] 18,86 unequal: No Solution Moving to Node #0,0,1 Current State: 86:[87, 25], Operations: ['93-46=47', '47-22=25'] Exploring Operation: 87*25=2175, Resulting Numbers: [2175] 2175,86 unequal: No Solution Exploring Operation: 87-25=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 87+25=112, Resulting Numbers: [112] 112,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[22, 40], Operations: ['93-46=47', '87-47=40'] Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,86 unequal: No Solution Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,86 unequal: No Solution Moving to Node #0,0,2 Current State: 86:[47, 65], Operations: ['93-46=47', '87-22=65'] Exploring Operation: 65-47=18, Resulting Numbers: [18] 18,86 unequal: No Solution Exploring Operation: 47+65=112, Resulting Numbers: [112] 112,86 unequal: No Solution Exploring Operation: 47*65=3055, Resulting Numbers: [3055] 3055,86 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 7, 31, 48, 62 ]
31
[ "31-7=24", "48/24=2", "62/2=31" ]
Current State: 31:[7, 31, 48, 62], Operations: [] Exploring Operation: 31-7=24, Resulting Numbers: [48, 62, 24] Generated Node #2: [48, 62, 24] from Operation: 31-7=24 Current State: 31:[48, 62, 24], Operations: ['31-7=24'] Exploring Operation: 48/24=2, Resulting Numbers: [62, 2] Generated Node #3: [62, 2] from Operation: 48/24=2 Current State: 31:[62, 2], Operations: ['31-7=24', '48/24=2'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[7, 31, 48, 62], Operations: [] Exploring Operation: 62-31=31, Resulting Numbers: [7, 48, 31] Generated Node #0,0: 31:[7, 48, 31] Operation: 62-31=31 Exploring Operation: 48-7=41, Resulting Numbers: [31, 62, 41] Generated Node #0,1: 31:[31, 62, 41] Operation: 48-7=41 Exploring Operation: 62-7=55, Resulting Numbers: [31, 48, 55] Generated Node #0,2: 31:[31, 48, 55] Operation: 62-7=55 Exploring Operation: 62-48=14, Resulting Numbers: [7, 31, 14] Generated Node #0,3: 31:[7, 31, 14] Operation: 62-48=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[7, 48, 31], Operations: ['62-31=31'] Exploring Operation: 48-7=41, Resulting Numbers: [31, 41] Generated Node #0,0,0: 31:[31, 41] Operation: 48-7=41 Exploring Operation: 31-7=24, Resulting Numbers: [48, 24] Generated Node #0,0,1: 31:[48, 24] Operation: 31-7=24 Exploring Operation: 7+31=38, Resulting Numbers: [48, 38] Generated Node #0,0,2: 31:[48, 38] Operation: 7+31=38 Exploring Operation: 7+48=55, Resulting Numbers: [31, 55] Generated Node #0,0,3: 31:[31, 55] Operation: 7+48=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[31, 41], Operations: ['62-31=31', '48-7=41'] Exploring Operation: 31+41=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 31*41=1271, Resulting Numbers: [1271] 1271,31 unequal: No Solution No 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: 31:[48, 24], Operations: ['62-31=31', '31-7=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,31 unequal: No Solution No 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: 31:[48, 38], Operations: ['62-31=31', '7+31=38'] Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,31 unequal: No Solution Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,31 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,31 unequal: No Solution No 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: 31:[31, 55], Operations: ['62-31=31', '7+48=55'] Exploring Operation: 31*55=1705, Resulting Numbers: [1705] 1705,31 unequal: No Solution Exploring Operation: 31+55=86, Resulting Numbers: [86] 86,31 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,31 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: 31:[31, 62, 41], Operations: ['48-7=41'] Exploring Operation: 41-31=10, Resulting Numbers: [62, 10] Generated Node #0,1,0: 31:[62, 10] Operation: 41-31=10 Exploring Operation: 62-31=31, Resulting Numbers: [41, 31] Generated Node #0,1,1: 31:[41, 31] Operation: 62-31=31 Exploring Operation: 62/31=2, Resulting Numbers: [41, 2] Generated Node #0,1,2: 31:[41, 2] Operation: 62/31=2 Exploring Operation: 62-41=21, Resulting Numbers: [31, 21] Generated Node #0,1,3: 31:[31, 21] Operation: 62-41=21 Moving to Node #0,1,1 Current State: 31:[41, 31], Operations: ['48-7=41', '62-31=31'] Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,31 unequal: No Solution Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[31, 21], Operations: ['48-7=41', '62-41=21'] Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,31 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[41, 2], Operations: ['48-7=41', '62/31=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,31 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[62, 10], Operations: ['48-7=41', '41-31=10'] Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,31 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[31, 48, 55], Operations: ['62-7=55'] Exploring Operation: 31+48=79, Resulting Numbers: [55, 79] Generated Node #0,2,0: 31:[55, 79] Operation: 31+48=79 Exploring Operation: 55-48=7, Resulting Numbers: [31, 7] Generated Node #0,2,1: 31:[31, 7] Operation: 55-48=7 Exploring Operation: 48-31=17, Resulting Numbers: [55, 17] Generated Node #0,2,2: 31:[55, 17] Operation: 48-31=17 Exploring Operation: 55-31=24, Resulting Numbers: [48, 24] Generated Node #0,2,3: 31:[48, 24] Operation: 55-31=24 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 31:[31, 7], Operations: ['62-7=55', '55-48=7'] Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,31 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,31 unequal: No Solution No 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: 31:[48, 24], Operations: ['62-7=55', '55-31=24'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,31 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,31 unequal: No Solution No 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: 31:[55, 17], Operations: ['62-7=55', '48-31=17'] Exploring Operation: 55*17=935, Resulting Numbers: [935] 935,31 unequal: No Solution Exploring Operation: 55+17=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 55-17=38, Resulting Numbers: [38] 38,31 unequal: No Solution No 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: 31:[55, 79], Operations: ['62-7=55', '31+48=79'] Exploring Operation: 79-55=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 55*79=4345, Resulting Numbers: [4345] 4345,31 unequal: No Solution Exploring Operation: 55+79=134, Resulting Numbers: [134] 134,31 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: 31:[7, 31, 14], Operations: ['62-48=14'] Exploring Operation: 7+14=21, Resulting Numbers: [31, 21] Generated Node #0,3,0: 31:[31, 21] Operation: 7+14=21 Exploring Operation: 31-7=24, Resulting Numbers: [14, 24] Generated Node #0,3,1: 31:[14, 24] Operation: 31-7=24 Exploring Operation: 7+31=38, Resulting Numbers: [14, 38] Generated Node #0,3,2: 31:[14, 38] Operation: 7+31=38 Exploring Operation: 14-7=7, Resulting Numbers: [31, 7] Generated Node #0,3,3: 31:[31, 7] Operation: 14-7=7 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[31, 21], Operations: ['62-48=14', '7+14=21'] Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,31 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,31 unequal: No Solution No 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: 31:[14, 24], Operations: ['62-48=14', '31-7=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,31 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 14*24=336, Resulting Numbers: [336] 336,31 unequal: No Solution No 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: 31:[14, 38], Operations: ['62-48=14', '7+31=38'] Exploring Operation: 14*38=532, Resulting Numbers: [532] 532,31 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,31 unequal: No Solution No 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: 31:[31, 7], Operations: ['62-48=14', '14-7=7'] Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 17, 57, 55, 63 ]
66
[ "17+57=74", "63-55=8", "74-8=66" ]
Current State: 66:[17, 57, 55, 63], Operations: [] Exploring Operation: 17+57=74, Resulting Numbers: [55, 63, 74] Generated Node #2: [55, 63, 74] from Operation: 17+57=74 Current State: 66:[55, 63, 74], Operations: ['17+57=74'] Exploring Operation: 63-55=8, Resulting Numbers: [74, 8] Generated Node #3: [74, 8] from Operation: 63-55=8 Current State: 66:[74, 8], Operations: ['17+57=74', '63-55=8'] Exploring Operation: 74-8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[17, 57, 55, 63], Operations: [] Exploring Operation: 17+55=72, Resulting Numbers: [57, 63, 72] Generated Node #0,0: 66:[57, 63, 72] Operation: 17+55=72 Exploring Operation: 57-55=2, Resulting Numbers: [17, 63, 2] Generated Node #0,1: 66:[17, 63, 2] Operation: 57-55=2 Exploring Operation: 55-17=38, Resulting Numbers: [57, 63, 38] Generated Node #0,2: 66:[57, 63, 38] Operation: 55-17=38 Exploring Operation: 63-57=6, Resulting Numbers: [17, 55, 6] Generated Node #0,3: 66:[17, 55, 6] Operation: 63-57=6 Exploring Operation: 63-55=8, Resulting Numbers: [17, 57, 8] Generated Node #0,4: 66:[17, 57, 8] Operation: 63-55=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[17, 63, 2], Operations: ['57-55=2'] Exploring Operation: 63+2=65, Resulting Numbers: [17, 65] Generated Node #0,1,0: 66:[17, 65] Operation: 63+2=65 Exploring Operation: 63-2=61, Resulting Numbers: [17, 61] Generated Node #0,1,1: 66:[17, 61] Operation: 63-2=61 Exploring Operation: 17+2=19, Resulting Numbers: [63, 19] Generated Node #0,1,2: 66:[63, 19] Operation: 17+2=19 Exploring Operation: 17*2=34, Resulting Numbers: [63, 34] Generated Node #0,1,3: 66:[63, 34] Operation: 17*2=34 Exploring Operation: 17-2=15, Resulting Numbers: [63, 15] Generated Node #0,1,4: 66:[63, 15] Operation: 17-2=15 Moving to Node #0,1,3 Current State: 66:[63, 34], Operations: ['57-55=2', '17*2=34'] Exploring Operation: 63*34=2142, Resulting Numbers: [2142] 2142,66 unequal: No Solution Exploring Operation: 63-34=29, Resulting Numbers: [29] 29,66 unequal: No Solution Exploring Operation: 63+34=97, Resulting Numbers: [97] 97,66 unequal: No Solution Moving to Node #0,1,2 Current State: 66:[63, 19], Operations: ['57-55=2', '17+2=19'] Exploring Operation: 63*19=1197, Resulting Numbers: [1197] 1197,66 unequal: No Solution Exploring Operation: 63+19=82, Resulting Numbers: [82] 82,66 unequal: No Solution Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,66 unequal: No Solution Moving to Node #0,1,0 Current State: 66:[17, 65], Operations: ['57-55=2', '63+2=65'] Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,66 unequal: No Solution Exploring Operation: 17*65=1105, Resulting Numbers: [1105] 1105,66 unequal: No Solution Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,66 unequal: No Solution Moving to Node #0,1,4 Current State: 66:[63, 15], Operations: ['57-55=2', '17-2=15'] Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,66 unequal: No Solution Exploring Operation: 63*15=945, Resulting Numbers: [945] 945,66 unequal: No Solution Exploring Operation: 63+15=78, Resulting Numbers: [78] 78,66 unequal: No Solution Moving to Node #0,1,1 Current State: 66:[17, 61], Operations: ['57-55=2', '63-2=61'] Exploring Operation: 17+61=78, Resulting Numbers: [78] 78,66 unequal: No Solution Exploring Operation: 17*61=1037, Resulting Numbers: [1037] 1037,66 unequal: No Solution Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 66:[17, 55, 6], Operations: ['63-57=6'] Exploring Operation: 17-6=11, Resulting Numbers: [55, 11] Generated Node #0,3,0: 66:[55, 11] Operation: 17-6=11 Exploring Operation: 55-17=38, Resulting Numbers: [6, 38] Generated Node #0,3,1: 66:[6, 38] Operation: 55-17=38 Exploring Operation: 17+55=72, Resulting Numbers: [6, 72] Generated Node #0,3,2: 66:[6, 72] Operation: 17+55=72 Exploring Operation: 55+6=61, Resulting Numbers: [17, 61] Generated Node #0,3,3: 66:[17, 61] Operation: 55+6=61 Exploring Operation: 17+6=23, Resulting Numbers: [55, 23] Generated Node #0,3,4: 66:[55, 23] Operation: 17+6=23 Moving to Node #0,3,1 Current State: 66:[6, 38], Operations: ['63-57=6', '55-17=38'] Exploring Operation: 6*38=228, Resulting Numbers: [228] 228,66 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,66 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,66 unequal: No Solution Moving to Node #0,3,2 Current State: 66:[6, 72], Operations: ['63-57=6', '17+55=72'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,66 unequal: No Solution Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[17, 57, 55, 63], Operations: [] Exploring Operation: 63-57=6, Resulting Numbers: [17, 55, 6] Generated Node #0,3: 66:[17, 55, 6] Operation: 63-57=6 Moving to Node #0,3 Current State: 66:[17, 55, 6], Operations: ['63-57=6'] Exploring Operation: 17+55=72, Resulting Numbers: [6, 72] Generated Node #0,3,2: 66:[6, 72] Operation: 17+55=72 Moving to Node #0,3,2 Current State: 66:[6, 72], Operations: ['63-57=6', '17+55=72'] Exploring Operation: 72-6=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
sum_heuristic
[ 30, 72, 16, 87 ]
32
[ "30*16=480", "87-72=15", "480/15=32" ]
