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
[ 84, 68, 4, 63 ]
55
[ "68*63=4284", "4284/84=51", "4+51=55" ]
Current State: 55:[84, 68, 4, 63], Operations: [] Exploring Operation: 68*63=4284, Resulting Numbers: [84, 4, 4284] Generated Node #2: [84, 4, 4284] from Operation: 68*63=4284 Current State: 55:[84, 4, 4284], Operations: ['68*63=4284'] Exploring Operation: 4284/84=51, Resulting Numbers: [4, 51] Generated Node #3: [4, 51] from Operation: 4284/84=51 Current State: 55:[4, 51], Operations: ['68*63=4284', '4284/84=51'] Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[84, 68, 4, 63], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [4, 63, 16] Generated Node #0,0: 55:[4, 63, 16] Operation: 84-68=16 Exploring Operation: 84-63=21, Resulting Numbers: [68, 4, 21] Generated Node #0,1: 55:[68, 4, 21] Operation: 84-63=21 Exploring Operation: 84/4=21, Resulting Numbers: [68, 63, 21] Generated Node #0,2: 55:[68, 63, 21] Operation: 84/4=21 Exploring Operation: 68-63=5, Resulting Numbers: [84, 4, 5] Generated Node #0,3: 55:[84, 4, 5] Operation: 68-63=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[4, 63, 16], Operations: ['84-68=16'] Exploring Operation: 63-4=59, Resulting Numbers: [16, 59] Generated Node #0,0,0: 55:[16, 59] Operation: 63-4=59 Exploring Operation: 16-4=12, Resulting Numbers: [63, 12] Generated Node #0,0,1: 55:[63, 12] Operation: 16-4=12 Exploring Operation: 63-16=47, Resulting Numbers: [4, 47] Generated Node #0,0,2: 55:[4, 47] Operation: 63-16=47 Exploring Operation: 16/4=4, Resulting Numbers: [63, 4] Generated Node #0,0,3: 55:[63, 4] Operation: 16/4=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[16, 59], Operations: ['84-68=16', '63-4=59'] Exploring Operation: 59-16=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 16+59=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 16*59=944, Resulting Numbers: [944] 944,55 unequal: No Solution No 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: 55:[63, 12], Operations: ['84-68=16', '16-4=12'] Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 63*12=756, Resulting Numbers: [756] 756,55 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,55 unequal: No Solution No 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: 55:[4, 47], Operations: ['84-68=16', '63-16=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,55 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,55 unequal: No Solution No 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: 55:[63, 4], Operations: ['84-68=16', '16/4=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,55 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,55 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,55 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: 55:[68, 4, 21], Operations: ['84-63=21'] Exploring Operation: 21-4=17, Resulting Numbers: [68, 17] Generated Node #0,1,0: 55:[68, 17] Operation: 21-4=17 Exploring Operation: 68/4=17, Resulting Numbers: [21, 17] Generated Node #0,1,1: 55:[21, 17] Operation: 68/4=17 Exploring Operation: 68-21=47, Resulting Numbers: [4, 47] Generated Node #0,1,2: 55:[4, 47] Operation: 68-21=47 Exploring Operation: 68-4=64, Resulting Numbers: [21, 64] Generated Node #0,1,3: 55:[21, 64] Operation: 68-4=64 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[4, 47], Operations: ['84-63=21', '68-21=47'] Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,55 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,55 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,55 unequal: No Solution No 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: 55:[21, 17], Operations: ['84-63=21', '68/4=17'] Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,55 unequal: No Solution Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,55 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,55 unequal: No Solution No 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: 55:[68, 17], Operations: ['84-63=21', '21-4=17'] Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,55 unequal: No Solution Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,55 unequal: No Solution Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,55 unequal: No Solution No 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: 55:[21, 64], Operations: ['84-63=21', '68-4=64'] Exploring Operation: 64-21=43, Resulting Numbers: [43] 43,55 unequal: No Solution Exploring Operation: 21*64=1344, Resulting Numbers: [1344] 1344,55 unequal: No Solution Exploring Operation: 21+64=85, Resulting Numbers: [85] 85,55 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: 55:[84, 4, 5], Operations: ['68-63=5'] Exploring Operation: 84/4=21, Resulting Numbers: [5, 21] Generated Node #0,3,0: 55:[5, 21] Operation: 84/4=21 Exploring Operation: 84-5=79, Resulting Numbers: [4, 79] Generated Node #0,3,1: 55:[4, 79] Operation: 84-5=79 Exploring Operation: 4+5=9, Resulting Numbers: [84, 9] Generated Node #0,3,2: 55:[84, 9] Operation: 4+5=9 Exploring Operation: 84-4=80, Resulting Numbers: [5, 80] Generated Node #0,3,3: 55:[5, 80] Operation: 84-4=80 Moving to Node #0,3,0 Current State: 55:[5, 21], Operations: ['68-63=5', '84/4=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 5*21=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 5+21=26, Resulting Numbers: [26] 26,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[5, 80], Operations: ['68-63=5', '84-4=80'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,55 unequal: No Solution Exploring Operation: 5*80=400, Resulting Numbers: [400] 400,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[4, 79], Operations: ['68-63=5', '84-5=79'] Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,55 unequal: No Solution Exploring Operation: 4*79=316, Resulting Numbers: [316] 316,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[84, 9], Operations: ['68-63=5', '4+5=9'] Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,55 unequal: No Solution Exploring Operation: 84*9=756, Resulting Numbers: [756] 756,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[68, 63, 21], Operations: ['84/4=21'] Exploring Operation: 63/21=3, Resulting Numbers: [68, 3] Generated Node #0,2,0: 55:[68, 3] Operation: 63/21=3 Exploring Operation: 63-21=42, Resulting Numbers: [68, 42] Generated Node #0,2,1: 55:[68, 42] Operation: 63-21=42 Exploring Operation: 68-63=5, Resulting Numbers: [21, 5] Generated Node #0,2,2: 55:[21, 5] Operation: 68-63=5 Exploring Operation: 68-21=47, Resulting Numbers: [63, 47] Generated Node #0,2,3: 55:[63, 47] Operation: 68-21=47 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[21, 5], Operations: ['84/4=21', '68-63=5'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 21*5=105, Resulting Numbers: [105] 105,55 unequal: No Solution Exploring Operation: 21+5=26, Resulting Numbers: [26] 26,55 unequal: No Solution No 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: 55:[68, 3], Operations: ['84/4=21', '63/21=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,55 unequal: No Solution Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,55 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,55 unequal: No Solution No 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: 55:[63, 47], Operations: ['84/4=21', '68-21=47'] Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 63+47=110, Resulting Numbers: [110] 110,55 unequal: No Solution Exploring Operation: 63*47=2961, Resulting Numbers: [2961] 2961,55 unequal: No Solution No 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: 55:[68, 42], Operations: ['84/4=21', '63-21=42'] Exploring Operation: 68*42=2856, Resulting Numbers: [2856] 2856,55 unequal: No Solution Exploring Operation: 68+42=110, Resulting Numbers: [110] 110,55 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,55 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
[ 16, 16, 24, 28 ]
10
[ "16*16=256", "24+256=280", "280/28=10" ]
Current State: 10:[16, 16, 24, 28], Operations: [] Exploring Operation: 16*16=256, Resulting Numbers: [24, 28, 256] Generated Node #2: [24, 28, 256] from Operation: 16*16=256 Current State: 10:[24, 28, 256], Operations: ['16*16=256'] Exploring Operation: 24+256=280, Resulting Numbers: [28, 280] Generated Node #3: [28, 280] from Operation: 24+256=280 Current State: 10:[28, 280], Operations: ['16*16=256', '24+256=280'] Exploring Operation: 280/28=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[16, 16, 24, 28], Operations: [] Exploring Operation: 28-16=12, Resulting Numbers: [16, 24, 12] Generated Node #0,0: 10:[16, 24, 12] Operation: 28-16=12 Exploring Operation: 28-16=12, Resulting Numbers: [16, 24, 12] Generated Node #0,1: 10:[16, 24, 12] Operation: 28-16=12 Exploring Operation: 28-24=4, Resulting Numbers: [16, 16, 4] Generated Node #0,2: 10:[16, 16, 4] Operation: 28-24=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[16, 16, 4], Operations: ['28-24=4'] Exploring Operation: 16/4=4, Resulting Numbers: [16, 4] Generated Node #0,2,0: 10:[16, 4] Operation: 16/4=4 Exploring Operation: 16-16=0, Resulting Numbers: [4, 0] Generated Node #0,2,1: 10:[4, 0] Operation: 16-16=0 Exploring Operation: 16/16=1, Resulting Numbers: [4, 1] Generated Node #0,2,2: 10:[4, 1] Operation: 16/16=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 10:[4, 1], Operations: ['28-24=4', '16/16=1'] Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,10 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,10 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 #0,2,1 Current State: 10:[4, 0], Operations: ['28-24=4', '16-16=0'] Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,10 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 #0,2,0 Current State: 10:[16, 4], Operations: ['28-24=4', '16/4=4'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,10 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:[16, 24, 12], Operations: ['28-16=12'] Exploring Operation: 24-16=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 10:[12, 8] Operation: 24-16=8 Exploring Operation: 24-12=12, Resulting Numbers: [16, 12] Generated Node #0,0,1: 10:[16, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [16, 2] Generated Node #0,0,2: 10:[16, 2] Operation: 24/12=2 Moving to Node #0,0,0 Current State: 10:[12, 8], Operations: ['28-16=12', '24-16=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,10 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[16, 2], Operations: ['28-16=12', '24/12=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,10 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,10 unequal: No Solution Moving to Node #0,0,1 Current State: 10:[16, 12], Operations: ['28-16=12', '24-12=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,10 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 16+12=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 #0,1 Current State: 10:[16, 24, 12], Operations: ['28-16=12'] Exploring Operation: 24-12=12, Resulting Numbers: [16, 12] Generated Node #0,1,0: 10:[16, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [16, 2] Generated Node #0,1,1: 10:[16, 2] Operation: 24/12=2 Exploring Operation: 24-16=8, Resulting Numbers: [12, 8] Generated Node #0,1,2: 10:[12, 8] Operation: 24-16=8 Moving to Node #0,1,2 Current State: 10:[12, 8], Operations: ['28-16=12', '24-16=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[16, 2], Operations: ['28-16=12', '24/12=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,10 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[16, 12], Operations: ['28-16=12', '24-12=12'] Exploring Operation: 16*12=192, Resulting Numbers: [192] 192,10 unequal: No Solution Exploring Operation: 16+12=28, Resulting Numbers: [28] 28,10 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 91, 24, 72, 3 ]
59
[ "24+72=96", "96/3=32", "91-32=59" ]
Current State: 59:[91, 24, 72, 3], Operations: [] Exploring Operation: 24+72=96, Resulting Numbers: [91, 3, 96] Generated Node #2: [91, 3, 96] from Operation: 24+72=96 Current State: 59:[91, 3, 96], Operations: ['24+72=96'] Exploring Operation: 96/3=32, Resulting Numbers: [91, 32] Generated Node #3: [91, 32] from Operation: 96/3=32 Current State: 59:[91, 32], Operations: ['24+72=96', '96/3=32'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[91, 24, 72, 3], Operations: [] Exploring Operation: 24*3=72, Resulting Numbers: [91, 72, 72] Generated Node #0,0: 59:[91, 72, 72] Operation: 24*3=72 Exploring Operation: 91-24=67, Resulting Numbers: [72, 3, 67] Generated Node #0,1: 59:[72, 3, 67] Operation: 91-24=67 Exploring Operation: 72-3=69, Resulting Numbers: [91, 24, 69] Generated Node #0,2: 59:[91, 24, 69] Operation: 72-3=69 Exploring Operation: 91-3=88, Resulting Numbers: [24, 72, 88] Generated Node #0,3: 59:[24, 72, 88] Operation: 91-3=88 Exploring Operation: 24+3=27, Resulting Numbers: [91, 72, 27] Generated Node #0,4: 59:[91, 72, 27] Operation: 24+3=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[91, 72, 72], Operations: ['24*3=72'] Exploring Operation: 91-72=19, Resulting Numbers: [72, 19] Generated Node #0,0,0: 59:[72, 19] Operation: 91-72=19 Exploring Operation: 72/72=1, Resulting Numbers: [91, 1] Generated Node #0,0,1: 59:[91, 1] Operation: 72/72=1 Exploring Operation: 72-72=0, Resulting Numbers: [91, 0] Generated Node #0,0,2: 59:[91, 0] Operation: 72-72=0 Exploring Operation: 91+72=163, Resulting Numbers: [72, 163] Generated Node #0,0,3: 59:[72, 163] Operation: 91+72=163 Exploring Operation: 91-72=19, Resulting Numbers: [72, 19] Generated Node #0,0,4: 59:[72, 19] Operation: 91-72=19 Moving to Node #0,0,0 Current State: 59:[72, 19], Operations: ['24*3=72', '91-72=19'] Exploring Operation: 72*19=1368, Resulting Numbers: [1368] 1368,59 unequal: No Solution Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[72, 19], Operations: ['24*3=72', '91-72=19'] Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 72*19=1368, Resulting Numbers: [1368] 1368,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[91, 1], Operations: ['24*3=72', '72/72=1'] Exploring Operation: 91*1=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 91-1=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 91/1=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 91+1=92, Resulting Numbers: [92] 92,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[91, 0], Operations: ['24*3=72', '72-72=0'] Exploring Operation: 91+0=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 91*0=0, Resulting Numbers: [0] 0,59 unequal: No Solution Exploring Operation: 91-0=91, Resulting Numbers: [91] 91,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[72, 163], Operations: ['24*3=72', '91+72=163'] Exploring Operation: 72*163=11736, Resulting Numbers: [11736] 11736,59 unequal: No Solution Exploring Operation: 72+163=235, Resulting Numbers: [235] 235,59 unequal: No Solution Exploring Operation: 163-72=91, Resulting Numbers: [91] 91,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[72, 3, 67], Operations: ['91-24=67'] Exploring Operation: 3+67=70, Resulting Numbers: [72, 70] Generated Node #0,1,0: 59:[72, 70] Operation: 3+67=70 Exploring Operation: 72/3=24, Resulting Numbers: [67, 24] Generated Node #0,1,1: 59:[67, 24] Operation: 72/3=24 Exploring Operation: 72+3=75, Resulting Numbers: [67, 75] Generated Node #0,1,2: 59:[67, 75] Operation: 72+3=75 Exploring Operation: 72-3=69, Resulting Numbers: [67, 69] Generated Node #0,1,3: 59:[67, 69] Operation: 72-3=69 Exploring Operation: 67-3=64, Resulting Numbers: [72, 64] Generated Node #0,1,4: 59:[72, 64] Operation: 67-3=64 Moving to Node #0,1,3 Current State: 59:[67, 69], Operations: ['91-24=67', '72-3=69'] Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 67*69=4623, Resulting Numbers: [4623] 4623,59 unequal: No Solution Exploring Operation: 67+69=136, Resulting Numbers: [136] 136,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[72, 64], Operations: ['91-24=67', '67-3=64'] Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,59 unequal: No Solution Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[72, 70], Operations: ['91-24=67', '3+67=70'] Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,59 unequal: No Solution Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[67, 75], Operations: ['91-24=67', '72+3=75'] Exploring Operation: 67*75=5025, Resulting Numbers: [5025] 5025,59 unequal: No Solution Exploring Operation: 67+75=142, Resulting Numbers: [142] 142,59 unequal: No Solution Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[67, 24], Operations: ['91-24=67', '72/3=24'] Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 67*24=1608, Resulting Numbers: [1608] 1608,59 unequal: No Solution Exploring Operation: 67+24=91, Resulting Numbers: [91] 91,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[91, 24, 69], Operations: ['72-3=69'] Exploring Operation: 24+69=93, Resulting Numbers: [91, 93] Generated Node #0,2,0: 59:[91, 93] Operation: 24+69=93 Exploring Operation: 69-24=45, Resulting Numbers: [91, 45] Generated Node #0,2,1: 59:[91, 45] Operation: 69-24=45 Exploring Operation: 91-24=67, Resulting Numbers: [69, 67] Generated Node #0,2,2: 59:[69, 67] Operation: 91-24=67 Exploring Operation: 91-69=22, Resulting Numbers: [24, 22] Generated Node #0,2,3: 59:[24, 22] Operation: 91-69=22 Exploring Operation: 91+24=115, Resulting Numbers: [69, 115] Generated Node #0,2,4: 59:[69, 115] Operation: 91+24=115 Moving to Node #0,2,2 Current State: 59:[69, 67], Operations: ['72-3=69', '91-24=67'] Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[91, 45], Operations: ['72-3=69', '69-24=45'] Exploring Operation: 91*45=4095, Resulting Numbers: [4095] 4095,59 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[91, 93], Operations: ['72-3=69', '24+69=93'] Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,59 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,59 unequal: No Solution Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,2,4 Current State: 59:[69, 115], Operations: ['72-3=69', '91+24=115'] Exploring Operation: 69*115=7935, Resulting Numbers: [7935] 7935,59 unequal: No Solution Exploring Operation: 115-69=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 69+115=184, Resulting Numbers: [184] 184,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[24, 22], Operations: ['72-3=69', '91-69=22'] Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 24*22=528, Resulting Numbers: [528] 528,59 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[24, 72, 88], Operations: ['91-3=88'] Exploring Operation: 24+72=96, Resulting Numbers: [88, 96] Generated Node #0,3,0: 59:[88, 96] Operation: 24+72=96 Exploring Operation: 24+88=112, Resulting Numbers: [72, 112] Generated Node #0,3,1: 59:[72, 112] Operation: 24+88=112 Exploring Operation: 72-24=48, Resulting Numbers: [88, 48] Generated Node #0,3,2: 59:[88, 48] Operation: 72-24=48 Exploring Operation: 88-72=16, Resulting Numbers: [24, 16] Generated Node #0,3,3: 59:[24, 16] Operation: 88-72=16 Exploring Operation: 88-24=64, Resulting Numbers: [72, 64] Generated Node #0,3,4: 59:[72, 64] Operation: 88-24=64 Moving to Node #0,3,4 Current State: 59:[72, 64], Operations: ['91-3=88', '88-24=64'] Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[88, 48], Operations: ['91-3=88', '72-24=48'] Exploring Operation: 88+48=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 88-48=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 88*48=4224, Resulting Numbers: [4224] 4224,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[88, 96], Operations: ['91-3=88', '24+72=96'] Exploring Operation: 88+96=184, Resulting Numbers: [184] 184,59 unequal: No Solution Exploring Operation: 88*96=8448, Resulting Numbers: [8448] 8448,59 unequal: No Solution Exploring Operation: 96-88=8, Resulting Numbers: [8] 8,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[72, 112], Operations: ['91-3=88', '24+88=112'] Exploring Operation: 72+112=184, Resulting Numbers: [184] 184,59 unequal: No Solution Exploring Operation: 72*112=8064, Resulting Numbers: [8064] 8064,59 unequal: No Solution Exploring Operation: 112-72=40, Resulting Numbers: [40] 40,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[24, 16], Operations: ['91-3=88', '88-72=16'] Exploring Operation: 24*16=384, Resulting Numbers: [384] 384,59 unequal: No Solution Exploring Operation: 24+16=40, Resulting Numbers: [40] 40,59 unequal: No Solution Exploring Operation: 24-16=8, Resulting Numbers: [8] 8,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 59:[91, 72, 27], Operations: ['24+3=27'] Exploring Operation: 91-72=19, Resulting Numbers: [27, 19] Generated Node #0,4,0: 59:[27, 19] Operation: 91-72=19 Exploring Operation: 72+27=99, Resulting Numbers: [91, 99] Generated Node #0,4,1: 59:[91, 99] Operation: 72+27=99 Exploring Operation: 91-27=64, Resulting Numbers: [72, 64] Generated Node #0,4,2: 59:[72, 64] Operation: 91-27=64 Exploring Operation: 91+27=118, Resulting Numbers: [72, 118] Generated Node #0,4,3: 59:[72, 118] Operation: 91+27=118 Exploring Operation: 72-27=45, Resulting Numbers: [91, 45] Generated Node #0,4,4: 59:[91, 45] Operation: 72-27=45 Moving to Node #0,4,2 Current State: 59:[72, 64], Operations: ['24+3=27', '91-27=64'] Exploring Operation: 72*64=4608, Resulting Numbers: [4608] 4608,59 unequal: No Solution Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 72+64=136, Resulting Numbers: [136] 136,59 unequal: No Solution Moving to Node #0,4,4 Current State: 59:[91, 45], Operations: ['24+3=27', '72-27=45'] Exploring Operation: 91+45=136, Resulting Numbers: [136] 136,59 unequal: No Solution Exploring Operation: 91*45=4095, Resulting Numbers: [4095] 4095,59 unequal: No Solution Exploring Operation: 91-45=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[27, 19], Operations: ['24+3=27', '91-72=19'] Exploring Operation: 27*19=513, Resulting Numbers: [513] 513,59 unequal: No Solution Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 27+19=46, Resulting Numbers: [46] 46,59 unequal: No Solution Moving to Node #0,4,1 Current State: 59:[91, 99], Operations: ['24+3=27', '72+27=99'] Exploring Operation: 99-91=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 91+99=190, Resulting Numbers: [190] 190,59 unequal: No Solution Exploring Operation: 91*99=9009, Resulting Numbers: [9009] 9009,59 unequal: No Solution Moving to Node #0,4,3 Current State: 59:[72, 118], Operations: ['24+3=27', '91+27=118'] Exploring Operation: 118-72=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 72+118=190, Resulting Numbers: [190] 190,59 unequal: No Solution Exploring Operation: 72*118=8496, Resulting Numbers: [8496] 8496,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 6, 75, 77, 33 ]
29
[ "6+75=81", "77+33=110", "110-81=29" ]
Current State: 29:[6, 75, 77, 33], Operations: [] Exploring Operation: 6+75=81, Resulting Numbers: [77, 33, 81] Generated Node #2: [77, 33, 81] from Operation: 6+75=81 Current State: 29:[77, 33, 81], Operations: ['6+75=81'] Exploring Operation: 77+33=110, Resulting Numbers: [81, 110] Generated Node #3: [81, 110] from Operation: 77+33=110 Current State: 29:[81, 110], Operations: ['6+75=81', '77+33=110'] Exploring Operation: 110-81=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[6, 75, 77, 33], Operations: [] Exploring Operation: 75-6=69, Resulting Numbers: [77, 33, 69] Generated Node #0,0: 29:[77, 33, 69] Operation: 75-6=69 Exploring Operation: 77-33=44, Resulting Numbers: [6, 75, 44] Generated Node #0,1: 29:[6, 75, 44] Operation: 77-33=44 Exploring Operation: 75-33=42, Resulting Numbers: [6, 77, 42] Generated Node #0,2: 29:[6, 77, 42] Operation: 75-33=42 Exploring Operation: 77-75=2, Resulting Numbers: [6, 33, 2] Generated Node #0,3: 29:[6, 33, 2] Operation: 77-75=2 Moving to Node #0,3 Current State: 29:[6, 33, 2], Operations: ['77-75=2'] Exploring Operation: 33-6=27, Resulting Numbers: [2, 27] Generated Node #0,3,0: 29:[2, 27] Operation: 33-6=27 Exploring Operation: 33-2=31, Resulting Numbers: [6, 31] Generated Node #0,3,1: 29:[6, 31] Operation: 33-2=31 Exploring Operation: 6+2=8, Resulting Numbers: [33, 8] Generated Node #0,3,2: 29:[33, 8] Operation: 6+2=8 Exploring Operation: 6*2=12, Resulting Numbers: [33, 12] Generated Node #0,3,3: 29:[33, 12] Operation: 6*2=12 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 29:[33, 12], Operations: ['77-75=2', '6*2=12'] Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,29 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,29 unequal: No Solution Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 29:[6, 31], Operations: ['77-75=2', '33-2=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,29 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,29 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 29:[33, 8], Operations: ['77-75=2', '6+2=8'] Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,29 unequal: No Solution Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,29 unequal: No Solution Exploring Operation: 33*8=264, Resulting Numbers: [264] 264,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 29:[2, 27], Operations: ['77-75=2', '33-6=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[6, 75, 77, 33], Operations: [] Exploring Operation: 77-75=2, Resulting Numbers: [6, 33, 2] Generated Node #0,3: 29:[6, 33, 2] Operation: 77-75=2 Moving to Node #0,3 Current State: 29:[6, 33, 2], Operations: ['77-75=2'] Exploring Operation: 33-6=27, Resulting Numbers: [2, 27] Generated Node #0,3,0: 29:[2, 27] Operation: 33-6=27 Moving to Node #0,3,0 Current State: 29:[2, 27], Operations: ['77-75=2', '33-6=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 67, 13, 41, 27 ]
80
[ "41*27=1107", "1107-67=1040", "1040/13=80" ]
Current State: 80:[67, 13, 41, 27], Operations: [] Exploring Operation: 41*27=1107, Resulting Numbers: [67, 13, 1107] Generated Node #2: [67, 13, 1107] from Operation: 41*27=1107 Current State: 80:[67, 13, 1107], Operations: ['41*27=1107'] Exploring Operation: 1107-67=1040, Resulting Numbers: [13, 1040] Generated Node #3: [13, 1040] from Operation: 1107-67=1040 Current State: 80:[13, 1040], Operations: ['41*27=1107', '1107-67=1040'] Exploring Operation: 1040/13=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[67, 13, 41, 27], Operations: [] Exploring Operation: 67-27=40, Resulting Numbers: [13, 41, 40] Generated Node #0,0: 80:[13, 41, 40] Operation: 67-27=40 Moving to Node #0,0 Current State: 80:[13, 41, 40], Operations: ['67-27=40'] Exploring Operation: 41+40=81, Resulting Numbers: [13, 81] Generated Node #0,0,0: 80:[13, 81] Operation: 41+40=81 Moving to Node #0,0,0 Current State: 80:[13, 81], Operations: ['67-27=40', '41+40=81'] Exploring Operation: 81-13=68, Resulting Numbers: [68] 68,80 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 4, 72, 97, 8 ]
23
[ "8/4=2", "97-72=25", "25-2=23" ]
Current State: 23:[4, 72, 97, 8], Operations: [] Exploring Operation: 8/4=2, Resulting Numbers: [72, 97, 2] Generated Node #2: [72, 97, 2] from Operation: 8/4=2 Current State: 23:[72, 97, 2], Operations: ['8/4=2'] Exploring Operation: 97-72=25, Resulting Numbers: [2, 25] Generated Node #3: [2, 25] from Operation: 97-72=25 Current State: 23:[2, 25], Operations: ['8/4=2', '97-72=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[4, 72, 97, 8], Operations: [] Exploring Operation: 97-72=25, Resulting Numbers: [4, 8, 25] Generated Node #0,0: 23:[4, 8, 25] Operation: 97-72=25 Exploring Operation: 4*8=32, Resulting Numbers: [72, 97, 32] Generated Node #0,1: 23:[72, 97, 32] Operation: 4*8=32 Exploring Operation: 72/4=18, Resulting Numbers: [97, 8, 18] Generated Node #0,2: 23:[97, 8, 18] Operation: 72/4=18 Exploring Operation: 72-4=68, Resulting Numbers: [97, 8, 68] Generated Node #0,3: 23:[97, 8, 68] Operation: 72-4=68 Exploring Operation: 72/8=9, Resulting Numbers: [4, 97, 9] Generated Node #0,4: 23:[4, 97, 9] Operation: 72/8=9 Moving to Node #0,0 Current State: 23:[4, 8, 25], Operations: ['97-72=25'] Exploring Operation: 4+25=29, Resulting Numbers: [8, 29] Generated Node #0,0,0: 23:[8, 29] Operation: 4+25=29 Exploring Operation: 25-4=21, Resulting Numbers: [8, 21] Generated Node #0,0,1: 23:[8, 21] Operation: 25-4=21 Exploring Operation: 8-4=4, Resulting Numbers: [25, 4] Generated Node #0,0,2: 23:[25, 4] Operation: 8-4=4 Exploring Operation: 4*8=32, Resulting Numbers: [25, 32] Generated Node #0,0,3: 23:[25, 32] Operation: 4*8=32 Exploring Operation: 4+8=12, Resulting Numbers: [25, 12] Generated Node #0,0,4: 23:[25, 12] Operation: 4+8=12 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 23:[25, 32], Operations: ['97-72=25', '4*8=32'] Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 25+32=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 25*32=800, Resulting Numbers: [800] 800,23 unequal: No Solution No 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: 23:[25, 12], Operations: ['97-72=25', '4+8=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,23 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,23 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,23 unequal: No Solution No 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: 23:[8, 21], Operations: ['97-72=25', '25-4=21'] Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 8*21=168, Resulting Numbers: [168] 168,23 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,23 unequal: No Solution No 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: 23:[8, 29], Operations: ['97-72=25', '4+25=29'] Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,23 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,23 unequal: No Solution No 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: 23:[25, 4], Operations: ['97-72=25', '8-4=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,23 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,23 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: 23:[97, 8, 18], Operations: ['72/4=18'] Exploring Operation: 97+8=105, Resulting Numbers: [18, 105] Generated Node #0,2,0: 23:[18, 105] Operation: 97+8=105 Exploring Operation: 97-18=79, Resulting Numbers: [8, 79] Generated Node #0,2,1: 23:[8, 79] Operation: 97-18=79 Exploring Operation: 97-8=89, Resulting Numbers: [18, 89] Generated Node #0,2,2: 23:[18, 89] Operation: 97-8=89 Exploring Operation: 8+18=26, Resulting Numbers: [97, 26] Generated Node #0,2,3: 23:[97, 26] Operation: 8+18=26 Exploring Operation: 18-8=10, Resulting Numbers: [97, 10] Generated Node #0,2,4: 23:[97, 10] Operation: 18-8=10 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[8, 79], Operations: ['72/4=18', '97-18=79'] Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 8+79=87, Resulting Numbers: [87] 87,23 unequal: No Solution Exploring Operation: 8*79=632, Resulting Numbers: [632] 632,23 unequal: No Solution No 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: 23:[18, 89], Operations: ['72/4=18', '97-8=89'] Exploring Operation: 18+89=107, Resulting Numbers: [107] 107,23 unequal: No Solution Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 18*89=1602, Resulting Numbers: [1602] 1602,23 unequal: No Solution No 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: 23:[97, 26], Operations: ['72/4=18', '8+18=26'] Exploring Operation: 97-26=71, Resulting Numbers: [71] 71,23 unequal: No Solution Exploring Operation: 97*26=2522, Resulting Numbers: [2522] 2522,23 unequal: No Solution Exploring Operation: 97+26=123, Resulting Numbers: [123] 123,23 unequal: No Solution No 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: 23:[18, 105], Operations: ['72/4=18', '97+8=105'] Exploring Operation: 18*105=1890, Resulting Numbers: [1890] 1890,23 unequal: No Solution Exploring Operation: 18+105=123, Resulting Numbers: [123] 123,23 unequal: No Solution Exploring Operation: 105-18=87, Resulting Numbers: [87] 87,23 unequal: No Solution No 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: 23:[97, 10], Operations: ['72/4=18', '18-8=10'] Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,23 unequal: No Solution Exploring Operation: 97*10=970, Resulting Numbers: [970] 970,23 unequal: No Solution Exploring Operation: 97+10=107, Resulting Numbers: [107] 107,23 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: 23:[4, 97, 9], Operations: ['72/8=9'] Exploring Operation: 4*9=36, Resulting Numbers: [97, 36] Generated Node #0,4,0: 23:[97, 36] Operation: 4*9=36 Exploring Operation: 4+97=101, Resulting Numbers: [9, 101] Generated Node #0,4,1: 23:[9, 101] Operation: 4+97=101 Exploring Operation: 4+9=13, Resulting Numbers: [97, 13] Generated Node #0,4,2: 23:[97, 13] Operation: 4+9=13 Exploring Operation: 97-4=93, Resulting Numbers: [9, 93] Generated Node #0,4,3: 23:[9, 93] Operation: 97-4=93 Exploring Operation: 97-9=88, Resulting Numbers: [4, 88] Generated Node #0,4,4: 23:[4, 88] Operation: 97-9=88 Moving to Node #0,1 Current State: 23:[72, 97, 32], Operations: ['4*8=32'] Exploring Operation: 72-32=40, Resulting Numbers: [97, 40] Generated Node #0,1,0: 23:[97, 40] Operation: 72-32=40 Exploring Operation: 97-32=65, Resulting Numbers: [72, 65] Generated Node #0,1,1: 23:[72, 65] Operation: 97-32=65 Exploring Operation: 97-72=25, Resulting Numbers: [32, 25] Generated Node #0,1,2: 23:[32, 25] Operation: 97-72=25 Exploring Operation: 72+97=169, Resulting Numbers: [32, 169] Generated Node #0,1,3: 23:[32, 169] Operation: 72+97=169 Exploring Operation: 72+32=104, Resulting Numbers: [97, 104] Generated Node #0,1,4: 23:[97, 104] Operation: 72+32=104 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[32, 25], Operations: ['4*8=32', '97-72=25'] Exploring Operation: 32*25=800, Resulting Numbers: [800] 800,23 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 32+25=57, Resulting Numbers: [57] 57,23 unequal: No Solution No 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: 23:[97, 40], Operations: ['4*8=32', '72-32=40'] Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,23 unequal: No Solution Exploring Operation: 97*40=3880, Resulting Numbers: [3880] 3880,23 unequal: No Solution Exploring Operation: 97+40=137, Resulting Numbers: [137] 137,23 unequal: No Solution No 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: 23:[72, 65], Operations: ['4*8=32', '97-32=65'] Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,23 unequal: No Solution Exploring Operation: 72*65=4680, Resulting Numbers: [4680] 4680,23 unequal: No Solution Exploring Operation: 72+65=137, Resulting Numbers: [137] 137,23 unequal: No Solution No 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: 23:[32, 169], Operations: ['4*8=32', '72+97=169'] Exploring Operation: 32+169=201, Resulting Numbers: [201] 201,23 unequal: No Solution Exploring Operation: 32*169=5408, Resulting Numbers: [5408] 5408,23 unequal: No Solution Exploring Operation: 169-32=137, Resulting Numbers: [137] 137,23 unequal: No Solution No 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: 23:[97, 104], Operations: ['4*8=32', '72+32=104'] Exploring Operation: 97+104=201, Resulting Numbers: [201] 201,23 unequal: No Solution Exploring Operation: 97*104=10088, Resulting Numbers: [10088] 10088,23 unequal: No Solution Exploring Operation: 104-97=7, Resulting Numbers: [7] 7,23 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: 23:[97, 8, 68], Operations: ['72-4=68'] Exploring Operation: 8+68=76, Resulting Numbers: [97, 76] Generated Node #0,3,0: 23:[97, 76] Operation: 8+68=76 Exploring Operation: 68-8=60, Resulting Numbers: [97, 60] Generated Node #0,3,1: 23:[97, 60] Operation: 68-8=60 Exploring Operation: 97-68=29, Resulting Numbers: [8, 29] Generated Node #0,3,2: 23:[8, 29] Operation: 97-68=29 Exploring Operation: 97+8=105, Resulting Numbers: [68, 105] Generated Node #0,3,3: 23:[68, 105] Operation: 97+8=105 Exploring Operation: 97-8=89, Resulting Numbers: [68, 89] Generated Node #0,3,4: 23:[68, 89] Operation: 97-8=89 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[8, 29], Operations: ['72-4=68', '97-68=29'] Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 8*29=232, Resulting Numbers: [232] 232,23 unequal: No Solution Exploring Operation: 8+29=37, Resulting Numbers: [37] 37,23 unequal: No Solution No 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: 23:[97, 60], Operations: ['72-4=68', '68-8=60'] Exploring Operation: 97*60=5820, Resulting Numbers: [5820] 5820,23 unequal: No Solution Exploring Operation: 97-60=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 97+60=157, Resulting Numbers: [157] 157,23 unequal: No Solution No 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: 23:[68, 89], Operations: ['72-4=68', '97-8=89'] Exploring Operation: 68+89=157, Resulting Numbers: [157] 157,23 unequal: No Solution Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 68*89=6052, Resulting Numbers: [6052] 6052,23 unequal: No Solution No 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: 23:[97, 76], Operations: ['72-4=68', '8+68=76'] Exploring Operation: 97-76=21, Resulting Numbers: [21] 21,23 unequal: No Solution Exploring Operation: 97+76=173, Resulting Numbers: [173] 173,23 unequal: No Solution Exploring Operation: 97*76=7372, Resulting Numbers: [7372] 7372,23 unequal: No Solution No 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: 23:[68, 105], Operations: ['72-4=68', '97+8=105'] Exploring Operation: 105-68=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 68*105=7140, Resulting Numbers: [7140] 7140,23 unequal: No Solution Exploring Operation: 68+105=173, Resulting Numbers: [173] 173,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,2 Current State: 23:[97, 13], Operations: ['72/8=9', '4+9=13'] Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,23 unequal: No Solution Exploring Operation: 97*13=1261, Resulting Numbers: [1261] 1261,23 unequal: No Solution Exploring Operation: 97+13=110, Resulting Numbers: [110] 110,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[4, 88], Operations: ['72/8=9', '97-9=88'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,23 unequal: No Solution Exploring Operation: 4*88=352, Resulting Numbers: [352] 352,23 unequal: No Solution Exploring Operation: 4+88=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[9, 93], Operations: ['72/8=9', '97-4=93'] Exploring Operation: 93-9=84, Resulting Numbers: [84] 84,23 unequal: No Solution Exploring Operation: 9+93=102, Resulting Numbers: [102] 102,23 unequal: No Solution Exploring Operation: 9*93=837, Resulting Numbers: [837] 837,23 unequal: No Solution Moving to Node #0,4,0 Current State: 23:[97, 36], Operations: ['72/8=9', '4*9=36'] Exploring Operation: 97-36=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 97+36=133, Resulting Numbers: [133] 133,23 unequal: No Solution Exploring Operation: 97*36=3492, Resulting Numbers: [3492] 3492,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[9, 101], Operations: ['72/8=9', '4+97=101'] Exploring Operation: 101-9=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 9*101=909, Resulting Numbers: [909] 909,23 unequal: No Solution Exploring Operation: 9+101=110, Resulting Numbers: [110] 110,23 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 29, 60, 40, 84 ]
97
[ "60*84=5040", "5040/40=126", "126-29=97" ]
Current State: 97:[29, 60, 40, 84], Operations: [] Exploring Operation: 60*84=5040, Resulting Numbers: [29, 40, 5040] Generated Node #2: [29, 40, 5040] from Operation: 60*84=5040 Current State: 97:[29, 40, 5040], Operations: ['60*84=5040'] Exploring Operation: 5040/40=126, Resulting Numbers: [29, 126] Generated Node #3: [29, 126] from Operation: 5040/40=126 Current State: 97:[29, 126], Operations: ['60*84=5040', '5040/40=126'] Exploring Operation: 126-29=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[29, 60, 40, 84], Operations: [] Exploring Operation: 29+40=69, Resulting Numbers: [60, 84, 69] Generated Node #0,0: 97:[60, 84, 69] Operation: 29+40=69 Exploring Operation: 29+60=89, Resulting Numbers: [40, 84, 89] Generated Node #0,1: 97:[40, 84, 89] Operation: 29+60=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[60, 84, 69], Operations: ['29+40=69'] Exploring Operation: 60+69=129, Resulting Numbers: [84, 129] Generated Node #0,0,0: 97:[84, 129] Operation: 60+69=129 Exploring Operation: 60+84=144, Resulting Numbers: [69, 144] Generated Node #0,0,1: 97:[69, 144] Operation: 60+84=144 Moving to Node #0,0,0 Current State: 97:[84, 129], Operations: ['29+40=69', '60+69=129'] Exploring Operation: 129-84=45, Resulting Numbers: [45] 45,97 unequal: No Solution Exploring Operation: 84+129=213, Resulting Numbers: [213] 213,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[69, 144], Operations: ['29+40=69', '60+84=144'] Exploring Operation: 144-69=75, Resulting Numbers: [75] 75,97 unequal: No Solution Exploring Operation: 69+144=213, Resulting Numbers: [213] 213,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[40, 84, 89], Operations: ['29+60=89'] Exploring Operation: 40+84=124, Resulting Numbers: [89, 124] Generated Node #0,1,0: 97:[89, 124] Operation: 40+84=124 Exploring Operation: 40+89=129, Resulting Numbers: [84, 129] Generated Node #0,1,1: 97:[84, 129] Operation: 40+89=129 Moving to Node #0,1,0 Current State: 97:[89, 124], Operations: ['29+60=89', '40+84=124'] Exploring Operation: 124-89=35, Resulting Numbers: [35] 35,97 unequal: No Solution Exploring Operation: 89+124=213, Resulting Numbers: [213] 213,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[84, 129], Operations: ['29+60=89', '40+89=129'] Exploring Operation: 84+129=213, Resulting Numbers: [213] 213,97 unequal: No Solution Exploring Operation: 129-84=45, Resulting Numbers: [45] 45,97 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
[ 96, 32, 23, 10 ]
16
[ "96/32=3", "23-10=13", "3+13=16" ]
Current State: 16:[96, 32, 23, 10], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [23, 10, 3] Generated Node #2: [23, 10, 3] from Operation: 96/32=3 Current State: 16:[23, 10, 3], Operations: ['96/32=3'] Exploring Operation: 23-10=13, Resulting Numbers: [3, 13] Generated Node #3: [3, 13] from Operation: 23-10=13 Current State: 16:[3, 13], Operations: ['96/32=3', '23-10=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[96, 32, 23, 10], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [23, 10, 3] Generated Node #0,0: 16:[23, 10, 3] Operation: 96/32=3 Exploring Operation: 96-32=64, Resulting Numbers: [23, 10, 64] Generated Node #0,1: 16:[23, 10, 64] Operation: 96-32=64 Moving to Node #0,0 Current State: 16:[23, 10, 3], Operations: ['96/32=3'] Exploring Operation: 23-3=20, Resulting Numbers: [10, 20] Generated Node #0,0,0: 16:[10, 20] Operation: 23-3=20 Exploring Operation: 23-10=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 16:[3, 13] Operation: 23-10=13 Moving to Node #0,1 Current State: 16:[23, 10, 64], Operations: ['96-32=64'] Exploring Operation: 64-23=41, Resulting Numbers: [10, 41] Generated Node #0,1,0: 16:[10, 41] Operation: 64-23=41 Exploring Operation: 64-10=54, Resulting Numbers: [23, 54] Generated Node #0,1,1: 16:[23, 54] Operation: 64-10=54 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[10, 41], Operations: ['96-32=64', '64-23=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[23, 54], Operations: ['96-32=64', '64-10=54'] Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,16 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: 16:[3, 13], Operations: ['96/32=3', '23-10=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,16 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[96, 32, 23, 10], Operations: [] Exploring Operation: 96/32=3, Resulting Numbers: [23, 10, 3] Generated Node #0,0: 16:[23, 10, 3] Operation: 96/32=3 Moving to Node #0,0 Current State: 16:[23, 10, 3], Operations: ['96/32=3'] Exploring Operation: 23-10=13, Resulting Numbers: [3, 13] Generated Node #0,0,1: 16:[3, 13] Operation: 23-10=13 Moving to Node #0,0,1 Current State: 16:[3, 13], Operations: ['96/32=3', '23-10=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 60, 20, 58, 4 ]
36
[ "60-58=2", "20*2=40", "40-4=36" ]
Current State: 36:[60, 20, 58, 4], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [20, 4, 2] Generated Node #2: [20, 4, 2] from Operation: 60-58=2 Current State: 36:[20, 4, 2], Operations: ['60-58=2'] Exploring Operation: 20*2=40, Resulting Numbers: [4, 40] Generated Node #3: [4, 40] from Operation: 20*2=40 Current State: 36:[4, 40], Operations: ['60-58=2', '20*2=40'] Exploring Operation: 40-4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[60, 20, 58, 4], Operations: [] Exploring Operation: 60-20=40, Resulting Numbers: [58, 4, 40] Generated Node #0,0: 36:[58, 4, 40] Operation: 60-20=40 Exploring Operation: 60/20=3, Resulting Numbers: [58, 4, 3] Generated Node #0,1: 36:[58, 4, 3] Operation: 60/20=3 Exploring Operation: 60-58=2, Resulting Numbers: [20, 4, 2] Generated Node #0,2: 36:[20, 4, 2] Operation: 60-58=2 Moving to Node #0,2 Current State: 36:[20, 4, 2], Operations: ['60-58=2'] Exploring Operation: 20/2=10, Resulting Numbers: [4, 10] Generated Node #0,2,0: 36:[4, 10] Operation: 20/2=10 Exploring Operation: 20/4=5, Resulting Numbers: [2, 5] Generated Node #0,2,1: 36:[2, 5] Operation: 20/4=5 Exploring Operation: 20-2=18, Resulting Numbers: [4, 18] Generated Node #0,2,2: 36:[4, 18] Operation: 20-2=18 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 36:[4, 18], Operations: ['60-58=2', '20-2=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,36 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,36 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 #0,2,0 Current State: 36:[4, 10], Operations: ['60-58=2', '20/2=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,36 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,36 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 #0,2,1 Current State: 36:[2, 5], Operations: ['60-58=2', '20/4=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,36 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,36 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: 36:[58, 4, 3], Operations: ['60/20=3'] Exploring Operation: 4*3=12, Resulting Numbers: [58, 12] Generated Node #0,1,0: 36:[58, 12] Operation: 4*3=12 Exploring Operation: 58-4=54, Resulting Numbers: [3, 54] Generated Node #0,1,1: 36:[3, 54] Operation: 58-4=54 Exploring Operation: 58-3=55, Resulting Numbers: [4, 55] Generated Node #0,1,2: 36:[4, 55] Operation: 58-3=55 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 36:[3, 54], Operations: ['60/20=3', '58-4=54'] Exploring Operation: 3+54=57, Resulting Numbers: [57] 57,36 unequal: No Solution Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 54-3=51, Resulting Numbers: [51] 51,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 36:[4, 55], Operations: ['60/20=3', '58-3=55'] Exploring Operation: 55-4=51, Resulting Numbers: [51] 51,36 unequal: No Solution Exploring Operation: 4*55=220, Resulting Numbers: [220] 220,36 unequal: No Solution Exploring Operation: 4+55=59, Resulting Numbers: [59] 59,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[58, 12], Operations: ['60/20=3', '4*3=12'] Exploring Operation: 58*12=696, Resulting Numbers: [696] 696,36 unequal: No Solution Exploring Operation: 58-12=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 58+12=70, Resulting Numbers: [70] 70,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 36:[58, 4, 40], Operations: ['60-20=40'] Exploring Operation: 58-40=18, Resulting Numbers: [4, 18] Generated Node #0,0,0: 36:[4, 18] Operation: 58-40=18 Exploring Operation: 58-4=54, Resulting Numbers: [40, 54] Generated Node #0,0,1: 36:[40, 54] Operation: 58-4=54 Exploring Operation: 40-4=36, Resulting Numbers: [58, 36] Generated Node #0,0,2: 36:[58, 36] Operation: 40-4=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 36:[4, 18], Operations: ['60-20=40', '58-40=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,36 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,36 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[40, 54], Operations: ['60-20=40', '58-4=54'] Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,36 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,36 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 36:[58, 36], Operations: ['60-20=40', '40-4=36'] Exploring Operation: 58*36=2088, Resulting Numbers: [2088] 2088,36 unequal: No Solution Exploring Operation: 58+36=94, Resulting Numbers: [94] 94,36 unequal: No Solution Exploring Operation: 58-36=22, Resulting Numbers: [22] 22,36 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