Current State: 32:[30, 72, 16, 87], Operations: [] Exploring Operation: 30*16=480, Resulting Numbers: [72, 87, 480] Generated Node #2: [72, 87, 480] from Operation: 30*16=480 Current State: 32:[72, 87, 480], Operations: ['30*16=480'] Exploring Operation: 87-72=15, Resulting Numbers: [480, 15] Generated Node #3: [480, 15] from Operation: 87-72=15 Current State: 32:[480, 15], Operations: ['30*16=480', '87-72=15'] Exploring Operation: 480/15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[30, 72, 16, 87], Operations: [] Exploring Operation: 72-30=42, Resulting Numbers: [16, 87, 42] Generated Node #0,0: 32:[16, 87, 42] Operation: 72-30=42 Exploring Operation: 87-72=15, Resulting Numbers: [30, 16, 15] Generated Node #0,1: 32:[30, 16, 15] Operation: 87-72=15 Moving to Node #0,1 Current State: 32:[30, 16, 15], Operations: ['87-72=15'] Exploring Operation: 30-15=15, Resulting Numbers: [16, 15] Generated Node #0,1,0: 32:[16, 15] Operation: 30-15=15 Exploring Operation: 30/15=2, Resulting Numbers: [16, 2] Generated Node #0,1,1: 32:[16, 2] Operation: 30/15=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 32:[16, 2], Operations: ['87-72=15', '30/15=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[30, 72, 16, 87], Operations: [] Exploring Operation: 87-72=15, Resulting Numbers: [30, 16, 15] Generated Node #0,1: 32:[30, 16, 15] Operation: 87-72=15 Moving to Node #0,1 Current State: 32:[30, 16, 15], Operations: ['87-72=15'] Exploring Operation: 30/15=2, Resulting Numbers: [16, 2] Generated Node #0,1,1: 32:[16, 2] Operation: 30/15=2 Moving to Node #0,1,1 Current State: 32:[16, 2], Operations: ['87-72=15', '30/15=2'] Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 4, 63, 51, 1 ]
30
[ "4-1=3", "63/3=21", "51-21=30" ]
Current State: 30:[4, 63, 51, 1], Operations: [] Exploring Operation: 4-1=3, Resulting Numbers: [63, 51, 3] Generated Node #2: [63, 51, 3] from Operation: 4-1=3 Current State: 30:[63, 51, 3], Operations: ['4-1=3'] Exploring Operation: 63/3=21, Resulting Numbers: [51, 21] Generated Node #3: [51, 21] from Operation: 63/3=21 Current State: 30:[51, 21], Operations: ['4-1=3', '63/3=21'] Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[4, 63, 51, 1], Operations: [] Exploring Operation: 63-4=59, Resulting Numbers: [51, 1, 59] Generated Node #0,0: 30:[51, 1, 59] Operation: 63-4=59 Exploring Operation: 63-51=12, Resulting Numbers: [4, 1, 12] Generated Node #0,1: 30:[4, 1, 12] Operation: 63-51=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[4, 1, 12], Operations: ['63-51=12'] Exploring Operation: 4+1=5, Resulting Numbers: [12, 5] Generated Node #0,1,0: 30:[12, 5] Operation: 4+1=5 Exploring Operation: 12/4=3, Resulting Numbers: [1, 3] Generated Node #0,1,1: 30:[1, 3] Operation: 12/4=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[1, 3], Operations: ['63-51=12', '12/4=3'] Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[12, 5], Operations: ['63-51=12', '4+1=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[51, 1, 59], Operations: ['63-4=59'] Exploring Operation: 59-51=8, Resulting Numbers: [1, 8] Generated Node #0,0,0: 30:[1, 8] Operation: 59-51=8 Exploring Operation: 51-1=50, Resulting Numbers: [59, 50] Generated Node #0,0,1: 30:[59, 50] Operation: 51-1=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[1, 8], Operations: ['63-4=59', '59-51=8'] Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[59, 50], Operations: ['63-4=59', '51-1=50'] Exploring Operation: 59+50=109, Resulting Numbers: [109] 109,30 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 50, 52, 4, 2 ]
10
[ "52-50=2", "4*2=8", "2+8=10" ]
Current State: 10:[50, 52, 4, 2], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [4, 2, 2] Generated Node #2: [4, 2, 2] from Operation: 52-50=2 Current State: 10:[4, 2, 2], Operations: ['52-50=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,10 equal: Goal Reached Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[50, 52, 4, 2], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [50, 4, 26] Generated Node #0,0: 10:[50, 4, 26] Operation: 52/2=26 Exploring Operation: 50/2=25, Resulting Numbers: [52, 4, 25] Generated Node #0,1: 10:[52, 4, 25] Operation: 50/2=25 Exploring Operation: 52-50=2, Resulting Numbers: [4, 2, 2] Generated Node #0,2: 10:[4, 2, 2] Operation: 52-50=2 Exploring Operation: 52/4=13, Resulting Numbers: [50, 2, 13] Generated Node #0,3: 10:[50, 2, 13] Operation: 52/4=13 Moving to Node #0,2 Current State: 10:[4, 2, 2], Operations: ['52-50=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2, 2] Generated Node #0,2,0: 10:[2, 2] Operation: 4-2=2 Exploring Operation: 4-2=2, Resulting Numbers: [2, 2] Generated Node #0,2,1: 10:[2, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [2, 2] Generated Node #0,2,2: 10:[2, 2] Operation: 4/2=2 Exploring Operation: 4/2=2, Resulting Numbers: [2, 2] Generated Node #0,2,3: 10:[2, 2] Operation: 4/2=2 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 10:[2, 2], Operations: ['52-50=2', '4-2=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 10:[2, 2], Operations: ['52-50=2', '4-2=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 10:[2, 2], Operations: ['52-50=2', '4/2=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 10:[2, 2], Operations: ['52-50=2', '4/2=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 10:[50, 2, 13], Operations: ['52/4=13'] Exploring Operation: 50-2=48, Resulting Numbers: [13, 48] Generated Node #0,3,0: 10:[13, 48] Operation: 50-2=48 Exploring Operation: 50/2=25, Resulting Numbers: [13, 25] Generated Node #0,3,1: 10:[13, 25] Operation: 50/2=25 Exploring Operation: 13-2=11, Resulting Numbers: [50, 11] Generated Node #0,3,2: 10:[50, 11] Operation: 13-2=11 Exploring Operation: 50-13=37, Resulting Numbers: [2, 37] Generated Node #0,3,3: 10:[2, 37] Operation: 50-13=37 Moving to Node #0,0 Current State: 10:[50, 4, 26], Operations: ['52/2=26'] Exploring Operation: 26-4=22, Resulting Numbers: [50, 22] Generated Node #0,0,0: 10:[50, 22] Operation: 26-4=22 Exploring Operation: 50-4=46, Resulting Numbers: [26, 46] Generated Node #0,0,1: 10:[26, 46] Operation: 50-4=46 Exploring Operation: 50+4=54, Resulting Numbers: [26, 54] Generated Node #0,0,2: 10:[26, 54] Operation: 50+4=54 Exploring Operation: 50-26=24, Resulting Numbers: [4, 24] Generated Node #0,0,3: 10:[4, 24] Operation: 50-26=24 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 10:[4, 24], Operations: ['52/2=26', '50-26=24'] Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,10 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[50, 22], Operations: ['52/2=26', '26-4=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,10 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,10 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 10:[26, 46], Operations: ['52/2=26', '50-4=46'] Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,10 unequal: No Solution Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,10 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[26, 54], Operations: ['52/2=26', '50+4=54'] Exploring Operation: 26+54=80, Resulting Numbers: [80] 80,10 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,10 unequal: No Solution Exploring Operation: 26*54=1404, Resulting Numbers: [1404] 1404,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 10:[52, 4, 25], Operations: ['50/2=25'] Exploring Operation: 52-25=27, Resulting Numbers: [4, 27] Generated Node #0,1,0: 10:[4, 27] Operation: 52-25=27 Exploring Operation: 25-4=21, Resulting Numbers: [52, 21] Generated Node #0,1,1: 10:[52, 21] Operation: 25-4=21 Exploring Operation: 52/4=13, Resulting Numbers: [25, 13] Generated Node #0,1,2: 10:[25, 13] Operation: 52/4=13 Exploring Operation: 52-4=48, Resulting Numbers: [25, 48] Generated Node #0,1,3: 10:[25, 48] Operation: 52-4=48 Moving to Node #0,3,1 Current State: 10:[13, 25], Operations: ['52/4=13', '50/2=25'] Exploring Operation: 13+25=38, Resulting Numbers: [38] 38,10 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 13*25=325, Resulting Numbers: [325] 325,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[25, 13], Operations: ['50/2=25', '52/4=13'] Exploring Operation: 25+13=38, Resulting Numbers: [38] 38,10 unequal: No Solution Exploring Operation: 25*13=325, Resulting Numbers: [325] 325,10 unequal: No Solution Exploring Operation: 25-13=12, Resulting Numbers: [12] 12,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[4, 27], Operations: ['50/2=25', '52-25=27'] Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,10 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,10 unequal: No Solution Moving to Node #0,3,3 Current State: 10:[2, 37], Operations: ['52/4=13', '50-13=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,10 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,10 unequal: No Solution Moving to Node #0,3,0 Current State: 10:[13, 48], Operations: ['52/4=13', '50-2=48'] Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,10 unequal: No Solution Exploring Operation: 13*48=624, Resulting Numbers: [624] 624,10 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[50, 11], Operations: ['52/4=13', '13-2=11'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,10 unequal: No Solution Exploring Operation: 50+11=61, Resulting Numbers: [61] 61,10 unequal: No Solution Exploring Operation: 50*11=550, Resulting Numbers: [550] 550,10 unequal: No Solution Moving to Node #0,1,3 Current State: 10:[25, 48], Operations: ['50/2=25', '52-4=48'] Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,10 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,10 unequal: No Solution Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[52, 21], Operations: ['50/2=25', '25-4=21'] Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,10 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,10 unequal: No Solution Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,10 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 37, 76, 34, 36 ]
32
[ "37-34=3", "36*3=108", "108-76=32" ]
Current State: 32:[37, 76, 34, 36], Operations: [] Exploring Operation: 37-34=3, Resulting Numbers: [76, 36, 3] Generated Node #2: [76, 36, 3] from Operation: 37-34=3 Current State: 32:[76, 36, 3], Operations: ['37-34=3'] Exploring Operation: 36*3=108, Resulting Numbers: [76, 108] Generated Node #3: [76, 108] from Operation: 36*3=108 Current State: 32:[76, 108], Operations: ['37-34=3', '36*3=108'] Exploring Operation: 108-76=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[37, 76, 34, 36], Operations: [] Exploring Operation: 37-36=1, Resulting Numbers: [76, 34, 1] Generated Node #0,0: 32:[76, 34, 1] Operation: 37-36=1 Exploring Operation: 76-37=39, Resulting Numbers: [34, 36, 39] Generated Node #0,1: 32:[34, 36, 39] Operation: 76-37=39 Exploring Operation: 76-34=42, Resulting Numbers: [37, 36, 42] Generated Node #0,2: 32:[37, 36, 42] Operation: 76-34=42 Exploring Operation: 76-36=40, Resulting Numbers: [37, 34, 40] Generated Node #0,3: 32:[37, 34, 40] Operation: 76-36=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[34, 36, 39], Operations: ['76-37=39'] Exploring Operation: 36-34=2, Resulting Numbers: [39, 2] Generated Node #0,1,0: 32:[39, 2] Operation: 36-34=2 Exploring Operation: 34+36=70, Resulting Numbers: [39, 70] Generated Node #0,1,1: 32:[39, 70] Operation: 34+36=70 Exploring Operation: 39-36=3, Resulting Numbers: [34, 3] Generated Node #0,1,2: 32:[34, 3] Operation: 39-36=3 Exploring Operation: 39-34=5, Resulting Numbers: [36, 5] Generated Node #0,1,3: 32:[36, 5] Operation: 39-34=5 Moving to Node #0,1,2 Current State: 32:[34, 3], Operations: ['76-37=39', '39-36=3'] Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,32 unequal: No Solution Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[36, 5], Operations: ['76-37=39', '39-34=5'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[39, 2], Operations: ['76-37=39', '36-34=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,32 unequal: No Solution Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[39, 70], Operations: ['76-37=39', '34+36=70'] Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,32 unequal: No Solution Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,32 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[37, 34, 40], Operations: ['76-36=40'] Exploring Operation: 37-34=3, Resulting Numbers: [40, 3] Generated Node #0,3,0: 32:[40, 3] Operation: 37-34=3 Exploring Operation: 40-37=3, Resulting Numbers: [34, 3] Generated Node #0,3,1: 32:[34, 3] Operation: 40-37=3 Exploring Operation: 40-34=6, Resulting Numbers: [37, 6] Generated Node #0,3,2: 32:[37, 6] Operation: 40-34=6 Exploring Operation: 37+34=71, Resulting Numbers: [40, 71] Generated Node #0,3,3: 32:[40, 71] Operation: 37+34=71 Moving to Node #0,3,1 Current State: 32:[34, 3], Operations: ['76-36=40', '40-37=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,32 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[37, 6], Operations: ['76-36=40', '40-34=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,32 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[40, 3], Operations: ['76-36=40', '37-34=3'] Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,32 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,32 unequal: No Solution Moving to Node #0,3,3 Current State: 32:[40, 71], Operations: ['76-36=40', '37+34=71'] Exploring Operation: 40+71=111, Resulting Numbers: [111] 111,32 unequal: No Solution Exploring Operation: 40*71=2840, Resulting Numbers: [2840] 2840,32 unequal: No Solution Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[37, 36, 42], Operations: ['76-34=42'] Exploring Operation: 42-36=6, Resulting Numbers: [37, 6] Generated Node #0,2,0: 32:[37, 6] Operation: 42-36=6 Exploring Operation: 37-36=1, Resulting Numbers: [42, 1] Generated Node #0,2,1: 32:[42, 1] Operation: 37-36=1 Exploring Operation: 37+36=73, Resulting Numbers: [42, 73] Generated Node #0,2,2: 32:[42, 73] Operation: 37+36=73 Exploring Operation: 42-37=5, Resulting Numbers: [36, 5] Generated Node #0,2,3: 32:[36, 5] Operation: 42-37=5 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 32:[36, 5], Operations: ['76-34=42', '42-37=5'] Exploring Operation: 36*5=180, Resulting Numbers: [180] 180,32 unequal: No Solution Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,32 unequal: No Solution No 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: 32:[37, 6], Operations: ['76-34=42', '42-36=6'] Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,32 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,32 unequal: No Solution No 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: 32:[42, 1], Operations: ['76-34=42', '37-36=1'] Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 42*1=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,32 unequal: No Solution Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,32 unequal: No Solution No 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: 32:[42, 73], Operations: ['76-34=42', '37+36=73'] Exploring Operation: 73-42=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 42+73=115, Resulting Numbers: [115] 115,32 unequal: No Solution Exploring Operation: 42*73=3066, Resulting Numbers: [3066] 3066,32 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: 32:[76, 34, 1], Operations: ['37-36=1'] Exploring Operation: 76-1=75, Resulting Numbers: [34, 75] Generated Node #0,0,0: 32:[34, 75] Operation: 76-1=75 Exploring Operation: 76-34=42, Resulting Numbers: [1, 42] Generated Node #0,0,1: 32:[1, 42] Operation: 76-34=42 Exploring Operation: 34-1=33, Resulting Numbers: [76, 33] Generated Node #0,0,2: 32:[76, 33] Operation: 34-1=33 Exploring Operation: 76*1=76, Resulting Numbers: [34, 76] Generated Node #0,0,3: 32:[34, 76] Operation: 76*1=76 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[1, 42], Operations: ['37-36=1', '76-34=42'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 1*42=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 1+42=43, Resulting Numbers: [43] 43,32 unequal: No Solution No 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: 32:[34, 75], Operations: ['37-36=1', '76-1=75'] Exploring Operation: 34*75=2550, Resulting Numbers: [2550] 2550,32 unequal: No Solution Exploring Operation: 75-34=41, Resulting Numbers: [41] 41,32 unequal: No Solution Exploring Operation: 34+75=109, Resulting Numbers: [109] 109,32 unequal: No Solution No 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: 32:[76, 33], Operations: ['37-36=1', '34-1=33'] Exploring Operation: 76*33=2508, Resulting Numbers: [2508] 2508,32 unequal: No Solution Exploring Operation: 76+33=109, Resulting Numbers: [109] 109,32 unequal: No Solution Exploring Operation: 76-33=43, Resulting Numbers: [43] 43,32 unequal: No Solution No 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: 32:[34, 76], Operations: ['37-36=1', '76*1=76'] Exploring Operation: 34+76=110, Resulting Numbers: [110] 110,32 unequal: No Solution Exploring Operation: 76-34=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 34*76=2584, Resulting Numbers: [2584] 2584,32 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
[ 35, 65, 70, 19 ]
49
[ "35+65=100", "70-19=51", "100-51=49" ]
Current State: 49:[35, 65, 70, 19], Operations: [] Exploring Operation: 35+65=100, Resulting Numbers: [70, 19, 100] Generated Node #2: [70, 19, 100] from Operation: 35+65=100 Current State: 49:[70, 19, 100], Operations: ['35+65=100'] Exploring Operation: 70-19=51, Resulting Numbers: [100, 51] Generated Node #3: [100, 51] from Operation: 70-19=51 Current State: 49:[100, 51], Operations: ['35+65=100', '70-19=51'] Exploring Operation: 100-51=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[35, 65, 70, 19], Operations: [] Exploring Operation: 70-19=51, Resulting Numbers: [35, 65, 51] Generated Node #0,0: 49:[35, 65, 51] Operation: 70-19=51 Exploring Operation: 70-65=5, Resulting Numbers: [35, 19, 5] Generated Node #0,1: 49:[35, 19, 5] Operation: 70-65=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[35, 19, 5], Operations: ['70-65=5'] Exploring Operation: 35-19=16, Resulting Numbers: [5, 16] Generated Node #0,1,0: 49:[5, 16] Operation: 35-19=16 Exploring Operation: 35+19=54, Resulting Numbers: [5, 54] Generated Node #0,1,1: 49:[5, 54] Operation: 35+19=54 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[5, 54], Operations: ['70-65=5', '35+19=54'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[35, 65, 70, 19], Operations: [] Exploring Operation: 70-65=5, Resulting Numbers: [35, 19, 5] Generated Node #0,1: 49:[35, 19, 5] Operation: 70-65=5 Moving to Node #0,1 Current State: 49:[35, 19, 5], Operations: ['70-65=5'] Exploring Operation: 35+19=54, Resulting Numbers: [5, 54] Generated Node #0,1,1: 49:[5, 54] Operation: 35+19=54 Moving to Node #0,1,1 Current State: 49:[5, 54], Operations: ['70-65=5', '35+19=54'] Exploring Operation: 54-5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 35, 94, 24, 66 ]
100
[ "35-24=11", "66/11=6", "94+6=100" ]
Current State: 100:[35, 94, 24, 66], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [94, 66, 11] Generated Node #2: [94, 66, 11] from Operation: 35-24=11 Current State: 100:[94, 66, 11], Operations: ['35-24=11'] Exploring Operation: 66/11=6, Resulting Numbers: [94, 6] Generated Node #3: [94, 6] from Operation: 66/11=6 Current State: 100:[94, 6], Operations: ['35-24=11', '66/11=6'] Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[35, 94, 24, 66], Operations: [] Exploring Operation: 35+66=101, Resulting Numbers: [94, 24, 101] Generated Node #0,0: 100:[94, 24, 101] Operation: 35+66=101 Exploring Operation: 66-35=31, Resulting Numbers: [94, 24, 31] Generated Node #0,1: 100:[94, 24, 31] Operation: 66-35=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[94, 24, 101], Operations: ['35+66=101'] Exploring Operation: 94+24=118, Resulting Numbers: [101, 118] Generated Node #0,0,0: 100:[101, 118] Operation: 94+24=118 Exploring Operation: 101-94=7, Resulting Numbers: [24, 7] Generated Node #0,0,1: 100:[24, 7] Operation: 101-94=7 Moving to Node #0,0,1 Current State: 100:[24, 7], Operations: ['35+66=101', '101-94=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,100 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[101, 118], Operations: ['35+66=101', '94+24=118'] Exploring Operation: 118-101=17, Resulting Numbers: [17] 17,100 unequal: No Solution Exploring Operation: 101+118=219, Resulting Numbers: [219] 219,100 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 #0,1 Current State: 100:[94, 24, 31], Operations: ['66-35=31'] Exploring Operation: 31-24=7, Resulting Numbers: [94, 7] Generated Node #0,1,0: 100:[94, 7] Operation: 31-24=7 Exploring Operation: 24+31=55, Resulting Numbers: [94, 55] Generated Node #0,1,1: 100:[94, 55] Operation: 24+31=55 Moving to Node #0,1,0 Current State: 100:[94, 7], Operations: ['66-35=31', '31-24=7'] Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,100 unequal: No Solution Exploring Operation: 94+7=101, Resulting Numbers: [101] 101,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[94, 55], Operations: ['66-35=31', '24+31=55'] Exploring Operation: 94-55=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 94+55=149, Resulting Numbers: [149] 149,100 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
[ 89, 72, 31, 29 ]
34
[ "89-72=17", "31-29=2", "17*2=34" ]
Current State: 34:[89, 72, 31, 29], Operations: [] Exploring Operation: 89-72=17, Resulting Numbers: [31, 29, 17] Generated Node #2: [31, 29, 17] from Operation: 89-72=17 Current State: 34:[31, 29, 17], Operations: ['89-72=17'] Exploring Operation: 31-29=2, Resulting Numbers: [17, 2] Generated Node #3: [17, 2] from Operation: 31-29=2 Current State: 34:[17, 2], Operations: ['89-72=17', '31-29=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[89, 72, 31, 29], Operations: [] Exploring Operation: 89-29=60, Resulting Numbers: [72, 31, 60] Generated Node #0,0: 34:[72, 31, 60] Operation: 89-29=60 Exploring Operation: 89-72=17, Resulting Numbers: [31, 29, 17] Generated Node #0,1: 34:[31, 29, 17] Operation: 89-72=17 Exploring Operation: 89-31=58, Resulting Numbers: [72, 29, 58] Generated Node #0,2: 34:[72, 29, 58] Operation: 89-31=58 Moving to Node #0,1 Current State: 34:[31, 29, 17], Operations: ['89-72=17'] Exploring Operation: 29-17=12, Resulting Numbers: [31, 12] Generated Node #0,1,0: 34:[31, 12] Operation: 29-17=12 Exploring Operation: 31-29=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 34:[17, 2] Operation: 31-29=2 Exploring Operation: 31-17=14, Resulting Numbers: [29, 14] Generated Node #0,1,2: 34:[29, 14] Operation: 31-17=14 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 34:[17, 2], Operations: ['89-72=17', '31-29=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,34 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[89, 72, 31, 29], Operations: [] Exploring Operation: 89-72=17, Resulting Numbers: [31, 29, 17] Generated Node #0,1: 34:[31, 29, 17] Operation: 89-72=17 Moving to Node #0,1 Current State: 34:[31, 29, 17], Operations: ['89-72=17'] Exploring Operation: 31-29=2, Resulting Numbers: [17, 2] Generated Node #0,1,1: 34:[17, 2] Operation: 31-29=2 Moving to Node #0,1,1 Current State: 34:[17, 2], Operations: ['89-72=17', '31-29=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 17, 3, 97, 93 ]
65
[ "97-93=4", "17*4=68", "68-3=65" ]
Current State: 65:[17, 3, 97, 93], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [17, 3, 4] Generated Node #2: [17, 3, 4] from Operation: 97-93=4 Current State: 65:[17, 3, 4], Operations: ['97-93=4'] Exploring Operation: 17*4=68, Resulting Numbers: [3, 68] Generated Node #3: [3, 68] from Operation: 17*4=68 Current State: 65:[3, 68], Operations: ['97-93=4', '17*4=68'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[17, 3, 97, 93], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [17, 3, 4] Generated Node #0,0: 65:[17, 3, 4] Operation: 97-93=4 Exploring Operation: 17-3=14, Resulting Numbers: [97, 93, 14] Generated Node #0,1: 65:[97, 93, 14] Operation: 17-3=14 Exploring Operation: 93/3=31, Resulting Numbers: [17, 97, 31] Generated Node #0,2: 65:[17, 97, 31] Operation: 93/3=31 Exploring Operation: 97-17=80, Resulting Numbers: [3, 93, 80] Generated Node #0,3: 65:[3, 93, 80] Operation: 97-17=80 Exploring Operation: 93-17=76, Resulting Numbers: [3, 97, 76] Generated Node #0,4: 65:[3, 97, 76] Operation: 93-17=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[17, 3, 4], Operations: ['97-93=4'] Exploring Operation: 3*4=12, Resulting Numbers: [17, 12] Generated Node #0,0,0: 65:[17, 12] Operation: 3*4=12 Exploring Operation: 17*4=68, Resulting Numbers: [3, 68] Generated Node #0,0,1: 65:[3, 68] Operation: 17*4=68 Exploring Operation: 17-3=14, Resulting Numbers: [4, 14] Generated Node #0,0,2: 65:[4, 14] Operation: 17-3=14 Exploring Operation: 17-4=13, Resulting Numbers: [3, 13] Generated Node #0,0,3: 65:[3, 13] Operation: 17-4=13 Exploring Operation: 3+4=7, Resulting Numbers: [17, 7] Generated Node #0,0,4: 65:[17, 7] Operation: 3+4=7 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 65:[4, 14], Operations: ['97-93=4', '17-3=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,65 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,65 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 #0,0,3 Current State: 65:[3, 13], Operations: ['97-93=4', '17-4=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,65 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,65 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:[17, 12], Operations: ['97-93=4', '3*4=12'] Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,65 unequal: No Solution Exploring Operation: 17*12=204, Resulting Numbers: [204] 204,65 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 #0,0,1 Current State: 65:[3, 68], Operations: ['97-93=4', '17*4=68'] Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,65 unequal: No Solution Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,65 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[17, 3, 97, 93], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [17, 3, 4] Generated Node #0,0: 65:[17, 3, 4] Operation: 97-93=4 Moving to Node #0,0 Current State: 65:[17, 3, 4], Operations: ['97-93=4'] Exploring Operation: 17*4=68, Resulting Numbers: [3, 68] Generated Node #0,0,1: 65:[3, 68] Operation: 17*4=68 Moving to Node #0,0,1 Current State: 65:[3, 68], Operations: ['97-93=4', '17*4=68'] 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
0.977431
hs_5
sum_heuristic
[ 39, 47, 24, 90 ]
58
[ "47-39=8", "90-24=66", "66-8=58" ]