[ 82, 17, 76, 81 ]
58
[ "82+17=99", "76+81=157", "157-99=58" ]
Current State: 58:[82, 17, 76, 81], Operations: [] Exploring Operation: 82+17=99, Resulting Numbers: [76, 81, 99] Generated Node #2: [76, 81, 99] from Operation: 82+17=99 Current State: 58:[76, 81, 99], Operations: ['82+17=99'] Exploring Operation: 76+81=157, Resulting Numbers: [99, 157] Generated Node #3: [99, 157] from Operation: 76+81=157 Current State: 58:[99, 157], Operations: ['82+17=99', '76+81=157'] Exploring Operation: 157-99=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[82, 17, 76, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [17, 76, 1] Generated Node #0,0: 58:[17, 76, 1] Operation: 82-81=1 Exploring Operation: 76-17=59, Resulting Numbers: [82, 81, 59] Generated Node #0,1: 58:[82, 81, 59] Operation: 76-17=59 Exploring Operation: 82-76=6, Resulting Numbers: [17, 81, 6] Generated Node #0,2: 58:[17, 81, 6] Operation: 82-76=6 Exploring Operation: 82-17=65, Resulting Numbers: [76, 81, 65] Generated Node #0,3: 58:[76, 81, 65] Operation: 82-17=65 Exploring Operation: 81-76=5, Resulting Numbers: [82, 17, 5] Generated Node #0,4: 58:[82, 17, 5] Operation: 81-76=5 Moving to Node #0,0 Current State: 58:[17, 76, 1], Operations: ['82-81=1'] Exploring Operation: 76-1=75, Resulting Numbers: [17, 75] Generated Node #0,0,0: 58:[17, 75] Operation: 76-1=75 Exploring Operation: 17/1=17, Resulting Numbers: [76, 17] Generated Node #0,0,1: 58:[76, 17] Operation: 17/1=17 Exploring Operation: 76-17=59, Resulting Numbers: [1, 59] Generated Node #0,0,2: 58:[1, 59] Operation: 76-17=59 Exploring Operation: 17+1=18, Resulting Numbers: [76, 18] Generated Node #0,0,3: 58:[76, 18] Operation: 17+1=18 Exploring Operation: 17*1=17, Resulting Numbers: [76, 17] Generated Node #0,0,4: 58:[76, 17] Operation: 17*1=17 Moving to Node #0,4 Current State: 58:[82, 17, 5], Operations: ['81-76=5'] Exploring Operation: 17-5=12, Resulting Numbers: [82, 12] Generated Node #0,4,0: 58:[82, 12] Operation: 17-5=12 Exploring Operation: 17+5=22, Resulting Numbers: [82, 22] Generated Node #0,4,1: 58:[82, 22] Operation: 17+5=22 Exploring Operation: 82-17=65, Resulting Numbers: [5, 65] Generated Node #0,4,2: 58:[5, 65] Operation: 82-17=65 Exploring Operation: 82-5=77, Resulting Numbers: [17, 77] Generated Node #0,4,3: 58:[17, 77] Operation: 82-5=77 Exploring Operation: 82+5=87, Resulting Numbers: [17, 87] Generated Node #0,4,4: 58:[17, 87] Operation: 82+5=87 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 58:[5, 65], Operations: ['81-76=5', '82-17=65'] Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,58 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 5*65=325, Resulting Numbers: [325] 325,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 58:[82, 22], Operations: ['81-76=5', '17+5=22'] Exploring Operation: 82*22=1804, Resulting Numbers: [1804] 1804,58 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 82+22=104, Resulting Numbers: [104] 104,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 58:[17, 77], Operations: ['81-76=5', '82-5=77'] Exploring Operation: 17*77=1309, Resulting Numbers: [1309] 1309,58 unequal: No Solution Exploring Operation: 17+77=94, Resulting Numbers: [94] 94,58 unequal: No Solution Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 58:[82, 12], Operations: ['81-76=5', '17-5=12'] Exploring Operation: 82+12=94, Resulting Numbers: [94] 94,58 unequal: No Solution Exploring Operation: 82*12=984, Resulting Numbers: [984] 984,58 unequal: No Solution Exploring Operation: 82-12=70, Resulting Numbers: [70] 70,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 58:[17, 87], Operations: ['81-76=5', '82+5=87'] Exploring Operation: 17*87=1479, Resulting Numbers: [1479] 1479,58 unequal: No Solution Exploring Operation: 17+87=104, Resulting Numbers: [104] 104,58 unequal: No Solution Exploring Operation: 87-17=70, Resulting Numbers: [70] 70,58 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: 58:[17, 81, 6], Operations: ['82-76=6'] Exploring Operation: 81+6=87, Resulting Numbers: [17, 87] Generated Node #0,2,0: 58:[17, 87] Operation: 81+6=87 Exploring Operation: 81-6=75, Resulting Numbers: [17, 75] Generated Node #0,2,1: 58:[17, 75] Operation: 81-6=75 Exploring Operation: 81-17=64, Resulting Numbers: [6, 64] Generated Node #0,2,2: 58:[6, 64] Operation: 81-17=64 Exploring Operation: 17-6=11, Resulting Numbers: [81, 11] Generated Node #0,2,3: 58:[81, 11] Operation: 17-6=11 Exploring Operation: 17+6=23, Resulting Numbers: [81, 23] Generated Node #0,2,4: 58:[81, 23] Operation: 17+6=23 Moving to Node #0,1 Current State: 58:[82, 81, 59], Operations: ['76-17=59'] Exploring Operation: 82+81=163, Resulting Numbers: [59, 163] Generated Node #0,1,0: 58:[59, 163] Operation: 82+81=163 Exploring Operation: 82-59=23, Resulting Numbers: [81, 23] Generated Node #0,1,1: 58:[81, 23] Operation: 82-59=23 Exploring Operation: 82-81=1, Resulting Numbers: [59, 1] Generated Node #0,1,2: 58:[59, 1] Operation: 82-81=1 Exploring Operation: 82+59=141, Resulting Numbers: [81, 141] Generated Node #0,1,3: 58:[81, 141] Operation: 82+59=141 Exploring Operation: 81-59=22, Resulting Numbers: [82, 22] Generated Node #0,1,4: 58:[82, 22] Operation: 81-59=22 Moving to Node #0,3 Current State: 58:[76, 81, 65], Operations: ['82-17=65'] Exploring Operation: 76-65=11, Resulting Numbers: [81, 11] Generated Node #0,3,0: 58:[81, 11] Operation: 76-65=11 Exploring Operation: 76+81=157, Resulting Numbers: [65, 157] Generated Node #0,3,1: 58:[65, 157] Operation: 76+81=157 Exploring Operation: 81-65=16, Resulting Numbers: [76, 16] Generated Node #0,3,2: 58:[76, 16] Operation: 81-65=16 Exploring Operation: 76+65=141, Resulting Numbers: [81, 141] Generated Node #0,3,3: 58:[81, 141] Operation: 76+65=141 Exploring Operation: 81-76=5, Resulting Numbers: [65, 5] Generated Node #0,3,4: 58:[65, 5] Operation: 81-76=5 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 58:[65, 5], Operations: ['82-17=65', '81-76=5'] Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 65+5=70, Resulting Numbers: [70] 70,58 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 65*5=325, Resulting Numbers: [325] 325,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 58:[76, 16], Operations: ['82-17=65', '81-65=16'] Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,58 unequal: No Solution Exploring Operation: 76-16=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 76*16=1216, Resulting Numbers: [1216] 1216,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 58:[81, 11], Operations: ['82-17=65', '76-65=11'] Exploring Operation: 81*11=891, Resulting Numbers: [891] 891,58 unequal: No Solution Exploring Operation: 81+11=92, Resulting Numbers: [92] 92,58 unequal: No Solution Exploring Operation: 81-11=70, Resulting Numbers: [70] 70,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 58:[65, 157], Operations: ['82-17=65', '76+81=157'] Exploring Operation: 65+157=222, Resulting Numbers: [222] 222,58 unequal: No Solution Exploring Operation: 157-65=92, Resulting Numbers: [92] 92,58 unequal: No Solution Exploring Operation: 65*157=10205, Resulting Numbers: [10205] 10205,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 58:[81, 141], Operations: ['82-17=65', '76+65=141'] Exploring Operation: 81*141=11421, Resulting Numbers: [11421] 11421,58 unequal: No Solution Exploring Operation: 141-81=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 81+141=222, Resulting Numbers: [222] 222,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 58:[1, 59], Operations: ['82-81=1', '76-17=59'] Exploring Operation: 59/1=59, Resulting Numbers: [59] 59,58 unequal: No Solution Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,58 unequal: No Solution Exploring Operation: 1*59=59, Resulting Numbers: [59] 59,58 unequal: No Solution Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[82, 17, 76, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [17, 76, 1] Generated Node #0,0: 58:[17, 76, 1] Operation: 82-81=1 Moving to Node #0,0 Current State: 58:[17, 76, 1], Operations: ['82-81=1'] Exploring Operation: 76-17=59, Resulting Numbers: [1, 59] Generated Node #0,0,2: 58:[1, 59] Operation: 76-17=59 Moving to Node #0,0,2 Current State: 58:[1, 59], Operations: ['82-81=1', '76-17=59'] Exploring Operation: 59-1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.939236
hs_5
mult_heuristic
[ 40, 37, 55, 86 ]
64
[ "40+37=77", "55+86=141", "141-77=64" ]
Current State: 64:[40, 37, 55, 86], Operations: [] Exploring Operation: 40+37=77, Resulting Numbers: [55, 86, 77] Generated Node #2: [55, 86, 77] from Operation: 40+37=77 Current State: 64:[55, 86, 77], Operations: ['40+37=77'] Exploring Operation: 55+86=141, Resulting Numbers: [77, 141] Generated Node #3: [77, 141] from Operation: 55+86=141 Current State: 64:[77, 141], Operations: ['40+37=77', '55+86=141'] Exploring Operation: 141-77=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[40, 37, 55, 86], Operations: [] Exploring Operation: 55-40=15, Resulting Numbers: [37, 86, 15] Generated Node #0,0: 64:[37, 86, 15] Operation: 55-40=15 Exploring Operation: 86-55=31, Resulting Numbers: [40, 37, 31] Generated Node #0,1: 64:[40, 37, 31] Operation: 86-55=31 Moving to Node #0,1 Current State: 64:[40, 37, 31], Operations: ['86-55=31'] Exploring Operation: 40-37=3, Resulting Numbers: [31, 3] Generated Node #0,1,0: 64:[31, 3] Operation: 40-37=3 Exploring Operation: 40-31=9, Resulting Numbers: [37, 9] Generated Node #0,1,1: 64:[37, 9] Operation: 40-31=9 Moving to Node #0,0 Current State: 64:[37, 86, 15], Operations: ['55-40=15'] Exploring Operation: 86-15=71, Resulting Numbers: [37, 71] Generated Node #0,0,0: 64:[37, 71] Operation: 86-15=71 Exploring Operation: 86-37=49, Resulting Numbers: [15, 49] Generated Node #0,0,1: 64:[15, 49] Operation: 86-37=49 Moving to Node #0,1,0 Current State: 64:[31, 3], Operations: ['86-55=31', '40-37=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,64 unequal: No Solution Moving to Node #0,1,1 Current State: 64:[37, 9], Operations: ['86-55=31', '40-31=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,64 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,64 unequal: No Solution Moving to Node #0,0,0 Current State: 64:[37, 71], Operations: ['55-40=15', '86-15=71'] Exploring Operation: 71-37=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 37+71=108, Resulting Numbers: [108] 108,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[15, 49], Operations: ['55-40=15', '86-37=49'] Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[40, 37, 55, 86], Operations: [] Exploring Operation: 55-40=15, Resulting Numbers: [37, 86, 15] Generated Node #0,0: 64:[37, 86, 15] Operation: 55-40=15 Moving to Node #0,0 Current State: 64:[37, 86, 15], Operations: ['55-40=15'] Exploring Operation: 86-37=49, Resulting Numbers: [15, 49] Generated Node #0,0,1: 64:[15, 49] Operation: 86-37=49 Moving to Node #0,0,1 Current State: 64:[15, 49], Operations: ['55-40=15', '86-37=49'] Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
0.985243
hs_2
sum_heuristic
[ 48, 49, 2, 75 ]
50
[ "48/2=24", "75-49=26", "24+26=50" ]
Current State: 50:[48, 49, 2, 75], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [49, 75, 24] Generated Node #2: [49, 75, 24] from Operation: 48/2=24 Current State: 50:[49, 75, 24], Operations: ['48/2=24'] Exploring Operation: 75-49=26, Resulting Numbers: [24, 26] Generated Node #3: [24, 26] from Operation: 75-49=26 Current State: 50:[24, 26], Operations: ['48/2=24', '75-49=26'] Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[48, 49, 2, 75], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [49, 2, 27] Generated Node #0,0: 50:[49, 2, 27] Operation: 75-48=27 Moving to Node #0,0 Current State: 50:[49, 2, 27], Operations: ['75-48=27'] Exploring Operation: 27-2=25, Resulting Numbers: [49, 25] Generated Node #0,0,0: 50:[49, 25] Operation: 27-2=25 Moving to Node #0,0,0 Current State: 50:[49, 25], Operations: ['75-48=27', '27-2=25'] Exploring Operation: 49-25=24, Resulting Numbers: [24] 24,50 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 82, 44, 23, 41 ]
56
[ "82-44=38", "41-23=18", "38+18=56" ]
Current State: 56:[82, 44, 23, 41], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [23, 41, 38] Generated Node #2: [23, 41, 38] from Operation: 82-44=38 Current State: 56:[23, 41, 38], Operations: ['82-44=38'] Exploring Operation: 41-23=18, Resulting Numbers: [38, 18] Generated Node #3: [38, 18] from Operation: 41-23=18 Current State: 56:[38, 18], Operations: ['82-44=38', '41-23=18'] Exploring Operation: 38+18=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[82, 44, 23, 41], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [82, 23, 3] Generated Node #0,0: 56:[82, 23, 3] Operation: 44-41=3 Exploring Operation: 82-41=41, Resulting Numbers: [44, 23, 41] Generated Node #0,1: 56:[44, 23, 41] Operation: 82-41=41 Exploring Operation: 82/41=2, Resulting Numbers: [44, 23, 2] Generated Node #0,2: 56:[44, 23, 2] Operation: 82/41=2 Exploring Operation: 82-44=38, Resulting Numbers: [23, 41, 38] Generated Node #0,3: 56:[23, 41, 38] Operation: 82-44=38 Exploring Operation: 82-23=59, Resulting Numbers: [44, 41, 59] Generated Node #0,4: 56:[44, 41, 59] Operation: 82-23=59 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[44, 23, 2], Operations: ['82/41=2'] Exploring Operation: 44+23=67, Resulting Numbers: [2, 67] Generated Node #0,2,0: 56:[2, 67] Operation: 44+23=67 Exploring Operation: 44/2=22, Resulting Numbers: [23, 22] Generated Node #0,2,1: 56:[23, 22] Operation: 44/2=22 Exploring Operation: 44+2=46, Resulting Numbers: [23, 46] Generated Node #0,2,2: 56:[23, 46] Operation: 44+2=46 Exploring Operation: 23+2=25, Resulting Numbers: [44, 25] Generated Node #0,2,3: 56:[44, 25] Operation: 23+2=25 Exploring Operation: 44-23=21, Resulting Numbers: [2, 21] Generated Node #0,2,4: 56:[2, 21] Operation: 44-23=21 Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 56:[2, 21], Operations: ['82/41=2', '44-23=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,56 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,56 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 56:[2, 67], Operations: ['82/41=2', '44+23=67'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,56 unequal: No Solution Exploring Operation: 2+67=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 2*67=134, Resulting Numbers: [134] 134,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 56:[23, 22], Operations: ['82/41=2', '44/2=22'] Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,56 unequal: No Solution Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,56 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 56:[23, 46], Operations: ['82/41=2', '44+2=46'] Exploring Operation: 23*46=1058, Resulting Numbers: [1058] 1058,56 unequal: No Solution Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,56 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,56 unequal: No Solution Exploring Operation: 23+46=69, Resulting Numbers: [69] 69,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 56:[44, 25], Operations: ['82/41=2', '23+2=25'] Exploring Operation: 44+25=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 44*25=1100, Resulting Numbers: [1100] 1100,56 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 56:[23, 41, 38], Operations: ['82-44=38'] Exploring Operation: 41-23=18, Resulting Numbers: [38, 18] Generated Node #0,3,0: 56:[38, 18] Operation: 41-23=18 Exploring Operation: 23+38=61, Resulting Numbers: [41, 61] Generated Node #0,3,1: 56:[41, 61] Operation: 23+38=61 Exploring Operation: 41-38=3, Resulting Numbers: [23, 3] Generated Node #0,3,2: 56:[23, 3] Operation: 41-38=3 Exploring Operation: 38-23=15, Resulting Numbers: [41, 15] Generated Node #0,3,3: 56:[41, 15] Operation: 38-23=15 Exploring Operation: 23+41=64, Resulting Numbers: [38, 64] Generated Node #0,3,4: 56:[38, 64] Operation: 23+41=64 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 56:[23, 3], Operations: ['82-44=38', '41-38=3'] Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,56 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,56 unequal: No Solution Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,56 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 56:[38, 18], Operations: ['82-44=38', '41-23=18'] Exploring Operation: 38+18=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[82, 44, 23, 41], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [23, 41, 38] Generated Node #0,3: 56:[23, 41, 38] Operation: 82-44=38 Moving to Node #0,3 Current State: 56:[23, 41, 38], Operations: ['82-44=38'] Exploring Operation: 41-23=18, Resulting Numbers: [38, 18] Generated Node #0,3,0: 56:[38, 18] Operation: 41-23=18 Moving to Node #0,3,0 Current State: 56:[38, 18], Operations: ['82-44=38', '41-23=18'] Exploring Operation: 38+18=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 21, 18, 14, 6 ]
23
[ "21-18=3", "14+6=20", "3+20=23" ]
Current State: 23:[21, 18, 14, 6], Operations: [] Exploring Operation: 21-18=3, Resulting Numbers: [14, 6, 3] Generated Node #2: [14, 6, 3] from Operation: 21-18=3 Current State: 23:[14, 6, 3], Operations: ['21-18=3'] Exploring Operation: 14+6=20, Resulting Numbers: [3, 20] Generated Node #3: [3, 20] from Operation: 14+6=20 Current State: 23:[3, 20], Operations: ['21-18=3', '14+6=20'] Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[21, 18, 14, 6], Operations: [] Exploring Operation: 18+6=24, Resulting Numbers: [21, 14, 24] Generated Node #0,0: 23:[21, 14, 24] Operation: 18+6=24 Exploring Operation: 14+6=20, Resulting Numbers: [21, 18, 20] Generated Node #0,1: 23:[21, 18, 20] Operation: 14+6=20 Moving to Node #0,1 Current State: 23:[21, 18, 20], Operations: ['14+6=20'] Exploring Operation: 18+20=38, Resulting Numbers: [21, 38] Generated Node #0,1,0: 23:[21, 38] Operation: 18+20=38 Exploring Operation: 21+18=39, Resulting Numbers: [20, 39] Generated Node #0,1,1: 23:[20, 39] Operation: 21+18=39 Moving to Node #0,0 Current State: 23:[21, 14, 24], Operations: ['18+6=24'] Exploring Operation: 24-14=10, Resulting Numbers: [21, 10] Generated Node #0,0,0: 23:[21, 10] Operation: 24-14=10 Exploring Operation: 21+14=35, Resulting Numbers: [24, 35] Generated Node #0,0,1: 23:[24, 35] Operation: 21+14=35 Moving to Node #0,0,1 Current State: 23:[24, 35], Operations: ['18+6=24', '21+14=35'] Exploring Operation: 24+35=59, Resulting Numbers: [59] 59,23 unequal: No Solution Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[21, 10], Operations: ['18+6=24', '24-14=10'] Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,23 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,23 unequal: No Solution Moving to Node #0,1,0 Current State: 23:[21, 38], Operations: ['14+6=20', '18+20=38'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[20, 39], Operations: ['14+6=20', '21+18=39'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,23 unequal: No Solution Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,23 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 88, 12, 5, 71 ]
97
[ "88-71=17", "5*17=85", "12+85=97" ]
Current State: 97:[88, 12, 5, 71], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [12, 5, 17] Generated Node #2: [12, 5, 17] from Operation: 88-71=17 Current State: 97:[12, 5, 17], Operations: ['88-71=17'] Exploring Operation: 5*17=85, Resulting Numbers: [12, 85] Generated Node #3: [12, 85] from Operation: 5*17=85 Current State: 97:[12, 85], Operations: ['88-71=17', '5*17=85'] Exploring Operation: 12+85=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[88, 12, 5, 71], Operations: [] Exploring Operation: 12*5=60, Resulting Numbers: [88, 71, 60] Generated Node #0,0: 97:[88, 71, 60] Operation: 12*5=60 Exploring Operation: 12+5=17, Resulting Numbers: [88, 71, 17] Generated Node #0,1: 97:[88, 71, 17] Operation: 12+5=17 Exploring Operation: 88+5=93, Resulting Numbers: [12, 71, 93] Generated Node #0,2: 97:[12, 71, 93] Operation: 88+5=93 Moving to Node #0,0 Current State: 97:[88, 71, 60], Operations: ['12*5=60'] Exploring Operation: 88-60=28, Resulting Numbers: [71, 28] Generated Node #0,0,0: 97:[71, 28] Operation: 88-60=28 Exploring Operation: 88+60=148, Resulting Numbers: [71, 148] Generated Node #0,0,1: 97:[71, 148] Operation: 88+60=148 Exploring Operation: 71+60=131, Resulting Numbers: [88, 131] Generated Node #0,0,2: 97:[88, 131] Operation: 71+60=131 Moving to Node #0,1 Current State: 97:[88, 71, 17], Operations: ['12+5=17'] Exploring Operation: 88+17=105, Resulting Numbers: [71, 105] Generated Node #0,1,0: 97:[71, 105] Operation: 88+17=105 Exploring Operation: 71+17=88, Resulting Numbers: [88, 88] Generated Node #0,1,1: 97:[88, 88] Operation: 71+17=88 Exploring Operation: 88-17=71, Resulting Numbers: [71, 71] Generated Node #0,1,2: 97:[71, 71] Operation: 88-17=71 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[88, 88], Operations: ['12+5=17', '71+17=88'] Exploring Operation: 88+88=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 88/88=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 88-88=0, Resulting Numbers: [0] 0,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[71, 105], Operations: ['12+5=17', '88+17=105'] Exploring Operation: 105-71=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 71+105=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 71*105=7455, Resulting Numbers: [7455] 7455,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[71, 71], Operations: ['12+5=17', '88-17=71'] Exploring Operation: 71/71=1, Resulting Numbers: [1] 1,97 unequal: No Solution Exploring Operation: 71+71=142, Resulting Numbers: [142] 142,97 unequal: No Solution Exploring Operation: 71-71=0, Resulting Numbers: [0] 0,97 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: 97:[12, 71, 93], Operations: ['88+5=93'] Exploring Operation: 12+93=105, Resulting Numbers: [71, 105] Generated Node #0,2,0: 97:[71, 105] Operation: 12+93=105 Exploring Operation: 12+71=83, Resulting Numbers: [93, 83] Generated Node #0,2,1: 97:[93, 83] Operation: 12+71=83 Exploring Operation: 71-12=59, Resulting Numbers: [93, 59] Generated Node #0,2,2: 97:[93, 59] Operation: 71-12=59 Moving to Node #0,2,1 Current State: 97:[93, 83], Operations: ['88+5=93', '12+71=83'] Exploring Operation: 93*83=7719, Resulting Numbers: [7719] 7719,97 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,97 unequal: No Solution Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[71, 105], Operations: ['88+5=93', '12+93=105'] Exploring Operation: 71+105=176, Resulting Numbers: [176] 176,97 unequal: No Solution Exploring Operation: 105-71=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 71*105=7455, Resulting Numbers: [7455] 7455,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[93, 59], Operations: ['88+5=93', '71-12=59'] Exploring Operation: 93-59=34, Resulting Numbers: [34] 34,97 unequal: No Solution Exploring Operation: 93+59=152, Resulting Numbers: [152] 152,97 unequal: No Solution Exploring Operation: 93*59=5487, Resulting Numbers: [5487] 5487,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[88, 131], Operations: ['12*5=60', '71+60=131'] Exploring Operation: 88+131=219, Resulting Numbers: [219] 219,97 unequal: No Solution Exploring Operation: 88*131=11528, Resulting Numbers: [11528] 11528,97 unequal: No Solution Exploring Operation: 131-88=43, Resulting Numbers: [43] 43,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[71, 148], Operations: ['12*5=60', '88+60=148'] Exploring Operation: 148-71=77, Resulting Numbers: [77] 77,97 unequal: No Solution Exploring Operation: 71+148=219, Resulting Numbers: [219] 219,97 unequal: No Solution Exploring Operation: 71*148=10508, Resulting Numbers: [10508] 10508,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[71, 28], Operations: ['12*5=60', '88-60=28'] Exploring Operation: 71*28=1988, Resulting Numbers: [1988] 1988,97 unequal: No Solution Exploring Operation: 71+28=99, Resulting Numbers: [99] 99,97 unequal: No Solution Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,97 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 68, 33, 2, 25 ]
52
[ "33-25=8", "2*8=16", "68-16=52" ]
Current State: 52:[68, 33, 2, 25], Operations: [] Exploring Operation: 33-25=8, Resulting Numbers: [68, 2, 8] Generated Node #2: [68, 2, 8] from Operation: 33-25=8 Current State: 52:[68, 2, 8], Operations: ['33-25=8'] Exploring Operation: 2*8=16, Resulting Numbers: [68, 16] Generated Node #3: [68, 16] from Operation: 2*8=16 Current State: 52:[68, 16], Operations: ['33-25=8', '2*8=16'] Exploring Operation: 68-16=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[68, 33, 2, 25], Operations: [] Exploring Operation: 33-25=8, Resulting Numbers: [68, 2, 8] Generated Node #0,0: 52:[68, 2, 8] Operation: 33-25=8 Exploring Operation: 68-25=43, Resulting Numbers: [33, 2, 43] Generated Node #0,1: 52:[33, 2, 43] Operation: 68-25=43 Exploring Operation: 68-33=35, Resulting Numbers: [2, 25, 35] Generated Node #0,2: 52:[2, 25, 35] Operation: 68-33=35 Exploring Operation: 68/2=34, Resulting Numbers: [33, 25, 34] Generated Node #0,3: 52:[33, 25, 34] Operation: 68/2=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[2, 25, 35], Operations: ['68-33=35'] Exploring Operation: 2+25=27, Resulting Numbers: [35, 27] Generated Node #0,2,0: 52:[35, 27] Operation: 2+25=27 Exploring Operation: 35-2=33, Resulting Numbers: [25, 33] Generated Node #0,2,1: 52:[25, 33] Operation: 35-2=33 Exploring Operation: 25+35=60, Resulting Numbers: [2, 60] Generated Node #0,2,2: 52:[2, 60] Operation: 25+35=60 Exploring Operation: 35-25=10, Resulting Numbers: [2, 10] Generated Node #0,2,3: 52:[2, 10] Operation: 35-25=10 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[2, 10], Operations: ['68-33=35', '35-25=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,52 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:[25, 33], Operations: ['68-33=35', '35-2=33'] Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,52 unequal: No Solution Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,52 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 #0,2,2 Current State: 52:[2, 60], Operations: ['68-33=35', '25+35=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,52 unequal: No Solution Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,52 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,52 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:[35, 27], Operations: ['68-33=35', '2+25=27'] Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,52 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,52 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:[33, 2, 43], Operations: ['68-25=43'] Exploring Operation: 33-2=31, Resulting Numbers: [43, 31] Generated Node #0,1,0: 52:[43, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [43, 35] Generated Node #0,1,1: 52:[43, 35] Operation: 33+2=35 Exploring Operation: 43-33=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 52:[2, 10] Operation: 43-33=10 Exploring Operation: 2+43=45, Resulting Numbers: [33, 45] Generated Node #0,1,3: 52:[33, 45] Operation: 2+43=45 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[2, 10], Operations: ['68-25=43', '43-33=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,52 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,52 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:[43, 31], Operations: ['68-25=43', '33-2=31'] Exploring Operation: 43-31=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 43*31=1333, Resulting Numbers: [1333] 1333,52 unequal: No Solution Exploring Operation: 43+31=74, Resulting Numbers: [74] 74,52 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:[33, 45], Operations: ['68-25=43', '2+43=45'] Exploring Operation: 33*45=1485, Resulting Numbers: [1485] 1485,52 unequal: No Solution Exploring Operation: 45-33=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 33+45=78, Resulting Numbers: [78] 78,52 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 #0,1,1 Current State: 52:[43, 35], Operations: ['68-25=43', '33+2=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,52 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,52 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,52 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 #0,3 Current State: 52:[33, 25, 34], Operations: ['68/2=34'] Exploring Operation: 33+25=58, Resulting Numbers: [34, 58] Generated Node #0,3,0: 52:[34, 58] Operation: 33+25=58 Exploring Operation: 34-33=1, Resulting Numbers: [25, 1] Generated Node #0,3,1: 52:[25, 1] Operation: 34-33=1 Exploring Operation: 33-25=8, Resulting Numbers: [34, 8] Generated Node #0,3,2: 52:[34, 8] Operation: 33-25=8 Exploring Operation: 34-25=9, Resulting Numbers: [33, 9] Generated Node #0,3,3: 52:[33, 9] Operation: 34-25=9 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[25, 1], Operations: ['68/2=34', '34-33=1'] Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,52 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,52 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 #0,3,3 Current State: 52:[33, 9], Operations: ['68/2=34', '34-25=9'] Exploring Operation: 33+9=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 33-9=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 33*9=297, Resulting Numbers: [297] 297,52 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 #0,3,2 Current State: 52:[34, 8], Operations: ['68/2=34', '33-25=8'] Exploring Operation: 34*8=272, Resulting Numbers: [272] 272,52 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,52 unequal: No Solution Exploring Operation: 34+8=42, Resulting Numbers: [42] 42,52 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 #0,3,0 Current State: 52:[34, 58], Operations: ['68/2=34', '33+25=58'] Exploring Operation: 34*58=1972, Resulting Numbers: [1972] 1972,52 unequal: No Solution Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 34+58=92, Resulting Numbers: [92] 92,52 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 #0,0 Current State: 52:[68, 2, 8], Operations: ['33-25=8'] Exploring Operation: 68/2=34, Resulting Numbers: [8, 34] Generated Node #0,0,0: 52:[8, 34] Operation: 68/2=34 Exploring Operation: 8/2=4, Resulting Numbers: [68, 4] Generated Node #0,0,1: 52:[68, 4] Operation: 8/2=4 Exploring Operation: 68-8=60, Resulting Numbers: [2, 60] Generated Node #0,0,2: 52:[2, 60] Operation: 68-8=60 Exploring Operation: 68-2=66, Resulting Numbers: [8, 66] Generated Node #0,0,3: 52:[8, 66] Operation: 68-2=66 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[2, 60], Operations: ['33-25=8', '68-8=60'] Exploring Operation: 2+60=62, Resulting Numbers: [62] 62,52 unequal: No Solution Exploring Operation: 2*60=120, Resulting Numbers: [120] 120,52 unequal: No Solution Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,52 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,52 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:[8, 34], Operations: ['33-25=8', '68/2=34'] Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,52 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,52 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,52 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:[68, 4], Operations: ['33-25=8', '8/2=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 68*4=272, Resulting Numbers: [272] 272,52 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 68/4=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 #0,0,3 Current State: 52:[8, 66], Operations: ['33-25=8', '68-2=66'] Exploring Operation: 66-8=58, Resulting Numbers: [58] 58,52 unequal: No Solution Exploring Operation: 8*66=528, Resulting Numbers: [528] 528,52 unequal: No Solution Exploring Operation: 8+66=74, Resulting Numbers: [74] 74,52 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_4
mult_heuristic
[ 97, 45, 68, 80 ]
49
[ "97-80=17", "68/17=4", "45+4=49" ]
Current State: 49:[97, 45, 68, 80], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [45, 68, 17] Generated Node #2: [45, 68, 17] from Operation: 97-80=17 Current State: 49:[45, 68, 17], Operations: ['97-80=17'] Exploring Operation: 68/17=4, Resulting Numbers: [45, 4] Generated Node #3: [45, 4] from Operation: 68/17=4 Current State: 49:[45, 4], Operations: ['97-80=17', '68/17=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[97, 45, 68, 80], Operations: [] Exploring Operation: 97-68=29, Resulting Numbers: [45, 80, 29] Generated Node #0,0: 49:[45, 80, 29] Operation: 97-68=29 Exploring Operation: 97-80=17, Resulting Numbers: [45, 68, 17] Generated Node #0,1: 49:[45, 68, 17] Operation: 97-80=17 Exploring Operation: 80-68=12, Resulting Numbers: [97, 45, 12] Generated Node #0,2: 49:[97, 45, 12] Operation: 80-68=12 Exploring Operation: 97-45=52, Resulting Numbers: [68, 80, 52] Generated Node #0,3: 49:[68, 80, 52] Operation: 97-45=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[45, 68, 17], Operations: ['97-80=17'] Exploring Operation: 68/17=4, Resulting Numbers: [45, 4] Generated Node #0,1,0: 49:[45, 4] Operation: 68/17=4 Exploring Operation: 45+17=62, Resulting Numbers: [68, 62] Generated Node #0,1,1: 49:[68, 62] Operation: 45+17=62 Exploring Operation: 68-45=23, Resulting Numbers: [17, 23] Generated Node #0,1,2: 49:[17, 23] Operation: 68-45=23 Exploring Operation: 68-17=51, Resulting Numbers: [45, 51] Generated Node #0,1,3: 49:[45, 51] Operation: 68-17=51 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 49:[45, 51], Operations: ['97-80=17', '68-17=51'] Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,49 unequal: No Solution Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 45*51=2295, Resulting Numbers: [2295] 2295,49 unequal: No Solution No 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: 49:[45, 4], Operations: ['97-80=17', '68/17=4'] Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[97, 45, 68, 80], Operations: [] Exploring Operation: 97-80=17, Resulting Numbers: [45, 68, 17] Generated Node #0,1: 49:[45, 68, 17] Operation: 97-80=17 Moving to Node #0,1 Current State: 49:[45, 68, 17], Operations: ['97-80=17'] Exploring Operation: 68/17=4, Resulting Numbers: [45, 4] Generated Node #0,1,0: 49:[45, 4] Operation: 68/17=4 Moving to Node #0,1,0 Current State: 49:[45, 4], Operations: ['97-80=17', '68/17=4'] Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 76, 56, 2, 36 ]
12
[ "76-36=40", "56/2=28", "40-28=12" ]
Current State: 12:[76, 56, 2, 36], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [56, 2, 40] Generated Node #2: [56, 2, 40] from Operation: 76-36=40 Current State: 12:[56, 2, 40], Operations: ['76-36=40'] Exploring Operation: 56/2=28, Resulting Numbers: [40, 28] Generated Node #3: [40, 28] from Operation: 56/2=28 Current State: 12:[40, 28], Operations: ['76-36=40', '56/2=28'] Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[76, 56, 2, 36], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [56, 2, 40] Generated Node #0,0: 12:[56, 2, 40] Operation: 76-36=40 Exploring Operation: 76-56=20, Resulting Numbers: [2, 36, 20] Generated Node #0,1: 12:[2, 36, 20] Operation: 76-56=20 Moving to Node #0,1 Current State: 12:[2, 36, 20], Operations: ['76-56=20'] Exploring Operation: 36/2=18, Resulting Numbers: [20, 18] Generated Node #0,1,0: 12:[20, 18] Operation: 36/2=18 Exploring Operation: 36-20=16, Resulting Numbers: [2, 16] Generated Node #0,1,1: 12:[2, 16] Operation: 36-20=16 Moving to Node #0,0 Current State: 12:[56, 2, 40], Operations: ['76-36=40'] Exploring Operation: 56/2=28, Resulting Numbers: [40, 28] Generated Node #0,0,0: 12:[40, 28] Operation: 56/2=28 Exploring Operation: 56-40=16, Resulting Numbers: [2, 16] Generated Node #0,0,1: 12:[2, 16] Operation: 56-40=16 Moving to Node #0,1,1 Current State: 12:[2, 16], Operations: ['76-56=20', '36-20=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[2, 16], Operations: ['76-36=40', '56-40=16'] Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[20, 18], Operations: ['76-56=20', '36/2=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[40, 28], Operations: ['76-36=40', '56/2=28'] Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,12 unequal: No Solution Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[76, 56, 2, 36], Operations: [] Exploring Operation: 76-36=40, Resulting Numbers: [56, 2, 40] Generated Node #0,0: 12:[56, 2, 40] Operation: 76-36=40 Moving to Node #0,0 Current State: 12:[56, 2, 40], Operations: ['76-36=40'] Exploring Operation: 56/2=28, Resulting Numbers: [40, 28] Generated Node #0,0,0: 12:[40, 28] Operation: 56/2=28 Moving to Node #0,0,0 Current State: 12:[40, 28], Operations: ['76-36=40', '56/2=28'] Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.984375
hs_2
sum_heuristic
[ 8, 94, 64, 70 ]
92
[ "94-8=86", "70-64=6", "86+6=92" ]
Current State: 92:[8, 94, 64, 70], Operations: [] Exploring Operation: 94-8=86, Resulting Numbers: [64, 70, 86] Generated Node #2: [64, 70, 86] from Operation: 94-8=86 Current State: 92:[64, 70, 86], Operations: ['94-8=86'] Exploring Operation: 70-64=6, Resulting Numbers: [86, 6] Generated Node #3: [86, 6] from Operation: 70-64=6 Current State: 92:[86, 6], Operations: ['94-8=86', '70-64=6'] Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[8, 94, 64, 70], Operations: [] Exploring Operation: 94-70=24, Resulting Numbers: [8, 64, 24] Generated Node #0,0: 92:[8, 64, 24] Operation: 94-70=24 Exploring Operation: 70-64=6, Resulting Numbers: [8, 94, 6] Generated Node #0,1: 92:[8, 94, 6] Operation: 70-64=6 Moving to Node #0,1 Current State: 92:[8, 94, 6], Operations: ['70-64=6'] Exploring Operation: 8-6=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 92:[94, 2] Operation: 8-6=2 Exploring Operation: 8*6=48, Resulting Numbers: [94, 48] Generated Node #0,1,1: 92:[94, 48] Operation: 8*6=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[94, 2], Operations: ['70-64=6', '8-6=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[8, 94, 64, 70], Operations: [] Exploring Operation: 70-64=6, Resulting Numbers: [8, 94, 6] Generated Node #0,1: 92:[8, 94, 6] Operation: 70-64=6 Moving to Node #0,1 Current State: 92:[8, 94, 6], Operations: ['70-64=6'] Exploring Operation: 8-6=2, Resulting Numbers: [94, 2] Generated Node #0,1,0: 92:[94, 2] Operation: 8-6=2 Moving to Node #0,1,0 Current State: 92:[94, 2], Operations: ['70-64=6', '8-6=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 31, 2, 32, 87 ]
79
[ "87-32=55", "2*55=110", "110-31=79" ]
Current State: 79:[31, 2, 32, 87], Operations: [] Exploring Operation: 87-32=55, Resulting Numbers: [31, 2, 55] Generated Node #2: [31, 2, 55] from Operation: 87-32=55 Current State: 79:[31, 2, 55], Operations: ['87-32=55'] Exploring Operation: 2*55=110, Resulting Numbers: [31, 110] Generated Node #3: [31, 110] from Operation: 2*55=110 Current State: 79:[31, 110], Operations: ['87-32=55', '2*55=110'] Exploring Operation: 110-31=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[31, 2, 32, 87], Operations: [] Exploring Operation: 31+2=33, Resulting Numbers: [32, 87, 33] Generated Node #0,0: 79:[32, 87, 33] Operation: 31+2=33 Exploring Operation: 31*2=62, Resulting Numbers: [32, 87, 62] Generated Node #0,1: 79:[32, 87, 62] Operation: 31*2=62 Exploring Operation: 2*32=64, Resulting Numbers: [31, 87, 64] Generated Node #0,2: 79:[31, 87, 64] Operation: 2*32=64 Exploring Operation: 31+32=63, Resulting Numbers: [2, 87, 63] Generated Node #0,3: 79:[2, 87, 63] Operation: 31+32=63 Moving to Node #0,2 Current State: 79:[31, 87, 64], Operations: ['2*32=64'] Exploring Operation: 31+64=95, Resulting Numbers: [87, 95] Generated Node #0,2,0: 79:[87, 95] Operation: 31+64=95 Exploring Operation: 31+87=118, Resulting Numbers: [64, 118] Generated Node #0,2,1: 79:[64, 118] Operation: 31+87=118 Exploring Operation: 64-31=33, Resulting Numbers: [87, 33] Generated Node #0,2,2: 79:[87, 33] Operation: 64-31=33 Exploring Operation: 87-31=56, Resulting Numbers: [64, 56] Generated Node #0,2,3: 79:[64, 56] Operation: 87-31=56 Moving to Node #0,1 Current State: 79:[32, 87, 62], Operations: ['31*2=62'] Exploring Operation: 32+62=94, Resulting Numbers: [87, 94] Generated Node #0,1,0: 79:[87, 94] Operation: 32+62=94 Exploring Operation: 32+87=119, Resulting Numbers: [62, 119] Generated Node #0,1,1: 79:[62, 119] Operation: 32+87=119 Exploring Operation: 87-32=55, Resulting Numbers: [62, 55] Generated Node #0,1,2: 79:[62, 55] Operation: 87-32=55 Exploring Operation: 62-32=30, Resulting Numbers: [87, 30] Generated Node #0,1,3: 79:[87, 30] Operation: 62-32=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[87, 94], Operations: ['31*2=62', '32+62=94'] Exploring Operation: 87+94=181, Resulting Numbers: [181] 181,79 unequal: No Solution Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 87*94=8178, Resulting Numbers: [8178] 8178,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[62, 55], Operations: ['31*2=62', '87-32=55'] Exploring Operation: 62-55=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 62+55=117, Resulting Numbers: [117] 117,79 unequal: No Solution Exploring Operation: 62*55=3410, Resulting Numbers: [3410] 3410,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[62, 119], Operations: ['31*2=62', '32+87=119'] Exploring Operation: 119-62=57, Resulting Numbers: [57] 57,79 unequal: No Solution Exploring Operation: 62+119=181, Resulting Numbers: [181] 181,79 unequal: No Solution Exploring Operation: 62*119=7378, Resulting Numbers: [7378] 7378,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[87, 30], Operations: ['31*2=62', '62-32=30'] Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,79 unequal: No Solution Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,79 unequal: No Solution Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,79 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: 79:[2, 87, 63], Operations: ['31+32=63'] Exploring Operation: 2+87=89, Resulting Numbers: [63, 89] Generated Node #0,3,0: 79:[63, 89] Operation: 2+87=89 Exploring Operation: 87-2=85, Resulting Numbers: [63, 85] Generated Node #0,3,1: 79:[63, 85] Operation: 87-2=85 Exploring Operation: 2+63=65, Resulting Numbers: [87, 65] Generated Node #0,3,2: 79:[87, 65] Operation: 2+63=65 Exploring Operation: 63-2=61, Resulting Numbers: [87, 61] Generated Node #0,3,3: 79:[87, 61] Operation: 63-2=61 Moving to Node #0,0 Current State: 79:[32, 87, 33], Operations: ['31+2=33'] Exploring Operation: 32+87=119, Resulting Numbers: [33, 119] Generated Node #0,0,0: 79:[33, 119] Operation: 32+87=119 Exploring Operation: 87-32=55, Resulting Numbers: [33, 55] Generated Node #0,0,1: 79:[33, 55] Operation: 87-32=55 Exploring Operation: 32+33=65, Resulting Numbers: [87, 65] Generated Node #0,0,2: 79:[87, 65] Operation: 32+33=65 Exploring Operation: 87-33=54, Resulting Numbers: [32, 54] Generated Node #0,0,3: 79:[32, 54] Operation: 87-33=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[87, 65], Operations: ['31+2=33', '32+33=65'] Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,79 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,79 unequal: No Solution Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,79 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 #0,0,1 Current State: 79:[33, 55], Operations: ['31+2=33', '87-32=55'] Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,79 unequal: No Solution Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,79 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,79 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 #0,0,3 Current State: 79:[32, 54], Operations: ['31+2=33', '87-33=54'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,79 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,79 unequal: No Solution Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,79 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:[33, 119], Operations: ['31+2=33', '32+87=119'] Exploring Operation: 119-33=86, Resulting Numbers: [86] 86,79 unequal: No Solution Exploring Operation: 33*119=3927, Resulting Numbers: [3927] 3927,79 unequal: No Solution Exploring Operation: 33+119=152, Resulting Numbers: [152] 152,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 79:[63, 85], Operations: ['31+32=63', '87-2=85'] Exploring Operation: 63+85=148, Resulting Numbers: [148] 148,79 unequal: No Solution Exploring Operation: 63*85=5355, Resulting Numbers: [5355] 5355,79 unequal: No Solution Exploring Operation: 85-63=22, Resulting Numbers: [22] 22,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[87, 65], Operations: ['31+32=63', '2+63=65'] Exploring Operation: 87+65=152, Resulting Numbers: [152] 152,79 unequal: No Solution Exploring Operation: 87-65=22, Resulting Numbers: [22] 22,79 unequal: No Solution Exploring Operation: 87*65=5655, Resulting Numbers: [5655] 5655,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[87, 95], Operations: ['2*32=64', '31+64=95'] Exploring Operation: 95-87=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 87*95=8265, Resulting Numbers: [8265] 8265,79 unequal: No Solution Exploring Operation: 87+95=182, Resulting Numbers: [182] 182,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[63, 89], Operations: ['31+32=63', '2+87=89'] Exploring Operation: 63*89=5607, Resulting Numbers: [5607] 5607,79 unequal: No Solution Exploring Operation: 63+89=152, Resulting Numbers: [152] 152,79 unequal: No Solution Exploring Operation: 89-63=26, Resulting Numbers: [26] 26,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[87, 61], Operations: ['31+32=63', '63-2=61'] Exploring Operation: 87+61=148, Resulting Numbers: [148] 148,79 unequal: No Solution Exploring Operation: 87-61=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 87*61=5307, Resulting Numbers: [5307] 5307,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[64, 56], Operations: ['2*32=64', '87-31=56'] Exploring Operation: 64*56=3584, Resulting Numbers: [3584] 3584,79 unequal: No Solution Exploring Operation: 64+56=120, Resulting Numbers: [120] 120,79 unequal: No Solution Exploring Operation: 64-56=8, Resulting Numbers: [8] 8,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[87, 33], Operations: ['2*32=64', '64-31=33'] Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,79 unequal: No Solution Exploring Operation: 87*33=2871, Resulting Numbers: [2871] 2871,79 unequal: No Solution Exploring Operation: 87+33=120, Resulting Numbers: [120] 120,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[64, 118], Operations: ['2*32=64', '31+87=118'] Exploring Operation: 64*118=7552, Resulting Numbers: [7552] 7552,79 unequal: No Solution Exploring Operation: 64+118=182, Resulting Numbers: [182] 182,79 unequal: No Solution Exploring Operation: 118-64=54, Resulting Numbers: [54] 54,79 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 24, 67, 69, 24 ]
48
[ "24*67=1608", "69*24=1656", "1656-1608=48" ]