Current State: 58:[39, 47, 24, 90], Operations: [] Exploring Operation: 47-39=8, Resulting Numbers: [24, 90, 8] Generated Node #2: [24, 90, 8] from Operation: 47-39=8 Current State: 58:[24, 90, 8], Operations: ['47-39=8'] Exploring Operation: 90-24=66, Resulting Numbers: [8, 66] Generated Node #3: [8, 66] from Operation: 90-24=66 Current State: 58:[8, 66], Operations: ['47-39=8', '90-24=66'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[39, 47, 24, 90], Operations: [] Exploring Operation: 90-39=51, Resulting Numbers: [47, 24, 51] Generated Node #0,0: 58:[47, 24, 51] Operation: 90-39=51 Moving to Node #0,0 Current State: 58:[47, 24, 51], Operations: ['90-39=51'] Exploring Operation: 51-47=4, Resulting Numbers: [24, 4] Generated Node #0,0,0: 58:[24, 4] Operation: 51-47=4 Moving to Node #0,0,0 Current State: 58:[24, 4], Operations: ['90-39=51', '51-47=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,58 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 49, 65, 84, 67 ]
91
[ "67-65=2", "84/2=42", "49+42=91" ]
Current State: 91:[49, 65, 84, 67], Operations: [] Exploring Operation: 67-65=2, Resulting Numbers: [49, 84, 2] Generated Node #2: [49, 84, 2] from Operation: 67-65=2 Current State: 91:[49, 84, 2], Operations: ['67-65=2'] Exploring Operation: 84/2=42, Resulting Numbers: [49, 42] Generated Node #3: [49, 42] from Operation: 84/2=42 Current State: 91:[49, 42], Operations: ['67-65=2', '84/2=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[49, 65, 84, 67], Operations: [] Exploring Operation: 67-49=18, Resulting Numbers: [65, 84, 18] Generated Node #0,0: 91:[65, 84, 18] Operation: 67-49=18 Exploring Operation: 65-49=16, Resulting Numbers: [84, 67, 16] Generated Node #0,1: 91:[84, 67, 16] Operation: 65-49=16 Exploring Operation: 49+67=116, Resulting Numbers: [65, 84, 116] Generated Node #0,2: 91:[65, 84, 116] Operation: 49+67=116 Exploring Operation: 49+65=114, Resulting Numbers: [84, 67, 114] Generated Node #0,3: 91:[84, 67, 114] Operation: 49+65=114 Exploring Operation: 67-65=2, Resulting Numbers: [49, 84, 2] Generated Node #0,4: 91:[49, 84, 2] Operation: 67-65=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 91:[84, 67, 16], Operations: ['65-49=16'] Exploring Operation: 84+16=100, Resulting Numbers: [67, 100] Generated Node #0,1,0: 91:[67, 100] Operation: 84+16=100 Exploring Operation: 67-16=51, Resulting Numbers: [84, 51] Generated Node #0,1,1: 91:[84, 51] Operation: 67-16=51 Exploring Operation: 67+16=83, Resulting Numbers: [84, 83] Generated Node #0,1,2: 91:[84, 83] Operation: 67+16=83 Exploring Operation: 84-16=68, Resulting Numbers: [67, 68] Generated Node #0,1,3: 91:[67, 68] Operation: 84-16=68 Exploring Operation: 84-67=17, Resulting Numbers: [16, 17] Generated Node #0,1,4: 91:[16, 17] Operation: 84-67=17 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 91:[16, 17], Operations: ['65-49=16', '84-67=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,91 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 91:[84, 83], Operations: ['65-49=16', '67+16=83'] Exploring Operation: 84-83=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 84+83=167, Resulting Numbers: [167] 167,91 unequal: No Solution Exploring Operation: 84*83=6972, Resulting Numbers: [6972] 6972,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 91:[67, 100], Operations: ['65-49=16', '84+16=100'] Exploring Operation: 67*100=6700, Resulting Numbers: [6700] 6700,91 unequal: No Solution Exploring Operation: 67+100=167, Resulting Numbers: [167] 167,91 unequal: No Solution Exploring Operation: 100-67=33, Resulting Numbers: [33] 33,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 91:[84, 51], Operations: ['65-49=16', '67-16=51'] Exploring Operation: 84*51=4284, Resulting Numbers: [4284] 4284,91 unequal: No Solution Exploring Operation: 84+51=135, Resulting Numbers: [135] 135,91 unequal: No Solution Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 91:[67, 68], Operations: ['65-49=16', '84-16=68'] Exploring Operation: 68-67=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 67+68=135, Resulting Numbers: [135] 135,91 unequal: No Solution Exploring Operation: 67*68=4556, Resulting Numbers: [4556] 4556,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 91:[65, 84, 18], Operations: ['67-49=18'] Exploring Operation: 65+18=83, Resulting Numbers: [84, 83] Generated Node #0,0,0: 91:[84, 83] Operation: 65+18=83 Exploring Operation: 84-18=66, Resulting Numbers: [65, 66] Generated Node #0,0,1: 91:[65, 66] Operation: 84-18=66 Exploring Operation: 84+18=102, Resulting Numbers: [65, 102] Generated Node #0,0,2: 91:[65, 102] Operation: 84+18=102 Exploring Operation: 84-65=19, Resulting Numbers: [18, 19] Generated Node #0,0,3: 91:[18, 19] Operation: 84-65=19 Exploring Operation: 65-18=47, Resulting Numbers: [84, 47] Generated Node #0,0,4: 91:[84, 47] Operation: 65-18=47 Moving to Node #0,0,3 Current State: 91:[18, 19], Operations: ['67-49=18', '84-65=19'] Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,91 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,91 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[84, 83], Operations: ['67-49=18', '65+18=83'] Exploring Operation: 84*83=6972, Resulting Numbers: [6972] 6972,91 unequal: No Solution Exploring Operation: 84+83=167, Resulting Numbers: [167] 167,91 unequal: No Solution Exploring Operation: 84-83=1, Resulting Numbers: [1] 1,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[65, 102], Operations: ['67-49=18', '84+18=102'] Exploring Operation: 65*102=6630, Resulting Numbers: [6630] 6630,91 unequal: No Solution Exploring Operation: 102-65=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 65+102=167, Resulting Numbers: [167] 167,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[84, 47], Operations: ['67-49=18', '65-18=47'] Exploring Operation: 84*47=3948, Resulting Numbers: [3948] 3948,91 unequal: No Solution Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 84+47=131, Resulting Numbers: [131] 131,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[65, 66], Operations: ['67-49=18', '84-18=66'] Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,91 unequal: No Solution Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,91 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,91 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 #0,4 Current State: 91:[49, 84, 2], Operations: ['67-65=2'] Exploring Operation: 84+2=86, Resulting Numbers: [49, 86] Generated Node #0,4,0: 91:[49, 86] Operation: 84+2=86 Exploring Operation: 49+2=51, Resulting Numbers: [84, 51] Generated Node #0,4,1: 91:[84, 51] Operation: 49+2=51 Exploring Operation: 49*2=98, Resulting Numbers: [84, 98] Generated Node #0,4,2: 91:[84, 98] Operation: 49*2=98 Exploring Operation: 49-2=47, Resulting Numbers: [84, 47] Generated Node #0,4,3: 91:[84, 47] Operation: 49-2=47 Exploring Operation: 84-49=35, Resulting Numbers: [2, 35] Generated Node #0,4,4: 91:[2, 35] Operation: 84-49=35 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 91:[84, 98], Operations: ['67-65=2', '49*2=98'] Exploring Operation: 84+98=182, Resulting Numbers: [182] 182,91 unequal: No Solution Exploring Operation: 98-84=14, Resulting Numbers: [14] 14,91 unequal: No Solution Exploring Operation: 84*98=8232, Resulting Numbers: [8232] 8232,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 91:[2, 35], Operations: ['67-65=2', '84-49=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,91 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 91:[49, 86], Operations: ['67-65=2', '84+2=86'] Exploring Operation: 49*86=4214, Resulting Numbers: [4214] 4214,91 unequal: No Solution Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 49+86=135, Resulting Numbers: [135] 135,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 91:[84, 47], Operations: ['67-65=2', '49-2=47'] Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 84+47=131, Resulting Numbers: [131] 131,91 unequal: No Solution Exploring Operation: 84*47=3948, Resulting Numbers: [3948] 3948,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 91:[84, 51], Operations: ['67-65=2', '49+2=51'] Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 84+51=135, Resulting Numbers: [135] 135,91 unequal: No Solution Exploring Operation: 84*51=4284, Resulting Numbers: [4284] 4284,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[84, 67, 114], Operations: ['49+65=114'] Exploring Operation: 84-67=17, Resulting Numbers: [114, 17] Generated Node #0,3,0: 91:[114, 17] Operation: 84-67=17 Exploring Operation: 67+114=181, Resulting Numbers: [84, 181] Generated Node #0,3,1: 91:[84, 181] Operation: 67+114=181 Exploring Operation: 114-84=30, Resulting Numbers: [67, 30] Generated Node #0,3,2: 91:[67, 30] Operation: 114-84=30 Exploring Operation: 84+67=151, Resulting Numbers: [114, 151] Generated Node #0,3,3: 91:[114, 151] Operation: 84+67=151 Exploring Operation: 114-67=47, Resulting Numbers: [84, 47] Generated Node #0,3,4: 91:[84, 47] Operation: 114-67=47 Moving to Node #0,3,0 Current State: 91:[114, 17], Operations: ['49+65=114', '84-67=17'] Exploring Operation: 114-17=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 114*17=1938, Resulting Numbers: [1938] 1938,91 unequal: No Solution Exploring Operation: 114+17=131, Resulting Numbers: [131] 131,91 unequal: No Solution Moving to Node #0,3,4 Current State: 91:[84, 47], Operations: ['49+65=114', '114-67=47'] Exploring Operation: 84*47=3948, Resulting Numbers: [3948] 3948,91 unequal: No Solution Exploring Operation: 84+47=131, Resulting Numbers: [131] 131,91 unequal: No Solution Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[67, 30], Operations: ['49+65=114', '114-84=30'] Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,91 unequal: No Solution Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[114, 151], Operations: ['49+65=114', '84+67=151'] Exploring Operation: 114+151=265, Resulting Numbers: [265] 265,91 unequal: No Solution Exploring Operation: 114*151=17214, Resulting Numbers: [17214] 17214,91 unequal: No Solution Exploring Operation: 151-114=37, Resulting Numbers: [37] 37,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[84, 181], Operations: ['49+65=114', '67+114=181'] Exploring Operation: 84+181=265, Resulting Numbers: [265] 265,91 unequal: No Solution Exploring Operation: 84*181=15204, Resulting Numbers: [15204] 15204,91 unequal: No Solution Exploring Operation: 181-84=97, Resulting Numbers: [97] 97,91 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 Current State: 91:[65, 84, 116], Operations: ['49+67=116'] Exploring Operation: 65+116=181, Resulting Numbers: [84, 181] Generated Node #0,2,0: 91:[84, 181] Operation: 65+116=181 Exploring Operation: 116-65=51, Resulting Numbers: [84, 51] Generated Node #0,2,1: 91:[84, 51] Operation: 116-65=51 Exploring Operation: 84-65=19, Resulting Numbers: [116, 19] Generated Node #0,2,2: 91:[116, 19] Operation: 84-65=19 Exploring Operation: 65+84=149, Resulting Numbers: [116, 149] Generated Node #0,2,3: 91:[116, 149] Operation: 65+84=149 Exploring Operation: 116-84=32, Resulting Numbers: [65, 32] Generated Node #0,2,4: 91:[65, 32] Operation: 116-84=32 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 91:[116, 19], Operations: ['49+67=116', '84-65=19'] Exploring Operation: 116+19=135, Resulting Numbers: [135] 135,91 unequal: No Solution Exploring Operation: 116*19=2204, Resulting Numbers: [2204] 2204,91 unequal: No Solution Exploring Operation: 116-19=97, Resulting Numbers: [97] 97,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 91:[84, 51], Operations: ['49+67=116', '116-65=51'] Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 84*51=4284, Resulting Numbers: [4284] 4284,91 unequal: No Solution Exploring Operation: 84+51=135, Resulting Numbers: [135] 135,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 91:[65, 32], Operations: ['49+67=116', '116-84=32'] Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,91 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 91:[116, 149], Operations: ['49+67=116', '65+84=149'] Exploring Operation: 116+149=265, Resulting Numbers: [265] 265,91 unequal: No Solution Exploring Operation: 116*149=17284, Resulting Numbers: [17284] 17284,91 unequal: No Solution Exploring Operation: 149-116=33, Resulting Numbers: [33] 33,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 91:[84, 181], Operations: ['49+67=116', '65+116=181'] Exploring Operation: 181-84=97, Resulting Numbers: [97] 97,91 unequal: No Solution Exploring Operation: 84*181=15204, Resulting Numbers: [15204] 15204,91 unequal: No Solution Exploring Operation: 84+181=265, Resulting Numbers: [265] 265,91 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 4, 3, 29, 47 ]
23
[ "4*29=116", "116-47=69", "69/3=23" ]
Current State: 23:[4, 3, 29, 47], Operations: [] Exploring Operation: 4*29=116, Resulting Numbers: [3, 47, 116] Generated Node #2: [3, 47, 116] from Operation: 4*29=116 Current State: 23:[3, 47, 116], Operations: ['4*29=116'] Exploring Operation: 116-47=69, Resulting Numbers: [3, 69] Generated Node #3: [3, 69] from Operation: 116-47=69 Current State: 23:[3, 69], Operations: ['4*29=116', '116-47=69'] Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[4, 3, 29, 47], Operations: [] Exploring Operation: 4*3=12, Resulting Numbers: [29, 47, 12] Generated Node #0,0: 23:[29, 47, 12] Operation: 4*3=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[29, 47, 12], Operations: ['4*3=12'] Exploring Operation: 47-29=18, Resulting Numbers: [12, 18] Generated Node #0,0,0: 23:[12, 18] Operation: 47-29=18 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[12, 18], Operations: ['4*3=12', '47-29=18'] Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 61, 51, 51, 49 ]