Current State: 48:[24, 67, 69, 24], Operations: [] Exploring Operation: 24*67=1608, Resulting Numbers: [69, 1608] Generated Node #2: [69, 1608] from Operation: 24*67=1608 Current State: 48:[69, 1608], Operations: ['24*67=1608'] Exploring Operation: 69*24=1656, Resulting Numbers: [1608, 1656] Generated Node #3: [1608, 1656] from Operation: 69*24=1656 Current State: 48:[1608, 1656], Operations: ['24*67=1608', '69*24=1656'] Exploring Operation: 1656-1608=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[24, 67, 69, 24], Operations: [] Exploring Operation: 69-24=45, Resulting Numbers: [67, 24, 45] Generated Node #0,0: 48:[67, 24, 45] Operation: 69-24=45 Exploring Operation: 69-67=2, Resulting Numbers: [24, 24, 2] Generated Node #0,1: 48:[24, 24, 2] Operation: 69-67=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[24, 24, 2], Operations: ['69-67=2'] Exploring Operation: 24+24=48, Resulting Numbers: [2, 48] Generated Node #0,1,0: 48:[2, 48] Operation: 24+24=48 Exploring Operation: 24*2=48, Resulting Numbers: [24, 48] Generated Node #0,1,1: 48:[24, 48] Operation: 24*2=48 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 48:[2, 48], Operations: ['69-67=2', '24+24=48'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,48 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,48 unequal: No Solution No 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: 48:[24, 48], Operations: ['69-67=2', '24*2=48'] Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,48 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: 48:[67, 24, 45], Operations: ['69-24=45'] Exploring Operation: 67-24=43, Resulting Numbers: [45, 43] Generated Node #0,0,0: 48:[45, 43] Operation: 67-24=43 Exploring Operation: 67-45=22, Resulting Numbers: [24, 22] Generated Node #0,0,1: 48:[24, 22] Operation: 67-45=22 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[24, 22], Operations: ['69-24=45', '67-45=22'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,48 unequal: No Solution Exploring Operation: 24+22=46, Resulting Numbers: [46] 46,48 unequal: No Solution No 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: 48:[45, 43], Operations: ['69-24=45', '67-24=43'] Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,48 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,48 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
[ 78, 28, 3, 77 ]
31
[ "78-77=1", "28+3=31", "1*31=31" ]
Current State: 31:[78, 28, 3, 77], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [28, 3, 1] Generated Node #2: [28, 3, 1] from Operation: 78-77=1 Current State: 31:[28, 3, 1], Operations: ['78-77=1'] Exploring Operation: 28+3=31, Resulting Numbers: [1, 31] Generated Node #3: [1, 31] from Operation: 28+3=31 Current State: 31:[1, 31], Operations: ['78-77=1', '28+3=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[78, 28, 3, 77], Operations: [] Exploring Operation: 78/3=26, Resulting Numbers: [28, 77, 26] Generated Node #0,0: 31:[28, 77, 26] Operation: 78/3=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[28, 77, 26], Operations: ['78/3=26'] Exploring Operation: 77-28=49, Resulting Numbers: [26, 49] Generated Node #0,0,0: 31:[26, 49] Operation: 77-28=49 Moving to Node #0,0,0 Current State: 31:[26, 49], Operations: ['78/3=26', '77-28=49'] Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 48, 26, 33, 73 ]
18
[ "48-26=22", "73-33=40", "40-22=18" ]
Current State: 18:[48, 26, 33, 73], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [33, 73, 22] Generated Node #2: [33, 73, 22] from Operation: 48-26=22 Current State: 18:[33, 73, 22], Operations: ['48-26=22'] Exploring Operation: 73-33=40, Resulting Numbers: [22, 40] Generated Node #3: [22, 40] from Operation: 73-33=40 Current State: 18:[22, 40], Operations: ['48-26=22', '73-33=40'] Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[48, 26, 33, 73], Operations: [] Exploring Operation: 73-33=40, Resulting Numbers: [48, 26, 40] Generated Node #0,0: 18:[48, 26, 40] Operation: 73-33=40 Exploring Operation: 73-48=25, Resulting Numbers: [26, 33, 25] Generated Node #0,1: 18:[26, 33, 25] Operation: 73-48=25 Moving to Node #0,1 Current State: 18:[26, 33, 25], Operations: ['73-48=25'] Exploring Operation: 33-26=7, Resulting Numbers: [25, 7] Generated Node #0,1,0: 18:[25, 7] Operation: 33-26=7 Exploring Operation: 33-25=8, Resulting Numbers: [26, 8] Generated Node #0,1,1: 18:[26, 8] Operation: 33-25=8 Moving to Node #0,0 Current State: 18:[48, 26, 40], Operations: ['73-33=40'] Exploring Operation: 48-26=22, Resulting Numbers: [40, 22] Generated Node #0,0,0: 18:[40, 22] Operation: 48-26=22 Exploring Operation: 48-40=8, Resulting Numbers: [26, 8] Generated Node #0,0,1: 18:[26, 8] Operation: 48-40=8 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[26, 8], Operations: ['73-33=40', '48-40=8'] Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[48, 26, 33, 73], Operations: [] Exploring Operation: 73-33=40, Resulting Numbers: [48, 26, 40] Generated Node #0,0: 18:[48, 26, 40] Operation: 73-33=40 Moving to Node #0,0 Current State: 18:[48, 26, 40], Operations: ['73-33=40'] Exploring Operation: 48-40=8, Resulting Numbers: [26, 8] Generated Node #0,0,1: 18:[26, 8] Operation: 48-40=8 Moving to Node #0,0,1 Current State: 18:[26, 8], Operations: ['73-33=40', '48-40=8'] Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 71, 71, 47, 10 ]
10
[ "71-71=0", "47*0=0", "10+0=10" ]
Current State: 10:[71, 71, 47, 10], Operations: [] Exploring Operation: 71-71=0, Resulting Numbers: [47, 10, 0] Generated Node #2: [47, 10, 0] from Operation: 71-71=0 Current State: 10:[47, 10, 0], Operations: ['71-71=0'] Exploring Operation: 47*0=0, Resulting Numbers: [10, 0] Generated Node #3: [10, 0] from Operation: 47*0=0 Current State: 10:[10, 0], Operations: ['71-71=0', '47*0=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[71, 71, 47, 10], Operations: [] Exploring Operation: 71-47=24, Resulting Numbers: [71, 10, 24] Generated Node #0,0: 10:[71, 10, 24] Operation: 71-47=24 Exploring Operation: 71-47=24, Resulting Numbers: [71, 10, 24] Generated Node #0,1: 10:[71, 10, 24] Operation: 71-47=24 Exploring Operation: 71-71=0, Resulting Numbers: [47, 10, 0] Generated Node #0,2: 10:[47, 10, 0] Operation: 71-71=0 Exploring Operation: 71/71=1, Resulting Numbers: [47, 10, 1] Generated Node #0,3: 10:[47, 10, 1] Operation: 71/71=1 Moving to Node #0,3 Current State: 10:[47, 10, 1], Operations: ['71/71=1'] Exploring Operation: 47/1=47, Resulting Numbers: [10, 47] Generated Node #0,3,0: 10:[10, 47] Operation: 47/1=47 Exploring Operation: 47-10=37, Resulting Numbers: [1, 37] Generated Node #0,3,1: 10:[1, 37] Operation: 47-10=37 Exploring Operation: 47*1=47, Resulting Numbers: [10, 47] Generated Node #0,3,2: 10:[10, 47] Operation: 47*1=47 Exploring Operation: 47-1=46, Resulting Numbers: [10, 46] Generated Node #0,3,3: 10:[10, 46] Operation: 47-1=46 Moving to Node #0,2 Current State: 10:[47, 10, 0], Operations: ['71-71=0'] Exploring Operation: 47+0=47, Resulting Numbers: [10, 47] Generated Node #0,2,0: 10:[10, 47] Operation: 47+0=47 Exploring Operation: 47*0=0, Resulting Numbers: [10, 0] Generated Node #0,2,1: 10:[10, 0] Operation: 47*0=0 Exploring Operation: 47-10=37, Resulting Numbers: [0, 37] Generated Node #0,2,2: 10:[0, 37] Operation: 47-10=37 Exploring Operation: 47-0=47, Resulting Numbers: [10, 47] Generated Node #0,2,3: 10:[10, 47] Operation: 47-0=47 Moving to Node #0,1 Current State: 10:[71, 10, 24], Operations: ['71-47=24'] Exploring Operation: 71-24=47, Resulting Numbers: [10, 47] Generated Node #0,1,0: 10:[10, 47] Operation: 71-24=47 Exploring Operation: 24-10=14, Resulting Numbers: [71, 14] Generated Node #0,1,1: 10:[71, 14] Operation: 24-10=14 Exploring Operation: 71-10=61, Resulting Numbers: [24, 61] Generated Node #0,1,2: 10:[24, 61] Operation: 71-10=61 Exploring Operation: 71+10=81, Resulting Numbers: [24, 81] Generated Node #0,1,3: 10:[24, 81] Operation: 71+10=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[10, 47], Operations: ['71-47=24', '71-24=47'] Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,10 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[71, 14], Operations: ['71-47=24', '24-10=14'] Exploring Operation: 71*14=994, Resulting Numbers: [994] 994,10 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 71+14=85, Resulting Numbers: [85] 85,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 10:[24, 61], Operations: ['71-47=24', '71-10=61'] Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,10 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 10:[24, 81], Operations: ['71-47=24', '71+10=81'] Exploring Operation: 24+81=105, Resulting Numbers: [105] 105,10 unequal: No Solution Exploring Operation: 24*81=1944, Resulting Numbers: [1944] 1944,10 unequal: No Solution Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,10 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: 10:[71, 10, 24], Operations: ['71-47=24'] Exploring Operation: 24-10=14, Resulting Numbers: [71, 14] Generated Node #0,0,0: 10:[71, 14] Operation: 24-10=14 Exploring Operation: 71-10=61, Resulting Numbers: [24, 61] Generated Node #0,0,1: 10:[24, 61] Operation: 71-10=61 Exploring Operation: 71-24=47, Resulting Numbers: [10, 47] Generated Node #0,0,2: 10:[10, 47] Operation: 71-24=47 Exploring Operation: 71+10=81, Resulting Numbers: [24, 81] Generated Node #0,0,3: 10:[24, 81] Operation: 71+10=81 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[10, 47], Operations: ['71-47=24', '71-24=47'] Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,10 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,10 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:[71, 14], Operations: ['71-47=24', '24-10=14'] Exploring Operation: 71*14=994, Resulting Numbers: [994] 994,10 unequal: No Solution Exploring Operation: 71+14=85, Resulting Numbers: [85] 85,10 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,10 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:[24, 61], Operations: ['71-47=24', '71-10=61'] Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,10 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,10 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 #0,0,3 Current State: 10:[24, 81], Operations: ['71-47=24', '71+10=81'] Exploring Operation: 81-24=57, Resulting Numbers: [57] 57,10 unequal: No Solution Exploring Operation: 24*81=1944, Resulting Numbers: [1944] 1944,10 unequal: No Solution Exploring Operation: 24+81=105, Resulting Numbers: [105] 105,10 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: 10:[10, 0], Operations: ['71-71=0', '47*0=0'] Exploring Operation: 10*0=0, Resulting Numbers: [0] 0,10 unequal: No Solution Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[71, 71, 47, 10], Operations: [] Exploring Operation: 71-71=0, Resulting Numbers: [47, 10, 0] Generated Node #0,2: 10:[47, 10, 0] Operation: 71-71=0 Moving to Node #0,2 Current State: 10:[47, 10, 0], Operations: ['71-71=0'] Exploring Operation: 47*0=0, Resulting Numbers: [10, 0] Generated Node #0,2,1: 10:[10, 0] Operation: 47*0=0 Moving to Node #0,2,1 Current State: 10:[10, 0], Operations: ['71-71=0', '47*0=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.956597
hs_4
mult_heuristic
[ 2, 73, 55, 50 ]
16
[ "73-55=18", "50-18=32", "32/2=16" ]
Current State: 16:[2, 73, 55, 50], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [2, 50, 18] Generated Node #2: [2, 50, 18] from Operation: 73-55=18 Current State: 16:[2, 50, 18], Operations: ['73-55=18'] Exploring Operation: 50-18=32, Resulting Numbers: [2, 32] Generated Node #3: [2, 32] from Operation: 50-18=32 Current State: 16:[2, 32], Operations: ['73-55=18', '50-18=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[2, 73, 55, 50], Operations: [] Exploring Operation: 73-50=23, Resulting Numbers: [2, 55, 23] Generated Node #0,0: 16:[2, 55, 23] Operation: 73-50=23 Exploring Operation: 73-55=18, Resulting Numbers: [2, 50, 18] Generated Node #0,1: 16:[2, 50, 18] Operation: 73-55=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[2, 50, 18], Operations: ['73-55=18'] Exploring Operation: 50-18=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 16:[2, 32] Operation: 50-18=32 Exploring Operation: 50/2=25, Resulting Numbers: [18, 25] Generated Node #0,1,1: 16:[18, 25] Operation: 50/2=25 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[18, 25], Operations: ['73-55=18', '50/2=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,16 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,16 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 #0,1,0 Current State: 16:[2, 32], Operations: ['73-55=18', '50-18=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[2, 73, 55, 50], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [2, 50, 18] Generated Node #0,1: 16:[2, 50, 18] Operation: 73-55=18 Moving to Node #0,1 Current State: 16:[2, 50, 18], Operations: ['73-55=18'] Exploring Operation: 50-18=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 16:[2, 32] Operation: 50-18=32 Moving to Node #0,1,0 Current State: 16:[2, 32], Operations: ['73-55=18', '50-18=32'] Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 65, 61, 53, 26 ]
83
[ "65-61=4", "53+26=79", "4+79=83" ]
Current State: 83:[65, 61, 53, 26], Operations: [] Exploring Operation: 65-61=4, Resulting Numbers: [53, 26, 4] Generated Node #2: [53, 26, 4] from Operation: 65-61=4 Current State: 83:[53, 26, 4], Operations: ['65-61=4'] Exploring Operation: 53+26=79, Resulting Numbers: [4, 79] Generated Node #3: [4, 79] from Operation: 53+26=79 Current State: 83:[4, 79], Operations: ['65-61=4', '53+26=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[65, 61, 53, 26], Operations: [] Exploring Operation: 65+26=91, Resulting Numbers: [61, 53, 91] Generated Node #0,0: 83:[61, 53, 91] Operation: 65+26=91 Exploring Operation: 61+26=87, Resulting Numbers: [65, 53, 87] Generated Node #0,1: 83:[65, 53, 87] Operation: 61+26=87 Exploring Operation: 53+26=79, Resulting Numbers: [65, 61, 79] Generated Node #0,2: 83:[65, 61, 79] Operation: 53+26=79 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[65, 61, 79], Operations: ['53+26=79'] Exploring Operation: 61+79=140, Resulting Numbers: [65, 140] Generated Node #0,2,0: 83:[65, 140] Operation: 61+79=140 Exploring Operation: 65-61=4, Resulting Numbers: [79, 4] Generated Node #0,2,1: 83:[79, 4] Operation: 65-61=4 Exploring Operation: 65+61=126, Resulting Numbers: [79, 126] Generated Node #0,2,2: 83:[79, 126] Operation: 65+61=126 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[79, 126], Operations: ['53+26=79', '65+61=126'] Exploring Operation: 79*126=9954, Resulting Numbers: [9954] 9954,83 unequal: No Solution Exploring Operation: 79+126=205, Resulting Numbers: [205] 205,83 unequal: No Solution Exploring Operation: 126-79=47, Resulting Numbers: [47] 47,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[65, 140], Operations: ['53+26=79', '61+79=140'] Exploring Operation: 65*140=9100, Resulting Numbers: [9100] 9100,83 unequal: No Solution Exploring Operation: 65+140=205, Resulting Numbers: [205] 205,83 unequal: No Solution Exploring Operation: 140-65=75, Resulting Numbers: [75] 75,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[79, 4], Operations: ['53+26=79', '65-61=4'] Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,83 unequal: No Solution Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[65, 61, 53, 26], Operations: [] Exploring Operation: 53+26=79, Resulting Numbers: [65, 61, 79] Generated Node #0,2: 83:[65, 61, 79] Operation: 53+26=79 Moving to Node #0,2 Current State: 83:[65, 61, 79], Operations: ['53+26=79'] Exploring Operation: 65-61=4, Resulting Numbers: [79, 4] Generated Node #0,2,1: 83:[79, 4] Operation: 65-61=4 Moving to Node #0,2,1 Current State: 83:[79, 4], Operations: ['53+26=79', '65-61=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 25, 5, 90, 14 ]
63
[ "25-5=20", "90*14=1260", "1260/20=63" ]
Current State: 63:[25, 5, 90, 14], Operations: [] Exploring Operation: 25-5=20, Resulting Numbers: [90, 14, 20] Generated Node #2: [90, 14, 20] from Operation: 25-5=20 Current State: 63:[90, 14, 20], Operations: ['25-5=20'] Exploring Operation: 90*14=1260, Resulting Numbers: [20, 1260] Generated Node #3: [20, 1260] from Operation: 90*14=1260 Current State: 63:[20, 1260], Operations: ['25-5=20', '90*14=1260'] Exploring Operation: 1260/20=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[25, 5, 90, 14], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [5, 14, 65] Generated Node #0,0: 63:[5, 14, 65] Operation: 90-25=65 Exploring Operation: 90-14=76, Resulting Numbers: [25, 5, 76] Generated Node #0,1: 63:[25, 5, 76] Operation: 90-14=76 Exploring Operation: 90/5=18, Resulting Numbers: [25, 14, 18] Generated Node #0,2: 63:[25, 14, 18] Operation: 90/5=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[5, 14, 65], Operations: ['90-25=65'] Exploring Operation: 65-5=60, Resulting Numbers: [14, 60] Generated Node #0,0,0: 63:[14, 60] Operation: 65-5=60 Exploring Operation: 5+14=19, Resulting Numbers: [65, 19] Generated Node #0,0,1: 63:[65, 19] Operation: 5+14=19 Exploring Operation: 14-5=9, Resulting Numbers: [65, 9] Generated Node #0,0,2: 63:[65, 9] Operation: 14-5=9 Moving to Node #0,0,2 Current State: 63:[65, 9], Operations: ['90-25=65', '14-5=9'] Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 65+9=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 65*9=585, Resulting Numbers: [585] 585,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[65, 19], Operations: ['90-25=65', '5+14=19'] Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 65*19=1235, Resulting Numbers: [1235] 1235,63 unequal: No Solution Exploring Operation: 65+19=84, Resulting Numbers: [84] 84,63 unequal: No Solution Moving to Node #0,0,0 Current State: 63:[14, 60], Operations: ['90-25=65', '65-5=60'] Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 14*60=840, Resulting Numbers: [840] 840,63 unequal: No Solution Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 63:[25, 14, 18], Operations: ['90/5=18'] Exploring Operation: 18-14=4, Resulting Numbers: [25, 4] Generated Node #0,2,0: 63:[25, 4] Operation: 18-14=4 Exploring Operation: 25-14=11, Resulting Numbers: [18, 11] Generated Node #0,2,1: 63:[18, 11] Operation: 25-14=11 Exploring Operation: 25-18=7, Resulting Numbers: [14, 7] Generated Node #0,2,2: 63:[14, 7] Operation: 25-18=7 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 63:[25, 4], Operations: ['90/5=18', '18-14=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 63:[18, 11], Operations: ['90/5=18', '25-14=11'] Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,63 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,63 unequal: No Solution Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[14, 7], Operations: ['90/5=18', '25-18=7'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,63 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[25, 5, 76], Operations: ['90-14=76'] Exploring Operation: 76-25=51, Resulting Numbers: [5, 51] Generated Node #0,1,0: 63:[5, 51] Operation: 76-25=51 Exploring Operation: 25-5=20, Resulting Numbers: [76, 20] Generated Node #0,1,1: 63:[76, 20] Operation: 25-5=20 Exploring Operation: 76-5=71, Resulting Numbers: [25, 71] Generated Node #0,1,2: 63:[25, 71] Operation: 76-5=71 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 63:[25, 71], Operations: ['90-14=76', '76-5=71'] Exploring Operation: 25*71=1775, Resulting Numbers: [1775] 1775,63 unequal: No Solution Exploring Operation: 71-25=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 25+71=96, Resulting Numbers: [96] 96,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 63:[5, 51], Operations: ['90-14=76', '76-25=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 63:[76, 20], Operations: ['90-14=76', '25-5=20'] Exploring Operation: 76*20=1520, Resulting Numbers: [1520] 1520,63 unequal: No Solution Exploring Operation: 76+20=96, Resulting Numbers: [96] 96,63 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,63 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 5, 87, 55, 41 ]
78
[ "5+87=92", "55-41=14", "92-14=78" ]
Current State: 78:[5, 87, 55, 41], Operations: [] Exploring Operation: 5+87=92, Resulting Numbers: [55, 41, 92] Generated Node #2: [55, 41, 92] from Operation: 5+87=92 Current State: 78:[55, 41, 92], Operations: ['5+87=92'] Exploring Operation: 55-41=14, Resulting Numbers: [92, 14] Generated Node #3: [92, 14] from Operation: 55-41=14 Current State: 78:[92, 14], Operations: ['5+87=92', '55-41=14'] Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[5, 87, 55, 41], Operations: [] Exploring Operation: 87-55=32, Resulting Numbers: [5, 41, 32] Generated Node #0,0: 78:[5, 41, 32] Operation: 87-55=32 Exploring Operation: 55-41=14, Resulting Numbers: [5, 87, 14] Generated Node #0,1: 78:[5, 87, 14] Operation: 55-41=14 Exploring Operation: 55/5=11, Resulting Numbers: [87, 41, 11] Generated Node #0,2: 78:[87, 41, 11] Operation: 55/5=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[5, 41, 32], Operations: ['87-55=32'] Exploring Operation: 41-32=9, Resulting Numbers: [5, 9] Generated Node #0,0,0: 78:[5, 9] Operation: 41-32=9 Exploring Operation: 32-5=27, Resulting Numbers: [41, 27] Generated Node #0,0,1: 78:[41, 27] Operation: 32-5=27 Exploring Operation: 5+32=37, Resulting Numbers: [41, 37] Generated Node #0,0,2: 78:[41, 37] Operation: 5+32=37 Moving to Node #0,0,1 Current State: 78:[41, 27], Operations: ['87-55=32', '32-5=27'] Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,78 unequal: No Solution Exploring Operation: 41*27=1107, Resulting Numbers: [1107] 1107,78 unequal: No Solution Exploring Operation: 41+27=68, Resulting Numbers: [68] 68,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[5, 9], Operations: ['87-55=32', '41-32=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,78 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[41, 37], Operations: ['87-55=32', '5+32=37'] Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[5, 87, 55, 41], Operations: [] Exploring Operation: 87-55=32, Resulting Numbers: [5, 41, 32] Generated Node #0,0: 78:[5, 41, 32] Operation: 87-55=32 Moving to Node #0,0 Current State: 78:[5, 41, 32], Operations: ['87-55=32'] Exploring Operation: 5+32=37, Resulting Numbers: [41, 37] Generated Node #0,0,2: 78:[41, 37] Operation: 5+32=37 Moving to Node #0,0,2 Current State: 78:[41, 37], Operations: ['87-55=32', '5+32=37'] Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 40, 69, 50, 18 ]
39
[ "69-40=29", "50+18=68", "68-29=39" ]
Current State: 39:[40, 69, 50, 18], Operations: [] Exploring Operation: 69-40=29, Resulting Numbers: [50, 18, 29] Generated Node #2: [50, 18, 29] from Operation: 69-40=29 Current State: 39:[50, 18, 29], Operations: ['69-40=29'] Exploring Operation: 50+18=68, Resulting Numbers: [29, 68] Generated Node #3: [29, 68] from Operation: 50+18=68 Current State: 39:[29, 68], Operations: ['69-40=29', '50+18=68'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[40, 69, 50, 18], Operations: [] Exploring Operation: 69-18=51, Resulting Numbers: [40, 50, 51] Generated Node #0,0: 39:[40, 50, 51] Operation: 69-18=51 Exploring Operation: 69-40=29, Resulting Numbers: [50, 18, 29] Generated Node #0,1: 39:[50, 18, 29] Operation: 69-40=29 Exploring Operation: 69-50=19, Resulting Numbers: [40, 18, 19] Generated Node #0,2: 39:[40, 18, 19] Operation: 69-50=19 Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[40, 18, 19], Operations: ['69-50=19'] Exploring Operation: 40-19=21, Resulting Numbers: [18, 21] Generated Node #0,2,0: 39:[18, 21] Operation: 40-19=21 Exploring Operation: 19-18=1, Resulting Numbers: [40, 1] Generated Node #0,2,1: 39:[40, 1] Operation: 19-18=1 Exploring Operation: 18+19=37, Resulting Numbers: [40, 37] Generated Node #0,2,2: 39:[40, 37] Operation: 18+19=37 Moving to Node #0,2,1 Current State: 39:[40, 1], Operations: ['69-50=19', '19-18=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[40, 69, 50, 18], Operations: [] Exploring Operation: 69-50=19, Resulting Numbers: [40, 18, 19] Generated Node #0,2: 39:[40, 18, 19] Operation: 69-50=19 Moving to Node #0,2 Current State: 39:[40, 18, 19], Operations: ['69-50=19'] Exploring Operation: 19-18=1, Resulting Numbers: [40, 1] Generated Node #0,2,1: 39:[40, 1] Operation: 19-18=1 Moving to Node #0,2,1 Current State: 39:[40, 1], Operations: ['69-50=19', '19-18=1'] Exploring Operation: 40-1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 2, 85, 62, 53 ]
63
[ "62/2=31", "85-53=32", "31+32=63" ]
Current State: 63:[2, 85, 62, 53], Operations: [] Exploring Operation: 62/2=31, Resulting Numbers: [85, 53, 31] Generated Node #2: [85, 53, 31] from Operation: 62/2=31 Current State: 63:[85, 53, 31], Operations: ['62/2=31'] Exploring Operation: 85-53=32, Resulting Numbers: [31, 32] Generated Node #3: [31, 32] from Operation: 85-53=32 Current State: 63:[31, 32], Operations: ['62/2=31', '85-53=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[2, 85, 62, 53], Operations: [] Exploring Operation: 85-62=23, Resulting Numbers: [2, 53, 23] Generated Node #0,0: 63:[2, 53, 23] Operation: 85-62=23 Exploring Operation: 85-53=32, Resulting Numbers: [2, 62, 32] Generated Node #0,1: 63:[2, 62, 32] Operation: 85-53=32 Moving to Node #0,0 Current State: 63:[2, 53, 23], Operations: ['85-62=23'] Exploring Operation: 2+53=55, Resulting Numbers: [23, 55] Generated Node #0,0,0: 63:[23, 55] Operation: 2+53=55 Exploring Operation: 23-2=21, Resulting Numbers: [53, 21] Generated Node #0,0,1: 63:[53, 21] Operation: 23-2=21 Moving to Node #0,1 Current State: 63:[2, 62, 32], Operations: ['85-53=32'] Exploring Operation: 2*32=64, Resulting Numbers: [62, 64] Generated Node #0,1,0: 63:[62, 64] Operation: 2*32=64 Exploring Operation: 32/2=16, Resulting Numbers: [62, 16] Generated Node #0,1,1: 63:[62, 16] Operation: 32/2=16 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[62, 64], Operations: ['85-53=32', '2*32=64'] Exploring Operation: 64-62=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 62+64=126, Resulting Numbers: [126] 126,63 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:[62, 16], Operations: ['85-53=32', '32/2=16'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,63 unequal: No Solution Exploring Operation: 62+16=78, Resulting Numbers: [78] 78,63 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: 63:[23, 55], Operations: ['85-62=23', '2+53=55'] Exploring Operation: 23+55=78, Resulting Numbers: [78] 78,63 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[53, 21], Operations: ['85-62=23', '23-2=21'] Exploring Operation: 53+21=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 53-21=32, Resulting Numbers: [32] 32,63 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 36, 77, 3, 78 ]
39
[ "36+3=39", "78-77=1", "39*1=39" ]
Current State: 39:[36, 77, 3, 78], Operations: [] Exploring Operation: 36+3=39, Resulting Numbers: [77, 78, 39] Generated Node #2: [77, 78, 39] from Operation: 36+3=39 Current State: 39:[77, 78, 39], Operations: ['36+3=39'] Exploring Operation: 78-77=1, Resulting Numbers: [39, 1] Generated Node #3: [39, 1] from Operation: 78-77=1 Current State: 39:[39, 1], Operations: ['36+3=39', '78-77=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[36, 77, 3, 78], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [36, 3, 1] Generated Node #0,0: 39:[36, 3, 1] Operation: 78-77=1 Exploring Operation: 77-36=41, Resulting Numbers: [3, 78, 41] Generated Node #0,1: 39:[3, 78, 41] Operation: 77-36=41 Exploring Operation: 78-36=42, Resulting Numbers: [77, 3, 42] Generated Node #0,2: 39:[77, 3, 42] Operation: 78-36=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[36, 3, 1], Operations: ['78-77=1'] Exploring Operation: 36+1=37, Resulting Numbers: [3, 37] Generated Node #0,0,0: 39:[3, 37] Operation: 36+1=37 Exploring Operation: 36/3=12, Resulting Numbers: [1, 12] Generated Node #0,0,1: 39:[1, 12] Operation: 36/3=12 Exploring Operation: 36+3=39, Resulting Numbers: [1, 39] Generated Node #0,0,2: 39:[1, 39] Operation: 36+3=39 Moving to Node #0,0,0 Current State: 39:[3, 37], Operations: ['78-77=1', '36+1=37'] Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,39 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[1, 39], Operations: ['78-77=1', '36+3=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[36, 77, 3, 78], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [36, 3, 1] Generated Node #0,0: 39:[36, 3, 1] Operation: 78-77=1 Moving to Node #0,0 Current State: 39:[36, 3, 1], Operations: ['78-77=1'] Exploring Operation: 36+3=39, Resulting Numbers: [1, 39] Generated Node #0,0,2: 39:[1, 39] Operation: 36+3=39 Moving to Node #0,0,2 Current State: 39:[1, 39], Operations: ['78-77=1', '36+3=39'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 56, 92, 76, 26 ]
98
[ "56+92=148", "76-26=50", "148-50=98" ]
Current State: 98:[56, 92, 76, 26], Operations: [] Exploring Operation: 56+92=148, Resulting Numbers: [76, 26, 148] Generated Node #2: [76, 26, 148] from Operation: 56+92=148 Current State: 98:[76, 26, 148], Operations: ['56+92=148'] Exploring Operation: 76-26=50, Resulting Numbers: [148, 50] Generated Node #3: [148, 50] from Operation: 76-26=50 Current State: 98:[148, 50], Operations: ['56+92=148', '76-26=50'] Exploring Operation: 148-50=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[56, 92, 76, 26], Operations: [] Exploring Operation: 76+26=102, Resulting Numbers: [56, 92, 102] Generated Node #0,0: 98:[56, 92, 102] Operation: 76+26=102 Exploring Operation: 92-76=16, Resulting Numbers: [56, 26, 16] Generated Node #0,1: 98:[56, 26, 16] Operation: 92-76=16 Exploring Operation: 76-56=20, Resulting Numbers: [92, 26, 20] Generated Node #0,2: 98:[92, 26, 20] Operation: 76-56=20 Exploring Operation: 76-26=50, Resulting Numbers: [56, 92, 50] Generated Node #0,3: 98:[56, 92, 50] Operation: 76-26=50 Moving to Node #0,3 Current State: 98:[56, 92, 50], Operations: ['76-26=50'] Exploring Operation: 92-56=36, Resulting Numbers: [50, 36] Generated Node #0,3,0: 98:[50, 36] Operation: 92-56=36 Exploring Operation: 56+50=106, Resulting Numbers: [92, 106] Generated Node #0,3,1: 98:[92, 106] Operation: 56+50=106 Exploring Operation: 92-50=42, Resulting Numbers: [56, 42] Generated Node #0,3,2: 98:[56, 42] Operation: 92-50=42 Exploring Operation: 56-50=6, Resulting Numbers: [92, 6] Generated Node #0,3,3: 98:[92, 6] Operation: 56-50=6 Moving to Node #0,0 Current State: 98:[56, 92, 102], Operations: ['76+26=102'] Exploring Operation: 92-56=36, Resulting Numbers: [102, 36] Generated Node #0,0,0: 98:[102, 36] Operation: 92-56=36 Exploring Operation: 56+92=148, Resulting Numbers: [102, 148] Generated Node #0,0,1: 98:[102, 148] Operation: 56+92=148 Exploring Operation: 102-56=46, Resulting Numbers: [92, 46] Generated Node #0,0,2: 98:[92, 46] Operation: 102-56=46 Exploring Operation: 102-92=10, Resulting Numbers: [56, 10] Generated Node #0,0,3: 98:[56, 10] Operation: 102-92=10 Moving to Node #0,1 Current State: 98:[56, 26, 16], Operations: ['92-76=16'] Exploring Operation: 26-16=10, Resulting Numbers: [56, 10] Generated Node #0,1,0: 98:[56, 10] Operation: 26-16=10 Exploring Operation: 56+26=82, Resulting Numbers: [16, 82] Generated Node #0,1,1: 98:[16, 82] Operation: 56+26=82 Exploring Operation: 26+16=42, Resulting Numbers: [56, 42] Generated Node #0,1,2: 98:[56, 42] Operation: 26+16=42 Exploring Operation: 56-26=30, Resulting Numbers: [16, 30] Generated Node #0,1,3: 98:[16, 30] Operation: 56-26=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[56, 10], Operations: ['92-76=16', '26-16=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,98 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,98 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 98:[56, 42], Operations: ['92-76=16', '26+16=42'] Exploring Operation: 56*42=2352, Resulting Numbers: [2352] 2352,98 unequal: No Solution Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[56, 92, 76, 26], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [56, 26, 16] Generated Node #0,1: 98:[56, 26, 16] Operation: 92-76=16 Moving to Node #0,1 Current State: 98:[56, 26, 16], Operations: ['92-76=16'] Exploring Operation: 26+16=42, Resulting Numbers: [56, 42] Generated Node #0,1,2: 98:[56, 42] Operation: 26+16=42 Moving to Node #0,1,2 Current State: 98:[56, 42], Operations: ['92-76=16', '26+16=42'] Exploring Operation: 56+42=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 68, 60, 90, 96 ]
58
[ "68+60=128", "90+96=186", "186-128=58" ]
Current State: 58:[68, 60, 90, 96], Operations: [] Exploring Operation: 68+60=128, Resulting Numbers: [90, 96, 128] Generated Node #2: [90, 96, 128] from Operation: 68+60=128 Current State: 58:[90, 96, 128], Operations: ['68+60=128'] Exploring Operation: 90+96=186, Resulting Numbers: [128, 186] Generated Node #3: [128, 186] from Operation: 90+96=186 Current State: 58:[128, 186], Operations: ['68+60=128', '90+96=186'] Exploring Operation: 186-128=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[68, 60, 90, 96], Operations: [] Exploring Operation: 96-90=6, Resulting Numbers: [68, 60, 6] Generated Node #0,0: 58:[68, 60, 6] Operation: 96-90=6 Exploring Operation: 90-60=30, Resulting Numbers: [68, 96, 30] Generated Node #0,1: 58:[68, 96, 30] Operation: 90-60=30 Exploring Operation: 90-68=22, Resulting Numbers: [60, 96, 22] Generated Node #0,2: 58:[60, 96, 22] Operation: 90-68=22 Exploring Operation: 96-68=28, Resulting Numbers: [60, 90, 28] Generated Node #0,3: 58:[60, 90, 28] Operation: 96-68=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[68, 60, 6], Operations: ['96-90=6'] Exploring Operation: 68-60=8, Resulting Numbers: [6, 8] Generated Node #0,0,0: 58:[6, 8] Operation: 68-60=8 Exploring Operation: 60-6=54, Resulting Numbers: [68, 54] Generated Node #0,0,1: 58:[68, 54] Operation: 60-6=54 Exploring Operation: 68-6=62, Resulting Numbers: [60, 62] Generated Node #0,0,2: 58:[60, 62] Operation: 68-6=62 Exploring Operation: 68+6=74, Resulting Numbers: [60, 74] Generated Node #0,0,3: 58:[60, 74] Operation: 68+6=74 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 58:[60, 62], Operations: ['96-90=6', '68-6=62'] Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,58 unequal: No Solution Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,58 unequal: No Solution No 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: 58:[6, 8], Operations: ['96-90=6', '68-60=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,58 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,58 unequal: No Solution No 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: 58:[68, 54], Operations: ['96-90=6', '60-6=54'] Exploring Operation: 68+54=122, Resulting Numbers: [122] 122,58 unequal: No Solution Exploring Operation: 68-54=14, Resulting Numbers: [14] 14,58 unequal: No Solution Exploring Operation: 68*54=3672, Resulting Numbers: [3672] 3672,58 unequal: No Solution No 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: 58:[60, 74], Operations: ['96-90=6', '68+6=74'] Exploring Operation: 74-60=14, Resulting Numbers: [14] 14,58 unequal: No Solution Exploring Operation: 60*74=4440, Resulting Numbers: [4440] 4440,58 unequal: No Solution Exploring Operation: 60+74=134, Resulting Numbers: [134] 134,58 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: 58:[60, 90, 28], Operations: ['96-68=28'] Exploring Operation: 90-60=30, Resulting Numbers: [28, 30] Generated Node #0,3,0: 58:[28, 30] Operation: 90-60=30 Exploring Operation: 90-28=62, Resulting Numbers: [60, 62] Generated Node #0,3,1: 58:[60, 62] Operation: 90-28=62 Exploring Operation: 60+28=88, Resulting Numbers: [90, 88] Generated Node #0,3,2: 58:[90, 88] Operation: 60+28=88 Exploring Operation: 60-28=32, Resulting Numbers: [90, 32] Generated Node #0,3,3: 58:[90, 32] Operation: 60-28=32 Moving to Node #0,3,0 Current State: 58:[28, 30], Operations: ['96-68=28', '90-60=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[68, 60, 90, 96], Operations: [] Exploring Operation: 96-68=28, Resulting Numbers: [60, 90, 28] Generated Node #0,3: 58:[60, 90, 28] Operation: 96-68=28 Moving to Node #0,3 Current State: 58:[60, 90, 28], Operations: ['96-68=28'] Exploring Operation: 90-60=30, Resulting Numbers: [28, 30] Generated Node #0,3,0: 58:[28, 30] Operation: 90-60=30 Moving to Node #0,3,0 Current State: 58:[28, 30], Operations: ['96-68=28', '90-60=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 64, 82, 80, 96 ]
69
[ "82*80=6560", "64+6560=6624", "6624/96=69" ]
Current State: 69:[64, 82, 80, 96], Operations: [] Exploring Operation: 82*80=6560, Resulting Numbers: [64, 96, 6560] Generated Node #2: [64, 96, 6560] from Operation: 82*80=6560 Current State: 69:[64, 96, 6560], Operations: ['82*80=6560'] Exploring Operation: 64+6560=6624, Resulting Numbers: [96, 6624] Generated Node #3: [96, 6624] from Operation: 64+6560=6624 Current State: 69:[96, 6624], Operations: ['82*80=6560', '64+6560=6624'] Exploring Operation: 6624/96=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[64, 82, 80, 96], Operations: [] Exploring Operation: 96-64=32, Resulting Numbers: [82, 80, 32] Generated Node #0,0: 69:[82, 80, 32] Operation: 96-64=32 Exploring Operation: 96-80=16, Resulting Numbers: [64, 82, 16] Generated Node #0,1: 69:[64, 82, 16] Operation: 96-80=16 Exploring Operation: 96-82=14, Resulting Numbers: [64, 80, 14] Generated Node #0,2: 69:[64, 80, 14] Operation: 96-82=14 Moving to Node #0,1 Current State: 69:[64, 82, 16], Operations: ['96-80=16'] Exploring Operation: 64/16=4, Resulting Numbers: [82, 4] Generated Node #0,1,0: 69:[82, 4] Operation: 64/16=4 Exploring Operation: 82-16=66, Resulting Numbers: [64, 66] Generated Node #0,1,1: 69:[64, 66] Operation: 82-16=66 Exploring Operation: 82-64=18, Resulting Numbers: [16, 18] Generated Node #0,1,2: 69:[16, 18] Operation: 82-64=18 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[64, 66], Operations: ['96-80=16', '82-16=66'] Exploring Operation: 64+66=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 64*66=4224, Resulting Numbers: [4224] 4224,69 unequal: No Solution Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[16, 18], Operations: ['96-80=16', '82-64=18'] Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,69 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[82, 4], Operations: ['96-80=16', '64/16=4'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,69 unequal: No Solution Exploring Operation: 82+4=86, Resulting Numbers: [86] 86,69 unequal: No Solution Exploring Operation: 82*4=328, Resulting Numbers: [328] 328,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[64, 80, 14], Operations: ['96-82=14'] Exploring Operation: 80-64=16, Resulting Numbers: [14, 16] Generated Node #0,2,0: 69:[14, 16] Operation: 80-64=16 Exploring Operation: 64+14=78, Resulting Numbers: [80, 78] Generated Node #0,2,1: 69:[80, 78] Operation: 64+14=78 Exploring Operation: 80-14=66, Resulting Numbers: [64, 66] Generated Node #0,2,2: 69:[64, 66] Operation: 80-14=66 Moving to Node #0,0 Current State: 69:[82, 80, 32], Operations: ['96-64=32'] Exploring Operation: 82-80=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 69:[32, 2] Operation: 82-80=2 Exploring Operation: 80-32=48, Resulting Numbers: [82, 48] Generated Node #0,0,1: 69:[82, 48] Operation: 80-32=48 Exploring Operation: 82-32=50, Resulting Numbers: [80, 50] Generated Node #0,0,2: 69:[80, 50] Operation: 82-32=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[32, 2], Operations: ['96-64=32', '82-80=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[80, 50], Operations: ['96-64=32', '82-32=50'] Exploring Operation: 80-50=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 80+50=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 80*50=4000, Resulting Numbers: [4000] 4000,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[82, 48], Operations: ['96-64=32', '80-32=48'] Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,69 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 69:[64, 66], Operations: ['96-82=14', '80-14=66'] Exploring Operation: 66-64=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 64+66=130, Resulting Numbers: [130] 130,69 unequal: No Solution Exploring Operation: 64*66=4224, Resulting Numbers: [4224] 4224,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[14, 16], Operations: ['96-82=14', '80-64=16'] Exploring Operation: 14*16=224, Resulting Numbers: [224] 224,69 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,69 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[80, 78], Operations: ['96-82=14', '64+14=78'] Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 80*78=6240, Resulting Numbers: [6240] 6240,69 unequal: No Solution Exploring Operation: 80+78=158, Resulting Numbers: [158] 158,69 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 32, 54, 62, 4 ]
61
[ "54+62=116", "116/4=29", "32+29=61" ]
Current State: 61:[32, 54, 62, 4], Operations: [] Exploring Operation: 54+62=116, Resulting Numbers: [32, 4, 116] Generated Node #2: [32, 4, 116] from Operation: 54+62=116 Current State: 61:[32, 4, 116], Operations: ['54+62=116'] Exploring Operation: 116/4=29, Resulting Numbers: [32, 29] Generated Node #3: [32, 29] from Operation: 116/4=29 Current State: 61:[32, 29], Operations: ['54+62=116', '116/4=29'] Exploring Operation: 32+29=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[32, 54, 62, 4], Operations: [] Exploring Operation: 54+4=58, Resulting Numbers: [32, 62, 58] Generated Node #0,0: 61:[32, 62, 58] Operation: 54+4=58 Exploring Operation: 32+4=36, Resulting Numbers: [54, 62, 36] Generated Node #0,1: 61:[54, 62, 36] Operation: 32+4=36 Exploring Operation: 62-4=58, Resulting Numbers: [32, 54, 58] Generated Node #0,2: 61:[32, 54, 58] Operation: 62-4=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[32, 62, 58], Operations: ['54+4=58'] Exploring Operation: 62-32=30, Resulting Numbers: [58, 30] Generated Node #0,0,0: 61:[58, 30] Operation: 62-32=30 Exploring Operation: 32+58=90, Resulting Numbers: [62, 90] Generated Node #0,0,1: 61:[62, 90] Operation: 32+58=90 Exploring Operation: 32+62=94, Resulting Numbers: [58, 94] Generated Node #0,0,2: 61:[58, 94] Operation: 32+62=94 Moving to Node #0,0,1 Current State: 61:[62, 90], Operations: ['54+4=58', '32+58=90'] Exploring Operation: 62+90=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 62*90=5580, Resulting Numbers: [5580] 5580,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[58, 30], Operations: ['54+4=58', '62-32=30'] Exploring Operation: 58*30=1740, Resulting Numbers: [1740] 1740,61 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[58, 94], Operations: ['54+4=58', '32+62=94'] Exploring Operation: 58+94=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 94-58=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 58*94=5452, Resulting Numbers: [5452] 5452,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[54, 62, 36], Operations: ['32+4=36'] Exploring Operation: 62-36=26, Resulting Numbers: [54, 26] Generated Node #0,1,0: 61:[54, 26] Operation: 62-36=26 Exploring Operation: 54+36=90, Resulting Numbers: [62, 90] Generated Node #0,1,1: 61:[62, 90] Operation: 54+36=90 Exploring Operation: 54-36=18, Resulting Numbers: [62, 18] Generated Node #0,1,2: 61:[62, 18] Operation: 54-36=18 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[62, 90], Operations: ['32+4=36', '54+36=90'] Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 62*90=5580, Resulting Numbers: [5580] 5580,61 unequal: No Solution Exploring Operation: 62+90=152, Resulting Numbers: [152] 152,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[54, 26], Operations: ['32+4=36', '62-36=26'] Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,61 unequal: No Solution Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[62, 18], Operations: ['32+4=36', '54-36=18'] Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,61 unequal: No Solution Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,61 unequal: No Solution Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[32, 54, 58], Operations: ['62-4=58'] Exploring Operation: 32+58=90, Resulting Numbers: [54, 90] Generated Node #0,2,0: 61:[54, 90] Operation: 32+58=90 Exploring Operation: 32+54=86, Resulting Numbers: [58, 86] Generated Node #0,2,1: 61:[58, 86] Operation: 32+54=86 Exploring Operation: 54-32=22, Resulting Numbers: [58, 22] Generated Node #0,2,2: 61:[58, 22] Operation: 54-32=22 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[58, 86], Operations: ['62-4=58', '32+54=86'] Exploring Operation: 86-58=28, Resulting Numbers: [28] 28,61 unequal: No Solution Exploring Operation: 58*86=4988, Resulting Numbers: [4988] 4988,61 unequal: No Solution Exploring Operation: 58+86=144, Resulting Numbers: [144] 144,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[54, 90], Operations: ['62-4=58', '32+58=90'] Exploring Operation: 54*90=4860, Resulting Numbers: [4860] 4860,61 unequal: No Solution Exploring Operation: 90-54=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 54+90=144, Resulting Numbers: [144] 144,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[58, 22], Operations: ['62-4=58', '54-32=22'] Exploring Operation: 58*22=1276, Resulting Numbers: [1276] 1276,61 unequal: No Solution Exploring Operation: 58-22=36, Resulting Numbers: [36] 36,61 unequal: No Solution Exploring Operation: 58+22=80, Resulting Numbers: [80] 80,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 87, 80, 84, 13 ]
90
[ "87-80=7", "84+13=97", "97-7=90" ]
Current State: 90:[87, 80, 84, 13], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [84, 13, 7] Generated Node #2: [84, 13, 7] from Operation: 87-80=7 Current State: 90:[84, 13, 7], Operations: ['87-80=7'] Exploring Operation: 84+13=97, Resulting Numbers: [7, 97] Generated Node #3: [7, 97] from Operation: 84+13=97 Current State: 90:[7, 97], Operations: ['87-80=7', '84+13=97'] Exploring Operation: 97-7=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[87, 80, 84, 13], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [84, 13, 7] Generated Node #0,0: 90:[84, 13, 7] Operation: 87-80=7 Exploring Operation: 84-80=4, Resulting Numbers: [87, 13, 4] Generated Node #0,1: 90:[87, 13, 4] Operation: 84-80=4 Exploring Operation: 87-84=3, Resulting Numbers: [80, 13, 3] Generated Node #0,2: 90:[80, 13, 3] Operation: 87-84=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[87, 13, 4], Operations: ['84-80=4'] Exploring Operation: 13+4=17, Resulting Numbers: [87, 17] Generated Node #0,1,0: 90:[87, 17] Operation: 13+4=17 Exploring Operation: 13-4=9, Resulting Numbers: [87, 9] Generated Node #0,1,1: 90:[87, 9] Operation: 13-4=9 Exploring Operation: 87+4=91, Resulting Numbers: [13, 91] Generated Node #0,1,2: 90:[13, 91] Operation: 87+4=91 Moving to Node #0,1,1 Current State: 90:[87, 9], Operations: ['84-80=4', '13-4=9'] Exploring Operation: 87*9=783, Resulting Numbers: [783] 783,90 unequal: No Solution Exploring Operation: 87+9=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 87-9=78, Resulting Numbers: [78] 78,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[13, 91], Operations: ['84-80=4', '87+4=91'] Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,90 unequal: No Solution Exploring Operation: 13+91=104, Resulting Numbers: [104] 104,90 unequal: No Solution Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[87, 17], Operations: ['84-80=4', '13+4=17'] Exploring Operation: 87*17=1479, Resulting Numbers: [1479] 1479,90 unequal: No Solution Exploring Operation: 87+17=104, Resulting Numbers: [104] 104,90 unequal: No Solution Exploring Operation: 87-17=70, Resulting Numbers: [70] 70,90 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:[84, 13, 7], Operations: ['87-80=7'] Exploring Operation: 13-7=6, Resulting Numbers: [84, 6] Generated Node #0,0,0: 90:[84, 6] Operation: 13-7=6 Exploring Operation: 84/7=12, Resulting Numbers: [13, 12] Generated Node #0,0,1: 90:[13, 12] Operation: 84/7=12 Exploring Operation: 84+7=91, Resulting Numbers: [13, 91] Generated Node #0,0,2: 90:[13, 91] Operation: 84+7=91 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[13, 91], Operations: ['87-80=7', '84+7=91'] Exploring Operation: 13+91=104, Resulting Numbers: [104] 104,90 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,90 unequal: No Solution Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,90 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 #0,0,1 Current State: 90:[13, 12], Operations: ['87-80=7', '84/7=12'] Exploring Operation: 13+12=25, Resulting Numbers: [25] 25,90 unequal: No Solution Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 13*12=156, Resulting Numbers: [156] 156,90 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:[84, 6], Operations: ['87-80=7', '13-7=6'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,90 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[87, 80, 84, 13], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [84, 13, 7] Generated Node #0,0: 90:[84, 13, 7] Operation: 87-80=7 Moving to Node #0,0 Current State: 90:[84, 13, 7], Operations: ['87-80=7'] Exploring Operation: 13-7=6, Resulting Numbers: [84, 6] Generated Node #0,0,0: 90:[84, 6] Operation: 13-7=6 Moving to Node #0,0,0 Current State: 90:[84, 6], Operations: ['87-80=7', '13-7=6'] Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 10, 2, 8, 27 ]