13
[ "61-49=12", "51/51=1", "12+1=13" ]
Current State: 13:[61, 51, 51, 49], Operations: [] Exploring Operation: 61-49=12, Resulting Numbers: [51, 51, 12] Generated Node #2: [51, 51, 12] from Operation: 61-49=12 Current State: 13:[51, 51, 12], Operations: ['61-49=12'] Exploring Operation: 51/51=1, Resulting Numbers: [12, 1] Generated Node #3: [12, 1] from Operation: 51/51=1 Current State: 13:[12, 1], Operations: ['61-49=12', '51/51=1'] Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[61, 51, 51, 49], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [51, 49, 10] Generated Node #0,0: 13:[51, 49, 10] Operation: 61-51=10 Exploring Operation: 61-51=10, Resulting Numbers: [51, 49, 10] Generated Node #0,1: 13:[51, 49, 10] Operation: 61-51=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[51, 49, 10], Operations: ['61-51=10'] Exploring Operation: 51-49=2, Resulting Numbers: [10, 2] Generated Node #0,0,0: 13:[10, 2] Operation: 51-49=2 Exploring Operation: 51-10=41, Resulting Numbers: [49, 41] Generated Node #0,0,1: 13:[49, 41] Operation: 51-10=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[10, 2], Operations: ['61-51=10', '51-49=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,13 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,13 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 #0,0,1 Current State: 13:[49, 41], Operations: ['61-51=10', '51-10=41'] Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,13 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: 13:[51, 49, 10], Operations: ['61-51=10'] Exploring Operation: 51-49=2, Resulting Numbers: [10, 2] Generated Node #0,1,0: 13:[10, 2] Operation: 51-49=2 Exploring Operation: 51-10=41, Resulting Numbers: [49, 41] Generated Node #0,1,1: 13:[49, 41] Operation: 51-10=41 Moving to Node #0,1,0 Current State: 13:[10, 2], Operations: ['61-51=10', '51-49=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[49, 41], Operations: ['61-51=10', '51-10=41'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,13 unequal: No Solution Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,13 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
[ 38, 17, 14, 57 ]
98
[ "38+17=55", "57-14=43", "55+43=98" ]
Current State: 98:[38, 17, 14, 57], Operations: [] Exploring Operation: 38+17=55, Resulting Numbers: [14, 57, 55] Generated Node #2: [14, 57, 55] from Operation: 38+17=55 Current State: 98:[14, 57, 55], Operations: ['38+17=55'] Exploring Operation: 57-14=43, Resulting Numbers: [55, 43] Generated Node #3: [55, 43] from Operation: 57-14=43 Current State: 98:[55, 43], Operations: ['38+17=55', '57-14=43'] Exploring Operation: 55+43=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[38, 17, 14, 57], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [17, 14, 19] Generated Node #0,0: 98:[17, 14, 19] Operation: 57-38=19 Exploring Operation: 38+57=95, Resulting Numbers: [17, 14, 95] Generated Node #0,1: 98:[17, 14, 95] Operation: 38+57=95 Exploring Operation: 38+17=55, Resulting Numbers: [14, 57, 55] Generated Node #0,2: 98:[14, 57, 55] Operation: 38+17=55 Moving to Node #0,1 Current State: 98:[17, 14, 95], Operations: ['38+57=95'] Exploring Operation: 17+95=112, Resulting Numbers: [14, 112] Generated Node #0,1,0: 98:[14, 112] Operation: 17+95=112 Exploring Operation: 17-14=3, Resulting Numbers: [95, 3] Generated Node #0,1,1: 98:[95, 3] Operation: 17-14=3 Exploring Operation: 14+95=109, Resulting Numbers: [17, 109] Generated Node #0,1,2: 98:[17, 109] Operation: 14+95=109 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[95, 3], Operations: ['38+57=95', '17-14=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[38, 17, 14, 57], Operations: [] Exploring Operation: 38+57=95, Resulting Numbers: [17, 14, 95] Generated Node #0,1: 98:[17, 14, 95] Operation: 38+57=95 Moving to Node #0,1 Current State: 98:[17, 14, 95], Operations: ['38+57=95'] Exploring Operation: 17-14=3, Resulting Numbers: [95, 3] Generated Node #0,1,1: 98:[95, 3] Operation: 17-14=3 Moving to Node #0,1,1 Current State: 98:[95, 3], Operations: ['38+57=95', '17-14=3'] Exploring Operation: 95+3=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 11, 30, 39, 22 ]
48
[ "22/11=2", "39*2=78", "78-30=48" ]
Current State: 48:[11, 30, 39, 22], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [30, 39, 2] Generated Node #2: [30, 39, 2] from Operation: 22/11=2 Current State: 48:[30, 39, 2], Operations: ['22/11=2'] Exploring Operation: 39*2=78, Resulting Numbers: [30, 78] Generated Node #3: [30, 78] from Operation: 39*2=78 Current State: 48:[30, 78], Operations: ['22/11=2', '39*2=78'] Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[11, 30, 39, 22], Operations: [] Exploring Operation: 39-22=17, Resulting Numbers: [11, 30, 17] Generated Node #0,0: 48:[11, 30, 17] Operation: 39-22=17 Exploring Operation: 39-30=9, Resulting Numbers: [11, 22, 9] Generated Node #0,1: 48:[11, 22, 9] Operation: 39-30=9 Exploring Operation: 11+39=50, Resulting Numbers: [30, 22, 50] Generated Node #0,2: 48:[30, 22, 50] Operation: 11+39=50 Moving to Node #0,1 Current State: 48:[11, 22, 9], Operations: ['39-30=9'] Exploring Operation: 22/11=2, Resulting Numbers: [9, 2] Generated Node #0,1,0: 48:[9, 2] Operation: 22/11=2 Exploring Operation: 22-11=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 48:[9, 11] Operation: 22-11=11 Exploring Operation: 11-9=2, Resulting Numbers: [22, 2] Generated Node #0,1,2: 48:[22, 2] Operation: 11-9=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 48:[9, 2], Operations: ['39-30=9', '22/11=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,48 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,48 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 #0,1,1 Current State: 48:[9, 11], Operations: ['39-30=9', '22-11=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,48 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,48 unequal: No Solution Exploring Operation: 11-9=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 #0,1,2 Current State: 48:[22, 2], Operations: ['39-30=9', '11-9=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,48 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: 48:[11, 30, 17], Operations: ['39-22=17'] Exploring Operation: 30-11=19, Resulting Numbers: [17, 19] Generated Node #0,0,0: 48:[17, 19] Operation: 30-11=19 Exploring Operation: 30-17=13, Resulting Numbers: [11, 13] Generated Node #0,0,1: 48:[11, 13] Operation: 30-17=13 Exploring Operation: 30+17=47, Resulting Numbers: [11, 47] Generated Node #0,0,2: 48:[11, 47] Operation: 30+17=47 Moving to Node #0,2 Current State: 48:[30, 22, 50], Operations: ['11+39=50'] Exploring Operation: 30+22=52, Resulting Numbers: [50, 52] Generated Node #0,2,0: 48:[50, 52] Operation: 30+22=52 Exploring Operation: 50-30=20, Resulting Numbers: [22, 20] Generated Node #0,2,1: 48:[22, 20] Operation: 50-30=20 Exploring Operation: 30-22=8, Resulting Numbers: [50, 8] Generated Node #0,2,2: 48:[50, 8] Operation: 30-22=8 Moving to Node #0,0,1 Current State: 48:[11, 13], Operations: ['39-22=17', '30-17=13'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,48 unequal: No Solution Moving to Node #0,0,2 Current State: 48:[11, 47], Operations: ['39-22=17', '30+17=47'] Exploring Operation: 11*47=517, Resulting Numbers: [517] 517,48 unequal: No Solution Exploring Operation: 11+47=58, Resulting Numbers: [58] 58,48 unequal: No Solution Exploring Operation: 47-11=36, Resulting Numbers: [36] 36,48 unequal: No Solution Moving to Node #0,2,2 Current State: 48:[50, 8], Operations: ['11+39=50', '30-22=8'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,48 unequal: No Solution Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,48 unequal: No Solution Moving to Node #0,0,0 Current State: 48:[17, 19], Operations: ['39-22=17', '30-11=19'] Exploring Operation: 17+19=36, Resulting Numbers: [36] 36,48 unequal: No Solution Exploring Operation: 17*19=323, Resulting Numbers: [323] 323,48 unequal: No Solution Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[22, 20], Operations: ['11+39=50', '50-30=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,48 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[50, 52], Operations: ['11+39=50', '30+22=52'] Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,48 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,48 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,48 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 66, 92, 58, 43 ]
75
[ "92-66=26", "58+43=101", "101-26=75" ]
Current State: 75:[66, 92, 58, 43], Operations: [] Exploring Operation: 92-66=26, Resulting Numbers: [58, 43, 26] Generated Node #2: [58, 43, 26] from Operation: 92-66=26 Current State: 75:[58, 43, 26], Operations: ['92-66=26'] Exploring Operation: 58+43=101, Resulting Numbers: [26, 101] Generated Node #3: [26, 101] from Operation: 58+43=101 Current State: 75:[26, 101], Operations: ['92-66=26', '58+43=101'] Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[66, 92, 58, 43], Operations: [] Exploring Operation: 58-43=15, Resulting Numbers: [66, 92, 15] Generated Node #0,0: 75:[66, 92, 15] Operation: 58-43=15 Exploring Operation: 92-66=26, Resulting Numbers: [58, 43, 26] Generated Node #0,1: 75:[58, 43, 26] Operation: 92-66=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[66, 92, 15], Operations: ['58-43=15'] Exploring Operation: 92-66=26, Resulting Numbers: [15, 26] Generated Node #0,0,0: 75:[15, 26] Operation: 92-66=26 Exploring Operation: 92-15=77, Resulting Numbers: [66, 77] Generated Node #0,0,1: 75:[66, 77] Operation: 92-15=77 Moving to Node #0,0,0 Current State: 75:[15, 26], Operations: ['58-43=15', '92-66=26'] Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 15+26=41, Resulting Numbers: [41] 41,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[66, 77], Operations: ['58-43=15', '92-15=77'] Exploring Operation: 66+77=143, Resulting Numbers: [143] 143,75 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[58, 43, 26], Operations: ['92-66=26'] Exploring Operation: 43-26=17, Resulting Numbers: [58, 17] Generated Node #0,1,0: 75:[58, 17] Operation: 43-26=17 Exploring Operation: 58-43=15, Resulting Numbers: [26, 15] Generated Node #0,1,1: 75:[26, 15] Operation: 58-43=15 Moving to Node #0,1,1 Current State: 75:[26, 15], Operations: ['92-66=26', '58-43=15'] Exploring Operation: 26+15=41, Resulting Numbers: [41] 41,75 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[58, 17], Operations: ['92-66=26', '43-26=17'] Exploring Operation: 58+17=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[66, 92, 58, 43], Operations: [] Exploring Operation: 92-66=26, Resulting Numbers: [58, 43, 26] Generated Node #0,1: 75:[58, 43, 26] Operation: 92-66=26 Moving to Node #0,1 Current State: 75:[58, 43, 26], Operations: ['92-66=26'] Exploring Operation: 43-26=17, Resulting Numbers: [58, 17] Generated Node #0,1,0: 75:[58, 17] Operation: 43-26=17 Moving to Node #0,1,0 Current State: 75:[58, 17], Operations: ['92-66=26', '43-26=17'] Exploring Operation: 58+17=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 38, 16, 24, 57 ]
12
[ "24-16=8", "57*8=456", "456/38=12" ]
Current State: 12:[38, 16, 24, 57], Operations: [] Exploring Operation: 24-16=8, Resulting Numbers: [38, 57, 8] Generated Node #2: [38, 57, 8] from Operation: 24-16=8 Current State: 12:[38, 57, 8], Operations: ['24-16=8'] Exploring Operation: 57*8=456, Resulting Numbers: [38, 456] Generated Node #3: [38, 456] from Operation: 57*8=456 Current State: 12:[38, 456], Operations: ['24-16=8', '57*8=456'] Exploring Operation: 456/38=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[38, 16, 24, 57], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [16, 24, 19] Generated Node #0,0: 12:[16, 24, 19] Operation: 57-38=19 Exploring Operation: 57-24=33, Resulting Numbers: [38, 16, 33] Generated Node #0,1: 12:[38, 16, 33] Operation: 57-24=33 Exploring Operation: 38-24=14, Resulting Numbers: [16, 57, 14] Generated Node #0,2: 12:[16, 57, 14] Operation: 38-24=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[16, 24, 19], Operations: ['57-38=19'] Exploring Operation: 24-19=5, Resulting Numbers: [16, 5] Generated Node #0,0,0: 12:[16, 5] Operation: 24-19=5 Exploring Operation: 19-16=3, Resulting Numbers: [24, 3] Generated Node #0,0,1: 12:[24, 3] Operation: 19-16=3 Exploring Operation: 24-16=8, Resulting Numbers: [19, 8] Generated Node #0,0,2: 12:[19, 8] Operation: 24-16=8 Moving to Node #0,0,0 Current State: 12:[16, 5], Operations: ['57-38=19', '24-19=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,12 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[19, 8], Operations: ['57-38=19', '24-16=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[24, 3], Operations: ['57-38=19', '19-16=3'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[38, 16, 33], Operations: ['57-24=33'] Exploring Operation: 38-16=22, Resulting Numbers: [33, 22] Generated Node #0,1,0: 12:[33, 22] Operation: 38-16=22 Exploring Operation: 38-33=5, Resulting Numbers: [16, 5] Generated Node #0,1,1: 12:[16, 5] Operation: 38-33=5 Exploring Operation: 33-16=17, Resulting Numbers: [38, 17] Generated Node #0,1,2: 12:[38, 17] Operation: 33-16=17 Moving to Node #0,1,1 Current State: 12:[16, 5], Operations: ['57-24=33', '38-33=5'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[33, 22], Operations: ['57-24=33', '38-16=22'] Exploring Operation: 33+22=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,12 unequal: No Solution Exploring Operation: 33*22=726, Resulting Numbers: [726] 726,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[38, 17], Operations: ['57-24=33', '33-16=17'] Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,12 unequal: No Solution Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 38*17=646, Resulting Numbers: [646] 646,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[16, 57, 14], Operations: ['38-24=14'] Exploring Operation: 57-16=41, Resulting Numbers: [14, 41] Generated Node #0,2,0: 12:[14, 41] Operation: 57-16=41 Exploring Operation: 16-14=2, Resulting Numbers: [57, 2] Generated Node #0,2,1: 12:[57, 2] Operation: 16-14=2 Exploring Operation: 57-14=43, Resulting Numbers: [16, 43] Generated Node #0,2,2: 12:[16, 43] Operation: 57-14=43 Moving to Node #0,2,0 Current State: 12:[14, 41], Operations: ['38-24=14', '57-16=41'] Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,12 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[16, 43], Operations: ['38-24=14', '57-14=43'] Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 16*43=688, Resulting Numbers: [688] 688,12 unequal: No Solution Exploring Operation: 16+43=59, Resulting Numbers: [59] 59,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[57, 2], Operations: ['38-24=14', '16-14=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,12 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,12 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 60, 79, 37, 13 ]