31
[ "10+2=12", "27-8=19", "12+19=31" ]
Current State: 31:[10, 2, 8, 27], Operations: [] Exploring Operation: 10+2=12, Resulting Numbers: [8, 27, 12] Generated Node #2: [8, 27, 12] from Operation: 10+2=12 Current State: 31:[8, 27, 12], Operations: ['10+2=12'] Exploring Operation: 27-8=19, Resulting Numbers: [12, 19] Generated Node #3: [12, 19] from Operation: 27-8=19 Current State: 31:[12, 19], Operations: ['10+2=12', '27-8=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[10, 2, 8, 27], Operations: [] Exploring Operation: 10+2=12, Resulting Numbers: [8, 27, 12] Generated Node #0,0: 31:[8, 27, 12] Operation: 10+2=12 Exploring Operation: 2*8=16, Resulting Numbers: [10, 27, 16] Generated Node #0,1: 31:[10, 27, 16] Operation: 2*8=16 Exploring Operation: 10*2=20, Resulting Numbers: [8, 27, 20] Generated Node #0,2: 31:[8, 27, 20] Operation: 10*2=20 Exploring Operation: 10+8=18, Resulting Numbers: [2, 27, 18] Generated Node #0,3: 31:[2, 27, 18] Operation: 10+8=18 Moving to Node #0,2 Current State: 31:[8, 27, 20], Operations: ['10*2=20'] Exploring Operation: 27-8=19, Resulting Numbers: [20, 19] Generated Node #0,2,0: 31:[20, 19] Operation: 27-8=19 Exploring Operation: 8+20=28, Resulting Numbers: [27, 28] Generated Node #0,2,1: 31:[27, 28] Operation: 8+20=28 Exploring Operation: 20-8=12, Resulting Numbers: [27, 12] Generated Node #0,2,2: 31:[27, 12] Operation: 20-8=12 Exploring Operation: 8+27=35, Resulting Numbers: [20, 35] Generated Node #0,2,3: 31:[20, 35] Operation: 8+27=35 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[27, 28], Operations: ['10*2=20', '8+20=28'] Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[20, 35], Operations: ['10*2=20', '8+27=35'] Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[20, 19], Operations: ['10*2=20', '27-8=19'] Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,31 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[27, 12], Operations: ['10*2=20', '20-8=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,31 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,31 unequal: No Solution Exploring Operation: 27*12=324, Resulting Numbers: [324] 324,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 31:[10, 27, 16], Operations: ['2*8=16'] Exploring Operation: 10+16=26, Resulting Numbers: [27, 26] Generated Node #0,1,0: 31:[27, 26] Operation: 10+16=26 Exploring Operation: 27-10=17, Resulting Numbers: [16, 17] Generated Node #0,1,1: 31:[16, 17] Operation: 27-10=17 Exploring Operation: 16-10=6, Resulting Numbers: [27, 6] Generated Node #0,1,2: 31:[27, 6] Operation: 16-10=6 Exploring Operation: 10+27=37, Resulting Numbers: [16, 37] Generated Node #0,1,3: 31:[16, 37] Operation: 10+27=37 Moving to Node #0,3 Current State: 31:[2, 27, 18], Operations: ['10+8=18'] Exploring Operation: 2+27=29, Resulting Numbers: [18, 29] Generated Node #0,3,0: 31:[18, 29] Operation: 2+27=29 Exploring Operation: 27-2=25, Resulting Numbers: [18, 25] Generated Node #0,3,1: 31:[18, 25] Operation: 27-2=25 Exploring Operation: 2+18=20, Resulting Numbers: [27, 20] Generated Node #0,3,2: 31:[27, 20] Operation: 2+18=20 Exploring Operation: 2*18=36, Resulting Numbers: [27, 36] Generated Node #0,3,3: 31:[27, 36] Operation: 2*18=36 Moving to Node #0,0 Current State: 31:[8, 27, 12], Operations: ['10+2=12'] Exploring Operation: 27-8=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 31:[12, 19] Operation: 27-8=19 Exploring Operation: 8+27=35, Resulting Numbers: [12, 35] Generated Node #0,0,1: 31:[12, 35] Operation: 8+27=35 Exploring Operation: 12-8=4, Resulting Numbers: [27, 4] Generated Node #0,0,2: 31:[27, 4] Operation: 12-8=4 Exploring Operation: 8+12=20, Resulting Numbers: [27, 20] Generated Node #0,0,3: 31:[27, 20] Operation: 8+12=20 Moving to Node #0,1,0 Current State: 31:[27, 26], Operations: ['2*8=16', '10+16=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,31 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,31 unequal: No Solution Moving to Node #0,3,3 Current State: 31:[27, 36], Operations: ['10+8=18', '2*18=36'] Exploring Operation: 36-27=9, Resulting Numbers: [9] 9,31 unequal: No Solution Exploring Operation: 27*36=972, Resulting Numbers: [972] 972,31 unequal: No Solution Exploring Operation: 27+36=63, Resulting Numbers: [63] 63,31 unequal: No Solution Moving to Node #0,3,0 Current State: 31:[18, 29], Operations: ['10+8=18', '2+27=29'] Exploring Operation: 18*29=522, Resulting Numbers: [522] 522,31 unequal: No Solution Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,31 unequal: No Solution Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,31 unequal: No Solution Moving to Node #0,3,2 Current State: 31:[27, 20], Operations: ['10+8=18', '2+18=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,31 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[27, 20], Operations: ['10+2=12', '8+12=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,31 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,31 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,31 unequal: No Solution Moving to Node #0,3,1 Current State: 31:[18, 25], Operations: ['10+8=18', '27-2=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,31 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[16, 37], Operations: ['2*8=16', '10+27=37'] Exploring Operation: 16+37=53, Resulting Numbers: [53] 53,31 unequal: No Solution Exploring Operation: 16*37=592, Resulting Numbers: [592] 592,31 unequal: No Solution Exploring Operation: 37-16=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[12, 35], Operations: ['10+2=12', '8+27=35'] Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,31 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,31 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[16, 17], Operations: ['2*8=16', '27-10=17'] Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,31 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,31 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,31 unequal: No Solution Moving to Node #0,1,2 Current State: 31:[27, 6], Operations: ['2*8=16', '16-10=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,31 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,31 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,31 unequal: No Solution Moving to Node #0,0,0 Current State: 31:[12, 19], Operations: ['10+2=12', '27-8=19'] Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,31 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,31 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[10, 2, 8, 27], Operations: [] Exploring Operation: 10+2=12, Resulting Numbers: [8, 27, 12] Generated Node #0,0: 31:[8, 27, 12] Operation: 10+2=12 Moving to Node #0,0 Current State: 31:[8, 27, 12], Operations: ['10+2=12'] Exploring Operation: 27-8=19, Resulting Numbers: [12, 19] Generated Node #0,0,0: 31:[12, 19] Operation: 27-8=19 Moving to Node #0,0,0 Current State: 31:[12, 19], Operations: ['10+2=12', '27-8=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
0.940104
hs_4
mult_heuristic
[ 16, 39, 56, 24 ]
25
[ "16+39=55", "56+24=80", "80-55=25" ]
Current State: 25:[16, 39, 56, 24], Operations: [] Exploring Operation: 16+39=55, Resulting Numbers: [56, 24, 55] Generated Node #2: [56, 24, 55] from Operation: 16+39=55 Current State: 25:[56, 24, 55], Operations: ['16+39=55'] Exploring Operation: 56+24=80, Resulting Numbers: [55, 80] Generated Node #3: [55, 80] from Operation: 56+24=80 Current State: 25:[55, 80], Operations: ['16+39=55', '56+24=80'] Exploring Operation: 80-55=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[16, 39, 56, 24], Operations: [] Exploring Operation: 56-39=17, Resulting Numbers: [16, 24, 17] Generated Node #0,0: 25:[16, 24, 17] Operation: 56-39=17 Exploring Operation: 56-24=32, Resulting Numbers: [16, 39, 32] Generated Node #0,1: 25:[16, 39, 32] Operation: 56-24=32 Exploring Operation: 56-16=40, Resulting Numbers: [39, 24, 40] Generated Node #0,2: 25:[39, 24, 40] Operation: 56-16=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[16, 24, 17], Operations: ['56-39=17'] Exploring Operation: 24-16=8, Resulting Numbers: [17, 8] Generated Node #0,0,0: 25:[17, 8] Operation: 24-16=8 Exploring Operation: 16+17=33, Resulting Numbers: [24, 33] Generated Node #0,0,1: 25:[24, 33] Operation: 16+17=33 Exploring Operation: 17-16=1, Resulting Numbers: [24, 1] Generated Node #0,0,2: 25:[24, 1] Operation: 17-16=1 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[24, 1], Operations: ['56-39=17', '17-16=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[16, 39, 56, 24], Operations: [] Exploring Operation: 56-39=17, Resulting Numbers: [16, 24, 17] Generated Node #0,0: 25:[16, 24, 17] Operation: 56-39=17 Moving to Node #0,0 Current State: 25:[16, 24, 17], Operations: ['56-39=17'] Exploring Operation: 17-16=1, Resulting Numbers: [24, 1] Generated Node #0,0,2: 25:[24, 1] Operation: 17-16=1 Moving to Node #0,0,2 Current State: 25:[24, 1], Operations: ['56-39=17', '17-16=1'] Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 32, 10, 47, 68 ]
93
[ "32-10=22", "47+68=115", "115-22=93" ]
Current State: 93:[32, 10, 47, 68], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [47, 68, 22] Generated Node #2: [47, 68, 22] from Operation: 32-10=22 Current State: 93:[47, 68, 22], Operations: ['32-10=22'] Exploring Operation: 47+68=115, Resulting Numbers: [22, 115] Generated Node #3: [22, 115] from Operation: 47+68=115 Current State: 93:[22, 115], Operations: ['32-10=22', '47+68=115'] Exploring Operation: 115-22=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[32, 10, 47, 68], Operations: [] Exploring Operation: 32+68=100, Resulting Numbers: [10, 47, 100] Generated Node #0,0: 93:[10, 47, 100] Operation: 32+68=100 Exploring Operation: 68-32=36, Resulting Numbers: [10, 47, 36] Generated Node #0,1: 93:[10, 47, 36] Operation: 68-32=36 Exploring Operation: 68-47=21, Resulting Numbers: [32, 10, 21] Generated Node #0,2: 93:[32, 10, 21] Operation: 68-47=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[32, 10, 21], Operations: ['68-47=21'] Exploring Operation: 21-10=11, Resulting Numbers: [32, 11] Generated Node #0,2,0: 93:[32, 11] Operation: 21-10=11 Exploring Operation: 10+21=31, Resulting Numbers: [32, 31] Generated Node #0,2,1: 93:[32, 31] Operation: 10+21=31 Exploring Operation: 32-21=11, Resulting Numbers: [10, 11] Generated Node #0,2,2: 93:[10, 11] Operation: 32-21=11 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 93:[32, 31], Operations: ['68-47=21', '10+21=31'] Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,93 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,93 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,93 unequal: No Solution No 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: 93:[32, 11], Operations: ['68-47=21', '21-10=11'] Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,93 unequal: No Solution Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,93 unequal: No Solution Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,93 unequal: No Solution No 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: 93:[10, 11], Operations: ['68-47=21', '32-21=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,93 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,93 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: 93:[10, 47, 36], Operations: ['68-32=36'] Exploring Operation: 47-10=37, Resulting Numbers: [36, 37] Generated Node #0,1,0: 93:[36, 37] Operation: 47-10=37 Exploring Operation: 47-36=11, Resulting Numbers: [10, 11] Generated Node #0,1,1: 93:[10, 11] Operation: 47-36=11 Exploring Operation: 47+36=83, Resulting Numbers: [10, 83] Generated Node #0,1,2: 93:[10, 83] Operation: 47+36=83 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[36, 37], Operations: ['68-32=36', '47-10=37'] Exploring Operation: 36*37=1332, Resulting Numbers: [1332] 1332,93 unequal: No Solution Exploring Operation: 36+37=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,93 unequal: No Solution No 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: 93:[10, 11], Operations: ['68-32=36', '47-36=11'] Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,93 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,93 unequal: No Solution No 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: 93:[10, 83], Operations: ['68-32=36', '47+36=83'] Exploring Operation: 10*83=830, Resulting Numbers: [830] 830,93 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,93 unequal: No Solution Exploring Operation: 10+83=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[32, 10, 47, 68], Operations: [] Exploring Operation: 68-32=36, Resulting Numbers: [10, 47, 36] Generated Node #0,1: 93:[10, 47, 36] Operation: 68-32=36 Moving to Node #0,1 Current State: 93:[10, 47, 36], Operations: ['68-32=36'] Exploring Operation: 47+36=83, Resulting Numbers: [10, 83] Generated Node #0,1,2: 93:[10, 83] Operation: 47+36=83 Moving to Node #0,1,2 Current State: 93:[10, 83], Operations: ['68-32=36', '47+36=83'] Exploring Operation: 10+83=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_3
mult_heuristic
[ 2, 45, 57, 88 ]
55
[ "2*45=90", "57+88=145", "145-90=55" ]
Current State: 55:[2, 45, 57, 88], Operations: [] Exploring Operation: 2*45=90, Resulting Numbers: [57, 88, 90] Generated Node #2: [57, 88, 90] from Operation: 2*45=90 Current State: 55:[57, 88, 90], Operations: ['2*45=90'] Exploring Operation: 57+88=145, Resulting Numbers: [90, 145] Generated Node #3: [90, 145] from Operation: 57+88=145 Current State: 55:[90, 145], Operations: ['2*45=90', '57+88=145'] Exploring Operation: 145-90=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[2, 45, 57, 88], Operations: [] Exploring Operation: 88-45=43, Resulting Numbers: [2, 57, 43] Generated Node #0,0: 55:[2, 57, 43] Operation: 88-45=43 Exploring Operation: 88-57=31, Resulting Numbers: [2, 45, 31] Generated Node #0,1: 55:[2, 45, 31] Operation: 88-57=31 Exploring Operation: 88/2=44, Resulting Numbers: [45, 57, 44] Generated Node #0,2: 55:[45, 57, 44] Operation: 88/2=44 Moving to Node #0,0 Current State: 55:[2, 57, 43], Operations: ['88-45=43'] Exploring Operation: 2+43=45, Resulting Numbers: [57, 45] Generated Node #0,0,0: 55:[57, 45] Operation: 2+43=45 Exploring Operation: 57-2=55, Resulting Numbers: [43, 55] Generated Node #0,0,1: 55:[43, 55] Operation: 57-2=55 Exploring Operation: 57-43=14, Resulting Numbers: [2, 14] Generated Node #0,0,2: 55:[2, 14] Operation: 57-43=14 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 55:[2, 14], Operations: ['88-45=43', '57-43=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 55:[57, 45], Operations: ['88-45=43', '2+43=45'] Exploring Operation: 57*45=2565, Resulting Numbers: [2565] 2565,55 unequal: No Solution Exploring Operation: 57+45=102, Resulting Numbers: [102] 102,55 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 55:[43, 55], Operations: ['88-45=43', '57-2=55'] Exploring Operation: 43+55=98, Resulting Numbers: [98] 98,55 unequal: No Solution Exploring Operation: 55-43=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 43*55=2365, Resulting Numbers: [2365] 2365,55 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: 55:[45, 57, 44], Operations: ['88/2=44'] Exploring Operation: 45-44=1, Resulting Numbers: [57, 1] Generated Node #0,2,0: 55:[57, 1] Operation: 45-44=1 Exploring Operation: 57-44=13, Resulting Numbers: [45, 13] Generated Node #0,2,1: 55:[45, 13] Operation: 57-44=13 Exploring Operation: 57-45=12, Resulting Numbers: [44, 12] Generated Node #0,2,2: 55:[44, 12] Operation: 57-45=12 Moving to Node #0,1 Current State: 55:[2, 45, 31], Operations: ['88-57=31'] Exploring Operation: 2*31=62, Resulting Numbers: [45, 62] Generated Node #0,1,0: 55:[45, 62] Operation: 2*31=62 Exploring Operation: 45-31=14, Resulting Numbers: [2, 14] Generated Node #0,1,1: 55:[2, 14] Operation: 45-31=14 Exploring Operation: 45+31=76, Resulting Numbers: [2, 76] Generated Node #0,1,2: 55:[2, 76] Operation: 45+31=76 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 55:[2, 14], Operations: ['88-57=31', '45-31=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[45, 62], Operations: ['88-57=31', '2*31=62'] Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 45*62=2790, Resulting Numbers: [2790] 2790,55 unequal: No Solution Exploring Operation: 45+62=107, Resulting Numbers: [107] 107,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 55:[2, 76], Operations: ['88-57=31', '45+31=76'] Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,55 unequal: No Solution Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,55 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 55:[57, 1], Operations: ['88/2=44', '45-44=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,55 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[45, 13], Operations: ['88/2=44', '57-44=13'] Exploring Operation: 45+13=58, Resulting Numbers: [58] 58,55 unequal: No Solution Exploring Operation: 45-13=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 45*13=585, Resulting Numbers: [585] 585,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[44, 12], Operations: ['88/2=44', '57-45=12'] Exploring Operation: 44*12=528, Resulting Numbers: [528] 528,55 unequal: No Solution Exploring Operation: 44+12=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 26, 3, 76, 67 ]
99
[ "26+76=102", "3*67=201", "201-102=99" ]
Current State: 99:[26, 3, 76, 67], Operations: [] Exploring Operation: 26+76=102, Resulting Numbers: [3, 67, 102] Generated Node #2: [3, 67, 102] from Operation: 26+76=102 Current State: 99:[3, 67, 102], Operations: ['26+76=102'] Exploring Operation: 3*67=201, Resulting Numbers: [102, 201] Generated Node #3: [102, 201] from Operation: 3*67=201 Current State: 99:[102, 201], Operations: ['26+76=102', '3*67=201'] Exploring Operation: 201-102=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[26, 3, 76, 67], Operations: [] Exploring Operation: 26+67=93, Resulting Numbers: [3, 76, 93] Generated Node #0,0: 99:[3, 76, 93] Operation: 26+67=93 Exploring Operation: 67-26=41, Resulting Numbers: [3, 76, 41] Generated Node #0,1: 99:[3, 76, 41] Operation: 67-26=41 Exploring Operation: 76-67=9, Resulting Numbers: [26, 3, 9] Generated Node #0,2: 99:[26, 3, 9] Operation: 76-67=9 Moving to Node #0,2 Current State: 99:[26, 3, 9], Operations: ['76-67=9'] Exploring Operation: 26-9=17, Resulting Numbers: [3, 17] Generated Node #0,2,0: 99:[3, 17] Operation: 26-9=17 Exploring Operation: 26+3=29, Resulting Numbers: [9, 29] Generated Node #0,2,1: 99:[9, 29] Operation: 26+3=29 Exploring Operation: 26+9=35, Resulting Numbers: [3, 35] Generated Node #0,2,2: 99:[3, 35] Operation: 26+9=35 Moving to Node #0,0 Current State: 99:[3, 76, 93], Operations: ['26+67=93'] Exploring Operation: 93/3=31, Resulting Numbers: [76, 31] Generated Node #0,0,0: 99:[76, 31] Operation: 93/3=31 Exploring Operation: 93-76=17, Resulting Numbers: [3, 17] Generated Node #0,0,1: 99:[3, 17] Operation: 93-76=17 Exploring Operation: 3+76=79, Resulting Numbers: [93, 79] Generated Node #0,0,2: 99:[93, 79] Operation: 3+76=79 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[3, 17], Operations: ['26+67=93', '93-76=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,99 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,99 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 #0,0,0 Current State: 99:[76, 31], Operations: ['26+67=93', '93/3=31'] Exploring Operation: 76*31=2356, Resulting Numbers: [2356] 2356,99 unequal: No Solution Exploring Operation: 76+31=107, Resulting Numbers: [107] 107,99 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,99 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 #0,0,2 Current State: 99:[93, 79], Operations: ['26+67=93', '3+76=79'] Exploring Operation: 93-79=14, Resulting Numbers: [14] 14,99 unequal: No Solution Exploring Operation: 93*79=7347, Resulting Numbers: [7347] 7347,99 unequal: No Solution Exploring Operation: 93+79=172, Resulting Numbers: [172] 172,99 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: 99:[3, 76, 41], Operations: ['67-26=41'] Exploring Operation: 76-41=35, Resulting Numbers: [3, 35] Generated Node #0,1,0: 99:[3, 35] Operation: 76-41=35 Exploring Operation: 76+41=117, Resulting Numbers: [3, 117] Generated Node #0,1,1: 99:[3, 117] Operation: 76+41=117 Exploring Operation: 3+76=79, Resulting Numbers: [41, 79] Generated Node #0,1,2: 99:[41, 79] Operation: 3+76=79 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[3, 35], Operations: ['67-26=41', '76-41=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,99 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:[3, 117], Operations: ['67-26=41', '76+41=117'] Exploring Operation: 117/3=39, Resulting Numbers: [39] 39,99 unequal: No Solution Exploring Operation: 117-3=114, Resulting Numbers: [114] 114,99 unequal: No Solution Exploring Operation: 3+117=120, Resulting Numbers: [120] 120,99 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 #0,1,2 Current State: 99:[41, 79], Operations: ['67-26=41', '3+76=79'] Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 41+79=120, Resulting Numbers: [120] 120,99 unequal: No Solution Exploring Operation: 41*79=3239, Resulting Numbers: [3239] 3239,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 99:[3, 35], Operations: ['76-67=9', '26+9=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,99 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,99 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[9, 29], Operations: ['76-67=9', '26+3=29'] Exploring Operation: 9+29=38, Resulting Numbers: [38] 38,99 unequal: No Solution Exploring Operation: 29-9=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 9*29=261, Resulting Numbers: [261] 261,99 unequal: No Solution Moving to Node #0,2,0 Current State: 99:[3, 17], Operations: ['76-67=9', '26-9=17'] Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,99 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,99 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 88, 7, 92, 4 ]
60
[ "88+92=180", "7-4=3", "180/3=60" ]
Current State: 60:[88, 7, 92, 4], Operations: [] Exploring Operation: 88+92=180, Resulting Numbers: [7, 4, 180] Generated Node #2: [7, 4, 180] from Operation: 88+92=180 Current State: 60:[7, 4, 180], Operations: ['88+92=180'] Exploring Operation: 7-4=3, Resulting Numbers: [180, 3] Generated Node #3: [180, 3] from Operation: 7-4=3 Current State: 60:[180, 3], Operations: ['88+92=180', '7-4=3'] Exploring Operation: 180/3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[88, 7, 92, 4], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [88, 7, 23] Generated Node #0,0: 60:[88, 7, 23] Operation: 92/4=23 Exploring Operation: 88/4=22, Resulting Numbers: [7, 92, 22] Generated Node #0,1: 60:[7, 92, 22] Operation: 88/4=22 Exploring Operation: 92-7=85, Resulting Numbers: [88, 4, 85] Generated Node #0,2: 60:[88, 4, 85] Operation: 92-7=85 Exploring Operation: 92-88=4, Resulting Numbers: [7, 4, 4] Generated Node #0,3: 60:[7, 4, 4] Operation: 92-88=4 Exploring Operation: 88-7=81, Resulting Numbers: [92, 4, 81] Generated Node #0,4: 60:[92, 4, 81] Operation: 88-7=81 Start Sub Search at level 1: Moving to Node #0,3 Current State: 60:[7, 4, 4], Operations: ['92-88=4'] Exploring Operation: 7+4=11, Resulting Numbers: [4, 11] Generated Node #0,3,0: 60:[4, 11] Operation: 7+4=11 Exploring Operation: 7+4=11, Resulting Numbers: [4, 11] Generated Node #0,3,1: 60:[4, 11] Operation: 7+4=11 Exploring Operation: 7*4=28, Resulting Numbers: [4, 28] Generated Node #0,3,2: 60:[4, 28] Operation: 7*4=28 Exploring Operation: 7-4=3, Resulting Numbers: [4, 3] Generated Node #0,3,3: 60:[4, 3] Operation: 7-4=3 Exploring Operation: 7-4=3, Resulting Numbers: [4, 3] Generated Node #0,3,4: 60:[4, 3] Operation: 7-4=3 Moving to Node #0,3,3 Current State: 60:[4, 3], Operations: ['92-88=4', '7-4=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,3,4 Current State: 60:[4, 3], Operations: ['92-88=4', '7-4=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,60 unequal: No Solution Moving to Node #0,3,0 Current State: 60:[4, 11], Operations: ['92-88=4', '7+4=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,60 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[4, 11], Operations: ['92-88=4', '7+4=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[4, 28], Operations: ['92-88=4', '7*4=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[88, 7, 23], Operations: ['92/4=23'] Exploring Operation: 23-7=16, Resulting Numbers: [88, 16] Generated Node #0,0,0: 60:[88, 16] Operation: 23-7=16 Exploring Operation: 7+23=30, Resulting Numbers: [88, 30] Generated Node #0,0,1: 60:[88, 30] Operation: 7+23=30 Exploring Operation: 88+7=95, Resulting Numbers: [23, 95] Generated Node #0,0,2: 60:[23, 95] Operation: 88+7=95 Exploring Operation: 88-23=65, Resulting Numbers: [7, 65] Generated Node #0,0,3: 60:[7, 65] Operation: 88-23=65 Exploring Operation: 88-7=81, Resulting Numbers: [23, 81] Generated Node #0,0,4: 60:[23, 81] Operation: 88-7=81 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 60:[7, 65], Operations: ['92/4=23', '88-23=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,60 unequal: No Solution Exploring Operation: 7*65=455, Resulting Numbers: [455] 455,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 60:[23, 81], Operations: ['92/4=23', '88-7=81'] Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 23+81=104, Resulting Numbers: [104] 104,60 unequal: No Solution Exploring Operation: 23*81=1863, Resulting Numbers: [1863] 1863,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 60:[88, 30], Operations: ['92/4=23', '7+23=30'] Exploring Operation: 88+30=118, Resulting Numbers: [118] 118,60 unequal: No Solution Exploring Operation: 88*30=2640, Resulting Numbers: [2640] 2640,60 unequal: No Solution Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[88, 16], Operations: ['92/4=23', '23-7=16'] Exploring Operation: 88*16=1408, Resulting Numbers: [1408] 1408,60 unequal: No Solution Exploring Operation: 88+16=104, Resulting Numbers: [104] 104,60 unequal: No Solution Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 60:[23, 95], Operations: ['92/4=23', '88+7=95'] Exploring Operation: 23+95=118, Resulting Numbers: [118] 118,60 unequal: No Solution Exploring Operation: 23*95=2185, Resulting Numbers: [2185] 2185,60 unequal: No Solution Exploring Operation: 95-23=72, Resulting Numbers: [72] 72,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 60:[7, 92, 22], Operations: ['88/4=22'] Exploring Operation: 7+22=29, Resulting Numbers: [92, 29] Generated Node #0,1,0: 60:[92, 29] Operation: 7+22=29 Exploring Operation: 7+92=99, Resulting Numbers: [22, 99] Generated Node #0,1,1: 60:[22, 99] Operation: 7+92=99 Exploring Operation: 22-7=15, Resulting Numbers: [92, 15] Generated Node #0,1,2: 60:[92, 15] Operation: 22-7=15 Exploring Operation: 92-7=85, Resulting Numbers: [22, 85] Generated Node #0,1,3: 60:[22, 85] Operation: 92-7=85 Exploring Operation: 92-22=70, Resulting Numbers: [7, 70] Generated Node #0,1,4: 60:[7, 70] Operation: 92-22=70 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 60:[7, 70], Operations: ['88/4=22', '92-22=70'] Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,60 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 7*70=490, Resulting Numbers: [490] 490,60 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 60:[22, 85], Operations: ['88/4=22', '92-7=85'] Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 22+85=107, Resulting Numbers: [107] 107,60 unequal: No Solution Exploring Operation: 22*85=1870, Resulting Numbers: [1870] 1870,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 60:[92, 15], Operations: ['88/4=22', '22-7=15'] Exploring Operation: 92*15=1380, Resulting Numbers: [1380] 1380,60 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,60 unequal: No Solution Exploring Operation: 92+15=107, Resulting Numbers: [107] 107,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 60:[92, 29], Operations: ['88/4=22', '7+22=29'] Exploring Operation: 92-29=63, Resulting Numbers: [63] 63,60 unequal: No Solution Exploring Operation: 92*29=2668, Resulting Numbers: [2668] 2668,60 unequal: No Solution Exploring Operation: 92+29=121, Resulting Numbers: [121] 121,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 60:[22, 99], Operations: ['88/4=22', '7+92=99'] Exploring Operation: 22+99=121, Resulting Numbers: [121] 121,60 unequal: No Solution Exploring Operation: 99-22=77, Resulting Numbers: [77] 77,60 unequal: No Solution Exploring Operation: 22*99=2178, Resulting Numbers: [2178] 2178,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[88, 4, 85], Operations: ['92-7=85'] Exploring Operation: 88-4=84, Resulting Numbers: [85, 84] Generated Node #0,2,0: 60:[85, 84] Operation: 88-4=84 Exploring Operation: 88/4=22, Resulting Numbers: [85, 22] Generated Node #0,2,1: 60:[85, 22] Operation: 88/4=22 Exploring Operation: 88-85=3, Resulting Numbers: [4, 3] Generated Node #0,2,2: 60:[4, 3] Operation: 88-85=3 Exploring Operation: 88+4=92, Resulting Numbers: [85, 92] Generated Node #0,2,3: 60:[85, 92] Operation: 88+4=92 Exploring Operation: 85-4=81, Resulting Numbers: [88, 81] Generated Node #0,2,4: 60:[88, 81] Operation: 85-4=81 Moving to Node #0,2,2 Current State: 60:[4, 3], Operations: ['92-7=85', '88-85=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[85, 22], Operations: ['92-7=85', '88/4=22'] Exploring Operation: 85+22=107, Resulting Numbers: [107] 107,60 unequal: No Solution Exploring Operation: 85*22=1870, Resulting Numbers: [1870] 1870,60 unequal: No Solution Exploring Operation: 85-22=63, Resulting Numbers: [63] 63,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[85, 84], Operations: ['92-7=85', '88-4=84'] Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 85*84=7140, Resulting Numbers: [7140] 7140,60 unequal: No Solution Exploring Operation: 85+84=169, Resulting Numbers: [169] 169,60 unequal: No Solution Moving to Node #0,2,4 Current State: 60:[88, 81], Operations: ['92-7=85', '85-4=81'] Exploring Operation: 88+81=169, Resulting Numbers: [169] 169,60 unequal: No Solution Exploring Operation: 88*81=7128, Resulting Numbers: [7128] 7128,60 unequal: No Solution Exploring Operation: 88-81=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[85, 92], Operations: ['92-7=85', '88+4=92'] Exploring Operation: 85+92=177, Resulting Numbers: [177] 177,60 unequal: No Solution Exploring Operation: 85*92=7820, Resulting Numbers: [7820] 7820,60 unequal: No Solution Exploring Operation: 92-85=7, Resulting Numbers: [7] 7,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 60:[92, 4, 81], Operations: ['88-7=81'] Exploring Operation: 92/4=23, Resulting Numbers: [81, 23] Generated Node #0,4,0: 60:[81, 23] Operation: 92/4=23 Exploring Operation: 92+4=96, Resulting Numbers: [81, 96] Generated Node #0,4,1: 60:[81, 96] Operation: 92+4=96 Exploring Operation: 92-81=11, Resulting Numbers: [4, 11] Generated Node #0,4,2: 60:[4, 11] Operation: 92-81=11 Exploring Operation: 81-4=77, Resulting Numbers: [92, 77] Generated Node #0,4,3: 60:[92, 77] Operation: 81-4=77 Exploring Operation: 92-4=88, Resulting Numbers: [81, 88] Generated Node #0,4,4: 60:[81, 88] Operation: 92-4=88 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 60:[4, 11], Operations: ['88-7=81', '92-81=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,60 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,60 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 60:[81, 23], Operations: ['88-7=81', '92/4=23'] Exploring Operation: 81*23=1863, Resulting Numbers: [1863] 1863,60 unequal: No Solution Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,60 unequal: No Solution Exploring Operation: 81+23=104, Resulting Numbers: [104] 104,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 60:[92, 77], Operations: ['88-7=81', '81-4=77'] Exploring Operation: 92-77=15, Resulting Numbers: [15] 15,60 unequal: No Solution Exploring Operation: 92+77=169, Resulting Numbers: [169] 169,60 unequal: No Solution Exploring Operation: 92*77=7084, Resulting Numbers: [7084] 7084,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 60:[81, 88], Operations: ['88-7=81', '92-4=88'] Exploring Operation: 81+88=169, Resulting Numbers: [169] 169,60 unequal: No Solution Exploring Operation: 88-81=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 81*88=7128, Resulting Numbers: [7128] 7128,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 60:[81, 96], Operations: ['88-7=81', '92+4=96'] Exploring Operation: 96-81=15, Resulting Numbers: [15] 15,60 unequal: No Solution Exploring Operation: 81+96=177, Resulting Numbers: [177] 177,60 unequal: No Solution Exploring Operation: 81*96=7776, Resulting Numbers: [7776] 7776,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 54, 4, 45, 77 ]
30
[ "54*45=2430", "4+77=81", "2430/81=30" ]
Current State: 30:[54, 4, 45, 77], Operations: [] Exploring Operation: 54*45=2430, Resulting Numbers: [4, 77, 2430] Generated Node #2: [4, 77, 2430] from Operation: 54*45=2430 Current State: 30:[4, 77, 2430], Operations: ['54*45=2430'] Exploring Operation: 4+77=81, Resulting Numbers: [2430, 81] Generated Node #3: [2430, 81] from Operation: 4+77=81 Current State: 30:[2430, 81], Operations: ['54*45=2430', '4+77=81'] Exploring Operation: 2430/81=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[54, 4, 45, 77], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [4, 45, 23] Generated Node #0,0: 30:[4, 45, 23] Operation: 77-54=23 Exploring Operation: 77-45=32, Resulting Numbers: [54, 4, 32] Generated Node #0,1: 30:[54, 4, 32] Operation: 77-45=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[4, 45, 23], Operations: ['77-54=23'] Exploring Operation: 45-4=41, Resulting Numbers: [23, 41] Generated Node #0,0,0: 30:[23, 41] Operation: 45-4=41 Exploring Operation: 45-23=22, Resulting Numbers: [4, 22] Generated Node #0,0,1: 30:[4, 22] Operation: 45-23=22 Moving to Node #0,0,1 Current State: 30:[4, 22], Operations: ['77-54=23', '45-23=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[23, 41], Operations: ['77-54=23', '45-4=41'] Exploring Operation: 23+41=64, Resulting Numbers: [64] 64,30 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[54, 4, 32], Operations: ['77-45=32'] Exploring Operation: 54-4=50, Resulting Numbers: [32, 50] Generated Node #0,1,0: 30:[32, 50] Operation: 54-4=50 Exploring Operation: 54-32=22, Resulting Numbers: [4, 22] Generated Node #0,1,1: 30:[4, 22] Operation: 54-32=22 Moving to Node #0,1,1 Current State: 30:[4, 22], Operations: ['77-45=32', '54-32=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[32, 50], Operations: ['77-45=32', '54-4=50'] Exploring Operation: 32+50=82, Resulting Numbers: [82] 82,30 unequal: No Solution Exploring Operation: 50-32=18, Resulting Numbers: [18] 18,30 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
[ 41, 32, 77, 46 ]
42
[ "41+32=73", "77-46=31", "73-31=42" ]
Current State: 42:[41, 32, 77, 46], Operations: [] Exploring Operation: 41+32=73, Resulting Numbers: [77, 46, 73] Generated Node #2: [77, 46, 73] from Operation: 41+32=73 Current State: 42:[77, 46, 73], Operations: ['41+32=73'] Exploring Operation: 77-46=31, Resulting Numbers: [73, 31] Generated Node #3: [73, 31] from Operation: 77-46=31 Current State: 42:[73, 31], Operations: ['41+32=73', '77-46=31'] Exploring Operation: 73-31=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[41, 32, 77, 46], Operations: [] Exploring Operation: 77-41=36, Resulting Numbers: [32, 46, 36] Generated Node #0,0: 42:[32, 46, 36] Operation: 77-41=36 Exploring Operation: 77-46=31, Resulting Numbers: [41, 32, 31] Generated Node #0,1: 42:[41, 32, 31] Operation: 77-46=31 Exploring Operation: 77-32=45, Resulting Numbers: [41, 46, 45] Generated Node #0,2: 42:[41, 46, 45] Operation: 77-32=45 Moving to Node #0,2 Current State: 42:[41, 46, 45], Operations: ['77-32=45'] Exploring Operation: 46-45=1, Resulting Numbers: [41, 1] Generated Node #0,2,0: 42:[41, 1] Operation: 46-45=1 Exploring Operation: 46-41=5, Resulting Numbers: [45, 5] Generated Node #0,2,1: 42:[45, 5] Operation: 46-41=5 Exploring Operation: 45-41=4, Resulting Numbers: [46, 4] Generated Node #0,2,2: 42:[46, 4] Operation: 45-41=4 Moving to Node #0,0 Current State: 42:[32, 46, 36], Operations: ['77-41=36'] Exploring Operation: 36-32=4, Resulting Numbers: [46, 4] Generated Node #0,0,0: 42:[46, 4] Operation: 36-32=4 Exploring Operation: 46-32=14, Resulting Numbers: [36, 14] Generated Node #0,0,1: 42:[36, 14] Operation: 46-32=14 Exploring Operation: 46-36=10, Resulting Numbers: [32, 10] Generated Node #0,0,2: 42:[32, 10] Operation: 46-36=10 Moving to Node #0,1 Current State: 42:[41, 32, 31], Operations: ['77-46=31'] Exploring Operation: 41-32=9, Resulting Numbers: [31, 9] Generated Node #0,1,0: 42:[31, 9] Operation: 41-32=9 Exploring Operation: 32-31=1, Resulting Numbers: [41, 1] Generated Node #0,1,1: 42:[41, 1] Operation: 32-31=1 Exploring Operation: 41-31=10, Resulting Numbers: [32, 10] Generated Node #0,1,2: 42:[32, 10] Operation: 41-31=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 42:[41, 1], Operations: ['77-46=31', '32-31=1'] Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,42 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[41, 32, 77, 46], Operations: [] Exploring Operation: 77-46=31, Resulting Numbers: [41, 32, 31] Generated Node #0,1: 42:[41, 32, 31] Operation: 77-46=31 Moving to Node #0,1 Current State: 42:[41, 32, 31], Operations: ['77-46=31'] Exploring Operation: 32-31=1, Resulting Numbers: [41, 1] Generated Node #0,1,1: 42:[41, 1] Operation: 32-31=1 Moving to Node #0,1,1 Current State: 42:[41, 1], Operations: ['77-46=31', '32-31=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 32, 30, 5, 26 ]
29
[ "32-30=2", "5+26=31", "31-2=29" ]
Current State: 29:[32, 30, 5, 26], Operations: [] Exploring Operation: 32-30=2, Resulting Numbers: [5, 26, 2] Generated Node #2: [5, 26, 2] from Operation: 32-30=2 Current State: 29:[5, 26, 2], Operations: ['32-30=2'] Exploring Operation: 5+26=31, Resulting Numbers: [2, 31] Generated Node #3: [2, 31] from Operation: 5+26=31 Current State: 29:[2, 31], Operations: ['32-30=2', '5+26=31'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[32, 30, 5, 26], Operations: [] Exploring Operation: 32-5=27, Resulting Numbers: [30, 26, 27] Generated Node #0,0: 29:[30, 26, 27] Operation: 32-5=27 Exploring Operation: 30-5=25, Resulting Numbers: [32, 26, 25] Generated Node #0,1: 29:[32, 26, 25] Operation: 30-5=25 Exploring Operation: 5+26=31, Resulting Numbers: [32, 30, 31] Generated Node #0,2: 29:[32, 30, 31] Operation: 5+26=31 Moving to Node #0,0 Current State: 29:[30, 26, 27], Operations: ['32-5=27'] Exploring Operation: 26+27=53, Resulting Numbers: [30, 53] Generated Node #0,0,0: 29:[30, 53] Operation: 26+27=53 Exploring Operation: 30+26=56, Resulting Numbers: [27, 56] Generated Node #0,0,1: 29:[27, 56] Operation: 30+26=56 Exploring Operation: 30-26=4, Resulting Numbers: [27, 4] Generated Node #0,0,2: 29:[27, 4] Operation: 30-26=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[30, 53], Operations: ['32-5=27', '26+27=53'] Exploring Operation: 30*53=1590, Resulting Numbers: [1590] 1590,29 unequal: No Solution Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,29 unequal: No Solution Exploring Operation: 30+53=83, Resulting Numbers: [83] 83,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 29:[27, 4], Operations: ['32-5=27', '30-26=4'] Exploring Operation: 27+4=31, Resulting Numbers: [31] 31,29 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,29 unequal: No Solution Exploring Operation: 27*4=108, Resulting Numbers: [108] 108,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[27, 56], Operations: ['32-5=27', '30+26=56'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[32, 30, 5, 26], Operations: [] Exploring Operation: 32-5=27, Resulting Numbers: [30, 26, 27] Generated Node #0,0: 29:[30, 26, 27] Operation: 32-5=27 Moving to Node #0,0 Current State: 29:[30, 26, 27], Operations: ['32-5=27'] Exploring Operation: 30+26=56, Resulting Numbers: [27, 56] Generated Node #0,0,1: 29:[27, 56] Operation: 30+26=56 Moving to Node #0,0,1 Current State: 29:[27, 56], Operations: ['32-5=27', '30+26=56'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 66, 90, 6, 28 ]
35
[ "66+6=72", "90*28=2520", "2520/72=35" ]
Current State: 35:[66, 90, 6, 28], Operations: [] Exploring Operation: 66+6=72, Resulting Numbers: [90, 28, 72] Generated Node #2: [90, 28, 72] from Operation: 66+6=72 Current State: 35:[90, 28, 72], Operations: ['66+6=72'] Exploring Operation: 90*28=2520, Resulting Numbers: [72, 2520] Generated Node #3: [72, 2520] from Operation: 90*28=2520 Current State: 35:[72, 2520], Operations: ['66+6=72', '90*28=2520'] Exploring Operation: 2520/72=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[66, 90, 6, 28], Operations: [] Exploring Operation: 90-66=24, Resulting Numbers: [6, 28, 24] Generated Node #0,0: 35:[6, 28, 24] Operation: 90-66=24 Moving to Node #0,0 Current State: 35:[6, 28, 24], Operations: ['90-66=24'] Exploring Operation: 28-24=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 35:[6, 4] Operation: 28-24=4 Moving to Node #0,0,0 Current State: 35:[6, 4], Operations: ['90-66=24', '28-24=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,35 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 63, 64, 5, 26 ]
45
[ "64+26=90", "90/5=18", "63-18=45" ]
Current State: 45:[63, 64, 5, 26], Operations: [] Exploring Operation: 64+26=90, Resulting Numbers: [63, 5, 90] Generated Node #2: [63, 5, 90] from Operation: 64+26=90 Current State: 45:[63, 5, 90], Operations: ['64+26=90'] Exploring Operation: 90/5=18, Resulting Numbers: [63, 18] Generated Node #3: [63, 18] from Operation: 90/5=18 Current State: 45:[63, 18], Operations: ['64+26=90', '90/5=18'] Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[63, 64, 5, 26], Operations: [] Exploring Operation: 64-63=1, Resulting Numbers: [5, 26, 1] Generated Node #0,0: 45:[5, 26, 1] Operation: 64-63=1 Exploring Operation: 64-26=38, Resulting Numbers: [63, 5, 38] Generated Node #0,1: 45:[63, 5, 38] Operation: 64-26=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[5, 26, 1], Operations: ['64-63=1'] Exploring Operation: 26-5=21, Resulting Numbers: [1, 21] Generated Node #0,0,0: 45:[1, 21] Operation: 26-5=21 Exploring Operation: 26-1=25, Resulting Numbers: [5, 25] Generated Node #0,0,1: 45:[5, 25] Operation: 26-1=25 Moving to Node #0,0,0 Current State: 45:[1, 21], Operations: ['64-63=1', '26-5=21'] Exploring Operation: 21-1=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 1*21=21, Resulting Numbers: [21] 21,45 unequal: No Solution Moving to Node #0,0,1 Current State: 45:[5, 25], Operations: ['64-63=1', '26-1=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[63, 5, 38], Operations: ['64-26=38'] Exploring Operation: 63-5=58, Resulting Numbers: [38, 58] Generated Node #0,1,0: 45:[38, 58] Operation: 63-5=58 Exploring Operation: 63-38=25, Resulting Numbers: [5, 25] Generated Node #0,1,1: 45:[5, 25] Operation: 63-38=25 Moving to Node #0,1,1 Current State: 45:[5, 25], Operations: ['64-26=38', '63-38=25'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[38, 58], Operations: ['64-26=38', '63-5=58'] Exploring Operation: 58-38=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 38+58=96, Resulting Numbers: [96] 96,45 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
[ 13, 24, 58, 94 ]
47
[ "24-13=11", "94-58=36", "11+36=47" ]
Current State: 47:[13, 24, 58, 94], Operations: [] Exploring Operation: 24-13=11, Resulting Numbers: [58, 94, 11] Generated Node #2: [58, 94, 11] from Operation: 24-13=11 Current State: 47:[58, 94, 11], Operations: ['24-13=11'] Exploring Operation: 94-58=36, Resulting Numbers: [11, 36] Generated Node #3: [11, 36] from Operation: 94-58=36 Current State: 47:[11, 36], Operations: ['24-13=11', '94-58=36'] Exploring Operation: 11+36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[13, 24, 58, 94], Operations: [] Exploring Operation: 94-13=81, Resulting Numbers: [24, 58, 81] Generated Node #0,0: 47:[24, 58, 81] Operation: 94-13=81 Exploring Operation: 13+24=37, Resulting Numbers: [58, 94, 37] Generated Node #0,1: 47:[58, 94, 37] Operation: 13+24=37 Exploring Operation: 58-13=45, Resulting Numbers: [24, 94, 45] Generated Node #0,2: 47:[24, 94, 45] Operation: 58-13=45 Exploring Operation: 94-58=36, Resulting Numbers: [13, 24, 36] Generated Node #0,3: 47:[13, 24, 36] Operation: 94-58=36 Exploring Operation: 94-24=70, Resulting Numbers: [13, 58, 70] Generated Node #0,4: 47:[13, 58, 70] Operation: 94-24=70 Moving to Node #0,0 Current State: 47:[24, 58, 81], Operations: ['94-13=81'] Exploring Operation: 81-24=57, Resulting Numbers: [58, 57] Generated Node #0,0,0: 47:[58, 57] Operation: 81-24=57 Exploring Operation: 24+58=82, Resulting Numbers: [81, 82] Generated Node #0,0,1: 47:[81, 82] Operation: 24+58=82 Exploring Operation: 58-24=34, Resulting Numbers: [81, 34] Generated Node #0,0,2: 47:[81, 34] Operation: 58-24=34 Exploring Operation: 81-58=23, Resulting Numbers: [24, 23] Generated Node #0,0,3: 47:[24, 23] Operation: 81-58=23 Exploring Operation: 24+81=105, Resulting Numbers: [58, 105] Generated Node #0,0,4: 47:[58, 105] Operation: 24+81=105 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[58, 57], Operations: ['94-13=81', '81-24=57'] Exploring Operation: 58*57=3306, Resulting Numbers: [3306] 3306,47 unequal: No Solution Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 58+57=115, Resulting Numbers: [115] 115,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[81, 34], Operations: ['94-13=81', '58-24=34'] Exploring Operation: 81+34=115, Resulting Numbers: [115] 115,47 unequal: No Solution Exploring Operation: 81*34=2754, Resulting Numbers: [2754] 2754,47 unequal: No Solution Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[13, 24, 58, 94], Operations: [] Exploring Operation: 94-13=81, Resulting Numbers: [24, 58, 81] Generated Node #0,0: 47:[24, 58, 81] Operation: 94-13=81 Moving to Node #0,0 Current State: 47:[24, 58, 81], Operations: ['94-13=81'] Exploring Operation: 58-24=34, Resulting Numbers: [81, 34] Generated Node #0,0,2: 47:[81, 34] Operation: 58-24=34 Moving to Node #0,0,2 Current State: 47:[81, 34], Operations: ['94-13=81', '58-24=34'] Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 33, 1, 56, 40 ]
49
[ "33*1=33", "56-40=16", "33+16=49" ]
Current State: 49:[33, 1, 56, 40], Operations: [] Exploring Operation: 33*1=33, Resulting Numbers: [56, 40, 33] Generated Node #2: [56, 40, 33] from Operation: 33*1=33 Current State: 49:[56, 40, 33], Operations: ['33*1=33'] Exploring Operation: 56-40=16, Resulting Numbers: [33, 16] Generated Node #3: [33, 16] from Operation: 56-40=16 Current State: 49:[33, 16], Operations: ['33*1=33', '56-40=16'] Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[33, 1, 56, 40], Operations: [] Exploring Operation: 56-33=23, Resulting Numbers: [1, 40, 23] Generated Node #0,0: 49:[1, 40, 23] Operation: 56-33=23 Exploring Operation: 33+1=34, Resulting Numbers: [56, 40, 34] Generated Node #0,1: 49:[56, 40, 34] Operation: 33+1=34 Exploring Operation: 56-1=55, Resulting Numbers: [33, 40, 55] Generated Node #0,2: 49:[33, 40, 55] Operation: 56-1=55 Exploring Operation: 1+40=41, Resulting Numbers: [33, 56, 41] Generated Node #0,3: 49:[33, 56, 41] Operation: 1+40=41 Exploring Operation: 40-33=7, Resulting Numbers: [1, 56, 7] Generated Node #0,4: 49:[1, 56, 7] Operation: 40-33=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[1, 56, 7], Operations: ['40-33=7'] Exploring Operation: 1*56=56, Resulting Numbers: [7, 56] Generated Node #0,4,0: 49:[7, 56] Operation: 1*56=56 Exploring Operation: 56-7=49, Resulting Numbers: [1, 49] Generated Node #0,4,1: 49:[1, 49] Operation: 56-7=49 Exploring Operation: 1*7=7, Resulting Numbers: [56, 7] Generated Node #0,4,2: 49:[56, 7] Operation: 1*7=7 Exploring Operation: 56/1=56, Resulting Numbers: [7, 56] Generated Node #0,4,3: 49:[7, 56] Operation: 56/1=56 Exploring Operation: 56-1=55, Resulting Numbers: [7, 55] Generated Node #0,4,4: 49:[7, 55] Operation: 56-1=55 Moving to Node #0,4,1 Current State: 49:[1, 49], Operations: ['40-33=7', '56-7=49'] Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[33, 1, 56, 40], Operations: [] Exploring Operation: 40-33=7, Resulting Numbers: [1, 56, 7] Generated Node #0,4: 49:[1, 56, 7] Operation: 40-33=7 Moving to Node #0,4 Current State: 49:[1, 56, 7], Operations: ['40-33=7'] Exploring Operation: 56-7=49, Resulting Numbers: [1, 49] Generated Node #0,4,1: 49:[1, 49] Operation: 56-7=49 Moving to Node #0,4,1 Current State: 49:[1, 49], Operations: ['40-33=7', '56-7=49'] Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 71, 19, 83, 16 ]
47
[ "71-19=52", "83+16=99", "99-52=47" ]
Current State: 47:[71, 19, 83, 16], Operations: [] Exploring Operation: 71-19=52, Resulting Numbers: [83, 16, 52] Generated Node #2: [83, 16, 52] from Operation: 71-19=52 Current State: 47:[83, 16, 52], Operations: ['71-19=52'] Exploring Operation: 83+16=99, Resulting Numbers: [52, 99] Generated Node #3: [52, 99] from Operation: 83+16=99 Current State: 47:[52, 99], Operations: ['71-19=52', '83+16=99'] Exploring Operation: 99-52=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[71, 19, 83, 16], Operations: [] Exploring Operation: 83-19=64, Resulting Numbers: [71, 16, 64] Generated Node #0,0: 47:[71, 16, 64] Operation: 83-19=64 Exploring Operation: 71-19=52, Resulting Numbers: [83, 16, 52] Generated Node #0,1: 47:[83, 16, 52] Operation: 71-19=52 Exploring Operation: 71-16=55, Resulting Numbers: [19, 83, 55] Generated Node #0,2: 47:[19, 83, 55] Operation: 71-16=55 Exploring Operation: 19+16=35, Resulting Numbers: [71, 83, 35] Generated Node #0,3: 47:[71, 83, 35] Operation: 19+16=35 Moving to Node #0,0 Current State: 47:[71, 16, 64], Operations: ['83-19=64'] Exploring Operation: 71+16=87, Resulting Numbers: [64, 87] Generated Node #0,0,0: 47:[64, 87] Operation: 71+16=87 Exploring Operation: 71-16=55, Resulting Numbers: [64, 55] Generated Node #0,0,1: 47:[64, 55] Operation: 71-16=55 Exploring Operation: 64-16=48, Resulting Numbers: [71, 48] Generated Node #0,0,2: 47:[71, 48] Operation: 64-16=48 Exploring Operation: 16+64=80, Resulting Numbers: [71, 80] Generated Node #0,0,3: 47:[71, 80] Operation: 16+64=80 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[64, 55], Operations: ['83-19=64', '71-16=55'] Exploring Operation: 64+55=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 64*55=3520, Resulting Numbers: [3520] 3520,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[71, 48], Operations: ['83-19=64', '64-16=48'] Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 71+48=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 71*48=3408, Resulting Numbers: [3408] 3408,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[64, 87], Operations: ['83-19=64', '71+16=87'] Exploring Operation: 64+87=151, Resulting Numbers: [151] 151,47 unequal: No Solution Exploring Operation: 87-64=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 64*87=5568, Resulting Numbers: [5568] 5568,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[71, 80], Operations: ['83-19=64', '16+64=80'] Exploring Operation: 71*80=5680, Resulting Numbers: [5680] 5680,47 unequal: No Solution Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 71+80=151, Resulting Numbers: [151] 151,47 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: 47:[19, 83, 55], Operations: ['71-16=55'] Exploring Operation: 83-19=64, Resulting Numbers: [55, 64] Generated Node #0,2,0: 47:[55, 64] Operation: 83-19=64 Exploring Operation: 19+83=102, Resulting Numbers: [55, 102] Generated Node #0,2,1: 47:[55, 102] Operation: 19+83=102 Exploring Operation: 55-19=36, Resulting Numbers: [83, 36] Generated Node #0,2,2: 47:[83, 36] Operation: 55-19=36 Exploring Operation: 83-55=28, Resulting Numbers: [19, 28] Generated Node #0,2,3: 47:[19, 28] Operation: 83-55=28 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[55, 64], Operations: ['71-16=55', '83-19=64'] Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[83, 36], Operations: ['71-16=55', '55-19=36'] Exploring Operation: 83+36=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[71, 19, 83, 16], Operations: [] Exploring Operation: 71-16=55, Resulting Numbers: [19, 83, 55] Generated Node #0,2: 47:[19, 83, 55] Operation: 71-16=55 Moving to Node #0,2 Current State: 47:[19, 83, 55], Operations: ['71-16=55'] Exploring Operation: 55-19=36, Resulting Numbers: [83, 36] Generated Node #0,2,2: 47:[83, 36] Operation: 55-19=36 Moving to Node #0,2,2 Current State: 47:[83, 36], Operations: ['71-16=55', '55-19=36'] Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
mult_heuristic
[ 47, 44, 27, 63 ]
18
[ "47-44=3", "27*3=81", "81-63=18" ]
Current State: 18:[47, 44, 27, 63], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [27, 63, 3] Generated Node #2: [27, 63, 3] from Operation: 47-44=3 Current State: 18:[27, 63, 3], Operations: ['47-44=3'] Exploring Operation: 27*3=81, Resulting Numbers: [63, 81] Generated Node #3: [63, 81] from Operation: 27*3=81 Current State: 18:[63, 81], Operations: ['47-44=3', '27*3=81'] Exploring Operation: 81-63=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[47, 44, 27, 63], Operations: [] Exploring Operation: 47-44=3, Resulting Numbers: [27, 63, 3] Generated Node #0,0: 18:[27, 63, 3] Operation: 47-44=3 Exploring Operation: 47-27=20, Resulting Numbers: [44, 63, 20] Generated Node #0,1: 18:[44, 63, 20] Operation: 47-27=20 Exploring Operation: 63-44=19, Resulting Numbers: [47, 27, 19] Generated Node #0,2: 18:[47, 27, 19] Operation: 63-44=19 Exploring Operation: 63-47=16, Resulting Numbers: [44, 27, 16] Generated Node #0,3: 18:[44, 27, 16] Operation: 63-47=16 Moving to Node #0,3 Current State: 18:[44, 27, 16], Operations: ['63-47=16'] Exploring Operation: 44+16=60, Resulting Numbers: [27, 60] Generated Node #0,3,0: 18:[27, 60] Operation: 44+16=60 Exploring Operation: 44-27=17, Resulting Numbers: [16, 17] Generated Node #0,3,1: 18:[16, 17] Operation: 44-27=17 Exploring Operation: 27-16=11, Resulting Numbers: [44, 11] Generated Node #0,3,2: 18:[44, 11] Operation: 27-16=11 Exploring Operation: 44-16=28, Resulting Numbers: [27, 28] Generated Node #0,3,3: 18:[27, 28] Operation: 44-16=28 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[16, 17], Operations: ['63-47=16', '44-27=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,18 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,18 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:[27, 28], Operations: ['63-47=16', '44-16=28'] Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,18 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,18 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:[44, 11], Operations: ['63-47=16', '27-16=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 44*11=484, Resulting Numbers: [484] 484,18 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,18 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:[27, 60], Operations: ['63-47=16', '44+16=60'] Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 27+60=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 27*60=1620, Resulting Numbers: [1620] 1620,18 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:[47, 27, 19], Operations: ['63-44=19'] Exploring Operation: 47+27=74, Resulting Numbers: [19, 74] Generated Node #0,2,0: 18:[19, 74] Operation: 47+27=74 Exploring Operation: 47-27=20, Resulting Numbers: [19, 20] Generated Node #0,2,1: 18:[19, 20] Operation: 47-27=20 Exploring Operation: 47-19=28, Resulting Numbers: [27, 28] Generated Node #0,2,2: 18:[27, 28] Operation: 47-19=28 Exploring Operation: 27-19=8, Resulting Numbers: [47, 8] Generated Node #0,2,3: 18:[47, 8] Operation: 27-19=8 Moving to Node #0,0 Current State: 18:[27, 63, 3], Operations: ['47-44=3'] Exploring Operation: 27-3=24, Resulting Numbers: [63, 24] Generated Node #0,0,0: 18:[63, 24] Operation: 27-3=24 Exploring Operation: 27/3=9, Resulting Numbers: [63, 9] Generated Node #0,0,1: 18:[63, 9] Operation: 27/3=9 Exploring Operation: 63/3=21, Resulting Numbers: [27, 21] Generated Node #0,0,2: 18:[27, 21] Operation: 63/3=21 Exploring Operation: 63-27=36, Resulting Numbers: [3, 36] Generated Node #0,0,3: 18:[3, 36] Operation: 63-27=36 Moving to Node #0,1 Current State: 18:[44, 63, 20], Operations: ['47-27=20'] Exploring Operation: 44+63=107, Resulting Numbers: [20, 107] Generated Node #0,1,0: 18:[20, 107] Operation: 44+63=107 Exploring Operation: 63-20=43, Resulting Numbers: [44, 43] Generated Node #0,1,1: 18:[44, 43] Operation: 63-20=43 Exploring Operation: 63-44=19, Resulting Numbers: [20, 19] Generated Node #0,1,2: 18:[20, 19] Operation: 63-44=19 Exploring Operation: 44-20=24, Resulting Numbers: [63, 24] Generated Node #0,1,3: 18:[63, 24] Operation: 44-20=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[20, 19], Operations: ['47-27=20', '63-44=19'] Exploring Operation: 20*19=380, Resulting Numbers: [380] 380,18 unequal: No Solution Exploring Operation: 20+19=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,18 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:[44, 43], Operations: ['47-27=20', '63-20=43'] Exploring Operation: 44*43=1892, Resulting Numbers: [1892] 1892,18 unequal: No Solution Exploring Operation: 44+43=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,18 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:[63, 24], Operations: ['47-27=20', '44-20=24'] Exploring Operation: 63+24=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 63*24=1512, Resulting Numbers: [1512] 1512,18 unequal: No Solution Exploring Operation: 63-24=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 #0,1,0 Current State: 18:[20, 107], Operations: ['47-27=20', '44+63=107'] Exploring Operation: 20*107=2140, Resulting Numbers: [2140] 2140,18 unequal: No Solution Exploring Operation: 20+107=127, Resulting Numbers: [127] 127,18 unequal: No Solution Exploring Operation: 107-20=87, Resulting Numbers: [87] 87,18 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: 18:[19, 20], Operations: ['63-44=19', '47-27=20'] Exploring Operation: 19*20=380, Resulting Numbers: [380] 380,18 unequal: No Solution Exploring Operation: 19+20=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 20-19=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[27, 21], Operations: ['47-44=3', '63/3=21'] Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,18 unequal: No Solution Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[3, 36], Operations: ['47-44=3', '63-27=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,18 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[27, 28], Operations: ['63-44=19', '47-19=28'] Exploring Operation: 27*28=756, Resulting Numbers: [756] 756,18 unequal: No Solution Exploring Operation: 28-27=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 27+28=55, Resulting Numbers: [55] 55,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[47, 8], Operations: ['63-44=19', '27-19=8'] Exploring Operation: 47+8=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 47*8=376, Resulting Numbers: [376] 376,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[63, 9], Operations: ['47-44=3', '27/3=9'] Exploring Operation: 63*9=567, Resulting Numbers: [567] 567,18 unequal: No Solution Exploring Operation: 63/9=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 63-9=54, Resulting Numbers: [54] 54,18 unequal: No Solution Exploring Operation: 63+9=72, Resulting Numbers: [72] 72,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[63, 24], Operations: ['47-44=3', '27-3=24'] Exploring Operation: 63+24=87, Resulting Numbers: [87] 87,18 unequal: No Solution Exploring Operation: 63-24=39, Resulting Numbers: [39] 39,18 unequal: No Solution Exploring Operation: 63*24=1512, Resulting Numbers: [1512] 1512,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[19, 74], Operations: ['63-44=19', '47+27=74'] Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,18 unequal: No Solution Exploring Operation: 19*74=1406, Resulting Numbers: [1406] 1406,18 unequal: No Solution Exploring Operation: 19+74=93, Resulting Numbers: [93] 93,18 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 50, 60, 32, 44 ]
22
[ "60-50=10", "44-32=12", "10+12=22" ]
Current State: 22:[50, 60, 32, 44], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [32, 44, 10] Generated Node #2: [32, 44, 10] from Operation: 60-50=10 Current State: 22:[32, 44, 10], Operations: ['60-50=10'] Exploring Operation: 44-32=12, Resulting Numbers: [10, 12] Generated Node #3: [10, 12] from Operation: 44-32=12 Current State: 22:[10, 12], Operations: ['60-50=10', '44-32=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[50, 60, 32, 44], Operations: [] Exploring Operation: 50-44=6, Resulting Numbers: [60, 32, 6] Generated Node #0,0: 22:[60, 32, 6] Operation: 50-44=6 Exploring Operation: 60-50=10, Resulting Numbers: [32, 44, 10] Generated Node #0,1: 22:[32, 44, 10] Operation: 60-50=10 Exploring Operation: 60-44=16, Resulting Numbers: [50, 32, 16] Generated Node #0,2: 22:[50, 32, 16] Operation: 60-44=16 Exploring Operation: 60-32=28, Resulting Numbers: [50, 44, 28] Generated Node #0,3: 22:[50, 44, 28] Operation: 60-32=28 Moving to Node #0,1 Current State: 22:[32, 44, 10], Operations: ['60-50=10'] Exploring Operation: 44-32=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 22:[10, 12] Operation: 44-32=12 Exploring Operation: 44-10=34, Resulting Numbers: [32, 34] Generated Node #0,1,1: 22:[32, 34] Operation: 44-10=34 Exploring Operation: 32-10=22, Resulting Numbers: [44, 22] Generated Node #0,1,2: 22:[44, 22] Operation: 32-10=22 Exploring Operation: 32+10=42, Resulting Numbers: [44, 42] Generated Node #0,1,3: 22:[44, 42] Operation: 32+10=42 Moving to Node #0,2 Current State: 22:[50, 32, 16], Operations: ['60-44=16'] Exploring Operation: 32/16=2, Resulting Numbers: [50, 2] Generated Node #0,2,0: 22:[50, 2] Operation: 32/16=2 Exploring Operation: 50-16=34, Resulting Numbers: [32, 34] Generated Node #0,2,1: 22:[32, 34] Operation: 50-16=34 Exploring Operation: 32-16=16, Resulting Numbers: [50, 16] Generated Node #0,2,2: 22:[50, 16] Operation: 32-16=16 Exploring Operation: 50-32=18, Resulting Numbers: [16, 18] Generated Node #0,2,3: 22:[16, 18] Operation: 50-32=18 Moving to Node #0,0 Current State: 22:[60, 32, 6], Operations: ['50-44=6'] Exploring Operation: 60/6=10, Resulting Numbers: [32, 10] Generated Node #0,0,0: 22:[32, 10] Operation: 60/6=10 Exploring Operation: 32-6=26, Resulting Numbers: [60, 26] Generated Node #0,0,1: 22:[60, 26] Operation: 32-6=26 Exploring Operation: 60-32=28, Resulting Numbers: [6, 28] Generated Node #0,0,2: 22:[6, 28] Operation: 60-32=28 Exploring Operation: 60-6=54, Resulting Numbers: [32, 54] Generated Node #0,0,3: 22:[32, 54] Operation: 60-6=54 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[6, 28], Operations: ['50-44=6', '60-32=28'] Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,22 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[50, 60, 32, 44], Operations: [] Exploring Operation: 50-44=6, Resulting Numbers: [60, 32, 6] Generated Node #0,0: 22:[60, 32, 6] Operation: 50-44=6 Moving to Node #0,0 Current State: 22:[60, 32, 6], Operations: ['50-44=6'] Exploring Operation: 60-32=28, Resulting Numbers: [6, 28] Generated Node #0,0,2: 22:[6, 28] Operation: 60-32=28 Moving to Node #0,0,2 Current State: 22:[6, 28], Operations: ['50-44=6', '60-32=28'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 29, 8, 19, 21 ]
77
[ "29+8=37", "19+21=40", "37+40=77" ]
Current State: 77:[29, 8, 19, 21], Operations: [] Exploring Operation: 29+8=37, Resulting Numbers: [19, 21, 37] Generated Node #2: [19, 21, 37] from Operation: 29+8=37 Current State: 77:[19, 21, 37], Operations: ['29+8=37'] Exploring Operation: 19+21=40, Resulting Numbers: [37, 40] Generated Node #3: [37, 40] from Operation: 19+21=40 Current State: 77:[37, 40], Operations: ['29+8=37', '19+21=40'] Exploring Operation: 37+40=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[29, 8, 19, 21], Operations: [] Exploring Operation: 21-19=2, Resulting Numbers: [29, 8, 2] Generated Node #0,0: 77:[29, 8, 2] Operation: 21-19=2 Exploring Operation: 29-21=8, Resulting Numbers: [8, 19, 8] Generated Node #0,1: 77:[8, 19, 8] Operation: 29-21=8 Exploring Operation: 29-8=21, Resulting Numbers: [19, 21, 21] Generated Node #0,2: 77:[19, 21, 21] Operation: 29-8=21 Exploring Operation: 29-19=10, Resulting Numbers: [8, 21, 10] Generated Node #0,3: 77:[8, 21, 10] Operation: 29-19=10 Exploring Operation: 19-8=11, Resulting Numbers: [29, 21, 11] Generated Node #0,4: 77:[29, 21, 11] Operation: 19-8=11 Moving to Node #0,1 Current State: 77:[8, 19, 8], Operations: ['29-21=8'] Exploring Operation: 8/8=1, Resulting Numbers: [19, 1] Generated Node #0,1,0: 77:[19, 1] Operation: 8/8=1 Exploring Operation: 19-8=11, Resulting Numbers: [8, 11] Generated Node #0,1,1: 77:[8, 11] Operation: 19-8=11 Exploring Operation: 19-8=11, Resulting Numbers: [8, 11] Generated Node #0,1,2: 77:[8, 11] Operation: 19-8=11 Exploring Operation: 8+8=16, Resulting Numbers: [19, 16] Generated Node #0,1,3: 77:[19, 16] Operation: 8+8=16 Exploring Operation: 8-8=0, Resulting Numbers: [19, 0] Generated Node #0,1,4: 77:[19, 0] Operation: 8-8=0 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[8, 11], Operations: ['29-21=8', '19-8=11'] Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 77:[8, 11], Operations: ['29-21=8', '19-8=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 77:[19, 16], Operations: ['29-21=8', '8+8=16'] Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,77 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[19, 1], Operations: ['29-21=8', '8/8=1'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 77:[19, 0], Operations: ['29-21=8', '8-8=0'] Exploring Operation: 19*0=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 19+0=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 19-0=19, Resulting Numbers: [19] 19,77 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: 77:[8, 21, 10], Operations: ['29-19=10'] Exploring Operation: 10-8=2, Resulting Numbers: [21, 2] Generated Node #0,3,0: 77:[21, 2] Operation: 10-8=2 Exploring Operation: 8+10=18, Resulting Numbers: [21, 18] Generated Node #0,3,1: 77:[21, 18] Operation: 8+10=18 Exploring Operation: 8*10=80, Resulting Numbers: [21, 80] Generated Node #0,3,2: 77:[21, 80] Operation: 8*10=80 Exploring Operation: 21-10=11, Resulting Numbers: [8, 11] Generated Node #0,3,3: 77:[8, 11] Operation: 21-10=11 Exploring Operation: 21-8=13, Resulting Numbers: [10, 13] Generated Node #0,3,4: 77:[10, 13] Operation: 21-8=13 Moving to Node #0,0 Current State: 77:[29, 8, 2], Operations: ['21-19=2'] Exploring Operation: 29*2=58, Resulting Numbers: [8, 58] Generated Node #0,0,0: 77:[8, 58] Operation: 29*2=58 Exploring Operation: 8-2=6, Resulting Numbers: [29, 6] Generated Node #0,0,1: 77:[29, 6] Operation: 8-2=6 Exploring Operation: 29-2=27, Resulting Numbers: [8, 27] Generated Node #0,0,2: 77:[8, 27] Operation: 29-2=27 Exploring Operation: 29-8=21, Resulting Numbers: [2, 21] Generated Node #0,0,3: 77:[2, 21] Operation: 29-8=21 Exploring Operation: 8+2=10, Resulting Numbers: [29, 10] Generated Node #0,0,4: 77:[29, 10] Operation: 8+2=10 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 77:[2, 21], Operations: ['21-19=2', '29-8=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 77:[8, 27], Operations: ['21-19=2', '29-2=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,77 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[29, 6], Operations: ['21-19=2', '8-2=6'] Exploring Operation: 29+6=35, Resulting Numbers: [35] 35,77 unequal: No Solution Exploring Operation: 29*6=174, Resulting Numbers: [174] 174,77 unequal: No Solution Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 77:[29, 10], Operations: ['21-19=2', '8+2=10'] Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,77 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[8, 58], Operations: ['21-19=2', '29*2=58'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,77 unequal: No Solution Exploring Operation: 8*58=464, Resulting Numbers: [464] 464,77 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,77 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: 77:[19, 21, 21], Operations: ['29-8=21'] Exploring Operation: 21-19=2, Resulting Numbers: [21, 2] Generated Node #0,2,0: 77:[21, 2] Operation: 21-19=2 Exploring Operation: 21-21=0, Resulting Numbers: [19, 0] Generated Node #0,2,1: 77:[19, 0] Operation: 21-21=0 Exploring Operation: 21-19=2, Resulting Numbers: [21, 2] Generated Node #0,2,2: 77:[21, 2] Operation: 21-19=2 Exploring Operation: 19+21=40, Resulting Numbers: [21, 40] Generated Node #0,2,3: 77:[21, 40] Operation: 19+21=40 Exploring Operation: 21/21=1, Resulting Numbers: [19, 1] Generated Node #0,2,4: 77:[19, 1] Operation: 21/21=1 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 77:[19, 1], Operations: ['29-8=21', '21/21=1'] Exploring Operation: 19*1=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 19+1=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 77:[21, 2], Operations: ['29-8=21', '21-19=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 77:[19, 0], Operations: ['29-8=21', '21-21=0'] Exploring Operation: 19+0=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 19*0=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 19-0=19, Resulting Numbers: [19] 19,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 77:[21, 2], Operations: ['29-8=21', '21-19=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 77:[21, 40], Operations: ['29-8=21', '19+21=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,77 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,77 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: 77:[29, 21, 11], Operations: ['19-8=11'] Exploring Operation: 29-11=18, Resulting Numbers: [21, 18] Generated Node #0,4,0: 77:[21, 18] Operation: 29-11=18 Exploring Operation: 29+21=50, Resulting Numbers: [11, 50] Generated Node #0,4,1: 77:[11, 50] Operation: 29+21=50 Exploring Operation: 21-11=10, Resulting Numbers: [29, 10] Generated Node #0,4,2: 77:[29, 10] Operation: 21-11=10 Exploring Operation: 29-21=8, Resulting Numbers: [11, 8] Generated Node #0,4,3: 77:[11, 8] Operation: 29-21=8 Exploring Operation: 29+11=40, Resulting Numbers: [21, 40] Generated Node #0,4,4: 77:[21, 40] Operation: 29+11=40 Moving to Node #0,3,3 Current State: 77:[8, 11], Operations: ['29-19=10', '21-10=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 8+11=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,4,3 Current State: 77:[11, 8], Operations: ['19-8=11', '29-21=8'] Exploring Operation: 11*8=88, Resulting Numbers: [88] 88,77 unequal: No Solution Exploring Operation: 11+8=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 11-8=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,3,4 Current State: 77:[10, 13], Operations: ['29-19=10', '21-8=13'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,77 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[21, 80], Operations: ['29-19=10', '8*10=80'] Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,77 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,77 unequal: No Solution Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[21, 2], Operations: ['29-19=10', '10-8=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,77 unequal: No Solution Moving to Node #0,4,0 Current State: 77:[21, 18], Operations: ['19-8=11', '29-11=18'] Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,77 unequal: No Solution Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,77 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,3,1 Current State: 77:[21, 18], Operations: ['29-19=10', '8+10=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,77 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,77 unequal: No Solution Moving to Node #0,4,2 Current State: 77:[29, 10], Operations: ['19-8=11', '21-11=10'] Exploring Operation: 29*10=290, Resulting Numbers: [290] 290,77 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 29+10=39, Resulting Numbers: [39] 39,77 unequal: No Solution Moving to Node #0,4,1 Current State: 77:[11, 50], Operations: ['19-8=11', '29+21=50'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,77 unequal: No Solution Exploring Operation: 11*50=550, Resulting Numbers: [550] 550,77 unequal: No Solution Exploring Operation: 11+50=61, Resulting Numbers: [61] 61,77 unequal: No Solution Moving to Node #0,4,4 Current State: 77:[21, 40], Operations: ['19-8=11', '29+11=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,77 unequal: No Solution Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,77 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 87, 33, 70, 27 ]
77
[ "87+33=120", "70-27=43", "120-43=77" ]
Current State: 77:[87, 33, 70, 27], Operations: [] Exploring Operation: 87+33=120, Resulting Numbers: [70, 27, 120] Generated Node #2: [70, 27, 120] from Operation: 87+33=120 Current State: 77:[70, 27, 120], Operations: ['87+33=120'] Exploring Operation: 70-27=43, Resulting Numbers: [120, 43] Generated Node #3: [120, 43] from Operation: 70-27=43 Current State: 77:[120, 43], Operations: ['87+33=120', '70-27=43'] Exploring Operation: 120-43=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[87, 33, 70, 27], Operations: [] Exploring Operation: 87-33=54, Resulting Numbers: [70, 27, 54] Generated Node #0,0: 77:[70, 27, 54] Operation: 87-33=54 Exploring Operation: 87-70=17, Resulting Numbers: [33, 27, 17] Generated Node #0,1: 77:[33, 27, 17] Operation: 87-70=17 Exploring Operation: 33-27=6, Resulting Numbers: [87, 70, 6] Generated Node #0,2: 77:[87, 70, 6] Operation: 33-27=6 Exploring Operation: 33+27=60, Resulting Numbers: [87, 70, 60] Generated Node #0,3: 77:[87, 70, 60] Operation: 33+27=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[87, 70, 6], Operations: ['33-27=6'] Exploring Operation: 70+6=76, Resulting Numbers: [87, 76] Generated Node #0,2,0: 77:[87, 76] Operation: 70+6=76 Exploring Operation: 87-70=17, Resulting Numbers: [6, 17] Generated Node #0,2,1: 77:[6, 17] Operation: 87-70=17 Exploring Operation: 87-6=81, Resulting Numbers: [70, 81] Generated Node #0,2,2: 77:[70, 81] Operation: 87-6=81 Exploring Operation: 87+6=93, Resulting Numbers: [70, 93] Generated Node #0,2,3: 77:[70, 93] Operation: 87+6=93 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 77:[6, 17], Operations: ['33-27=6', '87-70=17'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 77:[87, 76], Operations: ['33-27=6', '70+6=76'] Exploring Operation: 87+76=163, Resulting Numbers: [163] 163,77 unequal: No Solution Exploring Operation: 87-76=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 87*76=6612, Resulting Numbers: [6612] 6612,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 77:[70, 81], Operations: ['33-27=6', '87-6=81'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,77 unequal: No Solution Exploring Operation: 70+81=151, Resulting Numbers: [151] 151,77 unequal: No Solution Exploring Operation: 70*81=5670, Resulting Numbers: [5670] 5670,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 77:[70, 93], Operations: ['33-27=6', '87+6=93'] Exploring Operation: 93-70=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 70+93=163, Resulting Numbers: [163] 163,77 unequal: No Solution Exploring Operation: 70*93=6510, Resulting Numbers: [6510] 6510,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[87, 70, 60], Operations: ['33+27=60'] Exploring Operation: 70+60=130, Resulting Numbers: [87, 130] Generated Node #0,3,0: 77:[87, 130] Operation: 70+60=130 Exploring Operation: 87-70=17, Resulting Numbers: [60, 17] Generated Node #0,3,1: 77:[60, 17] Operation: 87-70=17 Exploring Operation: 87-60=27, Resulting Numbers: [70, 27] Generated Node #0,3,2: 77:[70, 27] Operation: 87-60=27 Exploring Operation: 70-60=10, Resulting Numbers: [87, 10] Generated Node #0,3,3: 77:[87, 10] Operation: 70-60=10 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 77:[87, 10], Operations: ['33+27=60', '70-60=10'] Exploring Operation: 87*10=870, Resulting Numbers: [870] 870,77 unequal: No Solution Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[87, 33, 70, 27], Operations: [] Exploring Operation: 33+27=60, Resulting Numbers: [87, 70, 60] Generated Node #0,3: 77:[87, 70, 60] Operation: 33+27=60 Moving to Node #0,3 Current State: 77:[87, 70, 60], Operations: ['33+27=60'] Exploring Operation: 70-60=10, Resulting Numbers: [87, 10] Generated Node #0,3,3: 77:[87, 10] Operation: 70-60=10 Moving to Node #0,3,3 Current State: 77:[87, 10], Operations: ['33+27=60', '70-60=10'] Exploring Operation: 87-10=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 44, 33, 41, 54 ]
43
[ "44-41=3", "33/3=11", "54-11=43" ]
Current State: 43:[44, 33, 41, 54], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [33, 54, 3] Generated Node #2: [33, 54, 3] from Operation: 44-41=3 Current State: 43:[33, 54, 3], Operations: ['44-41=3'] Exploring Operation: 33/3=11, Resulting Numbers: [54, 11] Generated Node #3: [54, 11] from Operation: 33/3=11 Current State: 43:[54, 11], Operations: ['44-41=3', '33/3=11'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[44, 33, 41, 54], Operations: [] Exploring Operation: 54-41=13, Resulting Numbers: [44, 33, 13] Generated Node #0,0: 43:[44, 33, 13] Operation: 54-41=13 Exploring Operation: 54-33=21, Resulting Numbers: [44, 41, 21] Generated Node #0,1: 43:[44, 41, 21] Operation: 54-33=21 Moving to Node #0,1 Current State: 43:[44, 41, 21], Operations: ['54-33=21'] Exploring Operation: 41+21=62, Resulting Numbers: [44, 62] Generated Node #0,1,0: 43:[44, 62] Operation: 41+21=62 Exploring Operation: 44-21=23, Resulting Numbers: [41, 23] Generated Node #0,1,1: 43:[41, 23] Operation: 44-21=23 Moving to Node #0,0 Current State: 43:[44, 33, 13], Operations: ['54-41=13'] Exploring Operation: 44-13=31, Resulting Numbers: [33, 31] Generated Node #0,0,0: 43:[33, 31] Operation: 44-13=31 Exploring Operation: 33+13=46, Resulting Numbers: [44, 46] Generated Node #0,0,1: 43:[44, 46] Operation: 33+13=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[44, 46], Operations: ['54-41=13', '33+13=46'] Exploring Operation: 46-44=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 44+46=90, Resulting Numbers: [90] 90,43 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 #0,0,0 Current State: 43:[33, 31], Operations: ['54-41=13', '44-13=31'] Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,43 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,43 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: 43:[44, 62], Operations: ['54-33=21', '41+21=62'] Exploring Operation: 62-44=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 44+62=106, Resulting Numbers: [106] 106,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[41, 23], Operations: ['54-33=21', '44-21=23'] Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,43 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 46, 45, 30, 71 ]
54
[ "71-46=25", "45*30=1350", "1350/25=54" ]
Current State: 54:[46, 45, 30, 71], Operations: [] Exploring Operation: 71-46=25, Resulting Numbers: [45, 30, 25] Generated Node #2: [45, 30, 25] from Operation: 71-46=25 Current State: 54:[45, 30, 25], Operations: ['71-46=25'] Exploring Operation: 45*30=1350, Resulting Numbers: [25, 1350] Generated Node #3: [25, 1350] from Operation: 45*30=1350 Current State: 54:[25, 1350], Operations: ['71-46=25', '45*30=1350'] Exploring Operation: 1350/25=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[46, 45, 30, 71], Operations: [] Exploring Operation: 71-46=25, Resulting Numbers: [45, 30, 25] Generated Node #0,0: 54:[45, 30, 25] Operation: 71-46=25 Exploring Operation: 71-45=26, Resulting Numbers: [46, 30, 26] Generated Node #0,1: 54:[46, 30, 26] Operation: 71-45=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[46, 30, 26], Operations: ['71-45=26'] Exploring Operation: 46-26=20, Resulting Numbers: [30, 20] Generated Node #0,1,0: 54:[30, 20] Operation: 46-26=20 Exploring Operation: 46-30=16, Resulting Numbers: [26, 16] Generated Node #0,1,1: 54:[26, 16] Operation: 46-30=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 54:[26, 16], Operations: ['71-45=26', '46-30=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,54 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:[30, 20], Operations: ['71-45=26', '46-26=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[45, 30, 25], Operations: ['71-46=25'] Exploring Operation: 45-30=15, Resulting Numbers: [25, 15] Generated Node #0,0,0: 54:[25, 15] Operation: 45-30=15 Exploring Operation: 45-25=20, Resulting Numbers: [30, 20] Generated Node #0,0,1: 54:[30, 20] Operation: 45-25=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[25, 15], Operations: ['71-46=25', '45-30=15'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[30, 20], Operations: ['71-46=25', '45-25=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,54 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,54 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_2
sum_heuristic
[ 21, 32, 88, 30 ]
47
[ "32-21=11", "88-30=58", "58-11=47" ]
Current State: 47:[21, 32, 88, 30], Operations: [] Exploring Operation: 32-21=11, Resulting Numbers: [88, 30, 11] Generated Node #2: [88, 30, 11] from Operation: 32-21=11 Current State: 47:[88, 30, 11], Operations: ['32-21=11'] Exploring Operation: 88-30=58, Resulting Numbers: [11, 58] Generated Node #3: [11, 58] from Operation: 88-30=58 Current State: 47:[11, 58], Operations: ['32-21=11', '88-30=58'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[21, 32, 88, 30], Operations: [] Exploring Operation: 88-32=56, Resulting Numbers: [21, 30, 56] Generated Node #0,0: 47:[21, 30, 56] Operation: 88-32=56 Exploring Operation: 88-21=67, Resulting Numbers: [32, 30, 67] Generated Node #0,1: 47:[32, 30, 67] Operation: 88-21=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[21, 30, 56], Operations: ['88-32=56'] Exploring Operation: 21+30=51, Resulting Numbers: [56, 51] Generated Node #0,0,0: 47:[56, 51] Operation: 21+30=51 Exploring Operation: 56-21=35, Resulting Numbers: [30, 35] Generated Node #0,0,1: 47:[30, 35] Operation: 56-21=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[56, 51], Operations: ['88-32=56', '21+30=51'] Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 56+51=107, Resulting Numbers: [107] 107,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[30, 35], Operations: ['88-32=56', '56-21=35'] Exploring Operation: 30+35=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[32, 30, 67], Operations: ['88-21=67'] Exploring Operation: 67-30=37, Resulting Numbers: [32, 37] Generated Node #0,1,0: 47:[32, 37] Operation: 67-30=37 Exploring Operation: 67-32=35, Resulting Numbers: [30, 35] Generated Node #0,1,1: 47:[30, 35] Operation: 67-32=35 Moving to Node #0,1,0 Current State: 47:[32, 37], Operations: ['88-21=67', '67-30=37'] Exploring Operation: 37-32=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[30, 35], Operations: ['88-21=67', '67-32=35'] Exploring Operation: 30+35=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,47 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
[ 91, 94, 30, 44 ]
71
[ "94-91=3", "30+44=74", "74-3=71" ]
Current State: 71:[91, 94, 30, 44], Operations: [] Exploring Operation: 94-91=3, Resulting Numbers: [30, 44, 3] Generated Node #2: [30, 44, 3] from Operation: 94-91=3 Current State: 71:[30, 44, 3], Operations: ['94-91=3'] Exploring Operation: 30+44=74, Resulting Numbers: [3, 74] Generated Node #3: [3, 74] from Operation: 30+44=74 Current State: 71:[3, 74], Operations: ['94-91=3', '30+44=74'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[91, 94, 30, 44], Operations: [] Exploring Operation: 30+44=74, Resulting Numbers: [91, 94, 74] Generated Node #0,0: 71:[91, 94, 74] Operation: 30+44=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[91, 94, 74], Operations: ['30+44=74'] Exploring Operation: 94-91=3, Resulting Numbers: [74, 3] Generated Node #0,0,0: 71:[74, 3] Operation: 94-91=3 Moving to Node #0,0,0 Current State: 71:[74, 3], Operations: ['30+44=74', '94-91=3'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[91, 94, 30, 44], Operations: [] Exploring Operation: 30+44=74, Resulting Numbers: [91, 94, 74] Generated Node #0,0: 71:[91, 94, 74] Operation: 30+44=74 Moving to Node #0,0 Current State: 71:[91, 94, 74], Operations: ['30+44=74'] Exploring Operation: 94-91=3, Resulting Numbers: [74, 3] Generated Node #0,0,0: 71:[74, 3] Operation: 94-91=3 Moving to Node #0,0,0 Current State: 71:[74, 3], Operations: ['30+44=74', '94-91=3'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 65, 90, 63, 55 ]
10
[ "65-63=2", "90/2=45", "55-45=10" ]
Current State: 10:[65, 90, 63, 55], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [90, 55, 2] Generated Node #2: [90, 55, 2] from Operation: 65-63=2 Current State: 10:[90, 55, 2], Operations: ['65-63=2'] Exploring Operation: 90/2=45, Resulting Numbers: [55, 45] Generated Node #3: [55, 45] from Operation: 90/2=45 Current State: 10:[55, 45], Operations: ['65-63=2', '90/2=45'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[65, 90, 63, 55], Operations: [] Exploring Operation: 90-63=27, Resulting Numbers: [65, 55, 27] Generated Node #0,0: 10:[65, 55, 27] Operation: 90-63=27 Exploring Operation: 90-65=25, Resulting Numbers: [63, 55, 25] Generated Node #0,1: 10:[63, 55, 25] Operation: 90-65=25 Exploring Operation: 65-63=2, Resulting Numbers: [90, 55, 2] Generated Node #0,2: 10:[90, 55, 2] Operation: 65-63=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[63, 55, 25], Operations: ['90-65=25'] Exploring Operation: 63-55=8, Resulting Numbers: [25, 8] Generated Node #0,1,0: 10:[25, 8] Operation: 63-55=8 Exploring Operation: 55-25=30, Resulting Numbers: [63, 30] Generated Node #0,1,1: 10:[63, 30] Operation: 55-25=30 Exploring Operation: 63-25=38, Resulting Numbers: [55, 38] Generated Node #0,1,2: 10:[55, 38] Operation: 63-25=38 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[25, 8], Operations: ['90-65=25', '63-55=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,10 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,10 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:[63, 30], Operations: ['90-65=25', '55-25=30'] Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,10 unequal: No Solution Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,10 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:[55, 38], Operations: ['90-65=25', '63-25=38'] Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,10 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:[65, 55, 27], Operations: ['90-63=27'] Exploring Operation: 65-55=10, Resulting Numbers: [27, 10] Generated Node #0,0,0: 10:[27, 10] Operation: 65-55=10 Exploring Operation: 55-27=28, Resulting Numbers: [65, 28] Generated Node #0,0,1: 10:[65, 28] Operation: 55-27=28 Exploring Operation: 65-27=38, Resulting Numbers: [55, 38] Generated Node #0,0,2: 10:[55, 38] Operation: 65-27=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[27, 10], Operations: ['90-63=27', '65-55=10'] Exploring Operation: 27+10=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 27*10=270, Resulting Numbers: [270] 270,10 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,10 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:[65, 28], Operations: ['90-63=27', '55-27=28'] Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,10 unequal: No Solution Exploring Operation: 65*28=1820, Resulting Numbers: [1820] 1820,10 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:[55, 38], Operations: ['90-63=27', '65-27=38'] Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,10 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,10 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:[90, 55, 2], Operations: ['65-63=2'] Exploring Operation: 90-55=35, Resulting Numbers: [2, 35] Generated Node #0,2,0: 10:[2, 35] Operation: 90-55=35 Exploring Operation: 90/2=45, Resulting Numbers: [55, 45] Generated Node #0,2,1: 10:[55, 45] Operation: 90/2=45 Exploring Operation: 90-2=88, Resulting Numbers: [55, 88] Generated Node #0,2,2: 10:[55, 88] Operation: 90-2=88 Moving to Node #0,2,0 Current State: 10:[2, 35], Operations: ['65-63=2', '90-55=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,10 unequal: No Solution Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,10 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[55, 45], Operations: ['65-63=2', '90/2=45'] Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,10 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[65, 90, 63, 55], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [90, 55, 2] Generated Node #0,2: 10:[90, 55, 2] Operation: 65-63=2 Moving to Node #0,2 Current State: 10:[90, 55, 2], Operations: ['65-63=2'] Exploring Operation: 90/2=45, Resulting Numbers: [55, 45] Generated Node #0,2,1: 10:[55, 45] Operation: 90/2=45 Moving to Node #0,2,1 Current State: 10:[55, 45], Operations: ['65-63=2', '90/2=45'] Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_3
sum_heuristic
[ 92, 71, 10, 37 ]
26
[ "92-71=21", "10+37=47", "47-21=26" ]
Current State: 26:[92, 71, 10, 37], Operations: [] Exploring Operation: 92-71=21, Resulting Numbers: [10, 37, 21] Generated Node #2: [10, 37, 21] from Operation: 92-71=21 Current State: 26:[10, 37, 21], Operations: ['92-71=21'] Exploring Operation: 10+37=47, Resulting Numbers: [21, 47] Generated Node #3: [21, 47] from Operation: 10+37=47 Current State: 26:[21, 47], Operations: ['92-71=21', '10+37=47'] Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[92, 71, 10, 37], Operations: [] Exploring Operation: 71-37=34, Resulting Numbers: [92, 10, 34] Generated Node #0,0: 26:[92, 10, 34] Operation: 71-37=34 Exploring Operation: 92-71=21, Resulting Numbers: [10, 37, 21] Generated Node #0,1: 26:[10, 37, 21] Operation: 92-71=21 Exploring Operation: 92-37=55, Resulting Numbers: [71, 10, 55] Generated Node #0,2: 26:[71, 10, 55] Operation: 92-37=55 Start Sub Search at level 1: Moving to Node #0,1 Current State: 26:[10, 37, 21], Operations: ['92-71=21'] Exploring Operation: 21-10=11, Resulting Numbers: [37, 11] Generated Node #0,1,0: 26:[37, 11] Operation: 21-10=11 Exploring Operation: 37-21=16, Resulting Numbers: [10, 16] Generated Node #0,1,1: 26:[10, 16] Operation: 37-21=16 Exploring Operation: 37-10=27, Resulting Numbers: [21, 27] Generated Node #0,1,2: 26:[21, 27] Operation: 37-10=27 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 26:[10, 16], Operations: ['92-71=21', '37-21=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[92, 71, 10, 37], Operations: [] Exploring Operation: 92-71=21, Resulting Numbers: [10, 37, 21] Generated Node #0,1: 26:[10, 37, 21] Operation: 92-71=21 Moving to Node #0,1 Current State: 26:[10, 37, 21], Operations: ['92-71=21'] Exploring Operation: 37-21=16, Resulting Numbers: [10, 16] Generated Node #0,1,1: 26:[10, 16] Operation: 37-21=16 Moving to Node #0,1,1 Current State: 26:[10, 16], Operations: ['92-71=21', '37-21=16'] Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 59, 65, 69, 16 ]
39
[ "59+65=124", "69+16=85", "124-85=39" ]
Current State: 39:[59, 65, 69, 16], Operations: [] Exploring Operation: 59+65=124, Resulting Numbers: [69, 16, 124] Generated Node #2: [69, 16, 124] from Operation: 59+65=124 Current State: 39:[69, 16, 124], Operations: ['59+65=124'] Exploring Operation: 69+16=85, Resulting Numbers: [124, 85] Generated Node #3: [124, 85] from Operation: 69+16=85 Current State: 39:[124, 85], Operations: ['59+65=124', '69+16=85'] Exploring Operation: 124-85=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[59, 65, 69, 16], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [59, 16, 4] Generated Node #0,0: 39:[59, 16, 4] Operation: 69-65=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[59, 16, 4], Operations: ['69-65=4'] Exploring Operation: 59-16=43, Resulting Numbers: [4, 43] Generated Node #0,0,0: 39:[4, 43] Operation: 59-16=43 Moving to Node #0,0,0 Current State: 39:[4, 43], Operations: ['69-65=4', '59-16=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[59, 65, 69, 16], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [59, 16, 4] Generated Node #0,0: 39:[59, 16, 4] Operation: 69-65=4 Moving to Node #0,0 Current State: 39:[59, 16, 4], Operations: ['69-65=4'] Exploring Operation: 59-16=43, Resulting Numbers: [4, 43] Generated Node #0,0,0: 39:[4, 43] Operation: 59-16=43 Moving to Node #0,0,0 Current State: 39:[4, 43], Operations: ['69-65=4', '59-16=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 51, 6, 75, 21 ]
99
[ "51-6=45", "75-21=54", "45+54=99" ]
Current State: 99:[51, 6, 75, 21], Operations: [] Exploring Operation: 51-6=45, Resulting Numbers: [75, 21, 45] Generated Node #2: [75, 21, 45] from Operation: 51-6=45 Current State: 99:[75, 21, 45], Operations: ['51-6=45'] Exploring Operation: 75-21=54, Resulting Numbers: [45, 54] Generated Node #3: [45, 54] from Operation: 75-21=54 Current State: 99:[45, 54], Operations: ['51-6=45', '75-21=54'] Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[51, 6, 75, 21], Operations: [] Exploring Operation: 75-51=24, Resulting Numbers: [6, 21, 24] Generated Node #0,0: 99:[6, 21, 24] Operation: 75-51=24 Moving to Node #0,0 Current State: 99:[6, 21, 24], Operations: ['75-51=24'] Exploring Operation: 24-21=3, Resulting Numbers: [6, 3] Generated Node #0,0,0: 99:[6, 3] Operation: 24-21=3 Moving to Node #0,0,0 Current State: 99:[6, 3], Operations: ['75-51=24', '24-21=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 75, 63, 26, 78 ]
36
[ "75-63=12", "78/26=3", "12*3=36" ]
Current State: 36:[75, 63, 26, 78], Operations: [] Exploring Operation: 75-63=12, Resulting Numbers: [26, 78, 12] Generated Node #2: [26, 78, 12] from Operation: 75-63=12 Current State: 36:[26, 78, 12], Operations: ['75-63=12'] Exploring Operation: 78/26=3, Resulting Numbers: [12, 3] Generated Node #3: [12, 3] from Operation: 78/26=3 Current State: 36:[12, 3], Operations: ['75-63=12', '78/26=3'] Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[75, 63, 26, 78], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [63, 26, 3] Generated Node #0,0: 36:[63, 26, 3] Operation: 78-75=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[63, 26, 3], Operations: ['78-75=3'] Exploring Operation: 63-26=37, Resulting Numbers: [3, 37] Generated Node #0,0,0: 36:[3, 37] Operation: 63-26=37 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[3, 37], Operations: ['78-75=3', '63-26=37'] Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 48, 48, 60, 56 ]
69
[ "60*56=3360", "3360-48=3312", "3312/48=69" ]