69
[ "79-60=19", "37+13=50", "19+50=69" ]
Current State: 69:[60, 79, 37, 13], Operations: [] Exploring Operation: 79-60=19, Resulting Numbers: [37, 13, 19] Generated Node #2: [37, 13, 19] from Operation: 79-60=19 Current State: 69:[37, 13, 19], Operations: ['79-60=19'] Exploring Operation: 37+13=50, Resulting Numbers: [19, 50] Generated Node #3: [19, 50] from Operation: 37+13=50 Current State: 69:[19, 50], Operations: ['79-60=19', '37+13=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[60, 79, 37, 13], Operations: [] Exploring Operation: 37-13=24, Resulting Numbers: [60, 79, 24] Generated Node #0,0: 69:[60, 79, 24] Operation: 37-13=24 Exploring Operation: 60-37=23, Resulting Numbers: [79, 13, 23] Generated Node #0,1: 69:[79, 13, 23] Operation: 60-37=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[60, 79, 24], Operations: ['37-13=24'] Exploring Operation: 60-24=36, Resulting Numbers: [79, 36] Generated Node #0,0,0: 69:[79, 36] Operation: 60-24=36 Exploring Operation: 79-60=19, Resulting Numbers: [24, 19] Generated Node #0,0,1: 69:[24, 19] Operation: 79-60=19 Moving to Node #0,0,1 Current State: 69:[24, 19], Operations: ['37-13=24', '79-60=19'] Exploring Operation: 24+19=43, Resulting Numbers: [43] 43,69 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[79, 36], Operations: ['37-13=24', '60-24=36'] Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,69 unequal: No Solution Exploring Operation: 79+36=115, Resulting Numbers: [115] 115,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[79, 13, 23], Operations: ['60-37=23'] Exploring Operation: 79-13=66, Resulting Numbers: [23, 66] Generated Node #0,1,0: 69:[23, 66] Operation: 79-13=66 Exploring Operation: 23-13=10, Resulting Numbers: [79, 10] Generated Node #0,1,1: 69:[79, 10] Operation: 23-13=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[23, 66], Operations: ['60-37=23', '79-13=66'] Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,69 unequal: No Solution Exploring Operation: 23+66=89, Resulting Numbers: [89] 89,69 unequal: No Solution No 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: 69:[79, 10], Operations: ['60-37=23', '23-13=10'] Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,69 unequal: No Solution Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[60, 79, 37, 13], Operations: [] Exploring Operation: 60-37=23, Resulting Numbers: [79, 13, 23] Generated Node #0,1: 69:[79, 13, 23] Operation: 60-37=23 Moving to Node #0,1 Current State: 69:[79, 13, 23], Operations: ['60-37=23'] Exploring Operation: 23-13=10, Resulting Numbers: [79, 10] Generated Node #0,1,1: 69:[79, 10] Operation: 23-13=10 Moving to Node #0,1,1 Current State: 69:[79, 10], Operations: ['60-37=23', '23-13=10'] Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 79, 71, 28, 80 ]
43
[ "80-79=1", "71-28=43", "1*43=43" ]
Current State: 43:[79, 71, 28, 80], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [71, 28, 1] Generated Node #2: [71, 28, 1] from Operation: 80-79=1 Current State: 43:[71, 28, 1], Operations: ['80-79=1'] Exploring Operation: 71-28=43, Resulting Numbers: [1, 43] Generated Node #3: [1, 43] from Operation: 71-28=43 Current State: 43:[1, 43], Operations: ['80-79=1', '71-28=43'] Exploring Operation: 1*43=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[79, 71, 28, 80], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [71, 28, 1] Generated Node #0,0: 43:[71, 28, 1] Operation: 80-79=1 Exploring Operation: 80-28=52, Resulting Numbers: [79, 71, 52] Generated Node #0,1: 43:[79, 71, 52] Operation: 80-28=52 Exploring Operation: 79-28=51, Resulting Numbers: [71, 80, 51] Generated Node #0,2: 43:[71, 80, 51] Operation: 79-28=51 Exploring Operation: 71-28=43, Resulting Numbers: [79, 80, 43] Generated Node #0,3: 43:[79, 80, 43] Operation: 71-28=43 Moving to Node #0,1 Current State: 43:[79, 71, 52], Operations: ['80-28=52'] Exploring Operation: 71-52=19, Resulting Numbers: [79, 19] Generated Node #0,1,0: 43:[79, 19] Operation: 71-52=19 Exploring Operation: 79+71=150, Resulting Numbers: [52, 150] Generated Node #0,1,1: 43:[52, 150] Operation: 79+71=150 Exploring Operation: 79-71=8, Resulting Numbers: [52, 8] Generated Node #0,1,2: 43:[52, 8] Operation: 79-71=8 Exploring Operation: 79-52=27, Resulting Numbers: [71, 27] Generated Node #0,1,3: 43:[71, 27] Operation: 79-52=27 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[52, 8], Operations: ['80-28=52', '79-71=8'] Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,43 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 #0,1,3 Current State: 43:[71, 27], Operations: ['80-28=52', '79-52=27'] Exploring Operation: 71-27=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 71+27=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 71*27=1917, Resulting Numbers: [1917] 1917,43 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 #0,1,0 Current State: 43:[79, 19], Operations: ['80-28=52', '71-52=19'] Exploring Operation: 79*19=1501, Resulting Numbers: [1501] 1501,43 unequal: No Solution Exploring Operation: 79+19=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,43 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 #0,1,1 Current State: 43:[52, 150], Operations: ['80-28=52', '79+71=150'] Exploring Operation: 52*150=7800, Resulting Numbers: [7800] 7800,43 unequal: No Solution Exploring Operation: 52+150=202, Resulting Numbers: [202] 202,43 unequal: No Solution Exploring Operation: 150-52=98, Resulting Numbers: [98] 98,43 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: 43:[79, 80, 43], Operations: ['71-28=43'] Exploring Operation: 79-43=36, Resulting Numbers: [80, 36] Generated Node #0,3,0: 43:[80, 36] Operation: 79-43=36 Exploring Operation: 79+80=159, Resulting Numbers: [43, 159] Generated Node #0,3,1: 43:[43, 159] Operation: 79+80=159 Exploring Operation: 80-79=1, Resulting Numbers: [43, 1] Generated Node #0,3,2: 43:[43, 1] Operation: 80-79=1 Exploring Operation: 80-43=37, Resulting Numbers: [79, 37] Generated Node #0,3,3: 43:[79, 37] Operation: 80-43=37 Moving to Node #0,2 Current State: 43:[71, 80, 51], Operations: ['79-28=51'] Exploring Operation: 71-51=20, Resulting Numbers: [80, 20] Generated Node #0,2,0: 43:[80, 20] Operation: 71-51=20 Exploring Operation: 71+80=151, Resulting Numbers: [51, 151] Generated Node #0,2,1: 43:[51, 151] Operation: 71+80=151 Exploring Operation: 80-71=9, Resulting Numbers: [51, 9] Generated Node #0,2,2: 43:[51, 9] Operation: 80-71=9 Exploring Operation: 80-51=29, Resulting Numbers: [71, 29] Generated Node #0,2,3: 43:[71, 29] Operation: 80-51=29 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[51, 9], Operations: ['79-28=51', '80-71=9'] Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,43 unequal: No Solution Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,43 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 #0,2,3 Current State: 43:[71, 29], Operations: ['79-28=51', '80-51=29'] Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,43 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,43 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 #0,2,0 Current State: 43:[80, 20], Operations: ['79-28=51', '71-51=20'] Exploring Operation: 80*20=1600, Resulting Numbers: [1600] 1600,43 unequal: No Solution Exploring Operation: 80+20=100, Resulting Numbers: [100] 100,43 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,43 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 #0,2,1 Current State: 43:[51, 151], Operations: ['79-28=51', '71+80=151'] Exploring Operation: 151-51=100, Resulting Numbers: [100] 100,43 unequal: No Solution Exploring Operation: 51+151=202, Resulting Numbers: [202] 202,43 unequal: No Solution Exploring Operation: 51*151=7701, Resulting Numbers: [7701] 7701,43 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: 43:[71, 28, 1], Operations: ['80-79=1'] Exploring Operation: 28+1=29, Resulting Numbers: [71, 29] Generated Node #0,0,0: 43:[71, 29] Operation: 28+1=29 Exploring Operation: 71-1=70, Resulting Numbers: [28, 70] Generated Node #0,0,1: 43:[28, 70] Operation: 71-1=70 Exploring Operation: 71*1=71, Resulting Numbers: [28, 71] Generated Node #0,0,2: 43:[28, 71] Operation: 71*1=71 Exploring Operation: 71-28=43, Resulting Numbers: [1, 43] Generated Node #0,0,3: 43:[1, 43] Operation: 71-28=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[71, 29], Operations: ['80-79=1', '28+1=29'] Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,43 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,43 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 #0,0,1 Current State: 43:[28, 70], Operations: ['80-79=1', '71-1=70'] Exploring Operation: 28*70=1960, Resulting Numbers: [1960] 1960,43 unequal: No Solution Exploring Operation: 28+70=98, Resulting Numbers: [98] 98,43 unequal: No Solution Exploring Operation: 70-28=42, Resulting Numbers: [42] 42,43 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 #0,0,3 Current State: 43:[1, 43], Operations: ['80-79=1', '71-28=43'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[79, 71, 28, 80], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [71, 28, 1] Generated Node #0,0: 43:[71, 28, 1] Operation: 80-79=1 Moving to Node #0,0 Current State: 43:[71, 28, 1], Operations: ['80-79=1'] Exploring Operation: 71-28=43, Resulting Numbers: [1, 43] Generated Node #0,0,3: 43:[1, 43] Operation: 71-28=43 Moving to Node #0,0,3 Current State: 43:[1, 43], Operations: ['80-79=1', '71-28=43'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_4
sum_heuristic
[ 99, 53, 5, 87 ]
70
[ "99+53=152", "87-5=82", "152-82=70" ]
Current State: 70:[99, 53, 5, 87], Operations: [] Exploring Operation: 99+53=152, Resulting Numbers: [5, 87, 152] Generated Node #2: [5, 87, 152] from Operation: 99+53=152 Current State: 70:[5, 87, 152], Operations: ['99+53=152'] Exploring Operation: 87-5=82, Resulting Numbers: [152, 82] Generated Node #3: [152, 82] from Operation: 87-5=82 Current State: 70:[152, 82], Operations: ['99+53=152', '87-5=82'] Exploring Operation: 152-82=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[99, 53, 5, 87], Operations: [] Exploring Operation: 99-53=46, Resulting Numbers: [5, 87, 46] Generated Node #0,0: 70:[5, 87, 46] Operation: 99-53=46 Exploring Operation: 87-53=34, Resulting Numbers: [99, 5, 34] Generated Node #0,1: 70:[99, 5, 34] Operation: 87-53=34 Exploring Operation: 99-87=12, Resulting Numbers: [53, 5, 12] Generated Node #0,2: 70:[53, 5, 12] Operation: 99-87=12 Moving to Node #0,2 Current State: 70:[53, 5, 12], Operations: ['99-87=12'] Exploring Operation: 53+12=65, Resulting Numbers: [5, 65] Generated Node #0,2,0: 70:[5, 65] Operation: 53+12=65 Exploring Operation: 53-12=41, Resulting Numbers: [5, 41] Generated Node #0,2,1: 70:[5, 41] Operation: 53-12=41 Exploring Operation: 53+5=58, Resulting Numbers: [12, 58] Generated Node #0,2,2: 70:[12, 58] Operation: 53+5=58 Moving to Node #0,0 Current State: 70:[5, 87, 46], Operations: ['99-53=46'] Exploring Operation: 46-5=41, Resulting Numbers: [87, 41] Generated Node #0,0,0: 70:[87, 41] Operation: 46-5=41 Exploring Operation: 87-5=82, Resulting Numbers: [46, 82] Generated Node #0,0,1: 70:[46, 82] Operation: 87-5=82 Exploring Operation: 87-46=41, Resulting Numbers: [5, 41] Generated Node #0,0,2: 70:[5, 41] Operation: 87-46=41 Moving to Node #0,1 Current State: 70:[99, 5, 34], Operations: ['87-53=34'] Exploring Operation: 99-5=94, Resulting Numbers: [34, 94] Generated Node #0,1,0: 70:[34, 94] Operation: 99-5=94 Exploring Operation: 99-34=65, Resulting Numbers: [5, 65] Generated Node #0,1,1: 70:[5, 65] Operation: 99-34=65 Exploring Operation: 5+34=39, Resulting Numbers: [99, 39] Generated Node #0,1,2: 70:[99, 39] Operation: 5+34=39 Moving to Node #0,2,0 Current State: 70:[5, 65], Operations: ['99-87=12', '53+12=65'] Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,70 unequal: No Solution Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[99, 53, 5, 87], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [53, 5, 12] Generated Node #0,2: 70:[53, 5, 12] Operation: 99-87=12 Moving to Node #0,2 Current State: 70:[53, 5, 12], Operations: ['99-87=12'] Exploring Operation: 53+12=65, Resulting Numbers: [5, 65] Generated Node #0,2,0: 70:[5, 65] Operation: 53+12=65 Moving to Node #0,2,0 Current State: 70:[5, 65], Operations: ['99-87=12', '53+12=65'] Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 54, 27, 50, 14 ]