Current State: 69:[48, 48, 60, 56], Operations: [] Exploring Operation: 60*56=3360, Resulting Numbers: [48, 48, 3360] Generated Node #2: [48, 48, 3360] from Operation: 60*56=3360 Current State: 69:[48, 48, 3360], Operations: ['60*56=3360'] Exploring Operation: 3360-48=3312, Resulting Numbers: [3312] 3312,69 equal: Goal Reached Exploring Operation: 3312/48=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[48, 48, 60, 56], Operations: [] Exploring Operation: 48-48=0, Resulting Numbers: [60, 56, 0] Generated Node #0,0: 69:[60, 56, 0] Operation: 48-48=0 Exploring Operation: 56-48=8, Resulting Numbers: [48, 60, 8] Generated Node #0,1: 69:[48, 60, 8] Operation: 56-48=8 Exploring Operation: 56-48=8, Resulting Numbers: [48, 60, 8] Generated Node #0,2: 69:[48, 60, 8] Operation: 56-48=8 Exploring Operation: 48/48=1, Resulting Numbers: [60, 56, 1] Generated Node #0,3: 69:[60, 56, 1] Operation: 48/48=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[60, 56, 1], Operations: ['48/48=1'] Exploring Operation: 60+1=61, Resulting Numbers: [56, 61] Generated Node #0,3,0: 69:[56, 61] Operation: 60+1=61 Exploring Operation: 60-56=4, Resulting Numbers: [1, 4] Generated Node #0,3,1: 69:[1, 4] Operation: 60-56=4 Exploring Operation: 60*1=60, Resulting Numbers: [56, 60] Generated Node #0,3,2: 69:[56, 60] Operation: 60*1=60 Exploring Operation: 56+1=57, Resulting Numbers: [60, 57] Generated Node #0,3,3: 69:[60, 57] Operation: 56+1=57 Moving to Node #0,3,1 Current State: 69:[1, 4], Operations: ['48/48=1', '60-56=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[60, 57], Operations: ['48/48=1', '56+1=57'] Exploring Operation: 60+57=117, Resulting Numbers: [117] 117,69 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 60*57=3420, Resulting Numbers: [3420] 3420,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[56, 61], Operations: ['48/48=1', '60+1=61'] Exploring Operation: 56+61=117, Resulting Numbers: [117] 117,69 unequal: No Solution Exploring Operation: 61-56=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 56*61=3416, Resulting Numbers: [3416] 3416,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[56, 60], Operations: ['48/48=1', '60*1=60'] Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,69 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[60, 56, 0], Operations: ['48-48=0'] Exploring Operation: 60+0=60, Resulting Numbers: [56, 60] Generated Node #0,0,0: 69:[56, 60] Operation: 60+0=60 Exploring Operation: 60-56=4, Resulting Numbers: [0, 4] Generated Node #0,0,1: 69:[0, 4] Operation: 60-56=4 Exploring Operation: 56*0=0, Resulting Numbers: [60, 0] Generated Node #0,0,2: 69:[60, 0] Operation: 56*0=0 Exploring Operation: 60*0=0, Resulting Numbers: [56, 0] Generated Node #0,0,3: 69:[56, 0] Operation: 60*0=0 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 69:[0, 4], Operations: ['48-48=0', '60-56=4'] Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 0*4=0, Resulting Numbers: [0] 0,69 unequal: No Solution Exploring Operation: 0+4=4, Resulting Numbers: [4] 4,69 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 #0,0,2 Current State: 69:[60, 0], Operations: ['48-48=0', '56*0=0'] Exploring Operation: 60+0=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 60*0=0, Resulting Numbers: [0] 0,69 unequal: No Solution Exploring Operation: 60-0=60, Resulting Numbers: [60] 60,69 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 #0,0,3 Current State: 69:[56, 0], Operations: ['48-48=0', '60*0=0'] Exploring Operation: 56+0=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 56*0=0, Resulting Numbers: [0] 0,69 unequal: No Solution Exploring Operation: 56-0=56, Resulting Numbers: [56] 56,69 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 #0,0,0 Current State: 69:[56, 60], Operations: ['48-48=0', '60+0=60'] Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,69 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: 69:[48, 60, 8], Operations: ['56-48=8'] Exploring Operation: 60-48=12, Resulting Numbers: [8, 12] Generated Node #0,1,0: 69:[8, 12] Operation: 60-48=12 Exploring Operation: 48+8=56, Resulting Numbers: [60, 56] Generated Node #0,1,1: 69:[60, 56] Operation: 48+8=56 Exploring Operation: 60+8=68, Resulting Numbers: [48, 68] Generated Node #0,1,2: 69:[48, 68] Operation: 60+8=68 Exploring Operation: 48/8=6, Resulting Numbers: [60, 6] Generated Node #0,1,3: 69:[60, 6] Operation: 48/8=6 Moving to Node #0,1,3 Current State: 69:[60, 6], Operations: ['56-48=8', '48/8=6'] Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,69 unequal: No Solution Exploring Operation: 60*6=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[8, 12], Operations: ['56-48=8', '60-48=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[48, 68], Operations: ['56-48=8', '60+8=68'] Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 48*68=3264, Resulting Numbers: [3264] 3264,69 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[60, 56], Operations: ['56-48=8', '48+8=56'] Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[48, 60, 8], Operations: ['56-48=8'] Exploring Operation: 48/8=6, Resulting Numbers: [60, 6] Generated Node #0,2,0: 69:[60, 6] Operation: 48/8=6 Exploring Operation: 48+8=56, Resulting Numbers: [60, 56] Generated Node #0,2,1: 69:[60, 56] Operation: 48+8=56 Exploring Operation: 60-48=12, Resulting Numbers: [8, 12] Generated Node #0,2,2: 69:[8, 12] Operation: 60-48=12 Exploring Operation: 60+8=68, Resulting Numbers: [48, 68] Generated Node #0,2,3: 69:[48, 68] Operation: 60+8=68 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 69:[60, 6], Operations: ['56-48=8', '48/8=6'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,69 unequal: No Solution Exploring Operation: 60*6=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,69 unequal: No Solution Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,69 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 #0,2,2 Current State: 69:[8, 12], Operations: ['56-48=8', '60-48=12'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 8*12=96, Resulting Numbers: [96] 96,69 unequal: No Solution Exploring Operation: 8+12=20, Resulting Numbers: [20] 20,69 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 #0,2,1 Current State: 69:[60, 56], Operations: ['56-48=8', '48+8=56'] Exploring Operation: 60+56=116, Resulting Numbers: [116] 116,69 unequal: No Solution Exploring Operation: 60*56=3360, Resulting Numbers: [3360] 3360,69 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,69 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 #0,2,3 Current State: 69:[48, 68], Operations: ['56-48=8', '60+8=68'] Exploring Operation: 48*68=3264, Resulting Numbers: [3264] 3264,69 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,69 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
[ 3, 94, 97, 43 ]
80
[ "94-43=51", "51/3=17", "97-17=80" ]
Current State: 80:[3, 94, 97, 43], Operations: [] Exploring Operation: 94-43=51, Resulting Numbers: [3, 97, 51] Generated Node #2: [3, 97, 51] from Operation: 94-43=51 Current State: 80:[3, 97, 51], Operations: ['94-43=51'] Exploring Operation: 51/3=17, Resulting Numbers: [97, 17] Generated Node #3: [97, 17] from Operation: 51/3=17 Current State: 80:[97, 17], Operations: ['94-43=51', '51/3=17'] Exploring Operation: 97-17=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[3, 94, 97, 43], Operations: [] Exploring Operation: 94-3=91, Resulting Numbers: [97, 43, 91] Generated Node #0,0: 80:[97, 43, 91] Operation: 94-3=91 Exploring Operation: 94-43=51, Resulting Numbers: [3, 97, 51] Generated Node #0,1: 80:[3, 97, 51] Operation: 94-43=51 Exploring Operation: 97-43=54, Resulting Numbers: [3, 94, 54] Generated Node #0,2: 80:[3, 94, 54] Operation: 97-43=54 Exploring Operation: 97-94=3, Resulting Numbers: [3, 43, 3] Generated Node #0,3: 80:[3, 43, 3] Operation: 97-94=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 80:[3, 43, 3], Operations: ['97-94=3'] Exploring Operation: 43-3=40, Resulting Numbers: [3, 40] Generated Node #0,3,0: 80:[3, 40] Operation: 43-3=40 Exploring Operation: 3+3=6, Resulting Numbers: [43, 6] Generated Node #0,3,1: 80:[43, 6] Operation: 3+3=6 Exploring Operation: 43-3=40, Resulting Numbers: [3, 40] Generated Node #0,3,2: 80:[3, 40] Operation: 43-3=40 Exploring Operation: 3*3=9, Resulting Numbers: [43, 9] Generated Node #0,3,3: 80:[43, 9] Operation: 3*3=9 Moving to Node #0,3,0 Current State: 80:[3, 40], Operations: ['97-94=3', '43-3=40'] Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[3, 40], Operations: ['97-94=3', '43-3=40'] Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 3*40=120, Resulting Numbers: [120] 120,80 unequal: No Solution Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[43, 9], Operations: ['97-94=3', '3*3=9'] Exploring Operation: 43*9=387, Resulting Numbers: [387] 387,80 unequal: No Solution Exploring Operation: 43+9=52, Resulting Numbers: [52] 52,80 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[43, 6], Operations: ['97-94=3', '3+3=6'] Exploring Operation: 43*6=258, Resulting Numbers: [258] 258,80 unequal: No Solution Exploring Operation: 43+6=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 43-6=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[3, 97, 51], Operations: ['94-43=51'] Exploring Operation: 97-3=94, Resulting Numbers: [51, 94] Generated Node #0,1,0: 80:[51, 94] Operation: 97-3=94 Exploring Operation: 97-51=46, Resulting Numbers: [3, 46] Generated Node #0,1,1: 80:[3, 46] Operation: 97-51=46 Exploring Operation: 51-3=48, Resulting Numbers: [97, 48] Generated Node #0,1,2: 80:[97, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [97, 17] Generated Node #0,1,3: 80:[97, 17] Operation: 51/3=17 Moving to Node #0,1,1 Current State: 80:[3, 46], Operations: ['94-43=51', '97-51=46'] Exploring Operation: 3*46=138, Resulting Numbers: [138] 138,80 unequal: No Solution Exploring Operation: 3+46=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 46-3=43, Resulting Numbers: [43] 43,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[97, 17], Operations: ['94-43=51', '51/3=17'] Exploring Operation: 97-17=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[3, 94, 97, 43], Operations: [] Exploring Operation: 94-43=51, Resulting Numbers: [3, 97, 51] Generated Node #0,1: 80:[3, 97, 51] Operation: 94-43=51 Moving to Node #0,1 Current State: 80:[3, 97, 51], Operations: ['94-43=51'] Exploring Operation: 51/3=17, Resulting Numbers: [97, 17] Generated Node #0,1,3: 80:[97, 17] Operation: 51/3=17 Moving to Node #0,1,3 Current State: 80:[97, 17], Operations: ['94-43=51', '51/3=17'] Exploring Operation: 97-17=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
sum_heuristic
[ 76, 17, 52, 58 ]
87
[ "76+17=93", "58-52=6", "93-6=87" ]
Current State: 87:[76, 17, 52, 58], Operations: [] Exploring Operation: 76+17=93, Resulting Numbers: [52, 58, 93] Generated Node #2: [52, 58, 93] from Operation: 76+17=93 Current State: 87:[52, 58, 93], Operations: ['76+17=93'] Exploring Operation: 58-52=6, Resulting Numbers: [93, 6] Generated Node #3: [93, 6] from Operation: 58-52=6 Current State: 87:[93, 6], Operations: ['76+17=93', '58-52=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[76, 17, 52, 58], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [76, 17, 6] Generated Node #0,0: 87:[76, 17, 6] Operation: 58-52=6 Moving to Node #0,0 Current State: 87:[76, 17, 6], Operations: ['58-52=6'] Exploring Operation: 76+17=93, Resulting Numbers: [6, 93] Generated Node #0,0,0: 87:[6, 93] Operation: 76+17=93 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[6, 93], Operations: ['58-52=6', '76+17=93'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[76, 17, 52, 58], Operations: [] Exploring Operation: 58-52=6, Resulting Numbers: [76, 17, 6] Generated Node #0,0: 87:[76, 17, 6] Operation: 58-52=6 Moving to Node #0,0 Current State: 87:[76, 17, 6], Operations: ['58-52=6'] Exploring Operation: 76+17=93, Resulting Numbers: [6, 93] Generated Node #0,0,0: 87:[6, 93] Operation: 76+17=93 Moving to Node #0,0,0 Current State: 87:[6, 93], Operations: ['58-52=6', '76+17=93'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 4, 5, 91, 3 ]
83
[ "5-3=2", "4*2=8", "91-8=83" ]
Current State: 83:[4, 5, 91, 3], Operations: [] Exploring Operation: 5-3=2, Resulting Numbers: [4, 91, 2] Generated Node #2: [4, 91, 2] from Operation: 5-3=2 Current State: 83:[4, 91, 2], Operations: ['5-3=2'] Exploring Operation: 4*2=8, Resulting Numbers: [91, 8] Generated Node #3: [91, 8] from Operation: 4*2=8 Current State: 83:[91, 8], Operations: ['5-3=2', '4*2=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[4, 5, 91, 3], Operations: [] Exploring Operation: 4*5=20, Resulting Numbers: [91, 3, 20] Generated Node #0,0: 83:[91, 3, 20] Operation: 4*5=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[91, 3, 20], Operations: ['4*5=20'] Exploring Operation: 3*20=60, Resulting Numbers: [91, 60] Generated Node #0,0,0: 83:[91, 60] Operation: 3*20=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[91, 60], Operations: ['4*5=20', '3*20=60'] Exploring Operation: 91-60=31, Resulting Numbers: [31] 31,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 35, 36, 53, 8 ]
46
[ "36-35=1", "53-8=45", "1+45=46" ]
Current State: 46:[35, 36, 53, 8], Operations: [] Exploring Operation: 36-35=1, Resulting Numbers: [53, 8, 1] Generated Node #2: [53, 8, 1] from Operation: 36-35=1 Current State: 46:[53, 8, 1], Operations: ['36-35=1'] Exploring Operation: 53-8=45, Resulting Numbers: [1, 45] Generated Node #3: [1, 45] from Operation: 53-8=45 Current State: 46:[1, 45], Operations: ['36-35=1', '53-8=45'] Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[35, 36, 53, 8], Operations: [] Exploring Operation: 36+8=44, Resulting Numbers: [35, 53, 44] Generated Node #0,0: 46:[35, 53, 44] Operation: 36+8=44 Exploring Operation: 35+8=43, Resulting Numbers: [36, 53, 43] Generated Node #0,1: 46:[36, 53, 43] Operation: 35+8=43 Exploring Operation: 36-35=1, Resulting Numbers: [53, 8, 1] Generated Node #0,2: 46:[53, 8, 1] Operation: 36-35=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[53, 8, 1], Operations: ['36-35=1'] Exploring Operation: 53-1=52, Resulting Numbers: [8, 52] Generated Node #0,2,0: 46:[8, 52] Operation: 53-1=52 Exploring Operation: 8-1=7, Resulting Numbers: [53, 7] Generated Node #0,2,1: 46:[53, 7] Operation: 8-1=7 Exploring Operation: 53-8=45, Resulting Numbers: [1, 45] Generated Node #0,2,2: 46:[1, 45] Operation: 53-8=45 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 46:[1, 45], Operations: ['36-35=1', '53-8=45'] Exploring Operation: 1*45=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,46 unequal: No Solution Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[35, 36, 53, 8], Operations: [] Exploring Operation: 36-35=1, Resulting Numbers: [53, 8, 1] Generated Node #0,2: 46:[53, 8, 1] Operation: 36-35=1 Moving to Node #0,2 Current State: 46:[53, 8, 1], Operations: ['36-35=1'] Exploring Operation: 53-8=45, Resulting Numbers: [1, 45] Generated Node #0,2,2: 46:[1, 45] Operation: 53-8=45 Moving to Node #0,2,2 Current State: 46:[1, 45], Operations: ['36-35=1', '53-8=45'] Exploring Operation: 1+45=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 32, 3, 54, 51 ]
69
[ "32+54=86", "51/3=17", "86-17=69" ]
Current State: 69:[32, 3, 54, 51], Operations: [] Exploring Operation: 32+54=86, Resulting Numbers: [3, 51, 86] Generated Node #2: [3, 51, 86] from Operation: 32+54=86 Current State: 69:[3, 51, 86], Operations: ['32+54=86'] Exploring Operation: 51/3=17, Resulting Numbers: [86, 17] Generated Node #3: [86, 17] from Operation: 51/3=17 Current State: 69:[86, 17], Operations: ['32+54=86', '51/3=17'] Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[32, 3, 54, 51], Operations: [] Exploring Operation: 54-32=22, Resulting Numbers: [3, 51, 22] Generated Node #0,0: 69:[3, 51, 22] Operation: 54-32=22 Exploring Operation: 54-51=3, Resulting Numbers: [32, 3, 3] Generated Node #0,1: 69:[32, 3, 3] Operation: 54-51=3 Moving to Node #0,1 Current State: 69:[32, 3, 3], Operations: ['54-51=3'] Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,1,0: 69:[3, 29] Operation: 32-3=29 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,1,1: 69:[3, 29] Operation: 32-3=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[3, 29], Operations: ['54-51=3', '32-3=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,69 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 #0,1,1 Current State: 69:[3, 29], Operations: ['54-51=3', '32-3=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 69:[3, 51, 22], Operations: ['54-32=22'] Exploring Operation: 51-22=29, Resulting Numbers: [3, 29] Generated Node #0,0,0: 69:[3, 29] Operation: 51-22=29 Exploring Operation: 51+22=73, Resulting Numbers: [3, 73] Generated Node #0,0,1: 69:[3, 73] Operation: 51+22=73 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[3, 73], Operations: ['54-32=22', '51+22=73'] Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[3, 29], Operations: ['54-32=22', '51-22=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,69 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,69 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
[ 84, 51, 91, 26 ]
84
[ "84-51=33", "91+26=117", "117-33=84" ]
Current State: 84:[84, 51, 91, 26], Operations: [] Exploring Operation: 84-51=33, Resulting Numbers: [91, 26, 33] Generated Node #2: [91, 26, 33] from Operation: 84-51=33 Current State: 84:[91, 26, 33], Operations: ['84-51=33'] Exploring Operation: 91+26=117, Resulting Numbers: [33, 117] Generated Node #3: [33, 117] from Operation: 91+26=117 Current State: 84:[33, 117], Operations: ['84-51=33', '91+26=117'] Exploring Operation: 117-33=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[84, 51, 91, 26], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [51, 26, 7] Generated Node #0,0: 84:[51, 26, 7] Operation: 91-84=7 Exploring Operation: 91-51=40, Resulting Numbers: [84, 26, 40] Generated Node #0,1: 84:[84, 26, 40] Operation: 91-51=40 Exploring Operation: 84-51=33, Resulting Numbers: [91, 26, 33] Generated Node #0,2: 84:[91, 26, 33] Operation: 84-51=33 Exploring Operation: 51-26=25, Resulting Numbers: [84, 91, 25] Generated Node #0,3: 84:[84, 91, 25] Operation: 51-26=25 Exploring Operation: 51+26=77, Resulting Numbers: [84, 91, 77] Generated Node #0,4: 84:[84, 91, 77] Operation: 51+26=77 Moving to Node #0,1 Current State: 84:[84, 26, 40], Operations: ['91-51=40'] Exploring Operation: 84+26=110, Resulting Numbers: [40, 110] Generated Node #0,1,0: 84:[40, 110] Operation: 84+26=110 Exploring Operation: 40-26=14, Resulting Numbers: [84, 14] Generated Node #0,1,1: 84:[84, 14] Operation: 40-26=14 Exploring Operation: 26+40=66, Resulting Numbers: [84, 66] Generated Node #0,1,2: 84:[84, 66] Operation: 26+40=66 Exploring Operation: 84-40=44, Resulting Numbers: [26, 44] Generated Node #0,1,3: 84:[26, 44] Operation: 84-40=44 Exploring Operation: 84-26=58, Resulting Numbers: [40, 58] Generated Node #0,1,4: 84:[40, 58] Operation: 84-26=58 Moving to Node #0,3 Current State: 84:[84, 91, 25], Operations: ['51-26=25'] Exploring Operation: 84-25=59, Resulting Numbers: [91, 59] Generated Node #0,3,0: 84:[91, 59] Operation: 84-25=59 Exploring Operation: 91+25=116, Resulting Numbers: [84, 116] Generated Node #0,3,1: 84:[84, 116] Operation: 91+25=116 Exploring Operation: 84+25=109, Resulting Numbers: [91, 109] Generated Node #0,3,2: 84:[91, 109] Operation: 84+25=109 Exploring Operation: 91-84=7, Resulting Numbers: [25, 7] Generated Node #0,3,3: 84:[25, 7] Operation: 91-84=7 Exploring Operation: 91-25=66, Resulting Numbers: [84, 66] Generated Node #0,3,4: 84:[84, 66] Operation: 91-25=66 Moving to Node #0,0 Current State: 84:[51, 26, 7], Operations: ['91-84=7'] Exploring Operation: 51+26=77, Resulting Numbers: [7, 77] Generated Node #0,0,0: 84:[7, 77] Operation: 51+26=77 Exploring Operation: 26-7=19, Resulting Numbers: [51, 19] Generated Node #0,0,1: 84:[51, 19] Operation: 26-7=19 Exploring Operation: 51-7=44, Resulting Numbers: [26, 44] Generated Node #0,0,2: 84:[26, 44] Operation: 51-7=44 Exploring Operation: 26+7=33, Resulting Numbers: [51, 33] Generated Node #0,0,3: 84:[51, 33] Operation: 26+7=33 Exploring Operation: 51-26=25, Resulting Numbers: [7, 25] Generated Node #0,0,4: 84:[7, 25] Operation: 51-26=25 Moving to Node #0,2 Current State: 84:[91, 26, 33], Operations: ['84-51=33'] Exploring Operation: 91-26=65, Resulting Numbers: [33, 65] Generated Node #0,2,0: 84:[33, 65] Operation: 91-26=65 Exploring Operation: 26+33=59, Resulting Numbers: [91, 59] Generated Node #0,2,1: 84:[91, 59] Operation: 26+33=59 Exploring Operation: 91-33=58, Resulting Numbers: [26, 58] Generated Node #0,2,2: 84:[26, 58] Operation: 91-33=58 Exploring Operation: 33-26=7, Resulting Numbers: [91, 7] Generated Node #0,2,3: 84:[91, 7] Operation: 33-26=7 Exploring Operation: 91+26=117, Resulting Numbers: [33, 117] Generated Node #0,2,4: 84:[33, 117] Operation: 91+26=117 Moving to Node #0,4 Current State: 84:[84, 91, 77], Operations: ['51+26=77'] Exploring Operation: 84+77=161, Resulting Numbers: [91, 161] Generated Node #0,4,0: 84:[91, 161] Operation: 84+77=161 Exploring Operation: 91-77=14, Resulting Numbers: [84, 14] Generated Node #0,4,1: 84:[84, 14] Operation: 91-77=14 Exploring Operation: 91+77=168, Resulting Numbers: [84, 168] Generated Node #0,4,2: 84:[84, 168] Operation: 91+77=168 Exploring Operation: 84-77=7, Resulting Numbers: [91, 7] Generated Node #0,4,3: 84:[91, 7] Operation: 84-77=7 Exploring Operation: 91-84=7, Resulting Numbers: [77, 7] Generated Node #0,4,4: 84:[77, 7] Operation: 91-84=7 Moving to Node #0,1,1 Current State: 84:[84, 14], Operations: ['91-51=40', '40-26=14'] Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,84 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 84*14=1176, Resulting Numbers: [1176] 1176,84 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,84 unequal: No Solution Moving to Node #0,4,1 Current State: 84:[84, 14], Operations: ['51+26=77', '91-77=14'] Exploring Operation: 84*14=1176, Resulting Numbers: [1176] 1176,84 unequal: No Solution Exploring Operation: 84/14=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 84-14=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 84+14=98, Resulting Numbers: [98] 98,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[25, 7], Operations: ['51-26=25', '91-84=7'] Exploring Operation: 25+7=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 25*7=175, Resulting Numbers: [175] 175,84 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,84 unequal: No Solution Moving to Node #0,0,4 Current State: 84:[7, 25], Operations: ['91-84=7', '51-26=25'] Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,84 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[26, 44], Operations: ['91-84=7', '51-7=44'] Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 26*44=1144, Resulting Numbers: [1144] 1144,84 unequal: No Solution Exploring Operation: 26+44=70, Resulting Numbers: [70] 70,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[26, 44], Operations: ['91-51=40', '84-40=44'] Exploring Operation: 26+44=70, Resulting Numbers: [70] 70,84 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 26*44=1144, Resulting Numbers: [1144] 1144,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[7, 77], Operations: ['91-84=7', '51+26=77'] Exploring Operation: 7+77=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[84, 51, 91, 26], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [51, 26, 7] Generated Node #0,0: 84:[51, 26, 7] Operation: 91-84=7 Moving to Node #0,0 Current State: 84:[51, 26, 7], Operations: ['91-84=7'] Exploring Operation: 51+26=77, Resulting Numbers: [7, 77] Generated Node #0,0,0: 84:[7, 77] Operation: 51+26=77 Moving to Node #0,0,0 Current State: 84:[7, 77], Operations: ['91-84=7', '51+26=77'] Exploring Operation: 7+77=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.952257
hs_5
sum_heuristic
[ 91, 52, 26, 95 ]
99
[ "52/26=2", "95*2=190", "190-91=99" ]
Current State: 99:[91, 52, 26, 95], Operations: [] Exploring Operation: 52/26=2, Resulting Numbers: [91, 95, 2] Generated Node #2: [91, 95, 2] from Operation: 52/26=2 Current State: 99:[91, 95, 2], Operations: ['52/26=2'] Exploring Operation: 95*2=190, Resulting Numbers: [91, 190] Generated Node #3: [91, 190] from Operation: 95*2=190 Current State: 99:[91, 190], Operations: ['52/26=2', '95*2=190'] Exploring Operation: 190-91=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[91, 52, 26, 95], Operations: [] Exploring Operation: 91-52=39, Resulting Numbers: [26, 95, 39] Generated Node #0,0: 99:[26, 95, 39] Operation: 91-52=39 Exploring Operation: 52/26=2, Resulting Numbers: [91, 95, 2] Generated Node #0,1: 99:[91, 95, 2] Operation: 52/26=2 Exploring Operation: 52-26=26, Resulting Numbers: [91, 95, 26] Generated Node #0,2: 99:[91, 95, 26] Operation: 52-26=26 Exploring Operation: 95-52=43, Resulting Numbers: [91, 26, 43] Generated Node #0,3: 99:[91, 26, 43] Operation: 95-52=43 Moving to Node #0,1 Current State: 99:[91, 95, 2], Operations: ['52/26=2'] Exploring Operation: 91-2=89, Resulting Numbers: [95, 89] Generated Node #0,1,0: 99:[95, 89] Operation: 91-2=89 Exploring Operation: 95-91=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 99:[2, 4] Operation: 95-91=4 Exploring Operation: 95+2=97, Resulting Numbers: [91, 97] Generated Node #0,1,2: 99:[91, 97] Operation: 95+2=97 Exploring Operation: 91+2=93, Resulting Numbers: [95, 93] Generated Node #0,1,3: 99:[95, 93] Operation: 91+2=93 Moving to Node #0,0 Current State: 99:[26, 95, 39], Operations: ['91-52=39'] Exploring Operation: 26+95=121, Resulting Numbers: [39, 121] Generated Node #0,0,0: 99:[39, 121] Operation: 26+95=121 Exploring Operation: 95-39=56, Resulting Numbers: [26, 56] Generated Node #0,0,1: 99:[26, 56] Operation: 95-39=56 Exploring Operation: 39-26=13, Resulting Numbers: [95, 13] Generated Node #0,0,2: 99:[95, 13] Operation: 39-26=13 Exploring Operation: 95-26=69, Resulting Numbers: [39, 69] Generated Node #0,0,3: 99:[39, 69] Operation: 95-26=69 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 99:[95, 13], Operations: ['91-52=39', '39-26=13'] Exploring Operation: 95-13=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 95+13=108, Resulting Numbers: [108] 108,99 unequal: No Solution Exploring Operation: 95*13=1235, Resulting Numbers: [1235] 1235,99 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 #0,0,0 Current State: 99:[39, 121], Operations: ['91-52=39', '26+95=121'] Exploring Operation: 121-39=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 39*121=4719, Resulting Numbers: [4719] 4719,99 unequal: No Solution Exploring Operation: 39+121=160, Resulting Numbers: [160] 160,99 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 #0,0,1 Current State: 99:[26, 56], Operations: ['91-52=39', '95-39=56'] Exploring Operation: 26*56=1456, Resulting Numbers: [1456] 1456,99 unequal: No Solution Exploring Operation: 26+56=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 56-26=30, Resulting Numbers: [30] 30,99 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 #0,0,3 Current State: 99:[39, 69], Operations: ['91-52=39', '95-26=69'] Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,99 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,99 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: 99:[91, 95, 26], Operations: ['52-26=26'] Exploring Operation: 95-91=4, Resulting Numbers: [26, 4] Generated Node #0,2,0: 99:[26, 4] Operation: 95-91=4 Exploring Operation: 91-26=65, Resulting Numbers: [95, 65] Generated Node #0,2,1: 99:[95, 65] Operation: 91-26=65 Exploring Operation: 95+26=121, Resulting Numbers: [91, 121] Generated Node #0,2,2: 99:[91, 121] Operation: 95+26=121 Exploring Operation: 91+26=117, Resulting Numbers: [95, 117] Generated Node #0,2,3: 99:[95, 117] Operation: 91+26=117 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[26, 4], Operations: ['52-26=26', '95-91=4'] Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,99 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,99 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 #0,2,3 Current State: 99:[95, 117], Operations: ['52-26=26', '91+26=117'] Exploring Operation: 95*117=11115, Resulting Numbers: [11115] 11115,99 unequal: No Solution Exploring Operation: 117-95=22, Resulting Numbers: [22] 22,99 unequal: No Solution Exploring Operation: 95+117=212, Resulting Numbers: [212] 212,99 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 #0,2,2 Current State: 99:[91, 121], Operations: ['52-26=26', '95+26=121'] Exploring Operation: 121-91=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 91+121=212, Resulting Numbers: [212] 212,99 unequal: No Solution Exploring Operation: 91*121=11011, Resulting Numbers: [11011] 11011,99 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 #0,2,1 Current State: 99:[95, 65], Operations: ['52-26=26', '91-26=65'] Exploring Operation: 95*65=6175, Resulting Numbers: [6175] 6175,99 unequal: No Solution Exploring Operation: 95-65=30, Resulting Numbers: [30] 30,99 unequal: No Solution Exploring Operation: 95+65=160, Resulting Numbers: [160] 160,99 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: 99:[91, 26, 43], Operations: ['95-52=43'] Exploring Operation: 91+26=117, Resulting Numbers: [43, 117] Generated Node #0,3,0: 99:[43, 117] Operation: 91+26=117 Exploring Operation: 43-26=17, Resulting Numbers: [91, 17] Generated Node #0,3,1: 99:[91, 17] Operation: 43-26=17 Exploring Operation: 91-43=48, Resulting Numbers: [26, 48] Generated Node #0,3,2: 99:[26, 48] Operation: 91-43=48 Exploring Operation: 26+43=69, Resulting Numbers: [91, 69] Generated Node #0,3,3: 99:[91, 69] Operation: 26+43=69 Moving to Node #0,1,1 Current State: 99:[2, 4], Operations: ['52/26=2', '95-91=4'] Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,99 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[95, 93], Operations: ['52/26=2', '91+2=93'] Exploring Operation: 95+93=188, Resulting Numbers: [188] 188,99 unequal: No Solution Exploring Operation: 95-93=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 95*93=8835, Resulting Numbers: [8835] 8835,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[91, 97], Operations: ['52/26=2', '95+2=97'] Exploring Operation: 91+97=188, Resulting Numbers: [188] 188,99 unequal: No Solution Exploring Operation: 97-91=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 91*97=8827, Resulting Numbers: [8827] 8827,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[91, 17], Operations: ['95-52=43', '43-26=17'] Exploring Operation: 91-17=74, Resulting Numbers: [74] 74,99 unequal: No Solution Exploring Operation: 91*17=1547, Resulting Numbers: [1547] 1547,99 unequal: No Solution Exploring Operation: 91+17=108, Resulting Numbers: [108] 108,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[95, 89], Operations: ['52/26=2', '91-2=89'] Exploring Operation: 95-89=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 95*89=8455, Resulting Numbers: [8455] 8455,99 unequal: No Solution Exploring Operation: 95+89=184, Resulting Numbers: [184] 184,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[26, 48], Operations: ['95-52=43', '91-43=48'] Exploring Operation: 48-26=22, Resulting Numbers: [22] 22,99 unequal: No Solution Exploring Operation: 26*48=1248, Resulting Numbers: [1248] 1248,99 unequal: No Solution Exploring Operation: 26+48=74, Resulting Numbers: [74] 74,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[43, 117], Operations: ['95-52=43', '91+26=117'] Exploring Operation: 43+117=160, Resulting Numbers: [160] 160,99 unequal: No Solution Exploring Operation: 117-43=74, Resulting Numbers: [74] 74,99 unequal: No Solution Exploring Operation: 43*117=5031, Resulting Numbers: [5031] 5031,99 unequal: No Solution Moving to Node #0,3,3 Current State: 99:[91, 69], Operations: ['95-52=43', '26+43=69'] Exploring Operation: 91-69=22, Resulting Numbers: [22] 22,99 unequal: No Solution Exploring Operation: 91*69=6279, Resulting Numbers: [6279] 6279,99 unequal: No Solution Exploring Operation: 91+69=160, Resulting Numbers: [160] 160,99 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 1, 82, 7, 30 ]
87
[ "7-1=6", "30/6=5", "82+5=87" ]
Current State: 87:[1, 82, 7, 30], Operations: [] Exploring Operation: 7-1=6, Resulting Numbers: [82, 30, 6] Generated Node #2: [82, 30, 6] from Operation: 7-1=6 Current State: 87:[82, 30, 6], Operations: ['7-1=6'] Exploring Operation: 30/6=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 30/6=5 Current State: 87:[82, 5], Operations: ['7-1=6', '30/6=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[1, 82, 7, 30], Operations: [] Exploring Operation: 82+7=89, Resulting Numbers: [1, 30, 89] Generated Node #0,0: 87:[1, 30, 89] Operation: 82+7=89 Exploring Operation: 1+82=83, Resulting Numbers: [7, 30, 83] Generated Node #0,1: 87:[7, 30, 83] Operation: 1+82=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[1, 30, 89], Operations: ['82+7=89'] Exploring Operation: 30-1=29, Resulting Numbers: [89, 29] Generated Node #0,0,0: 87:[89, 29] Operation: 30-1=29 Exploring Operation: 89-1=88, Resulting Numbers: [30, 88] Generated Node #0,0,1: 87:[30, 88] Operation: 89-1=88 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[89, 29], Operations: ['82+7=89', '30-1=29'] Exploring Operation: 89-29=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 89+29=118, Resulting Numbers: [118] 118,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[30, 88], Operations: ['82+7=89', '89-1=88'] Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,87 unequal: No Solution Exploring Operation: 30+88=118, Resulting Numbers: [118] 118,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[7, 30, 83], Operations: ['1+82=83'] Exploring Operation: 7+83=90, Resulting Numbers: [30, 90] Generated Node #0,1,0: 87:[30, 90] Operation: 7+83=90 Exploring Operation: 30-7=23, Resulting Numbers: [83, 23] Generated Node #0,1,1: 87:[83, 23] Operation: 30-7=23 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[30, 90], Operations: ['1+82=83', '7+83=90'] Exploring Operation: 90-30=60, Resulting Numbers: [60] 60,87 unequal: No Solution Exploring Operation: 90/30=3, Resulting Numbers: [3] 3,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[83, 23], Operations: ['1+82=83', '30-7=23'] Exploring Operation: 83+23=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 96, 89, 82, 17 ]
34
[ "96+82=178", "178/89=2", "17*2=34" ]
Current State: 34:[96, 89, 82, 17], Operations: [] Exploring Operation: 96+82=178, Resulting Numbers: [89, 17, 178] Generated Node #2: [89, 17, 178] from Operation: 96+82=178 Current State: 34:[89, 17, 178], Operations: ['96+82=178'] Exploring Operation: 178/89=2, Resulting Numbers: [17, 2] Generated Node #3: [17, 2] from Operation: 178/89=2 Current State: 34:[17, 2], Operations: ['96+82=178', '178/89=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[96, 89, 82, 17], Operations: [] Exploring Operation: 89-17=72, Resulting Numbers: [96, 82, 72] Generated Node #0,0: 34:[96, 82, 72] Operation: 89-17=72 Exploring Operation: 96-89=7, Resulting Numbers: [82, 17, 7] Generated Node #0,1: 34:[82, 17, 7] Operation: 96-89=7 Exploring Operation: 96-17=79, Resulting Numbers: [89, 82, 79] Generated Node #0,2: 34:[89, 82, 79] Operation: 96-17=79 Exploring Operation: 89-82=7, Resulting Numbers: [96, 17, 7] Generated Node #0,3: 34:[96, 17, 7] Operation: 89-82=7 Exploring Operation: 96-82=14, Resulting Numbers: [89, 17, 14] Generated Node #0,4: 34:[89, 17, 14] Operation: 96-82=14 Moving to Node #0,1 Current State: 34:[82, 17, 7], Operations: ['96-89=7'] Exploring Operation: 17-7=10, Resulting Numbers: [82, 10] Generated Node #0,1,0: 34:[82, 10] Operation: 17-7=10 Exploring Operation: 82-17=65, Resulting Numbers: [7, 65] Generated Node #0,1,1: 34:[7, 65] Operation: 82-17=65 Exploring Operation: 17+7=24, Resulting Numbers: [82, 24] Generated Node #0,1,2: 34:[82, 24] Operation: 17+7=24 Exploring Operation: 82+7=89, Resulting Numbers: [17, 89] Generated Node #0,1,3: 34:[17, 89] Operation: 82+7=89 Exploring Operation: 82-7=75, Resulting Numbers: [17, 75] Generated Node #0,1,4: 34:[17, 75] Operation: 82-7=75 Moving to Node #0,4 Current State: 34:[89, 17, 14], Operations: ['96-82=14'] Exploring Operation: 17+14=31, Resulting Numbers: [89, 31] Generated Node #0,4,0: 34:[89, 31] Operation: 17+14=31 Exploring Operation: 17-14=3, Resulting Numbers: [89, 3] Generated Node #0,4,1: 34:[89, 3] Operation: 17-14=3 Exploring Operation: 89-14=75, Resulting Numbers: [17, 75] Generated Node #0,4,2: 34:[17, 75] Operation: 89-14=75 Exploring Operation: 89+14=103, Resulting Numbers: [17, 103] Generated Node #0,4,3: 34:[17, 103] Operation: 89+14=103 Exploring Operation: 89-17=72, Resulting Numbers: [14, 72] Generated Node #0,4,4: 34:[14, 72] Operation: 89-17=72 Moving to Node #0,3 Current State: 34:[96, 17, 7], Operations: ['89-82=7'] Exploring Operation: 17-7=10, Resulting Numbers: [96, 10] Generated Node #0,3,0: 34:[96, 10] Operation: 17-7=10 Exploring Operation: 17+7=24, Resulting Numbers: [96, 24] Generated Node #0,3,1: 34:[96, 24] Operation: 17+7=24 Exploring Operation: 96+7=103, Resulting Numbers: [17, 103] Generated Node #0,3,2: 34:[17, 103] Operation: 96+7=103 Exploring Operation: 96-17=79, Resulting Numbers: [7, 79] Generated Node #0,3,3: 34:[7, 79] Operation: 96-17=79 Exploring Operation: 96-7=89, Resulting Numbers: [17, 89] Generated Node #0,3,4: 34:[17, 89] Operation: 96-7=89 Moving to Node #0,0 Current State: 34:[96, 82, 72], Operations: ['89-17=72'] Exploring Operation: 96+82=178, Resulting Numbers: [72, 178] Generated Node #0,0,0: 34:[72, 178] Operation: 96+82=178 Exploring Operation: 96-82=14, Resulting Numbers: [72, 14] Generated Node #0,0,1: 34:[72, 14] Operation: 96-82=14 Exploring Operation: 96-72=24, Resulting Numbers: [82, 24] Generated Node #0,0,2: 34:[82, 24] Operation: 96-72=24 Exploring Operation: 96+72=168, Resulting Numbers: [82, 168] Generated Node #0,0,3: 34:[82, 168] Operation: 96+72=168 Exploring Operation: 82-72=10, Resulting Numbers: [96, 10] Generated Node #0,0,4: 34:[96, 10] Operation: 82-72=10 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 34:[72, 14], Operations: ['89-17=72', '96-82=14'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,34 unequal: No Solution Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,34 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 #0,0,2 Current State: 34:[82, 24], Operations: ['89-17=72', '96-72=24'] Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 82*24=1968, Resulting Numbers: [1968] 1968,34 unequal: No Solution Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,34 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 #0,0,4 Current State: 34:[96, 10], Operations: ['89-17=72', '82-72=10'] Exploring Operation: 96*10=960, Resulting Numbers: [960] 960,34 unequal: No Solution Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 96+10=106, Resulting Numbers: [106] 106,34 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 #0,0,0 Current State: 34:[72, 178], Operations: ['89-17=72', '96+82=178'] Exploring Operation: 72+178=250, Resulting Numbers: [250] 250,34 unequal: No Solution Exploring Operation: 72*178=12816, Resulting Numbers: [12816] 12816,34 unequal: No Solution Exploring Operation: 178-72=106, Resulting Numbers: [106] 106,34 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 #0,0,3 Current State: 34:[82, 168], Operations: ['89-17=72', '96+72=168'] Exploring Operation: 168-82=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 82*168=13776, Resulting Numbers: [13776] 13776,34 unequal: No Solution Exploring Operation: 82+168=250, Resulting Numbers: [250] 250,34 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: 34:[89, 82, 79], Operations: ['96-17=79'] Exploring Operation: 82-79=3, Resulting Numbers: [89, 3] Generated Node #0,2,0: 34:[89, 3] Operation: 82-79=3 Exploring Operation: 89+82=171, Resulting Numbers: [79, 171] Generated Node #0,2,1: 34:[79, 171] Operation: 89+82=171 Exploring Operation: 89-82=7, Resulting Numbers: [79, 7] Generated Node #0,2,2: 34:[79, 7] Operation: 89-82=7 Exploring Operation: 89+79=168, Resulting Numbers: [82, 168] Generated Node #0,2,3: 34:[82, 168] Operation: 89+79=168 Exploring Operation: 89-79=10, Resulting Numbers: [82, 10] Generated Node #0,2,4: 34:[82, 10] Operation: 89-79=10 Moving to Node #0,1,1 Current State: 34:[7, 65], Operations: ['96-89=7', '82-17=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 7+65=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 7*65=455, Resulting Numbers: [455] 455,34 unequal: No Solution Moving to Node #0,4,2 Current State: 34:[17, 75], Operations: ['96-82=14', '89-14=75'] Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,34 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,34 unequal: No Solution Moving to Node #0,4,4 Current State: 34:[14, 72], Operations: ['96-82=14', '89-17=72'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 14*72=1008, Resulting Numbers: [1008] 1008,34 unequal: No Solution Exploring Operation: 14+72=86, Resulting Numbers: [86] 86,34 unequal: No Solution Moving to Node #0,1,4 Current State: 34:[17, 75], Operations: ['96-89=7', '82-7=75'] Exploring Operation: 75-17=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 17+75=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 17*75=1275, Resulting Numbers: [1275] 1275,34 unequal: No Solution Moving to Node #0,3,3 Current State: 34:[7, 79], Operations: ['89-82=7', '96-17=79'] Exploring Operation: 7*79=553, Resulting Numbers: [553] 553,34 unequal: No Solution Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[79, 7], Operations: ['96-17=79', '89-82=7'] Exploring Operation: 79*7=553, Resulting Numbers: [553] 553,34 unequal: No Solution Exploring Operation: 79+7=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[82, 10], Operations: ['96-89=7', '17-7=10'] Exploring Operation: 82+10=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 82*10=820, Resulting Numbers: [820] 820,34 unequal: No Solution Moving to Node #0,3,4 Current State: 34:[17, 89], Operations: ['89-82=7', '96-7=89'] Exploring Operation: 17+89=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 17*89=1513, Resulting Numbers: [1513] 1513,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[17, 89], Operations: ['96-89=7', '82+7=89'] Exploring Operation: 17+89=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 89-17=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 17*89=1513, Resulting Numbers: [1513] 1513,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[82, 24], Operations: ['96-89=7', '17+7=24'] Exploring Operation: 82-24=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 82*24=1968, Resulting Numbers: [1968] 1968,34 unequal: No Solution Exploring Operation: 82+24=106, Resulting Numbers: [106] 106,34 unequal: No Solution Moving to Node #0,2,4 Current State: 34:[82, 10], Operations: ['96-17=79', '89-79=10'] Exploring Operation: 82+10=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 82-10=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 82*10=820, Resulting Numbers: [820] 820,34 unequal: No Solution Moving to Node #0,4,1 Current State: 34:[89, 3], Operations: ['96-82=14', '17-14=3'] Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,34 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,34 unequal: No Solution Moving to Node #0,2,0 Current State: 34:[89, 3], Operations: ['96-17=79', '82-79=3'] Exploring Operation: 89*3=267, Resulting Numbers: [267] 267,34 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 89+3=92, Resulting Numbers: [92] 92,34 unequal: No Solution Moving to Node #0,4,0 Current State: 34:[89, 31], Operations: ['96-82=14', '17+14=31'] Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,34 unequal: No Solution Exploring Operation: 89*31=2759, Resulting Numbers: [2759] 2759,34 unequal: No Solution Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,34 unequal: No Solution Moving to Node #0,3,2 Current State: 34:[17, 103], Operations: ['89-82=7', '96+7=103'] Exploring Operation: 17*103=1751, Resulting Numbers: [1751] 1751,34 unequal: No Solution Exploring Operation: 17+103=120, Resulting Numbers: [120] 120,34 unequal: No Solution Exploring Operation: 103-17=86, Resulting Numbers: [86] 86,34 unequal: No Solution Moving to Node #0,3,0 Current State: 34:[96, 10], Operations: ['89-82=7', '17-7=10'] Exploring Operation: 96*10=960, Resulting Numbers: [960] 960,34 unequal: No Solution Exploring Operation: 96+10=106, Resulting Numbers: [106] 106,34 unequal: No Solution Exploring Operation: 96-10=86, Resulting Numbers: [86] 86,34 unequal: No Solution Moving to Node #0,3,1 Current State: 34:[96, 24], Operations: ['89-82=7', '17+7=24'] Exploring Operation: 96-24=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 96+24=120, Resulting Numbers: [120] 120,34 unequal: No Solution Exploring Operation: 96*24=2304, Resulting Numbers: [2304] 2304,34 unequal: No Solution Exploring Operation: 96/24=4, Resulting Numbers: [4] 4,34 unequal: No Solution Moving to Node #0,4,3 Current State: 34:[17, 103], Operations: ['96-82=14', '89+14=103'] Exploring Operation: 17*103=1751, Resulting Numbers: [1751] 1751,34 unequal: No Solution Exploring Operation: 17+103=120, Resulting Numbers: [120] 120,34 unequal: No Solution Exploring Operation: 103-17=86, Resulting Numbers: [86] 86,34 unequal: No Solution Moving to Node #0,2,3 Current State: 34:[82, 168], Operations: ['96-17=79', '89+79=168'] Exploring Operation: 168-82=86, Resulting Numbers: [86] 86,34 unequal: No Solution Exploring Operation: 82*168=13776, Resulting Numbers: [13776] 13776,34 unequal: No Solution Exploring Operation: 82+168=250, Resulting Numbers: [250] 250,34 unequal: No Solution Moving to Node #0,2,1 Current State: 34:[79, 171], Operations: ['96-17=79', '89+82=171'] Exploring Operation: 79+171=250, Resulting Numbers: [250] 250,34 unequal: No Solution Exploring Operation: 79*171=13509, Resulting Numbers: [13509] 13509,34 unequal: No Solution Exploring Operation: 171-79=92, Resulting Numbers: [92] 92,34 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 73, 49, 64, 24 ]
64
[ "73-49=24", "64+24=88", "88-24=64" ]
Current State: 64:[73, 49, 64, 24], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [64, 24, 24] Generated Node #2: [64, 24, 24] from Operation: 73-49=24 Current State: 64:[64, 24, 24], Operations: ['73-49=24'] Exploring Operation: 64+24=88, Resulting Numbers: [88] 88,64 equal: Goal Reached Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[73, 49, 64, 24], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [64, 24, 24] Generated Node #0,0: 64:[64, 24, 24] Operation: 73-49=24 Exploring Operation: 49-24=25, Resulting Numbers: [73, 64, 25] Generated Node #0,1: 64:[73, 64, 25] Operation: 49-24=25 Exploring Operation: 64-49=15, Resulting Numbers: [73, 24, 15] Generated Node #0,2: 64:[73, 24, 15] Operation: 64-49=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[64, 24, 24], Operations: ['73-49=24'] Exploring Operation: 64-24=40, Resulting Numbers: [24, 40] Generated Node #0,0,0: 64:[24, 40] Operation: 64-24=40 Exploring Operation: 24-24=0, Resulting Numbers: [64, 0] Generated Node #0,0,1: 64:[64, 0] Operation: 24-24=0 Exploring Operation: 24/24=1, Resulting Numbers: [64, 1] Generated Node #0,0,2: 64:[64, 1] Operation: 24/24=1 Moving to Node #0,0,2 Current State: 64:[64, 1], Operations: ['73-49=24', '24/24=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[73, 49, 64, 24], Operations: [] Exploring Operation: 73-49=24, Resulting Numbers: [64, 24, 24] Generated Node #0,0: 64:[64, 24, 24] Operation: 73-49=24 Moving to Node #0,0 Current State: 64:[64, 24, 24], Operations: ['73-49=24'] Exploring Operation: 24/24=1, Resulting Numbers: [64, 1] Generated Node #0,0,2: 64:[64, 1] Operation: 24/24=1 Moving to Node #0,0,2 Current State: 64:[64, 1], Operations: ['73-49=24', '24/24=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 63, 50, 75, 71 ]
78
[ "71-50=21", "63/21=3", "75+3=78" ]