62
[ "54/27=2", "50+14=64", "64-2=62" ]
Current State: 62:[54, 27, 50, 14], Operations: [] Exploring Operation: 54/27=2, Resulting Numbers: [50, 14, 2] Generated Node #2: [50, 14, 2] from Operation: 54/27=2 Current State: 62:[50, 14, 2], Operations: ['54/27=2'] Exploring Operation: 50+14=64, Resulting Numbers: [2, 64] Generated Node #3: [2, 64] from Operation: 50+14=64 Current State: 62:[2, 64], Operations: ['54/27=2', '50+14=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[54, 27, 50, 14], Operations: [] Exploring Operation: 54-50=4, Resulting Numbers: [27, 14, 4] Generated Node #0,0: 62:[27, 14, 4] Operation: 54-50=4 Exploring Operation: 50+14=64, Resulting Numbers: [54, 27, 64] Generated Node #0,1: 62:[54, 27, 64] Operation: 50+14=64 Exploring Operation: 50-14=36, Resulting Numbers: [54, 27, 36] Generated Node #0,2: 62:[54, 27, 36] Operation: 50-14=36 Moving to Node #0,1 Current State: 62:[54, 27, 64], Operations: ['50+14=64'] Exploring Operation: 64-54=10, Resulting Numbers: [27, 10] Generated Node #0,1,0: 62:[27, 10] Operation: 64-54=10 Exploring Operation: 54-27=27, Resulting Numbers: [64, 27] Generated Node #0,1,1: 62:[64, 27] Operation: 54-27=27 Exploring Operation: 54/27=2, Resulting Numbers: [64, 2] Generated Node #0,1,2: 62:[64, 2] Operation: 54/27=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[64, 2], Operations: ['50+14=64', '54/27=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[54, 27, 50, 14], Operations: [] Exploring Operation: 50+14=64, Resulting Numbers: [54, 27, 64] Generated Node #0,1: 62:[54, 27, 64] Operation: 50+14=64 Moving to Node #0,1 Current State: 62:[54, 27, 64], Operations: ['50+14=64'] Exploring Operation: 54/27=2, Resulting Numbers: [64, 2] Generated Node #0,1,2: 62:[64, 2] Operation: 54/27=2 Moving to Node #0,1,2 Current State: 62:[64, 2], Operations: ['50+14=64', '54/27=2'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 54, 38, 27, 32 ]
36
[ "38-32=6", "54/6=9", "27+9=36" ]
Current State: 36:[54, 38, 27, 32], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [54, 27, 6] Generated Node #2: [54, 27, 6] from Operation: 38-32=6 Current State: 36:[54, 27, 6], Operations: ['38-32=6'] Exploring Operation: 54/6=9, Resulting Numbers: [27, 9] Generated Node #3: [27, 9] from Operation: 54/6=9 Current State: 36:[27, 9], Operations: ['38-32=6', '54/6=9'] Exploring Operation: 27+9=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[54, 38, 27, 32], Operations: [] Exploring Operation: 54-38=16, Resulting Numbers: [27, 32, 16] Generated Node #0,0: 36:[27, 32, 16] Operation: 54-38=16 Exploring Operation: 54/27=2, Resulting Numbers: [38, 32, 2] Generated Node #0,1: 36:[38, 32, 2] Operation: 54/27=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[38, 32, 2], Operations: ['54/27=2'] Exploring Operation: 38-32=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 36:[2, 6] Operation: 38-32=6 Exploring Operation: 38-2=36, Resulting Numbers: [32, 36] Generated Node #0,1,1: 36:[32, 36] Operation: 38-2=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 36:[2, 6], Operations: ['54/27=2', '38-32=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 36:[32, 36], Operations: ['54/27=2', '38-2=36'] Exploring Operation: 32+36=68, Resulting Numbers: [68] 68,36 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[27, 32, 16], Operations: ['54-38=16'] Exploring Operation: 27-16=11, Resulting Numbers: [32, 11] Generated Node #0,0,0: 36:[32, 11] Operation: 27-16=11 Exploring Operation: 32-27=5, Resulting Numbers: [16, 5] Generated Node #0,0,1: 36:[16, 5] Operation: 32-27=5 Moving to Node #0,0,1 Current State: 36:[16, 5], Operations: ['54-38=16', '32-27=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,36 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[32, 11], Operations: ['54-38=16', '27-16=11'] Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,36 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,36 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
[ 57, 4, 39, 8 ]
67
[ "39-8=31", "4*31=124", "124-57=67" ]
Current State: 67:[57, 4, 39, 8], Operations: [] Exploring Operation: 39-8=31, Resulting Numbers: [57, 4, 31] Generated Node #2: [57, 4, 31] from Operation: 39-8=31 Current State: 67:[57, 4, 31], Operations: ['39-8=31'] Exploring Operation: 4*31=124, Resulting Numbers: [57, 124] Generated Node #3: [57, 124] from Operation: 4*31=124 Current State: 67:[57, 124], Operations: ['39-8=31', '4*31=124'] Exploring Operation: 124-57=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[57, 4, 39, 8], Operations: [] Exploring Operation: 4*8=32, Resulting Numbers: [57, 39, 32] Generated Node #0,0: 67:[57, 39, 32] Operation: 4*8=32 Moving to Node #0,0 Current State: 67:[57, 39, 32], Operations: ['4*8=32'] Exploring Operation: 39+32=71, Resulting Numbers: [57, 71] Generated Node #0,0,0: 67:[57, 71] Operation: 39+32=71 Moving to Node #0,0,0 Current State: 67:[57, 71], Operations: ['4*8=32', '39+32=71'] Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,67 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 29, 65, 59, 8 ]
31
[ "65-29=36", "59+8=67", "67-36=31" ]
Current State: 31:[29, 65, 59, 8], Operations: [] Exploring Operation: 65-29=36, Resulting Numbers: [59, 8, 36] Generated Node #2: [59, 8, 36] from Operation: 65-29=36 Current State: 31:[59, 8, 36], Operations: ['65-29=36'] Exploring Operation: 59+8=67, Resulting Numbers: [36, 67] Generated Node #3: [36, 67] from Operation: 59+8=67 Current State: 31:[36, 67], Operations: ['65-29=36', '59+8=67'] Exploring Operation: 67-36=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[29, 65, 59, 8], Operations: [] Exploring Operation: 65-29=36, Resulting Numbers: [59, 8, 36] Generated Node #0,0: 31:[59, 8, 36] Operation: 65-29=36 Exploring Operation: 65-59=6, Resulting Numbers: [29, 8, 6] Generated Node #0,1: 31:[29, 8, 6] Operation: 65-59=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[29, 8, 6], Operations: ['65-59=6'] Exploring Operation: 8+6=14, Resulting Numbers: [29, 14] Generated Node #0,1,0: 31:[29, 14] Operation: 8+6=14 Exploring Operation: 8*6=48, Resulting Numbers: [29, 48] Generated Node #0,1,1: 31:[29, 48] Operation: 8*6=48 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 31:[29, 14], Operations: ['65-59=6', '8+6=14'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,31 unequal: No Solution No 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: 31:[29, 48], Operations: ['65-59=6', '8*6=48'] Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,31 unequal: No Solution Exploring Operation: 29+48=77, Resulting Numbers: [77] 77,31 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: 31:[59, 8, 36], Operations: ['65-29=36'] Exploring Operation: 59-36=23, Resulting Numbers: [8, 23] Generated Node #0,0,0: 31:[8, 23] Operation: 59-36=23 Exploring Operation: 59-8=51, Resulting Numbers: [36, 51] Generated Node #0,0,1: 31:[36, 51] Operation: 59-8=51 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[36, 51], Operations: ['65-29=36', '59-8=51'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 36+51=87, Resulting Numbers: [87] 87,31 unequal: No Solution No 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: 31:[8, 23], Operations: ['65-29=36', '59-36=23'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[29, 65, 59, 8], Operations: [] Exploring Operation: 65-29=36, Resulting Numbers: [59, 8, 36] Generated Node #0,0: 31:[59, 8, 36] Operation: 65-29=36 Moving to Node #0,0 Current State: 31:[59, 8, 36], Operations: ['65-29=36'] Exploring Operation: 59-36=23, Resulting Numbers: [8, 23] Generated Node #0,0,0: 31:[8, 23] Operation: 59-36=23 Moving to Node #0,0,0 Current State: 31:[8, 23], Operations: ['65-29=36', '59-36=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 51, 45, 45, 23 ]
73
[ "51+23=74", "45/45=1", "74-1=73" ]
Current State: 73:[51, 45, 45, 23], Operations: [] Exploring Operation: 51+23=74, Resulting Numbers: [45, 45, 74] Generated Node #2: [45, 45, 74] from Operation: 51+23=74 Current State: 73:[45, 45, 74], Operations: ['51+23=74'] Exploring Operation: 45/45=1, Resulting Numbers: [74, 1] Generated Node #3: [74, 1] from Operation: 45/45=1 Current State: 73:[74, 1], Operations: ['51+23=74', '45/45=1'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[51, 45, 45, 23], Operations: [] Exploring Operation: 45+23=68, Resulting Numbers: [51, 45, 68] Generated Node #0,0: 73:[51, 45, 68] Operation: 45+23=68 Moving to Node #0,0 Current State: 73:[51, 45, 68], Operations: ['45+23=68'] Exploring Operation: 51+45=96, Resulting Numbers: [68, 96] Generated Node #0,0,0: 73:[68, 96] Operation: 51+45=96 Moving to Node #0,0,0 Current State: 73:[68, 96], Operations: ['45+23=68', '51+45=96'] Exploring Operation: 96-68=28, Resulting Numbers: [28] 28,73 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 15, 62, 45, 31 ]
63
[ "15+62=77", "45-31=14", "77-14=63" ]
Current State: 63:[15, 62, 45, 31], Operations: [] Exploring Operation: 15+62=77, Resulting Numbers: [45, 31, 77] Generated Node #2: [45, 31, 77] from Operation: 15+62=77 Current State: 63:[45, 31, 77], Operations: ['15+62=77'] Exploring Operation: 45-31=14, Resulting Numbers: [77, 14] Generated Node #3: [77, 14] from Operation: 45-31=14 Current State: 63:[77, 14], Operations: ['15+62=77', '45-31=14'] Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[15, 62, 45, 31], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [62, 31, 3] Generated Node #0,0: 63:[62, 31, 3] Operation: 45/15=3 Exploring Operation: 45-31=14, Resulting Numbers: [15, 62, 14] Generated Node #0,1: 63:[15, 62, 14] Operation: 45-31=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[62, 31, 3], Operations: ['45/15=3'] Exploring Operation: 31-3=28, Resulting Numbers: [62, 28] Generated Node #0,0,0: 63:[62, 28] Operation: 31-3=28 Exploring Operation: 62/31=2, Resulting Numbers: [3, 2] Generated Node #0,0,1: 63:[3, 2] Operation: 62/31=2 Moving to Node #0,0,1 Current State: 63:[3, 2], Operations: ['45/15=3', '62/31=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[62, 28], Operations: ['45/15=3', '31-3=28'] Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,63 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[15, 62, 14], Operations: ['45-31=14'] Exploring Operation: 15+14=29, Resulting Numbers: [62, 29] Generated Node #0,1,0: 63:[62, 29] Operation: 15+14=29 Exploring Operation: 15-14=1, Resulting Numbers: [62, 1] Generated Node #0,1,1: 63:[62, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[62, 1], Operations: ['45-31=14', '15-14=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[15, 62, 45, 31], Operations: [] Exploring Operation: 45-31=14, Resulting Numbers: [15, 62, 14] Generated Node #0,1: 63:[15, 62, 14] Operation: 45-31=14 Moving to Node #0,1 Current State: 63:[15, 62, 14], Operations: ['45-31=14'] Exploring Operation: 15-14=1, Resulting Numbers: [62, 1] Generated Node #0,1,1: 63:[62, 1] Operation: 15-14=1 Moving to Node #0,1,1 Current State: 63:[62, 1], Operations: ['45-31=14', '15-14=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 53, 5, 59, 81 ]
36
[ "53+5=58", "81-59=22", "58-22=36" ]
Current State: 36:[53, 5, 59, 81], Operations: [] Exploring Operation: 53+5=58, Resulting Numbers: [59, 81, 58] Generated Node #2: [59, 81, 58] from Operation: 53+5=58 Current State: 36:[59, 81, 58], Operations: ['53+5=58'] Exploring Operation: 81-59=22, Resulting Numbers: [58, 22] Generated Node #3: [58, 22] from Operation: 81-59=22 Current State: 36:[58, 22], Operations: ['53+5=58', '81-59=22'] Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[53, 5, 59, 81], Operations: [] Exploring Operation: 81-53=28, Resulting Numbers: [5, 59, 28] Generated Node #0,0: 36:[5, 59, 28] Operation: 81-53=28 Exploring Operation: 81-59=22, Resulting Numbers: [53, 5, 22] Generated Node #0,1: 36:[53, 5, 22] Operation: 81-59=22 Exploring Operation: 59-53=6, Resulting Numbers: [5, 81, 6] Generated Node #0,2: 36:[5, 81, 6] Operation: 59-53=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[53, 5, 22], Operations: ['81-59=22'] Exploring Operation: 22-5=17, Resulting Numbers: [53, 17] Generated Node #0,1,0: 36:[53, 17] Operation: 22-5=17 Exploring Operation: 53-5=48, Resulting Numbers: [22, 48] Generated Node #0,1,1: 36:[22, 48] Operation: 53-5=48 Exploring Operation: 53-22=31, Resulting Numbers: [5, 31] Generated Node #0,1,2: 36:[5, 31] Operation: 53-22=31 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 36:[5, 31], Operations: ['81-59=22', '53-22=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,36 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,36 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[53, 5, 59, 81], Operations: [] Exploring Operation: 81-59=22, Resulting Numbers: [53, 5, 22] Generated Node #0,1: 36:[53, 5, 22] Operation: 81-59=22 Moving to Node #0,1 Current State: 36:[53, 5, 22], Operations: ['81-59=22'] Exploring Operation: 53-22=31, Resulting Numbers: [5, 31] Generated Node #0,1,2: 36:[5, 31] Operation: 53-22=31 Moving to Node #0,1,2 Current State: 36:[5, 31], Operations: ['81-59=22', '53-22=31'] Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 4, 41, 90, 31 ]