Current State: 78:[63, 50, 75, 71], Operations: [] Exploring Operation: 71-50=21, Resulting Numbers: [63, 75, 21] Generated Node #2: [63, 75, 21] from Operation: 71-50=21 Current State: 78:[63, 75, 21], Operations: ['71-50=21'] Exploring Operation: 63/21=3, Resulting Numbers: [75, 3] Generated Node #3: [75, 3] from Operation: 63/21=3 Current State: 78:[75, 3], Operations: ['71-50=21', '63/21=3'] Exploring Operation: 75+3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[63, 50, 75, 71], Operations: [] Exploring Operation: 75-50=25, Resulting Numbers: [63, 71, 25] Generated Node #0,0: 78:[63, 71, 25] Operation: 75-50=25 Exploring Operation: 63-50=13, Resulting Numbers: [75, 71, 13] Generated Node #0,1: 78:[75, 71, 13] Operation: 63-50=13 Exploring Operation: 71-63=8, Resulting Numbers: [50, 75, 8] Generated Node #0,2: 78:[50, 75, 8] Operation: 71-63=8 Exploring Operation: 75-63=12, Resulting Numbers: [50, 71, 12] Generated Node #0,3: 78:[50, 71, 12] Operation: 75-63=12 Moving to Node #0,1 Current State: 78:[75, 71, 13], Operations: ['63-50=13'] Exploring Operation: 71+13=84, Resulting Numbers: [75, 84] Generated Node #0,1,0: 78:[75, 84] Operation: 71+13=84 Exploring Operation: 75-71=4, Resulting Numbers: [13, 4] Generated Node #0,1,1: 78:[13, 4] Operation: 75-71=4 Exploring Operation: 71-13=58, Resulting Numbers: [75, 58] Generated Node #0,1,2: 78:[75, 58] Operation: 71-13=58 Exploring Operation: 75+13=88, Resulting Numbers: [71, 88] Generated Node #0,1,3: 78:[71, 88] Operation: 75+13=88 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[13, 4], Operations: ['63-50=13', '75-71=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,78 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,78 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 #0,1,0 Current State: 78:[75, 84], Operations: ['63-50=13', '71+13=84'] Exploring Operation: 75+84=159, Resulting Numbers: [159] 159,78 unequal: No Solution Exploring Operation: 75*84=6300, Resulting Numbers: [6300] 6300,78 unequal: No Solution Exploring Operation: 84-75=9, Resulting Numbers: [9] 9,78 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 #0,1,3 Current State: 78:[71, 88], Operations: ['63-50=13', '75+13=88'] Exploring Operation: 71+88=159, Resulting Numbers: [159] 159,78 unequal: No Solution Exploring Operation: 71*88=6248, Resulting Numbers: [6248] 6248,78 unequal: No Solution Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,78 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 #0,1,2 Current State: 78:[75, 58], Operations: ['63-50=13', '71-13=58'] Exploring Operation: 75*58=4350, Resulting Numbers: [4350] 4350,78 unequal: No Solution Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 75+58=133, Resulting Numbers: [133] 133,78 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: 78:[50, 75, 8], Operations: ['71-63=8'] Exploring Operation: 50-8=42, Resulting Numbers: [75, 42] Generated Node #0,2,0: 78:[75, 42] Operation: 50-8=42 Exploring Operation: 50+8=58, Resulting Numbers: [75, 58] Generated Node #0,2,1: 78:[75, 58] Operation: 50+8=58 Exploring Operation: 75+8=83, Resulting Numbers: [50, 83] Generated Node #0,2,2: 78:[50, 83] Operation: 75+8=83 Exploring Operation: 75-50=25, Resulting Numbers: [8, 25] Generated Node #0,2,3: 78:[8, 25] Operation: 75-50=25 Moving to Node #0,3 Current State: 78:[50, 71, 12], Operations: ['75-63=12'] Exploring Operation: 71+12=83, Resulting Numbers: [50, 83] Generated Node #0,3,0: 78:[50, 83] Operation: 71+12=83 Exploring Operation: 50+12=62, Resulting Numbers: [71, 62] Generated Node #0,3,1: 78:[71, 62] Operation: 50+12=62 Exploring Operation: 71-50=21, Resulting Numbers: [12, 21] Generated Node #0,3,2: 78:[12, 21] Operation: 71-50=21 Exploring Operation: 50-12=38, Resulting Numbers: [71, 38] Generated Node #0,3,3: 78:[71, 38] Operation: 50-12=38 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[12, 21], Operations: ['75-63=12', '71-50=21'] Exploring Operation: 12+21=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 21-12=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 12*21=252, Resulting Numbers: [252] 252,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[71, 38], Operations: ['75-63=12', '50-12=38'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 71+38=109, Resulting Numbers: [109] 109,78 unequal: No Solution Exploring Operation: 71*38=2698, Resulting Numbers: [2698] 2698,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[50, 83], Operations: ['75-63=12', '71+12=83'] Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,78 unequal: No Solution Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,78 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[71, 62], Operations: ['75-63=12', '50+12=62'] Exploring Operation: 71*62=4402, Resulting Numbers: [4402] 4402,78 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 71+62=133, Resulting Numbers: [133] 133,78 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: 78:[63, 71, 25], Operations: ['75-50=25'] Exploring Operation: 71-25=46, Resulting Numbers: [63, 46] Generated Node #0,0,0: 78:[63, 46] Operation: 71-25=46 Exploring Operation: 63-25=38, Resulting Numbers: [71, 38] Generated Node #0,0,1: 78:[71, 38] Operation: 63-25=38 Exploring Operation: 63+25=88, Resulting Numbers: [71, 88] Generated Node #0,0,2: 78:[71, 88] Operation: 63+25=88 Exploring Operation: 71-63=8, Resulting Numbers: [25, 8] Generated Node #0,0,3: 78:[25, 8] Operation: 71-63=8 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[25, 8], Operations: ['75-50=25', '71-63=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,78 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,78 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 #0,0,1 Current State: 78:[71, 38], Operations: ['75-50=25', '63-25=38'] Exploring Operation: 71*38=2698, Resulting Numbers: [2698] 2698,78 unequal: No Solution Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 71+38=109, Resulting Numbers: [109] 109,78 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 #0,0,2 Current State: 78:[71, 88], Operations: ['75-50=25', '63+25=88'] Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 71*88=6248, Resulting Numbers: [6248] 6248,78 unequal: No Solution Exploring Operation: 71+88=159, Resulting Numbers: [159] 159,78 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:[63, 46], Operations: ['75-50=25', '71-25=46'] Exploring Operation: 63*46=2898, Resulting Numbers: [2898] 2898,78 unequal: No Solution Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 63+46=109, Resulting Numbers: [109] 109,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,3 Current State: 78:[8, 25], Operations: ['71-63=8', '75-50=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,78 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[75, 42], Operations: ['71-63=8', '50-8=42'] Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,78 unequal: No Solution Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,78 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[50, 83], Operations: ['71-63=8', '75+8=83'] Exploring Operation: 50+83=133, Resulting Numbers: [133] 133,78 unequal: No Solution Exploring Operation: 50*83=4150, Resulting Numbers: [4150] 4150,78 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,78 unequal: No Solution Moving to Node #0,2,1 Current State: 78:[75, 58], Operations: ['71-63=8', '50+8=58'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,78 unequal: No Solution Exploring Operation: 75+58=133, Resulting Numbers: [133] 133,78 unequal: No Solution Exploring Operation: 75*58=4350, Resulting Numbers: [4350] 4350,78 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 5, 92, 92, 80 ]
80
[ "92-92=0", "5*0=0", "80+0=80" ]
Current State: 80:[5, 92, 92, 80], Operations: [] Exploring Operation: 92-92=0, Resulting Numbers: [5, 80, 0] Generated Node #2: [5, 80, 0] from Operation: 92-92=0 Current State: 80:[5, 80, 0], Operations: ['92-92=0'] Exploring Operation: 5*0=0, Resulting Numbers: [80, 0] Generated Node #3: [80, 0] from Operation: 5*0=0 Current State: 80:[80, 0], Operations: ['92-92=0', '5*0=0'] Exploring Operation: 80+0=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[5, 92, 92, 80], Operations: [] Exploring Operation: 92/92=1, Resulting Numbers: [5, 80, 1] Generated Node #0,0: 80:[5, 80, 1] Operation: 92/92=1 Moving to Node #0,0 Current State: 80:[5, 80, 1], Operations: ['92/92=1'] Exploring Operation: 5*1=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 80:[80, 5] Operation: 5*1=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[80, 5], Operations: ['92/92=1', '5*1=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,80 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
[ 9, 19, 2, 44 ]
89
[ "9-2=7", "19*7=133", "133-44=89" ]
Current State: 89:[9, 19, 2, 44], Operations: [] Exploring Operation: 9-2=7, Resulting Numbers: [19, 44, 7] Generated Node #2: [19, 44, 7] from Operation: 9-2=7 Current State: 89:[19, 44, 7], Operations: ['9-2=7'] Exploring Operation: 19*7=133, Resulting Numbers: [44, 133] Generated Node #3: [44, 133] from Operation: 19*7=133 Current State: 89:[44, 133], Operations: ['9-2=7', '19*7=133'] Exploring Operation: 133-44=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[9, 19, 2, 44], Operations: [] Exploring Operation: 9*2=18, Resulting Numbers: [19, 44, 18] Generated Node #0,0: 89:[19, 44, 18] Operation: 9*2=18 Exploring Operation: 2*44=88, Resulting Numbers: [9, 19, 88] Generated Node #0,1: 89:[9, 19, 88] Operation: 2*44=88 Exploring Operation: 19*2=38, Resulting Numbers: [9, 44, 38] Generated Node #0,2: 89:[9, 44, 38] Operation: 19*2=38 Exploring Operation: 9+19=28, Resulting Numbers: [2, 44, 28] Generated Node #0,3: 89:[2, 44, 28] Operation: 9+19=28 Moving to Node #0,1 Current State: 89:[9, 19, 88], Operations: ['2*44=88'] Exploring Operation: 9+19=28, Resulting Numbers: [88, 28] Generated Node #0,1,0: 89:[88, 28] Operation: 9+19=28 Exploring Operation: 88-9=79, Resulting Numbers: [19, 79] Generated Node #0,1,1: 89:[19, 79] Operation: 88-9=79 Exploring Operation: 9+88=97, Resulting Numbers: [19, 97] Generated Node #0,1,2: 89:[19, 97] Operation: 9+88=97 Exploring Operation: 19-9=10, Resulting Numbers: [88, 10] Generated Node #0,1,3: 89:[88, 10] Operation: 19-9=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[88, 28], Operations: ['2*44=88', '9+19=28'] Exploring Operation: 88+28=116, Resulting Numbers: [116] 116,89 unequal: No Solution Exploring Operation: 88*28=2464, Resulting Numbers: [2464] 2464,89 unequal: No Solution Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[19, 97], Operations: ['2*44=88', '9+88=97'] Exploring Operation: 19*97=1843, Resulting Numbers: [1843] 1843,89 unequal: No Solution Exploring Operation: 19+97=116, Resulting Numbers: [116] 116,89 unequal: No Solution Exploring Operation: 97-19=78, Resulting Numbers: [78] 78,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[19, 79], Operations: ['2*44=88', '88-9=79'] Exploring Operation: 79-19=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 19*79=1501, Resulting Numbers: [1501] 1501,89 unequal: No Solution Exploring Operation: 19+79=98, Resulting Numbers: [98] 98,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 89:[88, 10], Operations: ['2*44=88', '19-9=10'] Exploring Operation: 88+10=98, Resulting Numbers: [98] 98,89 unequal: No Solution Exploring Operation: 88-10=78, Resulting Numbers: [78] 78,89 unequal: No Solution Exploring Operation: 88*10=880, Resulting Numbers: [880] 880,89 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: 89:[9, 44, 38], Operations: ['19*2=38'] Exploring Operation: 9+44=53, Resulting Numbers: [38, 53] Generated Node #0,2,0: 89:[38, 53] Operation: 9+44=53 Exploring Operation: 9+38=47, Resulting Numbers: [44, 47] Generated Node #0,2,1: 89:[44, 47] Operation: 9+38=47 Exploring Operation: 44+38=82, Resulting Numbers: [9, 82] Generated Node #0,2,2: 89:[9, 82] Operation: 44+38=82 Exploring Operation: 44-9=35, Resulting Numbers: [38, 35] Generated Node #0,2,3: 89:[38, 35] Operation: 44-9=35 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[38, 53], Operations: ['19*2=38', '9+44=53'] Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,89 unequal: No Solution Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,89 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[44, 47], Operations: ['19*2=38', '9+38=47'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,89 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,89 unequal: No Solution Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[9, 82], Operations: ['19*2=38', '44+38=82'] Exploring Operation: 9+82=91, Resulting Numbers: [91] 91,89 unequal: No Solution Exploring Operation: 9*82=738, Resulting Numbers: [738] 738,89 unequal: No Solution Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[38, 35], Operations: ['19*2=38', '44-9=35'] Exploring Operation: 38+35=73, Resulting Numbers: [73] 73,89 unequal: No Solution Exploring Operation: 38*35=1330, Resulting Numbers: [1330] 1330,89 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,89 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: 89:[19, 44, 18], Operations: ['9*2=18'] Exploring Operation: 19+18=37, Resulting Numbers: [44, 37] Generated Node #0,0,0: 89:[44, 37] Operation: 19+18=37 Exploring Operation: 19-18=1, Resulting Numbers: [44, 1] Generated Node #0,0,1: 89:[44, 1] Operation: 19-18=1 Exploring Operation: 19+44=63, Resulting Numbers: [18, 63] Generated Node #0,0,2: 89:[18, 63] Operation: 19+44=63 Exploring Operation: 44+18=62, Resulting Numbers: [19, 62] Generated Node #0,0,3: 89:[19, 62] Operation: 44+18=62 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[44, 37], Operations: ['9*2=18', '19+18=37'] Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,89 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[18, 63], Operations: ['9*2=18', '19+44=63'] Exploring Operation: 18*63=1134, Resulting Numbers: [1134] 1134,89 unequal: No Solution Exploring Operation: 18+63=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 63-18=45, Resulting Numbers: [45] 45,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[19, 62], Operations: ['9*2=18', '44+18=62'] Exploring Operation: 19*62=1178, Resulting Numbers: [1178] 1178,89 unequal: No Solution Exploring Operation: 19+62=81, Resulting Numbers: [81] 81,89 unequal: No Solution Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[44, 1], Operations: ['9*2=18', '19-18=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,89 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,89 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,89 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 89:[2, 44, 28], Operations: ['9+19=28'] Exploring Operation: 2+28=30, Resulting Numbers: [44, 30] Generated Node #0,3,0: 89:[44, 30] Operation: 2+28=30 Exploring Operation: 2+44=46, Resulting Numbers: [28, 46] Generated Node #0,3,1: 89:[28, 46] Operation: 2+44=46 Exploring Operation: 2*28=56, Resulting Numbers: [44, 56] Generated Node #0,3,2: 89:[44, 56] Operation: 2*28=56 Exploring Operation: 2*44=88, Resulting Numbers: [28, 88] Generated Node #0,3,3: 89:[28, 88] Operation: 2*44=88 Moving to Node #0,3,3 Current State: 89:[28, 88], Operations: ['9+19=28', '2*44=88'] Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,89 unequal: No Solution Exploring Operation: 28*88=2464, Resulting Numbers: [2464] 2464,89 unequal: No Solution Exploring Operation: 28+88=116, Resulting Numbers: [116] 116,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[44, 56], Operations: ['9+19=28', '2*28=56'] Exploring Operation: 44*56=2464, Resulting Numbers: [2464] 2464,89 unequal: No Solution Exploring Operation: 44+56=100, Resulting Numbers: [100] 100,89 unequal: No Solution Exploring Operation: 56-44=12, Resulting Numbers: [12] 12,89 unequal: No Solution Moving to Node #0,3,1 Current State: 89:[28, 46], Operations: ['9+19=28', '2+44=46'] Exploring Operation: 28*46=1288, Resulting Numbers: [1288] 1288,89 unequal: No Solution Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,89 unequal: No Solution Exploring Operation: 28+46=74, Resulting Numbers: [74] 74,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[44, 30], Operations: ['9+19=28', '2+28=30'] Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 44*30=1320, Resulting Numbers: [1320] 1320,89 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,89 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 89, 20, 15, 19 ]
75
[ "89+20=109", "15+19=34", "109-34=75" ]
Current State: 75:[89, 20, 15, 19], Operations: [] Exploring Operation: 89+20=109, Resulting Numbers: [15, 19, 109] Generated Node #2: [15, 19, 109] from Operation: 89+20=109 Current State: 75:[15, 19, 109], Operations: ['89+20=109'] Exploring Operation: 15+19=34, Resulting Numbers: [109, 34] Generated Node #3: [109, 34] from Operation: 15+19=34 Current State: 75:[109, 34], Operations: ['89+20=109', '15+19=34'] Exploring Operation: 109-34=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[89, 20, 15, 19], Operations: [] Exploring Operation: 89-19=70, Resulting Numbers: [20, 15, 70] Generated Node #0,0: 75:[20, 15, 70] Operation: 89-19=70 Exploring Operation: 89-15=74, Resulting Numbers: [20, 19, 74] Generated Node #0,1: 75:[20, 19, 74] Operation: 89-15=74 Exploring Operation: 89-20=69, Resulting Numbers: [15, 19, 69] Generated Node #0,2: 75:[15, 19, 69] Operation: 89-20=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[20, 15, 70], Operations: ['89-19=70'] Exploring Operation: 20+15=35, Resulting Numbers: [70, 35] Generated Node #0,0,0: 75:[70, 35] Operation: 20+15=35 Exploring Operation: 20-15=5, Resulting Numbers: [70, 5] Generated Node #0,0,1: 75:[70, 5] Operation: 20-15=5 Exploring Operation: 20+70=90, Resulting Numbers: [15, 90] Generated Node #0,0,2: 75:[15, 90] Operation: 20+70=90 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[70, 5], Operations: ['89-19=70', '20-15=5'] Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[89, 20, 15, 19], Operations: [] Exploring Operation: 89-19=70, Resulting Numbers: [20, 15, 70] Generated Node #0,0: 75:[20, 15, 70] Operation: 89-19=70 Moving to Node #0,0 Current State: 75:[20, 15, 70], Operations: ['89-19=70'] Exploring Operation: 20-15=5, Resulting Numbers: [70, 5] Generated Node #0,0,1: 75:[70, 5] Operation: 20-15=5 Moving to Node #0,0,1 Current State: 75:[70, 5], Operations: ['89-19=70', '20-15=5'] Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 41, 13, 15, 47 ]
38
[ "13*47=611", "611-41=570", "570/15=38" ]
Current State: 38:[41, 13, 15, 47], Operations: [] Exploring Operation: 13*47=611, Resulting Numbers: [41, 15, 611] Generated Node #2: [41, 15, 611] from Operation: 13*47=611 Current State: 38:[41, 15, 611], Operations: ['13*47=611'] Exploring Operation: 611-41=570, Resulting Numbers: [15, 570] Generated Node #3: [15, 570] from Operation: 611-41=570 Current State: 38:[15, 570], Operations: ['13*47=611', '611-41=570'] Exploring Operation: 570/15=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[41, 13, 15, 47], Operations: [] Exploring Operation: 15-13=2, Resulting Numbers: [41, 47, 2] Generated Node #0,0: 38:[41, 47, 2] Operation: 15-13=2 Exploring Operation: 47-13=34, Resulting Numbers: [41, 15, 34] Generated Node #0,1: 38:[41, 15, 34] Operation: 47-13=34 Moving to Node #0,1 Current State: 38:[41, 15, 34], Operations: ['47-13=34'] Exploring Operation: 41-34=7, Resulting Numbers: [15, 7] Generated Node #0,1,0: 38:[15, 7] Operation: 41-34=7 Exploring Operation: 34-15=19, Resulting Numbers: [41, 19] Generated Node #0,1,1: 38:[41, 19] Operation: 34-15=19 Moving to Node #0,0 Current State: 38:[41, 47, 2], Operations: ['15-13=2'] Exploring Operation: 47-41=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 38:[2, 6] Operation: 47-41=6 Exploring Operation: 41-2=39, Resulting Numbers: [47, 39] Generated Node #0,0,1: 38:[47, 39] Operation: 41-2=39 Moving to Node #0,1,1 Current State: 38:[41, 19], Operations: ['47-13=34', '34-15=19'] Exploring Operation: 41-19=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 41+19=60, Resulting Numbers: [60] 60,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[2, 6], Operations: ['15-13=2', '47-41=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[15, 7], Operations: ['47-13=34', '41-34=7'] Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,38 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,38 unequal: No Solution Moving to Node #0,0,1 Current State: 38:[47, 39], Operations: ['15-13=2', '41-2=39'] Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,38 unequal: No Solution Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,38 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 2, 19, 33, 57 ]
83
[ "19+33=52", "52/2=26", "57+26=83" ]
Current State: 83:[2, 19, 33, 57], Operations: [] Exploring Operation: 19+33=52, Resulting Numbers: [2, 57, 52] Generated Node #2: [2, 57, 52] from Operation: 19+33=52 Current State: 83:[2, 57, 52], Operations: ['19+33=52'] Exploring Operation: 52/2=26, Resulting Numbers: [57, 26] Generated Node #3: [57, 26] from Operation: 52/2=26 Current State: 83:[57, 26], Operations: ['19+33=52', '52/2=26'] Exploring Operation: 57+26=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[2, 19, 33, 57], Operations: [] Exploring Operation: 2*19=38, Resulting Numbers: [33, 57, 38] Generated Node #0,0: 83:[33, 57, 38] Operation: 2*19=38 Exploring Operation: 2*33=66, Resulting Numbers: [19, 57, 66] Generated Node #0,1: 83:[19, 57, 66] Operation: 2*33=66 Moving to Node #0,1 Current State: 83:[19, 57, 66], Operations: ['2*33=66'] Exploring Operation: 19+66=85, Resulting Numbers: [57, 85] Generated Node #0,1,0: 83:[57, 85] Operation: 19+66=85 Exploring Operation: 19+57=76, Resulting Numbers: [66, 76] Generated Node #0,1,1: 83:[66, 76] Operation: 19+57=76 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[66, 76], Operations: ['2*33=66', '19+57=76'] Exploring Operation: 66+76=142, Resulting Numbers: [142] 142,83 unequal: No Solution Exploring Operation: 76-66=10, Resulting Numbers: [10] 10,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[57, 85], Operations: ['2*33=66', '19+66=85'] Exploring Operation: 85-57=28, Resulting Numbers: [28] 28,83 unequal: No Solution Exploring Operation: 57+85=142, Resulting Numbers: [142] 142,83 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: 83:[33, 57, 38], Operations: ['2*19=38'] Exploring Operation: 33+38=71, Resulting Numbers: [57, 71] Generated Node #0,0,0: 83:[57, 71] Operation: 33+38=71 Exploring Operation: 33+57=90, Resulting Numbers: [38, 90] Generated Node #0,0,1: 83:[38, 90] Operation: 33+57=90 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[57, 71], Operations: ['2*19=38', '33+38=71'] Exploring Operation: 57+71=128, Resulting Numbers: [128] 128,83 unequal: No Solution Exploring Operation: 71-57=14, Resulting Numbers: [14] 14,83 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:[38, 90], Operations: ['2*19=38', '33+57=90'] Exploring Operation: 38+90=128, Resulting Numbers: [128] 128,83 unequal: No Solution Exploring Operation: 90-38=52, Resulting Numbers: [52] 52,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 14, 17, 12, 46 ]
12
[ "14-12=2", "17*2=34", "46-34=12" ]
Current State: 12:[14, 17, 12, 46], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [17, 46, 2] Generated Node #2: [17, 46, 2] from Operation: 14-12=2 Current State: 12:[17, 46, 2], Operations: ['14-12=2'] Exploring Operation: 17*2=34, Resulting Numbers: [46, 34] Generated Node #3: [46, 34] from Operation: 17*2=34 Current State: 12:[46, 34], Operations: ['14-12=2', '17*2=34'] Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[14, 17, 12, 46], Operations: [] Exploring Operation: 46-17=29, Resulting Numbers: [14, 12, 29] Generated Node #0,0: 12:[14, 12, 29] Operation: 46-17=29 Exploring Operation: 46-14=32, Resulting Numbers: [17, 12, 32] Generated Node #0,1: 12:[17, 12, 32] Operation: 46-14=32 Exploring Operation: 46-12=34, Resulting Numbers: [14, 17, 34] Generated Node #0,2: 12:[14, 17, 34] Operation: 46-12=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[14, 12, 29], Operations: ['46-17=29'] Exploring Operation: 14-12=2, Resulting Numbers: [29, 2] Generated Node #0,0,0: 12:[29, 2] Operation: 14-12=2 Exploring Operation: 29-14=15, Resulting Numbers: [12, 15] Generated Node #0,0,1: 12:[12, 15] Operation: 29-14=15 Exploring Operation: 29-12=17, Resulting Numbers: [14, 17] Generated Node #0,0,2: 12:[14, 17] Operation: 29-12=17 Moving to Node #0,0,1 Current State: 12:[12, 15], Operations: ['46-17=29', '29-14=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[14, 17], Operations: ['46-17=29', '29-12=17'] Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,12 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[29, 2], Operations: ['46-17=29', '14-12=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,12 unequal: No Solution Exploring Operation: 29+2=31, Resulting Numbers: [31] 31,12 unequal: No Solution Exploring Operation: 29-2=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:[17, 12, 32], Operations: ['46-14=32'] Exploring Operation: 17-12=5, Resulting Numbers: [32, 5] Generated Node #0,1,0: 12:[32, 5] Operation: 17-12=5 Exploring Operation: 32-12=20, Resulting Numbers: [17, 20] Generated Node #0,1,1: 12:[17, 20] Operation: 32-12=20 Exploring Operation: 32-17=15, Resulting Numbers: [12, 15] Generated Node #0,1,2: 12:[12, 15] Operation: 32-17=15 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 12:[12, 15], Operations: ['46-14=32', '32-17=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 12*15=180, Resulting Numbers: [180] 180,12 unequal: No Solution Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 12:[17, 20], Operations: ['46-14=32', '32-12=20'] Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,12 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 12:[32, 5], Operations: ['46-14=32', '17-12=5'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,12 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,12 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 12:[14, 17, 34], Operations: ['46-12=34'] Exploring Operation: 34/17=2, Resulting Numbers: [14, 2] Generated Node #0,2,0: 12:[14, 2] Operation: 34/17=2 Exploring Operation: 34-14=20, Resulting Numbers: [17, 20] Generated Node #0,2,1: 12:[17, 20] Operation: 34-14=20 Exploring Operation: 34-17=17, Resulting Numbers: [14, 17] Generated Node #0,2,2: 12:[14, 17] Operation: 34-17=17 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 12:[14, 2], Operations: ['46-12=34', '34/17=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[14, 17, 12, 46], Operations: [] Exploring Operation: 46-12=34, Resulting Numbers: [14, 17, 34] Generated Node #0,2: 12:[14, 17, 34] Operation: 46-12=34 Moving to Node #0,2 Current State: 12:[14, 17, 34], Operations: ['46-12=34'] Exploring Operation: 34/17=2, Resulting Numbers: [14, 2] Generated Node #0,2,0: 12:[14, 2] Operation: 34/17=2 Moving to Node #0,2,0 Current State: 12:[14, 2], Operations: ['46-12=34', '34/17=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_3
sum_heuristic
[ 3, 10, 25, 37 ]
100
[ "3+37=40", "40/10=4", "25*4=100" ]
Current State: 100:[3, 10, 25, 37], Operations: [] Exploring Operation: 3+37=40, Resulting Numbers: [10, 25, 40] Generated Node #2: [10, 25, 40] from Operation: 3+37=40 Current State: 100:[10, 25, 40], Operations: ['3+37=40'] Exploring Operation: 40/10=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 40/10=4 Current State: 100:[25, 4], Operations: ['3+37=40', '40/10=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[3, 10, 25, 37], Operations: [] Exploring Operation: 37-10=27, Resulting Numbers: [3, 25, 27] Generated Node #0,0: 100:[3, 25, 27] Operation: 37-10=27 Moving to Node #0,0 Current State: 100:[3, 25, 27], Operations: ['37-10=27'] Exploring Operation: 27-3=24, Resulting Numbers: [25, 24] Generated Node #0,0,0: 100:[25, 24] Operation: 27-3=24 Moving to Node #0,0,0 Current State: 100:[25, 24], Operations: ['37-10=27', '27-3=24'] Exploring Operation: 25+24=49, Resulting Numbers: [49] 49,100 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 2, 73, 56, 19 ]
77
[ "56+19=75", "2*75=150", "150-73=77" ]
Current State: 77:[2, 73, 56, 19], Operations: [] Exploring Operation: 56+19=75, Resulting Numbers: [2, 73, 75] Generated Node #2: [2, 73, 75] from Operation: 56+19=75 Current State: 77:[2, 73, 75], Operations: ['56+19=75'] Exploring Operation: 2*75=150, Resulting Numbers: [73, 150] Generated Node #3: [73, 150] from Operation: 2*75=150 Current State: 77:[73, 150], Operations: ['56+19=75', '2*75=150'] Exploring Operation: 150-73=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[2, 73, 56, 19], Operations: [] Exploring Operation: 2+73=75, Resulting Numbers: [56, 19, 75] Generated Node #0,0: 77:[56, 19, 75] Operation: 2+73=75 Exploring Operation: 56+19=75, Resulting Numbers: [2, 73, 75] Generated Node #0,1: 77:[2, 73, 75] Operation: 56+19=75 Exploring Operation: 56/2=28, Resulting Numbers: [73, 19, 28] Generated Node #0,2: 77:[73, 19, 28] Operation: 56/2=28 Exploring Operation: 73-56=17, Resulting Numbers: [2, 19, 17] Generated Node #0,3: 77:[2, 19, 17] Operation: 73-56=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[2, 73, 75], Operations: ['56+19=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73, 73] Generated Node #0,1,0: 77:[73, 73] Operation: 75-2=73 Exploring Operation: 73-2=71, Resulting Numbers: [75, 71] Generated Node #0,1,1: 77:[75, 71] Operation: 73-2=71 Exploring Operation: 2+75=77, Resulting Numbers: [73, 77] Generated Node #0,1,2: 77:[73, 77] Operation: 2+75=77 Exploring Operation: 2+73=75, Resulting Numbers: [75, 75] Generated Node #0,1,3: 77:[75, 75] Operation: 2+73=75 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 77:[73, 77], Operations: ['56+19=75', '2+75=77'] Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 77:[75, 75], Operations: ['56+19=75', '2+73=75'] Exploring Operation: 75*75=5625, Resulting Numbers: [5625] 5625,77 unequal: No Solution Exploring Operation: 75/75=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 75+75=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 75-75=0, Resulting Numbers: [0] 0,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 77:[73, 73], Operations: ['56+19=75', '75-2=73'] Exploring Operation: 73-73=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 73+73=146, Resulting Numbers: [146] 146,77 unequal: No Solution Exploring Operation: 73*73=5329, Resulting Numbers: [5329] 5329,77 unequal: No Solution Exploring Operation: 73/73=1, Resulting Numbers: [1] 1,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 77:[75, 71], Operations: ['56+19=75', '73-2=71'] Exploring Operation: 75+71=146, Resulting Numbers: [146] 146,77 unequal: No Solution Exploring Operation: 75-71=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 75*71=5325, Resulting Numbers: [5325] 5325,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[2, 19, 17], Operations: ['73-56=17'] Exploring Operation: 19-2=17, Resulting Numbers: [17, 17] Generated Node #0,3,0: 77:[17, 17] Operation: 19-2=17 Exploring Operation: 19-17=2, Resulting Numbers: [2, 2] Generated Node #0,3,1: 77:[2, 2] Operation: 19-17=2 Exploring Operation: 2+19=21, Resulting Numbers: [17, 21] Generated Node #0,3,2: 77:[17, 21] Operation: 2+19=21 Exploring Operation: 17-2=15, Resulting Numbers: [19, 15] Generated Node #0,3,3: 77:[19, 15] Operation: 17-2=15 Moving to Node #0,3,1 Current State: 77:[2, 2], Operations: ['73-56=17', '19-17=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[19, 15], Operations: ['73-56=17', '17-2=15'] Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,77 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,77 unequal: No Solution Moving to Node #0,3,0 Current State: 77:[17, 17], Operations: ['73-56=17', '19-2=17'] Exploring Operation: 17/17=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 17*17=289, Resulting Numbers: [289] 289,77 unequal: No Solution Exploring Operation: 17+17=34, Resulting Numbers: [34] 34,77 unequal: No Solution Exploring Operation: 17-17=0, Resulting Numbers: [0] 0,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[17, 21], Operations: ['73-56=17', '2+19=21'] Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,77 unequal: No Solution Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,77 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[73, 19, 28], Operations: ['56/2=28'] Exploring Operation: 73+19=92, Resulting Numbers: [28, 92] Generated Node #0,2,0: 77:[28, 92] Operation: 73+19=92 Exploring Operation: 73+28=101, Resulting Numbers: [19, 101] Generated Node #0,2,1: 77:[19, 101] Operation: 73+28=101 Exploring Operation: 28-19=9, Resulting Numbers: [73, 9] Generated Node #0,2,2: 77:[73, 9] Operation: 28-19=9 Exploring Operation: 19+28=47, Resulting Numbers: [73, 47] Generated Node #0,2,3: 77:[73, 47] Operation: 19+28=47 Moving to Node #0,2,2 Current State: 77:[73, 9], Operations: ['56/2=28', '28-19=9'] Exploring Operation: 73-9=64, Resulting Numbers: [64] 64,77 unequal: No Solution Exploring Operation: 73*9=657, Resulting Numbers: [657] 657,77 unequal: No Solution Exploring Operation: 73+9=82, Resulting Numbers: [82] 82,77 unequal: No Solution Moving to Node #0,2,1 Current State: 77:[19, 101], Operations: ['56/2=28', '73+28=101'] Exploring Operation: 19+101=120, Resulting Numbers: [120] 120,77 unequal: No Solution Exploring Operation: 101-19=82, Resulting Numbers: [82] 82,77 unequal: No Solution Exploring Operation: 19*101=1919, Resulting Numbers: [1919] 1919,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[28, 92], Operations: ['56/2=28', '73+19=92'] Exploring Operation: 28+92=120, Resulting Numbers: [120] 120,77 unequal: No Solution Exploring Operation: 28*92=2576, Resulting Numbers: [2576] 2576,77 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[73, 47], Operations: ['56/2=28', '19+28=47'] Exploring Operation: 73-47=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 73*47=3431, Resulting Numbers: [3431] 3431,77 unequal: No Solution Exploring Operation: 73+47=120, Resulting Numbers: [120] 120,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[56, 19, 75], Operations: ['2+73=75'] Exploring Operation: 56-19=37, Resulting Numbers: [75, 37] Generated Node #0,0,0: 77:[75, 37] Operation: 56-19=37 Exploring Operation: 56+19=75, Resulting Numbers: [75, 75] Generated Node #0,0,1: 77:[75, 75] Operation: 56+19=75 Exploring Operation: 75-56=19, Resulting Numbers: [19, 19] Generated Node #0,0,2: 77:[19, 19] Operation: 75-56=19 Exploring Operation: 19+75=94, Resulting Numbers: [56, 94] Generated Node #0,0,3: 77:[56, 94] Operation: 19+75=94 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 77:[75, 75], Operations: ['2+73=75', '56+19=75'] Exploring Operation: 75-75=0, Resulting Numbers: [0] 0,77 unequal: No Solution Exploring Operation: 75+75=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 75/75=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 75*75=5625, Resulting Numbers: [5625] 5625,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 77:[19, 19], Operations: ['2+73=75', '75-56=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,77 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,77 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[75, 37], Operations: ['2+73=75', '56-19=37'] Exploring Operation: 75*37=2775, Resulting Numbers: [2775] 2775,77 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,77 unequal: No Solution Exploring Operation: 75+37=112, Resulting Numbers: [112] 112,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 77:[56, 94], Operations: ['2+73=75', '19+75=94'] Exploring Operation: 56+94=150, Resulting Numbers: [150] 150,77 unequal: No Solution Exploring Operation: 94-56=38, Resulting Numbers: [38] 38,77 unequal: No Solution Exploring Operation: 56*94=5264, Resulting Numbers: [5264] 5264,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 48, 91, 86, 35 ]
88
[ "48+91=139", "86-35=51", "139-51=88" ]
Current State: 88:[48, 91, 86, 35], Operations: [] Exploring Operation: 48+91=139, Resulting Numbers: [86, 35, 139] Generated Node #2: [86, 35, 139] from Operation: 48+91=139 Current State: 88:[86, 35, 139], Operations: ['48+91=139'] Exploring Operation: 86-35=51, Resulting Numbers: [139, 51] Generated Node #3: [139, 51] from Operation: 86-35=51 Current State: 88:[139, 51], Operations: ['48+91=139', '86-35=51'] Exploring Operation: 139-51=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[48, 91, 86, 35], Operations: [] Exploring Operation: 48-35=13, Resulting Numbers: [91, 86, 13] Generated Node #0,0: 88:[91, 86, 13] Operation: 48-35=13 Exploring Operation: 48+35=83, Resulting Numbers: [91, 86, 83] Generated Node #0,1: 88:[91, 86, 83] Operation: 48+35=83 Exploring Operation: 91-86=5, Resulting Numbers: [48, 35, 5] Generated Node #0,2: 88:[48, 35, 5] Operation: 91-86=5 Exploring Operation: 91-48=43, Resulting Numbers: [86, 35, 43] Generated Node #0,3: 88:[86, 35, 43] Operation: 91-48=43 Moving to Node #0,0 Current State: 88:[91, 86, 13], Operations: ['48-35=13'] Exploring Operation: 91-86=5, Resulting Numbers: [13, 5] Generated Node #0,0,0: 88:[13, 5] Operation: 91-86=5 Exploring Operation: 86+13=99, Resulting Numbers: [91, 99] Generated Node #0,0,1: 88:[91, 99] Operation: 86+13=99 Exploring Operation: 91-13=78, Resulting Numbers: [86, 78] Generated Node #0,0,2: 88:[86, 78] Operation: 91-13=78 Exploring Operation: 91/13=7, Resulting Numbers: [86, 7] Generated Node #0,0,3: 88:[86, 7] Operation: 91/13=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[13, 5], Operations: ['48-35=13', '91-86=5'] Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 88:[86, 7], Operations: ['48-35=13', '91/13=7'] Exploring Operation: 86-7=79, Resulting Numbers: [79] 79,88 unequal: No Solution Exploring Operation: 86+7=93, Resulting Numbers: [93] 93,88 unequal: No Solution Exploring Operation: 86*7=602, Resulting Numbers: [602] 602,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 88:[86, 78], Operations: ['48-35=13', '91-13=78'] Exploring Operation: 86+78=164, Resulting Numbers: [164] 164,88 unequal: No Solution Exploring Operation: 86-78=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 86*78=6708, Resulting Numbers: [6708] 6708,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[91, 99], Operations: ['48-35=13', '86+13=99'] Exploring Operation: 91+99=190, Resulting Numbers: [190] 190,88 unequal: No Solution Exploring Operation: 91*99=9009, Resulting Numbers: [9009] 9009,88 unequal: No Solution Exploring Operation: 99-91=8, Resulting Numbers: [8] 8,88 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: 88:[91, 86, 83], Operations: ['48+35=83'] Exploring Operation: 86-83=3, Resulting Numbers: [91, 3] Generated Node #0,1,0: 88:[91, 3] Operation: 86-83=3 Exploring Operation: 86+83=169, Resulting Numbers: [91, 169] Generated Node #0,1,1: 88:[91, 169] Operation: 86+83=169 Exploring Operation: 91-83=8, Resulting Numbers: [86, 8] Generated Node #0,1,2: 88:[86, 8] Operation: 91-83=8 Exploring Operation: 91-86=5, Resulting Numbers: [83, 5] Generated Node #0,1,3: 88:[83, 5] Operation: 91-86=5 Moving to Node #0,3 Current State: 88:[86, 35, 43], Operations: ['91-48=43'] Exploring Operation: 86/43=2, Resulting Numbers: [35, 2] Generated Node #0,3,0: 88:[35, 2] Operation: 86/43=2 Exploring Operation: 43-35=8, Resulting Numbers: [86, 8] Generated Node #0,3,1: 88:[86, 8] Operation: 43-35=8 Exploring Operation: 86-35=51, Resulting Numbers: [43, 51] Generated Node #0,3,2: 88:[43, 51] Operation: 86-35=51 Exploring Operation: 86-43=43, Resulting Numbers: [35, 43] Generated Node #0,3,3: 88:[35, 43] Operation: 86-43=43 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 88:[86, 8], Operations: ['91-48=43', '43-35=8'] Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,88 unequal: No Solution Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 88:[43, 51], Operations: ['91-48=43', '86-35=51'] Exploring Operation: 43+51=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 43*51=2193, Resulting Numbers: [2193] 2193,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 88:[35, 2], Operations: ['91-48=43', '86/43=2'] Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,88 unequal: No Solution Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 88:[35, 43], Operations: ['91-48=43', '86-43=43'] Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 35*43=1505, Resulting Numbers: [1505] 1505,88 unequal: No Solution Exploring Operation: 35+43=78, Resulting Numbers: [78] 78,88 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: 88:[48, 35, 5], Operations: ['91-86=5'] Exploring Operation: 48+35=83, Resulting Numbers: [5, 83] Generated Node #0,2,0: 88:[5, 83] Operation: 48+35=83 Exploring Operation: 35/5=7, Resulting Numbers: [48, 7] Generated Node #0,2,1: 88:[48, 7] Operation: 35/5=7 Exploring Operation: 48-35=13, Resulting Numbers: [5, 13] Generated Node #0,2,2: 88:[5, 13] Operation: 48-35=13 Exploring Operation: 35+5=40, Resulting Numbers: [48, 40] Generated Node #0,2,3: 88:[48, 40] Operation: 35+5=40 Moving to Node #0,1,2 Current State: 88:[86, 8], Operations: ['48+35=83', '91-83=8'] Exploring Operation: 86+8=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 86*8=688, Resulting Numbers: [688] 688,88 unequal: No Solution Exploring Operation: 86-8=78, Resulting Numbers: [78] 78,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[5, 13], Operations: ['91-86=5', '48-35=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[91, 3], Operations: ['48+35=83', '86-83=3'] Exploring Operation: 91*3=273, Resulting Numbers: [273] 273,88 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[48, 91, 86, 35], Operations: [] Exploring Operation: 48+35=83, Resulting Numbers: [91, 86, 83] Generated Node #0,1: 88:[91, 86, 83] Operation: 48+35=83 Moving to Node #0,1 Current State: 88:[91, 86, 83], Operations: ['48+35=83'] Exploring Operation: 86-83=3, Resulting Numbers: [91, 3] Generated Node #0,1,0: 88:[91, 3] Operation: 86-83=3 Moving to Node #0,1,0 Current State: 88:[91, 3], Operations: ['48+35=83', '86-83=3'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
0.950521
hs_4
sum_heuristic
[ 78, 6, 23, 1 ]
61
[ "78+6=84", "23*1=23", "84-23=61" ]
Current State: 61:[78, 6, 23, 1], Operations: [] Exploring Operation: 78+6=84, Resulting Numbers: [23, 1, 84] Generated Node #2: [23, 1, 84] from Operation: 78+6=84 Current State: 61:[23, 1, 84], Operations: ['78+6=84'] Exploring Operation: 23*1=23, Resulting Numbers: [84, 23] Generated Node #3: [84, 23] from Operation: 23*1=23 Current State: 61:[84, 23], Operations: ['78+6=84', '23*1=23'] Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[78, 6, 23, 1], Operations: [] Exploring Operation: 23+1=24, Resulting Numbers: [78, 6, 24] Generated Node #0,0: 61:[78, 6, 24] Operation: 23+1=24 Exploring Operation: 78-1=77, Resulting Numbers: [6, 23, 77] Generated Node #0,1: 61:[6, 23, 77] Operation: 78-1=77 Exploring Operation: 6+1=7, Resulting Numbers: [78, 23, 7] Generated Node #0,2: 61:[78, 23, 7] Operation: 6+1=7 Exploring Operation: 78-6=72, Resulting Numbers: [23, 1, 72] Generated Node #0,3: 61:[23, 1, 72] Operation: 78-6=72 Exploring Operation: 6+23=29, Resulting Numbers: [78, 1, 29] Generated Node #0,4: 61:[78, 1, 29] Operation: 6+23=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[78, 6, 24], Operations: ['23+1=24'] Exploring Operation: 78+6=84, Resulting Numbers: [24, 84] Generated Node #0,0,0: 61:[24, 84] Operation: 78+6=84 Exploring Operation: 78-24=54, Resulting Numbers: [6, 54] Generated Node #0,0,1: 61:[6, 54] Operation: 78-24=54 Exploring Operation: 6+24=30, Resulting Numbers: [78, 30] Generated Node #0,0,2: 61:[78, 30] Operation: 6+24=30 Exploring Operation: 24-6=18, Resulting Numbers: [78, 18] Generated Node #0,0,3: 61:[78, 18] Operation: 24-6=18 Exploring Operation: 78-6=72, Resulting Numbers: [24, 72] Generated Node #0,0,4: 61:[24, 72] Operation: 78-6=72 Moving to Node #0,0,2 Current State: 61:[78, 30], Operations: ['23+1=24', '6+24=30'] Exploring Operation: 78*30=2340, Resulting Numbers: [2340] 2340,61 unequal: No Solution Exploring Operation: 78+30=108, Resulting Numbers: [108] 108,61 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[24, 72], Operations: ['23+1=24', '78-6=72'] Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 24+72=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 24*72=1728, Resulting Numbers: [1728] 1728,61 unequal: No Solution Exploring Operation: 72/24=3, Resulting Numbers: [3] 3,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[24, 84], Operations: ['23+1=24', '78+6=84'] Exploring Operation: 24*84=2016, Resulting Numbers: [2016] 2016,61 unequal: No Solution Exploring Operation: 24+84=108, Resulting Numbers: [108] 108,61 unequal: No Solution Exploring Operation: 84-24=60, Resulting Numbers: [60] 60,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[78, 18], Operations: ['23+1=24', '24-6=18'] Exploring Operation: 78+18=96, Resulting Numbers: [96] 96,61 unequal: No Solution Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 78*18=1404, Resulting Numbers: [1404] 1404,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[6, 54], Operations: ['23+1=24', '78-24=54'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[6, 23, 77], Operations: ['78-1=77'] Exploring Operation: 77-23=54, Resulting Numbers: [6, 54] Generated Node #0,1,0: 61:[6, 54] Operation: 77-23=54 Exploring Operation: 6+77=83, Resulting Numbers: [23, 83] Generated Node #0,1,1: 61:[23, 83] Operation: 6+77=83 Exploring Operation: 77-6=71, Resulting Numbers: [23, 71] Generated Node #0,1,2: 61:[23, 71] Operation: 77-6=71 Exploring Operation: 23-6=17, Resulting Numbers: [77, 17] Generated Node #0,1,3: 61:[77, 17] Operation: 23-6=17 Exploring Operation: 6+23=29, Resulting Numbers: [77, 29] Generated Node #0,1,4: 61:[77, 29] Operation: 6+23=29 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[23, 71], Operations: ['78-1=77', '77-6=71'] Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 23*71=1633, Resulting Numbers: [1633] 1633,61 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 61:[77, 29], Operations: ['78-1=77', '6+23=29'] Exploring Operation: 77+29=106, Resulting Numbers: [106] 106,61 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 77*29=2233, Resulting Numbers: [2233] 2233,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[23, 83], Operations: ['78-1=77', '6+77=83'] Exploring Operation: 23+83=106, Resulting Numbers: [106] 106,61 unequal: No Solution Exploring Operation: 23*83=1909, Resulting Numbers: [1909] 1909,61 unequal: No Solution Exploring Operation: 83-23=60, Resulting Numbers: [60] 60,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 61:[77, 17], Operations: ['78-1=77', '23-6=17'] Exploring Operation: 77-17=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 77+17=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 77*17=1309, Resulting Numbers: [1309] 1309,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[6, 54], Operations: ['78-1=77', '77-23=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 6*54=324, Resulting Numbers: [324] 324,61 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,61 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[78, 23, 7], Operations: ['6+1=7'] Exploring Operation: 23+7=30, Resulting Numbers: [78, 30] Generated Node #0,2,0: 61:[78, 30] Operation: 23+7=30 Exploring Operation: 23-7=16, Resulting Numbers: [78, 16] Generated Node #0,2,1: 61:[78, 16] Operation: 23-7=16 Exploring Operation: 78-7=71, Resulting Numbers: [23, 71] Generated Node #0,2,2: 61:[23, 71] Operation: 78-7=71 Exploring Operation: 78+7=85, Resulting Numbers: [23, 85] Generated Node #0,2,3: 61:[23, 85] Operation: 78+7=85 Exploring Operation: 78-23=55, Resulting Numbers: [7, 55] Generated Node #0,2,4: 61:[7, 55] Operation: 78-23=55 Moving to Node #0,2,0 Current State: 61:[78, 30], Operations: ['6+1=7', '23+7=30'] Exploring Operation: 78+30=108, Resulting Numbers: [108] 108,61 unequal: No Solution Exploring Operation: 78*30=2340, Resulting Numbers: [2340] 2340,61 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[23, 71], Operations: ['6+1=7', '78-7=71'] Exploring Operation: 23*71=1633, Resulting Numbers: [1633] 1633,61 unequal: No Solution Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,61 unequal: No Solution Moving to Node #0,2,4 Current State: 61:[7, 55], Operations: ['6+1=7', '78-23=55'] Exploring Operation: 7*55=385, Resulting Numbers: [385] 385,61 unequal: No Solution Exploring Operation: 7+55=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 55-7=48, Resulting Numbers: [48] 48,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[78, 16], Operations: ['6+1=7', '23-7=16'] Exploring Operation: 78-16=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 78*16=1248, Resulting Numbers: [1248] 1248,61 unequal: No Solution Exploring Operation: 78+16=94, Resulting Numbers: [94] 94,61 unequal: No Solution Moving to Node #0,2,3 Current State: 61:[23, 85], Operations: ['6+1=7', '78+7=85'] Exploring Operation: 23+85=108, Resulting Numbers: [108] 108,61 unequal: No Solution Exploring Operation: 85-23=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 23*85=1955, Resulting Numbers: [1955] 1955,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[23, 1, 72], Operations: ['78-6=72'] Exploring Operation: 1*72=72, Resulting Numbers: [23, 72] Generated Node #0,3,0: 61:[23, 72] Operation: 1*72=72 Exploring Operation: 72-1=71, Resulting Numbers: [23, 71] Generated Node #0,3,1: 61:[23, 71] Operation: 72-1=71 Exploring Operation: 23/1=23, Resulting Numbers: [72, 23] Generated Node #0,3,2: 61:[72, 23] Operation: 23/1=23 Exploring Operation: 23+1=24, Resulting Numbers: [72, 24] Generated Node #0,3,3: 61:[72, 24] Operation: 23+1=24 Exploring Operation: 23*1=23, Resulting Numbers: [72, 23] Generated Node #0,3,4: 61:[72, 23] Operation: 23*1=23 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 61:[23, 71], Operations: ['78-6=72', '72-1=71'] Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 23*71=1633, Resulting Numbers: [1633] 1633,61 unequal: No Solution Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 61:[72, 24], Operations: ['78-6=72', '23+1=24'] Exploring Operation: 72*24=1728, Resulting Numbers: [1728] 1728,61 unequal: No Solution Exploring Operation: 72/24=3, Resulting Numbers: [3] 3,61 unequal: No Solution Exploring Operation: 72-24=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 72+24=96, Resulting Numbers: [96] 96,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 61:[23, 72], Operations: ['78-6=72', '1*72=72'] Exploring Operation: 23*72=1656, Resulting Numbers: [1656] 1656,61 unequal: No Solution Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 23+72=95, Resulting Numbers: [95] 95,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 61:[72, 23], Operations: ['78-6=72', '23/1=23'] Exploring Operation: 72*23=1656, Resulting Numbers: [1656] 1656,61 unequal: No Solution Exploring Operation: 72+23=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 61:[72, 23], Operations: ['78-6=72', '23*1=23'] Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 72+23=95, Resulting Numbers: [95] 95,61 unequal: No Solution Exploring Operation: 72*23=1656, Resulting Numbers: [1656] 1656,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[78, 1, 29], Operations: ['6+23=29'] Exploring Operation: 78*1=78, Resulting Numbers: [29, 78] Generated Node #0,4,0: 61:[29, 78] Operation: 78*1=78 Exploring Operation: 78-1=77, Resulting Numbers: [29, 77] Generated Node #0,4,1: 61:[29, 77] Operation: 78-1=77 Exploring Operation: 78/1=78, Resulting Numbers: [29, 78] Generated Node #0,4,2: 61:[29, 78] Operation: 78/1=78 Exploring Operation: 1+29=30, Resulting Numbers: [78, 30] Generated Node #0,4,3: 61:[78, 30] Operation: 1+29=30 Exploring Operation: 1*29=29, Resulting Numbers: [78, 29] Generated Node #0,4,4: 61:[78, 29] Operation: 1*29=29 Moving to Node #0,4,1 Current State: 61:[29, 77], Operations: ['6+23=29', '78-1=77'] Exploring Operation: 29*77=2233, Resulting Numbers: [2233] 2233,61 unequal: No Solution Exploring Operation: 77-29=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 29+77=106, Resulting Numbers: [106] 106,61 unequal: No Solution Moving to Node #0,4,3 Current State: 61:[78, 30], Operations: ['6+23=29', '1+29=30'] Exploring Operation: 78*30=2340, Resulting Numbers: [2340] 2340,61 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,61 unequal: No Solution Exploring Operation: 78+30=108, Resulting Numbers: [108] 108,61 unequal: No Solution Moving to Node #0,4,0 Current State: 61:[29, 78], Operations: ['6+23=29', '78*1=78'] Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[29, 78], Operations: ['6+23=29', '78/1=78'] Exploring Operation: 29+78=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 29*78=2262, Resulting Numbers: [2262] 2262,61 unequal: No Solution Moving to Node #0,4,4 Current State: 61:[78, 29], Operations: ['6+23=29', '1*29=29'] Exploring Operation: 78+29=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 78-29=49, Resulting Numbers: [49] 49,61 unequal: No Solution Exploring Operation: 78*29=2262, Resulting Numbers: [2262] 2262,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 50, 44, 5, 16 ]
14
[ "50+44=94", "5*16=80", "94-80=14" ]
Current State: 14:[50, 44, 5, 16], Operations: [] Exploring Operation: 50+44=94, Resulting Numbers: [5, 16, 94] Generated Node #2: [5, 16, 94] from Operation: 50+44=94 Current State: 14:[5, 16, 94], Operations: ['50+44=94'] Exploring Operation: 5*16=80, Resulting Numbers: [94, 80] Generated Node #3: [94, 80] from Operation: 5*16=80 Current State: 14:[94, 80], Operations: ['50+44=94', '5*16=80'] Exploring Operation: 94-80=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[50, 44, 5, 16], Operations: [] Exploring Operation: 50-44=6, Resulting Numbers: [5, 16, 6] Generated Node #0,0: 14:[5, 16, 6] Operation: 50-44=6 Exploring Operation: 50-16=34, Resulting Numbers: [44, 5, 34] Generated Node #0,1: 14:[44, 5, 34] Operation: 50-16=34 Exploring Operation: 50/5=10, Resulting Numbers: [44, 16, 10] Generated Node #0,2: 14:[44, 16, 10] Operation: 50/5=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[5, 16, 6], Operations: ['50-44=6'] Exploring Operation: 6-5=1, Resulting Numbers: [16, 1] Generated Node #0,0,0: 14:[16, 1] Operation: 6-5=1 Exploring Operation: 16-5=11, Resulting Numbers: [6, 11] Generated Node #0,0,1: 14:[6, 11] Operation: 16-5=11 Exploring Operation: 5+6=11, Resulting Numbers: [16, 11] Generated Node #0,0,2: 14:[16, 11] Operation: 5+6=11 Moving to Node #0,0,0 Current State: 14:[16, 1], Operations: ['50-44=6', '6-5=1'] Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,14 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,14 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[6, 11], Operations: ['50-44=6', '16-5=11'] Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,14 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[16, 11], Operations: ['50-44=6', '5+6=11'] Exploring Operation: 16*11=176, Resulting Numbers: [176] 176,14 unequal: No Solution Exploring Operation: 16-11=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 16+11=27, Resulting Numbers: [27] 27,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[44, 16, 10], Operations: ['50/5=10'] Exploring Operation: 44-16=28, Resulting Numbers: [10, 28] Generated Node #0,2,0: 14:[10, 28] Operation: 44-16=28 Exploring Operation: 44-10=34, Resulting Numbers: [16, 34] Generated Node #0,2,1: 14:[16, 34] Operation: 44-10=34 Exploring Operation: 16-10=6, Resulting Numbers: [44, 6] Generated Node #0,2,2: 14:[44, 6] Operation: 16-10=6 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 14:[10, 28], Operations: ['50/5=10', '44-16=28'] Exploring Operation: 10+28=38, Resulting Numbers: [38] 38,14 unequal: No Solution Exploring Operation: 10*28=280, Resulting Numbers: [280] 280,14 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 14:[16, 34], Operations: ['50/5=10', '44-10=34'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 14:[44, 6], Operations: ['50/5=10', '16-10=6'] Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,14 unequal: No Solution Exploring Operation: 44*6=264, Resulting Numbers: [264] 264,14 unequal: No Solution Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[44, 5, 34], Operations: ['50-16=34'] Exploring Operation: 44-5=39, Resulting Numbers: [34, 39] Generated Node #0,1,0: 14:[34, 39] Operation: 44-5=39 Exploring Operation: 44-34=10, Resulting Numbers: [5, 10] Generated Node #0,1,1: 14:[5, 10] Operation: 44-34=10 Exploring Operation: 34-5=29, Resulting Numbers: [44, 29] Generated Node #0,1,2: 14:[44, 29] Operation: 34-5=29 Moving to Node #0,1,1 Current State: 14:[5, 10], Operations: ['50-16=34', '44-34=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[34, 39], Operations: ['50-16=34', '44-5=39'] Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,14 unequal: No Solution Exploring Operation: 34*39=1326, Resulting Numbers: [1326] 1326,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[44, 29], Operations: ['50-16=34', '34-5=29'] Exploring Operation: 44+29=73, Resulting Numbers: [73] 73,14 unequal: No Solution Exploring Operation: 44*29=1276, Resulting Numbers: [1276] 1276,14 unequal: No Solution Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,14 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
[ 7, 5, 38, 19 ]
88
[ "38-19=19", "5*19=95", "95-7=88" ]
Current State: 88:[7, 5, 38, 19], Operations: [] Exploring Operation: 38-19=19, Resulting Numbers: [7, 5, 19] Generated Node #2: [7, 5, 19] from Operation: 38-19=19 Current State: 88:[7, 5, 19], Operations: ['38-19=19'] Exploring Operation: 5*19=95, Resulting Numbers: [7, 95] Generated Node #3: [7, 95] from Operation: 5*19=95 Current State: 88:[7, 95], Operations: ['38-19=19', '5*19=95'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[7, 5, 38, 19], Operations: [] Exploring Operation: 7+38=45, Resulting Numbers: [5, 19, 45] Generated Node #0,0: 88:[5, 19, 45] Operation: 7+38=45 Exploring Operation: 38/19=2, Resulting Numbers: [7, 5, 2] Generated Node #0,1: 88:[7, 5, 2] Operation: 38/19=2 Moving to Node #0,1 Current State: 88:[7, 5, 2], Operations: ['38/19=2'] Exploring Operation: 7+5=12, Resulting Numbers: [2, 12] Generated Node #0,1,0: 88:[2, 12] Operation: 7+5=12 Exploring Operation: 7-5=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 88:[2, 2] Operation: 7-5=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[2, 2], Operations: ['38/19=2', '7-5=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[2, 12], Operations: ['38/19=2', '7+5=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,88 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: 88:[5, 19, 45], Operations: ['7+38=45'] Exploring Operation: 5+19=24, Resulting Numbers: [45, 24] Generated Node #0,0,0: 88:[45, 24] Operation: 5+19=24 Exploring Operation: 19-5=14, Resulting Numbers: [45, 14] Generated Node #0,0,1: 88:[45, 14] Operation: 19-5=14 Moving to Node #0,0,0 Current State: 88:[45, 24], Operations: ['7+38=45', '5+19=24'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 45+24=69, Resulting Numbers: [69] 69,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[45, 14], Operations: ['7+38=45', '19-5=14'] Exploring Operation: 45-14=31, Resulting Numbers: [31] 31,88 unequal: No Solution Exploring Operation: 45+14=59, Resulting Numbers: [59] 59,88 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 28, 51, 51, 78 ]
78
[ "51-51=0", "28*0=0", "78+0=78" ]
Current State: 78:[28, 51, 51, 78], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [28, 78, 0] Generated Node #2: [28, 78, 0] from Operation: 51-51=0 Current State: 78:[28, 78, 0], Operations: ['51-51=0'] Exploring Operation: 28*0=0, Resulting Numbers: [78, 0] Generated Node #3: [78, 0] from Operation: 28*0=0 Current State: 78:[78, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 78+0=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[28, 51, 51, 78], Operations: [] Exploring Operation: 51/51=1, Resulting Numbers: [28, 78, 1] Generated Node #0,0: 78:[28, 78, 1] Operation: 51/51=1 Exploring Operation: 51-51=0, Resulting Numbers: [28, 78, 0] Generated Node #0,1: 78:[28, 78, 0] Operation: 51-51=0 Moving to Node #0,0 Current State: 78:[28, 78, 1], Operations: ['51/51=1'] Exploring Operation: 28*1=28, Resulting Numbers: [78, 28] Generated Node #0,0,0: 78:[78, 28] Operation: 28*1=28 Exploring Operation: 28-1=27, Resulting Numbers: [78, 27] Generated Node #0,0,1: 78:[78, 27] Operation: 28-1=27 Moving to Node #0,1 Current State: 78:[28, 78, 0], Operations: ['51-51=0'] Exploring Operation: 28+0=28, Resulting Numbers: [78, 28] Generated Node #0,1,0: 78:[78, 28] Operation: 28+0=28 Exploring Operation: 28*0=0, Resulting Numbers: [78, 0] Generated Node #0,1,1: 78:[78, 0] Operation: 28*0=0 Moving to Node #0,0,1 Current State: 78:[78, 27], Operations: ['51/51=1', '28-1=27'] Exploring Operation: 78-27=51, Resulting Numbers: [51] 51,78 unequal: No Solution Exploring Operation: 78+27=105, Resulting Numbers: [105] 105,78 unequal: No Solution Moving to Node #0,1,0 Current State: 78:[78, 28], Operations: ['51-51=0', '28+0=28'] Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 78+28=106, Resulting Numbers: [106] 106,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[78, 28], Operations: ['51/51=1', '28*1=28'] Exploring Operation: 78+28=106, Resulting Numbers: [106] 106,78 unequal: No Solution Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[78, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 78+0=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[28, 51, 51, 78], Operations: [] Exploring Operation: 51-51=0, Resulting Numbers: [28, 78, 0] Generated Node #0,1: 78:[28, 78, 0] Operation: 51-51=0 Moving to Node #0,1 Current State: 78:[28, 78, 0], Operations: ['51-51=0'] Exploring Operation: 28*0=0, Resulting Numbers: [78, 0] Generated Node #0,1,1: 78:[78, 0] Operation: 28*0=0 Moving to Node #0,1,1 Current State: 78:[78, 0], Operations: ['51-51=0', '28*0=0'] Exploring Operation: 78+0=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 2, 81, 59, 21 ]
100
[ "59-21=38", "38/2=19", "81+19=100" ]
Current State: 100:[2, 81, 59, 21], Operations: [] Exploring Operation: 59-21=38, Resulting Numbers: [2, 81, 38] Generated Node #2: [2, 81, 38] from Operation: 59-21=38 Current State: 100:[2, 81, 38], Operations: ['59-21=38'] Exploring Operation: 38/2=19, Resulting Numbers: [81, 19] Generated Node #3: [81, 19] from Operation: 38/2=19 Current State: 100:[81, 19], Operations: ['59-21=38', '38/2=19'] Exploring Operation: 81+19=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[2, 81, 59, 21], Operations: [] Exploring Operation: 81-21=60, Resulting Numbers: [2, 59, 60] Generated Node #0,0: 100:[2, 59, 60] Operation: 81-21=60 Exploring Operation: 81+21=102, Resulting Numbers: [2, 59, 102] Generated Node #0,1: 100:[2, 59, 102] Operation: 81+21=102 Exploring Operation: 81-59=22, Resulting Numbers: [2, 21, 22] Generated Node #0,2: 100:[2, 21, 22] Operation: 81-59=22 Moving to Node #0,2 Current State: 100:[2, 21, 22], Operations: ['81-59=22'] Exploring Operation: 22-2=20, Resulting Numbers: [21, 20] Generated Node #0,2,0: 100:[21, 20] Operation: 22-2=20 Exploring Operation: 2+22=24, Resulting Numbers: [21, 24] Generated Node #0,2,1: 100:[21, 24] Operation: 2+22=24 Exploring Operation: 22-21=1, Resulting Numbers: [2, 1] Generated Node #0,2,2: 100:[2, 1] Operation: 22-21=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[21, 20], Operations: ['81-59=22', '22-2=20'] Exploring Operation: 21*20=420, Resulting Numbers: [420] 420,100 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,100 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:[2, 1], Operations: ['81-59=22', '22-21=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,100 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:[21, 24], Operations: ['81-59=22', '2+22=24'] Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,100 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,100 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: 100:[2, 59, 102], Operations: ['81+21=102'] Exploring Operation: 102-59=43, Resulting Numbers: [2, 43] Generated Node #0,1,0: 100:[2, 43] Operation: 102-59=43 Exploring Operation: 59-2=57, Resulting Numbers: [102, 57] Generated Node #0,1,1: 100:[102, 57] Operation: 59-2=57 Exploring Operation: 102-2=100, Resulting Numbers: [59, 100] Generated Node #0,1,2: 100:[59, 100] Operation: 102-2=100 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[2, 43], Operations: ['81+21=102', '102-59=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,100 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,100 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 #0,1,1 Current State: 100:[102, 57], Operations: ['81+21=102', '59-2=57'] Exploring Operation: 102-57=45, Resulting Numbers: [45] 45,100 unequal: No Solution Exploring Operation: 102*57=5814, Resulting Numbers: [5814] 5814,100 unequal: No Solution Exploring Operation: 102+57=159, Resulting Numbers: [159] 159,100 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 #0,1,2 Current State: 100:[59, 100], Operations: ['81+21=102', '102-2=100'] Exploring Operation: 59+100=159, Resulting Numbers: [159] 159,100 unequal: No Solution Exploring Operation: 59*100=5900, Resulting Numbers: [5900] 5900,100 unequal: No Solution Exploring Operation: 100-59=41, Resulting Numbers: [41] 41,100 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:[2, 59, 60], Operations: ['81-21=60'] Exploring Operation: 60/2=30, Resulting Numbers: [59, 30] Generated Node #0,0,0: 100:[59, 30] Operation: 60/2=30 Exploring Operation: 59-2=57, Resulting Numbers: [60, 57] Generated Node #0,0,1: 100:[60, 57] Operation: 59-2=57 Exploring Operation: 60-59=1, Resulting Numbers: [2, 1] Generated Node #0,0,2: 100:[2, 1] Operation: 60-59=1 Moving to Node #0,0,2 Current State: 100:[2, 1], Operations: ['81-21=60', '60-59=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[59, 30], Operations: ['81-21=60', '60/2=30'] Exploring Operation: 59+30=89, Resulting Numbers: [89] 89,100 unequal: No Solution Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,100 unequal: No Solution Exploring Operation: 59*30=1770, Resulting Numbers: [1770] 1770,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[60, 57], Operations: ['81-21=60', '59-2=57'] Exploring Operation: 60*57=3420, Resulting Numbers: [3420] 3420,100 unequal: No Solution Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 60+57=117, Resulting Numbers: [117] 117,100 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 55, 36, 15, 66 ]
10
[ "55+36=91", "15+66=81", "91-81=10" ]
Current State: 10:[55, 36, 15, 66], Operations: [] Exploring Operation: 55+36=91, Resulting Numbers: [15, 66, 91] Generated Node #2: [15, 66, 91] from Operation: 55+36=91 Current State: 10:[15, 66, 91], Operations: ['55+36=91'] Exploring Operation: 15+66=81, Resulting Numbers: [91, 81] Generated Node #3: [91, 81] from Operation: 15+66=81 Current State: 10:[91, 81], Operations: ['55+36=91', '15+66=81'] Exploring Operation: 91-81=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[55, 36, 15, 66], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [55, 15, 30] Generated Node #0,0: 10:[55, 15, 30] Operation: 66-36=30 Exploring Operation: 66-55=11, Resulting Numbers: [36, 15, 11] Generated Node #0,1: 10:[36, 15, 11] Operation: 66-55=11 Exploring Operation: 55-36=19, Resulting Numbers: [15, 66, 19] Generated Node #0,2: 10:[15, 66, 19] Operation: 55-36=19 Exploring Operation: 55-15=40, Resulting Numbers: [36, 66, 40] Generated Node #0,3: 10:[36, 66, 40] Operation: 55-15=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[36, 15, 11], Operations: ['66-55=11'] Exploring Operation: 36+15=51, Resulting Numbers: [11, 51] Generated Node #0,1,0: 10:[11, 51] Operation: 36+15=51 Exploring Operation: 36-11=25, Resulting Numbers: [15, 25] Generated Node #0,1,1: 10:[15, 25] Operation: 36-11=25 Exploring Operation: 15-11=4, Resulting Numbers: [36, 4] Generated Node #0,1,2: 10:[36, 4] Operation: 15-11=4 Exploring Operation: 36-15=21, Resulting Numbers: [11, 21] Generated Node #0,1,3: 10:[11, 21] Operation: 36-15=21 Moving to Node #0,1,3 Current State: 10:[11, 21], Operations: ['66-55=11', '36-15=21'] Exploring Operation: 11*21=231, Resulting Numbers: [231] 231,10 unequal: No Solution Exploring Operation: 11+21=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[55, 36, 15, 66], Operations: [] Exploring Operation: 66-55=11, Resulting Numbers: [36, 15, 11] Generated Node #0,1: 10:[36, 15, 11] Operation: 66-55=11 Moving to Node #0,1 Current State: 10:[36, 15, 11], Operations: ['66-55=11'] Exploring Operation: 36-15=21, Resulting Numbers: [11, 21] Generated Node #0,1,3: 10:[11, 21] Operation: 36-15=21 Moving to Node #0,1,3 Current State: 10:[11, 21], Operations: ['66-55=11', '36-15=21'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 4, 20, 15, 78 ]
12
[ "4*78=312", "20*15=300", "312-300=12" ]
Current State: 12:[4, 20, 15, 78], Operations: [] Exploring Operation: 4*78=312, Resulting Numbers: [20, 15, 312] Generated Node #2: [20, 15, 312] from Operation: 4*78=312 Current State: 12:[20, 15, 312], Operations: ['4*78=312'] Exploring Operation: 20*15=300, Resulting Numbers: [312, 300] Generated Node #3: [312, 300] from Operation: 20*15=300 Current State: 12:[312, 300], Operations: ['4*78=312', '20*15=300'] Exploring Operation: 312-300=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[4, 20, 15, 78], Operations: [] Exploring Operation: 78-20=58, Resulting Numbers: [4, 15, 58] Generated Node #0,0: 12:[4, 15, 58] Operation: 78-20=58 Exploring Operation: 20-15=5, Resulting Numbers: [4, 78, 5] Generated Node #0,1: 12:[4, 78, 5] Operation: 20-15=5 Exploring Operation: 78-15=63, Resulting Numbers: [4, 20, 63] Generated Node #0,2: 12:[4, 20, 63] Operation: 78-15=63 Moving to Node #0,0 Current State: 12:[4, 15, 58], Operations: ['78-20=58'] Exploring Operation: 15-4=11, Resulting Numbers: [58, 11] Generated Node #0,0,0: 12:[58, 11] Operation: 15-4=11 Exploring Operation: 58-4=54, Resulting Numbers: [15, 54] Generated Node #0,0,1: 12:[15, 54] Operation: 58-4=54 Exploring Operation: 58-15=43, Resulting Numbers: [4, 43] Generated Node #0,0,2: 12:[4, 43] Operation: 58-15=43 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[4, 43], Operations: ['78-20=58', '58-15=43'] Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,12 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[15, 54], Operations: ['78-20=58', '58-4=54'] Exploring Operation: 15*54=810, Resulting Numbers: [810] 810,12 unequal: No Solution Exploring Operation: 15+54=69, Resulting Numbers: [69] 69,12 unequal: No Solution Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[58, 11], Operations: ['78-20=58', '15-4=11'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 58*11=638, Resulting Numbers: [638] 638,12 unequal: No Solution Exploring Operation: 58+11=69, Resulting Numbers: [69] 69,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 12:[4, 20, 63], Operations: ['78-15=63'] Exploring Operation: 20/4=5, Resulting Numbers: [63, 5] Generated Node #0,2,0: 12:[63, 5] Operation: 20/4=5 Exploring Operation: 63-20=43, Resulting Numbers: [4, 43] Generated Node #0,2,1: 12:[4, 43] Operation: 63-20=43 Exploring Operation: 20-4=16, Resulting Numbers: [63, 16] Generated Node #0,2,2: 12:[63, 16] Operation: 20-4=16 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 12:[4, 43], Operations: ['78-15=63', '63-20=43'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,12 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,12 unequal: No Solution Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,12 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 #0,2,0 Current State: 12:[63, 5], Operations: ['78-15=63', '20/4=5'] Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,12 unequal: No Solution Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,12 unequal: No Solution Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 12:[63, 16], Operations: ['78-15=63', '20-4=16'] Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,12 unequal: No Solution Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,12 unequal: No Solution Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,12 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: 12:[4, 78, 5], Operations: ['20-15=5'] Exploring Operation: 78-4=74, Resulting Numbers: [5, 74] Generated Node #0,1,0: 12:[5, 74] Operation: 78-4=74 Exploring Operation: 78-5=73, Resulting Numbers: [4, 73] Generated Node #0,1,1: 12:[4, 73] Operation: 78-5=73 Exploring Operation: 5-4=1, Resulting Numbers: [78, 1] Generated Node #0,1,2: 12:[78, 1] Operation: 5-4=1 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 12:[4, 73], Operations: ['20-15=5', '78-5=73'] Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,12 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 12:[5, 74], Operations: ['20-15=5', '78-4=74'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,12 unequal: No Solution Exploring Operation: 5*74=370, Resulting Numbers: [370] 370,12 unequal: No Solution Exploring Operation: 5+74=79, Resulting Numbers: [79] 79,12 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 #0,1,2 Current State: 12:[78, 1], Operations: ['20-15=5', '5-4=1'] Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,12 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
[ 97, 53, 85, 17 ]
49
[ "97-53=44", "85/17=5", "44+5=49" ]
Current State: 49:[97, 53, 85, 17], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [85, 17, 44] Generated Node #2: [85, 17, 44] from Operation: 97-53=44 Current State: 49:[85, 17, 44], Operations: ['97-53=44'] Exploring Operation: 85/17=5, Resulting Numbers: [44, 5] Generated Node #3: [44, 5] from Operation: 85/17=5 Current State: 49:[44, 5], Operations: ['97-53=44', '85/17=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[97, 53, 85, 17], Operations: [] Exploring Operation: 85/17=5, Resulting Numbers: [97, 53, 5] Generated Node #0,0: 49:[97, 53, 5] Operation: 85/17=5 Exploring Operation: 97-53=44, Resulting Numbers: [85, 17, 44] Generated Node #0,1: 49:[85, 17, 44] Operation: 97-53=44 Exploring Operation: 97-85=12, Resulting Numbers: [53, 17, 12] Generated Node #0,2: 49:[53, 17, 12] Operation: 97-85=12 Exploring Operation: 97-17=80, Resulting Numbers: [53, 85, 80] Generated Node #0,3: 49:[53, 85, 80] Operation: 97-17=80 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[53, 17, 12], Operations: ['97-85=12'] Exploring Operation: 17+12=29, Resulting Numbers: [53, 29] Generated Node #0,2,0: 49:[53, 29] Operation: 17+12=29 Exploring Operation: 53-17=36, Resulting Numbers: [12, 36] Generated Node #0,2,1: 49:[12, 36] Operation: 53-17=36 Exploring Operation: 17-12=5, Resulting Numbers: [53, 5] Generated Node #0,2,2: 49:[53, 5] Operation: 17-12=5 Exploring Operation: 53-12=41, Resulting Numbers: [17, 41] Generated Node #0,2,3: 49:[17, 41] Operation: 53-12=41 Moving to Node #0,2,2 Current State: 49:[53, 5], Operations: ['97-85=12', '17-12=5'] Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 53*5=265, Resulting Numbers: [265] 265,49 unequal: No Solution Exploring Operation: 53+5=58, Resulting Numbers: [58] 58,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[17, 41], Operations: ['97-85=12', '53-12=41'] Exploring Operation: 41-17=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 17*41=697, Resulting Numbers: [697] 697,49 unequal: No Solution Exploring Operation: 17+41=58, Resulting Numbers: [58] 58,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[12, 36], Operations: ['97-85=12', '53-17=36'] Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,49 unequal: No Solution Exploring Operation: 12*36=432, Resulting Numbers: [432] 432,49 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,49 unequal: No Solution Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[53, 29], Operations: ['97-85=12', '17+12=29'] Exploring Operation: 53-29=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 53*29=1537, Resulting Numbers: [1537] 1537,49 unequal: No Solution Exploring Operation: 53+29=82, Resulting Numbers: [82] 82,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[85, 17, 44], Operations: ['97-53=44'] Exploring Operation: 85/17=5, Resulting Numbers: [44, 5] Generated Node #0,1,0: 49:[44, 5] Operation: 85/17=5 Exploring Operation: 85-17=68, Resulting Numbers: [44, 68] Generated Node #0,1,1: 49:[44, 68] Operation: 85-17=68 Exploring Operation: 85-44=41, Resulting Numbers: [17, 41] Generated Node #0,1,2: 49:[17, 41] Operation: 85-44=41 Exploring Operation: 17+44=61, Resulting Numbers: [85, 61] Generated Node #0,1,3: 49:[85, 61] Operation: 17+44=61 Moving to Node #0,1,0 Current State: 49:[44, 5], Operations: ['97-53=44', '85/17=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[97, 53, 85, 17], Operations: [] Exploring Operation: 97-53=44, Resulting Numbers: [85, 17, 44] Generated Node #0,1: 49:[85, 17, 44] Operation: 97-53=44 Moving to Node #0,1 Current State: 49:[85, 17, 44], Operations: ['97-53=44'] Exploring Operation: 85/17=5, Resulting Numbers: [44, 5] Generated Node #0,1,0: 49:[44, 5] Operation: 85/17=5 Moving to Node #0,1,0 Current State: 49:[44, 5], Operations: ['97-53=44', '85/17=5'] Exploring Operation: 44+5=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 20, 19, 97, 12 ]
11
[ "97-20=77", "19-12=7", "77/7=11" ]
Current State: 11:[20, 19, 97, 12], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [19, 12, 77] Generated Node #2: [19, 12, 77] from Operation: 97-20=77 Current State: 11:[19, 12, 77], Operations: ['97-20=77'] Exploring Operation: 19-12=7, Resulting Numbers: [77, 7] Generated Node #3: [77, 7] from Operation: 19-12=7 Current State: 11:[77, 7], Operations: ['97-20=77', '19-12=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[20, 19, 97, 12], Operations: [] Exploring Operation: 97-19=78, Resulting Numbers: [20, 12, 78] Generated Node #0,0: 11:[20, 12, 78] Operation: 97-19=78 Exploring Operation: 97-20=77, Resulting Numbers: [19, 12, 77] Generated Node #0,1: 11:[19, 12, 77] Operation: 97-20=77 Exploring Operation: 97-12=85, Resulting Numbers: [20, 19, 85] Generated Node #0,2: 11:[20, 19, 85] Operation: 97-12=85 Exploring Operation: 20-19=1, Resulting Numbers: [97, 12, 1] Generated Node #0,3: 11:[97, 12, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[19, 12, 77], Operations: ['97-20=77'] Exploring Operation: 77-19=58, Resulting Numbers: [12, 58] Generated Node #0,1,0: 11:[12, 58] Operation: 77-19=58 Exploring Operation: 19+12=31, Resulting Numbers: [77, 31] Generated Node #0,1,1: 11:[77, 31] Operation: 19+12=31 Exploring Operation: 19-12=7, Resulting Numbers: [77, 7] Generated Node #0,1,2: 11:[77, 7] Operation: 19-12=7 Exploring Operation: 77-12=65, Resulting Numbers: [19, 65] Generated Node #0,1,3: 11:[19, 65] Operation: 77-12=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[12, 58], Operations: ['97-20=77', '77-19=58'] Exploring Operation: 12*58=696, Resulting Numbers: [696] 696,11 unequal: No Solution Exploring Operation: 58-12=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 12+58=70, Resulting Numbers: [70] 70,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 11:[19, 65], Operations: ['97-20=77', '77-12=65'] Exploring Operation: 19*65=1235, Resulting Numbers: [1235] 1235,11 unequal: No Solution Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,11 unequal: No Solution Exploring Operation: 19+65=84, Resulting Numbers: [84] 84,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 11:[77, 7], Operations: ['97-20=77', '19-12=7'] Exploring Operation: 77*7=539, Resulting Numbers: [539] 539,11 unequal: No Solution Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,11 unequal: No Solution Exploring Operation: 77+7=84, Resulting Numbers: [84] 84,11 unequal: No Solution Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[20, 19, 97, 12], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [19, 12, 77] Generated Node #0,1: 11:[19, 12, 77] Operation: 97-20=77 Moving to Node #0,1 Current State: 11:[19, 12, 77], Operations: ['97-20=77'] Exploring Operation: 19-12=7, Resulting Numbers: [77, 7] Generated Node #0,1,2: 11:[77, 7] Operation: 19-12=7 Moving to Node #0,1,2 Current State: 11:[77, 7], Operations: ['97-20=77', '19-12=7'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_4
mult_heuristic
[ 82, 98, 58, 29 ]
13
[ "98-82=16", "58-29=29", "29-16=13" ]
Current State: 13:[82, 98, 58, 29], Operations: [] Exploring Operation: 98-82=16, Resulting Numbers: [58, 29, 16] Generated Node #2: [58, 29, 16] from Operation: 98-82=16 Current State: 13:[58, 29, 16], Operations: ['98-82=16'] Exploring Operation: 58-29=29, Resulting Numbers: [16, 29] Generated Node #3: [16, 29] from Operation: 58-29=29 Current State: 13:[16, 29], Operations: ['98-82=16', '58-29=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[82, 98, 58, 29], Operations: [] Exploring Operation: 98-82=16, Resulting Numbers: [58, 29, 16] Generated Node #0,0: 13:[58, 29, 16] Operation: 98-82=16 Exploring Operation: 82-58=24, Resulting Numbers: [98, 29, 24] Generated Node #0,1: 13:[98, 29, 24] Operation: 82-58=24 Exploring Operation: 98-58=40, Resulting Numbers: [82, 29, 40] Generated Node #0,2: 13:[82, 29, 40] Operation: 98-58=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[58, 29, 16], Operations: ['98-82=16'] Exploring Operation: 58-29=29, Resulting Numbers: [16, 29] Generated Node #0,0,0: 13:[16, 29] Operation: 58-29=29 Exploring Operation: 58/29=2, Resulting Numbers: [16, 2] Generated Node #0,0,1: 13:[16, 2] Operation: 58/29=2 Exploring Operation: 58-16=42, Resulting Numbers: [29, 42] Generated Node #0,0,2: 13:[29, 42] Operation: 58-16=42 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[16, 2], Operations: ['98-82=16', '58/29=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,13 unequal: No Solution Exploring Operation: 16/2=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 #0,0,0 Current State: 13:[16, 29], Operations: ['98-82=16', '58-29=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[82, 98, 58, 29], Operations: [] Exploring Operation: 98-82=16, Resulting Numbers: [58, 29, 16] Generated Node #0,0: 13:[58, 29, 16] Operation: 98-82=16 Moving to Node #0,0 Current State: 13:[58, 29, 16], Operations: ['98-82=16'] Exploring Operation: 58-29=29, Resulting Numbers: [16, 29] Generated Node #0,0,0: 13:[16, 29] Operation: 58-29=29 Moving to Node #0,0,0 Current State: 13:[16, 29], Operations: ['98-82=16', '58-29=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 22, 44, 74, 76 ]
22
[ "22*74=1628", "44+1628=1672", "1672/76=22" ]
Current State: 22:[22, 44, 74, 76], Operations: [] Exploring Operation: 22*74=1628, Resulting Numbers: [44, 76, 1628] Generated Node #2: [44, 76, 1628] from Operation: 22*74=1628 Current State: 22:[44, 76, 1628], Operations: ['22*74=1628'] Exploring Operation: 44+1628=1672, Resulting Numbers: [76, 1672] Generated Node #3: [76, 1672] from Operation: 44+1628=1672 Current State: 22:[76, 1672], Operations: ['22*74=1628', '44+1628=1672'] Exploring Operation: 1672/76=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[22, 44, 74, 76], Operations: [] Exploring Operation: 76-44=32, Resulting Numbers: [22, 74, 32] Generated Node #0,0: 22:[22, 74, 32] Operation: 76-44=32 Exploring Operation: 74-44=30, Resulting Numbers: [22, 76, 30] Generated Node #0,1: 22:[22, 76, 30] Operation: 74-44=30 Exploring Operation: 76-74=2, Resulting Numbers: [22, 44, 2] Generated Node #0,2: 22:[22, 44, 2] Operation: 76-74=2 Moving to Node #0,2 Current State: 22:[22, 44, 2], Operations: ['76-74=2'] Exploring Operation: 44/22=2, Resulting Numbers: [2, 2] Generated Node #0,2,0: 22:[2, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [2, 22] Generated Node #0,2,1: 22:[2, 22] Operation: 44-22=22 Exploring Operation: 44/2=22, Resulting Numbers: [22, 22] Generated Node #0,2,2: 22:[22, 22] Operation: 44/2=22 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[2, 2], Operations: ['76-74=2', '44/22=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,22 unequal: No Solution No 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: 22:[2, 22], Operations: ['76-74=2', '44-22=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,22 unequal: No Solution No 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: 22:[22, 22], Operations: ['76-74=2', '44/2=22'] Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,22 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,22 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: 22:[22, 74, 32], Operations: ['76-44=32'] Exploring Operation: 32-22=10, Resulting Numbers: [74, 10] Generated Node #0,0,0: 22:[74, 10] Operation: 32-22=10 Exploring Operation: 74-22=52, Resulting Numbers: [32, 52] Generated Node #0,0,1: 22:[32, 52] Operation: 74-22=52 Exploring Operation: 74-32=42, Resulting Numbers: [22, 42] Generated Node #0,0,2: 22:[22, 42] Operation: 74-32=42 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[22, 42], Operations: ['76-44=32', '74-32=42'] Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,22 unequal: No Solution Exploring Operation: 22*42=924, Resulting Numbers: [924] 924,22 unequal: No Solution No 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: 22:[32, 52], Operations: ['76-44=32', '74-22=52'] Exploring Operation: 32*52=1664, Resulting Numbers: [1664] 1664,22 unequal: No Solution Exploring Operation: 32+52=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,22 unequal: No Solution No 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: 22:[74, 10], Operations: ['76-44=32', '32-22=10'] Exploring Operation: 74-10=64, Resulting Numbers: [64] 64,22 unequal: No Solution Exploring Operation: 74*10=740, Resulting Numbers: [740] 740,22 unequal: No Solution Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,22 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: 22:[22, 76, 30], Operations: ['74-44=30'] Exploring Operation: 30-22=8, Resulting Numbers: [76, 8] Generated Node #0,1,0: 22:[76, 8] Operation: 30-22=8 Exploring Operation: 76-30=46, Resulting Numbers: [22, 46] Generated Node #0,1,1: 22:[22, 46] Operation: 76-30=46 Exploring Operation: 76-22=54, Resulting Numbers: [30, 54] Generated Node #0,1,2: 22:[30, 54] Operation: 76-22=54 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[22, 46], Operations: ['74-44=30', '76-30=46'] Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 22*46=1012, Resulting Numbers: [1012] 1012,22 unequal: No Solution No 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: 22:[30, 54], Operations: ['74-44=30', '76-22=54'] Exploring Operation: 54-30=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 30+54=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 30*54=1620, Resulting Numbers: [1620] 1620,22 unequal: No Solution No 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: 22:[76, 8], Operations: ['74-44=30', '30-22=8'] Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,22 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,22 unequal: No Solution Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,22 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
[ 55, 63, 34, 3 ]
16
[ "55+63=118", "34*3=102", "118-102=16" ]
Current State: 16:[55, 63, 34, 3], Operations: [] Exploring Operation: 55+63=118, Resulting Numbers: [34, 3, 118] Generated Node #2: [34, 3, 118] from Operation: 55+63=118 Current State: 16:[34, 3, 118], Operations: ['55+63=118'] Exploring Operation: 34*3=102, Resulting Numbers: [118, 102] Generated Node #3: [118, 102] from Operation: 34*3=102 Current State: 16:[118, 102], Operations: ['55+63=118', '34*3=102'] Exploring Operation: 118-102=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[55, 63, 34, 3], Operations: [] Exploring Operation: 63-55=8, Resulting Numbers: [34, 3, 8] Generated Node #0,0: 16:[34, 3, 8] Operation: 63-55=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[34, 3, 8], Operations: ['63-55=8'] Exploring Operation: 34-8=26, Resulting Numbers: [3, 26] Generated Node #0,0,0: 16:[3, 26] Operation: 34-8=26 Moving to Node #0,0,0 Current State: 16:[3, 26], Operations: ['63-55=8', '34-8=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,16 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
[ 2, 85, 77, 90 ]
37
[ "90/2=45", "85-77=8", "45-8=37" ]
Current State: 37:[2, 85, 77, 90], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [85, 77, 45] Generated Node #2: [85, 77, 45] from Operation: 90/2=45 Current State: 37:[85, 77, 45], Operations: ['90/2=45'] Exploring Operation: 85-77=8, Resulting Numbers: [45, 8] Generated Node #3: [45, 8] from Operation: 85-77=8 Current State: 37:[45, 8], Operations: ['90/2=45', '85-77=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[2, 85, 77, 90], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [2, 77, 5] Generated Node #0,0: 37:[2, 77, 5] Operation: 90-85=5 Exploring Operation: 90/2=45, Resulting Numbers: [85, 77, 45] Generated Node #0,1: 37:[85, 77, 45] Operation: 90/2=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[85, 77, 45], Operations: ['90/2=45'] Exploring Operation: 85-45=40, Resulting Numbers: [77, 40] Generated Node #0,1,0: 37:[77, 40] Operation: 85-45=40 Exploring Operation: 85-77=8, Resulting Numbers: [45, 8] Generated Node #0,1,1: 37:[45, 8] Operation: 85-77=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[45, 8], Operations: ['90/2=45', '85-77=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[2, 85, 77, 90], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [85, 77, 45] Generated Node #0,1: 37:[85, 77, 45] Operation: 90/2=45 Moving to Node #0,1 Current State: 37:[85, 77, 45], Operations: ['90/2=45'] Exploring Operation: 85-77=8, Resulting Numbers: [45, 8] Generated Node #0,1,1: 37:[45, 8] Operation: 85-77=8 Moving to Node #0,1,1 Current State: 37:[45, 8], Operations: ['90/2=45', '85-77=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 4, 95, 24, 35 ]
39
[ "95-35=60", "60/4=15", "24+15=39" ]
Current State: 39:[4, 95, 24, 35], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [4, 24, 60] Generated Node #2: [4, 24, 60] from Operation: 95-35=60 Current State: 39:[4, 24, 60], Operations: ['95-35=60'] Exploring Operation: 60/4=15, Resulting Numbers: [24, 15] Generated Node #3: [24, 15] from Operation: 60/4=15 Current State: 39:[24, 15], Operations: ['95-35=60', '60/4=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[4, 95, 24, 35], Operations: [] Exploring Operation: 95-35=60, Resulting Numbers: [4, 24, 60] Generated Node #0,0: 39:[4, 24, 60] Operation: 95-35=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[4, 24, 60], Operations: ['95-35=60'] Exploring Operation: 60-24=36, Resulting Numbers: [4, 36] Generated Node #0,0,0: 39:[4, 36] Operation: 60-24=36 Moving to Node #0,0,0 Current State: 39:[4, 36], Operations: ['95-35=60', '60-24=36'] Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 2, 4, 44, 36 ]
60
[ "4+44=48", "2*48=96", "96-36=60" ]
Current State: 60:[2, 4, 44, 36], Operations: [] Exploring Operation: 4+44=48, Resulting Numbers: [2, 36, 48] Generated Node #2: [2, 36, 48] from Operation: 4+44=48 Current State: 60:[2, 36, 48], Operations: ['4+44=48'] Exploring Operation: 2*48=96, Resulting Numbers: [36, 96] Generated Node #3: [36, 96] from Operation: 2*48=96 Current State: 60:[36, 96], Operations: ['4+44=48', '2*48=96'] Exploring Operation: 96-36=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[2, 4, 44, 36], Operations: [] Exploring Operation: 44-36=8, Resulting Numbers: [2, 4, 8] Generated Node #0,0: 60:[2, 4, 8] Operation: 44-36=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[2, 4, 8], Operations: ['44-36=8'] Exploring Operation: 2+8=10, Resulting Numbers: [4, 10] Generated Node #0,0,0: 60:[4, 10] Operation: 2+8=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[4, 10], Operations: ['44-36=8', '2+8=10'] Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 85, 2, 3, 36 ]
55
[ "85-36=49", "2*3=6", "49+6=55" ]
Current State: 55:[85, 2, 3, 36], Operations: [] Exploring Operation: 85-36=49, Resulting Numbers: [2, 3, 49] Generated Node #2: [2, 3, 49] from Operation: 85-36=49 Current State: 55:[2, 3, 49], Operations: ['85-36=49'] Exploring Operation: 2*3=6, Resulting Numbers: [49, 6] Generated Node #3: [49, 6] from Operation: 2*3=6 Current State: 55:[49, 6], Operations: ['85-36=49', '2*3=6'] Exploring Operation: 49+6=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[85, 2, 3, 36], Operations: [] Exploring Operation: 36/3=12, Resulting Numbers: [85, 2, 12] Generated Node #0,0: 55:[85, 2, 12] Operation: 36/3=12 Exploring Operation: 85-36=49, Resulting Numbers: [2, 3, 49] Generated Node #0,1: 55:[2, 3, 49] Operation: 85-36=49 Exploring Operation: 36/2=18, Resulting Numbers: [85, 3, 18] Generated Node #0,2: 55:[85, 3, 18] Operation: 36/2=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[2, 3, 49], Operations: ['85-36=49'] Exploring Operation: 3+49=52, Resulting Numbers: [2, 52] Generated Node #0,1,0: 55:[2, 52] Operation: 3+49=52 Exploring Operation: 2+3=5, Resulting Numbers: [49, 5] Generated Node #0,1,1: 55:[49, 5] Operation: 2+3=5 Exploring Operation: 2+49=51, Resulting Numbers: [3, 51] Generated Node #0,1,2: 55:[3, 51] Operation: 2+49=51 Moving to Node #0,1,0 Current State: 55:[2, 52], Operations: ['85-36=49', '3+49=52'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,55 unequal: No Solution Exploring Operation: 2+52=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[49, 5], Operations: ['85-36=49', '2+3=5'] Exploring Operation: 49-5=44, Resulting Numbers: [44] 44,55 unequal: No Solution Exploring Operation: 49*5=245, Resulting Numbers: [245] 245,55 unequal: No Solution Exploring Operation: 49+5=54, Resulting Numbers: [54] 54,55 unequal: No Solution Moving to Node #0,1,2 Current State: 55:[3, 51], Operations: ['85-36=49', '2+49=51'] Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,55 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[85, 2, 12], Operations: ['36/3=12'] Exploring Operation: 85-12=73, Resulting Numbers: [2, 73] Generated Node #0,0,0: 55:[2, 73] Operation: 85-12=73 Exploring Operation: 85-2=83, Resulting Numbers: [12, 83] Generated Node #0,0,1: 55:[12, 83] Operation: 85-2=83 Exploring Operation: 12-2=10, Resulting Numbers: [85, 10] Generated Node #0,0,2: 55:[85, 10] Operation: 12-2=10 Moving to Node #0,0,0 Current State: 55:[2, 73], Operations: ['36/3=12', '85-12=73'] Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,55 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,55 unequal: No Solution Moving to Node #0,0,1 Current State: 55:[12, 83], Operations: ['36/3=12', '85-2=83'] Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,55 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,55 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,55 unequal: No Solution Moving to Node #0,0,2 Current State: 55:[85, 10], Operations: ['36/3=12', '12-2=10'] Exploring Operation: 85*10=850, Resulting Numbers: [850] 850,55 unequal: No Solution Exploring Operation: 85-10=75, Resulting Numbers: [75] 75,55 unequal: No Solution Exploring Operation: 85+10=95, Resulting Numbers: [95] 95,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[85, 3, 18], Operations: ['36/2=18'] Exploring Operation: 85-18=67, Resulting Numbers: [3, 67] Generated Node #0,2,0: 55:[3, 67] Operation: 85-18=67 Exploring Operation: 18/3=6, Resulting Numbers: [85, 6] Generated Node #0,2,1: 55:[85, 6] Operation: 18/3=6 Exploring Operation: 3*18=54, Resulting Numbers: [85, 54] Generated Node #0,2,2: 55:[85, 54] Operation: 3*18=54 Moving to Node #0,2,0 Current State: 55:[3, 67], Operations: ['36/2=18', '85-18=67'] Exploring Operation: 3*67=201, Resulting Numbers: [201] 201,55 unequal: No Solution Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,55 unequal: No Solution Moving to Node #0,2,1 Current State: 55:[85, 6], Operations: ['36/2=18', '18/3=6'] Exploring Operation: 85*6=510, Resulting Numbers: [510] 510,55 unequal: No Solution Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,55 unequal: No Solution Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,55 unequal: No Solution Moving to Node #0,2,2 Current State: 55:[85, 54], Operations: ['36/2=18', '3*18=54'] Exploring Operation: 85+54=139, Resulting Numbers: [139] 139,55 unequal: No Solution Exploring Operation: 85-54=31, Resulting Numbers: [31] 31,55 unequal: No Solution Exploring Operation: 85*54=4590, Resulting Numbers: [4590] 4590,55 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