84
[ "41-4=37", "90+31=121", "121-37=84" ]
Current State: 84:[4, 41, 90, 31], Operations: [] Exploring Operation: 41-4=37, Resulting Numbers: [90, 31, 37] Generated Node #2: [90, 31, 37] from Operation: 41-4=37 Current State: 84:[90, 31, 37], Operations: ['41-4=37'] Exploring Operation: 90+31=121, Resulting Numbers: [37, 121] Generated Node #3: [37, 121] from Operation: 90+31=121 Current State: 84:[37, 121], Operations: ['41-4=37', '90+31=121'] Exploring Operation: 121-37=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[4, 41, 90, 31], Operations: [] Exploring Operation: 90-41=49, Resulting Numbers: [4, 31, 49] Generated Node #0,0: 84:[4, 31, 49] Operation: 90-41=49 Exploring Operation: 4+41=45, Resulting Numbers: [90, 31, 45] Generated Node #0,1: 84:[90, 31, 45] Operation: 4+41=45 Exploring Operation: 31-4=27, Resulting Numbers: [41, 90, 27] Generated Node #0,2: 84:[41, 90, 27] Operation: 31-4=27 Exploring Operation: 90-4=86, Resulting Numbers: [41, 31, 86] Generated Node #0,3: 84:[41, 31, 86] Operation: 90-4=86 Exploring Operation: 41-31=10, Resulting Numbers: [4, 90, 10] Generated Node #0,4: 84:[4, 90, 10] Operation: 41-31=10 Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[41, 31, 86], Operations: ['90-4=86'] Exploring Operation: 31+86=117, Resulting Numbers: [41, 117] Generated Node #0,3,0: 84:[41, 117] Operation: 31+86=117 Exploring Operation: 86-31=55, Resulting Numbers: [41, 55] Generated Node #0,3,1: 84:[41, 55] Operation: 86-31=55 Exploring Operation: 41-31=10, Resulting Numbers: [86, 10] Generated Node #0,3,2: 84:[86, 10] Operation: 41-31=10 Exploring Operation: 41+31=72, Resulting Numbers: [86, 72] Generated Node #0,3,3: 84:[86, 72] Operation: 41+31=72 Exploring Operation: 86-41=45, Resulting Numbers: [31, 45] Generated Node #0,3,4: 84:[31, 45] Operation: 86-41=45 Moving to Node #0,3,2 Current State: 84:[86, 10], Operations: ['90-4=86', '41-31=10'] Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,84 unequal: No Solution Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,84 unequal: No Solution Moving to Node #0,3,4 Current State: 84:[31, 45], Operations: ['90-4=86', '86-41=45'] Exploring Operation: 31*45=1395, Resulting Numbers: [1395] 1395,84 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,84 unequal: No Solution Moving to Node #0,3,1 Current State: 84:[41, 55], Operations: ['90-4=86', '86-31=55'] Exploring Operation: 41+55=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 55-41=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 41*55=2255, Resulting Numbers: [2255] 2255,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[86, 72], Operations: ['90-4=86', '41+31=72'] Exploring Operation: 86+72=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 86-72=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 86*72=6192, Resulting Numbers: [6192] 6192,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[41, 117], Operations: ['90-4=86', '31+86=117'] Exploring Operation: 41*117=4797, Resulting Numbers: [4797] 4797,84 unequal: No Solution Exploring Operation: 41+117=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 117-41=76, Resulting Numbers: [76] 76,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[41, 90, 27], Operations: ['31-4=27'] Exploring Operation: 90-27=63, Resulting Numbers: [41, 63] Generated Node #0,2,0: 84:[41, 63] Operation: 90-27=63 Exploring Operation: 41+27=68, Resulting Numbers: [90, 68] Generated Node #0,2,1: 84:[90, 68] Operation: 41+27=68 Exploring Operation: 90+27=117, Resulting Numbers: [41, 117] Generated Node #0,2,2: 84:[41, 117] Operation: 90+27=117 Exploring Operation: 90-41=49, Resulting Numbers: [27, 49] Generated Node #0,2,3: 84:[27, 49] Operation: 90-41=49 Exploring Operation: 41-27=14, Resulting Numbers: [90, 14] Generated Node #0,2,4: 84:[90, 14] Operation: 41-27=14 Moving to Node #0,2,4 Current State: 84:[90, 14], Operations: ['31-4=27', '41-27=14'] Exploring Operation: 90+14=104, Resulting Numbers: [104] 104,84 unequal: No Solution Exploring Operation: 90*14=1260, Resulting Numbers: [1260] 1260,84 unequal: No Solution Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[27, 49], Operations: ['31-4=27', '90-41=49'] Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,84 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[41, 63], Operations: ['31-4=27', '90-27=63'] Exploring Operation: 41*63=2583, Resulting Numbers: [2583] 2583,84 unequal: No Solution Exploring Operation: 41+63=104, Resulting Numbers: [104] 104,84 unequal: No Solution Exploring Operation: 63-41=22, Resulting Numbers: [22] 22,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[90, 68], Operations: ['31-4=27', '41+27=68'] Exploring Operation: 90+68=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 90-68=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 90*68=6120, Resulting Numbers: [6120] 6120,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[41, 117], Operations: ['31-4=27', '90+27=117'] Exploring Operation: 117-41=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 41+117=158, Resulting Numbers: [158] 158,84 unequal: No Solution Exploring Operation: 41*117=4797, Resulting Numbers: [4797] 4797,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 84:[4, 90, 10], Operations: ['41-31=10'] Exploring Operation: 4+10=14, Resulting Numbers: [90, 14] Generated Node #0,4,0: 84:[90, 14] Operation: 4+10=14 Exploring Operation: 10-4=6, Resulting Numbers: [90, 6] Generated Node #0,4,1: 84:[90, 6] Operation: 10-4=6 Exploring Operation: 90/10=9, Resulting Numbers: [4, 9] Generated Node #0,4,2: 84:[4, 9] Operation: 90/10=9 Exploring Operation: 90-10=80, Resulting Numbers: [4, 80] Generated Node #0,4,3: 84:[4, 80] Operation: 90-10=80 Exploring Operation: 90-4=86, Resulting Numbers: [10, 86] Generated Node #0,4,4: 84:[10, 86] Operation: 90-4=86 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 84:[4, 9], Operations: ['41-31=10', '90/10=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,84 unequal: No Solution No 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: 84:[4, 80], Operations: ['41-31=10', '90-10=80'] Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[4, 41, 90, 31], Operations: [] Exploring Operation: 41-31=10, Resulting Numbers: [4, 90, 10] Generated Node #0,4: 84:[4, 90, 10] Operation: 41-31=10 Moving to Node #0,4 Current State: 84:[4, 90, 10], Operations: ['41-31=10'] Exploring Operation: 90-10=80, Resulting Numbers: [4, 80] Generated Node #0,4,3: 84:[4, 80] Operation: 90-10=80 Moving to Node #0,4,3 Current State: 84:[4, 80], Operations: ['41-31=10', '90-10=80'] Exploring Operation: 4+80=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 42, 34, 52, 54 ]
39
[ "52-34=18", "54/18=3", "42-3=39" ]
Current State: 39:[42, 34, 52, 54], Operations: [] Exploring Operation: 52-34=18, Resulting Numbers: [42, 54, 18] Generated Node #2: [42, 54, 18] from Operation: 52-34=18 Current State: 39:[42, 54, 18], Operations: ['52-34=18'] Exploring Operation: 54/18=3, Resulting Numbers: [42, 3] Generated Node #3: [42, 3] from Operation: 54/18=3 Current State: 39:[42, 3], Operations: ['52-34=18', '54/18=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[42, 34, 52, 54], Operations: [] Exploring Operation: 52-42=10, Resulting Numbers: [34, 54, 10] Generated Node #0,0: 39:[34, 54, 10] Operation: 52-42=10 Exploring Operation: 54-42=12, Resulting Numbers: [34, 52, 12] Generated Node #0,1: 39:[34, 52, 12] Operation: 54-42=12 Exploring Operation: 54-52=2, Resulting Numbers: [42, 34, 2] Generated Node #0,2: 39:[42, 34, 2] Operation: 54-52=2 Moving to Node #0,2 Current State: 39:[42, 34, 2], Operations: ['54-52=2'] Exploring Operation: 34+2=36, Resulting Numbers: [42, 36] Generated Node #0,2,0: 39:[42, 36] Operation: 34+2=36 Exploring Operation: 42-2=40, Resulting Numbers: [34, 40] Generated Node #0,2,1: 39:[34, 40] Operation: 42-2=40 Exploring Operation: 42-34=8, Resulting Numbers: [2, 8] Generated Node #0,2,2: 39:[2, 8] Operation: 42-34=8 Moving to Node #0,1 Current State: 39:[34, 52, 12], Operations: ['54-42=12'] Exploring Operation: 52-34=18, Resulting Numbers: [12, 18] Generated Node #0,1,0: 39:[12, 18] Operation: 52-34=18 Exploring Operation: 52-12=40, Resulting Numbers: [34, 40] Generated Node #0,1,1: 39:[34, 40] Operation: 52-12=40 Exploring Operation: 34+12=46, Resulting Numbers: [52, 46] Generated Node #0,1,2: 39:[52, 46] Operation: 34+12=46 Moving to Node #0,0 Current State: 39:[34, 54, 10], Operations: ['52-42=10'] Exploring Operation: 54-34=20, Resulting Numbers: [10, 20] Generated Node #0,0,0: 39:[10, 20] Operation: 54-34=20 Exploring Operation: 34+10=44, Resulting Numbers: [54, 44] Generated Node #0,0,1: 39:[54, 44] Operation: 34+10=44 Exploring Operation: 54-10=44, Resulting Numbers: [34, 44] Generated Node #0,0,2: 39:[34, 44] Operation: 54-10=44 Moving to Node #0,2,0 Current State: 39:[42, 36], Operations: ['54-52=2', '34+2=36'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,39 unequal: No Solution Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[2, 8], Operations: ['54-52=2', '42-34=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,39 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[34, 40], Operations: ['54-52=2', '42-2=40'] Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,39 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[34, 40], Operations: ['54-42=12', '52-12=40'] Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,39 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[12, 18], Operations: ['54-42=12', '52-34=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,39 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[10, 20], Operations: ['52-42=10', '54-34=20'] Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[34, 44], Operations: ['52-42=10', '54-10=44'] Exploring Operation: 34*44=1496, Resulting Numbers: [1496] 1496,39 unequal: No Solution Exploring Operation: 34+44=78, Resulting Numbers: [78] 78,39 unequal: No Solution Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[54, 44], Operations: ['52-42=10', '34+10=44'] Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,39 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,39 unequal: No Solution Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[52, 46], Operations: ['54-42=12', '34+12=46'] Exploring Operation: 52-46=6, Resulting Numbers: [6] 6,39 unequal: No Solution Exploring Operation: 52*46=2392, Resulting Numbers: [2392] 2392,39 unequal: No Solution Exploring Operation: 52+46=98, Resulting Numbers: [98] 98,39 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 17, 4, 31, 74 ]
62
[ "17+31=48", "48/4=12", "74-12=62" ]
Current State: 62:[17, 4, 31, 74], Operations: [] Exploring Operation: 17+31=48, Resulting Numbers: [4, 74, 48] Generated Node #2: [4, 74, 48] from Operation: 17+31=48 Current State: 62:[4, 74, 48], Operations: ['17+31=48'] Exploring Operation: 48/4=12, Resulting Numbers: [74, 12] Generated Node #3: [74, 12] from Operation: 48/4=12 Current State: 62:[74, 12], Operations: ['17+31=48', '48/4=12'] Exploring Operation: 74-12=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[17, 4, 31, 74], Operations: [] Exploring Operation: 74-17=57, Resulting Numbers: [4, 31, 57] Generated Node #0,0: 62:[4, 31, 57] Operation: 74-17=57 Exploring Operation: 17*4=68, Resulting Numbers: [31, 74, 68] Generated Node #0,1: 62:[31, 74, 68] Operation: 17*4=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[4, 31, 57], Operations: ['74-17=57'] Exploring Operation: 57-31=26, Resulting Numbers: [4, 26] Generated Node #0,0,0: 62:[4, 26] Operation: 57-31=26 Exploring Operation: 4+57=61, Resulting Numbers: [31, 61] Generated Node #0,0,1: 62:[31, 61] Operation: 4+57=61 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[31, 61], Operations: ['74-17=57', '4+57=61'] Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,62 unequal: No Solution No 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: 62:[4, 26], Operations: ['74-17=57', '57-31=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,62 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,62 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: 62:[31, 74, 68], Operations: ['17*4=68'] Exploring Operation: 74-31=43, Resulting Numbers: [68, 43] Generated Node #0,1,0: 62:[68, 43] Operation: 74-31=43 Exploring Operation: 74-68=6, Resulting Numbers: [31, 6] Generated Node #0,1,1: 62:[31, 6] Operation: 74-68=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[31, 6], Operations: ['17*4=68', '74-68=6'] Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,62 unequal: No Solution No 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: 62:[68, 43], Operations: ['17*4=68', '74-31=43'] Exploring Operation: 68+43=111, Resulting Numbers: [111] 111,62 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic