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
[ 72, 10, 54, 80 ]
88
[ "72-10=62", "80-54=26", "62+26=88" ]
Current State: 88:[72, 10, 54, 80], Operations: [] Exploring Operation: 72-10=62, Resulting Numbers: [54, 80, 62] Generated Node #2: [54, 80, 62] from Operation: 72-10=62 Current State: 88:[54, 80, 62], Operations: ['72-10=62'] Exploring Operation: 80-54=26, Resulting Numbers: [62, 26] Generated Node #3: [62, 26] from Operation: 80-54=26 Current State: 88:[62, 26], Operations: ['72-10=62', '80-54=26'] Exploring Operation: 62+26=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[72, 10, 54, 80], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [10, 54, 8] Generated Node #0,0: 88:[10, 54, 8] Operation: 80-72=8 Exploring Operation: 72-54=18, Resulting Numbers: [10, 80, 18] Generated Node #0,1: 88:[10, 80, 18] Operation: 72-54=18 Exploring Operation: 80-54=26, Resulting Numbers: [72, 10, 26] Generated Node #0,2: 88:[72, 10, 26] Operation: 80-54=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[10, 54, 8], Operations: ['80-72=8'] Exploring Operation: 10-8=2, Resulting Numbers: [54, 2] Generated Node #0,0,0: 88:[54, 2] Operation: 10-8=2 Exploring Operation: 54-8=46, Resulting Numbers: [10, 46] Generated Node #0,0,1: 88:[10, 46] Operation: 54-8=46 Exploring Operation: 54-10=44, Resulting Numbers: [8, 44] Generated Node #0,0,2: 88:[8, 44] Operation: 54-10=44 Moving to Node #0,0,2 Current State: 88:[8, 44], Operations: ['80-72=8', '54-10=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,88 unequal: No Solution Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[10, 46], Operations: ['80-72=8', '54-8=46'] Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,88 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,88 unequal: No Solution Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[54, 2], Operations: ['80-72=8', '10-8=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,88 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[10, 80, 18], Operations: ['72-54=18'] Exploring Operation: 10+80=90, Resulting Numbers: [18, 90] Generated Node #0,1,0: 88:[18, 90] Operation: 10+80=90 Exploring Operation: 80/10=8, Resulting Numbers: [18, 8] Generated Node #0,1,1: 88:[18, 8] Operation: 80/10=8 Exploring Operation: 18-10=8, Resulting Numbers: [80, 8] Generated Node #0,1,2: 88:[80, 8] Operation: 18-10=8 Moving to Node #0,1,1 Current State: 88:[18, 8], Operations: ['72-54=18', '80/10=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[18, 90], Operations: ['72-54=18', '10+80=90'] Exploring Operation: 90-18=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 90/18=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 18+90=108, Resulting Numbers: [108] 108,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[80, 8], Operations: ['72-54=18', '18-10=8'] Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[72, 10, 54, 80], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [10, 80, 18] Generated Node #0,1: 88:[10, 80, 18] Operation: 72-54=18 Moving to Node #0,1 Current State: 88:[10, 80, 18], Operations: ['72-54=18'] Exploring Operation: 18-10=8, Resulting Numbers: [80, 8] Generated Node #0,1,2: 88:[80, 8] Operation: 18-10=8 Moving to Node #0,1,2 Current State: 88:[80, 8], Operations: ['72-54=18', '18-10=8'] Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 26, 1, 51, 40 ]
20
[ "26*40=1040", "1+51=52", "1040/52=20" ]
Current State: 20:[26, 1, 51, 40], Operations: [] Exploring Operation: 26*40=1040, Resulting Numbers: [1, 51, 1040] Generated Node #2: [1, 51, 1040] from Operation: 26*40=1040 Current State: 20:[1, 51, 1040], Operations: ['26*40=1040'] Exploring Operation: 1+51=52, Resulting Numbers: [1040, 52] Generated Node #3: [1040, 52] from Operation: 1+51=52 Current State: 20:[1040, 52], Operations: ['26*40=1040', '1+51=52'] Exploring Operation: 1040/52=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[26, 1, 51, 40], Operations: [] Exploring Operation: 51-40=11, Resulting Numbers: [26, 1, 11] Generated Node #0,0: 20:[26, 1, 11] Operation: 51-40=11 Moving to Node #0,0 Current State: 20:[26, 1, 11], Operations: ['51-40=11'] Exploring Operation: 26-1=25, Resulting Numbers: [11, 25] Generated Node #0,0,0: 20:[11, 25] Operation: 26-1=25 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[11, 25], Operations: ['51-40=11', '26-1=25'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,20 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
[ 54, 24, 74, 16 ]
16
[ "54+74=128", "24-16=8", "128/8=16" ]
Current State: 16:[54, 24, 74, 16], Operations: [] Exploring Operation: 54+74=128, Resulting Numbers: [24, 16, 128] Generated Node #2: [24, 16, 128] from Operation: 54+74=128 Current State: 16:[24, 16, 128], Operations: ['54+74=128'] Exploring Operation: 24-16=8, Resulting Numbers: [128, 8] Generated Node #3: [128, 8] from Operation: 24-16=8 Current State: 16:[128, 8], Operations: ['54+74=128', '24-16=8'] Exploring Operation: 128/8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[54, 24, 74, 16], Operations: [] Exploring Operation: 74-54=20, Resulting Numbers: [24, 16, 20] Generated Node #0,0: 16:[24, 16, 20] Operation: 74-54=20 Exploring Operation: 54-24=30, Resulting Numbers: [74, 16, 30] Generated Node #0,1: 16:[74, 16, 30] Operation: 54-24=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[24, 16, 20], Operations: ['74-54=20'] Exploring Operation: 24-16=8, Resulting Numbers: [20, 8] Generated Node #0,0,0: 16:[20, 8] Operation: 24-16=8 Exploring Operation: 24-20=4, Resulting Numbers: [16, 4] Generated Node #0,0,1: 16:[16, 4] Operation: 24-20=4 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 16:[16, 4], Operations: ['74-54=20', '24-20=4'] Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,16 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 16:[20, 8], Operations: ['74-54=20', '24-16=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[74, 16, 30], Operations: ['54-24=30'] Exploring Operation: 74-16=58, Resulting Numbers: [30, 58] Generated Node #0,1,0: 16:[30, 58] Operation: 74-16=58 Exploring Operation: 74-30=44, Resulting Numbers: [16, 44] Generated Node #0,1,1: 16:[16, 44] Operation: 74-30=44 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[16, 44], Operations: ['54-24=30', '74-30=44'] Exploring Operation: 16+44=60, Resulting Numbers: [60] 60,16 unequal: No Solution Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,16 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:[30, 58], Operations: ['54-24=30', '74-16=58'] Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 30+58=88, Resulting Numbers: [88] 88,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 17, 72, 51, 95 ]
99
[ "72-17=55", "95-51=44", "55+44=99" ]
Current State: 99:[17, 72, 51, 95], Operations: [] Exploring Operation: 72-17=55, Resulting Numbers: [51, 95, 55] Generated Node #2: [51, 95, 55] from Operation: 72-17=55 Current State: 99:[51, 95, 55], Operations: ['72-17=55'] Exploring Operation: 95-51=44, Resulting Numbers: [55, 44] Generated Node #3: [55, 44] from Operation: 95-51=44 Current State: 99:[55, 44], Operations: ['72-17=55', '95-51=44'] Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[17, 72, 51, 95], Operations: [] Exploring Operation: 72-51=21, Resulting Numbers: [17, 95, 21] Generated Node #0,0: 99:[17, 95, 21] Operation: 72-51=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[17, 95, 21], Operations: ['72-51=21'] Exploring Operation: 21-17=4, Resulting Numbers: [95, 4] Generated Node #0,0,0: 99:[95, 4] Operation: 21-17=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[95, 4], Operations: ['72-51=21', '21-17=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[17, 72, 51, 95], Operations: [] Exploring Operation: 72-51=21, Resulting Numbers: [17, 95, 21] Generated Node #0,0: 99:[17, 95, 21] Operation: 72-51=21 Moving to Node #0,0 Current State: 99:[17, 95, 21], Operations: ['72-51=21'] Exploring Operation: 21-17=4, Resulting Numbers: [95, 4] Generated Node #0,0,0: 99:[95, 4] Operation: 21-17=4 Moving to Node #0,0,0 Current State: 99:[95, 4], Operations: ['72-51=21', '21-17=4'] Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 20, 93, 4, 64 ]
53
[ "20+93=113", "64-4=60", "113-60=53" ]
Current State: 53:[20, 93, 4, 64], Operations: [] Exploring Operation: 20+93=113, Resulting Numbers: [4, 64, 113] Generated Node #2: [4, 64, 113] from Operation: 20+93=113 Current State: 53:[4, 64, 113], Operations: ['20+93=113'] Exploring Operation: 64-4=60, Resulting Numbers: [113, 60] Generated Node #3: [113, 60] from Operation: 64-4=60 Current State: 53:[113, 60], Operations: ['20+93=113', '64-4=60'] Exploring Operation: 113-60=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[20, 93, 4, 64], Operations: [] Exploring Operation: 93-20=73, Resulting Numbers: [4, 64, 73] Generated Node #0,0: 53:[4, 64, 73] Operation: 93-20=73 Exploring Operation: 20*4=80, Resulting Numbers: [93, 64, 80] Generated Node #0,1: 53:[93, 64, 80] Operation: 20*4=80 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[93, 64, 80], Operations: ['20*4=80'] Exploring Operation: 93-80=13, Resulting Numbers: [64, 13] Generated Node #0,1,0: 53:[64, 13] Operation: 93-80=13 Exploring Operation: 93-64=29, Resulting Numbers: [80, 29] Generated Node #0,1,1: 53:[80, 29] Operation: 93-64=29 Moving to Node #0,1,0 Current State: 53:[64, 13], Operations: ['20*4=80', '93-80=13'] Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,53 unequal: No Solution Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[80, 29], Operations: ['20*4=80', '93-64=29'] Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,53 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[4, 64, 73], Operations: ['93-20=73'] Exploring Operation: 73-4=69, Resulting Numbers: [64, 69] Generated Node #0,0,0: 53:[64, 69] Operation: 73-4=69 Exploring Operation: 64-4=60, Resulting Numbers: [73, 60] Generated Node #0,0,1: 53:[73, 60] Operation: 64-4=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[64, 69], Operations: ['93-20=73', '73-4=69'] Exploring Operation: 69-64=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 64+69=133, Resulting Numbers: [133] 133,53 unequal: No Solution No 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: 53:[73, 60], Operations: ['93-20=73', '64-4=60'] Exploring Operation: 73-60=13, Resulting Numbers: [13] 13,53 unequal: No Solution Exploring Operation: 73+60=133, Resulting Numbers: [133] 133,53 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
[ 4, 9, 23, 62 ]
59
[ "4+23=27", "27/9=3", "62-3=59" ]
Current State: 59:[4, 9, 23, 62], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [9, 62, 27] Generated Node #2: [9, 62, 27] from Operation: 4+23=27 Current State: 59:[9, 62, 27], Operations: ['4+23=27'] Exploring Operation: 27/9=3, Resulting Numbers: [62, 3] Generated Node #3: [62, 3] from Operation: 27/9=3 Current State: 59:[62, 3], Operations: ['4+23=27', '27/9=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[4, 9, 23, 62], Operations: [] Exploring Operation: 9+23=32, Resulting Numbers: [4, 62, 32] Generated Node #0,0: 59:[4, 62, 32] Operation: 9+23=32 Exploring Operation: 4*9=36, Resulting Numbers: [23, 62, 36] Generated Node #0,1: 59:[23, 62, 36] Operation: 4*9=36 Exploring Operation: 4*23=92, Resulting Numbers: [9, 62, 92] Generated Node #0,2: 59:[9, 62, 92] Operation: 4*23=92 Exploring Operation: 4+23=27, Resulting Numbers: [9, 62, 27] Generated Node #0,3: 59:[9, 62, 27] Operation: 4+23=27 Exploring Operation: 4+9=13, Resulting Numbers: [23, 62, 13] Generated Node #0,4: 59:[23, 62, 13] Operation: 4+9=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[23, 62, 36], Operations: ['4*9=36'] Exploring Operation: 23+62=85, Resulting Numbers: [36, 85] Generated Node #0,1,0: 59:[36, 85] Operation: 23+62=85 Exploring Operation: 23+36=59, Resulting Numbers: [62, 59] Generated Node #0,1,1: 59:[62, 59] Operation: 23+36=59 Exploring Operation: 62-36=26, Resulting Numbers: [23, 26] Generated Node #0,1,2: 59:[23, 26] Operation: 62-36=26 Exploring Operation: 62-23=39, Resulting Numbers: [36, 39] Generated Node #0,1,3: 59:[36, 39] Operation: 62-23=39 Exploring Operation: 36-23=13, Resulting Numbers: [62, 13] Generated Node #0,1,4: 59:[62, 13] Operation: 36-23=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 59:[62, 59], Operations: ['4*9=36', '23+36=59'] Exploring Operation: 62*59=3658, Resulting Numbers: [3658] 3658,59 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,59 unequal: No Solution No 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: 59:[36, 39], Operations: ['4*9=36', '62-23=39'] Exploring Operation: 36+39=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 39-36=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 36*39=1404, Resulting Numbers: [1404] 1404,59 unequal: No Solution No 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: 59:[36, 85], Operations: ['4*9=36', '23+62=85'] Exploring Operation: 36*85=3060, Resulting Numbers: [3060] 3060,59 unequal: No Solution Exploring Operation: 36+85=121, Resulting Numbers: [121] 121,59 unequal: No Solution Exploring Operation: 85-36=49, Resulting Numbers: [49] 49,59 unequal: No Solution No 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: 59:[62, 13], Operations: ['4*9=36', '36-23=13'] Exploring Operation: 62+13=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 62*13=806, Resulting Numbers: [806] 806,59 unequal: No Solution Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,59 unequal: No Solution No 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: 59:[23, 26], Operations: ['4*9=36', '62-36=26'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,59 unequal: No Solution Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,59 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: 59:[4, 62, 32], Operations: ['9+23=32'] Exploring Operation: 32-4=28, Resulting Numbers: [62, 28] Generated Node #0,0,0: 59:[62, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [62, 8] Generated Node #0,0,1: 59:[62, 8] Operation: 32/4=8 Exploring Operation: 4+62=66, Resulting Numbers: [32, 66] Generated Node #0,0,2: 59:[32, 66] Operation: 4+62=66 Exploring Operation: 4+32=36, Resulting Numbers: [62, 36] Generated Node #0,0,3: 59:[62, 36] Operation: 4+32=36 Exploring Operation: 62-4=58, Resulting Numbers: [32, 58] Generated Node #0,0,4: 59:[32, 58] Operation: 62-4=58 Moving to Node #0,0,3 Current State: 59:[62, 36], Operations: ['9+23=32', '4+32=36'] Exploring Operation: 62*36=2232, Resulting Numbers: [2232] 2232,59 unequal: No Solution Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,59 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[32, 58], Operations: ['9+23=32', '62-4=58'] Exploring Operation: 58-32=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 32+58=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 32*58=1856, Resulting Numbers: [1856] 1856,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[62, 28], Operations: ['9+23=32', '32-4=28'] Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,59 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,59 unequal: No Solution Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[32, 66], Operations: ['9+23=32', '4+62=66'] Exploring Operation: 32*66=2112, Resulting Numbers: [2112] 2112,59 unequal: No Solution Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,59 unequal: No Solution Exploring Operation: 32+66=98, Resulting Numbers: [98] 98,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[62, 8], Operations: ['9+23=32', '32/4=8'] Exploring Operation: 62+8=70, Resulting Numbers: [70] 70,59 unequal: No Solution Exploring Operation: 62*8=496, Resulting Numbers: [496] 496,59 unequal: No Solution Exploring Operation: 62-8=54, Resulting Numbers: [54] 54,59 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:[9, 62, 27], Operations: ['4+23=27'] Exploring Operation: 9+62=71, Resulting Numbers: [27, 71] Generated Node #0,3,0: 59:[27, 71] Operation: 9+62=71 Exploring Operation: 9+27=36, Resulting Numbers: [62, 36] Generated Node #0,3,1: 59:[62, 36] Operation: 9+27=36 Exploring Operation: 62-9=53, Resulting Numbers: [27, 53] Generated Node #0,3,2: 59:[27, 53] Operation: 62-9=53 Exploring Operation: 27-9=18, Resulting Numbers: [62, 18] Generated Node #0,3,3: 59:[62, 18] Operation: 27-9=18 Exploring Operation: 27/9=3, Resulting Numbers: [62, 3] Generated Node #0,3,4: 59:[62, 3] Operation: 27/9=3 Moving to Node #0,3,1 Current State: 59:[62, 36], Operations: ['4+23=27', '9+27=36'] Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,59 unequal: No Solution Exploring Operation: 62-36=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 62*36=2232, Resulting Numbers: [2232] 2232,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[27, 53], Operations: ['4+23=27', '62-9=53'] Exploring Operation: 27+53=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 53-27=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 27*53=1431, Resulting Numbers: [1431] 1431,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[27, 71], Operations: ['4+23=27', '9+62=71'] Exploring Operation: 71-27=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 27*71=1917, Resulting Numbers: [1917] 1917,59 unequal: No Solution Exploring Operation: 27+71=98, Resulting Numbers: [98] 98,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[62, 18], Operations: ['4+23=27', '27-9=18'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 62*18=1116, Resulting Numbers: [1116] 1116,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[62, 3], Operations: ['4+23=27', '27/9=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,59 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[4, 9, 23, 62], Operations: [] Exploring Operation: 4+23=27, Resulting Numbers: [9, 62, 27] Generated Node #0,3: 59:[9, 62, 27] Operation: 4+23=27 Moving to Node #0,3 Current State: 59:[9, 62, 27], Operations: ['4+23=27'] Exploring Operation: 27/9=3, Resulting Numbers: [62, 3] Generated Node #0,3,4: 59:[62, 3] Operation: 27/9=3 Moving to Node #0,3,4 Current State: 59:[62, 3], Operations: ['4+23=27', '27/9=3'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_5
mult_heuristic
[ 20, 30, 20, 68 ]
72
[ "68-20=48", "30*48=1440", "1440/20=72" ]
Current State: 72:[20, 30, 20, 68], Operations: [] Exploring Operation: 68-20=48, Resulting Numbers: [30, 48] Generated Node #2: [30, 48] from Operation: 68-20=48 Current State: 72:[30, 48], Operations: ['68-20=48'] Exploring Operation: 30*48=1440, Resulting Numbers: [1440] 1440,72 equal: Goal Reached Exploring Operation: 1440/20=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[20, 30, 20, 68], Operations: [] Exploring Operation: 30-20=10, Resulting Numbers: [20, 68, 10] Generated Node #0,0: 72:[20, 68, 10] Operation: 30-20=10 Exploring Operation: 68-30=38, Resulting Numbers: [20, 20, 38] Generated Node #0,1: 72:[20, 20, 38] Operation: 68-30=38 Exploring Operation: 30-20=10, Resulting Numbers: [20, 68, 10] Generated Node #0,2: 72:[20, 68, 10] Operation: 30-20=10 Exploring Operation: 20/20=1, Resulting Numbers: [30, 68, 1] Generated Node #0,3: 72:[30, 68, 1] Operation: 20/20=1 Moving to Node #0,1 Current State: 72:[20, 20, 38], Operations: ['68-30=38'] Exploring Operation: 38-20=18, Resulting Numbers: [20, 18] Generated Node #0,1,0: 72:[20, 18] Operation: 38-20=18 Exploring Operation: 20/20=1, Resulting Numbers: [38, 1] Generated Node #0,1,1: 72:[38, 1] Operation: 20/20=1 Exploring Operation: 20-20=0, Resulting Numbers: [38, 0] Generated Node #0,1,2: 72:[38, 0] Operation: 20-20=0 Exploring Operation: 38-20=18, Resulting Numbers: [20, 18] Generated Node #0,1,3: 72:[20, 18] Operation: 38-20=18 Moving to Node #0,2 Current State: 72:[20, 68, 10], Operations: ['30-20=10'] Exploring Operation: 20+10=30, Resulting Numbers: [68, 30] Generated Node #0,2,0: 72:[68, 30] Operation: 20+10=30 Exploring Operation: 20-10=10, Resulting Numbers: [68, 10] Generated Node #0,2,1: 72:[68, 10] Operation: 20-10=10 Exploring Operation: 68+10=78, Resulting Numbers: [20, 78] Generated Node #0,2,2: 72:[20, 78] Operation: 68+10=78 Exploring Operation: 20/10=2, Resulting Numbers: [68, 2] Generated Node #0,2,3: 72:[68, 2] Operation: 20/10=2 Moving to Node #0,0 Current State: 72:[20, 68, 10], Operations: ['30-20=10'] Exploring Operation: 68+10=78, Resulting Numbers: [20, 78] Generated Node #0,0,0: 72:[20, 78] Operation: 68+10=78 Exploring Operation: 20/10=2, Resulting Numbers: [68, 2] Generated Node #0,0,1: 72:[68, 2] Operation: 20/10=2 Exploring Operation: 20-10=10, Resulting Numbers: [68, 10] Generated Node #0,0,2: 72:[68, 10] Operation: 20-10=10 Exploring Operation: 20+10=30, Resulting Numbers: [68, 30] Generated Node #0,0,3: 72:[68, 30] Operation: 20+10=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[68, 2], Operations: ['30-20=10', '20/10=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 68*2=136, Resulting Numbers: [136] 136,72 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[68, 10], Operations: ['30-20=10', '20-10=10'] Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[20, 78], Operations: ['30-20=10', '68+10=78'] Exploring Operation: 20+78=98, Resulting Numbers: [98] 98,72 unequal: No Solution Exploring Operation: 20*78=1560, Resulting Numbers: [1560] 1560,72 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 72:[68, 30], Operations: ['30-20=10', '20+10=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,72 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,72 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,72 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: 72:[30, 68, 1], Operations: ['20/20=1'] Exploring Operation: 30-1=29, Resulting Numbers: [68, 29] Generated Node #0,3,0: 72:[68, 29] Operation: 30-1=29 Exploring Operation: 68+1=69, Resulting Numbers: [30, 69] Generated Node #0,3,1: 72:[30, 69] Operation: 68+1=69 Exploring Operation: 68-30=38, Resulting Numbers: [1, 38] Generated Node #0,3,2: 72:[1, 38] Operation: 68-30=38 Exploring Operation: 30+1=31, Resulting Numbers: [68, 31] Generated Node #0,3,3: 72:[68, 31] Operation: 30+1=31 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 72:[1, 38], Operations: ['20/20=1', '68-30=38'] Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 1+38=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 1*38=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[68, 29], Operations: ['20/20=1', '30-1=29'] Exploring Operation: 68*29=1972, Resulting Numbers: [1972] 1972,72 unequal: No Solution Exploring Operation: 68+29=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 72:[30, 69], Operations: ['20/20=1', '68+1=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,72 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,72 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 72:[68, 31], Operations: ['20/20=1', '30+1=31'] Exploring Operation: 68+31=99, Resulting Numbers: [99] 99,72 unequal: No Solution Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 68*31=2108, Resulting Numbers: [2108] 2108,72 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: 72:[20, 18], Operations: ['68-30=38', '38-20=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,72 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,72 unequal: No Solution Moving to Node #0,1,3 Current State: 72:[20, 18], Operations: ['68-30=38', '38-20=18'] Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,72 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,72 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[38, 1], Operations: ['68-30=38', '20/20=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 38/1=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38*1=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38+1=39, Resulting Numbers: [39] 39,72 unequal: No Solution Moving to Node #0,2,3 Current State: 72:[68, 2], Operations: ['30-20=10', '20/10=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,72 unequal: No Solution Exploring Operation: 68+2=70, Resulting Numbers: [70] 70,72 unequal: No Solution Exploring Operation: 68*2=136, Resulting Numbers: [136] 136,72 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[38, 0], Operations: ['68-30=38', '20-20=0'] Exploring Operation: 38+0=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38-0=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 38*0=0, Resulting Numbers: [0] 0,72 unequal: No Solution Moving to Node #0,2,1 Current State: 72:[68, 10], Operations: ['30-20=10', '20-10=10'] Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,72 unequal: No Solution Exploring Operation: 68*10=680, Resulting Numbers: [680] 680,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[20, 78], Operations: ['30-20=10', '68+10=78'] Exploring Operation: 20*78=1560, Resulting Numbers: [1560] 1560,72 unequal: No Solution Exploring Operation: 20+78=98, Resulting Numbers: [98] 98,72 unequal: No Solution Exploring Operation: 78-20=58, Resulting Numbers: [58] 58,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[68, 30], Operations: ['30-20=10', '20+10=30'] Exploring Operation: 68+30=98, Resulting Numbers: [98] 98,72 unequal: No Solution Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,72 unequal: No Solution Exploring Operation: 68*30=2040, Resulting Numbers: [2040] 2040,72 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 38, 61, 89, 88 ]
100
[ "38+61=99", "89-88=1", "99+1=100" ]
Current State: 100:[38, 61, 89, 88], Operations: [] Exploring Operation: 38+61=99, Resulting Numbers: [89, 88, 99] Generated Node #2: [89, 88, 99] from Operation: 38+61=99 Current State: 100:[89, 88, 99], Operations: ['38+61=99'] Exploring Operation: 89-88=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 89-88=1 Current State: 100:[99, 1], Operations: ['38+61=99', '89-88=1'] Exploring Operation: 99+1=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[38, 61, 89, 88], Operations: [] Exploring Operation: 88-38=50, Resulting Numbers: [61, 89, 50] Generated Node #0,0: 100:[61, 89, 50] Operation: 88-38=50 Moving to Node #0,0 Current State: 100:[61, 89, 50], Operations: ['88-38=50'] Exploring Operation: 89-61=28, Resulting Numbers: [50, 28] Generated Node #0,0,0: 100:[50, 28] Operation: 89-61=28 Moving to Node #0,0,0 Current State: 100:[50, 28], Operations: ['88-38=50', '89-61=28'] Exploring Operation: 50-28=22, Resulting Numbers: [22] 22,100 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 25, 2, 70, 2 ]
88
[ "70-25=45", "2*45=90", "90-2=88" ]
Current State: 88:[25, 2, 70, 2], Operations: [] Exploring Operation: 70-25=45, Resulting Numbers: [2, 2, 45] Generated Node #2: [2, 2, 45] from Operation: 70-25=45 Current State: 88:[2, 2, 45], Operations: ['70-25=45'] Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,88 equal: Goal Reached Exploring Operation: 90-2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[25, 2, 70, 2], Operations: [] Exploring Operation: 25-2=23, Resulting Numbers: [70, 2, 23] Generated Node #0,0: 88:[70, 2, 23] Operation: 25-2=23 Exploring Operation: 70/2=35, Resulting Numbers: [25, 2, 35] Generated Node #0,1: 88:[25, 2, 35] Operation: 70/2=35 Exploring Operation: 70-25=45, Resulting Numbers: [2, 2, 45] Generated Node #0,2: 88:[2, 2, 45] Operation: 70-25=45 Exploring Operation: 70/2=35, Resulting Numbers: [25, 2, 35] Generated Node #0,3: 88:[25, 2, 35] Operation: 70/2=35 Exploring Operation: 25+70=95, Resulting Numbers: [2, 2, 95] Generated Node #0,4: 88:[2, 2, 95] Operation: 25+70=95 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[2, 2, 45], Operations: ['70-25=45'] Exploring Operation: 2*2=4, Resulting Numbers: [45, 4] Generated Node #0,2,0: 88:[45, 4] Operation: 2*2=4 Exploring Operation: 45-2=43, Resulting Numbers: [2, 43] Generated Node #0,2,1: 88:[2, 43] Operation: 45-2=43 Exploring Operation: 45-2=43, Resulting Numbers: [2, 43] Generated Node #0,2,2: 88:[2, 43] Operation: 45-2=43 Exploring Operation: 2/2=1, Resulting Numbers: [45, 1] Generated Node #0,2,3: 88:[45, 1] Operation: 2/2=1 Exploring Operation: 2+2=4, Resulting Numbers: [45, 4] Generated Node #0,2,4: 88:[45, 4] Operation: 2+2=4 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[45, 4], Operations: ['70-25=45', '2*2=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,88 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[2, 43], Operations: ['70-25=45', '45-2=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 88:[2, 43], Operations: ['70-25=45', '45-2=43'] Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,88 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,88 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 88:[45, 4], Operations: ['70-25=45', '2+2=4'] Exploring Operation: 45*4=180, Resulting Numbers: [180] 180,88 unequal: No Solution Exploring Operation: 45+4=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 88:[45, 1], Operations: ['70-25=45', '2/2=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,88 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 88:[2, 2, 95], Operations: ['25+70=95'] Exploring Operation: 2*2=4, Resulting Numbers: [95, 4] Generated Node #0,4,0: 88:[95, 4] Operation: 2*2=4 Exploring Operation: 95-2=93, Resulting Numbers: [2, 93] Generated Node #0,4,1: 88:[2, 93] Operation: 95-2=93 Exploring Operation: 2+2=4, Resulting Numbers: [95, 4] Generated Node #0,4,2: 88:[95, 4] Operation: 2+2=4 Exploring Operation: 95-2=93, Resulting Numbers: [2, 93] Generated Node #0,4,3: 88:[2, 93] Operation: 95-2=93 Exploring Operation: 2/2=1, Resulting Numbers: [95, 1] Generated Node #0,4,4: 88:[95, 1] Operation: 2/2=1 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 88:[2, 93], Operations: ['25+70=95', '95-2=93'] Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,88 unequal: No Solution Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,88 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 88:[2, 93], Operations: ['25+70=95', '95-2=93'] Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,88 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 88:[95, 4], Operations: ['25+70=95', '2*2=4'] Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,88 unequal: No Solution Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 88:[95, 4], Operations: ['25+70=95', '2+2=4'] Exploring Operation: 95*4=380, Resulting Numbers: [380] 380,88 unequal: No Solution Exploring Operation: 95+4=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 88:[95, 1], Operations: ['25+70=95', '2/2=1'] Exploring Operation: 95*1=95, Resulting Numbers: [95] 95,88 unequal: No Solution Exploring Operation: 95-1=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 95/1=95, Resulting Numbers: [95] 95,88 unequal: No Solution Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[25, 2, 35], Operations: ['70/2=35'] Exploring Operation: 25+2=27, Resulting Numbers: [35, 27] Generated Node #0,1,0: 88:[35, 27] Operation: 25+2=27 Exploring Operation: 2+35=37, Resulting Numbers: [25, 37] Generated Node #0,1,1: 88:[25, 37] Operation: 2+35=37 Exploring Operation: 35-2=33, Resulting Numbers: [25, 33] Generated Node #0,1,2: 88:[25, 33] Operation: 35-2=33 Exploring Operation: 25-2=23, Resulting Numbers: [35, 23] Generated Node #0,1,3: 88:[35, 23] Operation: 25-2=23 Exploring Operation: 35-25=10, Resulting Numbers: [2, 10] Generated Node #0,1,4: 88:[2, 10] Operation: 35-25=10 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 88:[2, 10], Operations: ['70/2=35', '35-25=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 88:[25, 37], Operations: ['70/2=35', '2+35=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,88 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,88 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 88:[35, 23], Operations: ['70/2=35', '25-2=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,88 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 88:[35, 27], Operations: ['70/2=35', '25+2=27'] Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,88 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,88 unequal: No Solution Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 88:[25, 33], Operations: ['70/2=35', '35-2=33'] Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,88 unequal: No Solution Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[25, 2, 35], Operations: ['70/2=35'] Exploring Operation: 35-2=33, Resulting Numbers: [25, 33] Generated Node #0,3,0: 88:[25, 33] Operation: 35-2=33 Exploring Operation: 2+35=37, Resulting Numbers: [25, 37] Generated Node #0,3,1: 88:[25, 37] Operation: 2+35=37 Exploring Operation: 25-2=23, Resulting Numbers: [35, 23] Generated Node #0,3,2: 88:[35, 23] Operation: 25-2=23 Exploring Operation: 25+2=27, Resulting Numbers: [35, 27] Generated Node #0,3,3: 88:[35, 27] Operation: 25+2=27 Exploring Operation: 35-25=10, Resulting Numbers: [2, 10] Generated Node #0,3,4: 88:[2, 10] Operation: 35-25=10 Moving to Node #0,3,4 Current State: 88:[2, 10], Operations: ['70/2=35', '35-25=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[35, 23], Operations: ['70/2=35', '25-2=23'] Exploring Operation: 35*23=805, Resulting Numbers: [805] 805,88 unequal: No Solution Exploring Operation: 35+23=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[25, 37], Operations: ['70/2=35', '2+35=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,88 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[25, 33], Operations: ['70/2=35', '35-2=33'] Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,88 unequal: No Solution Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[35, 27], Operations: ['70/2=35', '25+2=27'] Exploring Operation: 35-27=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 35+27=62, Resulting Numbers: [62] 62,88 unequal: No Solution Exploring Operation: 35*27=945, Resulting Numbers: [945] 945,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[70, 2, 23], Operations: ['25-2=23'] Exploring Operation: 70+2=72, Resulting Numbers: [23, 72] Generated Node #0,0,0: 88:[23, 72] Operation: 70+2=72 Exploring Operation: 70/2=35, Resulting Numbers: [23, 35] Generated Node #0,0,1: 88:[23, 35] Operation: 70/2=35 Exploring Operation: 23-2=21, Resulting Numbers: [70, 21] Generated Node #0,0,2: 88:[70, 21] Operation: 23-2=21 Exploring Operation: 70+23=93, Resulting Numbers: [2, 93] Generated Node #0,0,3: 88:[2, 93] Operation: 70+23=93 Exploring Operation: 70-23=47, Resulting Numbers: [2, 47] Generated Node #0,0,4: 88:[2, 47] Operation: 70-23=47 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 88:[2, 47], Operations: ['25-2=23', '70-23=47'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 2*47=94, Resulting Numbers: [94] 94,88 unequal: No Solution Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 88:[2, 93], Operations: ['25-2=23', '70+23=93'] Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,88 unequal: No Solution Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,88 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[23, 35], Operations: ['25-2=23', '70/2=35'] Exploring Operation: 35-23=12, Resulting Numbers: [12] 12,88 unequal: No Solution Exploring Operation: 23+35=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 23*35=805, Resulting Numbers: [805] 805,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[23, 72], Operations: ['25-2=23', '70+2=72'] Exploring Operation: 23*72=1656, Resulting Numbers: [1656] 1656,88 unequal: No Solution Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 23+72=95, Resulting Numbers: [95] 95,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 88:[70, 21], Operations: ['25-2=23', '23-2=21'] Exploring Operation: 70+21=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 70-21=49, Resulting Numbers: [49] 49,88 unequal: No Solution Exploring Operation: 70*21=1470, Resulting Numbers: [1470] 1470,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 2, 62, 6, 32 ]
18
[ "2*6=12", "62-32=30", "30-12=18" ]
Current State: 18:[2, 62, 6, 32], Operations: [] Exploring Operation: 2*6=12, Resulting Numbers: [62, 32, 12] Generated Node #2: [62, 32, 12] from Operation: 2*6=12 Current State: 18:[62, 32, 12], Operations: ['2*6=12'] Exploring Operation: 62-32=30, Resulting Numbers: [12, 30] Generated Node #3: [12, 30] from Operation: 62-32=30 Current State: 18:[12, 30], Operations: ['2*6=12', '62-32=30'] Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[2, 62, 6, 32], Operations: [] Exploring Operation: 62-32=30, Resulting Numbers: [2, 6, 30] Generated Node #0,0: 18:[2, 6, 30] Operation: 62-32=30 Exploring Operation: 32/2=16, Resulting Numbers: [62, 6, 16] Generated Node #0,1: 18:[62, 6, 16] Operation: 32/2=16 Exploring Operation: 62/2=31, Resulting Numbers: [6, 32, 31] Generated Node #0,2: 18:[6, 32, 31] Operation: 62/2=31 Exploring Operation: 62-6=56, Resulting Numbers: [2, 32, 56] Generated Node #0,3: 18:[2, 32, 56] Operation: 62-6=56 Moving to Node #0,0 Current State: 18:[2, 6, 30], Operations: ['62-32=30'] Exploring Operation: 30-6=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 18:[2, 24] Operation: 30-6=24 Exploring Operation: 30/2=15, Resulting Numbers: [6, 15] Generated Node #0,0,1: 18:[6, 15] Operation: 30/2=15 Exploring Operation: 30-2=28, Resulting Numbers: [6, 28] Generated Node #0,0,2: 18:[6, 28] Operation: 30-2=28 Exploring Operation: 30/6=5, Resulting Numbers: [2, 5] Generated Node #0,0,3: 18:[2, 5] Operation: 30/6=5 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[2, 5], Operations: ['62-32=30', '30/6=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[6, 15], Operations: ['62-32=30', '30/2=15'] Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,18 unequal: No Solution Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[2, 24], Operations: ['62-32=30', '30-6=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[6, 28], Operations: ['62-32=30', '30-2=28'] Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,18 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 6*28=168, Resulting Numbers: [168] 168,18 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:[6, 32, 31], Operations: ['62/2=31'] Exploring Operation: 32-6=26, Resulting Numbers: [31, 26] Generated Node #0,2,0: 18:[31, 26] Operation: 32-6=26 Exploring Operation: 32-31=1, Resulting Numbers: [6, 1] Generated Node #0,2,1: 18:[6, 1] Operation: 32-31=1 Exploring Operation: 6+32=38, Resulting Numbers: [31, 38] Generated Node #0,2,2: 18:[31, 38] Operation: 6+32=38 Exploring Operation: 31-6=25, Resulting Numbers: [32, 25] Generated Node #0,2,3: 18:[32, 25] Operation: 31-6=25 Moving to Node #0,1 Current State: 18:[62, 6, 16], Operations: ['32/2=16'] Exploring Operation: 62-16=46, Resulting Numbers: [6, 46] Generated Node #0,1,0: 18:[6, 46] Operation: 62-16=46 Exploring Operation: 16-6=10, Resulting Numbers: [62, 10] Generated Node #0,1,1: 18:[62, 10] Operation: 16-6=10 Exploring Operation: 6+16=22, Resulting Numbers: [62, 22] Generated Node #0,1,2: 18:[62, 22] Operation: 6+16=22 Exploring Operation: 62-6=56, Resulting Numbers: [16, 56] Generated Node #0,1,3: 18:[16, 56] Operation: 62-6=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[6, 46], Operations: ['32/2=16', '62-16=46'] Exploring Operation: 6*46=276, Resulting Numbers: [276] 276,18 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 6+46=52, Resulting Numbers: [52] 52,18 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:[16, 56], Operations: ['32/2=16', '62-6=56'] Exploring Operation: 16*56=896, Resulting Numbers: [896] 896,18 unequal: No Solution Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,18 unequal: No Solution Exploring Operation: 16+56=72, Resulting Numbers: [72] 72,18 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:[62, 10], Operations: ['32/2=16', '16-6=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 62*10=620, Resulting Numbers: [620] 620,18 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 #0,1,2 Current State: 18:[62, 22], Operations: ['32/2=16', '6+16=22'] Exploring Operation: 62+22=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 62*22=1364, Resulting Numbers: [1364] 1364,18 unequal: No Solution Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 18:[2, 32, 56], Operations: ['62-6=56'] Exploring Operation: 32-2=30, Resulting Numbers: [56, 30] Generated Node #0,3,0: 18:[56, 30] Operation: 32-2=30 Exploring Operation: 56-32=24, Resulting Numbers: [2, 24] Generated Node #0,3,1: 18:[2, 24] Operation: 56-32=24 Exploring Operation: 56/2=28, Resulting Numbers: [32, 28] Generated Node #0,3,2: 18:[32, 28] Operation: 56/2=28 Exploring Operation: 32/2=16, Resulting Numbers: [56, 16] Generated Node #0,3,3: 18:[56, 16] Operation: 32/2=16 Moving to Node #0,2,1 Current State: 18:[6, 1], Operations: ['62/2=31', '32-31=1'] Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[2, 24], Operations: ['62-6=56', '56-32=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,18 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[32, 25], Operations: ['62/2=31', '31-6=25'] Exploring Operation: 32*25=800, Resulting Numbers: [800] 800,18 unequal: No Solution Exploring Operation: 32+25=57, Resulting Numbers: [57] 57,18 unequal: No Solution Exploring Operation: 32-25=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[31, 26], Operations: ['62/2=31', '32-6=26'] Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,18 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,18 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[32, 28], Operations: ['62-6=56', '56/2=28'] Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 32*28=896, Resulting Numbers: [896] 896,18 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[31, 38], Operations: ['62/2=31', '6+32=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,18 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[56, 16], Operations: ['62-6=56', '32/2=16'] Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 56*16=896, Resulting Numbers: [896] 896,18 unequal: No Solution Exploring Operation: 56-16=40, Resulting Numbers: [40] 40,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[56, 30], Operations: ['62-6=56', '32-2=30'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,18 unequal: No Solution Exploring Operation: 56*30=1680, Resulting Numbers: [1680] 1680,18 unequal: No Solution Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 66, 69, 87, 59 ]
88
[ "69-66=3", "87/3=29", "59+29=88" ]
Current State: 88:[66, 69, 87, 59], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [87, 59, 3] Generated Node #2: [87, 59, 3] from Operation: 69-66=3 Current State: 88:[87, 59, 3], Operations: ['69-66=3'] Exploring Operation: 87/3=29, Resulting Numbers: [59, 29] Generated Node #3: [59, 29] from Operation: 87/3=29 Current State: 88:[59, 29], Operations: ['69-66=3', '87/3=29'] Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[66, 69, 87, 59], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [87, 59, 3] Generated Node #0,0: 88:[87, 59, 3] Operation: 69-66=3 Exploring Operation: 66-59=7, Resulting Numbers: [69, 87, 7] Generated Node #0,1: 88:[69, 87, 7] Operation: 66-59=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[87, 59, 3], Operations: ['69-66=3'] Exploring Operation: 59-3=56, Resulting Numbers: [87, 56] Generated Node #0,0,0: 88:[87, 56] Operation: 59-3=56 Exploring Operation: 87-59=28, Resulting Numbers: [3, 28] Generated Node #0,0,1: 88:[3, 28] Operation: 87-59=28 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 88:[3, 28], Operations: ['69-66=3', '87-59=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[87, 56], Operations: ['69-66=3', '59-3=56'] Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,88 unequal: No Solution Exploring Operation: 87+56=143, Resulting Numbers: [143] 143,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[69, 87, 7], Operations: ['66-59=7'] Exploring Operation: 69+7=76, Resulting Numbers: [87, 76] Generated Node #0,1,0: 88:[87, 76] Operation: 69+7=76 Exploring Operation: 87-69=18, Resulting Numbers: [7, 18] Generated Node #0,1,1: 88:[7, 18] Operation: 87-69=18 Moving to Node #0,1,1 Current State: 88:[7, 18], Operations: ['66-59=7', '87-69=18'] Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[87, 76], Operations: ['66-59=7', '69+7=76'] Exploring Operation: 87+76=163, Resulting Numbers: [163] 163,88 unequal: No Solution Exploring Operation: 87-76=11, Resulting Numbers: [11] 11,88 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
[ 40, 84, 61, 80 ]
17
[ "40+84=124", "61+80=141", "141-124=17" ]
Current State: 17:[40, 84, 61, 80], Operations: [] Exploring Operation: 40+84=124, Resulting Numbers: [61, 80, 124] Generated Node #2: [61, 80, 124] from Operation: 40+84=124 Current State: 17:[61, 80, 124], Operations: ['40+84=124'] Exploring Operation: 61+80=141, Resulting Numbers: [124, 141] Generated Node #3: [124, 141] from Operation: 61+80=141 Current State: 17:[124, 141], Operations: ['40+84=124', '61+80=141'] Exploring Operation: 141-124=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[40, 84, 61, 80], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [40, 61, 4] Generated Node #0,0: 17:[40, 61, 4] Operation: 84-80=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[40, 61, 4], Operations: ['84-80=4'] Exploring Operation: 61-40=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 61-40=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['84-80=4', '61-40=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[40, 84, 61, 80], Operations: [] Exploring Operation: 84-80=4, Resulting Numbers: [40, 61, 4] Generated Node #0,0: 17:[40, 61, 4] Operation: 84-80=4 Moving to Node #0,0 Current State: 17:[40, 61, 4], Operations: ['84-80=4'] Exploring Operation: 61-40=21, Resulting Numbers: [4, 21] Generated Node #0,0,0: 17:[4, 21] Operation: 61-40=21 Moving to Node #0,0,0 Current State: 17:[4, 21], Operations: ['84-80=4', '61-40=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 27, 8, 19, 87 ]
22
[ "8+87=95", "95/19=5", "27-5=22" ]
Current State: 22:[27, 8, 19, 87], Operations: [] Exploring Operation: 8+87=95, Resulting Numbers: [27, 19, 95] Generated Node #2: [27, 19, 95] from Operation: 8+87=95 Current State: 22:[27, 19, 95], Operations: ['8+87=95'] Exploring Operation: 95/19=5, Resulting Numbers: [27, 5] Generated Node #3: [27, 5] from Operation: 95/19=5 Current State: 22:[27, 5], Operations: ['8+87=95', '95/19=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[27, 8, 19, 87], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [8, 19, 60] Generated Node #0,0: 22:[8, 19, 60] Operation: 87-27=60 Exploring Operation: 87-8=79, Resulting Numbers: [27, 19, 79] Generated Node #0,1: 22:[27, 19, 79] Operation: 87-8=79 Exploring Operation: 87-19=68, Resulting Numbers: [27, 8, 68] Generated Node #0,2: 22:[27, 8, 68] Operation: 87-19=68 Moving to Node #0,0 Current State: 22:[8, 19, 60], Operations: ['87-27=60'] Exploring Operation: 60-19=41, Resulting Numbers: [8, 41] Generated Node #0,0,0: 22:[8, 41] Operation: 60-19=41 Exploring Operation: 19-8=11, Resulting Numbers: [60, 11] Generated Node #0,0,1: 22:[60, 11] Operation: 19-8=11 Exploring Operation: 60-8=52, Resulting Numbers: [19, 52] Generated Node #0,0,2: 22:[19, 52] Operation: 60-8=52 Moving to Node #0,2 Current State: 22:[27, 8, 68], Operations: ['87-19=68'] Exploring Operation: 68-8=60, Resulting Numbers: [27, 60] Generated Node #0,2,0: 22:[27, 60] Operation: 68-8=60 Exploring Operation: 27-8=19, Resulting Numbers: [68, 19] Generated Node #0,2,1: 22:[68, 19] Operation: 27-8=19 Exploring Operation: 68-27=41, Resulting Numbers: [8, 41] Generated Node #0,2,2: 22:[8, 41] Operation: 68-27=41 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[8, 41], Operations: ['87-19=68', '68-27=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,22 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,22 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,22 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 #0,2,0 Current State: 22:[27, 60], Operations: ['87-19=68', '68-8=60'] Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 27*60=1620, Resulting Numbers: [1620] 1620,22 unequal: No Solution Exploring Operation: 27+60=87, Resulting Numbers: [87] 87,22 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:[68, 19], Operations: ['87-19=68', '27-8=19'] Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,22 unequal: No Solution Exploring Operation: 68+19=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 68*19=1292, Resulting Numbers: [1292] 1292,22 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:[27, 19, 79], Operations: ['87-8=79'] Exploring Operation: 79-19=60, Resulting Numbers: [27, 60] Generated Node #0,1,0: 22:[27, 60] Operation: 79-19=60 Exploring Operation: 27-19=8, Resulting Numbers: [79, 8] Generated Node #0,1,1: 22:[79, 8] Operation: 27-19=8 Exploring Operation: 79-27=52, Resulting Numbers: [19, 52] Generated Node #0,1,2: 22:[19, 52] Operation: 79-27=52 Moving to Node #0,0,0 Current State: 22:[8, 41], Operations: ['87-27=60', '60-19=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,22 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[19, 52], Operations: ['87-27=60', '60-8=52'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,22 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[19, 52], Operations: ['87-8=79', '79-27=52'] Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,22 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[60, 11], Operations: ['87-27=60', '19-8=11'] Exploring Operation: 60+11=71, Resulting Numbers: [71] 71,22 unequal: No Solution Exploring Operation: 60*11=660, Resulting Numbers: [660] 660,22 unequal: No Solution Exploring Operation: 60-11=49, Resulting Numbers: [49] 49,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[27, 60], Operations: ['87-8=79', '79-19=60'] Exploring Operation: 27+60=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 27*60=1620, Resulting Numbers: [1620] 1620,22 unequal: No Solution Exploring Operation: 60-27=33, Resulting Numbers: [33] 33,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[79, 8], Operations: ['87-8=79', '27-19=8'] Exploring Operation: 79-8=71, Resulting Numbers: [71] 71,22 unequal: No Solution Exploring Operation: 79+8=87, Resulting Numbers: [87] 87,22 unequal: No Solution Exploring Operation: 79*8=632, Resulting Numbers: [632] 632,22 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 44, 89, 15, 51 ]
21
[ "89-44=45", "15+51=66", "66-45=21" ]
Current State: 21:[44, 89, 15, 51], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [15, 51, 45] Generated Node #2: [15, 51, 45] from Operation: 89-44=45 Current State: 21:[15, 51, 45], Operations: ['89-44=45'] Exploring Operation: 15+51=66, Resulting Numbers: [45, 66] Generated Node #3: [45, 66] from Operation: 15+51=66 Current State: 21:[45, 66], Operations: ['89-44=45', '15+51=66'] Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[44, 89, 15, 51], Operations: [] Exploring Operation: 89-44=45, Resulting Numbers: [15, 51, 45] Generated Node #0,0: 21:[15, 51, 45] Operation: 89-44=45 Exploring Operation: 44-15=29, Resulting Numbers: [89, 51, 29] Generated Node #0,1: 21:[89, 51, 29] Operation: 44-15=29 Exploring Operation: 89-51=38, Resulting Numbers: [44, 15, 38] Generated Node #0,2: 21:[44, 15, 38] Operation: 89-51=38 Exploring Operation: 89-15=74, Resulting Numbers: [44, 51, 74] Generated Node #0,3: 21:[44, 51, 74] Operation: 89-15=74 Exploring Operation: 51-44=7, Resulting Numbers: [89, 15, 7] Generated Node #0,4: 21:[89, 15, 7] Operation: 51-44=7 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[44, 15, 38], Operations: ['89-51=38'] Exploring Operation: 44-15=29, Resulting Numbers: [38, 29] Generated Node #0,2,0: 21:[38, 29] Operation: 44-15=29 Exploring Operation: 44-38=6, Resulting Numbers: [15, 6] Generated Node #0,2,1: 21:[15, 6] Operation: 44-38=6 Exploring Operation: 15+38=53, Resulting Numbers: [44, 53] Generated Node #0,2,2: 21:[44, 53] Operation: 15+38=53 Exploring Operation: 38-15=23, Resulting Numbers: [44, 23] Generated Node #0,2,3: 21:[44, 23] Operation: 38-15=23 Exploring Operation: 44+15=59, Resulting Numbers: [38, 59] Generated Node #0,2,4: 21:[38, 59] Operation: 44+15=59 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[15, 6], Operations: ['89-51=38', '44-38=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[44, 89, 15, 51], Operations: [] Exploring Operation: 89-51=38, Resulting Numbers: [44, 15, 38] Generated Node #0,2: 21:[44, 15, 38] Operation: 89-51=38 Moving to Node #0,2 Current State: 21:[44, 15, 38], Operations: ['89-51=38'] Exploring Operation: 44-38=6, Resulting Numbers: [15, 6] Generated Node #0,2,1: 21:[15, 6] Operation: 44-38=6 Moving to Node #0,2,1 Current State: 21:[15, 6], Operations: ['89-51=38', '44-38=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 11, 82, 42, 2 ]
92
[ "82-11=71", "42/2=21", "71+21=92" ]
Current State: 92:[11, 82, 42, 2], Operations: [] Exploring Operation: 82-11=71, Resulting Numbers: [42, 2, 71] Generated Node #2: [42, 2, 71] from Operation: 82-11=71 Current State: 92:[42, 2, 71], Operations: ['82-11=71'] Exploring Operation: 42/2=21, Resulting Numbers: [71, 21] Generated Node #3: [71, 21] from Operation: 42/2=21 Current State: 92:[71, 21], Operations: ['82-11=71', '42/2=21'] Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[11, 82, 42, 2], Operations: [] Exploring Operation: 11+42=53, Resulting Numbers: [82, 2, 53] Generated Node #0,0: 92:[82, 2, 53] Operation: 11+42=53 Exploring Operation: 11+82=93, Resulting Numbers: [42, 2, 93] Generated Node #0,1: 92:[42, 2, 93] Operation: 11+82=93 Exploring Operation: 82/2=41, Resulting Numbers: [11, 42, 41] Generated Node #0,2: 92:[11, 42, 41] Operation: 82/2=41 Exploring Operation: 11*2=22, Resulting Numbers: [82, 42, 22] Generated Node #0,3: 92:[82, 42, 22] Operation: 11*2=22 Exploring Operation: 82-42=40, Resulting Numbers: [11, 2, 40] Generated Node #0,4: 92:[11, 2, 40] Operation: 82-42=40 Moving to Node #0,1 Current State: 92:[42, 2, 93], Operations: ['11+82=93'] Exploring Operation: 93-2=91, Resulting Numbers: [42, 91] Generated Node #0,1,0: 92:[42, 91] Operation: 93-2=91 Exploring Operation: 42+2=44, Resulting Numbers: [93, 44] Generated Node #0,1,1: 92:[93, 44] Operation: 42+2=44 Exploring Operation: 42/2=21, Resulting Numbers: [93, 21] Generated Node #0,1,2: 92:[93, 21] Operation: 42/2=21 Exploring Operation: 42-2=40, Resulting Numbers: [93, 40] Generated Node #0,1,3: 92:[93, 40] Operation: 42-2=40 Exploring Operation: 93-42=51, Resulting Numbers: [2, 51] Generated Node #0,1,4: 92:[2, 51] Operation: 93-42=51 Moving to Node #0,4 Current State: 92:[11, 2, 40], Operations: ['82-42=40'] Exploring Operation: 40/2=20, Resulting Numbers: [11, 20] Generated Node #0,4,0: 92:[11, 20] Operation: 40/2=20 Exploring Operation: 11+40=51, Resulting Numbers: [2, 51] Generated Node #0,4,1: 92:[2, 51] Operation: 11+40=51 Exploring Operation: 11-2=9, Resulting Numbers: [40, 9] Generated Node #0,4,2: 92:[40, 9] Operation: 11-2=9 Exploring Operation: 11*2=22, Resulting Numbers: [40, 22] Generated Node #0,4,3: 92:[40, 22] Operation: 11*2=22 Exploring Operation: 40-11=29, Resulting Numbers: [2, 29] Generated Node #0,4,4: 92:[2, 29] Operation: 40-11=29 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 92:[2, 51], Operations: ['82-42=40', '11+40=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,92 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,92 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 92:[2, 29], Operations: ['82-42=40', '40-11=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 92:[40, 22], Operations: ['82-42=40', '11*2=22'] Exploring Operation: 40*22=880, Resulting Numbers: [880] 880,92 unequal: No Solution Exploring Operation: 40+22=62, Resulting Numbers: [62] 62,92 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 92:[11, 20], Operations: ['82-42=40', '40/2=20'] Exploring Operation: 11*20=220, Resulting Numbers: [220] 220,92 unequal: No Solution Exploring Operation: 11+20=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 92:[40, 9], Operations: ['82-42=40', '11-2=9'] Exploring Operation: 40*9=360, Resulting Numbers: [360] 360,92 unequal: No Solution Exploring Operation: 40+9=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 40-9=31, Resulting Numbers: [31] 31,92 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: 92:[82, 42, 22], Operations: ['11*2=22'] Exploring Operation: 82-22=60, Resulting Numbers: [42, 60] Generated Node #0,3,0: 92:[42, 60] Operation: 82-22=60 Exploring Operation: 82-42=40, Resulting Numbers: [22, 40] Generated Node #0,3,1: 92:[22, 40] Operation: 82-42=40 Exploring Operation: 42-22=20, Resulting Numbers: [82, 20] Generated Node #0,3,2: 92:[82, 20] Operation: 42-22=20 Exploring Operation: 82+22=104, Resulting Numbers: [42, 104] Generated Node #0,3,3: 92:[42, 104] Operation: 82+22=104 Exploring Operation: 42+22=64, Resulting Numbers: [82, 64] Generated Node #0,3,4: 92:[82, 64] Operation: 42+22=64 Moving to Node #0,2 Current State: 92:[11, 42, 41], Operations: ['82/2=41'] Exploring Operation: 11+42=53, Resulting Numbers: [41, 53] Generated Node #0,2,0: 92:[41, 53] Operation: 11+42=53 Exploring Operation: 41-11=30, Resulting Numbers: [42, 30] Generated Node #0,2,1: 92:[42, 30] Operation: 41-11=30 Exploring Operation: 42-11=31, Resulting Numbers: [41, 31] Generated Node #0,2,2: 92:[41, 31] Operation: 42-11=31 Exploring Operation: 42-41=1, Resulting Numbers: [11, 1] Generated Node #0,2,3: 92:[11, 1] Operation: 42-41=1 Exploring Operation: 11+41=52, Resulting Numbers: [42, 52] Generated Node #0,2,4: 92:[42, 52] Operation: 11+41=52 Moving to Node #0,0 Current State: 92:[82, 2, 53], Operations: ['11+42=53'] Exploring Operation: 82-53=29, Resulting Numbers: [2, 29] Generated Node #0,0,0: 92:[2, 29] Operation: 82-53=29 Exploring Operation: 82-2=80, Resulting Numbers: [53, 80] Generated Node #0,0,1: 92:[53, 80] Operation: 82-2=80 Exploring Operation: 82/2=41, Resulting Numbers: [53, 41] Generated Node #0,0,2: 92:[53, 41] Operation: 82/2=41 Exploring Operation: 82+2=84, Resulting Numbers: [53, 84] Generated Node #0,0,3: 92:[53, 84] Operation: 82+2=84 Exploring Operation: 53-2=51, Resulting Numbers: [82, 51] Generated Node #0,0,4: 92:[82, 51] Operation: 53-2=51 Moving to Node #0,1,1 Current State: 92:[93, 44], Operations: ['11+82=93', '42+2=44'] Exploring Operation: 93+44=137, Resulting Numbers: [137] 137,92 unequal: No Solution Exploring Operation: 93-44=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 93*44=4092, Resulting Numbers: [4092] 4092,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[93, 21], Operations: ['11+82=93', '42/2=21'] Exploring Operation: 93*21=1953, Resulting Numbers: [1953] 1953,92 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 93+21=114, Resulting Numbers: [114] 114,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[42, 91], Operations: ['11+82=93', '93-2=91'] Exploring Operation: 42*91=3822, Resulting Numbers: [3822] 3822,92 unequal: No Solution Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 42+91=133, Resulting Numbers: [133] 133,92 unequal: No Solution Moving to Node #0,1,4 Current State: 92:[2, 51], Operations: ['11+82=93', '93-42=51'] Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,92 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,92 unequal: No Solution Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[2, 29], Operations: ['11+42=53', '82-53=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[22, 40], Operations: ['11*2=22', '82-42=40'] Exploring Operation: 22*40=880, Resulting Numbers: [880] 880,92 unequal: No Solution Exploring Operation: 22+40=62, Resulting Numbers: [62] 62,92 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[93, 40], Operations: ['11+82=93', '42-2=40'] Exploring Operation: 93+40=133, Resulting Numbers: [133] 133,92 unequal: No Solution Exploring Operation: 93-40=53, Resulting Numbers: [53] 53,92 unequal: No Solution Exploring Operation: 93*40=3720, Resulting Numbers: [3720] 3720,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[11, 1], Operations: ['82/2=41', '42-41=1'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11-1=10, Resulting Numbers: [10] 10,92 unequal: No Solution Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,92 unequal: No Solution Exploring Operation: 11+1=12, Resulting Numbers: [12] 12,92 unequal: No Solution Moving to Node #0,2,4 Current State: 92:[42, 52], Operations: ['82/2=41', '11+41=52'] Exploring Operation: 42*52=2184, Resulting Numbers: [2184] 2184,92 unequal: No Solution Exploring Operation: 52-42=10, Resulting Numbers: [10] 10,92 unequal: No Solution Exploring Operation: 42+52=94, Resulting Numbers: [94] 94,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[42, 30], Operations: ['82/2=41', '41-11=30'] Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,92 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,92 unequal: No Solution Moving to Node #0,2,0 Current State: 92:[41, 53], Operations: ['82/2=41', '11+42=53'] Exploring Operation: 41*53=2173, Resulting Numbers: [2173] 2173,92 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 41+53=94, Resulting Numbers: [94] 94,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[53, 41], Operations: ['11+42=53', '82/2=41'] Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,92 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,92 unequal: No Solution Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[41, 31], Operations: ['82/2=41', '42-11=31'] Exploring Operation: 41*31=1271, Resulting Numbers: [1271] 1271,92 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,92 unequal: No Solution Exploring Operation: 41+31=72, Resulting Numbers: [72] 72,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[82, 20], Operations: ['11*2=22', '42-22=20'] Exploring Operation: 82*20=1640, Resulting Numbers: [1640] 1640,92 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,92 unequal: No Solution Exploring Operation: 82+20=102, Resulting Numbers: [102] 102,92 unequal: No Solution Moving to Node #0,0,4 Current State: 92:[82, 51], Operations: ['11+42=53', '53-2=51'] Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 82+51=133, Resulting Numbers: [133] 133,92 unequal: No Solution Exploring Operation: 82*51=4182, Resulting Numbers: [4182] 4182,92 unequal: No Solution Moving to Node #0,0,3 Current State: 92:[53, 84], Operations: ['11+42=53', '82+2=84'] Exploring Operation: 53+84=137, Resulting Numbers: [137] 137,92 unequal: No Solution Exploring Operation: 84-53=31, Resulting Numbers: [31] 31,92 unequal: No Solution Exploring Operation: 53*84=4452, Resulting Numbers: [4452] 4452,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[42, 104], Operations: ['11*2=22', '82+22=104'] Exploring Operation: 42+104=146, Resulting Numbers: [146] 146,92 unequal: No Solution Exploring Operation: 104-42=62, Resulting Numbers: [62] 62,92 unequal: No Solution Exploring Operation: 42*104=4368, Resulting Numbers: [4368] 4368,92 unequal: No Solution Moving to Node #0,3,0 Current State: 92:[42, 60], Operations: ['11*2=22', '82-22=60'] Exploring Operation: 42*60=2520, Resulting Numbers: [2520] 2520,92 unequal: No Solution Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,92 unequal: No Solution Exploring Operation: 42+60=102, Resulting Numbers: [102] 102,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[53, 80], Operations: ['11+42=53', '82-2=80'] Exploring Operation: 53+80=133, Resulting Numbers: [133] 133,92 unequal: No Solution Exploring Operation: 80-53=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 53*80=4240, Resulting Numbers: [4240] 4240,92 unequal: No Solution Moving to Node #0,3,4 Current State: 92:[82, 64], Operations: ['11*2=22', '42+22=64'] Exploring Operation: 82+64=146, Resulting Numbers: [146] 146,92 unequal: No Solution Exploring Operation: 82*64=5248, Resulting Numbers: [5248] 5248,92 unequal: No Solution Exploring Operation: 82-64=18, Resulting Numbers: [18] 18,92 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 49, 65, 15, 10 ]
41
[ "65-49=16", "15+10=25", "16+25=41" ]
Current State: 41:[49, 65, 15, 10], Operations: [] Exploring Operation: 65-49=16, Resulting Numbers: [15, 10, 16] Generated Node #2: [15, 10, 16] from Operation: 65-49=16 Current State: 41:[15, 10, 16], Operations: ['65-49=16'] Exploring Operation: 15+10=25, Resulting Numbers: [16, 25] Generated Node #3: [16, 25] from Operation: 15+10=25 Current State: 41:[16, 25], Operations: ['65-49=16', '15+10=25'] Exploring Operation: 16+25=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[49, 65, 15, 10], Operations: [] Exploring Operation: 65-10=55, Resulting Numbers: [49, 15, 55] Generated Node #0,0: 41:[49, 15, 55] Operation: 65-10=55 Exploring Operation: 49-10=39, Resulting Numbers: [65, 15, 39] Generated Node #0,1: 41:[65, 15, 39] Operation: 49-10=39 Exploring Operation: 15+10=25, Resulting Numbers: [49, 65, 25] Generated Node #0,2: 41:[49, 65, 25] Operation: 15+10=25 Exploring Operation: 65-15=50, Resulting Numbers: [49, 10, 50] Generated Node #0,3: 41:[49, 10, 50] Operation: 65-15=50 Moving to Node #0,0 Current State: 41:[49, 15, 55], Operations: ['65-10=55'] Exploring Operation: 49+15=64, Resulting Numbers: [55, 64] Generated Node #0,0,0: 41:[55, 64] Operation: 49+15=64 Exploring Operation: 55-15=40, Resulting Numbers: [49, 40] Generated Node #0,0,1: 41:[49, 40] Operation: 55-15=40 Exploring Operation: 15+55=70, Resulting Numbers: [49, 70] Generated Node #0,0,2: 41:[49, 70] Operation: 15+55=70 Exploring Operation: 49-15=34, Resulting Numbers: [55, 34] Generated Node #0,0,3: 41:[55, 34] Operation: 49-15=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[49, 40], Operations: ['65-10=55', '55-15=40'] Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 41:[55, 34], Operations: ['65-10=55', '49-15=34'] Exploring Operation: 55*34=1870, Resulting Numbers: [1870] 1870,41 unequal: No Solution Exploring Operation: 55+34=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[55, 64], Operations: ['65-10=55', '49+15=64'] Exploring Operation: 55*64=3520, Resulting Numbers: [3520] 3520,41 unequal: No Solution Exploring Operation: 55+64=119, Resulting Numbers: [119] 119,41 unequal: No Solution Exploring Operation: 64-55=9, Resulting Numbers: [9] 9,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[49, 70], Operations: ['65-10=55', '15+55=70'] Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,41 unequal: No Solution Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,41 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: 41:[49, 10, 50], Operations: ['65-15=50'] Exploring Operation: 10+50=60, Resulting Numbers: [49, 60] Generated Node #0,3,0: 41:[49, 60] Operation: 10+50=60 Exploring Operation: 50-10=40, Resulting Numbers: [49, 40] Generated Node #0,3,1: 41:[49, 40] Operation: 50-10=40 Exploring Operation: 49-10=39, Resulting Numbers: [50, 39] Generated Node #0,3,2: 41:[50, 39] Operation: 49-10=39 Exploring Operation: 49+10=59, Resulting Numbers: [50, 59] Generated Node #0,3,3: 41:[50, 59] Operation: 49+10=59 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[49, 40], Operations: ['65-15=50', '50-10=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[50, 39], Operations: ['65-15=50', '49-10=39'] Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 50*39=1950, Resulting Numbers: [1950] 1950,41 unequal: No Solution Exploring Operation: 50+39=89, Resulting Numbers: [89] 89,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[49, 60], Operations: ['65-15=50', '10+50=60'] Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,41 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 41:[50, 59], Operations: ['65-15=50', '49+10=59'] Exploring Operation: 50*59=2950, Resulting Numbers: [2950] 2950,41 unequal: No Solution Exploring Operation: 50+59=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 59-50=9, Resulting Numbers: [9] 9,41 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: 41:[49, 65, 25], Operations: ['15+10=25'] Exploring Operation: 49+25=74, Resulting Numbers: [65, 74] Generated Node #0,2,0: 41:[65, 74] Operation: 49+25=74 Exploring Operation: 65-49=16, Resulting Numbers: [25, 16] Generated Node #0,2,1: 41:[25, 16] Operation: 65-49=16 Exploring Operation: 65-25=40, Resulting Numbers: [49, 40] Generated Node #0,2,2: 41:[49, 40] Operation: 65-25=40 Exploring Operation: 49-25=24, Resulting Numbers: [65, 24] Generated Node #0,2,3: 41:[65, 24] Operation: 49-25=24 Moving to Node #0,1 Current State: 41:[65, 15, 39], Operations: ['49-10=39'] Exploring Operation: 15+39=54, Resulting Numbers: [65, 54] Generated Node #0,1,0: 41:[65, 54] Operation: 15+39=54 Exploring Operation: 65+15=80, Resulting Numbers: [39, 80] Generated Node #0,1,1: 41:[39, 80] Operation: 65+15=80 Exploring Operation: 65-15=50, Resulting Numbers: [39, 50] Generated Node #0,1,2: 41:[39, 50] Operation: 65-15=50 Exploring Operation: 65-39=26, Resulting Numbers: [15, 26] Generated Node #0,1,3: 41:[15, 26] Operation: 65-39=26 Moving to Node #0,2,2 Current State: 41:[49, 40], Operations: ['15+10=25', '65-25=40'] Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[39, 50], Operations: ['49-10=39', '65-15=50'] Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 39*50=1950, Resulting Numbers: [1950] 1950,41 unequal: No Solution Exploring Operation: 39+50=89, Resulting Numbers: [89] 89,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[65, 54], Operations: ['49-10=39', '15+39=54'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 65+54=119, Resulting Numbers: [119] 119,41 unequal: No Solution Exploring Operation: 65*54=3510, Resulting Numbers: [3510] 3510,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[65, 24], Operations: ['15+10=25', '49-25=24'] Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,41 unequal: No Solution Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,41 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[49, 65, 15, 10], Operations: [] Exploring Operation: 15+10=25, Resulting Numbers: [49, 65, 25] Generated Node #0,2: 41:[49, 65, 25] Operation: 15+10=25 Moving to Node #0,2 Current State: 41:[49, 65, 25], Operations: ['15+10=25'] Exploring Operation: 49-25=24, Resulting Numbers: [65, 24] Generated Node #0,2,3: 41:[65, 24] Operation: 49-25=24 Moving to Node #0,2,3 Current State: 41:[65, 24], Operations: ['15+10=25', '49-25=24'] Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
0.947917
hs_4
mult_heuristic
[ 4, 1, 82, 29 ]
75
[ "29-1=28", "28/4=7", "82-7=75" ]
Current State: 75:[4, 1, 82, 29], Operations: [] Exploring Operation: 29-1=28, Resulting Numbers: [4, 82, 28] Generated Node #2: [4, 82, 28] from Operation: 29-1=28 Current State: 75:[4, 82, 28], Operations: ['29-1=28'] Exploring Operation: 28/4=7, Resulting Numbers: [82, 7] Generated Node #3: [82, 7] from Operation: 28/4=7 Current State: 75:[82, 7], Operations: ['29-1=28', '28/4=7'] Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[4, 1, 82, 29], Operations: [] Exploring Operation: 82-4=78, Resulting Numbers: [1, 29, 78] Generated Node #0,0: 75:[1, 29, 78] Operation: 82-4=78 Moving to Node #0,0 Current State: 75:[1, 29, 78], Operations: ['82-4=78'] Exploring Operation: 29-1=28, Resulting Numbers: [78, 28] Generated Node #0,0,0: 75:[78, 28] Operation: 29-1=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[78, 28], Operations: ['82-4=78', '29-1=28'] Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,75 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
[ 31, 84, 7, 54 ]
73
[ "31+54=85", "84/7=12", "85-12=73" ]
Current State: 73:[31, 84, 7, 54], Operations: [] Exploring Operation: 31+54=85, Resulting Numbers: [84, 7, 85] Generated Node #2: [84, 7, 85] from Operation: 31+54=85 Current State: 73:[84, 7, 85], Operations: ['31+54=85'] Exploring Operation: 84/7=12, Resulting Numbers: [85, 12] Generated Node #3: [85, 12] from Operation: 84/7=12 Current State: 73:[85, 12], Operations: ['31+54=85', '84/7=12'] Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[31, 84, 7, 54], Operations: [] Exploring Operation: 31+7=38, Resulting Numbers: [84, 54, 38] Generated Node #0,0: 73:[84, 54, 38] Operation: 31+7=38 Exploring Operation: 7+54=61, Resulting Numbers: [31, 84, 61] Generated Node #0,1: 73:[31, 84, 61] Operation: 7+54=61 Exploring Operation: 84-7=77, Resulting Numbers: [31, 54, 77] Generated Node #0,2: 73:[31, 54, 77] Operation: 84-7=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[84, 54, 38], Operations: ['31+7=38'] Exploring Operation: 84+38=122, Resulting Numbers: [54, 122] Generated Node #0,0,0: 73:[54, 122] Operation: 84+38=122 Exploring Operation: 54+38=92, Resulting Numbers: [84, 92] Generated Node #0,0,1: 73:[84, 92] Operation: 54+38=92 Exploring Operation: 84-38=46, Resulting Numbers: [54, 46] Generated Node #0,0,2: 73:[54, 46] Operation: 84-38=46 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[84, 92], Operations: ['31+7=38', '54+38=92'] Exploring Operation: 84+92=176, Resulting Numbers: [176] 176,73 unequal: No Solution Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 84*92=7728, Resulting Numbers: [7728] 7728,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[54, 46], Operations: ['31+7=38', '84-38=46'] Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,73 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[54, 122], Operations: ['31+7=38', '84+38=122'] Exploring Operation: 54*122=6588, Resulting Numbers: [6588] 6588,73 unequal: No Solution Exploring Operation: 54+122=176, Resulting Numbers: [176] 176,73 unequal: No Solution Exploring Operation: 122-54=68, Resulting Numbers: [68] 68,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[31, 84, 61], Operations: ['7+54=61'] Exploring Operation: 31+84=115, Resulting Numbers: [61, 115] Generated Node #0,1,0: 73:[61, 115] Operation: 31+84=115 Exploring Operation: 84-31=53, Resulting Numbers: [61, 53] Generated Node #0,1,1: 73:[61, 53] Operation: 84-31=53 Exploring Operation: 31+61=92, Resulting Numbers: [84, 92] Generated Node #0,1,2: 73:[84, 92] Operation: 31+61=92 Moving to Node #0,1,2 Current State: 73:[84, 92], Operations: ['7+54=61', '31+61=92'] Exploring Operation: 92-84=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 84+92=176, Resulting Numbers: [176] 176,73 unequal: No Solution Exploring Operation: 84*92=7728, Resulting Numbers: [7728] 7728,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[61, 53], Operations: ['7+54=61', '84-31=53'] Exploring Operation: 61-53=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 61+53=114, Resulting Numbers: [114] 114,73 unequal: No Solution Exploring Operation: 61*53=3233, Resulting Numbers: [3233] 3233,73 unequal: No Solution Moving to Node #0,1,0 Current State: 73:[61, 115], Operations: ['7+54=61', '31+84=115'] Exploring Operation: 115-61=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 61+115=176, Resulting Numbers: [176] 176,73 unequal: No Solution Exploring Operation: 61*115=7015, Resulting Numbers: [7015] 7015,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[31, 54, 77], Operations: ['84-7=77'] Exploring Operation: 77-31=46, Resulting Numbers: [54, 46] Generated Node #0,2,0: 73:[54, 46] Operation: 77-31=46 Exploring Operation: 31+54=85, Resulting Numbers: [77, 85] Generated Node #0,2,1: 73:[77, 85] Operation: 31+54=85 Exploring Operation: 54-31=23, Resulting Numbers: [77, 23] Generated Node #0,2,2: 73:[77, 23] Operation: 54-31=23 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 73:[77, 85], Operations: ['84-7=77', '31+54=85'] Exploring Operation: 85-77=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 77+85=162, Resulting Numbers: [162] 162,73 unequal: No Solution Exploring Operation: 77*85=6545, Resulting Numbers: [6545] 6545,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 73:[54, 46], Operations: ['84-7=77', '77-31=46'] Exploring Operation: 54*46=2484, Resulting Numbers: [2484] 2484,73 unequal: No Solution Exploring Operation: 54-46=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 54+46=100, Resulting Numbers: [100] 100,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 73:[77, 23], Operations: ['84-7=77', '54-31=23'] Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 77+23=100, Resulting Numbers: [100] 100,73 unequal: No Solution Exploring Operation: 77*23=1771, Resulting Numbers: [1771] 1771,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 25, 76, 75, 82 ]
18
[ "75/25=3", "82-76=6", "3*6=18" ]
Current State: 18:[25, 76, 75, 82], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [76, 82, 3] Generated Node #2: [76, 82, 3] from Operation: 75/25=3 Current State: 18:[76, 82, 3], Operations: ['75/25=3'] Exploring Operation: 82-76=6, Resulting Numbers: [3, 6] Generated Node #3: [3, 6] from Operation: 82-76=6 Current State: 18:[3, 6], Operations: ['75/25=3', '82-76=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[25, 76, 75, 82], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [76, 82, 3] Generated Node #0,0: 18:[76, 82, 3] Operation: 75/25=3 Exploring Operation: 76-75=1, Resulting Numbers: [25, 82, 1] Generated Node #0,1: 18:[25, 82, 1] Operation: 76-75=1 Exploring Operation: 82-75=7, Resulting Numbers: [25, 76, 7] Generated Node #0,2: 18:[25, 76, 7] Operation: 82-75=7 Exploring Operation: 76-25=51, Resulting Numbers: [75, 82, 51] Generated Node #0,3: 18:[75, 82, 51] Operation: 76-25=51 Exploring Operation: 82-76=6, Resulting Numbers: [25, 75, 6] Generated Node #0,4: 18:[25, 75, 6] Operation: 82-76=6 Start Sub Search at level 1: Moving to Node #0,4 Current State: 18:[25, 75, 6], Operations: ['82-76=6'] Exploring Operation: 75-6=69, Resulting Numbers: [25, 69] Generated Node #0,4,0: 18:[25, 69] Operation: 75-6=69 Exploring Operation: 75-25=50, Resulting Numbers: [6, 50] Generated Node #0,4,1: 18:[6, 50] Operation: 75-25=50 Exploring Operation: 25-6=19, Resulting Numbers: [75, 19] Generated Node #0,4,2: 18:[75, 19] Operation: 25-6=19 Exploring Operation: 75/25=3, Resulting Numbers: [6, 3] Generated Node #0,4,3: 18:[6, 3] Operation: 75/25=3 Exploring Operation: 25+6=31, Resulting Numbers: [75, 31] Generated Node #0,4,4: 18:[75, 31] Operation: 25+6=31 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 18:[6, 3], Operations: ['82-76=6', '75/25=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,18 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[25, 76, 75, 82], Operations: [] Exploring Operation: 82-76=6, Resulting Numbers: [25, 75, 6] Generated Node #0,4: 18:[25, 75, 6] Operation: 82-76=6 Moving to Node #0,4 Current State: 18:[25, 75, 6], Operations: ['82-76=6'] Exploring Operation: 75/25=3, Resulting Numbers: [6, 3] Generated Node #0,4,3: 18:[6, 3] Operation: 75/25=3 Moving to Node #0,4,3 Current State: 18:[6, 3], Operations: ['82-76=6', '75/25=3'] Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 8, 20, 81, 63 ]
45
[ "81-63=18", "20*18=360", "360/8=45" ]
Current State: 45:[8, 20, 81, 63], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [8, 20, 18] Generated Node #2: [8, 20, 18] from Operation: 81-63=18 Current State: 45:[8, 20, 18], Operations: ['81-63=18'] Exploring Operation: 20*18=360, Resulting Numbers: [8, 360] Generated Node #3: [8, 360] from Operation: 20*18=360 Current State: 45:[8, 360], Operations: ['81-63=18', '20*18=360'] Exploring Operation: 360/8=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[8, 20, 81, 63], Operations: [] Exploring Operation: 81-63=18, Resulting Numbers: [8, 20, 18] Generated Node #0,0: 45:[8, 20, 18] Operation: 81-63=18 Moving to Node #0,0 Current State: 45:[8, 20, 18], Operations: ['81-63=18'] Exploring Operation: 20-18=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 45:[8, 2] Operation: 20-18=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[8, 2], Operations: ['81-63=18', '20-18=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,45 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
[ 5, 24, 3, 2 ]
47
[ "24-3=21", "2*21=42", "5+42=47" ]
Current State: 47:[5, 24, 3, 2], Operations: [] Exploring Operation: 24-3=21, Resulting Numbers: [5, 2, 21] Generated Node #2: [5, 2, 21] from Operation: 24-3=21 Current State: 47:[5, 2, 21], Operations: ['24-3=21'] Exploring Operation: 2*21=42, Resulting Numbers: [5, 42] Generated Node #3: [5, 42] from Operation: 2*21=42 Current State: 47:[5, 42], Operations: ['24-3=21', '2*21=42'] Exploring Operation: 5+42=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[5, 24, 3, 2], Operations: [] Exploring Operation: 5*2=10, Resulting Numbers: [24, 3, 10] Generated Node #0,0: 47:[24, 3, 10] Operation: 5*2=10 Exploring Operation: 5*3=15, Resulting Numbers: [24, 2, 15] Generated Node #0,1: 47:[24, 2, 15] Operation: 5*3=15 Exploring Operation: 24*2=48, Resulting Numbers: [5, 3, 48] Generated Node #0,2: 47:[5, 3, 48] Operation: 24*2=48 Exploring Operation: 3*2=6, Resulting Numbers: [5, 24, 6] Generated Node #0,3: 47:[5, 24, 6] Operation: 3*2=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 47:[5, 3, 48], Operations: ['24*2=48'] Exploring Operation: 5*3=15, Resulting Numbers: [48, 15] Generated Node #0,2,0: 47:[48, 15] Operation: 5*3=15 Exploring Operation: 5+3=8, Resulting Numbers: [48, 8] Generated Node #0,2,1: 47:[48, 8] Operation: 5+3=8 Exploring Operation: 48-3=45, Resulting Numbers: [5, 45] Generated Node #0,2,2: 47:[5, 45] Operation: 48-3=45 Exploring Operation: 5-3=2, Resulting Numbers: [48, 2] Generated Node #0,2,3: 47:[48, 2] Operation: 5-3=2 Moving to Node #0,2,0 Current State: 47:[48, 15], Operations: ['24*2=48', '5*3=15'] Exploring Operation: 48*15=720, Resulting Numbers: [720] 720,47 unequal: No Solution Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,47 unequal: No Solution Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[48, 8], Operations: ['24*2=48', '5+3=8'] Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,47 unequal: No Solution Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 48-8=40, Resulting Numbers: [40] 40,47 unequal: No Solution Exploring Operation: 48*8=384, Resulting Numbers: [384] 384,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[5, 45], Operations: ['24*2=48', '48-3=45'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,47 unequal: No Solution Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 5*45=225, Resulting Numbers: [225] 225,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[48, 2], Operations: ['24*2=48', '5-3=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,47 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,47 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[24, 2, 15], Operations: ['5*3=15'] Exploring Operation: 2*15=30, Resulting Numbers: [24, 30] Generated Node #0,1,0: 47:[24, 30] Operation: 2*15=30 Exploring Operation: 24*2=48, Resulting Numbers: [15, 48] Generated Node #0,1,1: 47:[15, 48] Operation: 24*2=48 Exploring Operation: 24+15=39, Resulting Numbers: [2, 39] Generated Node #0,1,2: 47:[2, 39] Operation: 24+15=39 Exploring Operation: 24+2=26, Resulting Numbers: [15, 26] Generated Node #0,1,3: 47:[15, 26] Operation: 24+2=26 Moving to Node #0,1,1 Current State: 47:[15, 48], Operations: ['5*3=15', '24*2=48'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,47 unequal: No Solution Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,47 unequal: No Solution Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[24, 30], Operations: ['5*3=15', '2*15=30'] Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[15, 26], Operations: ['5*3=15', '24+2=26'] Exploring Operation: 15+26=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 15*26=390, Resulting Numbers: [390] 390,47 unequal: No Solution Exploring Operation: 26-15=11, Resulting Numbers: [11] 11,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[2, 39], Operations: ['5*3=15', '24+15=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,47 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 Current State: 47:[24, 3, 10], Operations: ['5*2=10'] Exploring Operation: 24+10=34, Resulting Numbers: [3, 34] Generated Node #0,0,0: 47:[3, 34] Operation: 24+10=34 Exploring Operation: 3*10=30, Resulting Numbers: [24, 30] Generated Node #0,0,1: 47:[24, 30] Operation: 3*10=30 Exploring Operation: 3+10=13, Resulting Numbers: [24, 13] Generated Node #0,0,2: 47:[24, 13] Operation: 3+10=13 Exploring Operation: 24+3=27, Resulting Numbers: [10, 27] Generated Node #0,0,3: 47:[10, 27] Operation: 24+3=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[24, 30], Operations: ['5*2=10', '3*10=30'] Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,47 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,47 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 #0,0,0 Current State: 47:[3, 34], Operations: ['5*2=10', '24+10=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,47 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 #0,0,2 Current State: 47:[24, 13], Operations: ['5*2=10', '3+10=13'] Exploring Operation: 24*13=312, Resulting Numbers: [312] 312,47 unequal: No Solution Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,47 unequal: No Solution Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,47 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 #0,0,3 Current State: 47:[10, 27], Operations: ['5*2=10', '24+3=27'] Exploring Operation: 10+27=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 27-10=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 10*27=270, Resulting Numbers: [270] 270,47 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 #0,3 Current State: 47:[5, 24, 6], Operations: ['3*2=6'] Exploring Operation: 5+6=11, Resulting Numbers: [24, 11] Generated Node #0,3,0: 47:[24, 11] Operation: 5+6=11 Exploring Operation: 24+6=30, Resulting Numbers: [5, 30] Generated Node #0,3,1: 47:[5, 30] Operation: 24+6=30 Exploring Operation: 5*6=30, Resulting Numbers: [24, 30] Generated Node #0,3,2: 47:[24, 30] Operation: 5*6=30 Exploring Operation: 5+24=29, Resulting Numbers: [6, 29] Generated Node #0,3,3: 47:[6, 29] Operation: 5+24=29 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 47:[24, 30], Operations: ['3*2=6', '5*6=30'] Exploring Operation: 24*30=720, Resulting Numbers: [720] 720,47 unequal: No Solution Exploring Operation: 24+30=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 30-24=6, Resulting Numbers: [6] 6,47 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 #0,3,0 Current State: 47:[24, 11], Operations: ['3*2=6', '5+6=11'] Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,47 unequal: No Solution Exploring Operation: 24*11=264, Resulting Numbers: [264] 264,47 unequal: No Solution Exploring Operation: 24+11=35, Resulting Numbers: [35] 35,47 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 #0,3,1 Current State: 47:[5, 30], Operations: ['3*2=6', '24+6=30'] Exploring Operation: 5*30=150, Resulting Numbers: [150] 150,47 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,47 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,47 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 #0,3,3 Current State: 47:[6, 29], Operations: ['3*2=6', '5+24=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,47 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 12, 17, 59, 94 ]
21
[ "59+94=153", "153/17=9", "12+9=21" ]
Current State: 21:[12, 17, 59, 94], Operations: [] Exploring Operation: 59+94=153, Resulting Numbers: [12, 17, 153] Generated Node #2: [12, 17, 153] from Operation: 59+94=153 Current State: 21:[12, 17, 153], Operations: ['59+94=153'] Exploring Operation: 153/17=9, Resulting Numbers: [12, 9] Generated Node #3: [12, 9] from Operation: 153/17=9 Current State: 21:[12, 9], Operations: ['59+94=153', '153/17=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[12, 17, 59, 94], Operations: [] Exploring Operation: 59-17=42, Resulting Numbers: [12, 94, 42] Generated Node #0,0: 21:[12, 94, 42] Operation: 59-17=42 Exploring Operation: 94-59=35, Resulting Numbers: [12, 17, 35] Generated Node #0,1: 21:[12, 17, 35] Operation: 94-59=35 Exploring Operation: 94-17=77, Resulting Numbers: [12, 59, 77] Generated Node #0,2: 21:[12, 59, 77] Operation: 94-17=77 Exploring Operation: 94-12=82, Resulting Numbers: [17, 59, 82] Generated Node #0,3: 21:[17, 59, 82] Operation: 94-12=82 Exploring Operation: 59-12=47, Resulting Numbers: [17, 94, 47] Generated Node #0,4: 21:[17, 94, 47] Operation: 59-12=47 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[12, 17, 35], Operations: ['94-59=35'] Exploring Operation: 12+17=29, Resulting Numbers: [35, 29] Generated Node #0,1,0: 21:[35, 29] Operation: 12+17=29 Exploring Operation: 12+35=47, Resulting Numbers: [17, 47] Generated Node #0,1,1: 21:[17, 47] Operation: 12+35=47 Exploring Operation: 17-12=5, Resulting Numbers: [35, 5] Generated Node #0,1,2: 21:[35, 5] Operation: 17-12=5 Exploring Operation: 35-12=23, Resulting Numbers: [17, 23] Generated Node #0,1,3: 21:[17, 23] Operation: 35-12=23 Exploring Operation: 35-17=18, Resulting Numbers: [12, 18] Generated Node #0,1,4: 21:[12, 18] Operation: 35-17=18 Moving to Node #0,1,3 Current State: 21:[17, 23], Operations: ['94-59=35', '35-12=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,21 unequal: No Solution Moving to Node #0,1,4 Current State: 21:[12, 18], Operations: ['94-59=35', '35-17=18'] Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[35, 5], Operations: ['94-59=35', '17-12=5'] Exploring Operation: 35+5=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 35*5=175, Resulting Numbers: [175] 175,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[35, 29], Operations: ['94-59=35', '12+17=29'] Exploring Operation: 35+29=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 35-29=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 35*29=1015, Resulting Numbers: [1015] 1015,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[17, 47], Operations: ['94-59=35', '12+35=47'] Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,21 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,21 unequal: No Solution No 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: 21:[12, 94, 42], Operations: ['59-17=42'] Exploring Operation: 94-12=82, Resulting Numbers: [42, 82] Generated Node #0,0,0: 21:[42, 82] Operation: 94-12=82 Exploring Operation: 42-12=30, Resulting Numbers: [94, 30] Generated Node #0,0,1: 21:[94, 30] Operation: 42-12=30 Exploring Operation: 12+42=54, Resulting Numbers: [94, 54] Generated Node #0,0,2: 21:[94, 54] Operation: 12+42=54 Exploring Operation: 12+94=106, Resulting Numbers: [42, 106] Generated Node #0,0,3: 21:[42, 106] Operation: 12+94=106 Exploring Operation: 94-42=52, Resulting Numbers: [12, 52] Generated Node #0,0,4: 21:[12, 52] Operation: 94-42=52 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 21:[12, 52], Operations: ['59-17=42', '94-42=52'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 12+52=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 12*52=624, Resulting Numbers: [624] 624,21 unequal: No Solution No 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: 21:[42, 82], Operations: ['59-17=42', '94-12=82'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 42+82=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 42*82=3444, Resulting Numbers: [3444] 3444,21 unequal: No Solution No 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: 21:[94, 30], Operations: ['59-17=42', '42-12=30'] Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,21 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,21 unequal: No Solution No 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: 21:[94, 54], Operations: ['59-17=42', '12+42=54'] Exploring Operation: 94+54=148, Resulting Numbers: [148] 148,21 unequal: No Solution Exploring Operation: 94*54=5076, Resulting Numbers: [5076] 5076,21 unequal: No Solution Exploring Operation: 94-54=40, Resulting Numbers: [40] 40,21 unequal: No Solution No 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: 21:[42, 106], Operations: ['59-17=42', '12+94=106'] Exploring Operation: 42*106=4452, Resulting Numbers: [4452] 4452,21 unequal: No Solution Exploring Operation: 106-42=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 42+106=148, Resulting Numbers: [148] 148,21 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: 21:[12, 59, 77], Operations: ['94-17=77'] Exploring Operation: 12+59=71, Resulting Numbers: [77, 71] Generated Node #0,2,0: 21:[77, 71] Operation: 12+59=71 Exploring Operation: 12+77=89, Resulting Numbers: [59, 89] Generated Node #0,2,1: 21:[59, 89] Operation: 12+77=89 Exploring Operation: 77-59=18, Resulting Numbers: [12, 18] Generated Node #0,2,2: 21:[12, 18] Operation: 77-59=18 Exploring Operation: 59-12=47, Resulting Numbers: [77, 47] Generated Node #0,2,3: 21:[77, 47] Operation: 59-12=47 Exploring Operation: 77-12=65, Resulting Numbers: [59, 65] Generated Node #0,2,4: 21:[59, 65] Operation: 77-12=65 Moving to Node #0,2,2 Current State: 21:[12, 18], Operations: ['94-17=77', '77-59=18'] Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,21 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[59, 65], Operations: ['94-17=77', '77-12=65'] Exploring Operation: 59+65=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 59*65=3835, Resulting Numbers: [3835] 3835,21 unequal: No Solution Moving to Node #0,2,3 Current State: 21:[77, 47], Operations: ['94-17=77', '59-12=47'] Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 77+47=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 77*47=3619, Resulting Numbers: [3619] 3619,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[77, 71], Operations: ['94-17=77', '12+59=71'] Exploring Operation: 77+71=148, Resulting Numbers: [148] 148,21 unequal: No Solution Exploring Operation: 77-71=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 77*71=5467, Resulting Numbers: [5467] 5467,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[59, 89], Operations: ['94-17=77', '12+77=89'] Exploring Operation: 59+89=148, Resulting Numbers: [148] 148,21 unequal: No Solution Exploring Operation: 59*89=5251, Resulting Numbers: [5251] 5251,21 unequal: No Solution Exploring Operation: 89-59=30, Resulting Numbers: [30] 30,21 unequal: No Solution No 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: 21:[17, 59, 82], Operations: ['94-12=82'] Exploring Operation: 17+59=76, Resulting Numbers: [82, 76] Generated Node #0,3,0: 21:[82, 76] Operation: 17+59=76 Exploring Operation: 17+82=99, Resulting Numbers: [59, 99] Generated Node #0,3,1: 21:[59, 99] Operation: 17+82=99 Exploring Operation: 59-17=42, Resulting Numbers: [82, 42] Generated Node #0,3,2: 21:[82, 42] Operation: 59-17=42 Exploring Operation: 82-17=65, Resulting Numbers: [59, 65] Generated Node #0,3,3: 21:[59, 65] Operation: 82-17=65 Exploring Operation: 82-59=23, Resulting Numbers: [17, 23] Generated Node #0,3,4: 21:[17, 23] Operation: 82-59=23 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 21:[17, 23], Operations: ['94-12=82', '82-59=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,21 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,21 unequal: No Solution No 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: 21:[82, 42], Operations: ['94-12=82', '59-17=42'] Exploring Operation: 82-42=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 82+42=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 82*42=3444, Resulting Numbers: [3444] 3444,21 unequal: No Solution No 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: 21:[59, 65], Operations: ['94-12=82', '82-17=65'] Exploring Operation: 59+65=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 59*65=3835, Resulting Numbers: [3835] 3835,21 unequal: No Solution Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,21 unequal: No Solution No 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: 21:[82, 76], Operations: ['94-12=82', '17+59=76'] Exploring Operation: 82+76=158, Resulting Numbers: [158] 158,21 unequal: No Solution Exploring Operation: 82*76=6232, Resulting Numbers: [6232] 6232,21 unequal: No Solution Exploring Operation: 82-76=6, Resulting Numbers: [6] 6,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 21:[59, 99], Operations: ['94-12=82', '17+82=99'] Exploring Operation: 99-59=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 59*99=5841, Resulting Numbers: [5841] 5841,21 unequal: No Solution Exploring Operation: 59+99=158, Resulting Numbers: [158] 158,21 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: 21:[17, 94, 47], Operations: ['59-12=47'] Exploring Operation: 94-17=77, Resulting Numbers: [47, 77] Generated Node #0,4,0: 21:[47, 77] Operation: 94-17=77 Exploring Operation: 94-47=47, Resulting Numbers: [17, 47] Generated Node #0,4,1: 21:[17, 47] Operation: 94-47=47 Exploring Operation: 47-17=30, Resulting Numbers: [94, 30] Generated Node #0,4,2: 21:[94, 30] Operation: 47-17=30 Exploring Operation: 17+94=111, Resulting Numbers: [47, 111] Generated Node #0,4,3: 21:[47, 111] Operation: 17+94=111 Exploring Operation: 94/47=2, Resulting Numbers: [17, 2] Generated Node #0,4,4: 21:[17, 2] Operation: 94/47=2 Moving to Node #0,4,4 Current State: 21:[17, 2], Operations: ['59-12=47', '94/47=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,21 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,21 unequal: No Solution Moving to Node #0,4,1 Current State: 21:[17, 47], Operations: ['59-12=47', '94-47=47'] Exploring Operation: 17*47=799, Resulting Numbers: [799] 799,21 unequal: No Solution Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,21 unequal: No Solution Moving to Node #0,4,0 Current State: 21:[47, 77], Operations: ['59-12=47', '94-17=77'] Exploring Operation: 47+77=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 47*77=3619, Resulting Numbers: [3619] 3619,21 unequal: No Solution Exploring Operation: 77-47=30, Resulting Numbers: [30] 30,21 unequal: No Solution Moving to Node #0,4,2 Current State: 21:[94, 30], Operations: ['59-12=47', '47-17=30'] Exploring Operation: 94*30=2820, Resulting Numbers: [2820] 2820,21 unequal: No Solution Exploring Operation: 94+30=124, Resulting Numbers: [124] 124,21 unequal: No Solution Exploring Operation: 94-30=64, Resulting Numbers: [64] 64,21 unequal: No Solution Moving to Node #0,4,3 Current State: 21:[47, 111], Operations: ['59-12=47', '17+94=111'] Exploring Operation: 47*111=5217, Resulting Numbers: [5217] 5217,21 unequal: No Solution Exploring Operation: 111-47=64, Resulting Numbers: [64] 64,21 unequal: No Solution Exploring Operation: 47+111=158, Resulting Numbers: [158] 158,21 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
[ 72, 31, 38, 36 ]
62
[ "72-38=34", "36-34=2", "31*2=62" ]
Current State: 62:[72, 31, 38, 36], Operations: [] Exploring Operation: 72-38=34, Resulting Numbers: [31, 36, 34] Generated Node #2: [31, 36, 34] from Operation: 72-38=34 Current State: 62:[31, 36, 34], Operations: ['72-38=34'] Exploring Operation: 36-34=2, Resulting Numbers: [31, 2] Generated Node #3: [31, 2] from Operation: 36-34=2 Current State: 62:[31, 2], Operations: ['72-38=34', '36-34=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[72, 31, 38, 36], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [31, 38, 2] Generated Node #0,0: 62:[31, 38, 2] Operation: 72/36=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[31, 38, 2], Operations: ['72/36=2'] Exploring Operation: 38-31=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 62:[2, 7] Operation: 38-31=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[2, 7], Operations: ['72/36=2', '38-31=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 36, 49, 64, 60 ]
95
[ "64-60=4", "36*4=144", "144-49=95" ]
Current State: 95:[36, 49, 64, 60], Operations: [] Exploring Operation: 64-60=4, Resulting Numbers: [36, 49, 4] Generated Node #2: [36, 49, 4] from Operation: 64-60=4 Current State: 95:[36, 49, 4], Operations: ['64-60=4'] Exploring Operation: 36*4=144, Resulting Numbers: [49, 144] Generated Node #3: [49, 144] from Operation: 36*4=144 Current State: 95:[49, 144], Operations: ['64-60=4', '36*4=144'] Exploring Operation: 144-49=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[36, 49, 64, 60], Operations: [] Exploring Operation: 64-60=4, Resulting Numbers: [36, 49, 4] Generated Node #0,0: 95:[36, 49, 4] Operation: 64-60=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[36, 49, 4], Operations: ['64-60=4'] Exploring Operation: 49-36=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 95:[4, 13] Operation: 49-36=13 Moving to Node #0,0,0 Current State: 95:[4, 13], Operations: ['64-60=4', '49-36=13'] Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,95 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
[ 10, 73, 15, 87 ]
39
[ "73-10=63", "15+87=102", "102-63=39" ]
Current State: 39:[10, 73, 15, 87], Operations: [] Exploring Operation: 73-10=63, Resulting Numbers: [15, 87, 63] Generated Node #2: [15, 87, 63] from Operation: 73-10=63 Current State: 39:[15, 87, 63], Operations: ['73-10=63'] Exploring Operation: 15+87=102, Resulting Numbers: [63, 102] Generated Node #3: [63, 102] from Operation: 15+87=102 Current State: 39:[63, 102], Operations: ['73-10=63', '15+87=102'] Exploring Operation: 102-63=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[10, 73, 15, 87], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [10, 15, 14] Generated Node #0,0: 39:[10, 15, 14] Operation: 87-73=14 Exploring Operation: 87-15=72, Resulting Numbers: [10, 73, 72] Generated Node #0,1: 39:[10, 73, 72] Operation: 87-15=72 Exploring Operation: 73-15=58, Resulting Numbers: [10, 87, 58] Generated Node #0,2: 39:[10, 87, 58] Operation: 73-15=58 Moving to Node #0,0 Current State: 39:[10, 15, 14], Operations: ['87-73=14'] Exploring Operation: 15-10=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 39:[14, 5] Operation: 15-10=5 Exploring Operation: 14-10=4, Resulting Numbers: [15, 4] Generated Node #0,0,1: 39:[15, 4] Operation: 14-10=4 Exploring Operation: 15-14=1, Resulting Numbers: [10, 1] Generated Node #0,0,2: 39:[10, 1] Operation: 15-14=1 Moving to Node #0,1 Current State: 39:[10, 73, 72], Operations: ['87-15=72'] Exploring Operation: 73-72=1, Resulting Numbers: [10, 1] Generated Node #0,1,0: 39:[10, 1] Operation: 73-72=1 Exploring Operation: 72-10=62, Resulting Numbers: [73, 62] Generated Node #0,1,1: 39:[73, 62] Operation: 72-10=62 Exploring Operation: 73-10=63, Resulting Numbers: [72, 63] Generated Node #0,1,2: 39:[72, 63] Operation: 73-10=63 Moving to Node #0,2 Current State: 39:[10, 87, 58], Operations: ['73-15=58'] Exploring Operation: 87-58=29, Resulting Numbers: [10, 29] Generated Node #0,2,0: 39:[10, 29] Operation: 87-58=29 Exploring Operation: 87-10=77, Resulting Numbers: [58, 77] Generated Node #0,2,1: 39:[58, 77] Operation: 87-10=77 Exploring Operation: 58-10=48, Resulting Numbers: [87, 48] Generated Node #0,2,2: 39:[87, 48] Operation: 58-10=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[10, 29], Operations: ['73-15=58', '87-58=29'] Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,39 unequal: No Solution Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[10, 73, 15, 87], Operations: [] Exploring Operation: 73-15=58, Resulting Numbers: [10, 87, 58] Generated Node #0,2: 39:[10, 87, 58] Operation: 73-15=58 Moving to Node #0,2 Current State: 39:[10, 87, 58], Operations: ['73-15=58'] Exploring Operation: 87-58=29, Resulting Numbers: [10, 29] Generated Node #0,2,0: 39:[10, 29] Operation: 87-58=29 Moving to Node #0,2,0 Current State: 39:[10, 29], Operations: ['73-15=58', '87-58=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 66, 62, 19, 89 ]
27
[ "66-62=4", "19+89=108", "108/4=27" ]
Current State: 27:[66, 62, 19, 89], Operations: [] Exploring Operation: 66-62=4, Resulting Numbers: [19, 89, 4] Generated Node #2: [19, 89, 4] from Operation: 66-62=4 Current State: 27:[19, 89, 4], Operations: ['66-62=4'] Exploring Operation: 19+89=108, Resulting Numbers: [4, 108] Generated Node #3: [4, 108] from Operation: 19+89=108 Current State: 27:[4, 108], Operations: ['66-62=4', '19+89=108'] Exploring Operation: 108/4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[66, 62, 19, 89], Operations: [] Exploring Operation: 89-62=27, Resulting Numbers: [66, 19, 27] Generated Node #0,0: 27:[66, 19, 27] Operation: 89-62=27 Exploring Operation: 89-66=23, Resulting Numbers: [62, 19, 23] Generated Node #0,1: 27:[62, 19, 23] Operation: 89-66=23 Moving to Node #0,0 Current State: 27:[66, 19, 27], Operations: ['89-62=27'] Exploring Operation: 66-19=47, Resulting Numbers: [27, 47] Generated Node #0,0,0: 27:[27, 47] Operation: 66-19=47 Exploring Operation: 66-27=39, Resulting Numbers: [19, 39] Generated Node #0,0,1: 27:[19, 39] Operation: 66-27=39 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[27, 47], Operations: ['89-62=27', '66-19=47'] Exploring Operation: 47-27=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 27+47=74, Resulting Numbers: [74] 74,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[19, 39], Operations: ['89-62=27', '66-27=39'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,27 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: 27:[62, 19, 23], Operations: ['89-66=23'] Exploring Operation: 62-19=43, Resulting Numbers: [23, 43] Generated Node #0,1,0: 27:[23, 43] Operation: 62-19=43 Exploring Operation: 62-23=39, Resulting Numbers: [19, 39] Generated Node #0,1,1: 27:[19, 39] Operation: 62-23=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[23, 43], Operations: ['89-66=23', '62-19=43'] Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 23+43=66, Resulting Numbers: [66] 66,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[19, 39], Operations: ['89-66=23', '62-23=39'] Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,27 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 84, 42, 24, 8 ]
74
[ "84-42=42", "24+8=32", "42+32=74" ]
Current State: 74:[84, 42, 24, 8], Operations: [] Exploring Operation: 84-42=42, Resulting Numbers: [24, 8, 42] Generated Node #2: [24, 8, 42] from Operation: 84-42=42 Current State: 74:[24, 8, 42], Operations: ['84-42=42'] Exploring Operation: 24+8=32, Resulting Numbers: [42, 32] Generated Node #3: [42, 32] from Operation: 24+8=32 Current State: 74:[42, 32], Operations: ['84-42=42', '24+8=32'] Exploring Operation: 42+32=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[84, 42, 24, 8], Operations: [] Exploring Operation: 24/8=3, Resulting Numbers: [84, 42, 3] Generated Node #0,0: 74:[84, 42, 3] Operation: 24/8=3 Exploring Operation: 84/42=2, Resulting Numbers: [24, 8, 2] Generated Node #0,1: 74:[24, 8, 2] Operation: 84/42=2 Exploring Operation: 84-8=76, Resulting Numbers: [42, 24, 76] Generated Node #0,2: 74:[42, 24, 76] Operation: 84-8=76 Exploring Operation: 24+8=32, Resulting Numbers: [84, 42, 32] Generated Node #0,3: 74:[84, 42, 32] Operation: 24+8=32 Moving to Node #0,0 Current State: 74:[84, 42, 3], Operations: ['24/8=3'] Exploring Operation: 84/42=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 74:[3, 2] Operation: 84/42=2 Exploring Operation: 42-3=39, Resulting Numbers: [84, 39] Generated Node #0,0,1: 74:[84, 39] Operation: 42-3=39 Exploring Operation: 84-3=81, Resulting Numbers: [42, 81] Generated Node #0,0,2: 74:[42, 81] Operation: 84-3=81 Exploring Operation: 84-42=42, Resulting Numbers: [3, 42] Generated Node #0,0,3: 74:[3, 42] Operation: 84-42=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[3, 2], Operations: ['24/8=3', '84/42=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[3, 42], Operations: ['24/8=3', '84-42=42'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,74 unequal: No Solution Exploring Operation: 3*42=126, Resulting Numbers: [126] 126,74 unequal: No Solution Exploring Operation: 3+42=45, Resulting Numbers: [45] 45,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[84, 39], Operations: ['24/8=3', '42-3=39'] Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 84+39=123, Resulting Numbers: [123] 123,74 unequal: No Solution Exploring Operation: 84*39=3276, Resulting Numbers: [3276] 3276,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[42, 81], Operations: ['24/8=3', '84-3=81'] Exploring Operation: 42+81=123, Resulting Numbers: [123] 123,74 unequal: No Solution Exploring Operation: 42*81=3402, Resulting Numbers: [3402] 3402,74 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 74:[24, 8, 2], Operations: ['84/42=2'] Exploring Operation: 24+8=32, Resulting Numbers: [2, 32] Generated Node #0,1,0: 74:[2, 32] Operation: 24+8=32 Exploring Operation: 24/8=3, Resulting Numbers: [2, 3] Generated Node #0,1,1: 74:[2, 3] Operation: 24/8=3 Exploring Operation: 8/2=4, Resulting Numbers: [24, 4] Generated Node #0,1,2: 74:[24, 4] Operation: 8/2=4 Exploring Operation: 24-8=16, Resulting Numbers: [2, 16] Generated Node #0,1,3: 74:[2, 16] Operation: 24-8=16 Moving to Node #0,3 Current State: 74:[84, 42, 32], Operations: ['24+8=32'] Exploring Operation: 84-42=42, Resulting Numbers: [32, 42] Generated Node #0,3,0: 74:[32, 42] Operation: 84-42=42 Exploring Operation: 42-32=10, Resulting Numbers: [84, 10] Generated Node #0,3,1: 74:[84, 10] Operation: 42-32=10 Exploring Operation: 84/42=2, Resulting Numbers: [32, 2] Generated Node #0,3,2: 74:[32, 2] Operation: 84/42=2 Exploring Operation: 42+32=74, Resulting Numbers: [84, 74] Generated Node #0,3,3: 74:[84, 74] Operation: 42+32=74 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[32, 2], Operations: ['24+8=32', '84/42=2'] Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,74 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,74 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[32, 42], Operations: ['24+8=32', '84-42=42'] Exploring Operation: 32*42=1344, Resulting Numbers: [1344] 1344,74 unequal: No Solution Exploring Operation: 32+42=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[84, 42, 24, 8], Operations: [] Exploring Operation: 24+8=32, Resulting Numbers: [84, 42, 32] Generated Node #0,3: 74:[84, 42, 32] Operation: 24+8=32 Moving to Node #0,3 Current State: 74:[84, 42, 32], Operations: ['24+8=32'] Exploring Operation: 84-42=42, Resulting Numbers: [32, 42] Generated Node #0,3,0: 74:[32, 42] Operation: 84-42=42 Moving to Node #0,3,0 Current State: 74:[32, 42], Operations: ['24+8=32', '84-42=42'] Exploring Operation: 32+42=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 8, 48, 16, 27 ]
57
[ "27-8=19", "48/16=3", "19*3=57" ]
Current State: 57:[8, 48, 16, 27], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [48, 16, 19] Generated Node #2: [48, 16, 19] from Operation: 27-8=19 Current State: 57:[48, 16, 19], Operations: ['27-8=19'] Exploring Operation: 48/16=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 48/16=3 Current State: 57:[19, 3], Operations: ['27-8=19', '48/16=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[8, 48, 16, 27], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [48, 16, 19] Generated Node #0,0: 57:[48, 16, 19] Operation: 27-8=19 Exploring Operation: 48-27=21, Resulting Numbers: [8, 16, 21] Generated Node #0,1: 57:[8, 16, 21] Operation: 48-27=21 Exploring Operation: 8+48=56, Resulting Numbers: [16, 27, 56] Generated Node #0,2: 57:[16, 27, 56] Operation: 8+48=56 Exploring Operation: 48/16=3, Resulting Numbers: [8, 27, 3] Generated Node #0,3: 57:[8, 27, 3] Operation: 48/16=3 Exploring Operation: 48/8=6, Resulting Numbers: [16, 27, 6] Generated Node #0,4: 57:[16, 27, 6] Operation: 48/8=6 Moving to Node #0,1 Current State: 57:[8, 16, 21], Operations: ['48-27=21'] Exploring Operation: 8+16=24, Resulting Numbers: [21, 24] Generated Node #0,1,0: 57:[21, 24] Operation: 8+16=24 Exploring Operation: 16-8=8, Resulting Numbers: [21, 8] Generated Node #0,1,1: 57:[21, 8] Operation: 16-8=8 Exploring Operation: 21-16=5, Resulting Numbers: [8, 5] Generated Node #0,1,2: 57:[8, 5] Operation: 21-16=5 Exploring Operation: 21-8=13, Resulting Numbers: [16, 13] Generated Node #0,1,3: 57:[16, 13] Operation: 21-8=13 Exploring Operation: 16/8=2, Resulting Numbers: [21, 2] Generated Node #0,1,4: 57:[21, 2] Operation: 16/8=2 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 57:[21, 2], Operations: ['48-27=21', '16/8=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,57 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[21, 24], Operations: ['48-27=21', '8+16=24'] Exploring Operation: 21*24=504, Resulting Numbers: [504] 504,57 unequal: No Solution Exploring Operation: 21+24=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[21, 8], Operations: ['48-27=21', '16-8=8'] Exploring Operation: 21+8=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 21*8=168, Resulting Numbers: [168] 168,57 unequal: No Solution Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[8, 5], Operations: ['48-27=21', '21-16=5'] Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 57:[16, 13], Operations: ['48-27=21', '21-8=13'] Exploring Operation: 16*13=208, Resulting Numbers: [208] 208,57 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 16+13=29, Resulting Numbers: [29] 29,57 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: 57:[16, 27, 56], Operations: ['8+48=56'] Exploring Operation: 16+27=43, Resulting Numbers: [56, 43] Generated Node #0,2,0: 57:[56, 43] Operation: 16+27=43 Exploring Operation: 56-27=29, Resulting Numbers: [16, 29] Generated Node #0,2,1: 57:[16, 29] Operation: 56-27=29 Exploring Operation: 56-16=40, Resulting Numbers: [27, 40] Generated Node #0,2,2: 57:[27, 40] Operation: 56-16=40 Exploring Operation: 16+56=72, Resulting Numbers: [27, 72] Generated Node #0,2,3: 57:[27, 72] Operation: 16+56=72 Exploring Operation: 27-16=11, Resulting Numbers: [56, 11] Generated Node #0,2,4: 57:[56, 11] Operation: 27-16=11 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 57:[56, 11], Operations: ['8+48=56', '27-16=11'] Exploring Operation: 56+11=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 56*11=616, Resulting Numbers: [616] 616,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 57:[16, 29], Operations: ['8+48=56', '56-27=29'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,57 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 57:[56, 43], Operations: ['8+48=56', '16+27=43'] Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,57 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,57 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 57:[27, 72], Operations: ['8+48=56', '16+56=72'] Exploring Operation: 27+72=99, Resulting Numbers: [99] 99,57 unequal: No Solution Exploring Operation: 27*72=1944, Resulting Numbers: [1944] 1944,57 unequal: No Solution Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 57:[27, 40], Operations: ['8+48=56', '56-16=40'] Exploring Operation: 27*40=1080, Resulting Numbers: [1080] 1080,57 unequal: No Solution Exploring Operation: 27+40=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,57 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: 57:[48, 16, 19], Operations: ['27-8=19'] Exploring Operation: 48+19=67, Resulting Numbers: [16, 67] Generated Node #0,0,0: 57:[16, 67] Operation: 48+19=67 Exploring Operation: 48-16=32, Resulting Numbers: [19, 32] Generated Node #0,0,1: 57:[19, 32] Operation: 48-16=32 Exploring Operation: 19-16=3, Resulting Numbers: [48, 3] Generated Node #0,0,2: 57:[48, 3] Operation: 19-16=3 Exploring Operation: 48/16=3, Resulting Numbers: [19, 3] Generated Node #0,0,3: 57:[19, 3] Operation: 48/16=3 Exploring Operation: 48+16=64, Resulting Numbers: [19, 64] Generated Node #0,0,4: 57:[19, 64] Operation: 48+16=64 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 57:[19, 3], Operations: ['27-8=19', '48/16=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,57 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,57 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[8, 48, 16, 27], Operations: [] Exploring Operation: 27-8=19, Resulting Numbers: [48, 16, 19] Generated Node #0,0: 57:[48, 16, 19] Operation: 27-8=19 Moving to Node #0,0 Current State: 57:[48, 16, 19], Operations: ['27-8=19'] Exploring Operation: 48/16=3, Resulting Numbers: [19, 3] Generated Node #0,0,3: 57:[19, 3] Operation: 48/16=3 Moving to Node #0,0,3 Current State: 57:[19, 3], Operations: ['27-8=19', '48/16=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 79, 2, 65, 7 ]
23
[ "79+2=81", "65-7=58", "81-58=23" ]
Current State: 23:[79, 2, 65, 7], Operations: [] Exploring Operation: 79+2=81, Resulting Numbers: [65, 7, 81] Generated Node #2: [65, 7, 81] from Operation: 79+2=81 Current State: 23:[65, 7, 81], Operations: ['79+2=81'] Exploring Operation: 65-7=58, Resulting Numbers: [81, 58] Generated Node #3: [81, 58] from Operation: 65-7=58 Current State: 23:[81, 58], Operations: ['79+2=81', '65-7=58'] Exploring Operation: 81-58=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[79, 2, 65, 7], Operations: [] Exploring Operation: 2*7=14, Resulting Numbers: [79, 65, 14] Generated Node #0,0: 23:[79, 65, 14] Operation: 2*7=14 Exploring Operation: 79-65=14, Resulting Numbers: [2, 7, 14] Generated Node #0,1: 23:[2, 7, 14] Operation: 79-65=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[2, 7, 14], Operations: ['79-65=14'] Exploring Operation: 2*14=28, Resulting Numbers: [7, 28] Generated Node #0,1,0: 23:[7, 28] Operation: 2*14=28 Exploring Operation: 2*7=14, Resulting Numbers: [14, 14] Generated Node #0,1,1: 23:[14, 14] Operation: 2*7=14 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[14, 14], Operations: ['79-65=14', '2*7=14'] Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[7, 28], Operations: ['79-65=14', '2*14=28'] Exploring Operation: 7+28=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[79, 65, 14], Operations: ['2*7=14'] Exploring Operation: 79-14=65, Resulting Numbers: [65, 65] Generated Node #0,0,0: 23:[65, 65] Operation: 79-14=65 Exploring Operation: 79-65=14, Resulting Numbers: [14, 14] Generated Node #0,0,1: 23:[14, 14] Operation: 79-65=14 Moving to Node #0,0,1 Current State: 23:[14, 14], Operations: ['2*7=14', '79-65=14'] Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,23 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[65, 65], Operations: ['2*7=14', '79-14=65'] Exploring Operation: 65-65=0, Resulting Numbers: [0] 0,23 unequal: No Solution Exploring Operation: 65/65=1, Resulting Numbers: [1] 1,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 89, 7, 86, 46 ]
25
[ "89-86=3", "7*3=21", "46-21=25" ]
Current State: 25:[89, 7, 86, 46], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [7, 46, 3] Generated Node #2: [7, 46, 3] from Operation: 89-86=3 Current State: 25:[7, 46, 3], Operations: ['89-86=3'] Exploring Operation: 7*3=21, Resulting Numbers: [46, 21] Generated Node #3: [46, 21] from Operation: 7*3=21 Current State: 25:[46, 21], Operations: ['89-86=3', '7*3=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[89, 7, 86, 46], Operations: [] Exploring Operation: 89-86=3, Resulting Numbers: [7, 46, 3] Generated Node #0,0: 25:[7, 46, 3] Operation: 89-86=3 Moving to Node #0,0 Current State: 25:[7, 46, 3], Operations: ['89-86=3'] Exploring Operation: 46-7=39, Resulting Numbers: [3, 39] Generated Node #0,0,0: 25:[3, 39] Operation: 46-7=39 Moving to Node #0,0,0 Current State: 25:[3, 39], Operations: ['89-86=3', '46-7=39'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,25 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 62, 64, 16, 80 ]
56
[ "64-62=2", "80/2=40", "16+40=56" ]
Current State: 56:[62, 64, 16, 80], Operations: [] Exploring Operation: 64-62=2, Resulting Numbers: [16, 80, 2] Generated Node #2: [16, 80, 2] from Operation: 64-62=2 Current State: 56:[16, 80, 2], Operations: ['64-62=2'] Exploring Operation: 80/2=40, Resulting Numbers: [16, 40] Generated Node #3: [16, 40] from Operation: 80/2=40 Current State: 56:[16, 40], Operations: ['64-62=2', '80/2=40'] Exploring Operation: 16+40=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[62, 64, 16, 80], Operations: [] Exploring Operation: 80/16=5, Resulting Numbers: [62, 64, 5] Generated Node #0,0: 56:[62, 64, 5] Operation: 80/16=5 Exploring Operation: 80-62=18, Resulting Numbers: [64, 16, 18] Generated Node #0,1: 56:[64, 16, 18] Operation: 80-62=18 Exploring Operation: 80-64=16, Resulting Numbers: [62, 16, 16] Generated Node #0,2: 56:[62, 16, 16] Operation: 80-64=16 Moving to Node #0,2 Current State: 56:[62, 16, 16], Operations: ['80-64=16'] Exploring Operation: 16+16=32, Resulting Numbers: [62, 32] Generated Node #0,2,0: 56:[62, 32] Operation: 16+16=32 Exploring Operation: 16-16=0, Resulting Numbers: [62, 0] Generated Node #0,2,1: 56:[62, 0] Operation: 16-16=0 Exploring Operation: 16/16=1, Resulting Numbers: [62, 1] Generated Node #0,2,2: 56:[62, 1] Operation: 16/16=1 Moving to Node #0,1 Current State: 56:[64, 16, 18], Operations: ['80-62=18'] Exploring Operation: 64/16=4, Resulting Numbers: [18, 4] Generated Node #0,1,0: 56:[18, 4] Operation: 64/16=4 Exploring Operation: 18-16=2, Resulting Numbers: [64, 2] Generated Node #0,1,1: 56:[64, 2] Operation: 18-16=2 Exploring Operation: 64-16=48, Resulting Numbers: [18, 48] Generated Node #0,1,2: 56:[18, 48] Operation: 64-16=48 Moving to Node #0,0 Current State: 56:[62, 64, 5], Operations: ['80/16=5'] Exploring Operation: 62-5=57, Resulting Numbers: [64, 57] Generated Node #0,0,0: 56:[64, 57] Operation: 62-5=57 Exploring Operation: 64-5=59, Resulting Numbers: [62, 59] Generated Node #0,0,1: 56:[62, 59] Operation: 64-5=59 Exploring Operation: 64-62=2, Resulting Numbers: [5, 2] Generated Node #0,0,2: 56:[5, 2] Operation: 64-62=2 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 56:[5, 2], Operations: ['80/16=5', '64-62=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,56 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[64, 57], Operations: ['80/16=5', '62-5=57'] Exploring Operation: 64+57=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 64*57=3648, Resulting Numbers: [3648] 3648,56 unequal: No Solution Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[62, 59], Operations: ['80/16=5', '64-5=59'] Exploring Operation: 62*59=3658, Resulting Numbers: [3658] 3658,56 unequal: No Solution Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 62+59=121, Resulting Numbers: [121] 121,56 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: 56:[18, 4], Operations: ['80-62=18', '64/16=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,56 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,56 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[62, 1], Operations: ['80-64=16', '16/16=1'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,56 unequal: No Solution Moving to Node #0,1,1 Current State: 56:[64, 2], Operations: ['80-62=18', '18-16=2'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,56 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[62, 0], Operations: ['80-64=16', '16-16=0'] Exploring Operation: 62-0=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 62+0=62, Resulting Numbers: [62] 62,56 unequal: No Solution Exploring Operation: 62*0=0, Resulting Numbers: [0] 0,56 unequal: No Solution Moving to Node #0,2,0 Current State: 56:[62, 32], Operations: ['80-64=16', '16+16=32'] Exploring Operation: 62+32=94, Resulting Numbers: [94] 94,56 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,56 unequal: No Solution Exploring Operation: 62*32=1984, Resulting Numbers: [1984] 1984,56 unequal: No Solution Moving to Node #0,1,2 Current State: 56:[18, 48], Operations: ['80-62=18', '64-16=48'] Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,56 unequal: No Solution Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,56 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,56 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 62, 60, 25, 86 ]
36
[ "62-60=2", "25*2=50", "86-50=36" ]
Current State: 36:[62, 60, 25, 86], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [25, 86, 2] Generated Node #2: [25, 86, 2] from Operation: 62-60=2 Current State: 36:[25, 86, 2], Operations: ['62-60=2'] Exploring Operation: 25*2=50, Resulting Numbers: [86, 50] Generated Node #3: [86, 50] from Operation: 25*2=50 Current State: 36:[86, 50], Operations: ['62-60=2', '25*2=50'] Exploring Operation: 86-50=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[62, 60, 25, 86], Operations: [] Exploring Operation: 86-60=26, Resulting Numbers: [62, 25, 26] Generated Node #0,0: 36:[62, 25, 26] Operation: 86-60=26 Exploring Operation: 86-62=24, Resulting Numbers: [60, 25, 24] Generated Node #0,1: 36:[60, 25, 24] Operation: 86-62=24 Moving to Node #0,1 Current State: 36:[60, 25, 24], Operations: ['86-62=24'] Exploring Operation: 60-25=35, Resulting Numbers: [24, 35] Generated Node #0,1,0: 36:[24, 35] Operation: 60-25=35 Exploring Operation: 60-24=36, Resulting Numbers: [25, 36] Generated Node #0,1,1: 36:[25, 36] Operation: 60-24=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[24, 35], Operations: ['86-62=24', '60-25=35'] Exploring Operation: 35-24=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 24+35=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 #0,1,1 Current State: 36:[25, 36], Operations: ['86-62=24', '60-24=36'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,36 unequal: No Solution Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,36 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:[62, 25, 26], Operations: ['86-60=26'] Exploring Operation: 62-25=37, Resulting Numbers: [26, 37] Generated Node #0,0,0: 36:[26, 37] Operation: 62-25=37 Exploring Operation: 62-26=36, Resulting Numbers: [25, 36] Generated Node #0,0,1: 36:[25, 36] Operation: 62-26=36 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[25, 36], Operations: ['86-60=26', '62-26=36'] Exploring Operation: 25+36=61, Resulting Numbers: [61] 61,36 unequal: No Solution Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,36 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 #0,0,0 Current State: 36:[26, 37], Operations: ['86-60=26', '62-25=37'] Exploring Operation: 26+37=63, Resulting Numbers: [63] 63,36 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,36 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 47, 57, 8, 87 ]
89
[ "57-47=10", "87-8=79", "10+79=89" ]
Current State: 89:[47, 57, 8, 87], Operations: [] Exploring Operation: 57-47=10, Resulting Numbers: [8, 87, 10] Generated Node #2: [8, 87, 10] from Operation: 57-47=10 Current State: 89:[8, 87, 10], Operations: ['57-47=10'] Exploring Operation: 87-8=79, Resulting Numbers: [10, 79] Generated Node #3: [10, 79] from Operation: 87-8=79 Current State: 89:[10, 79], Operations: ['57-47=10', '87-8=79'] Exploring Operation: 10+79=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[47, 57, 8, 87], Operations: [] Exploring Operation: 8+87=95, Resulting Numbers: [47, 57, 95] Generated Node #0,0: 89:[47, 57, 95] Operation: 8+87=95 Exploring Operation: 47+8=55, Resulting Numbers: [57, 87, 55] Generated Node #0,1: 89:[57, 87, 55] Operation: 47+8=55 Exploring Operation: 57+8=65, Resulting Numbers: [47, 87, 65] Generated Node #0,2: 89:[47, 87, 65] Operation: 57+8=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[57, 87, 55], Operations: ['47+8=55'] Exploring Operation: 87+55=142, Resulting Numbers: [57, 142] Generated Node #0,1,0: 89:[57, 142] Operation: 87+55=142 Exploring Operation: 57+87=144, Resulting Numbers: [55, 144] Generated Node #0,1,1: 89:[55, 144] Operation: 57+87=144 Exploring Operation: 57+55=112, Resulting Numbers: [87, 112] Generated Node #0,1,2: 89:[87, 112] Operation: 57+55=112 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[87, 112], Operations: ['47+8=55', '57+55=112'] Exploring Operation: 112-87=25, Resulting Numbers: [25] 25,89 unequal: No Solution Exploring Operation: 87+112=199, Resulting Numbers: [199] 199,89 unequal: No Solution Exploring Operation: 87*112=9744, Resulting Numbers: [9744] 9744,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[57, 142], Operations: ['47+8=55', '87+55=142'] Exploring Operation: 57+142=199, Resulting Numbers: [199] 199,89 unequal: No Solution Exploring Operation: 57*142=8094, Resulting Numbers: [8094] 8094,89 unequal: No Solution Exploring Operation: 142-57=85, Resulting Numbers: [85] 85,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[55, 144], Operations: ['47+8=55', '57+87=144'] Exploring Operation: 55*144=7920, Resulting Numbers: [7920] 7920,89 unequal: No Solution Exploring Operation: 55+144=199, Resulting Numbers: [199] 199,89 unequal: No Solution Exploring Operation: 144-55=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[47, 57, 8, 87], Operations: [] Exploring Operation: 47+8=55, Resulting Numbers: [57, 87, 55] Generated Node #0,1: 89:[57, 87, 55] Operation: 47+8=55 Moving to Node #0,1 Current State: 89:[57, 87, 55], Operations: ['47+8=55'] Exploring Operation: 57+87=144, Resulting Numbers: [55, 144] Generated Node #0,1,1: 89:[55, 144] Operation: 57+87=144 Moving to Node #0,1,1 Current State: 89:[55, 144], Operations: ['47+8=55', '57+87=144'] Exploring Operation: 144-55=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_3
mult_heuristic
[ 10, 8, 38, 39 ]
81
[ "10*8=80", "39-38=1", "80+1=81" ]
Current State: 81:[10, 8, 38, 39], Operations: [] Exploring Operation: 10*8=80, Resulting Numbers: [38, 39, 80] Generated Node #2: [38, 39, 80] from Operation: 10*8=80 Current State: 81:[38, 39, 80], Operations: ['10*8=80'] Exploring Operation: 39-38=1, Resulting Numbers: [80, 1] Generated Node #3: [80, 1] from Operation: 39-38=1 Current State: 81:[80, 1], Operations: ['10*8=80', '39-38=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[10, 8, 38, 39], Operations: [] Exploring Operation: 38+39=77, Resulting Numbers: [10, 8, 77] Generated Node #0,0: 81:[10, 8, 77] Operation: 38+39=77 Exploring Operation: 39-38=1, Resulting Numbers: [10, 8, 1] Generated Node #0,1: 81:[10, 8, 1] Operation: 39-38=1 Moving to Node #0,1 Current State: 81:[10, 8, 1], Operations: ['39-38=1'] Exploring Operation: 8+1=9, Resulting Numbers: [10, 9] Generated Node #0,1,0: 81:[10, 9] Operation: 8+1=9 Exploring Operation: 10-1=9, Resulting Numbers: [8, 9] Generated Node #0,1,1: 81:[8, 9] Operation: 10-1=9 Moving to Node #0,0 Current State: 81:[10, 8, 77], Operations: ['38+39=77'] Exploring Operation: 10*8=80, Resulting Numbers: [77, 80] Generated Node #0,0,0: 81:[77, 80] Operation: 10*8=80 Exploring Operation: 10-8=2, Resulting Numbers: [77, 2] Generated Node #0,0,1: 81:[77, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[77, 80], Operations: ['38+39=77', '10*8=80'] Exploring Operation: 77+80=157, Resulting Numbers: [157] 157,81 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,81 unequal: No Solution No 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: 81:[77, 2], Operations: ['38+39=77', '10-8=2'] Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,81 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,81 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: 81:[10, 9], Operations: ['39-38=1', '8+1=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,81 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[8, 9], Operations: ['39-38=1', '10-1=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,81 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 3, 43, 92, 53 ]
12
[ "92-43=49", "53-49=4", "3*4=12" ]
Current State: 12:[3, 43, 92, 53], Operations: [] Exploring Operation: 92-43=49, Resulting Numbers: [3, 53, 49] Generated Node #2: [3, 53, 49] from Operation: 92-43=49 Current State: 12:[3, 53, 49], Operations: ['92-43=49'] Exploring Operation: 53-49=4, Resulting Numbers: [3, 4] Generated Node #3: [3, 4] from Operation: 53-49=4 Current State: 12:[3, 4], Operations: ['92-43=49', '53-49=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[3, 43, 92, 53], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [3, 43, 39] Generated Node #0,0: 12:[3, 43, 39] Operation: 92-53=39 Exploring Operation: 53-43=10, Resulting Numbers: [3, 92, 10] Generated Node #0,1: 12:[3, 92, 10] Operation: 53-43=10 Exploring Operation: 92-43=49, Resulting Numbers: [3, 53, 49] Generated Node #0,2: 12:[3, 53, 49] Operation: 92-43=49 Moving to Node #0,0 Current State: 12:[3, 43, 39], Operations: ['92-53=39'] Exploring Operation: 43-39=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 12:[3, 4] Operation: 43-39=4 Exploring Operation: 43-3=40, Resulting Numbers: [39, 40] Generated Node #0,0,1: 12:[39, 40] Operation: 43-3=40 Exploring Operation: 39/3=13, Resulting Numbers: [43, 13] Generated Node #0,0,2: 12:[43, 13] Operation: 39/3=13 Moving to Node #0,2 Current State: 12:[3, 53, 49], Operations: ['92-43=49'] Exploring Operation: 49-3=46, Resulting Numbers: [53, 46] Generated Node #0,2,0: 12:[53, 46] Operation: 49-3=46 Exploring Operation: 53-49=4, Resulting Numbers: [3, 4] Generated Node #0,2,1: 12:[3, 4] Operation: 53-49=4 Exploring Operation: 53-3=50, Resulting Numbers: [49, 50] Generated Node #0,2,2: 12:[49, 50] Operation: 53-3=50 Moving to Node #0,1 Current State: 12:[3, 92, 10], Operations: ['53-43=10'] Exploring Operation: 92-10=82, Resulting Numbers: [3, 82] Generated Node #0,1,0: 12:[3, 82] Operation: 92-10=82 Exploring Operation: 3+10=13, Resulting Numbers: [92, 13] Generated Node #0,1,1: 12:[92, 13] Operation: 3+10=13 Exploring Operation: 92-3=89, Resulting Numbers: [10, 89] Generated Node #0,1,2: 12:[10, 89] Operation: 92-3=89 Moving to Node #0,0,0 Current State: 12:[3, 4], Operations: ['92-53=39', '43-39=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,12 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[3, 43, 92, 53], Operations: [] Exploring Operation: 92-53=39, Resulting Numbers: [3, 43, 39] Generated Node #0,0: 12:[3, 43, 39] Operation: 92-53=39 Moving to Node #0,0 Current State: 12:[3, 43, 39], Operations: ['92-53=39'] Exploring Operation: 43-39=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 12:[3, 4] Operation: 43-39=4 Moving to Node #0,0,0 Current State: 12:[3, 4], Operations: ['92-53=39', '43-39=4'] Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 6, 4, 12, 3 ]
72
[ "6-4=2", "12*3=36", "2*36=72" ]
Current State: 72:[6, 4, 12, 3], Operations: [] Exploring Operation: 6-4=2, Resulting Numbers: [12, 3, 2] Generated Node #2: [12, 3, 2] from Operation: 6-4=2 Current State: 72:[12, 3, 2], Operations: ['6-4=2'] Exploring Operation: 12*3=36, Resulting Numbers: [2, 36] Generated Node #3: [2, 36] from Operation: 12*3=36 Current State: 72:[2, 36], Operations: ['6-4=2', '12*3=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[6, 4, 12, 3], Operations: [] Exploring Operation: 6+12=18, Resulting Numbers: [4, 3, 18] Generated Node #0,0: 72:[4, 3, 18] Operation: 6+12=18 Exploring Operation: 6*4=24, Resulting Numbers: [12, 3, 24] Generated Node #0,1: 72:[12, 3, 24] Operation: 6*4=24 Exploring Operation: 6-4=2, Resulting Numbers: [12, 3, 2] Generated Node #0,2: 72:[12, 3, 2] Operation: 6-4=2 Exploring Operation: 12-6=6, Resulting Numbers: [4, 3, 6] Generated Node #0,3: 72:[4, 3, 6] Operation: 12-6=6 Exploring Operation: 6*12=72, Resulting Numbers: [4, 3, 72] Generated Node #0,4: 72:[4, 3, 72] Operation: 6*12=72 Moving to Node #0,0 Current State: 72:[4, 3, 18], Operations: ['6+12=18'] Exploring Operation: 4*3=12, Resulting Numbers: [18, 12] Generated Node #0,0,0: 72:[18, 12] Operation: 4*3=12 Exploring Operation: 18/3=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 72:[4, 6] Operation: 18/3=6 Exploring Operation: 4+3=7, Resulting Numbers: [18, 7] Generated Node #0,0,2: 72:[18, 7] Operation: 4+3=7 Exploring Operation: 4-3=1, Resulting Numbers: [18, 1] Generated Node #0,0,3: 72:[18, 1] Operation: 4-3=1 Exploring Operation: 4*18=72, Resulting Numbers: [3, 72] Generated Node #0,0,4: 72:[3, 72] Operation: 4*18=72 Moving to Node #0,2 Current State: 72:[12, 3, 2], Operations: ['6-4=2'] Exploring Operation: 12-3=9, Resulting Numbers: [2, 9] Generated Node #0,2,0: 72:[2, 9] Operation: 12-3=9 Exploring Operation: 12*2=24, Resulting Numbers: [3, 24] Generated Node #0,2,1: 72:[3, 24] Operation: 12*2=24 Exploring Operation: 12/3=4, Resulting Numbers: [2, 4] Generated Node #0,2,2: 72:[2, 4] Operation: 12/3=4 Exploring Operation: 12*3=36, Resulting Numbers: [2, 36] Generated Node #0,2,3: 72:[2, 36] Operation: 12*3=36 Exploring Operation: 12/2=6, Resulting Numbers: [3, 6] Generated Node #0,2,4: 72:[3, 6] Operation: 12/2=6 Moving to Node #0,4 Current State: 72:[4, 3, 72], Operations: ['6*12=72'] Exploring Operation: 4*3=12, Resulting Numbers: [72, 12] Generated Node #0,4,0: 72:[72, 12] Operation: 4*3=12 Exploring Operation: 4-3=1, Resulting Numbers: [72, 1] Generated Node #0,4,1: 72:[72, 1] Operation: 4-3=1 Exploring Operation: 72/4=18, Resulting Numbers: [3, 18] Generated Node #0,4,2: 72:[3, 18] Operation: 72/4=18 Exploring Operation: 72/3=24, Resulting Numbers: [4, 24] Generated Node #0,4,3: 72:[4, 24] Operation: 72/3=24 Exploring Operation: 4+3=7, Resulting Numbers: [72, 7] Generated Node #0,4,4: 72:[72, 7] Operation: 4+3=7 Moving to Node #0,1 Current State: 72:[12, 3, 24], Operations: ['6*4=24'] Exploring Operation: 24-12=12, Resulting Numbers: [3, 12] Generated Node #0,1,0: 72:[3, 12] Operation: 24-12=12 Exploring Operation: 12-3=9, Resulting Numbers: [24, 9] Generated Node #0,1,1: 72:[24, 9] Operation: 12-3=9 Exploring Operation: 12+24=36, Resulting Numbers: [3, 36] Generated Node #0,1,2: 72:[3, 36] Operation: 12+24=36 Exploring Operation: 12/3=4, Resulting Numbers: [24, 4] Generated Node #0,1,3: 72:[24, 4] Operation: 12/3=4 Exploring Operation: 12*3=36, Resulting Numbers: [24, 36] Generated Node #0,1,4: 72:[24, 36] Operation: 12*3=36 Moving to Node #0,3 Current State: 72:[4, 3, 6], Operations: ['12-6=6'] Exploring Operation: 3*6=18, Resulting Numbers: [4, 18] Generated Node #0,3,0: 72:[4, 18] Operation: 3*6=18 Exploring Operation: 4*3=12, Resulting Numbers: [6, 12] Generated Node #0,3,1: 72:[6, 12] Operation: 4*3=12 Exploring Operation: 3+6=9, Resulting Numbers: [4, 9] Generated Node #0,3,2: 72:[4, 9] Operation: 3+6=9 Exploring Operation: 4*6=24, Resulting Numbers: [3, 24] Generated Node #0,3,3: 72:[3, 24] Operation: 4*6=24 Exploring Operation: 6-4=2, Resulting Numbers: [3, 2] Generated Node #0,3,4: 72:[3, 2] Operation: 6-4=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[4, 18], Operations: ['12-6=6', '3*6=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,72 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[6, 4, 12, 3], Operations: [] Exploring Operation: 12-6=6, Resulting Numbers: [4, 3, 6] Generated Node #0,3: 72:[4, 3, 6] Operation: 12-6=6 Moving to Node #0,3 Current State: 72:[4, 3, 6], Operations: ['12-6=6'] Exploring Operation: 3*6=18, Resulting Numbers: [4, 18] Generated Node #0,3,0: 72:[4, 18] Operation: 3*6=18 Moving to Node #0,3,0 Current State: 72:[4, 18], Operations: ['12-6=6', '3*6=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 73, 45, 49, 52 ]
84
[ "73-45=28", "52-49=3", "28*3=84" ]
Current State: 84:[73, 45, 49, 52], Operations: [] Exploring Operation: 73-45=28, Resulting Numbers: [49, 52, 28] Generated Node #2: [49, 52, 28] from Operation: 73-45=28 Current State: 84:[49, 52, 28], Operations: ['73-45=28'] Exploring Operation: 52-49=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 52-49=3 Current State: 84:[28, 3], Operations: ['73-45=28', '52-49=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[73, 45, 49, 52], Operations: [] Exploring Operation: 73-52=21, Resulting Numbers: [45, 49, 21] Generated Node #0,0: 84:[45, 49, 21] Operation: 73-52=21 Exploring Operation: 52-49=3, Resulting Numbers: [73, 45, 3] Generated Node #0,1: 84:[73, 45, 3] Operation: 52-49=3 Moving to Node #0,0 Current State: 84:[45, 49, 21], Operations: ['73-52=21'] Exploring Operation: 49-45=4, Resulting Numbers: [21, 4] Generated Node #0,0,0: 84:[21, 4] Operation: 49-45=4 Exploring Operation: 49-21=28, Resulting Numbers: [45, 28] Generated Node #0,0,1: 84:[45, 28] Operation: 49-21=28 Moving to Node #0,1 Current State: 84:[73, 45, 3], Operations: ['52-49=3'] Exploring Operation: 73-45=28, Resulting Numbers: [3, 28] Generated Node #0,1,0: 84:[3, 28] Operation: 73-45=28 Exploring Operation: 73+3=76, Resulting Numbers: [45, 76] Generated Node #0,1,1: 84:[45, 76] Operation: 73+3=76 Moving to Node #0,0,0 Current State: 84:[21, 4], Operations: ['73-52=21', '49-45=4'] Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[73, 45, 49, 52], Operations: [] Exploring Operation: 73-52=21, Resulting Numbers: [45, 49, 21] Generated Node #0,0: 84:[45, 49, 21] Operation: 73-52=21 Moving to Node #0,0 Current State: 84:[45, 49, 21], Operations: ['73-52=21'] Exploring Operation: 49-45=4, Resulting Numbers: [21, 4] Generated Node #0,0,0: 84:[21, 4] Operation: 49-45=4 Moving to Node #0,0,0 Current State: 84:[21, 4], Operations: ['73-52=21', '49-45=4'] Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 81, 69, 39, 66 ]
93
[ "81-69=12", "39+66=105", "105-12=93" ]
Current State: 93:[81, 69, 39, 66], Operations: [] Exploring Operation: 81-69=12, Resulting Numbers: [39, 66, 12] Generated Node #2: [39, 66, 12] from Operation: 81-69=12 Current State: 93:[39, 66, 12], Operations: ['81-69=12'] Exploring Operation: 39+66=105, Resulting Numbers: [12, 105] Generated Node #3: [12, 105] from Operation: 39+66=105 Current State: 93:[12, 105], Operations: ['81-69=12', '39+66=105'] Exploring Operation: 105-12=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[81, 69, 39, 66], Operations: [] Exploring Operation: 69-39=30, Resulting Numbers: [81, 66, 30] Generated Node #0,0: 93:[81, 66, 30] Operation: 69-39=30 Exploring Operation: 69-66=3, Resulting Numbers: [81, 39, 3] Generated Node #0,1: 93:[81, 39, 3] Operation: 69-66=3 Exploring Operation: 81-66=15, Resulting Numbers: [69, 39, 15] Generated Node #0,2: 93:[69, 39, 15] Operation: 81-66=15 Exploring Operation: 81-69=12, Resulting Numbers: [39, 66, 12] Generated Node #0,3: 93:[39, 66, 12] Operation: 81-69=12 Exploring Operation: 66-39=27, Resulting Numbers: [81, 69, 27] Generated Node #0,4: 93:[81, 69, 27] Operation: 66-39=27 Moving to Node #0,1 Current State: 93:[81, 39, 3], Operations: ['69-66=3'] Exploring Operation: 39-3=36, Resulting Numbers: [81, 36] Generated Node #0,1,0: 93:[81, 36] Operation: 39-3=36 Exploring Operation: 39/3=13, Resulting Numbers: [81, 13] Generated Node #0,1,1: 93:[81, 13] Operation: 39/3=13 Exploring Operation: 81-39=42, Resulting Numbers: [3, 42] Generated Node #0,1,2: 93:[3, 42] Operation: 81-39=42 Exploring Operation: 81/3=27, Resulting Numbers: [39, 27] Generated Node #0,1,3: 93:[39, 27] Operation: 81/3=27 Exploring Operation: 81+3=84, Resulting Numbers: [39, 84] Generated Node #0,1,4: 93:[39, 84] Operation: 81+3=84 Moving to Node #0,4 Current State: 93:[81, 69, 27], Operations: ['66-39=27'] Exploring Operation: 69-27=42, Resulting Numbers: [81, 42] Generated Node #0,4,0: 93:[81, 42] Operation: 69-27=42 Exploring Operation: 81/27=3, Resulting Numbers: [69, 3] Generated Node #0,4,1: 93:[69, 3] Operation: 81/27=3 Exploring Operation: 81-69=12, Resulting Numbers: [27, 12] Generated Node #0,4,2: 93:[27, 12] Operation: 81-69=12 Exploring Operation: 69+27=96, Resulting Numbers: [81, 96] Generated Node #0,4,3: 93:[81, 96] Operation: 69+27=96 Exploring Operation: 81+27=108, Resulting Numbers: [69, 108] Generated Node #0,4,4: 93:[69, 108] Operation: 81+27=108 Moving to Node #0,0 Current State: 93:[81, 66, 30], Operations: ['69-39=30'] Exploring Operation: 66+30=96, Resulting Numbers: [81, 96] Generated Node #0,0,0: 93:[81, 96] Operation: 66+30=96 Exploring Operation: 66-30=36, Resulting Numbers: [81, 36] Generated Node #0,0,1: 93:[81, 36] Operation: 66-30=36 Exploring Operation: 81+30=111, Resulting Numbers: [66, 111] Generated Node #0,0,2: 93:[66, 111] Operation: 81+30=111 Exploring Operation: 81-66=15, Resulting Numbers: [30, 15] Generated Node #0,0,3: 93:[30, 15] Operation: 81-66=15 Exploring Operation: 81-30=51, Resulting Numbers: [66, 51] Generated Node #0,0,4: 93:[66, 51] Operation: 81-30=51 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 93:[30, 15], Operations: ['69-39=30', '81-66=15'] Exploring Operation: 30+15=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 30*15=450, Resulting Numbers: [450] 450,93 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[81, 96], Operations: ['69-39=30', '66+30=96'] Exploring Operation: 96-81=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 81*96=7776, Resulting Numbers: [7776] 7776,93 unequal: No Solution Exploring Operation: 81+96=177, Resulting Numbers: [177] 177,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[81, 36], Operations: ['69-39=30', '66-30=36'] Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 81*36=2916, Resulting Numbers: [2916] 2916,93 unequal: No Solution Exploring Operation: 81+36=117, Resulting Numbers: [117] 117,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 93:[66, 111], Operations: ['69-39=30', '81+30=111'] Exploring Operation: 111-66=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 66*111=7326, Resulting Numbers: [7326] 7326,93 unequal: No Solution Exploring Operation: 66+111=177, Resulting Numbers: [177] 177,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 93:[66, 51], Operations: ['69-39=30', '81-30=51'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 66+51=117, Resulting Numbers: [117] 117,93 unequal: No Solution Exploring Operation: 66*51=3366, Resulting Numbers: [3366] 3366,93 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: 93:[69, 39, 15], Operations: ['81-66=15'] Exploring Operation: 69+15=84, Resulting Numbers: [39, 84] Generated Node #0,2,0: 93:[39, 84] Operation: 69+15=84 Exploring Operation: 39-15=24, Resulting Numbers: [69, 24] Generated Node #0,2,1: 93:[69, 24] Operation: 39-15=24 Exploring Operation: 69-39=30, Resulting Numbers: [15, 30] Generated Node #0,2,2: 93:[15, 30] Operation: 69-39=30 Exploring Operation: 69+39=108, Resulting Numbers: [15, 108] Generated Node #0,2,3: 93:[15, 108] Operation: 69+39=108 Exploring Operation: 69-15=54, Resulting Numbers: [39, 54] Generated Node #0,2,4: 93:[39, 54] Operation: 69-15=54 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[15, 30], Operations: ['81-66=15', '69-39=30'] Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,93 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,93 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,93 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[39, 84], Operations: ['81-66=15', '69+15=84'] Exploring Operation: 39+84=123, Resulting Numbers: [123] 123,93 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 39*84=3276, Resulting Numbers: [3276] 3276,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[15, 108], Operations: ['81-66=15', '69+39=108'] Exploring Operation: 108-15=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[81, 69, 39, 66], Operations: [] Exploring Operation: 81-66=15, Resulting Numbers: [69, 39, 15] Generated Node #0,2: 93:[69, 39, 15] Operation: 81-66=15 Moving to Node #0,2 Current State: 93:[69, 39, 15], Operations: ['81-66=15'] Exploring Operation: 69+39=108, Resulting Numbers: [15, 108] Generated Node #0,2,3: 93:[15, 108] Operation: 69+39=108 Moving to Node #0,2,3 Current State: 93:[15, 108], Operations: ['81-66=15', '69+39=108'] Exploring Operation: 108-15=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.953993
hs_5
mult_heuristic
[ 63, 93, 10, 10 ]
93
[ "10-10=0", "63*0=0", "93+0=93" ]
Current State: 93:[63, 93, 10, 10], Operations: [] Exploring Operation: 10-10=0, Resulting Numbers: [63, 93, 0] Generated Node #2: [63, 93, 0] from Operation: 10-10=0 Current State: 93:[63, 93, 0], Operations: ['10-10=0'] Exploring Operation: 63*0=0, Resulting Numbers: [93, 0] Generated Node #3: [93, 0] from Operation: 63*0=0 Current State: 93:[93, 0], Operations: ['10-10=0', '63*0=0'] Exploring Operation: 93+0=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[63, 93, 10, 10], Operations: [] Exploring Operation: 63+10=73, Resulting Numbers: [93, 10, 73] Generated Node #0,0: 93:[93, 10, 73] Operation: 63+10=73 Exploring Operation: 93-63=30, Resulting Numbers: [10, 10, 30] Generated Node #0,1: 93:[10, 10, 30] Operation: 93-63=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[10, 10, 30], Operations: ['93-63=30'] Exploring Operation: 10-10=0, Resulting Numbers: [30, 0] Generated Node #0,1,0: 93:[30, 0] Operation: 10-10=0 Exploring Operation: 10/10=1, Resulting Numbers: [30, 1] Generated Node #0,1,1: 93:[30, 1] Operation: 10/10=1 Moving to Node #0,1,1 Current State: 93:[30, 1], Operations: ['93-63=30', '10/10=1'] Exploring Operation: 30*1=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 30+1=31, Resulting Numbers: [31] 31,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[30, 0], Operations: ['93-63=30', '10-10=0'] Exploring Operation: 30-0=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 30+0=30, Resulting Numbers: [30] 30,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[93, 10, 73], Operations: ['63+10=73'] Exploring Operation: 10+73=83, Resulting Numbers: [93, 83] Generated Node #0,0,0: 93:[93, 83] Operation: 10+73=83 Exploring Operation: 93-73=20, Resulting Numbers: [10, 20] Generated Node #0,0,1: 93:[10, 20] Operation: 93-73=20 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[93, 83], Operations: ['63+10=73', '10+73=83'] Exploring Operation: 93+83=176, Resulting Numbers: [176] 176,93 unequal: No Solution Exploring Operation: 93-83=10, Resulting Numbers: [10] 10,93 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 #0,0,1 Current State: 93:[10, 20], Operations: ['63+10=73', '93-73=20'] Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,93 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,93 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 No solution found.
0
hs_2
sum_heuristic
[ 38, 45, 48, 35 ]
43
[ "45-38=7", "35/7=5", "48-5=43" ]
Current State: 43:[38, 45, 48, 35], Operations: [] Exploring Operation: 45-38=7, Resulting Numbers: [48, 35, 7] Generated Node #2: [48, 35, 7] from Operation: 45-38=7 Current State: 43:[48, 35, 7], Operations: ['45-38=7'] Exploring Operation: 35/7=5, Resulting Numbers: [48, 5] Generated Node #3: [48, 5] from Operation: 35/7=5 Current State: 43:[48, 5], Operations: ['45-38=7', '35/7=5'] Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[38, 45, 48, 35], Operations: [] Exploring Operation: 38+35=73, Resulting Numbers: [45, 48, 73] Generated Node #0,0: 43:[45, 48, 73] Operation: 38+35=73 Exploring Operation: 48-38=10, Resulting Numbers: [45, 35, 10] Generated Node #0,1: 43:[45, 35, 10] Operation: 48-38=10 Exploring Operation: 48-35=13, Resulting Numbers: [38, 45, 13] Generated Node #0,2: 43:[38, 45, 13] Operation: 48-35=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[45, 48, 73], Operations: ['38+35=73'] Exploring Operation: 73-48=25, Resulting Numbers: [45, 25] Generated Node #0,0,0: 43:[45, 25] Operation: 73-48=25 Exploring Operation: 73-45=28, Resulting Numbers: [48, 28] Generated Node #0,0,1: 43:[48, 28] Operation: 73-45=28 Exploring Operation: 48-45=3, Resulting Numbers: [73, 3] Generated Node #0,0,2: 43:[73, 3] Operation: 48-45=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[45, 25], Operations: ['38+35=73', '73-48=25'] Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,43 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,43 unequal: No Solution No 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: 43:[48, 28], Operations: ['38+35=73', '73-45=28'] Exploring Operation: 48-28=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 48*28=1344, Resulting Numbers: [1344] 1344,43 unequal: No Solution Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,43 unequal: No Solution No 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: 43:[73, 3], Operations: ['38+35=73', '48-45=3'] Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,43 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,43 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: 43:[38, 45, 13], Operations: ['48-35=13'] Exploring Operation: 45-13=32, Resulting Numbers: [38, 32] Generated Node #0,2,0: 43:[38, 32] Operation: 45-13=32 Exploring Operation: 38+13=51, Resulting Numbers: [45, 51] Generated Node #0,2,1: 43:[45, 51] Operation: 38+13=51 Exploring Operation: 38-13=25, Resulting Numbers: [45, 25] Generated Node #0,2,2: 43:[45, 25] Operation: 38-13=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[45, 51], Operations: ['48-35=13', '38+13=51'] Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,43 unequal: No Solution Exploring Operation: 45*51=2295, Resulting Numbers: [2295] 2295,43 unequal: No Solution Exploring Operation: 51-45=6, Resulting Numbers: [6] 6,43 unequal: No Solution No 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: 43:[38, 32], Operations: ['48-35=13', '45-13=32'] Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,43 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,43 unequal: No Solution No 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: 43:[45, 25], Operations: ['48-35=13', '38-13=25'] Exploring Operation: 45*25=1125, Resulting Numbers: [1125] 1125,43 unequal: No Solution Exploring Operation: 45-25=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 45+25=70, Resulting Numbers: [70] 70,43 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: 43:[45, 35, 10], Operations: ['48-38=10'] Exploring Operation: 45+10=55, Resulting Numbers: [35, 55] Generated Node #0,1,0: 43:[35, 55] Operation: 45+10=55 Exploring Operation: 35+10=45, Resulting Numbers: [45, 45] Generated Node #0,1,1: 43:[45, 45] Operation: 35+10=45 Exploring Operation: 45-10=35, Resulting Numbers: [35, 35] Generated Node #0,1,2: 43:[35, 35] Operation: 45-10=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[45, 45], Operations: ['48-38=10', '35+10=45'] Exploring Operation: 45-45=0, Resulting Numbers: [0] 0,43 unequal: No Solution Exploring Operation: 45/45=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,43 unequal: No Solution No 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: 43:[35, 35], Operations: ['48-38=10', '45-10=35'] Exploring Operation: 35/35=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 35-35=0, Resulting Numbers: [0] 0,43 unequal: No Solution Exploring Operation: 35+35=70, Resulting Numbers: [70] 70,43 unequal: No Solution No 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: 43:[35, 55], Operations: ['48-38=10', '45+10=55'] Exploring Operation: 55-35=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 35*55=1925, Resulting Numbers: [1925] 1925,43 unequal: No Solution Exploring Operation: 35+55=90, Resulting Numbers: [90] 90,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 15, 41, 25, 4 ]
79
[ "41-15=26", "4*26=104", "104-25=79" ]
Current State: 79:[15, 41, 25, 4], Operations: [] Exploring Operation: 41-15=26, Resulting Numbers: [25, 4, 26] Generated Node #2: [25, 4, 26] from Operation: 41-15=26 Current State: 79:[25, 4, 26], Operations: ['41-15=26'] Exploring Operation: 4*26=104, Resulting Numbers: [25, 104] Generated Node #3: [25, 104] from Operation: 4*26=104 Current State: 79:[25, 104], Operations: ['41-15=26', '4*26=104'] Exploring Operation: 104-25=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[15, 41, 25, 4], Operations: [] Exploring Operation: 15+25=40, Resulting Numbers: [41, 4, 40] Generated Node #0,0: 79:[41, 4, 40] Operation: 15+25=40 Exploring Operation: 15+41=56, Resulting Numbers: [25, 4, 56] Generated Node #0,1: 79:[25, 4, 56] Operation: 15+41=56 Exploring Operation: 25*4=100, Resulting Numbers: [15, 41, 100] Generated Node #0,2: 79:[15, 41, 100] Operation: 25*4=100 Exploring Operation: 15*4=60, Resulting Numbers: [41, 25, 60] Generated Node #0,3: 79:[41, 25, 60] Operation: 15*4=60 Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[41, 25, 60], Operations: ['15*4=60'] Exploring Operation: 41-25=16, Resulting Numbers: [60, 16] Generated Node #0,3,0: 79:[60, 16] Operation: 41-25=16 Exploring Operation: 41+60=101, Resulting Numbers: [25, 101] Generated Node #0,3,1: 79:[25, 101] Operation: 41+60=101 Exploring Operation: 25+60=85, Resulting Numbers: [41, 85] Generated Node #0,3,2: 79:[41, 85] Operation: 25+60=85 Exploring Operation: 41+25=66, Resulting Numbers: [60, 66] Generated Node #0,3,3: 79:[60, 66] Operation: 41+25=66 Moving to Node #0,3,3 Current State: 79:[60, 66], Operations: ['15*4=60', '41+25=66'] Exploring Operation: 66-60=6, Resulting Numbers: [6] 6,79 unequal: No Solution Exploring Operation: 60*66=3960, Resulting Numbers: [3960] 3960,79 unequal: No Solution Exploring Operation: 60+66=126, Resulting Numbers: [126] 126,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[41, 85], Operations: ['15*4=60', '25+60=85'] Exploring Operation: 85-41=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 41+85=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 41*85=3485, Resulting Numbers: [3485] 3485,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[25, 101], Operations: ['15*4=60', '41+60=101'] Exploring Operation: 25*101=2525, Resulting Numbers: [2525] 2525,79 unequal: No Solution Exploring Operation: 25+101=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 101-25=76, Resulting Numbers: [76] 76,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[60, 16], Operations: ['15*4=60', '41-25=16'] Exploring Operation: 60-16=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 60+16=76, Resulting Numbers: [76] 76,79 unequal: No Solution Exploring Operation: 60*16=960, Resulting Numbers: [960] 960,79 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 #0,2 Current State: 79:[15, 41, 100], Operations: ['25*4=100'] Exploring Operation: 15+41=56, Resulting Numbers: [100, 56] Generated Node #0,2,0: 79:[100, 56] Operation: 15+41=56 Exploring Operation: 15+100=115, Resulting Numbers: [41, 115] Generated Node #0,2,1: 79:[41, 115] Operation: 15+100=115 Exploring Operation: 41-15=26, Resulting Numbers: [100, 26] Generated Node #0,2,2: 79:[100, 26] Operation: 41-15=26 Exploring Operation: 100-15=85, Resulting Numbers: [41, 85] Generated Node #0,2,3: 79:[41, 85] Operation: 100-15=85 Moving to Node #0,2,0 Current State: 79:[100, 56], Operations: ['25*4=100', '15+41=56'] Exploring Operation: 100*56=5600, Resulting Numbers: [5600] 5600,79 unequal: No Solution Exploring Operation: 100+56=156, Resulting Numbers: [156] 156,79 unequal: No Solution Exploring Operation: 100-56=44, Resulting Numbers: [44] 44,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[41, 85], Operations: ['25*4=100', '100-15=85'] Exploring Operation: 85-41=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 41+85=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 41*85=3485, Resulting Numbers: [3485] 3485,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[100, 26], Operations: ['25*4=100', '41-15=26'] Exploring Operation: 100-26=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 100+26=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 100*26=2600, Resulting Numbers: [2600] 2600,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[41, 115], Operations: ['25*4=100', '15+100=115'] Exploring Operation: 41*115=4715, Resulting Numbers: [4715] 4715,79 unequal: No Solution Exploring Operation: 115-41=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 41+115=156, Resulting Numbers: [156] 156,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[41, 4, 40], Operations: ['15+25=40'] Exploring Operation: 41-4=37, Resulting Numbers: [40, 37] Generated Node #0,0,0: 79:[40, 37] Operation: 41-4=37 Exploring Operation: 41+40=81, Resulting Numbers: [4, 81] Generated Node #0,0,1: 79:[4, 81] Operation: 41+40=81 Exploring Operation: 4+40=44, Resulting Numbers: [41, 44] Generated Node #0,0,2: 79:[41, 44] Operation: 4+40=44 Exploring Operation: 41+4=45, Resulting Numbers: [40, 45] Generated Node #0,0,3: 79:[40, 45] Operation: 41+4=45 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[41, 44], Operations: ['15+25=40', '4+40=44'] Exploring Operation: 41+44=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 41*44=1804, Resulting Numbers: [1804] 1804,79 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,79 unequal: No Solution No 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: 79:[40, 45], Operations: ['15+25=40', '41+4=45'] Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,79 unequal: No Solution Exploring Operation: 40*45=1800, Resulting Numbers: [1800] 1800,79 unequal: No Solution Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,79 unequal: No Solution No 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: 79:[4, 81], Operations: ['15+25=40', '41+40=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,79 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,79 unequal: No Solution No 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: 79:[40, 37], Operations: ['15+25=40', '41-4=37'] Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[25, 4, 56], Operations: ['15+41=56'] Exploring Operation: 25+4=29, Resulting Numbers: [56, 29] Generated Node #0,1,0: 79:[56, 29] Operation: 25+4=29 Exploring Operation: 25*4=100, Resulting Numbers: [56, 100] Generated Node #0,1,1: 79:[56, 100] Operation: 25*4=100 Exploring Operation: 4+56=60, Resulting Numbers: [25, 60] Generated Node #0,1,2: 79:[25, 60] Operation: 4+56=60 Exploring Operation: 25+56=81, Resulting Numbers: [4, 81] Generated Node #0,1,3: 79:[4, 81] Operation: 25+56=81 Moving to Node #0,1,1 Current State: 79:[56, 100], Operations: ['15+41=56', '25*4=100'] Exploring Operation: 56+100=156, Resulting Numbers: [156] 156,79 unequal: No Solution Exploring Operation: 100-56=44, Resulting Numbers: [44] 44,79 unequal: No Solution Exploring Operation: 56*100=5600, Resulting Numbers: [5600] 5600,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[25, 60], Operations: ['15+41=56', '4+56=60'] Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[56, 29], Operations: ['15+41=56', '25+4=29'] Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,79 unequal: No Solution Exploring Operation: 56*29=1624, Resulting Numbers: [1624] 1624,79 unequal: No Solution Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[4, 81], Operations: ['15+41=56', '25+56=81'] Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,79 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 78, 45, 98, 66 ]
41
[ "78+45=123", "98+66=164", "164-123=41" ]
Current State: 41:[78, 45, 98, 66], Operations: [] Exploring Operation: 78+45=123, Resulting Numbers: [98, 66, 123] Generated Node #2: [98, 66, 123] from Operation: 78+45=123 Current State: 41:[98, 66, 123], Operations: ['78+45=123'] Exploring Operation: 98+66=164, Resulting Numbers: [123, 164] Generated Node #3: [123, 164] from Operation: 98+66=164 Current State: 41:[123, 164], Operations: ['78+45=123', '98+66=164'] Exploring Operation: 164-123=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[78, 45, 98, 66], Operations: [] Exploring Operation: 98-78=20, Resulting Numbers: [45, 66, 20] Generated Node #0,0: 41:[45, 66, 20] Operation: 98-78=20 Moving to Node #0,0 Current State: 41:[45, 66, 20], Operations: ['98-78=20'] Exploring Operation: 66-20=46, Resulting Numbers: [45, 46] Generated Node #0,0,0: 41:[45, 46] Operation: 66-20=46 Moving to Node #0,0,0 Current State: 41:[45, 46], Operations: ['98-78=20', '66-20=46'] Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,41 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 12, 36, 86, 33 ]
75
[ "36/12=3", "33/3=11", "86-11=75" ]
Current State: 75:[12, 36, 86, 33], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [86, 33, 3] Generated Node #2: [86, 33, 3] from Operation: 36/12=3 Current State: 75:[86, 33, 3], Operations: ['36/12=3'] Exploring Operation: 33/3=11, Resulting Numbers: [86, 11] Generated Node #3: [86, 11] from Operation: 33/3=11 Current State: 75:[86, 11], Operations: ['36/12=3', '33/3=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[12, 36, 86, 33], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [12, 86, 3] Generated Node #0,0: 75:[12, 86, 3] Operation: 36-33=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[12, 86, 3], Operations: ['36-33=3'] Exploring Operation: 86-12=74, Resulting Numbers: [3, 74] Generated Node #0,0,0: 75:[3, 74] Operation: 86-12=74 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[3, 74], Operations: ['36-33=3', '86-12=74'] Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,75 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
[ 42, 68, 98, 2 ]
22
[ "98-42=56", "68/2=34", "56-34=22" ]
Current State: 22:[42, 68, 98, 2], Operations: [] Exploring Operation: 98-42=56, Resulting Numbers: [68, 2, 56] Generated Node #2: [68, 2, 56] from Operation: 98-42=56 Current State: 22:[68, 2, 56], Operations: ['98-42=56'] Exploring Operation: 68/2=34, Resulting Numbers: [56, 34] Generated Node #3: [56, 34] from Operation: 68/2=34 Current State: 22:[56, 34], Operations: ['98-42=56', '68/2=34'] Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[42, 68, 98, 2], Operations: [] Exploring Operation: 98-68=30, Resulting Numbers: [42, 2, 30] Generated Node #0,0: 22:[42, 2, 30] Operation: 98-68=30 Moving to Node #0,0 Current State: 22:[42, 2, 30], Operations: ['98-68=30'] Exploring Operation: 42-30=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 22:[2, 12] Operation: 42-30=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[2, 12], Operations: ['98-68=30', '42-30=12'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 43, 82, 60, 81 ]
17
[ "60-43=17", "82-81=1", "17*1=17" ]
Current State: 17:[43, 82, 60, 81], Operations: [] Exploring Operation: 60-43=17, Resulting Numbers: [82, 81, 17] Generated Node #2: [82, 81, 17] from Operation: 60-43=17 Current State: 17:[82, 81, 17], Operations: ['60-43=17'] Exploring Operation: 82-81=1, Resulting Numbers: [17, 1] Generated Node #3: [17, 1] from Operation: 82-81=1 Current State: 17:[17, 1], Operations: ['60-43=17', '82-81=1'] Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[43, 82, 60, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [43, 60, 1] Generated Node #0,0: 17:[43, 60, 1] Operation: 82-81=1 Exploring Operation: 81-60=21, Resulting Numbers: [43, 82, 21] Generated Node #0,1: 17:[43, 82, 21] Operation: 81-60=21 Exploring Operation: 82-60=22, Resulting Numbers: [43, 81, 22] Generated Node #0,2: 17:[43, 81, 22] Operation: 82-60=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[43, 60, 1], Operations: ['82-81=1'] Exploring Operation: 60-1=59, Resulting Numbers: [43, 59] Generated Node #0,0,0: 17:[43, 59] Operation: 60-1=59 Exploring Operation: 60-43=17, Resulting Numbers: [1, 17] Generated Node #0,0,1: 17:[1, 17] Operation: 60-43=17 Exploring Operation: 43-1=42, Resulting Numbers: [60, 42] Generated Node #0,0,2: 17:[60, 42] Operation: 43-1=42 Moving to Node #0,0,1 Current State: 17:[1, 17], Operations: ['82-81=1', '60-43=17'] Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[43, 82, 60, 81], Operations: [] Exploring Operation: 82-81=1, Resulting Numbers: [43, 60, 1] Generated Node #0,0: 17:[43, 60, 1] Operation: 82-81=1 Moving to Node #0,0 Current State: 17:[43, 60, 1], Operations: ['82-81=1'] Exploring Operation: 60-43=17, Resulting Numbers: [1, 17] Generated Node #0,0,1: 17:[1, 17] Operation: 60-43=17 Moving to Node #0,0,1 Current State: 17:[1, 17], Operations: ['82-81=1', '60-43=17'] Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 80, 13, 21, 52 ]
55
[ "80-21=59", "52/13=4", "59-4=55" ]
Current State: 55:[80, 13, 21, 52], Operations: [] Exploring Operation: 80-21=59, Resulting Numbers: [13, 52, 59] Generated Node #2: [13, 52, 59] from Operation: 80-21=59 Current State: 55:[13, 52, 59], Operations: ['80-21=59'] Exploring Operation: 52/13=4, Resulting Numbers: [59, 4] Generated Node #3: [59, 4] from Operation: 52/13=4 Current State: 55:[59, 4], Operations: ['80-21=59', '52/13=4'] Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[80, 13, 21, 52], Operations: [] Exploring Operation: 80-21=59, Resulting Numbers: [13, 52, 59] Generated Node #0,0: 55:[13, 52, 59] Operation: 80-21=59 Moving to Node #0,0 Current State: 55:[13, 52, 59], Operations: ['80-21=59'] Exploring Operation: 59-52=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 55:[13, 7] Operation: 59-52=7 Moving to Node #0,0,0 Current State: 55:[13, 7], Operations: ['80-21=59', '59-52=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,55 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 4, 64, 3, 34 ]
75
[ "4*34=136", "64-3=61", "136-61=75" ]
Current State: 75:[4, 64, 3, 34], Operations: [] Exploring Operation: 4*34=136, Resulting Numbers: [64, 3, 136] Generated Node #2: [64, 3, 136] from Operation: 4*34=136 Current State: 75:[64, 3, 136], Operations: ['4*34=136'] Exploring Operation: 64-3=61, Resulting Numbers: [136, 61] Generated Node #3: [136, 61] from Operation: 64-3=61 Current State: 75:[136, 61], Operations: ['4*34=136', '64-3=61'] Exploring Operation: 136-61=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[4, 64, 3, 34], Operations: [] Exploring Operation: 64-34=30, Resulting Numbers: [4, 3, 30] Generated Node #0,0: 75:[4, 3, 30] Operation: 64-34=30 Moving to Node #0,0 Current State: 75:[4, 3, 30], Operations: ['64-34=30'] Exploring Operation: 30-4=26, Resulting Numbers: [3, 26] Generated Node #0,0,0: 75:[3, 26] Operation: 30-4=26 Moving to Node #0,0,0 Current State: 75:[3, 26], Operations: ['64-34=30', '30-4=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,75 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 48, 27, 59, 42 ]
92
[ "48+27=75", "59-42=17", "75+17=92" ]
Current State: 92:[48, 27, 59, 42], Operations: [] Exploring Operation: 48+27=75, Resulting Numbers: [59, 42, 75] Generated Node #2: [59, 42, 75] from Operation: 48+27=75 Current State: 92:[59, 42, 75], Operations: ['48+27=75'] Exploring Operation: 59-42=17, Resulting Numbers: [75, 17] Generated Node #3: [75, 17] from Operation: 59-42=17 Current State: 92:[75, 17], Operations: ['48+27=75', '59-42=17'] Exploring Operation: 75+17=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[48, 27, 59, 42], Operations: [] Exploring Operation: 59-48=11, Resulting Numbers: [27, 42, 11] Generated Node #0,0: 92:[27, 42, 11] Operation: 59-48=11 Exploring Operation: 27+59=86, Resulting Numbers: [48, 42, 86] Generated Node #0,1: 92:[48, 42, 86] Operation: 27+59=86 Exploring Operation: 59-27=32, Resulting Numbers: [48, 42, 32] Generated Node #0,2: 92:[48, 42, 32] Operation: 59-27=32 Exploring Operation: 59+42=101, Resulting Numbers: [48, 27, 101] Generated Node #0,3: 92:[48, 27, 101] Operation: 59+42=101 Exploring Operation: 59-42=17, Resulting Numbers: [48, 27, 17] Generated Node #0,4: 92:[48, 27, 17] Operation: 59-42=17 Moving to Node #0,1 Current State: 92:[48, 42, 86], Operations: ['27+59=86'] Exploring Operation: 86-48=38, Resulting Numbers: [42, 38] Generated Node #0,1,0: 92:[42, 38] Operation: 86-48=38 Exploring Operation: 86-42=44, Resulting Numbers: [48, 44] Generated Node #0,1,1: 92:[48, 44] Operation: 86-42=44 Exploring Operation: 48+42=90, Resulting Numbers: [86, 90] Generated Node #0,1,2: 92:[86, 90] Operation: 48+42=90 Exploring Operation: 48-42=6, Resulting Numbers: [86, 6] Generated Node #0,1,3: 92:[86, 6] Operation: 48-42=6 Exploring Operation: 42+86=128, Resulting Numbers: [48, 128] Generated Node #0,1,4: 92:[48, 128] Operation: 42+86=128 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[48, 44], Operations: ['27+59=86', '86-42=44'] Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[48, 27, 59, 42], Operations: [] Exploring Operation: 27+59=86, Resulting Numbers: [48, 42, 86] Generated Node #0,1: 92:[48, 42, 86] Operation: 27+59=86 Moving to Node #0,1 Current State: 92:[48, 42, 86], Operations: ['27+59=86'] Exploring Operation: 86-42=44, Resulting Numbers: [48, 44] Generated Node #0,1,1: 92:[48, 44] Operation: 86-42=44 Moving to Node #0,1,1 Current State: 92:[48, 44], Operations: ['27+59=86', '86-42=44'] Exploring Operation: 48+44=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 44, 79, 1, 2 ]
62
[ "44+79=123", "1+123=124", "124/2=62" ]
Current State: 62:[44, 79, 1, 2], Operations: [] Exploring Operation: 44+79=123, Resulting Numbers: [1, 2, 123] Generated Node #2: [1, 2, 123] from Operation: 44+79=123 Current State: 62:[1, 2, 123], Operations: ['44+79=123'] Exploring Operation: 1+123=124, Resulting Numbers: [2, 124] Generated Node #3: [2, 124] from Operation: 1+123=124 Current State: 62:[2, 124], Operations: ['44+79=123', '1+123=124'] Exploring Operation: 124/2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[44, 79, 1, 2], Operations: [] Exploring Operation: 44-2=42, Resulting Numbers: [79, 1, 42] Generated Node #0,0: 62:[79, 1, 42] Operation: 44-2=42 Exploring Operation: 44-1=43, Resulting Numbers: [79, 2, 43] Generated Node #0,1: 62:[79, 2, 43] Operation: 44-1=43 Exploring Operation: 44/2=22, Resulting Numbers: [79, 1, 22] Generated Node #0,2: 62:[79, 1, 22] Operation: 44/2=22 Exploring Operation: 79-44=35, Resulting Numbers: [1, 2, 35] Generated Node #0,3: 62:[1, 2, 35] Operation: 79-44=35 Moving to Node #0,3 Current State: 62:[1, 2, 35], Operations: ['79-44=35'] Exploring Operation: 35-1=34, Resulting Numbers: [2, 34] Generated Node #0,3,0: 62:[2, 34] Operation: 35-1=34 Exploring Operation: 2/1=2, Resulting Numbers: [35, 2] Generated Node #0,3,1: 62:[35, 2] Operation: 2/1=2 Exploring Operation: 1*2=2, Resulting Numbers: [35, 2] Generated Node #0,3,2: 62:[35, 2] Operation: 1*2=2 Exploring Operation: 35-2=33, Resulting Numbers: [1, 33] Generated Node #0,3,3: 62:[1, 33] Operation: 35-2=33 Moving to Node #0,2 Current State: 62:[79, 1, 22], Operations: ['44/2=22'] Exploring Operation: 79-22=57, Resulting Numbers: [1, 57] Generated Node #0,2,0: 62:[1, 57] Operation: 79-22=57 Exploring Operation: 79*1=79, Resulting Numbers: [22, 79] Generated Node #0,2,1: 62:[22, 79] Operation: 79*1=79 Exploring Operation: 1+22=23, Resulting Numbers: [79, 23] Generated Node #0,2,2: 62:[79, 23] Operation: 1+22=23 Exploring Operation: 79-1=78, Resulting Numbers: [22, 78] Generated Node #0,2,3: 62:[22, 78] Operation: 79-1=78 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 62:[1, 57], Operations: ['44/2=22', '79-22=57'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,62 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[79, 23], Operations: ['44/2=22', '1+22=23'] Exploring Operation: 79*23=1817, Resulting Numbers: [1817] 1817,62 unequal: No Solution Exploring Operation: 79-23=56, Resulting Numbers: [56] 56,62 unequal: No Solution Exploring Operation: 79+23=102, Resulting Numbers: [102] 102,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 62:[22, 78], Operations: ['44/2=22', '79-1=78'] Exploring Operation: 22*78=1716, Resulting Numbers: [1716] 1716,62 unequal: No Solution Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,62 unequal: No Solution Exploring Operation: 78-22=56, Resulting Numbers: [56] 56,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[22, 79], Operations: ['44/2=22', '79*1=79'] Exploring Operation: 22*79=1738, Resulting Numbers: [1738] 1738,62 unequal: No Solution Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,62 unequal: No Solution Exploring Operation: 22+79=101, Resulting Numbers: [101] 101,62 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: 62:[79, 2, 43], Operations: ['44-1=43'] Exploring Operation: 79-43=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 62:[2, 36] Operation: 79-43=36 Exploring Operation: 43-2=41, Resulting Numbers: [79, 41] Generated Node #0,1,1: 62:[79, 41] Operation: 43-2=41 Exploring Operation: 79-2=77, Resulting Numbers: [43, 77] Generated Node #0,1,2: 62:[43, 77] Operation: 79-2=77 Exploring Operation: 79+2=81, Resulting Numbers: [43, 81] Generated Node #0,1,3: 62:[43, 81] Operation: 79+2=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[2, 36], Operations: ['44-1=43', '79-43=36'] Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,62 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 62:[79, 41], Operations: ['44-1=43', '43-2=41'] Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,62 unequal: No Solution Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 62:[43, 77], Operations: ['44-1=43', '79-2=77'] Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 43+77=120, Resulting Numbers: [120] 120,62 unequal: No Solution Exploring Operation: 43*77=3311, Resulting Numbers: [3311] 3311,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 62:[43, 81], Operations: ['44-1=43', '79+2=81'] Exploring Operation: 43+81=124, Resulting Numbers: [124] 124,62 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 43*81=3483, Resulting Numbers: [3483] 3483,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 62:[79, 1, 42], Operations: ['44-2=42'] Exploring Operation: 79-1=78, Resulting Numbers: [42, 78] Generated Node #0,0,0: 62:[42, 78] Operation: 79-1=78 Exploring Operation: 42-1=41, Resulting Numbers: [79, 41] Generated Node #0,0,1: 62:[79, 41] Operation: 42-1=41 Exploring Operation: 79-42=37, Resulting Numbers: [1, 37] Generated Node #0,0,2: 62:[1, 37] Operation: 79-42=37 Exploring Operation: 79*1=79, Resulting Numbers: [42, 79] Generated Node #0,0,3: 62:[42, 79] Operation: 79*1=79 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[1, 37], Operations: ['44-2=42', '79-42=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[42, 78], Operations: ['44-2=42', '79-1=78'] Exploring Operation: 42+78=120, Resulting Numbers: [120] 120,62 unequal: No Solution Exploring Operation: 78-42=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 42*78=3276, Resulting Numbers: [3276] 3276,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[79, 41], Operations: ['44-2=42', '42-1=41'] Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,62 unequal: No Solution Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,62 unequal: No Solution Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 62:[42, 79], Operations: ['44-2=42', '79*1=79'] Exploring Operation: 42+79=121, Resulting Numbers: [121] 121,62 unequal: No Solution Exploring Operation: 42*79=3318, Resulting Numbers: [3318] 3318,62 unequal: No Solution Exploring Operation: 79-42=37, Resulting Numbers: [37] 37,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 62:[2, 34], Operations: ['79-44=35', '35-1=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,62 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,62 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,62 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[1, 33], Operations: ['79-44=35', '35-2=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 1+33=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,62 unequal: No Solution Moving to Node #0,3,2 Current State: 62:[35, 2], Operations: ['79-44=35', '1*2=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,62 unequal: No Solution Moving to Node #0,3,1 Current State: 62:[35, 2], Operations: ['79-44=35', '2/1=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,62 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,62 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 39, 80, 51, 13 ]
26
[ "39/13=3", "80-51=29", "29-3=26" ]
Current State: 26:[39, 80, 51, 13], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [80, 51, 3] Generated Node #2: [80, 51, 3] from Operation: 39/13=3 Current State: 26:[80, 51, 3], Operations: ['39/13=3'] Exploring Operation: 80-51=29, Resulting Numbers: [3, 29] Generated Node #3: [3, 29] from Operation: 80-51=29 Current State: 26:[3, 29], Operations: ['39/13=3', '80-51=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[39, 80, 51, 13], Operations: [] Exploring Operation: 39-13=26, Resulting Numbers: [80, 51, 26] Generated Node #0,0: 26:[80, 51, 26] Operation: 39-13=26 Exploring Operation: 80-39=41, Resulting Numbers: [51, 13, 41] Generated Node #0,1: 26:[51, 13, 41] Operation: 80-39=41 Exploring Operation: 80-51=29, Resulting Numbers: [39, 13, 29] Generated Node #0,2: 26:[39, 13, 29] Operation: 80-51=29 Exploring Operation: 80-13=67, Resulting Numbers: [39, 51, 67] Generated Node #0,3: 26:[39, 51, 67] Operation: 80-13=67 Exploring Operation: 51-39=12, Resulting Numbers: [80, 13, 12] Generated Node #0,4: 26:[80, 13, 12] Operation: 51-39=12 Moving to Node #0,2 Current State: 26:[39, 13, 29], Operations: ['80-51=29'] Exploring Operation: 39/13=3, Resulting Numbers: [29, 3] Generated Node #0,2,0: 26:[29, 3] Operation: 39/13=3 Exploring Operation: 29-13=16, Resulting Numbers: [39, 16] Generated Node #0,2,1: 26:[39, 16] Operation: 29-13=16 Exploring Operation: 39+13=52, Resulting Numbers: [29, 52] Generated Node #0,2,2: 26:[29, 52] Operation: 39+13=52 Exploring Operation: 39-13=26, Resulting Numbers: [29, 26] Generated Node #0,2,3: 26:[29, 26] Operation: 39-13=26 Exploring Operation: 39-29=10, Resulting Numbers: [13, 10] Generated Node #0,2,4: 26:[13, 10] Operation: 39-29=10 Moving to Node #0,1 Current State: 26:[51, 13, 41], Operations: ['80-39=41'] Exploring Operation: 51+13=64, Resulting Numbers: [41, 64] Generated Node #0,1,0: 26:[41, 64] Operation: 51+13=64 Exploring Operation: 13+41=54, Resulting Numbers: [51, 54] Generated Node #0,1,1: 26:[51, 54] Operation: 13+41=54 Exploring Operation: 41-13=28, Resulting Numbers: [51, 28] Generated Node #0,1,2: 26:[51, 28] Operation: 41-13=28 Exploring Operation: 51-41=10, Resulting Numbers: [13, 10] Generated Node #0,1,3: 26:[13, 10] Operation: 51-41=10 Exploring Operation: 51-13=38, Resulting Numbers: [41, 38] Generated Node #0,1,4: 26:[41, 38] Operation: 51-13=38 Moving to Node #0,4 Current State: 26:[80, 13, 12], Operations: ['51-39=12'] Exploring Operation: 13+12=25, Resulting Numbers: [80, 25] Generated Node #0,4,0: 26:[80, 25] Operation: 13+12=25 Exploring Operation: 80-13=67, Resulting Numbers: [12, 67] Generated Node #0,4,1: 26:[12, 67] Operation: 80-13=67 Exploring Operation: 80+12=92, Resulting Numbers: [13, 92] Generated Node #0,4,2: 26:[13, 92] Operation: 80+12=92 Exploring Operation: 13-12=1, Resulting Numbers: [80, 1] Generated Node #0,4,3: 26:[80, 1] Operation: 13-12=1 Exploring Operation: 80-12=68, Resulting Numbers: [13, 68] Generated Node #0,4,4: 26:[13, 68] Operation: 80-12=68 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 26:[12, 67], Operations: ['51-39=12', '80-13=67'] Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,26 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 26:[13, 68], Operations: ['51-39=12', '80-12=68'] Exploring Operation: 13*68=884, Resulting Numbers: [884] 884,26 unequal: No Solution Exploring Operation: 13+68=81, Resulting Numbers: [81] 81,26 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 26:[80, 25], Operations: ['51-39=12', '13+12=25'] Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,26 unequal: No Solution Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 26:[80, 1], Operations: ['51-39=12', '13-12=1'] Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,26 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,26 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 26:[13, 92], Operations: ['51-39=12', '80+12=92'] Exploring Operation: 13*92=1196, Resulting Numbers: [1196] 1196,26 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,26 unequal: No Solution Exploring Operation: 13+92=105, Resulting Numbers: [105] 105,26 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: 26:[80, 51, 26], Operations: ['39-13=26'] Exploring Operation: 80-51=29, Resulting Numbers: [26, 29] Generated Node #0,0,0: 26:[26, 29] Operation: 80-51=29 Exploring Operation: 80+26=106, Resulting Numbers: [51, 106] Generated Node #0,0,1: 26:[51, 106] Operation: 80+26=106 Exploring Operation: 80-26=54, Resulting Numbers: [51, 54] Generated Node #0,0,2: 26:[51, 54] Operation: 80-26=54 Exploring Operation: 80+51=131, Resulting Numbers: [26, 131] Generated Node #0,0,3: 26:[26, 131] Operation: 80+51=131 Exploring Operation: 51-26=25, Resulting Numbers: [80, 25] Generated Node #0,0,4: 26:[80, 25] Operation: 51-26=25 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[26, 29], Operations: ['39-13=26', '80-51=29'] Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,26 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[51, 54], Operations: ['39-13=26', '80-26=54'] Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 51*54=2754, Resulting Numbers: [2754] 2754,26 unequal: No Solution Exploring Operation: 51+54=105, Resulting Numbers: [105] 105,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 26:[80, 25], Operations: ['39-13=26', '51-26=25'] Exploring Operation: 80+25=105, Resulting Numbers: [105] 105,26 unequal: No Solution Exploring Operation: 80*25=2000, Resulting Numbers: [2000] 2000,26 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[51, 106], Operations: ['39-13=26', '80+26=106'] Exploring Operation: 106-51=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 51+106=157, Resulting Numbers: [157] 157,26 unequal: No Solution Exploring Operation: 51*106=5406, Resulting Numbers: [5406] 5406,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 26:[26, 131], Operations: ['39-13=26', '80+51=131'] Exploring Operation: 26*131=3406, Resulting Numbers: [3406] 3406,26 unequal: No Solution Exploring Operation: 26+131=157, Resulting Numbers: [157] 157,26 unequal: No Solution Exploring Operation: 131-26=105, Resulting Numbers: [105] 105,26 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: 26:[39, 51, 67], Operations: ['80-13=67'] Exploring Operation: 39+67=106, Resulting Numbers: [51, 106] Generated Node #0,3,0: 26:[51, 106] Operation: 39+67=106 Exploring Operation: 39+51=90, Resulting Numbers: [67, 90] Generated Node #0,3,1: 26:[67, 90] Operation: 39+51=90 Exploring Operation: 51-39=12, Resulting Numbers: [67, 12] Generated Node #0,3,2: 26:[67, 12] Operation: 51-39=12 Exploring Operation: 67-39=28, Resulting Numbers: [51, 28] Generated Node #0,3,3: 26:[51, 28] Operation: 67-39=28 Exploring Operation: 67-51=16, Resulting Numbers: [39, 16] Generated Node #0,3,4: 26:[39, 16] Operation: 67-51=16 Moving to Node #0,2,3 Current State: 26:[29, 26], Operations: ['80-51=29', '39-13=26'] Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,26 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,26 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,1,3 Current State: 26:[13, 10], Operations: ['80-39=41', '51-41=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,26 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,26 unequal: No Solution Moving to Node #0,2,4 Current State: 26:[13, 10], Operations: ['80-51=29', '39-29=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,26 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,2,0 Current State: 26:[29, 3], Operations: ['80-51=29', '39/13=3'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[39, 80, 51, 13], Operations: [] Exploring Operation: 80-51=29, Resulting Numbers: [39, 13, 29] Generated Node #0,2: 26:[39, 13, 29] Operation: 80-51=29 Moving to Node #0,2 Current State: 26:[39, 13, 29], Operations: ['80-51=29'] Exploring Operation: 39/13=3, Resulting Numbers: [29, 3] Generated Node #0,2,0: 26:[29, 3] Operation: 39/13=3 Moving to Node #0,2,0 Current State: 26:[29, 3], Operations: ['80-51=29', '39/13=3'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
0.934896
hs_5
sum_heuristic
[ 20, 8, 55, 73 ]
51
[ "8*55=440", "440/20=22", "73-22=51" ]
Current State: 51:[20, 8, 55, 73], Operations: [] Exploring Operation: 8*55=440, Resulting Numbers: [20, 73, 440] Generated Node #2: [20, 73, 440] from Operation: 8*55=440 Current State: 51:[20, 73, 440], Operations: ['8*55=440'] Exploring Operation: 440/20=22, Resulting Numbers: [73, 22] Generated Node #3: [73, 22] from Operation: 440/20=22 Current State: 51:[73, 22], Operations: ['8*55=440', '440/20=22'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[20, 8, 55, 73], Operations: [] Exploring Operation: 73-20=53, Resulting Numbers: [8, 55, 53] Generated Node #0,0: 51:[8, 55, 53] Operation: 73-20=53 Exploring Operation: 73-55=18, Resulting Numbers: [20, 8, 18] Generated Node #0,1: 51:[20, 8, 18] Operation: 73-55=18 Exploring Operation: 73-8=65, Resulting Numbers: [20, 55, 65] Generated Node #0,2: 51:[20, 55, 65] Operation: 73-8=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[20, 8, 18], Operations: ['73-55=18'] Exploring Operation: 20-8=12, Resulting Numbers: [18, 12] Generated Node #0,1,0: 51:[18, 12] Operation: 20-8=12 Exploring Operation: 20-18=2, Resulting Numbers: [8, 2] Generated Node #0,1,1: 51:[8, 2] Operation: 20-18=2 Exploring Operation: 18-8=10, Resulting Numbers: [20, 10] Generated Node #0,1,2: 51:[20, 10] Operation: 18-8=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 51:[18, 12], Operations: ['73-55=18', '20-8=12'] Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,51 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,51 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[8, 2], Operations: ['73-55=18', '20-18=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 51:[20, 10], Operations: ['73-55=18', '18-8=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,51 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[8, 55, 53], Operations: ['73-20=53'] Exploring Operation: 53-8=45, Resulting Numbers: [55, 45] Generated Node #0,0,0: 51:[55, 45] Operation: 53-8=45 Exploring Operation: 55-8=47, Resulting Numbers: [53, 47] Generated Node #0,0,1: 51:[53, 47] Operation: 55-8=47 Exploring Operation: 55-53=2, Resulting Numbers: [8, 2] Generated Node #0,0,2: 51:[8, 2] Operation: 55-53=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[53, 47], Operations: ['73-20=53', '55-8=47'] Exploring Operation: 53+47=100, Resulting Numbers: [100] 100,51 unequal: No Solution Exploring Operation: 53*47=2491, Resulting Numbers: [2491] 2491,51 unequal: No Solution Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[8, 2], Operations: ['73-20=53', '55-53=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[55, 45], Operations: ['73-20=53', '53-8=45'] Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,51 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[20, 55, 65], Operations: ['73-8=65'] Exploring Operation: 65-20=45, Resulting Numbers: [55, 45] Generated Node #0,2,0: 51:[55, 45] Operation: 65-20=45 Exploring Operation: 55-20=35, Resulting Numbers: [65, 35] Generated Node #0,2,1: 51:[65, 35] Operation: 55-20=35 Exploring Operation: 65-55=10, Resulting Numbers: [20, 10] Generated Node #0,2,2: 51:[20, 10] Operation: 65-55=10 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 51:[55, 45], Operations: ['73-8=65', '65-20=45'] Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,51 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[20, 10], Operations: ['73-8=65', '65-55=10'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 51:[65, 35], Operations: ['73-8=65', '55-20=35'] Exploring Operation: 65+35=100, Resulting Numbers: [100] 100,51 unequal: No Solution Exploring Operation: 65*35=2275, Resulting Numbers: [2275] 2275,51 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 9, 71, 26, 3 ]
24
[ "71-26=45", "45/3=15", "9+15=24" ]
Current State: 24:[9, 71, 26, 3], Operations: [] Exploring Operation: 71-26=45, Resulting Numbers: [9, 3, 45] Generated Node #2: [9, 3, 45] from Operation: 71-26=45 Current State: 24:[9, 3, 45], Operations: ['71-26=45'] Exploring Operation: 45/3=15, Resulting Numbers: [9, 15] Generated Node #3: [9, 15] from Operation: 45/3=15 Current State: 24:[9, 15], Operations: ['71-26=45', '45/3=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[9, 71, 26, 3], Operations: [] Exploring Operation: 71-3=68, Resulting Numbers: [9, 26, 68] Generated Node #0,0: 24:[9, 26, 68] Operation: 71-3=68 Exploring Operation: 71-26=45, Resulting Numbers: [9, 3, 45] Generated Node #0,1: 24:[9, 3, 45] Operation: 71-26=45 Exploring Operation: 9+3=12, Resulting Numbers: [71, 26, 12] Generated Node #0,2: 24:[71, 26, 12] Operation: 9+3=12 Exploring Operation: 71-9=62, Resulting Numbers: [26, 3, 62] Generated Node #0,3: 24:[26, 3, 62] Operation: 71-9=62 Exploring Operation: 9-3=6, Resulting Numbers: [71, 26, 6] Generated Node #0,4: 24:[71, 26, 6] Operation: 9-3=6 Moving to Node #0,1 Current State: 24:[9, 3, 45], Operations: ['71-26=45'] Exploring Operation: 45/9=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 24:[3, 5] Operation: 45/9=5 Exploring Operation: 45-3=42, Resulting Numbers: [9, 42] Generated Node #0,1,1: 24:[9, 42] Operation: 45-3=42 Exploring Operation: 45/3=15, Resulting Numbers: [9, 15] Generated Node #0,1,2: 24:[9, 15] Operation: 45/3=15 Exploring Operation: 45-9=36, Resulting Numbers: [3, 36] Generated Node #0,1,3: 24:[3, 36] Operation: 45-9=36 Exploring Operation: 9+3=12, Resulting Numbers: [45, 12] Generated Node #0,1,4: 24:[45, 12] Operation: 9+3=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 24:[3, 5], Operations: ['71-26=45', '45/9=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,24 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,24 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[9, 15], Operations: ['71-26=45', '45/3=15'] Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,24 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[9, 71, 26, 3], Operations: [] Exploring Operation: 71-26=45, Resulting Numbers: [9, 3, 45] Generated Node #0,1: 24:[9, 3, 45] Operation: 71-26=45 Moving to Node #0,1 Current State: 24:[9, 3, 45], Operations: ['71-26=45'] Exploring Operation: 45/3=15, Resulting Numbers: [9, 15] Generated Node #0,1,2: 24:[9, 15] Operation: 45/3=15 Moving to Node #0,1,2 Current State: 24:[9, 15], Operations: ['71-26=45', '45/3=15'] Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 78, 85, 83, 30 ]
60
[ "85-78=7", "83-30=53", "7+53=60" ]
Current State: 60:[78, 85, 83, 30], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [83, 30, 7] Generated Node #2: [83, 30, 7] from Operation: 85-78=7 Current State: 60:[83, 30, 7], Operations: ['85-78=7'] Exploring Operation: 83-30=53, Resulting Numbers: [7, 53] Generated Node #3: [7, 53] from Operation: 83-30=53 Current State: 60:[7, 53], Operations: ['85-78=7', '83-30=53'] Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[78, 85, 83, 30], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [78, 30, 2] Generated Node #0,0: 60:[78, 30, 2] Operation: 85-83=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[78, 30, 2], Operations: ['85-83=2'] Exploring Operation: 78/2=39, Resulting Numbers: [30, 39] Generated Node #0,0,0: 60:[30, 39] Operation: 78/2=39 Moving to Node #0,0,0 Current State: 60:[30, 39], Operations: ['85-83=2', '78/2=39'] Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 21, 43, 76 ]
17
[ "37-21=16", "76-43=33", "33-16=17" ]
Current State: 17:[37, 21, 43, 76], Operations: [] Exploring Operation: 37-21=16, Resulting Numbers: [43, 76, 16] Generated Node #2: [43, 76, 16] from Operation: 37-21=16 Current State: 17:[43, 76, 16], Operations: ['37-21=16'] Exploring Operation: 76-43=33, Resulting Numbers: [16, 33] Generated Node #3: [16, 33] from Operation: 76-43=33 Current State: 17:[16, 33], Operations: ['37-21=16', '76-43=33'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[37, 21, 43, 76], Operations: [] Exploring Operation: 76-43=33, Resulting Numbers: [37, 21, 33] Generated Node #0,0: 17:[37, 21, 33] Operation: 76-43=33 Moving to Node #0,0 Current State: 17:[37, 21, 33], Operations: ['76-43=33'] Exploring Operation: 37-21=16, Resulting Numbers: [33, 16] Generated Node #0,0,0: 17:[33, 16] Operation: 37-21=16 Moving to Node #0,0,0 Current State: 17:[33, 16], Operations: ['76-43=33', '37-21=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[37, 21, 43, 76], Operations: [] Exploring Operation: 76-43=33, Resulting Numbers: [37, 21, 33] Generated Node #0,0: 17:[37, 21, 33] Operation: 76-43=33 Moving to Node #0,0 Current State: 17:[37, 21, 33], Operations: ['76-43=33'] Exploring Operation: 37-21=16, Resulting Numbers: [33, 16] Generated Node #0,0,0: 17:[33, 16] Operation: 37-21=16 Moving to Node #0,0,0 Current State: 17:[33, 16], Operations: ['76-43=33', '37-21=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 5, 51, 18, 45 ]
49
[ "5*18=90", "90/45=2", "51-2=49" ]
Current State: 49:[5, 51, 18, 45], Operations: [] Exploring Operation: 5*18=90, Resulting Numbers: [51, 45, 90] Generated Node #2: [51, 45, 90] from Operation: 5*18=90 Current State: 49:[51, 45, 90], Operations: ['5*18=90'] Exploring Operation: 90/45=2, Resulting Numbers: [51, 2] Generated Node #3: [51, 2] from Operation: 90/45=2 Current State: 49:[51, 2], Operations: ['5*18=90', '90/45=2'] Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[5, 51, 18, 45], Operations: [] Exploring Operation: 18-5=13, Resulting Numbers: [51, 45, 13] Generated Node #0,0: 49:[51, 45, 13] Operation: 18-5=13 Exploring Operation: 5+45=50, Resulting Numbers: [51, 18, 50] Generated Node #0,1: 49:[51, 18, 50] Operation: 5+45=50 Exploring Operation: 51-45=6, Resulting Numbers: [5, 18, 6] Generated Node #0,2: 49:[5, 18, 6] Operation: 51-45=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[51, 45, 13], Operations: ['18-5=13'] Exploring Operation: 45+13=58, Resulting Numbers: [51, 58] Generated Node #0,0,0: 49:[51, 58] Operation: 45+13=58 Exploring Operation: 51-13=38, Resulting Numbers: [45, 38] Generated Node #0,0,1: 49:[45, 38] Operation: 51-13=38 Exploring Operation: 51-45=6, Resulting Numbers: [13, 6] Generated Node #0,0,2: 49:[13, 6] Operation: 51-45=6 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[13, 6], Operations: ['18-5=13', '51-45=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,49 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 #0,0,0 Current State: 49:[51, 58], Operations: ['18-5=13', '45+13=58'] Exploring Operation: 58-51=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 51+58=109, Resulting Numbers: [109] 109,49 unequal: No Solution Exploring Operation: 51*58=2958, Resulting Numbers: [2958] 2958,49 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 #0,0,1 Current State: 49:[45, 38], Operations: ['18-5=13', '51-13=38'] Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,49 unequal: No Solution Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[51, 18, 50], Operations: ['5+45=50'] Exploring Operation: 50-18=32, Resulting Numbers: [51, 32] Generated Node #0,1,0: 49:[51, 32] Operation: 50-18=32 Exploring Operation: 51-50=1, Resulting Numbers: [18, 1] Generated Node #0,1,1: 49:[18, 1] Operation: 51-50=1 Exploring Operation: 51-18=33, Resulting Numbers: [50, 33] Generated Node #0,1,2: 49:[50, 33] Operation: 51-18=33 Moving to Node #0,1,1 Current State: 49:[18, 1], Operations: ['5+45=50', '51-50=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,49 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,49 unequal: No Solution Moving to Node #0,1,2 Current State: 49:[50, 33], Operations: ['5+45=50', '51-18=33'] Exploring Operation: 50*33=1650, Resulting Numbers: [1650] 1650,49 unequal: No Solution Exploring Operation: 50-33=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 50+33=83, Resulting Numbers: [83] 83,49 unequal: No Solution Moving to Node #0,1,0 Current State: 49:[51, 32], Operations: ['5+45=50', '50-18=32'] Exploring Operation: 51+32=83, Resulting Numbers: [83] 83,49 unequal: No Solution Exploring Operation: 51*32=1632, Resulting Numbers: [1632] 1632,49 unequal: No Solution Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,49 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 #0,2 Current State: 49:[5, 18, 6], Operations: ['51-45=6'] Exploring Operation: 18-5=13, Resulting Numbers: [6, 13] Generated Node #0,2,0: 49:[6, 13] Operation: 18-5=13 Exploring Operation: 18-6=12, Resulting Numbers: [5, 12] Generated Node #0,2,1: 49:[5, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [5, 3] Generated Node #0,2,2: 49:[5, 3] Operation: 18/6=3 Moving to Node #0,2,2 Current State: 49:[5, 3], Operations: ['51-45=6', '18/6=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,49 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[6, 13], Operations: ['51-45=6', '18-5=13'] Exploring Operation: 6*13=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,49 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[5, 12], Operations: ['51-45=6', '18-6=12'] Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,49 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,49 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
[ 13, 75, 93, 91 ]
25
[ "91/13=7", "93-75=18", "7+18=25" ]
Current State: 25:[13, 75, 93, 91], Operations: [] Exploring Operation: 91/13=7, Resulting Numbers: [75, 93, 7] Generated Node #2: [75, 93, 7] from Operation: 91/13=7 Current State: 25:[75, 93, 7], Operations: ['91/13=7'] Exploring Operation: 93-75=18, Resulting Numbers: [7, 18] Generated Node #3: [7, 18] from Operation: 93-75=18 Current State: 25:[7, 18], Operations: ['91/13=7', '93-75=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[13, 75, 93, 91], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [13, 75, 2] Generated Node #0,0: 25:[13, 75, 2] Operation: 93-91=2 Exploring Operation: 93-75=18, Resulting Numbers: [13, 91, 18] Generated Node #0,1: 25:[13, 91, 18] Operation: 93-75=18 Exploring Operation: 91-75=16, Resulting Numbers: [13, 93, 16] Generated Node #0,2: 25:[13, 93, 16] Operation: 91-75=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[13, 75, 2], Operations: ['93-91=2'] Exploring Operation: 13-2=11, Resulting Numbers: [75, 11] Generated Node #0,0,0: 25:[75, 11] Operation: 13-2=11 Exploring Operation: 13*2=26, Resulting Numbers: [75, 26] Generated Node #0,0,1: 25:[75, 26] Operation: 13*2=26 Exploring Operation: 75-13=62, Resulting Numbers: [2, 62] Generated Node #0,0,2: 25:[2, 62] Operation: 75-13=62 Moving to Node #0,0,2 Current State: 25:[2, 62], Operations: ['93-91=2', '75-13=62'] Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,25 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[75, 26], Operations: ['93-91=2', '13*2=26'] Exploring Operation: 75*26=1950, Resulting Numbers: [1950] 1950,25 unequal: No Solution Exploring Operation: 75+26=101, Resulting Numbers: [101] 101,25 unequal: No Solution Exploring Operation: 75-26=49, Resulting Numbers: [49] 49,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[75, 11], Operations: ['93-91=2', '13-2=11'] Exploring Operation: 75-11=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 75+11=86, Resulting Numbers: [86] 86,25 unequal: No Solution Exploring Operation: 75*11=825, Resulting Numbers: [825] 825,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[13, 91, 18], Operations: ['93-75=18'] Exploring Operation: 91-18=73, Resulting Numbers: [13, 73] Generated Node #0,1,0: 25:[13, 73] Operation: 91-18=73 Exploring Operation: 91/13=7, Resulting Numbers: [18, 7] Generated Node #0,1,1: 25:[18, 7] Operation: 91/13=7 Exploring Operation: 91-13=78, Resulting Numbers: [18, 78] Generated Node #0,1,2: 25:[18, 78] Operation: 91-13=78 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[18, 7], Operations: ['93-75=18', '91/13=7'] Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[13, 75, 93, 91], Operations: [] Exploring Operation: 93-75=18, Resulting Numbers: [13, 91, 18] Generated Node #0,1: 25:[13, 91, 18] Operation: 93-75=18 Moving to Node #0,1 Current State: 25:[13, 91, 18], Operations: ['93-75=18'] Exploring Operation: 91/13=7, Resulting Numbers: [18, 7] Generated Node #0,1,1: 25:[18, 7] Operation: 91/13=7 Moving to Node #0,1,1 Current State: 25:[18, 7], Operations: ['93-75=18', '91/13=7'] Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 80, 43, 91, 56 ]
88
[ "80+43=123", "91-56=35", "123-35=88" ]
Current State: 88:[80, 43, 91, 56], Operations: [] Exploring Operation: 80+43=123, Resulting Numbers: [91, 56, 123] Generated Node #2: [91, 56, 123] from Operation: 80+43=123 Current State: 88:[91, 56, 123], Operations: ['80+43=123'] Exploring Operation: 91-56=35, Resulting Numbers: [123, 35] Generated Node #3: [123, 35] from Operation: 91-56=35 Current State: 88:[123, 35], Operations: ['80+43=123', '91-56=35'] Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[80, 43, 91, 56], Operations: [] Exploring Operation: 56-43=13, Resulting Numbers: [80, 91, 13] Generated Node #0,0: 88:[80, 91, 13] Operation: 56-43=13 Exploring Operation: 91-80=11, Resulting Numbers: [43, 56, 11] Generated Node #0,1: 88:[43, 56, 11] Operation: 91-80=11 Exploring Operation: 80-56=24, Resulting Numbers: [43, 91, 24] Generated Node #0,2: 88:[43, 91, 24] Operation: 80-56=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[43, 91, 24], Operations: ['80-56=24'] Exploring Operation: 91-24=67, Resulting Numbers: [43, 67] Generated Node #0,2,0: 88:[43, 67] Operation: 91-24=67 Exploring Operation: 43-24=19, Resulting Numbers: [91, 19] Generated Node #0,2,1: 88:[91, 19] Operation: 43-24=19 Exploring Operation: 91-43=48, Resulting Numbers: [24, 48] Generated Node #0,2,2: 88:[24, 48] Operation: 91-43=48 Moving to Node #0,2,1 Current State: 88:[91, 19], Operations: ['80-56=24', '43-24=19'] Exploring Operation: 91*19=1729, Resulting Numbers: [1729] 1729,88 unequal: No Solution Exploring Operation: 91-19=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 91+19=110, Resulting Numbers: [110] 110,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[24, 48], Operations: ['80-56=24', '91-43=48'] Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,88 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[43, 67], Operations: ['80-56=24', '91-24=67'] Exploring Operation: 43+67=110, Resulting Numbers: [110] 110,88 unequal: No Solution Exploring Operation: 43*67=2881, Resulting Numbers: [2881] 2881,88 unequal: No Solution Exploring Operation: 67-43=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[80, 91, 13], Operations: ['56-43=13'] Exploring Operation: 91/13=7, Resulting Numbers: [80, 7] Generated Node #0,0,0: 88:[80, 7] Operation: 91/13=7 Exploring Operation: 80+13=93, Resulting Numbers: [91, 93] Generated Node #0,0,1: 88:[91, 93] Operation: 80+13=93 Exploring Operation: 91-80=11, Resulting Numbers: [13, 11] Generated Node #0,0,2: 88:[13, 11] Operation: 91-80=11 Moving to Node #0,0,2 Current State: 88:[13, 11], Operations: ['56-43=13', '91-80=11'] Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,88 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[91, 93], Operations: ['56-43=13', '80+13=93'] Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,88 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,88 unequal: No Solution Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[80, 7], Operations: ['56-43=13', '91/13=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,88 unequal: No Solution Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,88 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[43, 56, 11], Operations: ['91-80=11'] Exploring Operation: 56-43=13, Resulting Numbers: [11, 13] Generated Node #0,1,0: 88:[11, 13] Operation: 56-43=13 Exploring Operation: 56-11=45, Resulting Numbers: [43, 45] Generated Node #0,1,1: 88:[43, 45] Operation: 56-11=45 Exploring Operation: 43+56=99, Resulting Numbers: [11, 99] Generated Node #0,1,2: 88:[11, 99] Operation: 43+56=99 Moving to Node #0,1,0 Current State: 88:[11, 13], Operations: ['91-80=11', '56-43=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,88 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[43, 45], Operations: ['91-80=11', '56-11=45'] Exploring Operation: 43+45=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[80, 43, 91, 56], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [43, 56, 11] Generated Node #0,1: 88:[43, 56, 11] Operation: 91-80=11 Moving to Node #0,1 Current State: 88:[43, 56, 11], Operations: ['91-80=11'] Exploring Operation: 56-11=45, Resulting Numbers: [43, 45] Generated Node #0,1,1: 88:[43, 45] Operation: 56-11=45 Moving to Node #0,1,1 Current State: 88:[43, 45], Operations: ['91-80=11', '56-11=45'] Exploring Operation: 43+45=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_3
mult_heuristic
[ 12, 32, 10, 40 ]
24
[ "32-12=20", "40/10=4", "20+4=24" ]
Current State: 24:[12, 32, 10, 40], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [10, 40, 20] Generated Node #2: [10, 40, 20] from Operation: 32-12=20 Current State: 24:[10, 40, 20], Operations: ['32-12=20'] Exploring Operation: 40/10=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 40/10=4 Current State: 24:[20, 4], Operations: ['32-12=20', '40/10=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[12, 32, 10, 40], Operations: [] Exploring Operation: 40-32=8, Resulting Numbers: [12, 10, 8] Generated Node #0,0: 24:[12, 10, 8] Operation: 40-32=8 Exploring Operation: 40/10=4, Resulting Numbers: [12, 32, 4] Generated Node #0,1: 24:[12, 32, 4] Operation: 40/10=4 Moving to Node #0,0 Current State: 24:[12, 10, 8], Operations: ['40-32=8'] Exploring Operation: 12-10=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 24:[8, 2] Operation: 12-10=2 Exploring Operation: 10-8=2, Resulting Numbers: [12, 2] Generated Node #0,0,1: 24:[12, 2] Operation: 10-8=2 Moving to Node #0,1 Current State: 24:[12, 32, 4], Operations: ['40/10=4'] Exploring Operation: 32/4=8, Resulting Numbers: [12, 8] Generated Node #0,1,0: 24:[12, 8] Operation: 32/4=8 Exploring Operation: 32-12=20, Resulting Numbers: [4, 20] Generated Node #0,1,1: 24:[4, 20] Operation: 32-12=20 Moving to Node #0,0,0 Current State: 24:[8, 2], Operations: ['40-32=8', '12-10=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[12, 8], Operations: ['40/10=4', '32/4=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,24 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[12, 2], Operations: ['40-32=8', '10-8=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[12, 32, 10, 40], Operations: [] Exploring Operation: 40-32=8, Resulting Numbers: [12, 10, 8] Generated Node #0,0: 24:[12, 10, 8] Operation: 40-32=8 Moving to Node #0,0 Current State: 24:[12, 10, 8], Operations: ['40-32=8'] Exploring Operation: 10-8=2, Resulting Numbers: [12, 2] Generated Node #0,0,1: 24:[12, 2] Operation: 10-8=2 Moving to Node #0,0,1 Current State: 24:[12, 2], Operations: ['40-32=8', '10-8=2'] Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 40, 86, 23, 2 ]
67
[ "86-40=46", "23-2=21", "46+21=67" ]
Current State: 67:[40, 86, 23, 2], Operations: [] Exploring Operation: 86-40=46, Resulting Numbers: [23, 2, 46] Generated Node #2: [23, 2, 46] from Operation: 86-40=46 Current State: 67:[23, 2, 46], Operations: ['86-40=46'] Exploring Operation: 23-2=21, Resulting Numbers: [46, 21] Generated Node #3: [46, 21] from Operation: 23-2=21 Current State: 67:[46, 21], Operations: ['86-40=46', '23-2=21'] Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[40, 86, 23, 2], Operations: [] Exploring Operation: 40*2=80, Resulting Numbers: [86, 23, 80] Generated Node #0,0: 67:[86, 23, 80] Operation: 40*2=80 Exploring Operation: 23*2=46, Resulting Numbers: [40, 86, 46] Generated Node #0,1: 67:[40, 86, 46] Operation: 23*2=46 Exploring Operation: 40+2=42, Resulting Numbers: [86, 23, 42] Generated Node #0,2: 67:[86, 23, 42] Operation: 40+2=42 Exploring Operation: 40+23=63, Resulting Numbers: [86, 2, 63] Generated Node #0,3: 67:[86, 2, 63] Operation: 40+23=63 Exploring Operation: 86-2=84, Resulting Numbers: [40, 23, 84] Generated Node #0,4: 67:[40, 23, 84] Operation: 86-2=84 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[40, 86, 46], Operations: ['23*2=46'] Exploring Operation: 86-40=46, Resulting Numbers: [46, 46] Generated Node #0,1,0: 67:[46, 46] Operation: 86-40=46 Exploring Operation: 40+86=126, Resulting Numbers: [46, 126] Generated Node #0,1,1: 67:[46, 126] Operation: 40+86=126 Exploring Operation: 40+46=86, Resulting Numbers: [86, 86] Generated Node #0,1,2: 67:[86, 86] Operation: 40+46=86 Exploring Operation: 86-46=40, Resulting Numbers: [40, 40] Generated Node #0,1,3: 67:[40, 40] Operation: 86-46=40 Exploring Operation: 46-40=6, Resulting Numbers: [86, 6] Generated Node #0,1,4: 67:[86, 6] Operation: 46-40=6 Moving to Node #0,1,2 Current State: 67:[86, 86], Operations: ['23*2=46', '40+46=86'] Exploring Operation: 86+86=172, Resulting Numbers: [172] 172,67 unequal: No Solution Exploring Operation: 86/86=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 86-86=0, Resulting Numbers: [0] 0,67 unequal: No Solution Exploring Operation: 86*86=7396, Resulting Numbers: [7396] 7396,67 unequal: No Solution Moving to Node #0,1,0 Current State: 67:[46, 46], Operations: ['23*2=46', '86-40=46'] Exploring Operation: 46-46=0, Resulting Numbers: [0] 0,67 unequal: No Solution Exploring Operation: 46+46=92, Resulting Numbers: [92] 92,67 unequal: No Solution Exploring Operation: 46/46=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 46*46=2116, Resulting Numbers: [2116] 2116,67 unequal: No Solution Moving to Node #0,1,3 Current State: 67:[40, 40], Operations: ['23*2=46', '86-46=40'] Exploring Operation: 40-40=0, Resulting Numbers: [0] 0,67 unequal: No Solution Exploring Operation: 40*40=1600, Resulting Numbers: [1600] 1600,67 unequal: No Solution Exploring Operation: 40/40=1, Resulting Numbers: [1] 1,67 unequal: No Solution Exploring Operation: 40+40=80, Resulting Numbers: [80] 80,67 unequal: No Solution Moving to Node #0,1,1 Current State: 67:[46, 126], Operations: ['23*2=46', '40+86=126'] Exploring Operation: 126-46=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 46*126=5796, Resulting Numbers: [5796] 5796,67 unequal: No Solution Exploring Operation: 46+126=172, Resulting Numbers: [172] 172,67 unequal: No Solution Moving to Node #0,1,4 Current State: 67:[86, 6], Operations: ['23*2=46', '46-40=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 86*6=516, Resulting Numbers: [516] 516,67 unequal: No Solution Exploring Operation: 86+6=92, Resulting Numbers: [92] 92,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[86, 23, 80], Operations: ['40*2=80'] Exploring Operation: 86-23=63, Resulting Numbers: [80, 63] Generated Node #0,0,0: 67:[80, 63] Operation: 86-23=63 Exploring Operation: 23+80=103, Resulting Numbers: [86, 103] Generated Node #0,0,1: 67:[86, 103] Operation: 23+80=103 Exploring Operation: 80-23=57, Resulting Numbers: [86, 57] Generated Node #0,0,2: 67:[86, 57] Operation: 80-23=57 Exploring Operation: 86-80=6, Resulting Numbers: [23, 6] Generated Node #0,0,3: 67:[23, 6] Operation: 86-80=6 Exploring Operation: 86+23=109, Resulting Numbers: [80, 109] Generated Node #0,0,4: 67:[80, 109] Operation: 86+23=109 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 67:[80, 63], Operations: ['40*2=80', '86-23=63'] Exploring Operation: 80-63=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 80*63=5040, Resulting Numbers: [5040] 5040,67 unequal: No Solution Exploring Operation: 80+63=143, Resulting Numbers: [143] 143,67 unequal: No Solution No 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: 67:[86, 57], Operations: ['40*2=80', '80-23=57'] Exploring Operation: 86*57=4902, Resulting Numbers: [4902] 4902,67 unequal: No Solution Exploring Operation: 86+57=143, Resulting Numbers: [143] 143,67 unequal: No Solution Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,67 unequal: No Solution No 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: 67:[86, 103], Operations: ['40*2=80', '23+80=103'] Exploring Operation: 86*103=8858, Resulting Numbers: [8858] 8858,67 unequal: No Solution Exploring Operation: 103-86=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 86+103=189, Resulting Numbers: [189] 189,67 unequal: No Solution No 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: 67:[80, 109], Operations: ['40*2=80', '86+23=109'] Exploring Operation: 80*109=8720, Resulting Numbers: [8720] 8720,67 unequal: No Solution Exploring Operation: 109-80=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 80+109=189, Resulting Numbers: [189] 189,67 unequal: No Solution No 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: 67:[23, 6], Operations: ['40*2=80', '86-80=6'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,67 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,67 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,67 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: 67:[86, 23, 42], Operations: ['40+2=42'] Exploring Operation: 86+23=109, Resulting Numbers: [42, 109] Generated Node #0,2,0: 67:[42, 109] Operation: 86+23=109 Exploring Operation: 86-42=44, Resulting Numbers: [23, 44] Generated Node #0,2,1: 67:[23, 44] Operation: 86-42=44 Exploring Operation: 86-23=63, Resulting Numbers: [42, 63] Generated Node #0,2,2: 67:[42, 63] Operation: 86-23=63 Exploring Operation: 23+42=65, Resulting Numbers: [86, 65] Generated Node #0,2,3: 67:[86, 65] Operation: 23+42=65 Exploring Operation: 42-23=19, Resulting Numbers: [86, 19] Generated Node #0,2,4: 67:[86, 19] Operation: 42-23=19 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 67:[86, 65], Operations: ['40+2=42', '23+42=65'] Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,67 unequal: No Solution Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,67 unequal: No Solution No 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: 67:[42, 63], Operations: ['40+2=42', '86-23=63'] Exploring Operation: 42*63=2646, Resulting Numbers: [2646] 2646,67 unequal: No Solution Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,67 unequal: No Solution Exploring Operation: 42+63=105, Resulting Numbers: [105] 105,67 unequal: No Solution No 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: 67:[42, 109], Operations: ['40+2=42', '86+23=109'] Exploring Operation: 42+109=151, Resulting Numbers: [151] 151,67 unequal: No Solution Exploring Operation: 42*109=4578, Resulting Numbers: [4578] 4578,67 unequal: No Solution Exploring Operation: 109-42=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[40, 86, 23, 2], Operations: [] Exploring Operation: 40+2=42, Resulting Numbers: [86, 23, 42] Generated Node #0,2: 67:[86, 23, 42] Operation: 40+2=42 Moving to Node #0,2 Current State: 67:[86, 23, 42], Operations: ['40+2=42'] Exploring Operation: 86+23=109, Resulting Numbers: [42, 109] Generated Node #0,2,0: 67:[42, 109] Operation: 86+23=109 Moving to Node #0,2,0 Current State: 67:[42, 109], Operations: ['40+2=42', '86+23=109'] Exploring Operation: 109-42=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.942708
hs_5
mult_heuristic
[ 6, 94, 17, 34 ]
82
[ "6*34=204", "204/17=12", "94-12=82" ]
Current State: 82:[6, 94, 17, 34], Operations: [] Exploring Operation: 6*34=204, Resulting Numbers: [94, 17, 204] Generated Node #2: [94, 17, 204] from Operation: 6*34=204 Current State: 82:[94, 17, 204], Operations: ['6*34=204'] Exploring Operation: 204/17=12, Resulting Numbers: [94, 12] Generated Node #3: [94, 12] from Operation: 204/17=12 Current State: 82:[94, 12], Operations: ['6*34=204', '204/17=12'] Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[6, 94, 17, 34], Operations: [] Exploring Operation: 94-17=77, Resulting Numbers: [6, 34, 77] Generated Node #0,0: 82:[6, 34, 77] Operation: 94-17=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[6, 34, 77], Operations: ['94-17=77'] Exploring Operation: 6+34=40, Resulting Numbers: [77, 40] Generated Node #0,0,0: 82:[77, 40] Operation: 6+34=40 Moving to Node #0,0,0 Current State: 82:[77, 40], Operations: ['94-17=77', '6+34=40'] Exploring Operation: 77-40=37, Resulting Numbers: [37] 37,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 53, 55, 3, 19 ]
55
[ "53+55=108", "108/3=36", "19+36=55" ]
Current State: 55:[53, 55, 3, 19], Operations: [] Exploring Operation: 53+55=108, Resulting Numbers: [3, 19, 108] Generated Node #2: [3, 19, 108] from Operation: 53+55=108 Current State: 55:[3, 19, 108], Operations: ['53+55=108'] Exploring Operation: 108/3=36, Resulting Numbers: [19, 36] Generated Node #3: [19, 36] from Operation: 108/3=36 Current State: 55:[19, 36], Operations: ['53+55=108', '108/3=36'] Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[53, 55, 3, 19], Operations: [] Exploring Operation: 3*19=57, Resulting Numbers: [53, 55, 57] Generated Node #0,0: 55:[53, 55, 57] Operation: 3*19=57 Moving to Node #0,0 Current State: 55:[53, 55, 57], Operations: ['3*19=57'] Exploring Operation: 57-53=4, Resulting Numbers: [55, 4] Generated Node #0,0,0: 55:[55, 4] Operation: 57-53=4 Moving to Node #0,0,0 Current State: 55:[55, 4], Operations: ['3*19=57', '57-53=4'] Exploring Operation: 55+4=59, Resulting Numbers: [59] 59,55 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 15, 92, 58, 82 ]
18
[ "92+82=174", "174/58=3", "15+3=18" ]
Current State: 18:[15, 92, 58, 82], Operations: [] Exploring Operation: 92+82=174, Resulting Numbers: [15, 58, 174] Generated Node #2: [15, 58, 174] from Operation: 92+82=174 Current State: 18:[15, 58, 174], Operations: ['92+82=174'] Exploring Operation: 174/58=3, Resulting Numbers: [15, 3] Generated Node #3: [15, 3] from Operation: 174/58=3 Current State: 18:[15, 3], Operations: ['92+82=174', '174/58=3'] Exploring Operation: 15+3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[15, 92, 58, 82], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [15, 58, 10] Generated Node #0,0: 18:[15, 58, 10] Operation: 92-82=10 Exploring Operation: 82-58=24, Resulting Numbers: [15, 92, 24] Generated Node #0,1: 18:[15, 92, 24] Operation: 82-58=24 Exploring Operation: 92-58=34, Resulting Numbers: [15, 82, 34] Generated Node #0,2: 18:[15, 82, 34] Operation: 92-58=34 Moving to Node #0,0 Current State: 18:[15, 58, 10], Operations: ['92-82=10'] Exploring Operation: 15-10=5, Resulting Numbers: [58, 5] Generated Node #0,0,0: 18:[58, 5] Operation: 15-10=5 Exploring Operation: 58-10=48, Resulting Numbers: [15, 48] Generated Node #0,0,1: 18:[15, 48] Operation: 58-10=48 Exploring Operation: 58-15=43, Resulting Numbers: [10, 43] Generated Node #0,0,2: 18:[10, 43] Operation: 58-15=43 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[10, 43], Operations: ['92-82=10', '58-15=43'] Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 10+43=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 10*43=430, Resulting Numbers: [430] 430,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[15, 48], Operations: ['92-82=10', '58-10=48'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[58, 5], Operations: ['92-82=10', '15-10=5'] Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[15, 92, 24], Operations: ['82-58=24'] Exploring Operation: 92-15=77, Resulting Numbers: [24, 77] Generated Node #0,1,0: 18:[24, 77] Operation: 92-15=77 Exploring Operation: 24-15=9, Resulting Numbers: [92, 9] Generated Node #0,1,1: 18:[92, 9] Operation: 24-15=9 Exploring Operation: 92-24=68, Resulting Numbers: [15, 68] Generated Node #0,1,2: 18:[15, 68] Operation: 92-24=68 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[15, 68], Operations: ['82-58=24', '92-24=68'] Exploring Operation: 15*68=1020, Resulting Numbers: [1020] 1020,18 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 15+68=83, Resulting Numbers: [83] 83,18 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:[24, 77], Operations: ['82-58=24', '92-15=77'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,18 unequal: No Solution Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,18 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:[92, 9], Operations: ['82-58=24', '24-15=9'] Exploring Operation: 92*9=828, Resulting Numbers: [828] 828,18 unequal: No Solution Exploring Operation: 92+9=101, Resulting Numbers: [101] 101,18 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,18 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:[15, 82, 34], Operations: ['92-58=34'] Exploring Operation: 82-34=48, Resulting Numbers: [15, 48] Generated Node #0,2,0: 18:[15, 48] Operation: 82-34=48 Exploring Operation: 34-15=19, Resulting Numbers: [82, 19] Generated Node #0,2,1: 18:[82, 19] Operation: 34-15=19 Exploring Operation: 82-15=67, Resulting Numbers: [34, 67] Generated Node #0,2,2: 18:[34, 67] Operation: 82-15=67 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[15, 48], Operations: ['92-58=34', '82-34=48'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[82, 19], Operations: ['92-58=34', '34-15=19'] Exploring Operation: 82*19=1558, Resulting Numbers: [1558] 1558,18 unequal: No Solution Exploring Operation: 82-19=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 82+19=101, Resulting Numbers: [101] 101,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[34, 67], Operations: ['92-58=34', '82-15=67'] Exploring Operation: 67-34=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 34+67=101, Resulting Numbers: [101] 101,18 unequal: No Solution Exploring Operation: 34*67=2278, Resulting Numbers: [2278] 2278,18 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
[ 13, 34, 68, 91 ]
24
[ "13+34=47", "91-68=23", "47-23=24" ]
Current State: 24:[13, 34, 68, 91], Operations: [] Exploring Operation: 13+34=47, Resulting Numbers: [68, 91, 47] Generated Node #2: [68, 91, 47] from Operation: 13+34=47 Current State: 24:[68, 91, 47], Operations: ['13+34=47'] Exploring Operation: 91-68=23, Resulting Numbers: [47, 23] Generated Node #3: [47, 23] from Operation: 91-68=23 Current State: 24:[47, 23], Operations: ['13+34=47', '91-68=23'] Exploring Operation: 47-23=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[13, 34, 68, 91], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [13, 91, 2] Generated Node #0,0: 24:[13, 91, 2] Operation: 68/34=2 Exploring Operation: 91-68=23, Resulting Numbers: [13, 34, 23] Generated Node #0,1: 24:[13, 34, 23] Operation: 91-68=23 Exploring Operation: 91/13=7, Resulting Numbers: [34, 68, 7] Generated Node #0,2: 24:[34, 68, 7] Operation: 91/13=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[13, 34, 23], Operations: ['91-68=23'] Exploring Operation: 23-13=10, Resulting Numbers: [34, 10] Generated Node #0,1,0: 24:[34, 10] Operation: 23-13=10 Exploring Operation: 34-23=11, Resulting Numbers: [13, 11] Generated Node #0,1,1: 24:[13, 11] Operation: 34-23=11 Exploring Operation: 34-13=21, Resulting Numbers: [23, 21] Generated Node #0,1,2: 24:[23, 21] Operation: 34-13=21 Moving to Node #0,1,1 Current State: 24:[13, 11], Operations: ['91-68=23', '34-23=11'] Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,24 unequal: No Solution Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[13, 34, 68, 91], Operations: [] Exploring Operation: 91-68=23, Resulting Numbers: [13, 34, 23] Generated Node #0,1: 24:[13, 34, 23] Operation: 91-68=23 Moving to Node #0,1 Current State: 24:[13, 34, 23], Operations: ['91-68=23'] Exploring Operation: 34-23=11, Resulting Numbers: [13, 11] Generated Node #0,1,1: 24:[13, 11] Operation: 34-23=11 Moving to Node #0,1,1 Current State: 24:[13, 11], Operations: ['91-68=23', '34-23=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 77, 86, 82, 4 ]
95
[ "86-77=9", "82+4=86", "9+86=95" ]
Current State: 95:[77, 86, 82, 4], Operations: [] Exploring Operation: 86-77=9, Resulting Numbers: [82, 4, 9] Generated Node #2: [82, 4, 9] from Operation: 86-77=9 Current State: 95:[82, 4, 9], Operations: ['86-77=9'] Exploring Operation: 82+4=86, Resulting Numbers: [9, 86] Generated Node #3: [9, 86] from Operation: 82+4=86 Current State: 95:[9, 86], Operations: ['86-77=9', '82+4=86'] Exploring Operation: 9+86=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[77, 86, 82, 4], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [77, 4, 4] Generated Node #0,0: 95:[77, 4, 4] Operation: 86-82=4 Exploring Operation: 86-77=9, Resulting Numbers: [82, 4, 9] Generated Node #0,1: 95:[82, 4, 9] Operation: 86-77=9 Exploring Operation: 77+4=81, Resulting Numbers: [86, 82, 81] Generated Node #0,2: 95:[86, 82, 81] Operation: 77+4=81 Exploring Operation: 82-77=5, Resulting Numbers: [86, 4, 5] Generated Node #0,3: 95:[86, 4, 5] Operation: 82-77=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 95:[86, 4, 5], Operations: ['82-77=5'] Exploring Operation: 86-4=82, Resulting Numbers: [5, 82] Generated Node #0,3,0: 95:[5, 82] Operation: 86-4=82 Exploring Operation: 4*5=20, Resulting Numbers: [86, 20] Generated Node #0,3,1: 95:[86, 20] Operation: 4*5=20 Exploring Operation: 86+4=90, Resulting Numbers: [5, 90] Generated Node #0,3,2: 95:[5, 90] Operation: 86+4=90 Exploring Operation: 86+5=91, Resulting Numbers: [4, 91] Generated Node #0,3,3: 95:[4, 91] Operation: 86+5=91 Moving to Node #0,3,2 Current State: 95:[5, 90], Operations: ['82-77=5', '86+4=90'] Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[77, 86, 82, 4], Operations: [] Exploring Operation: 82-77=5, Resulting Numbers: [86, 4, 5] Generated Node #0,3: 95:[86, 4, 5] Operation: 82-77=5 Moving to Node #0,3 Current State: 95:[86, 4, 5], Operations: ['82-77=5'] Exploring Operation: 86+4=90, Resulting Numbers: [5, 90] Generated Node #0,3,2: 95:[5, 90] Operation: 86+4=90 Moving to Node #0,3,2 Current State: 95:[5, 90], Operations: ['82-77=5', '86+4=90'] Exploring Operation: 5+90=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 63, 41, 3, 76 ]
72
[ "63*3=189", "41+76=117", "189-117=72" ]
Current State: 72:[63, 41, 3, 76], Operations: [] Exploring Operation: 63*3=189, Resulting Numbers: [41, 76, 189] Generated Node #2: [41, 76, 189] from Operation: 63*3=189 Current State: 72:[41, 76, 189], Operations: ['63*3=189'] Exploring Operation: 41+76=117, Resulting Numbers: [189, 117] Generated Node #3: [189, 117] from Operation: 41+76=117 Current State: 72:[189, 117], Operations: ['63*3=189', '41+76=117'] Exploring Operation: 189-117=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[63, 41, 3, 76], Operations: [] Exploring Operation: 76-41=35, Resulting Numbers: [63, 3, 35] Generated Node #0,0: 72:[63, 3, 35] Operation: 76-41=35 Exploring Operation: 63-41=22, Resulting Numbers: [3, 76, 22] Generated Node #0,1: 72:[3, 76, 22] Operation: 63-41=22 Exploring Operation: 76-63=13, Resulting Numbers: [41, 3, 13] Generated Node #0,2: 72:[41, 3, 13] Operation: 76-63=13 Moving to Node #0,1 Current State: 72:[3, 76, 22], Operations: ['63-41=22'] Exploring Operation: 3+22=25, Resulting Numbers: [76, 25] Generated Node #0,1,0: 72:[76, 25] Operation: 3+22=25 Exploring Operation: 22-3=19, Resulting Numbers: [76, 19] Generated Node #0,1,1: 72:[76, 19] Operation: 22-3=19 Exploring Operation: 76-3=73, Resulting Numbers: [22, 73] Generated Node #0,1,2: 72:[22, 73] Operation: 76-3=73 Moving to Node #0,2 Current State: 72:[41, 3, 13], Operations: ['76-63=13'] Exploring Operation: 13-3=10, Resulting Numbers: [41, 10] Generated Node #0,2,0: 72:[41, 10] Operation: 13-3=10 Exploring Operation: 41-13=28, Resulting Numbers: [3, 28] Generated Node #0,2,1: 72:[3, 28] Operation: 41-13=28 Exploring Operation: 41-3=38, Resulting Numbers: [13, 38] Generated Node #0,2,2: 72:[13, 38] Operation: 41-3=38 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[13, 38], Operations: ['76-63=13', '41-3=38'] Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,72 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,72 unequal: No Solution Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[3, 28], Operations: ['76-63=13', '41-13=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,72 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[41, 10], Operations: ['76-63=13', '13-3=10'] Exploring Operation: 41*10=410, Resulting Numbers: [410] 410,72 unequal: No Solution Exploring Operation: 41+10=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,72 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: 72:[63, 3, 35], Operations: ['76-41=35'] Exploring Operation: 63-35=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 72:[3, 28] Operation: 63-35=28 Exploring Operation: 63+3=66, Resulting Numbers: [35, 66] Generated Node #0,0,1: 72:[35, 66] Operation: 63+3=66 Exploring Operation: 63/3=21, Resulting Numbers: [35, 21] Generated Node #0,0,2: 72:[35, 21] Operation: 63/3=21 Moving to Node #0,1,2 Current State: 72:[22, 73], Operations: ['63-41=22', '76-3=73'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 22+73=95, Resulting Numbers: [95] 95,72 unequal: No Solution Exploring Operation: 22*73=1606, Resulting Numbers: [1606] 1606,72 unequal: No Solution Moving to Node #0,0,0 Current State: 72:[3, 28], Operations: ['76-41=35', '63-35=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,72 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,72 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[35, 21], Operations: ['76-41=35', '63/3=21'] Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,72 unequal: No Solution Exploring Operation: 35+21=56, Resulting Numbers: [56] 56,72 unequal: No Solution Exploring Operation: 35*21=735, Resulting Numbers: [735] 735,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[76, 19], Operations: ['63-41=22', '22-3=19'] Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 76+19=95, Resulting Numbers: [95] 95,72 unequal: No Solution Moving to Node #0,1,0 Current State: 72:[76, 25], Operations: ['63-41=22', '3+22=25'] Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,72 unequal: No Solution Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,72 unequal: No Solution Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[35, 66], Operations: ['76-41=35', '63+3=66'] Exploring Operation: 35+66=101, Resulting Numbers: [101] 101,72 unequal: No Solution Exploring Operation: 35*66=2310, Resulting Numbers: [2310] 2310,72 unequal: No Solution Exploring Operation: 66-35=31, Resulting Numbers: [31] 31,72 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 78, 89, 97, 51 ]
57
[ "89-78=11", "97-51=46", "11+46=57" ]
Current State: 57:[78, 89, 97, 51], Operations: [] Exploring Operation: 89-78=11, Resulting Numbers: [97, 51, 11] Generated Node #2: [97, 51, 11] from Operation: 89-78=11 Current State: 57:[97, 51, 11], Operations: ['89-78=11'] Exploring Operation: 97-51=46, Resulting Numbers: [11, 46] Generated Node #3: [11, 46] from Operation: 97-51=46 Current State: 57:[11, 46], Operations: ['89-78=11', '97-51=46'] Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[78, 89, 97, 51], Operations: [] Exploring Operation: 97-78=19, Resulting Numbers: [89, 51, 19] Generated Node #0,0: 57:[89, 51, 19] Operation: 97-78=19 Exploring Operation: 97-89=8, Resulting Numbers: [78, 51, 8] Generated Node #0,1: 57:[78, 51, 8] Operation: 97-89=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[78, 51, 8], Operations: ['97-89=8'] Exploring Operation: 78-51=27, Resulting Numbers: [8, 27] Generated Node #0,1,0: 57:[8, 27] Operation: 78-51=27 Exploring Operation: 78-8=70, Resulting Numbers: [51, 70] Generated Node #0,1,1: 57:[51, 70] Operation: 78-8=70 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 57:[8, 27], Operations: ['97-89=8', '78-51=27'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,57 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 57:[51, 70], Operations: ['97-89=8', '78-8=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[89, 51, 19], Operations: ['97-78=19'] Exploring Operation: 89-19=70, Resulting Numbers: [51, 70] Generated Node #0,0,0: 57:[51, 70] Operation: 89-19=70 Exploring Operation: 89-51=38, Resulting Numbers: [19, 38] Generated Node #0,0,1: 57:[19, 38] Operation: 89-51=38 Moving to Node #0,0,0 Current State: 57:[51, 70], Operations: ['97-78=19', '89-19=70'] Exploring Operation: 51+70=121, Resulting Numbers: [121] 121,57 unequal: No Solution Exploring Operation: 70-51=19, Resulting Numbers: [19] 19,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[19, 38], Operations: ['97-78=19', '89-51=38'] Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[78, 89, 97, 51], Operations: [] Exploring Operation: 97-78=19, Resulting Numbers: [89, 51, 19] Generated Node #0,0: 57:[89, 51, 19] Operation: 97-78=19 Moving to Node #0,0 Current State: 57:[89, 51, 19], Operations: ['97-78=19'] Exploring Operation: 89-51=38, Resulting Numbers: [19, 38] Generated Node #0,0,1: 57:[19, 38] Operation: 89-51=38 Moving to Node #0,0,1 Current State: 57:[19, 38], Operations: ['97-78=19', '89-51=38'] Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 58, 38, 50, 22 ]
100
[ "58-38=20", "22-20=2", "50*2=100" ]
Current State: 100:[58, 38, 50, 22], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [50, 22, 20] Generated Node #2: [50, 22, 20] from Operation: 58-38=20 Current State: 100:[50, 22, 20], Operations: ['58-38=20'] Exploring Operation: 22-20=2, Resulting Numbers: [50, 2] Generated Node #3: [50, 2] from Operation: 22-20=2 Current State: 100:[50, 2], Operations: ['58-38=20', '22-20=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[58, 38, 50, 22], Operations: [] Exploring Operation: 38-22=16, Resulting Numbers: [58, 50, 16] Generated Node #0,0: 100:[58, 50, 16] Operation: 38-22=16 Exploring Operation: 50-38=12, Resulting Numbers: [58, 22, 12] Generated Node #0,1: 100:[58, 22, 12] Operation: 50-38=12 Exploring Operation: 58-38=20, Resulting Numbers: [50, 22, 20] Generated Node #0,2: 100:[50, 22, 20] Operation: 58-38=20 Exploring Operation: 58-50=8, Resulting Numbers: [38, 22, 8] Generated Node #0,3: 100:[38, 22, 8] Operation: 58-50=8 Exploring Operation: 58+38=96, Resulting Numbers: [50, 22, 96] Generated Node #0,4: 100:[50, 22, 96] Operation: 58+38=96 Moving to Node #0,2 Current State: 100:[50, 22, 20], Operations: ['58-38=20'] Exploring Operation: 50-22=28, Resulting Numbers: [20, 28] Generated Node #0,2,0: 100:[20, 28] Operation: 50-22=28 Exploring Operation: 22-20=2, Resulting Numbers: [50, 2] Generated Node #0,2,1: 100:[50, 2] Operation: 22-20=2 Exploring Operation: 22+20=42, Resulting Numbers: [50, 42] Generated Node #0,2,2: 100:[50, 42] Operation: 22+20=42 Exploring Operation: 50+22=72, Resulting Numbers: [20, 72] Generated Node #0,2,3: 100:[20, 72] Operation: 50+22=72 Exploring Operation: 50-20=30, Resulting Numbers: [22, 30] Generated Node #0,2,4: 100:[22, 30] Operation: 50-20=30 Moving to Node #0,4 Current State: 100:[50, 22, 96], Operations: ['58+38=96'] Exploring Operation: 96-22=74, Resulting Numbers: [50, 74] Generated Node #0,4,0: 100:[50, 74] Operation: 96-22=74 Exploring Operation: 22+96=118, Resulting Numbers: [50, 118] Generated Node #0,4,1: 100:[50, 118] Operation: 22+96=118 Exploring Operation: 50+22=72, Resulting Numbers: [96, 72] Generated Node #0,4,2: 100:[96, 72] Operation: 50+22=72 Exploring Operation: 50-22=28, Resulting Numbers: [96, 28] Generated Node #0,4,3: 100:[96, 28] Operation: 50-22=28 Exploring Operation: 96-50=46, Resulting Numbers: [22, 46] Generated Node #0,4,4: 100:[22, 46] Operation: 96-50=46 Moving to Node #0,0 Current State: 100:[58, 50, 16], Operations: ['38-22=16'] Exploring Operation: 58-16=42, Resulting Numbers: [50, 42] Generated Node #0,0,0: 100:[50, 42] Operation: 58-16=42 Exploring Operation: 58+50=108, Resulting Numbers: [16, 108] Generated Node #0,0,1: 100:[16, 108] Operation: 58+50=108 Exploring Operation: 58-50=8, Resulting Numbers: [16, 8] Generated Node #0,0,2: 100:[16, 8] Operation: 58-50=8 Exploring Operation: 58+16=74, Resulting Numbers: [50, 74] Generated Node #0,0,3: 100:[50, 74] Operation: 58+16=74 Exploring Operation: 50-16=34, Resulting Numbers: [58, 34] Generated Node #0,0,4: 100:[58, 34] Operation: 50-16=34 Moving to Node #0,1 Current State: 100:[58, 22, 12], Operations: ['50-38=12'] Exploring Operation: 22-12=10, Resulting Numbers: [58, 10] Generated Node #0,1,0: 100:[58, 10] Operation: 22-12=10 Exploring Operation: 58+22=80, Resulting Numbers: [12, 80] Generated Node #0,1,1: 100:[12, 80] Operation: 58+22=80 Exploring Operation: 58-12=46, Resulting Numbers: [22, 46] Generated Node #0,1,2: 100:[22, 46] Operation: 58-12=46 Exploring Operation: 58-22=36, Resulting Numbers: [12, 36] Generated Node #0,1,3: 100:[12, 36] Operation: 58-22=36 Exploring Operation: 22+12=34, Resulting Numbers: [58, 34] Generated Node #0,1,4: 100:[58, 34] Operation: 22+12=34 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[22, 46], Operations: ['50-38=12', '58-12=46'] Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 22*46=1012, Resulting Numbers: [1012] 1012,100 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 #0,1,0 Current State: 100:[58, 10], Operations: ['50-38=12', '22-12=10'] Exploring Operation: 58*10=580, Resulting Numbers: [580] 580,100 unequal: No Solution Exploring Operation: 58+10=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,100 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 #0,1,3 Current State: 100:[12, 36], Operations: ['50-38=12', '58-22=36'] Exploring Operation: 36-12=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 36/12=3, Resulting Numbers: [3] 3,100 unequal: No Solution Exploring Operation: 12*36=432, Resulting Numbers: [432] 432,100 unequal: No Solution Exploring Operation: 12+36=48, Resulting Numbers: [48] 48,100 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 #0,1,4 Current State: 100:[58, 34], Operations: ['50-38=12', '22+12=34'] Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 58*34=1972, Resulting Numbers: [1972] 1972,100 unequal: No Solution Exploring Operation: 58+34=92, Resulting Numbers: [92] 92,100 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:[12, 80], Operations: ['50-38=12', '58+22=80'] Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,100 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,100 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: 100:[38, 22, 8], Operations: ['58-50=8'] Exploring Operation: 38-8=30, Resulting Numbers: [22, 30] Generated Node #0,3,0: 100:[22, 30] Operation: 38-8=30 Exploring Operation: 22-8=14, Resulting Numbers: [38, 14] Generated Node #0,3,1: 100:[38, 14] Operation: 22-8=14 Exploring Operation: 38+8=46, Resulting Numbers: [22, 46] Generated Node #0,3,2: 100:[22, 46] Operation: 38+8=46 Exploring Operation: 38+22=60, Resulting Numbers: [8, 60] Generated Node #0,3,3: 100:[8, 60] Operation: 38+22=60 Exploring Operation: 38-22=16, Resulting Numbers: [8, 16] Generated Node #0,3,4: 100:[8, 16] Operation: 38-22=16 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 100:[22, 46], Operations: ['58-50=8', '38+8=46'] Exploring Operation: 46-22=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 22*46=1012, Resulting Numbers: [1012] 1012,100 unequal: No Solution Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 100:[8, 16], Operations: ['58-50=8', '38-22=16'] Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,100 unequal: No Solution Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 100:[22, 30], Operations: ['58-50=8', '38-8=30'] Exploring Operation: 22*30=660, Resulting Numbers: [660] 660,100 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 100:[8, 60], Operations: ['58-50=8', '38+22=60'] Exploring Operation: 8*60=480, Resulting Numbers: [480] 480,100 unequal: No Solution Exploring Operation: 8+60=68, Resulting Numbers: [68] 68,100 unequal: No Solution Exploring Operation: 60-8=52, Resulting Numbers: [52] 52,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 100:[38, 14], Operations: ['58-50=8', '22-8=14'] Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 38*14=532, Resulting Numbers: [532] 532,100 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: 100:[50, 2], Operations: ['58-38=20', '22-20=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[58, 38, 50, 22], Operations: [] Exploring Operation: 58-38=20, Resulting Numbers: [50, 22, 20] Generated Node #0,2: 100:[50, 22, 20] Operation: 58-38=20 Moving to Node #0,2 Current State: 100:[50, 22, 20], Operations: ['58-38=20'] Exploring Operation: 22-20=2, Resulting Numbers: [50, 2] Generated Node #0,2,1: 100:[50, 2] Operation: 22-20=2 Moving to Node #0,2,1 Current State: 100:[50, 2], Operations: ['58-38=20', '22-20=2'] Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 53, 63, 10, 37 ]
38
[ "63-53=10", "10/10=1", "37+1=38" ]
Current State: 38:[53, 63, 10, 37], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [10, 37, 10] Generated Node #2: [10, 37, 10] from Operation: 63-53=10 Current State: 38:[10, 37, 10], Operations: ['63-53=10'] Exploring Operation: 10/10=1, Resulting Numbers: [37, 1] Generated Node #3: [37, 1] from Operation: 10/10=1 Current State: 38:[37, 1], Operations: ['63-53=10', '10/10=1'] Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[53, 63, 10, 37], Operations: [] Exploring Operation: 53-10=43, Resulting Numbers: [63, 37, 43] Generated Node #0,0: 38:[63, 37, 43] Operation: 53-10=43 Exploring Operation: 63-53=10, Resulting Numbers: [10, 37, 10] Generated Node #0,1: 38:[10, 37, 10] Operation: 63-53=10 Exploring Operation: 63-37=26, Resulting Numbers: [53, 10, 26] Generated Node #0,2: 38:[53, 10, 26] Operation: 63-37=26 Exploring Operation: 63-10=53, Resulting Numbers: [53, 37, 53] Generated Node #0,3: 38:[53, 37, 53] Operation: 63-10=53 Moving to Node #0,1 Current State: 38:[10, 37, 10], Operations: ['63-53=10'] Exploring Operation: 10/10=1, Resulting Numbers: [37, 1] Generated Node #0,1,0: 38:[37, 1] Operation: 10/10=1 Exploring Operation: 10-10=0, Resulting Numbers: [37, 0] Generated Node #0,1,1: 38:[37, 0] Operation: 10-10=0 Exploring Operation: 37-10=27, Resulting Numbers: [10, 27] Generated Node #0,1,2: 38:[10, 27] Operation: 37-10=27 Exploring Operation: 10+10=20, Resulting Numbers: [37, 20] Generated Node #0,1,3: 38:[37, 20] Operation: 10+10=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[37, 1], Operations: ['63-53=10', '10/10=1'] Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[53, 63, 10, 37], Operations: [] Exploring Operation: 63-53=10, Resulting Numbers: [10, 37, 10] Generated Node #0,1: 38:[10, 37, 10] Operation: 63-53=10 Moving to Node #0,1 Current State: 38:[10, 37, 10], Operations: ['63-53=10'] Exploring Operation: 10/10=1, Resulting Numbers: [37, 1] Generated Node #0,1,0: 38:[37, 1] Operation: 10/10=1 Moving to Node #0,1,0 Current State: 38:[37, 1], Operations: ['63-53=10', '10/10=1'] Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 19, 57, 52, 10 ]
95
[ "57-52=5", "10-5=5", "19*5=95" ]
Current State: 95:[19, 57, 52, 10], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [19, 10, 5] Generated Node #2: [19, 10, 5] from Operation: 57-52=5 Current State: 95:[19, 10, 5], Operations: ['57-52=5'] Exploring Operation: 10-5=5, Resulting Numbers: [19, 5] Generated Node #3: [19, 5] from Operation: 10-5=5 Current State: 95:[19, 5], Operations: ['57-52=5', '10-5=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[19, 57, 52, 10], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [19, 10, 5] Generated Node #0,0: 95:[19, 10, 5] Operation: 57-52=5 Exploring Operation: 57+52=109, Resulting Numbers: [19, 10, 109] Generated Node #0,1: 95:[19, 10, 109] Operation: 57+52=109 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[19, 10, 5], Operations: ['57-52=5'] Exploring Operation: 10-5=5, Resulting Numbers: [19, 5] Generated Node #0,0,0: 95:[19, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [19, 2] Generated Node #0,0,1: 95:[19, 2] Operation: 10/5=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[19, 5], Operations: ['57-52=5', '10-5=5'] Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[19, 57, 52, 10], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [19, 10, 5] Generated Node #0,0: 95:[19, 10, 5] Operation: 57-52=5 Moving to Node #0,0 Current State: 95:[19, 10, 5], Operations: ['57-52=5'] Exploring Operation: 10-5=5, Resulting Numbers: [19, 5] Generated Node #0,0,0: 95:[19, 5] Operation: 10-5=5 Moving to Node #0,0,0 Current State: 95:[19, 5], Operations: ['57-52=5', '10-5=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 49, 24, 65, 40 ]
98
[ "49+24=73", "65-40=25", "73+25=98" ]
Current State: 98:[49, 24, 65, 40], Operations: [] Exploring Operation: 49+24=73, Resulting Numbers: [65, 40, 73] Generated Node #2: [65, 40, 73] from Operation: 49+24=73 Current State: 98:[65, 40, 73], Operations: ['49+24=73'] Exploring Operation: 65-40=25, Resulting Numbers: [73, 25] Generated Node #3: [73, 25] from Operation: 65-40=25 Current State: 98:[73, 25], Operations: ['49+24=73', '65-40=25'] Exploring Operation: 73+25=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[49, 24, 65, 40], Operations: [] Exploring Operation: 24+65=89, Resulting Numbers: [49, 40, 89] Generated Node #0,0: 98:[49, 40, 89] Operation: 24+65=89 Exploring Operation: 65-24=41, Resulting Numbers: [49, 40, 41] Generated Node #0,1: 98:[49, 40, 41] Operation: 65-24=41 Exploring Operation: 65+40=105, Resulting Numbers: [49, 24, 105] Generated Node #0,2: 98:[49, 24, 105] Operation: 65+40=105 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[49, 40, 41], Operations: ['65-24=41'] Exploring Operation: 41-40=1, Resulting Numbers: [49, 1] Generated Node #0,1,0: 98:[49, 1] Operation: 41-40=1 Exploring Operation: 49-40=9, Resulting Numbers: [41, 9] Generated Node #0,1,1: 98:[41, 9] Operation: 49-40=9 Exploring Operation: 49-41=8, Resulting Numbers: [40, 8] Generated Node #0,1,2: 98:[40, 8] Operation: 49-41=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 98:[49, 1], Operations: ['65-24=41', '41-40=1'] Exploring Operation: 49+1=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,98 unequal: No Solution Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 98:[41, 9], Operations: ['65-24=41', '49-40=9'] Exploring Operation: 41+9=50, Resulting Numbers: [50] 50,98 unequal: No Solution Exploring Operation: 41-9=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 41*9=369, Resulting Numbers: [369] 369,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[40, 8], Operations: ['65-24=41', '49-41=8'] Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,98 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[49, 24, 105], Operations: ['65+40=105'] Exploring Operation: 105-49=56, Resulting Numbers: [24, 56] Generated Node #0,2,0: 98:[24, 56] Operation: 105-49=56 Exploring Operation: 105-24=81, Resulting Numbers: [49, 81] Generated Node #0,2,1: 98:[49, 81] Operation: 105-24=81 Exploring Operation: 49-24=25, Resulting Numbers: [105, 25] Generated Node #0,2,2: 98:[105, 25] Operation: 49-24=25 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[24, 56], Operations: ['65+40=105', '105-49=56'] Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 98:[49, 81], Operations: ['65+40=105', '105-24=81'] Exploring Operation: 81-49=32, Resulting Numbers: [32] 32,98 unequal: No Solution Exploring Operation: 49+81=130, Resulting Numbers: [130] 130,98 unequal: No Solution Exploring Operation: 49*81=3969, Resulting Numbers: [3969] 3969,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 98:[105, 25], Operations: ['65+40=105', '49-24=25'] Exploring Operation: 105*25=2625, Resulting Numbers: [2625] 2625,98 unequal: No Solution Exploring Operation: 105-25=80, Resulting Numbers: [80] 80,98 unequal: No Solution Exploring Operation: 105+25=130, Resulting Numbers: [130] 130,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[49, 40, 89], Operations: ['24+65=89'] Exploring Operation: 49-40=9, Resulting Numbers: [89, 9] Generated Node #0,0,0: 98:[89, 9] Operation: 49-40=9 Exploring Operation: 49+40=89, Resulting Numbers: [89, 89] Generated Node #0,0,1: 98:[89, 89] Operation: 49+40=89 Exploring Operation: 89-40=49, Resulting Numbers: [49, 49] Generated Node #0,0,2: 98:[49, 49] Operation: 89-40=49 Moving to Node #0,0,2 Current State: 98:[49, 49], Operations: ['24+65=89', '89-40=49'] Exploring Operation: 49-49=0, Resulting Numbers: [0] 0,98 unequal: No Solution Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[49, 24, 65, 40], Operations: [] Exploring Operation: 24+65=89, Resulting Numbers: [49, 40, 89] Generated Node #0,0: 98:[49, 40, 89] Operation: 24+65=89 Moving to Node #0,0 Current State: 98:[49, 40, 89], Operations: ['24+65=89'] Exploring Operation: 89-40=49, Resulting Numbers: [49, 49] Generated Node #0,0,2: 98:[49, 49] Operation: 89-40=49 Moving to Node #0,0,2 Current State: 98:[49, 49], Operations: ['24+65=89', '89-40=49'] Exploring Operation: 49+49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
mult_heuristic
[ 85, 16, 16, 38 ]
47
[ "85+16=101", "16+38=54", "101-54=47" ]
Current State: 47:[85, 16, 16, 38], Operations: [] Exploring Operation: 85+16=101, Resulting Numbers: [38, 101] Generated Node #2: [38, 101] from Operation: 85+16=101 Current State: 47:[38, 101], Operations: ['85+16=101'] Exploring Operation: 16+38=54, Resulting Numbers: [101, 54] Generated Node #3: [101, 54] from Operation: 16+38=54 Current State: 47:[101, 54], Operations: ['85+16=101', '16+38=54'] Exploring Operation: 101-54=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[85, 16, 16, 38], Operations: [] Exploring Operation: 16+16=32, Resulting Numbers: [85, 38, 32] Generated Node #0,0: 47:[85, 38, 32] Operation: 16+16=32 Exploring Operation: 85-16=69, Resulting Numbers: [16, 38, 69] Generated Node #0,1: 47:[16, 38, 69] Operation: 85-16=69 Exploring Operation: 85-16=69, Resulting Numbers: [16, 38, 69] Generated Node #0,2: 47:[16, 38, 69] Operation: 85-16=69 Exploring Operation: 16+38=54, Resulting Numbers: [85, 16, 54] Generated Node #0,3: 47:[85, 16, 54] Operation: 16+38=54 Exploring Operation: 85-38=47, Resulting Numbers: [16, 16, 47] Generated Node #0,4: 47:[16, 16, 47] Operation: 85-38=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[85, 38, 32], Operations: ['16+16=32'] Exploring Operation: 38+32=70, Resulting Numbers: [85, 70] Generated Node #0,0,0: 47:[85, 70] Operation: 38+32=70 Exploring Operation: 85-32=53, Resulting Numbers: [38, 53] Generated Node #0,0,1: 47:[38, 53] Operation: 85-32=53 Exploring Operation: 85-38=47, Resulting Numbers: [32, 47] Generated Node #0,0,2: 47:[32, 47] Operation: 85-38=47 Exploring Operation: 85+32=117, Resulting Numbers: [38, 117] Generated Node #0,0,3: 47:[38, 117] Operation: 85+32=117 Exploring Operation: 38-32=6, Resulting Numbers: [85, 6] Generated Node #0,0,4: 47:[85, 6] Operation: 38-32=6 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[38, 53], Operations: ['16+16=32', '85-32=53'] Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,47 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,47 unequal: No Solution Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,47 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 #0,0,2 Current State: 47:[32, 47], Operations: ['16+16=32', '85-38=47'] Exploring Operation: 47-32=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 32+47=79, Resulting Numbers: [79] 79,47 unequal: No Solution Exploring Operation: 32*47=1504, Resulting Numbers: [1504] 1504,47 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 #0,0,0 Current State: 47:[85, 70], Operations: ['16+16=32', '38+32=70'] Exploring Operation: 85*70=5950, Resulting Numbers: [5950] 5950,47 unequal: No Solution Exploring Operation: 85+70=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 85-70=15, Resulting Numbers: [15] 15,47 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 #0,0,3 Current State: 47:[38, 117], Operations: ['16+16=32', '85+32=117'] Exploring Operation: 117-38=79, Resulting Numbers: [79] 79,47 unequal: No Solution Exploring Operation: 38+117=155, Resulting Numbers: [155] 155,47 unequal: No Solution Exploring Operation: 38*117=4446, Resulting Numbers: [4446] 4446,47 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 #0,0,4 Current State: 47:[85, 6], Operations: ['16+16=32', '38-32=6'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,47 unequal: No Solution Exploring Operation: 85+6=91, Resulting Numbers: [91] 91,47 unequal: No Solution Exploring Operation: 85*6=510, Resulting Numbers: [510] 510,47 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:[16, 38, 69], Operations: ['85-16=69'] Exploring Operation: 69-16=53, Resulting Numbers: [38, 53] Generated Node #0,1,0: 47:[38, 53] Operation: 69-16=53 Exploring Operation: 16+69=85, Resulting Numbers: [38, 85] Generated Node #0,1,1: 47:[38, 85] Operation: 16+69=85 Exploring Operation: 38-16=22, Resulting Numbers: [69, 22] Generated Node #0,1,2: 47:[69, 22] Operation: 38-16=22 Exploring Operation: 16+38=54, Resulting Numbers: [69, 54] Generated Node #0,1,3: 47:[69, 54] Operation: 16+38=54 Exploring Operation: 69-38=31, Resulting Numbers: [16, 31] Generated Node #0,1,4: 47:[16, 31] Operation: 69-38=31 Moving to Node #0,1,0 Current State: 47:[38, 53], Operations: ['85-16=69', '69-16=53'] Exploring Operation: 53-38=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 38*53=2014, Resulting Numbers: [2014] 2014,47 unequal: No Solution Exploring Operation: 38+53=91, Resulting Numbers: [91] 91,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[69, 54], Operations: ['85-16=69', '16+38=54'] Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,47 unequal: No Solution Exploring Operation: 69+54=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 69*54=3726, Resulting Numbers: [3726] 3726,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[38, 85], Operations: ['85-16=69', '16+69=85'] Exploring Operation: 38+85=123, Resulting Numbers: [123] 123,47 unequal: No Solution Exploring Operation: 38*85=3230, Resulting Numbers: [3230] 3230,47 unequal: No Solution Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[85, 16, 16, 38], Operations: [] Exploring Operation: 85-16=69, Resulting Numbers: [16, 38, 69] Generated Node #0,1: 47:[16, 38, 69] Operation: 85-16=69 Moving to Node #0,1 Current State: 47:[16, 38, 69], Operations: ['85-16=69'] Exploring Operation: 16+69=85, Resulting Numbers: [38, 85] Generated Node #0,1,1: 47:[38, 85] Operation: 16+69=85 Moving to Node #0,1,1 Current State: 47:[38, 85], Operations: ['85-16=69', '16+69=85'] Exploring Operation: 85-38=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 3, 63, 44, 9 ]
57
[ "9/3=3", "63-44=19", "3*19=57" ]
Current State: 57:[3, 63, 44, 9], Operations: [] Exploring Operation: 9/3=3, Resulting Numbers: [63, 44, 3] Generated Node #2: [63, 44, 3] from Operation: 9/3=3 Current State: 57:[63, 44, 3], Operations: ['9/3=3'] Exploring Operation: 63-44=19, Resulting Numbers: [3, 19] Generated Node #3: [3, 19] from Operation: 63-44=19 Current State: 57:[3, 19], Operations: ['9/3=3', '63-44=19'] Exploring Operation: 3*19=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[3, 63, 44, 9], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [3, 44, 7] Generated Node #0,0: 57:[3, 44, 7] Operation: 63/9=7 Exploring Operation: 9/3=3, Resulting Numbers: [63, 44, 3] Generated Node #0,1: 57:[63, 44, 3] Operation: 9/3=3 Exploring Operation: 63-9=54, Resulting Numbers: [3, 44, 54] Generated Node #0,2: 57:[3, 44, 54] Operation: 63-9=54 Exploring Operation: 63-44=19, Resulting Numbers: [3, 9, 19] Generated Node #0,3: 57:[3, 9, 19] Operation: 63-44=19 Exploring Operation: 44+9=53, Resulting Numbers: [3, 63, 53] Generated Node #0,4: 57:[3, 63, 53] Operation: 44+9=53 Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[3, 9, 19], Operations: ['63-44=19'] Exploring Operation: 9-3=6, Resulting Numbers: [19, 6] Generated Node #0,3,0: 57:[19, 6] Operation: 9-3=6 Exploring Operation: 3*19=57, Resulting Numbers: [9, 57] Generated Node #0,3,1: 57:[9, 57] Operation: 3*19=57 Exploring Operation: 9/3=3, Resulting Numbers: [19, 3] Generated Node #0,3,2: 57:[19, 3] Operation: 9/3=3 Exploring Operation: 19-9=10, Resulting Numbers: [3, 10] Generated Node #0,3,3: 57:[3, 10] Operation: 19-9=10 Exploring Operation: 3+9=12, Resulting Numbers: [19, 12] Generated Node #0,3,4: 57:[19, 12] Operation: 3+9=12 Moving to Node #0,3,2 Current State: 57:[19, 3], Operations: ['63-44=19', '9/3=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[3, 63, 44, 9], Operations: [] Exploring Operation: 63-44=19, Resulting Numbers: [3, 9, 19] Generated Node #0,3: 57:[3, 9, 19] Operation: 63-44=19 Moving to Node #0,3 Current State: 57:[3, 9, 19], Operations: ['63-44=19'] Exploring Operation: 9/3=3, Resulting Numbers: [19, 3] Generated Node #0,3,2: 57:[19, 3] Operation: 9/3=3 Moving to Node #0,3,2 Current State: 57:[19, 3], Operations: ['63-44=19', '9/3=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 78, 62, 72, 93 ]
25
[ "78+62=140", "72+93=165", "165-140=25" ]
Current State: 25:[78, 62, 72, 93], Operations: [] Exploring Operation: 78+62=140, Resulting Numbers: [72, 93, 140] Generated Node #2: [72, 93, 140] from Operation: 78+62=140 Current State: 25:[72, 93, 140], Operations: ['78+62=140'] Exploring Operation: 72+93=165, Resulting Numbers: [140, 165] Generated Node #3: [140, 165] from Operation: 72+93=165 Current State: 25:[140, 165], Operations: ['78+62=140', '72+93=165'] Exploring Operation: 165-140=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[78, 62, 72, 93], Operations: [] Exploring Operation: 93-78=15, Resulting Numbers: [62, 72, 15] Generated Node #0,0: 25:[62, 72, 15] Operation: 93-78=15 Exploring Operation: 78-72=6, Resulting Numbers: [62, 93, 6] Generated Node #0,1: 25:[62, 93, 6] Operation: 78-72=6 Exploring Operation: 78-62=16, Resulting Numbers: [72, 93, 16] Generated Node #0,2: 25:[72, 93, 16] Operation: 78-62=16 Exploring Operation: 93-72=21, Resulting Numbers: [78, 62, 21] Generated Node #0,3: 25:[78, 62, 21] Operation: 93-72=21 Exploring Operation: 93-62=31, Resulting Numbers: [78, 72, 31] Generated Node #0,4: 25:[78, 72, 31] Operation: 93-62=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[62, 72, 15], Operations: ['93-78=15'] Exploring Operation: 62-15=47, Resulting Numbers: [72, 47] Generated Node #0,0,0: 25:[72, 47] Operation: 62-15=47 Exploring Operation: 62+15=77, Resulting Numbers: [72, 77] Generated Node #0,0,1: 25:[72, 77] Operation: 62+15=77 Exploring Operation: 72-15=57, Resulting Numbers: [62, 57] Generated Node #0,0,2: 25:[62, 57] Operation: 72-15=57 Exploring Operation: 72+15=87, Resulting Numbers: [62, 87] Generated Node #0,0,3: 25:[62, 87] Operation: 72+15=87 Exploring Operation: 72-62=10, Resulting Numbers: [15, 10] Generated Node #0,0,4: 25:[15, 10] Operation: 72-62=10 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 25:[15, 10], Operations: ['93-78=15', '72-62=10'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,25 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,25 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[78, 62, 72, 93], Operations: [] Exploring Operation: 93-78=15, Resulting Numbers: [62, 72, 15] Generated Node #0,0: 25:[62, 72, 15] Operation: 93-78=15 Moving to Node #0,0 Current State: 25:[62, 72, 15], Operations: ['93-78=15'] Exploring Operation: 72-62=10, Resulting Numbers: [15, 10] Generated Node #0,0,4: 25:[15, 10] Operation: 72-62=10 Moving to Node #0,0,4 Current State: 25:[15, 10], Operations: ['93-78=15', '72-62=10'] Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 79, 87, 56, 49 ]
56
[ "87-79=8", "56-49=7", "8*7=56" ]
Current State: 56:[79, 87, 56, 49], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [56, 49, 8] Generated Node #2: [56, 49, 8] from Operation: 87-79=8 Current State: 56:[56, 49, 8], Operations: ['87-79=8'] Exploring Operation: 56-49=7, Resulting Numbers: [8, 7] Generated Node #3: [8, 7] from Operation: 56-49=7 Current State: 56:[8, 7], Operations: ['87-79=8', '56-49=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[79, 87, 56, 49], Operations: [] Exploring Operation: 79-49=30, Resulting Numbers: [87, 56, 30] Generated Node #0,0: 56:[87, 56, 30] Operation: 79-49=30 Exploring Operation: 87-79=8, Resulting Numbers: [56, 49, 8] Generated Node #0,1: 56:[56, 49, 8] Operation: 87-79=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[56, 49, 8], Operations: ['87-79=8'] Exploring Operation: 56-49=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 56:[8, 7] Operation: 56-49=7 Exploring Operation: 49+8=57, Resulting Numbers: [56, 57] Generated Node #0,1,1: 56:[56, 57] Operation: 49+8=57 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[8, 7], Operations: ['87-79=8', '56-49=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[79, 87, 56, 49], Operations: [] Exploring Operation: 87-79=8, Resulting Numbers: [56, 49, 8] Generated Node #0,1: 56:[56, 49, 8] Operation: 87-79=8 Moving to Node #0,1 Current State: 56:[56, 49, 8], Operations: ['87-79=8'] Exploring Operation: 56-49=7, Resulting Numbers: [8, 7] Generated Node #0,1,0: 56:[8, 7] Operation: 56-49=7 Moving to Node #0,1,0 Current State: 56:[8, 7], Operations: ['87-79=8', '56-49=7'] Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 24, 56, 40, 88 ]
38
[ "24+88=112", "112/56=2", "40-2=38" ]
Current State: 38:[24, 56, 40, 88], Operations: [] Exploring Operation: 24+88=112, Resulting Numbers: [56, 40, 112] Generated Node #2: [56, 40, 112] from Operation: 24+88=112 Current State: 38:[56, 40, 112], Operations: ['24+88=112'] Exploring Operation: 112/56=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 112/56=2 Current State: 38:[40, 2], Operations: ['24+88=112', '112/56=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[24, 56, 40, 88], Operations: [] Exploring Operation: 88-56=32, Resulting Numbers: [24, 40, 32] Generated Node #0,0: 38:[24, 40, 32] Operation: 88-56=32 Moving to Node #0,0 Current State: 38:[24, 40, 32], Operations: ['88-56=32'] Exploring Operation: 32-24=8, Resulting Numbers: [40, 8] Generated Node #0,0,0: 38:[40, 8] Operation: 32-24=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[40, 8], Operations: ['88-56=32', '32-24=8'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 69, 50, 9, 5 ]
22
[ "69+50=119", "119-9=110", "110/5=22" ]
Current State: 22:[69, 50, 9, 5], Operations: [] Exploring Operation: 69+50=119, Resulting Numbers: [9, 5, 119] Generated Node #2: [9, 5, 119] from Operation: 69+50=119 Current State: 22:[9, 5, 119], Operations: ['69+50=119'] Exploring Operation: 119-9=110, Resulting Numbers: [5, 110] Generated Node #3: [5, 110] from Operation: 119-9=110 Current State: 22:[5, 110], Operations: ['69+50=119', '119-9=110'] Exploring Operation: 110/5=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[69, 50, 9, 5], Operations: [] Exploring Operation: 69-9=60, Resulting Numbers: [50, 5, 60] Generated Node #0,0: 22:[50, 5, 60] Operation: 69-9=60 Exploring Operation: 50/5=10, Resulting Numbers: [69, 9, 10] Generated Node #0,1: 22:[69, 9, 10] Operation: 50/5=10 Exploring Operation: 69-5=64, Resulting Numbers: [50, 9, 64] Generated Node #0,2: 22:[50, 9, 64] Operation: 69-5=64 Exploring Operation: 69-50=19, Resulting Numbers: [9, 5, 19] Generated Node #0,3: 22:[9, 5, 19] Operation: 69-50=19 Exploring Operation: 50-9=41, Resulting Numbers: [69, 5, 41] Generated Node #0,4: 22:[69, 5, 41] Operation: 50-9=41 Start Sub Search at level 1: Moving to Node #0,3 Current State: 22:[9, 5, 19], Operations: ['69-50=19'] Exploring Operation: 9+5=14, Resulting Numbers: [19, 14] Generated Node #0,3,0: 22:[19, 14] Operation: 9+5=14 Exploring Operation: 5+19=24, Resulting Numbers: [9, 24] Generated Node #0,3,1: 22:[9, 24] Operation: 5+19=24 Exploring Operation: 19-9=10, Resulting Numbers: [5, 10] Generated Node #0,3,2: 22:[5, 10] Operation: 19-9=10 Exploring Operation: 19-5=14, Resulting Numbers: [9, 14] Generated Node #0,3,3: 22:[9, 14] Operation: 19-5=14 Exploring Operation: 9-5=4, Resulting Numbers: [19, 4] Generated Node #0,3,4: 22:[19, 4] Operation: 9-5=4 Moving to Node #0,3,1 Current State: 22:[9, 24], Operations: ['69-50=19', '5+19=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,22 unequal: No Solution Moving to Node #0,3,2 Current State: 22:[5, 10], Operations: ['69-50=19', '19-9=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,3,3 Current State: 22:[9, 14], Operations: ['69-50=19', '19-5=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,3,4 Current State: 22:[19, 4], Operations: ['69-50=19', '9-5=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,22 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,22 unequal: No Solution Moving to Node #0,3,0 Current State: 22:[19, 14], Operations: ['69-50=19', '9+5=14'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 19+14=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 19*14=266, Resulting Numbers: [266] 266,22 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 Current State: 22:[69, 9, 10], Operations: ['50/5=10'] Exploring Operation: 69-10=59, Resulting Numbers: [9, 59] Generated Node #0,1,0: 22:[9, 59] Operation: 69-10=59 Exploring Operation: 10-9=1, Resulting Numbers: [69, 1] Generated Node #0,1,1: 22:[69, 1] Operation: 10-9=1 Exploring Operation: 69-9=60, Resulting Numbers: [10, 60] Generated Node #0,1,2: 22:[10, 60] Operation: 69-9=60 Exploring Operation: 9+10=19, Resulting Numbers: [69, 19] Generated Node #0,1,3: 22:[69, 19] Operation: 9+10=19 Exploring Operation: 69+9=78, Resulting Numbers: [10, 78] Generated Node #0,1,4: 22:[10, 78] Operation: 69+9=78 Moving to Node #0,1,0 Current State: 22:[9, 59], Operations: ['50/5=10', '69-10=59'] Exploring Operation: 9*59=531, Resulting Numbers: [531] 531,22 unequal: No Solution Exploring Operation: 9+59=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 59-9=50, Resulting Numbers: [50] 50,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[10, 60], Operations: ['50/5=10', '69-9=60'] Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 10*60=600, Resulting Numbers: [600] 600,22 unequal: No Solution Exploring Operation: 10+60=70, Resulting Numbers: [70] 70,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[69, 1], Operations: ['50/5=10', '10-9=1'] Exploring Operation: 69+1=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 69*1=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[69, 19], Operations: ['50/5=10', '9+10=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,22 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,22 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,22 unequal: No Solution Moving to Node #0,1,4 Current State: 22:[10, 78], Operations: ['50/5=10', '69+9=78'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,22 unequal: No Solution Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,22 unequal: No Solution Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,22 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 Current State: 22:[50, 5, 60], Operations: ['69-9=60'] Exploring Operation: 50/5=10, Resulting Numbers: [60, 10] Generated Node #0,0,0: 22:[60, 10] Operation: 50/5=10 Exploring Operation: 60-5=55, Resulting Numbers: [50, 55] Generated Node #0,0,1: 22:[50, 55] Operation: 60-5=55 Exploring Operation: 60/5=12, Resulting Numbers: [50, 12] Generated Node #0,0,2: 22:[50, 12] Operation: 60/5=12 Exploring Operation: 60-50=10, Resulting Numbers: [5, 10] Generated Node #0,0,3: 22:[5, 10] Operation: 60-50=10 Exploring Operation: 50-5=45, Resulting Numbers: [60, 45] Generated Node #0,0,4: 22:[60, 45] Operation: 50-5=45 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 22:[5, 10], Operations: ['69-9=60', '60-50=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,22 unequal: No Solution No 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: 22:[50, 12], Operations: ['69-9=60', '60/5=12'] Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,22 unequal: No Solution Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,22 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,22 unequal: No Solution No 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: 22:[60, 10], Operations: ['69-9=60', '50/5=10'] Exploring Operation: 60-10=50, Resulting Numbers: [50] 50,22 unequal: No Solution Exploring Operation: 60/10=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 60+10=70, Resulting Numbers: [70] 70,22 unequal: No Solution Exploring Operation: 60*10=600, Resulting Numbers: [600] 600,22 unequal: No Solution No 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: 22:[50, 55], Operations: ['69-9=60', '60-5=55'] Exploring Operation: 50+55=105, Resulting Numbers: [105] 105,22 unequal: No Solution Exploring Operation: 50*55=2750, Resulting Numbers: [2750] 2750,22 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,22 unequal: No Solution No 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: 22:[60, 45], Operations: ['69-9=60', '50-5=45'] Exploring Operation: 60*45=2700, Resulting Numbers: [2700] 2700,22 unequal: No Solution Exploring Operation: 60-45=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 60+45=105, Resulting Numbers: [105] 105,22 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: 22:[69, 5, 41], Operations: ['50-9=41'] Exploring Operation: 69-5=64, Resulting Numbers: [41, 64] Generated Node #0,4,0: 22:[41, 64] Operation: 69-5=64 Exploring Operation: 41-5=36, Resulting Numbers: [69, 36] Generated Node #0,4,1: 22:[69, 36] Operation: 41-5=36 Exploring Operation: 69-41=28, Resulting Numbers: [5, 28] Generated Node #0,4,2: 22:[5, 28] Operation: 69-41=28 Exploring Operation: 5+41=46, Resulting Numbers: [69, 46] Generated Node #0,4,3: 22:[69, 46] Operation: 5+41=46 Exploring Operation: 69+5=74, Resulting Numbers: [41, 74] Generated Node #0,4,4: 22:[41, 74] Operation: 69+5=74 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 22:[5, 28], Operations: ['50-9=41', '69-41=28'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,22 unequal: No Solution No 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: 22:[41, 64], Operations: ['50-9=41', '69-5=64'] Exploring Operation: 41*64=2624, Resulting Numbers: [2624] 2624,22 unequal: No Solution Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 41+64=105, Resulting Numbers: [105] 105,22 unequal: No Solution No 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: 22:[69, 36], Operations: ['50-9=41', '41-5=36'] Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,22 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,22 unequal: No Solution No 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: 22:[69, 46], Operations: ['50-9=41', '5+41=46'] Exploring Operation: 69*46=3174, Resulting Numbers: [3174] 3174,22 unequal: No Solution Exploring Operation: 69+46=115, Resulting Numbers: [115] 115,22 unequal: No Solution Exploring Operation: 69-46=23, Resulting Numbers: [23] 23,22 unequal: No Solution No 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: 22:[41, 74], Operations: ['50-9=41', '69+5=74'] Exploring Operation: 41*74=3034, Resulting Numbers: [3034] 3034,22 unequal: No Solution Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 41+74=115, Resulting Numbers: [115] 115,22 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: 22:[50, 9, 64], Operations: ['69-5=64'] Exploring Operation: 50-9=41, Resulting Numbers: [64, 41] Generated Node #0,2,0: 22:[64, 41] Operation: 50-9=41 Exploring Operation: 64-50=14, Resulting Numbers: [9, 14] Generated Node #0,2,1: 22:[9, 14] Operation: 64-50=14 Exploring Operation: 64-9=55, Resulting Numbers: [50, 55] Generated Node #0,2,2: 22:[50, 55] Operation: 64-9=55 Exploring Operation: 9+64=73, Resulting Numbers: [50, 73] Generated Node #0,2,3: 22:[50, 73] Operation: 9+64=73 Exploring Operation: 50+9=59, Resulting Numbers: [64, 59] Generated Node #0,2,4: 22:[64, 59] Operation: 50+9=59 Moving to Node #0,2,1 Current State: 22:[9, 14], Operations: ['69-5=64', '64-50=14'] Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[50, 55], Operations: ['69-5=64', '64-9=55'] Exploring Operation: 50*55=2750, Resulting Numbers: [2750] 2750,22 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 50+55=105, Resulting Numbers: [105] 105,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[64, 41], Operations: ['69-5=64', '50-9=41'] Exploring Operation: 64*41=2624, Resulting Numbers: [2624] 2624,22 unequal: No Solution Exploring Operation: 64+41=105, Resulting Numbers: [105] 105,22 unequal: No Solution Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[50, 73], Operations: ['69-5=64', '9+64=73'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,22 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,22 unequal: No Solution Moving to Node #0,2,4 Current State: 22:[64, 59], Operations: ['69-5=64', '50+9=59'] Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,22 unequal: No Solution Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,22 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
[ 82, 48, 45, 1 ]
80
[ "82-48=34", "45+1=46", "34+46=80" ]
Current State: 80:[82, 48, 45, 1], Operations: [] Exploring Operation: 82-48=34, Resulting Numbers: [45, 1, 34] Generated Node #2: [45, 1, 34] from Operation: 82-48=34 Current State: 80:[45, 1, 34], Operations: ['82-48=34'] Exploring Operation: 45+1=46, Resulting Numbers: [34, 46] Generated Node #3: [34, 46] from Operation: 45+1=46 Current State: 80:[34, 46], Operations: ['82-48=34', '45+1=46'] Exploring Operation: 34+46=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[82, 48, 45, 1], Operations: [] Exploring Operation: 48-45=3, Resulting Numbers: [82, 1, 3] Generated Node #0,0: 80:[82, 1, 3] Operation: 48-45=3 Exploring Operation: 82-48=34, Resulting Numbers: [45, 1, 34] Generated Node #0,1: 80:[45, 1, 34] Operation: 82-48=34 Moving to Node #0,0 Current State: 80:[82, 1, 3], Operations: ['48-45=3'] Exploring Operation: 82-1=81, Resulting Numbers: [3, 81] Generated Node #0,0,0: 80:[3, 81] Operation: 82-1=81 Exploring Operation: 82-3=79, Resulting Numbers: [1, 79] Generated Node #0,0,1: 80:[1, 79] Operation: 82-3=79 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[3, 81], Operations: ['48-45=3', '82-1=81'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 3+81=84, Resulting Numbers: [84] 84,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[1, 79], Operations: ['48-45=3', '82-3=79'] Exploring Operation: 1*79=79, Resulting Numbers: [79] 79,80 unequal: No Solution Exploring Operation: 1+79=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[82, 48, 45, 1], Operations: [] Exploring Operation: 48-45=3, Resulting Numbers: [82, 1, 3] Generated Node #0,0: 80:[82, 1, 3] Operation: 48-45=3 Moving to Node #0,0 Current State: 80:[82, 1, 3], Operations: ['48-45=3'] Exploring Operation: 82-3=79, Resulting Numbers: [1, 79] Generated Node #0,0,1: 80:[1, 79] Operation: 82-3=79 Moving to Node #0,0,1 Current State: 80:[1, 79], Operations: ['48-45=3', '82-3=79'] Exploring Operation: 1+79=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 91, 90, 47, 60 ]
92
[ "91+47=138", "60*138=8280", "8280/90=92" ]
Current State: 92:[91, 90, 47, 60], Operations: [] Exploring Operation: 91+47=138, Resulting Numbers: [90, 60, 138] Generated Node #2: [90, 60, 138] from Operation: 91+47=138 Current State: 92:[90, 60, 138], Operations: ['91+47=138'] Exploring Operation: 60*138=8280, Resulting Numbers: [90, 8280] Generated Node #3: [90, 8280] from Operation: 60*138=8280 Current State: 92:[90, 8280], Operations: ['91+47=138', '60*138=8280'] Exploring Operation: 8280/90=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[91, 90, 47, 60], Operations: [] Exploring Operation: 90-60=30, Resulting Numbers: [91, 47, 30] Generated Node #0,0: 92:[91, 47, 30] Operation: 90-60=30 Moving to Node #0,0 Current State: 92:[91, 47, 30], Operations: ['90-60=30'] Exploring Operation: 47-30=17, Resulting Numbers: [91, 17] Generated Node #0,0,0: 92:[91, 17] Operation: 47-30=17 Moving to Node #0,0,0 Current State: 92:[91, 17], Operations: ['90-60=30', '47-30=17'] Exploring Operation: 91+17=108, Resulting Numbers: [108] 108,92 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 30, 23, 89, 70 ]
79
[ "30-23=7", "70/7=10", "89-10=79" ]
Current State: 79:[30, 23, 89, 70], Operations: [] Exploring Operation: 30-23=7, Resulting Numbers: [89, 70, 7] Generated Node #2: [89, 70, 7] from Operation: 30-23=7 Current State: 79:[89, 70, 7], Operations: ['30-23=7'] Exploring Operation: 70/7=10, Resulting Numbers: [89, 10] Generated Node #3: [89, 10] from Operation: 70/7=10 Current State: 79:[89, 10], Operations: ['30-23=7', '70/7=10'] Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[30, 23, 89, 70], Operations: [] Exploring Operation: 30+23=53, Resulting Numbers: [89, 70, 53] Generated Node #0,0: 79:[89, 70, 53] Operation: 30+23=53 Exploring Operation: 89-23=66, Resulting Numbers: [30, 70, 66] Generated Node #0,1: 79:[30, 70, 66] Operation: 89-23=66 Moving to Node #0,0 Current State: 79:[89, 70, 53], Operations: ['30+23=53'] Exploring Operation: 89-53=36, Resulting Numbers: [70, 36] Generated Node #0,0,0: 79:[70, 36] Operation: 89-53=36 Exploring Operation: 70+53=123, Resulting Numbers: [89, 123] Generated Node #0,0,1: 79:[89, 123] Operation: 70+53=123 Moving to Node #0,1 Current State: 79:[30, 70, 66], Operations: ['89-23=66'] Exploring Operation: 30+70=100, Resulting Numbers: [66, 100] Generated Node #0,1,0: 79:[66, 100] Operation: 30+70=100 Exploring Operation: 30+66=96, Resulting Numbers: [70, 96] Generated Node #0,1,1: 79:[70, 96] Operation: 30+66=96 Moving to Node #0,1,1 Current State: 79:[70, 96], Operations: ['89-23=66', '30+66=96'] Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 70+96=166, Resulting Numbers: [166] 166,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[66, 100], Operations: ['89-23=66', '30+70=100'] Exploring Operation: 100-66=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 66+100=166, Resulting Numbers: [166] 166,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[70, 36], Operations: ['30+23=53', '89-53=36'] Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,79 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[89, 123], Operations: ['30+23=53', '70+53=123'] Exploring Operation: 123-89=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 89+123=212, Resulting Numbers: [212] 212,79 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 74, 77, 2, 34 ]
57
[ "74-34=40", "40/2=20", "77-20=57" ]
Current State: 57:[74, 77, 2, 34], Operations: [] Exploring Operation: 74-34=40, Resulting Numbers: [77, 2, 40] Generated Node #2: [77, 2, 40] from Operation: 74-34=40 Current State: 57:[77, 2, 40], Operations: ['74-34=40'] Exploring Operation: 40/2=20, Resulting Numbers: [77, 20] Generated Node #3: [77, 20] from Operation: 40/2=20 Current State: 57:[77, 20], Operations: ['74-34=40', '40/2=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[74, 77, 2, 34], Operations: [] Exploring Operation: 77-34=43, Resulting Numbers: [74, 2, 43] Generated Node #0,0: 57:[74, 2, 43] Operation: 77-34=43 Exploring Operation: 77-74=3, Resulting Numbers: [2, 34, 3] Generated Node #0,1: 57:[2, 34, 3] Operation: 77-74=3 Exploring Operation: 74-34=40, Resulting Numbers: [77, 2, 40] Generated Node #0,2: 57:[77, 2, 40] Operation: 74-34=40 Moving to Node #0,1 Current State: 57:[2, 34, 3], Operations: ['77-74=3'] Exploring Operation: 2*34=68, Resulting Numbers: [3, 68] Generated Node #0,1,0: 57:[3, 68] Operation: 2*34=68 Exploring Operation: 34/2=17, Resulting Numbers: [3, 17] Generated Node #0,1,1: 57:[3, 17] Operation: 34/2=17 Exploring Operation: 34-2=32, Resulting Numbers: [3, 32] Generated Node #0,1,2: 57:[3, 32] Operation: 34-2=32 Moving to Node #0,0 Current State: 57:[74, 2, 43], Operations: ['77-34=43'] Exploring Operation: 2+43=45, Resulting Numbers: [74, 45] Generated Node #0,0,0: 57:[74, 45] Operation: 2+43=45 Exploring Operation: 74-2=72, Resulting Numbers: [43, 72] Generated Node #0,0,1: 57:[43, 72] Operation: 74-2=72 Exploring Operation: 74-43=31, Resulting Numbers: [2, 31] Generated Node #0,0,2: 57:[2, 31] Operation: 74-43=31 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 57:[2, 31], Operations: ['77-34=43', '74-43=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,57 unequal: No Solution Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[74, 45], Operations: ['77-34=43', '2+43=45'] Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 74*45=3330, Resulting Numbers: [3330] 3330,57 unequal: No Solution Exploring Operation: 74+45=119, Resulting Numbers: [119] 119,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 57:[43, 72], Operations: ['77-34=43', '74-2=72'] Exploring Operation: 72-43=29, Resulting Numbers: [29] 29,57 unequal: No Solution Exploring Operation: 43*72=3096, Resulting Numbers: [3096] 3096,57 unequal: No Solution Exploring Operation: 43+72=115, Resulting Numbers: [115] 115,57 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: 57:[77, 2, 40], Operations: ['74-34=40'] Exploring Operation: 77-2=75, Resulting Numbers: [40, 75] Generated Node #0,2,0: 57:[40, 75] Operation: 77-2=75 Exploring Operation: 77-40=37, Resulting Numbers: [2, 37] Generated Node #0,2,1: 57:[2, 37] Operation: 77-40=37 Exploring Operation: 40/2=20, Resulting Numbers: [77, 20] Generated Node #0,2,2: 57:[77, 20] Operation: 40/2=20 Moving to Node #0,1,1 Current State: 57:[3, 17], Operations: ['77-74=3', '34/2=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,57 unequal: No Solution Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,57 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[3, 68], Operations: ['77-74=3', '2*34=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,57 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,57 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[3, 32], Operations: ['77-74=3', '34-2=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,57 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[2, 37], Operations: ['74-34=40', '77-40=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,57 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,57 unequal: No Solution Exploring Operation: 2*37=74, Resulting Numbers: [74] 74,57 unequal: No Solution Moving to Node #0,2,2 Current State: 57:[77, 20], Operations: ['74-34=40', '40/2=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[74, 77, 2, 34], Operations: [] Exploring Operation: 74-34=40, Resulting Numbers: [77, 2, 40] Generated Node #0,2: 57:[77, 2, 40] Operation: 74-34=40 Moving to Node #0,2 Current State: 57:[77, 2, 40], Operations: ['74-34=40'] Exploring Operation: 40/2=20, Resulting Numbers: [77, 20] Generated Node #0,2,2: 57:[77, 20] Operation: 40/2=20 Moving to Node #0,2,2 Current State: 57:[77, 20], Operations: ['74-34=40', '40/2=20'] Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.967014
hs_3
sum_heuristic
[ 68, 34, 17, 40 ]
38
[ "68-34=34", "34/17=2", "40-2=38" ]
Current State: 38:[68, 34, 17, 40], Operations: [] Exploring Operation: 68-34=34, Resulting Numbers: [17, 40, 34] Generated Node #2: [17, 40, 34] from Operation: 68-34=34 Current State: 38:[17, 40, 34], Operations: ['68-34=34'] Exploring Operation: 34/17=2, Resulting Numbers: [40, 2] Generated Node #3: [40, 2] from Operation: 34/17=2 Current State: 38:[40, 2], Operations: ['68-34=34', '34/17=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[68, 34, 17, 40], Operations: [] Exploring Operation: 68/17=4, Resulting Numbers: [34, 40, 4] Generated Node #0,0: 38:[34, 40, 4] Operation: 68/17=4 Exploring Operation: 68-40=28, Resulting Numbers: [34, 17, 28] Generated Node #0,1: 38:[34, 17, 28] Operation: 68-40=28 Exploring Operation: 68/34=2, Resulting Numbers: [17, 40, 2] Generated Node #0,2: 38:[17, 40, 2] Operation: 68/34=2 Exploring Operation: 68-34=34, Resulting Numbers: [17, 40, 34] Generated Node #0,3: 38:[17, 40, 34] Operation: 68-34=34 Exploring Operation: 68-17=51, Resulting Numbers: [34, 40, 51] Generated Node #0,4: 38:[34, 40, 51] Operation: 68-17=51 Start Sub Search at level 1: Moving to Node #0,2 Current State: 38:[17, 40, 2], Operations: ['68/34=2'] Exploring Operation: 17+2=19, Resulting Numbers: [40, 19] Generated Node #0,2,0: 38:[40, 19] Operation: 17+2=19 Exploring Operation: 40-17=23, Resulting Numbers: [2, 23] Generated Node #0,2,1: 38:[2, 23] Operation: 40-17=23 Exploring Operation: 40-2=38, Resulting Numbers: [17, 38] Generated Node #0,2,2: 38:[17, 38] Operation: 40-2=38 Exploring Operation: 40/2=20, Resulting Numbers: [17, 20] Generated Node #0,2,3: 38:[17, 20] Operation: 40/2=20 Exploring Operation: 17*2=34, Resulting Numbers: [40, 34] Generated Node #0,2,4: 38:[40, 34] Operation: 17*2=34 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 38:[40, 19], Operations: ['68/34=2', '17+2=19'] Exploring Operation: 40+19=59, Resulting Numbers: [59] 59,38 unequal: No Solution Exploring Operation: 40-19=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 40*19=760, Resulting Numbers: [760] 760,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 38:[17, 38], Operations: ['68/34=2', '40-2=38'] Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,38 unequal: No Solution Exploring Operation: 17*38=646, Resulting Numbers: [646] 646,38 unequal: No Solution Exploring Operation: 17+38=55, Resulting Numbers: [55] 55,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 38:[17, 20], Operations: ['68/34=2', '40/2=20'] Exploring Operation: 17*20=340, Resulting Numbers: [340] 340,38 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,38 unequal: No Solution Exploring Operation: 17+20=37, Resulting Numbers: [37] 37,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 38:[2, 23], Operations: ['68/34=2', '40-17=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 38:[40, 34], Operations: ['68/34=2', '17*2=34'] Exploring Operation: 40*34=1360, Resulting Numbers: [1360] 1360,38 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 40+34=74, Resulting Numbers: [74] 74,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 38:[34, 40, 4], Operations: ['68/17=4'] Exploring Operation: 40+4=44, Resulting Numbers: [34, 44] Generated Node #0,0,0: 38:[34, 44] Operation: 40+4=44 Exploring Operation: 40-34=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 38:[4, 6] Operation: 40-34=6 Exploring Operation: 34-4=30, Resulting Numbers: [40, 30] Generated Node #0,0,2: 38:[40, 30] Operation: 34-4=30 Exploring Operation: 34+4=38, Resulting Numbers: [40, 38] Generated Node #0,0,3: 38:[40, 38] Operation: 34+4=38 Exploring Operation: 40-4=36, Resulting Numbers: [34, 36] Generated Node #0,0,4: 38:[34, 36] Operation: 40-4=36 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 38:[40, 38], Operations: ['68/17=4', '34+4=38'] Exploring Operation: 40*38=1520, Resulting Numbers: [1520] 1520,38 unequal: No Solution Exploring Operation: 40+38=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 38:[4, 6], Operations: ['68/17=4', '40-34=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 38:[34, 36], Operations: ['68/17=4', '40-4=36'] Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,38 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,38 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 38:[34, 44], Operations: ['68/17=4', '40+4=44'] Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,38 unequal: No Solution Exploring Operation: 34+44=78, Resulting Numbers: [78] 78,38 unequal: No Solution Exploring Operation: 34*44=1496, Resulting Numbers: [1496] 1496,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 38:[40, 30], Operations: ['68/17=4', '34-4=30'] Exploring Operation: 40*30=1200, Resulting Numbers: [1200] 1200,38 unequal: No Solution Exploring Operation: 40+30=70, Resulting Numbers: [70] 70,38 unequal: No Solution Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,38 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 38:[17, 40, 34], Operations: ['68-34=34'] Exploring Operation: 17+34=51, Resulting Numbers: [40, 51] Generated Node #0,3,0: 38:[40, 51] Operation: 17+34=51 Exploring Operation: 34/17=2, Resulting Numbers: [40, 2] Generated Node #0,3,1: 38:[40, 2] Operation: 34/17=2 Exploring Operation: 40-17=23, Resulting Numbers: [34, 23] Generated Node #0,3,2: 38:[34, 23] Operation: 40-17=23 Exploring Operation: 34-17=17, Resulting Numbers: [40, 17] Generated Node #0,3,3: 38:[40, 17] Operation: 34-17=17 Exploring Operation: 40-34=6, Resulting Numbers: [17, 6] Generated Node #0,3,4: 38:[17, 6] Operation: 40-34=6 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 38:[40, 2], Operations: ['68-34=34', '34/17=2'] Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,38 unequal: No Solution Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,38 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[68, 34, 17, 40], Operations: [] Exploring Operation: 68-34=34, Resulting Numbers: [17, 40, 34] Generated Node #0,3: 38:[17, 40, 34] Operation: 68-34=34 Moving to Node #0,3 Current State: 38:[17, 40, 34], Operations: ['68-34=34'] Exploring Operation: 34/17=2, Resulting Numbers: [40, 2] Generated Node #0,3,1: 38:[40, 2] Operation: 34/17=2 Moving to Node #0,3,1 Current State: 38:[40, 2], Operations: ['68-34=34', '34/17=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 5, 89, 39, 96 ]
78
[ "5+89=94", "96-94=2", "39*2=78" ]
Current State: 78:[5, 89, 39, 96], Operations: [] Exploring Operation: 5+89=94, Resulting Numbers: [39, 96, 94] Generated Node #2: [39, 96, 94] from Operation: 5+89=94 Current State: 78:[39, 96, 94], Operations: ['5+89=94'] Exploring Operation: 96-94=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 96-94=2 Current State: 78:[39, 2], Operations: ['5+89=94', '96-94=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[5, 89, 39, 96], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [5, 39, 7] Generated Node #0,0: 78:[5, 39, 7] Operation: 96-89=7 Exploring Operation: 96-5=91, Resulting Numbers: [89, 39, 91] Generated Node #0,1: 78:[89, 39, 91] Operation: 96-5=91 Exploring Operation: 89-5=84, Resulting Numbers: [39, 96, 84] Generated Node #0,2: 78:[39, 96, 84] Operation: 89-5=84 Exploring Operation: 89-39=50, Resulting Numbers: [5, 96, 50] Generated Node #0,3: 78:[5, 96, 50] Operation: 89-39=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[5, 39, 7], Operations: ['96-89=7'] Exploring Operation: 5+39=44, Resulting Numbers: [7, 44] Generated Node #0,0,0: 78:[7, 44] Operation: 5+39=44 Exploring Operation: 7-5=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 78:[39, 2] Operation: 7-5=2 Exploring Operation: 5+7=12, Resulting Numbers: [39, 12] Generated Node #0,0,2: 78:[39, 12] Operation: 5+7=12 Exploring Operation: 5*7=35, Resulting Numbers: [39, 35] Generated Node #0,0,3: 78:[39, 35] Operation: 5*7=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 78:[39, 2], Operations: ['96-89=7', '7-5=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,78 unequal: No Solution Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[5, 89, 39, 96], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [5, 39, 7] Generated Node #0,0: 78:[5, 39, 7] Operation: 96-89=7 Moving to Node #0,0 Current State: 78:[5, 39, 7], Operations: ['96-89=7'] Exploring Operation: 7-5=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 78:[39, 2] Operation: 7-5=2 Moving to Node #0,0,1 Current State: 78:[39, 2], Operations: ['96-89=7', '7-5=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 40, 17, 10, 20 ]
11
[ "40+20=60", "60/10=6", "17-6=11" ]
Current State: 11:[40, 17, 10, 20], Operations: [] Exploring Operation: 40+20=60, Resulting Numbers: [17, 10, 60] Generated Node #2: [17, 10, 60] from Operation: 40+20=60 Current State: 11:[17, 10, 60], Operations: ['40+20=60'] Exploring Operation: 60/10=6, Resulting Numbers: [17, 6] Generated Node #3: [17, 6] from Operation: 60/10=6 Current State: 11:[17, 6], Operations: ['40+20=60', '60/10=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[40, 17, 10, 20], Operations: [] Exploring Operation: 40-20=20, Resulting Numbers: [17, 10, 20] Generated Node #0,0: 11:[17, 10, 20] Operation: 40-20=20 Exploring Operation: 40-17=23, Resulting Numbers: [10, 20, 23] Generated Node #0,1: 11:[10, 20, 23] Operation: 40-17=23 Exploring Operation: 40/20=2, Resulting Numbers: [17, 10, 2] Generated Node #0,2: 11:[17, 10, 2] Operation: 40/20=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[17, 10, 20], Operations: ['40-20=20'] Exploring Operation: 20-10=10, Resulting Numbers: [17, 10] Generated Node #0,0,0: 11:[17, 10] Operation: 20-10=10 Exploring Operation: 20-17=3, Resulting Numbers: [10, 3] Generated Node #0,0,1: 11:[10, 3] Operation: 20-17=3 Exploring Operation: 17-10=7, Resulting Numbers: [20, 7] Generated Node #0,0,2: 11:[20, 7] Operation: 17-10=7 Moving to Node #0,0,0 Current State: 11:[17, 10], Operations: ['40-20=20', '20-10=10'] Exploring Operation: 17*10=170, Resulting Numbers: [170] 170,11 unequal: No Solution Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,11 unequal: No Solution Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[10, 3], Operations: ['40-20=20', '20-17=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,0,2 Current State: 11:[20, 7], Operations: ['40-20=20', '17-10=7'] Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 20*7=140, Resulting Numbers: [140] 140,11 unequal: No Solution Exploring Operation: 20+7=27, Resulting Numbers: [27] 27,11 unequal: No Solution No 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: 11:[17, 10, 2], Operations: ['40/20=2'] Exploring Operation: 10+2=12, Resulting Numbers: [17, 12] Generated Node #0,2,0: 11:[17, 12] Operation: 10+2=12 Exploring Operation: 17+2=19, Resulting Numbers: [10, 19] Generated Node #0,2,1: 11:[10, 19] Operation: 17+2=19 Exploring Operation: 17-2=15, Resulting Numbers: [10, 15] Generated Node #0,2,2: 11:[10, 15] Operation: 17-2=15 Moving to Node #0,2,2 Current State: 11:[10, 15], Operations: ['40/20=2', '17-2=15'] Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,11 unequal: No Solution Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[17, 12], Operations: ['40/20=2', '10+2=12'] Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,11 unequal: No Solution Exploring Operation: 17*12=204, Resulting Numbers: [204] 204,11 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[10, 19], Operations: ['40/20=2', '17+2=19'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,11 unequal: No Solution Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,11 unequal: No Solution Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,11 unequal: No Solution No solution 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: 11:[10, 20, 23], Operations: ['40-17=23'] Exploring Operation: 23-10=13, Resulting Numbers: [20, 13] Generated Node #0,1,0: 11:[20, 13] Operation: 23-10=13 Exploring Operation: 23-20=3, Resulting Numbers: [10, 3] Generated Node #0,1,1: 11:[10, 3] Operation: 23-20=3 Exploring Operation: 20-10=10, Resulting Numbers: [23, 10] Generated Node #0,1,2: 11:[23, 10] Operation: 20-10=10 Moving to Node #0,1,1 Current State: 11:[10, 3], Operations: ['40-17=23', '23-20=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,11 unequal: No Solution Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[20, 13], Operations: ['40-17=23', '23-10=13'] Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,11 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[23, 10], Operations: ['40-17=23', '20-10=10'] Exploring Operation: 23*10=230, Resulting Numbers: [230] 230,11 unequal: No Solution Exploring Operation: 23+10=33, Resulting Numbers: [33] 33,11 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,11 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
[ 41, 5, 4, 41 ]
41
[ "41*5=205", "4*41=164", "205-164=41" ]
Current State: 41:[41, 5, 4, 41], Operations: [] Exploring Operation: 41*5=205, Resulting Numbers: [4, 205] Generated Node #2: [4, 205] from Operation: 41*5=205 Current State: 41:[4, 205], Operations: ['41*5=205'] Exploring Operation: 4*41=164, Resulting Numbers: [205, 164] Generated Node #3: [205, 164] from Operation: 4*41=164 Current State: 41:[205, 164], Operations: ['41*5=205', '4*41=164'] Exploring Operation: 205-164=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[41, 5, 4, 41], Operations: [] Exploring Operation: 41+4=45, Resulting Numbers: [5, 41, 45] Generated Node #0,0: 41:[5, 41, 45] Operation: 41+4=45 Exploring Operation: 5+4=9, Resulting Numbers: [41, 41, 9] Generated Node #0,1: 41:[41, 41, 9] Operation: 5+4=9 Exploring Operation: 41-4=37, Resulting Numbers: [5, 41, 37] Generated Node #0,2: 41:[5, 41, 37] Operation: 41-4=37 Exploring Operation: 5*4=20, Resulting Numbers: [41, 41, 20] Generated Node #0,3: 41:[41, 41, 20] Operation: 5*4=20 Moving to Node #0,3 Current State: 41:[41, 41, 20], Operations: ['5*4=20'] Exploring Operation: 41-20=21, Resulting Numbers: [41, 21] Generated Node #0,3,0: 41:[41, 21] Operation: 41-20=21 Exploring Operation: 41-20=21, Resulting Numbers: [41, 21] Generated Node #0,3,1: 41:[41, 21] Operation: 41-20=21 Exploring Operation: 41+20=61, Resulting Numbers: [41, 61] Generated Node #0,3,2: 41:[41, 61] Operation: 41+20=61 Exploring Operation: 41+20=61, Resulting Numbers: [41, 61] Generated Node #0,3,3: 41:[41, 61] Operation: 41+20=61 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[41, 21], Operations: ['5*4=20', '41-20=21'] Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,41 unequal: No Solution Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[41, 21], Operations: ['5*4=20', '41-20=21'] Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,41 unequal: No Solution Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,41 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[41, 61], Operations: ['5*4=20', '41+20=61'] Exploring Operation: 61-41=20, Resulting Numbers: [20] 20,41 unequal: No Solution Exploring Operation: 41*61=2501, Resulting Numbers: [2501] 2501,41 unequal: No Solution Exploring Operation: 41+61=102, Resulting Numbers: [102] 102,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 41:[41, 61], Operations: ['5*4=20', '41+20=61'] Exploring Operation: 41*61=2501, Resulting Numbers: [2501] 2501,41 unequal: No Solution Exploring Operation: 41+61=102, Resulting Numbers: [102] 102,41 unequal: No Solution Exploring Operation: 61-41=20, Resulting Numbers: [20] 20,41 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: 41:[41, 41, 9], Operations: ['5+4=9'] Exploring Operation: 41+9=50, Resulting Numbers: [41, 50] Generated Node #0,1,0: 41:[41, 50] Operation: 41+9=50 Exploring Operation: 41-9=32, Resulting Numbers: [41, 32] Generated Node #0,1,1: 41:[41, 32] Operation: 41-9=32 Exploring Operation: 41+9=50, Resulting Numbers: [41, 50] Generated Node #0,1,2: 41:[41, 50] Operation: 41+9=50 Exploring Operation: 41-9=32, Resulting Numbers: [41, 32] Generated Node #0,1,3: 41:[41, 32] Operation: 41-9=32 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[41, 50], Operations: ['5+4=9', '41+9=50'] Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 41+50=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 41*50=2050, Resulting Numbers: [2050] 2050,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[41, 32], Operations: ['5+4=9', '41-9=32'] Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 41+32=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 41*32=1312, Resulting Numbers: [1312] 1312,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[41, 50], Operations: ['5+4=9', '41+9=50'] Exploring Operation: 41*50=2050, Resulting Numbers: [2050] 2050,41 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 41+50=91, Resulting Numbers: [91] 91,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[41, 32], Operations: ['5+4=9', '41-9=32'] Exploring Operation: 41*32=1312, Resulting Numbers: [1312] 1312,41 unequal: No Solution Exploring Operation: 41+32=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,41 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: 41:[5, 41, 37], Operations: ['41-4=37'] Exploring Operation: 41-5=36, Resulting Numbers: [37, 36] Generated Node #0,2,0: 41:[37, 36] Operation: 41-5=36 Exploring Operation: 37-5=32, Resulting Numbers: [41, 32] Generated Node #0,2,1: 41:[41, 32] Operation: 37-5=32 Exploring Operation: 5+37=42, Resulting Numbers: [41, 42] Generated Node #0,2,2: 41:[41, 42] Operation: 5+37=42 Exploring Operation: 5+41=46, Resulting Numbers: [37, 46] Generated Node #0,2,3: 41:[37, 46] Operation: 5+41=46 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[41, 42], Operations: ['41-4=37', '5+37=42'] Exploring Operation: 41+42=83, Resulting Numbers: [83] 83,41 unequal: No Solution Exploring Operation: 41*42=1722, Resulting Numbers: [1722] 1722,41 unequal: No Solution Exploring Operation: 42-41=1, Resulting Numbers: [1] 1,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[37, 36], Operations: ['41-4=37', '41-5=36'] Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,41 unequal: No Solution Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 41:[41, 32], Operations: ['41-4=37', '37-5=32'] Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 41*32=1312, Resulting Numbers: [1312] 1312,41 unequal: No Solution Exploring Operation: 41+32=73, Resulting Numbers: [73] 73,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 41:[37, 46], Operations: ['41-4=37', '5+41=46'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,41 unequal: No Solution Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,41 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: 41:[5, 41, 45], Operations: ['41+4=45'] Exploring Operation: 5+41=46, Resulting Numbers: [45, 46] Generated Node #0,0,0: 41:[45, 46] Operation: 5+41=46 Exploring Operation: 41-5=36, Resulting Numbers: [45, 36] Generated Node #0,0,1: 41:[45, 36] Operation: 41-5=36 Exploring Operation: 5+45=50, Resulting Numbers: [41, 50] Generated Node #0,0,2: 41:[41, 50] Operation: 5+45=50 Exploring Operation: 45-5=40, Resulting Numbers: [41, 40] Generated Node #0,0,3: 41:[41, 40] Operation: 45-5=40 Moving to Node #0,0,3 Current State: 41:[41, 40], Operations: ['41+4=45', '45-5=40'] Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,41 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,41 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[45, 36], Operations: ['41+4=45', '41-5=36'] Exploring Operation: 45+36=81, Resulting Numbers: [81] 81,41 unequal: No Solution Exploring Operation: 45*36=1620, Resulting Numbers: [1620] 1620,41 unequal: No Solution Exploring Operation: 45-36=9, Resulting Numbers: [9] 9,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[45, 46], Operations: ['41+4=45', '5+41=46'] Exploring Operation: 45+46=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 45*46=2070, Resulting Numbers: [2070] 2070,41 unequal: No Solution Exploring Operation: 46-45=1, Resulting Numbers: [1] 1,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[41, 50], Operations: ['41+4=45', '5+45=50'] Exploring Operation: 41*50=2050, Resulting Numbers: [2050] 2050,41 unequal: No Solution Exploring Operation: 41+50=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,41 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 66, 54, 91, 93 ]
64
[ "66+54=120", "91+93=184", "184-120=64" ]
Current State: 64:[66, 54, 91, 93], Operations: [] Exploring Operation: 66+54=120, Resulting Numbers: [91, 93, 120] Generated Node #2: [91, 93, 120] from Operation: 66+54=120 Current State: 64:[91, 93, 120], Operations: ['66+54=120'] Exploring Operation: 91+93=184, Resulting Numbers: [120, 184] Generated Node #3: [120, 184] from Operation: 91+93=184 Current State: 64:[120, 184], Operations: ['66+54=120', '91+93=184'] Exploring Operation: 184-120=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[66, 54, 91, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [66, 54, 2] Generated Node #0,0: 64:[66, 54, 2] Operation: 93-91=2 Exploring Operation: 91-54=37, Resulting Numbers: [66, 93, 37] Generated Node #0,1: 64:[66, 93, 37] Operation: 91-54=37 Exploring Operation: 93-54=39, Resulting Numbers: [66, 91, 39] Generated Node #0,2: 64:[66, 91, 39] Operation: 93-54=39 Exploring Operation: 93-66=27, Resulting Numbers: [54, 91, 27] Generated Node #0,3: 64:[54, 91, 27] Operation: 93-66=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[66, 54, 2], Operations: ['93-91=2'] Exploring Operation: 66-54=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 64:[2, 12] Operation: 66-54=12 Exploring Operation: 54/2=27, Resulting Numbers: [66, 27] Generated Node #0,0,1: 64:[66, 27] Operation: 54/2=27 Exploring Operation: 54+2=56, Resulting Numbers: [66, 56] Generated Node #0,0,2: 64:[66, 56] Operation: 54+2=56 Exploring Operation: 66-2=64, Resulting Numbers: [54, 64] Generated Node #0,0,3: 64:[54, 64] Operation: 66-2=64 Moving to Node #0,0,0 Current State: 64:[2, 12], Operations: ['93-91=2', '66-54=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,64 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,64 unequal: No Solution Moving to Node #0,0,1 Current State: 64:[66, 27], Operations: ['93-91=2', '54/2=27'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,64 unequal: No Solution Exploring Operation: 66*27=1782, Resulting Numbers: [1782] 1782,64 unequal: No Solution Exploring Operation: 66+27=93, Resulting Numbers: [93] 93,64 unequal: No Solution Moving to Node #0,0,3 Current State: 64:[54, 64], Operations: ['93-91=2', '66-2=64'] Exploring Operation: 54*64=3456, Resulting Numbers: [3456] 3456,64 unequal: No Solution Exploring Operation: 64-54=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 54+64=118, Resulting Numbers: [118] 118,64 unequal: No Solution Moving to Node #0,0,2 Current State: 64:[66, 56], Operations: ['93-91=2', '54+2=56'] Exploring Operation: 66+56=122, Resulting Numbers: [122] 122,64 unequal: No Solution Exploring Operation: 66*56=3696, Resulting Numbers: [3696] 3696,64 unequal: No Solution Exploring Operation: 66-56=10, Resulting Numbers: [10] 10,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[66, 93, 37], Operations: ['91-54=37'] Exploring Operation: 66-37=29, Resulting Numbers: [93, 29] Generated Node #0,1,0: 64:[93, 29] Operation: 66-37=29 Exploring Operation: 66+37=103, Resulting Numbers: [93, 103] Generated Node #0,1,1: 64:[93, 103] Operation: 66+37=103 Exploring Operation: 93-66=27, Resulting Numbers: [37, 27] Generated Node #0,1,2: 64:[37, 27] Operation: 93-66=27 Exploring Operation: 93-37=56, Resulting Numbers: [66, 56] Generated Node #0,1,3: 64:[66, 56] Operation: 93-37=56 Moving to Node #0,1,2 Current State: 64:[37, 27], Operations: ['91-54=37', '93-66=27'] Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,64 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,64 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[66, 54, 91, 93], Operations: [] Exploring Operation: 91-54=37, Resulting Numbers: [66, 93, 37] Generated Node #0,1: 64:[66, 93, 37] Operation: 91-54=37 Moving to Node #0,1 Current State: 64:[66, 93, 37], Operations: ['91-54=37'] Exploring Operation: 93-66=27, Resulting Numbers: [37, 27] Generated Node #0,1,2: 64:[37, 27] Operation: 93-66=27 Moving to Node #0,1,2 Current State: 64:[37, 27], Operations: ['91-54=37', '93-66=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 84, 52, 30, 62 ]
87
[ "62-52=10", "30/10=3", "84+3=87" ]
Current State: 87:[84, 52, 30, 62], Operations: [] Exploring Operation: 62-52=10, Resulting Numbers: [84, 30, 10] Generated Node #2: [84, 30, 10] from Operation: 62-52=10 Current State: 87:[84, 30, 10], Operations: ['62-52=10'] Exploring Operation: 30/10=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 30/10=3 Current State: 87:[84, 3], Operations: ['62-52=10', '30/10=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[84, 52, 30, 62], Operations: [] Exploring Operation: 62-52=10, Resulting Numbers: [84, 30, 10] Generated Node #0,0: 87:[84, 30, 10] Operation: 62-52=10 Moving to Node #0,0 Current State: 87:[84, 30, 10], Operations: ['62-52=10'] Exploring Operation: 30/10=3, Resulting Numbers: [84, 3] Generated Node #0,0,0: 87:[84, 3] Operation: 30/10=3 Moving to Node #0,0,0 Current State: 87:[84, 3], Operations: ['62-52=10', '30/10=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[84, 52, 30, 62], Operations: [] Exploring Operation: 62-52=10, Resulting Numbers: [84, 30, 10] Generated Node #0,0: 87:[84, 30, 10] Operation: 62-52=10 Moving to Node #0,0 Current State: 87:[84, 30, 10], Operations: ['62-52=10'] Exploring Operation: 30/10=3, Resulting Numbers: [84, 3] Generated Node #0,0,0: 87:[84, 3] Operation: 30/10=3 Moving to Node #0,0,0 Current State: 87:[84, 3], Operations: ['62-52=10', '30/10=3'] Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 69, 45, 1, 60 ]
53
[ "69+45=114", "1+60=61", "114-61=53" ]
Current State: 53:[69, 45, 1, 60], Operations: [] Exploring Operation: 69+45=114, Resulting Numbers: [1, 60, 114] Generated Node #2: [1, 60, 114] from Operation: 69+45=114 Current State: 53:[1, 60, 114], Operations: ['69+45=114'] Exploring Operation: 1+60=61, Resulting Numbers: [114, 61] Generated Node #3: [114, 61] from Operation: 1+60=61 Current State: 53:[114, 61], Operations: ['69+45=114', '1+60=61'] Exploring Operation: 114-61=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[69, 45, 1, 60], Operations: [] Exploring Operation: 69-1=68, Resulting Numbers: [45, 60, 68] Generated Node #0,0: 53:[45, 60, 68] Operation: 69-1=68 Exploring Operation: 69*1=69, Resulting Numbers: [45, 60, 69] Generated Node #0,1: 53:[45, 60, 69] Operation: 69*1=69 Exploring Operation: 60-1=59, Resulting Numbers: [69, 45, 59] Generated Node #0,2: 53:[69, 45, 59] Operation: 60-1=59 Exploring Operation: 45+1=46, Resulting Numbers: [69, 60, 46] Generated Node #0,3: 53:[69, 60, 46] Operation: 45+1=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[45, 60, 68], Operations: ['69-1=68'] Exploring Operation: 60-45=15, Resulting Numbers: [68, 15] Generated Node #0,0,0: 53:[68, 15] Operation: 60-45=15 Exploring Operation: 68-45=23, Resulting Numbers: [60, 23] Generated Node #0,0,1: 53:[60, 23] Operation: 68-45=23 Exploring Operation: 45+60=105, Resulting Numbers: [68, 105] Generated Node #0,0,2: 53:[68, 105] Operation: 45+60=105 Exploring Operation: 68-60=8, Resulting Numbers: [45, 8] Generated Node #0,0,3: 53:[45, 8] Operation: 68-60=8 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[60, 23], Operations: ['69-1=68', '68-45=23'] Exploring Operation: 60*23=1380, Resulting Numbers: [1380] 1380,53 unequal: No Solution Exploring Operation: 60-23=37, Resulting Numbers: [37] 37,53 unequal: No Solution Exploring Operation: 60+23=83, Resulting Numbers: [83] 83,53 unequal: No Solution No 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: 53:[68, 15], Operations: ['69-1=68', '60-45=15'] Exploring Operation: 68+15=83, Resulting Numbers: [83] 83,53 unequal: No Solution Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[69, 45, 1, 60], Operations: [] Exploring Operation: 69-1=68, Resulting Numbers: [45, 60, 68] Generated Node #0,0: 53:[45, 60, 68] Operation: 69-1=68 Moving to Node #0,0 Current State: 53:[45, 60, 68], Operations: ['69-1=68'] Exploring Operation: 60-45=15, Resulting Numbers: [68, 15] Generated Node #0,0,0: 53:[68, 15] Operation: 60-45=15 Moving to Node #0,0,0 Current State: 53:[68, 15], Operations: ['69-1=68', '60-45=15'] Exploring Operation: 68-15=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 68, 56, 75, 52 ]
44
[ "75-68=7", "56/7=8", "52-8=44" ]
Current State: 44:[68, 56, 75, 52], Operations: [] Exploring Operation: 75-68=7, Resulting Numbers: [56, 52, 7] Generated Node #2: [56, 52, 7] from Operation: 75-68=7 Current State: 44:[56, 52, 7], Operations: ['75-68=7'] Exploring Operation: 56/7=8, Resulting Numbers: [52, 8] Generated Node #3: [52, 8] from Operation: 56/7=8 Current State: 44:[52, 8], Operations: ['75-68=7', '56/7=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[68, 56, 75, 52], Operations: [] Exploring Operation: 75-56=19, Resulting Numbers: [68, 52, 19] Generated Node #0,0: 44:[68, 52, 19] Operation: 75-56=19 Exploring Operation: 75-52=23, Resulting Numbers: [68, 56, 23] Generated Node #0,1: 44:[68, 56, 23] Operation: 75-52=23 Exploring Operation: 68-56=12, Resulting Numbers: [75, 52, 12] Generated Node #0,2: 44:[75, 52, 12] Operation: 68-56=12 Exploring Operation: 68-52=16, Resulting Numbers: [56, 75, 16] Generated Node #0,3: 44:[56, 75, 16] Operation: 68-52=16 Exploring Operation: 75-68=7, Resulting Numbers: [56, 52, 7] Generated Node #0,4: 44:[56, 52, 7] Operation: 75-68=7 Start Sub Search at level 1: Moving to Node #0,4 Current State: 44:[56, 52, 7], Operations: ['75-68=7'] Exploring Operation: 56-52=4, Resulting Numbers: [7, 4] Generated Node #0,4,0: 44:[7, 4] Operation: 56-52=4 Exploring Operation: 52-7=45, Resulting Numbers: [56, 45] Generated Node #0,4,1: 44:[56, 45] Operation: 52-7=45 Exploring Operation: 56-7=49, Resulting Numbers: [52, 49] Generated Node #0,4,2: 44:[52, 49] Operation: 56-7=49 Exploring Operation: 56/7=8, Resulting Numbers: [52, 8] Generated Node #0,4,3: 44:[52, 8] Operation: 56/7=8 Exploring Operation: 56+7=63, Resulting Numbers: [52, 63] Generated Node #0,4,4: 44:[52, 63] Operation: 56+7=63 Moving to Node #0,4,0 Current State: 44:[7, 4], Operations: ['75-68=7', '56-52=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,44 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,44 unequal: No Solution Moving to Node #0,4,3 Current State: 44:[52, 8], Operations: ['75-68=7', '56/7=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[68, 56, 75, 52], Operations: [] Exploring Operation: 75-68=7, Resulting Numbers: [56, 52, 7] Generated Node #0,4: 44:[56, 52, 7] Operation: 75-68=7 Moving to Node #0,4 Current State: 44:[56, 52, 7], Operations: ['75-68=7'] Exploring Operation: 56/7=8, Resulting Numbers: [52, 8] Generated Node #0,4,3: 44:[52, 8] Operation: 56/7=8 Moving to Node #0,4,3 Current State: 44:[52, 8], Operations: ['75-68=7', '56/7=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 14, 2, 18, 73 ]
71
[ "14+2=16", "73-18=55", "16+55=71" ]
Current State: 71:[14, 2, 18, 73], Operations: [] Exploring Operation: 14+2=16, Resulting Numbers: [18, 73, 16] Generated Node #2: [18, 73, 16] from Operation: 14+2=16 Current State: 71:[18, 73, 16], Operations: ['14+2=16'] Exploring Operation: 73-18=55, Resulting Numbers: [16, 55] Generated Node #3: [16, 55] from Operation: 73-18=55 Current State: 71:[16, 55], Operations: ['14+2=16', '73-18=55'] Exploring Operation: 16+55=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[14, 2, 18, 73], Operations: [] Exploring Operation: 14+2=16, Resulting Numbers: [18, 73, 16] Generated Node #0,0: 71:[18, 73, 16] Operation: 14+2=16 Exploring Operation: 14+18=32, Resulting Numbers: [2, 73, 32] Generated Node #0,1: 71:[2, 73, 32] Operation: 14+18=32 Exploring Operation: 2*18=36, Resulting Numbers: [14, 73, 36] Generated Node #0,2: 71:[14, 73, 36] Operation: 2*18=36 Exploring Operation: 14*2=28, Resulting Numbers: [18, 73, 28] Generated Node #0,3: 71:[18, 73, 28] Operation: 14*2=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[14, 73, 36], Operations: ['2*18=36'] Exploring Operation: 36-14=22, Resulting Numbers: [73, 22] Generated Node #0,2,0: 71:[73, 22] Operation: 36-14=22 Exploring Operation: 14+73=87, Resulting Numbers: [36, 87] Generated Node #0,2,1: 71:[36, 87] Operation: 14+73=87 Exploring Operation: 14+36=50, Resulting Numbers: [73, 50] Generated Node #0,2,2: 71:[73, 50] Operation: 14+36=50 Exploring Operation: 73-14=59, Resulting Numbers: [36, 59] Generated Node #0,2,3: 71:[36, 59] Operation: 73-14=59 Moving to Node #0,2,2 Current State: 71:[73, 50], Operations: ['2*18=36', '14+36=50'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,71 unequal: No Solution Exploring Operation: 73+50=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 73*50=3650, Resulting Numbers: [3650] 3650,71 unequal: No Solution Moving to Node #0,2,3 Current State: 71:[36, 59], Operations: ['2*18=36', '73-14=59'] Exploring Operation: 36*59=2124, Resulting Numbers: [2124] 2124,71 unequal: No Solution Exploring Operation: 36+59=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[36, 87], Operations: ['2*18=36', '14+73=87'] Exploring Operation: 87-36=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 36+87=123, Resulting Numbers: [123] 123,71 unequal: No Solution Exploring Operation: 36*87=3132, Resulting Numbers: [3132] 3132,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[73, 22], Operations: ['2*18=36', '36-14=22'] Exploring Operation: 73*22=1606, Resulting Numbers: [1606] 1606,71 unequal: No Solution Exploring Operation: 73+22=95, Resulting Numbers: [95] 95,71 unequal: No Solution Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,71 unequal: No Solution No 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: 71:[18, 73, 28], Operations: ['14*2=28'] Exploring Operation: 28-18=10, Resulting Numbers: [73, 10] Generated Node #0,3,0: 71:[73, 10] Operation: 28-18=10 Exploring Operation: 18+28=46, Resulting Numbers: [73, 46] Generated Node #0,3,1: 71:[73, 46] Operation: 18+28=46 Exploring Operation: 73-18=55, Resulting Numbers: [28, 55] Generated Node #0,3,2: 71:[28, 55] Operation: 73-18=55 Exploring Operation: 18+73=91, Resulting Numbers: [28, 91] Generated Node #0,3,3: 71:[28, 91] Operation: 18+73=91 Moving to Node #0,3,1 Current State: 71:[73, 46], Operations: ['14*2=28', '18+28=46'] Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,71 unequal: No Solution Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,71 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,71 unequal: No Solution Moving to Node #0,3,2 Current State: 71:[28, 55], Operations: ['14*2=28', '73-18=55'] Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,71 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,71 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,71 unequal: No Solution Moving to Node #0,3,3 Current State: 71:[28, 91], Operations: ['14*2=28', '18+73=91'] Exploring Operation: 28+91=119, Resulting Numbers: [119] 119,71 unequal: No Solution Exploring Operation: 91-28=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 28*91=2548, Resulting Numbers: [2548] 2548,71 unequal: No Solution Moving to Node #0,3,0 Current State: 71:[73, 10], Operations: ['14*2=28', '28-18=10'] Exploring Operation: 73-10=63, Resulting Numbers: [63] 63,71 unequal: No Solution Exploring Operation: 73*10=730, Resulting Numbers: [730] 730,71 unequal: No Solution Exploring Operation: 73+10=83, Resulting Numbers: [83] 83,71 unequal: No Solution No 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: 71:[18, 73, 16], Operations: ['14+2=16'] Exploring Operation: 18+16=34, Resulting Numbers: [73, 34] Generated Node #0,0,0: 71:[73, 34] Operation: 18+16=34 Exploring Operation: 73-16=57, Resulting Numbers: [18, 57] Generated Node #0,0,1: 71:[18, 57] Operation: 73-16=57 Exploring Operation: 18-16=2, Resulting Numbers: [73, 2] Generated Node #0,0,2: 71:[73, 2] Operation: 18-16=2 Exploring Operation: 73-18=55, Resulting Numbers: [16, 55] Generated Node #0,0,3: 71:[16, 55] Operation: 73-18=55 Moving to Node #0,0,0 Current State: 71:[73, 34], Operations: ['14+2=16', '18+16=34'] Exploring Operation: 73-34=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 73*34=2482, Resulting Numbers: [2482] 2482,71 unequal: No Solution Exploring Operation: 73+34=107, Resulting Numbers: [107] 107,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[18, 57], Operations: ['14+2=16', '73-16=57'] Exploring Operation: 57-18=39, Resulting Numbers: [39] 39,71 unequal: No Solution Exploring Operation: 18*57=1026, Resulting Numbers: [1026] 1026,71 unequal: No Solution Exploring Operation: 18+57=75, Resulting Numbers: [75] 75,71 unequal: No Solution Moving to Node #0,0,3 Current State: 71:[16, 55], Operations: ['14+2=16', '73-18=55'] Exploring Operation: 16+55=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[14, 2, 18, 73], Operations: [] Exploring Operation: 14+2=16, Resulting Numbers: [18, 73, 16] Generated Node #0,0: 71:[18, 73, 16] Operation: 14+2=16 Moving to Node #0,0 Current State: 71:[18, 73, 16], Operations: ['14+2=16'] Exploring Operation: 73-18=55, Resulting Numbers: [16, 55] Generated Node #0,0,3: 71:[16, 55] Operation: 73-18=55 Moving to Node #0,0,3 Current State: 71:[16, 55], Operations: ['14+2=16', '73-18=55'] Exploring Operation: 16+55=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
mult_heuristic
[ 38, 75, 1, 73 ]
41
[ "38+75=113", "73-1=72", "113-72=41" ]
Current State: 41:[38, 75, 1, 73], Operations: [] Exploring Operation: 38+75=113, Resulting Numbers: [1, 73, 113] Generated Node #2: [1, 73, 113] from Operation: 38+75=113 Current State: 41:[1, 73, 113], Operations: ['38+75=113'] Exploring Operation: 73-1=72, Resulting Numbers: [113, 72] Generated Node #3: [113, 72] from Operation: 73-1=72 Current State: 41:[113, 72], Operations: ['38+75=113', '73-1=72'] Exploring Operation: 113-72=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[38, 75, 1, 73], Operations: [] Exploring Operation: 38+1=39, Resulting Numbers: [75, 73, 39] Generated Node #0,0: 41:[75, 73, 39] Operation: 38+1=39 Exploring Operation: 75-1=74, Resulting Numbers: [38, 73, 74] Generated Node #0,1: 41:[38, 73, 74] Operation: 75-1=74 Moving to Node #0,0 Current State: 41:[75, 73, 39], Operations: ['38+1=39'] Exploring Operation: 75-39=36, Resulting Numbers: [73, 36] Generated Node #0,0,0: 41:[73, 36] Operation: 75-39=36 Exploring Operation: 75-73=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 41:[39, 2] Operation: 75-73=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[73, 36], Operations: ['38+1=39', '75-39=36'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 73+36=109, Resulting Numbers: [109] 109,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[39, 2], Operations: ['38+1=39', '75-73=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[38, 75, 1, 73], Operations: [] Exploring Operation: 38+1=39, Resulting Numbers: [75, 73, 39] Generated Node #0,0: 41:[75, 73, 39] Operation: 38+1=39 Moving to Node #0,0 Current State: 41:[75, 73, 39], Operations: ['38+1=39'] Exploring Operation: 75-73=2, Resulting Numbers: [39, 2] Generated Node #0,0,1: 41:[39, 2] Operation: 75-73=2 Moving to Node #0,0,1 Current State: 41:[39, 2], Operations: ['38+1=39', '75-73=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 12, 23, 23, 57 ]
20
[ "12+57=69", "69/23=3", "23-3=20" ]
Current State: 20:[12, 23, 23, 57], Operations: [] Exploring Operation: 12+57=69, Resulting Numbers: [23, 23, 69] Generated Node #2: [23, 23, 69] from Operation: 12+57=69 Current State: 20:[23, 23, 69], Operations: ['12+57=69'] Exploring Operation: 69/23=3, Resulting Numbers: [3] 3,20 equal: Goal Reached Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[12, 23, 23, 57], Operations: [] Exploring Operation: 57-23=34, Resulting Numbers: [12, 23, 34] Generated Node #0,0: 20:[12, 23, 34] Operation: 57-23=34 Moving to Node #0,0 Current State: 20:[12, 23, 34], Operations: ['57-23=34'] Exploring Operation: 34-23=11, Resulting Numbers: [12, 11] Generated Node #0,0,0: 20:[12, 11] Operation: 34-23=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 20:[12, 11], Operations: ['57-23=34', '34-23=11'] Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 31, 96, 19, 13 ]
21
[ "31-19=12", "96/12=8", "13+8=21" ]
Current State: 21:[31, 96, 19, 13], Operations: [] Exploring Operation: 31-19=12, Resulting Numbers: [96, 13, 12] Generated Node #2: [96, 13, 12] from Operation: 31-19=12 Current State: 21:[96, 13, 12], Operations: ['31-19=12'] Exploring Operation: 96/12=8, Resulting Numbers: [13, 8] Generated Node #3: [13, 8] from Operation: 96/12=8 Current State: 21:[13, 8], Operations: ['31-19=12', '96/12=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[31, 96, 19, 13], Operations: [] Exploring Operation: 96-13=83, Resulting Numbers: [31, 19, 83] Generated Node #0,0: 21:[31, 19, 83] Operation: 96-13=83 Exploring Operation: 96-19=77, Resulting Numbers: [31, 13, 77] Generated Node #0,1: 21:[31, 13, 77] Operation: 96-19=77 Exploring Operation: 96-31=65, Resulting Numbers: [19, 13, 65] Generated Node #0,2: 21:[19, 13, 65] Operation: 96-31=65 Exploring Operation: 31-13=18, Resulting Numbers: [96, 19, 18] Generated Node #0,3: 21:[96, 19, 18] Operation: 31-13=18 Moving to Node #0,2 Current State: 21:[19, 13, 65], Operations: ['96-31=65'] Exploring Operation: 19-13=6, Resulting Numbers: [65, 6] Generated Node #0,2,0: 21:[65, 6] Operation: 19-13=6 Exploring Operation: 65/13=5, Resulting Numbers: [19, 5] Generated Node #0,2,1: 21:[19, 5] Operation: 65/13=5 Exploring Operation: 65-13=52, Resulting Numbers: [19, 52] Generated Node #0,2,2: 21:[19, 52] Operation: 65-13=52 Exploring Operation: 65-19=46, Resulting Numbers: [13, 46] Generated Node #0,2,3: 21:[13, 46] Operation: 65-19=46 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[19, 5], Operations: ['96-31=65', '65/13=5'] Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,21 unequal: No Solution No 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: 21:[13, 46], Operations: ['96-31=65', '65-19=46'] Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,21 unequal: No Solution Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,21 unequal: No Solution No 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: 21:[19, 52], Operations: ['96-31=65', '65-13=52'] Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,21 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,21 unequal: No Solution No 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: 21:[65, 6], Operations: ['96-31=65', '19-13=6'] Exploring Operation: 65*6=390, Resulting Numbers: [390] 390,21 unequal: No Solution Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 65-6=59, Resulting Numbers: [59] 59,21 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: 21:[31, 13, 77], Operations: ['96-19=77'] Exploring Operation: 31-13=18, Resulting Numbers: [77, 18] Generated Node #0,1,0: 21:[77, 18] Operation: 31-13=18 Exploring Operation: 77-13=64, Resulting Numbers: [31, 64] Generated Node #0,1,1: 21:[31, 64] Operation: 77-13=64 Exploring Operation: 77-31=46, Resulting Numbers: [13, 46] Generated Node #0,1,2: 21:[13, 46] Operation: 77-31=46 Exploring Operation: 31+13=44, Resulting Numbers: [77, 44] Generated Node #0,1,3: 21:[77, 44] Operation: 31+13=44 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[13, 46], Operations: ['96-19=77', '77-31=46'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,21 unequal: No Solution No solution 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: 21:[31, 64], Operations: ['96-19=77', '77-13=64'] Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 31*64=1984, Resulting Numbers: [1984] 1984,21 unequal: No Solution Exploring Operation: 31+64=95, Resulting Numbers: [95] 95,21 unequal: No Solution No solution 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: 21:[77, 18], Operations: ['96-19=77', '31-13=18'] Exploring Operation: 77+18=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 77*18=1386, Resulting Numbers: [1386] 1386,21 unequal: No Solution No solution 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: 21:[77, 44], Operations: ['96-19=77', '31+13=44'] Exploring Operation: 77+44=121, Resulting Numbers: [121] 121,21 unequal: No Solution Exploring Operation: 77*44=3388, Resulting Numbers: [3388] 3388,21 unequal: No Solution Exploring Operation: 77-44=33, Resulting Numbers: [33] 33,21 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: 21:[31, 19, 83], Operations: ['96-13=83'] Exploring Operation: 83-19=64, Resulting Numbers: [31, 64] Generated Node #0,0,0: 21:[31, 64] Operation: 83-19=64 Exploring Operation: 31+19=50, Resulting Numbers: [83, 50] Generated Node #0,0,1: 21:[83, 50] Operation: 31+19=50 Exploring Operation: 31-19=12, Resulting Numbers: [83, 12] Generated Node #0,0,2: 21:[83, 12] Operation: 31-19=12 Exploring Operation: 83-31=52, Resulting Numbers: [19, 52] Generated Node #0,0,3: 21:[19, 52] Operation: 83-31=52 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 21:[19, 52], Operations: ['96-13=83', '83-31=52'] Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,21 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,21 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,21 unequal: No Solution No 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: 21:[31, 64], Operations: ['96-13=83', '83-19=64'] Exploring Operation: 31+64=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 31*64=1984, Resulting Numbers: [1984] 1984,21 unequal: No Solution Exploring Operation: 64-31=33, Resulting Numbers: [33] 33,21 unequal: No Solution No 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: 21:[83, 12], Operations: ['96-13=83', '31-19=12'] Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,21 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,21 unequal: No Solution No 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: 21:[83, 50], Operations: ['96-13=83', '31+19=50'] Exploring Operation: 83*50=4150, Resulting Numbers: [4150] 4150,21 unequal: No Solution Exploring Operation: 83+50=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 83-50=33, Resulting Numbers: [33] 33,21 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: 21:[96, 19, 18], Operations: ['31-13=18'] Exploring Operation: 96-19=77, Resulting Numbers: [18, 77] Generated Node #0,3,0: 21:[18, 77] Operation: 96-19=77 Exploring Operation: 19+18=37, Resulting Numbers: [96, 37] Generated Node #0,3,1: 21:[96, 37] Operation: 19+18=37 Exploring Operation: 96-18=78, Resulting Numbers: [19, 78] Generated Node #0,3,2: 21:[19, 78] Operation: 96-18=78 Exploring Operation: 19-18=1, Resulting Numbers: [96, 1] Generated Node #0,3,3: 21:[96, 1] Operation: 19-18=1 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 21:[18, 77], Operations: ['31-13=18', '96-19=77'] Exploring Operation: 18*77=1386, Resulting Numbers: [1386] 1386,21 unequal: No Solution Exploring Operation: 18+77=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,21 unequal: No Solution No 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: 21:[19, 78], Operations: ['31-13=18', '96-18=78'] Exploring Operation: 19*78=1482, Resulting Numbers: [1482] 1482,21 unequal: No Solution Exploring Operation: 19+78=97, Resulting Numbers: [97] 97,21 unequal: No Solution Exploring Operation: 78-19=59, Resulting Numbers: [59] 59,21 unequal: No Solution No 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: 21:[96, 1], Operations: ['31-13=18', '19-18=1'] Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 96+1=97, Resulting Numbers: [97] 97,21 unequal: No Solution Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,21 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,21 unequal: No Solution No 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: 21:[96, 37], Operations: ['31-13=18', '19+18=37'] Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 96*37=3552, Resulting Numbers: [3552] 3552,21 unequal: No Solution Exploring Operation: 96+37=133, Resulting Numbers: [133] 133,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 22, 64, 3, 28 ]
10
[ "64*3=192", "28+192=220", "220/22=10" ]
Current State: 10:[22, 64, 3, 28], Operations: [] Exploring Operation: 64*3=192, Resulting Numbers: [22, 28, 192] Generated Node #2: [22, 28, 192] from Operation: 64*3=192 Current State: 10:[22, 28, 192], Operations: ['64*3=192'] Exploring Operation: 28+192=220, Resulting Numbers: [22, 220] Generated Node #3: [22, 220] from Operation: 28+192=220 Current State: 10:[22, 220], Operations: ['64*3=192', '28+192=220'] Exploring Operation: 220/22=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[22, 64, 3, 28], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [64, 3, 6] Generated Node #0,0: 10:[64, 3, 6] Operation: 28-22=6 Exploring Operation: 64-28=36, Resulting Numbers: [22, 3, 36] Generated Node #0,1: 10:[22, 3, 36] Operation: 64-28=36 Exploring Operation: 64-22=42, Resulting Numbers: [3, 28, 42] Generated Node #0,2: 10:[3, 28, 42] Operation: 64-22=42 Exploring Operation: 22-3=19, Resulting Numbers: [64, 28, 19] Generated Node #0,3: 10:[64, 28, 19] Operation: 22-3=19 Moving to Node #0,1 Current State: 10:[22, 3, 36], Operations: ['64-28=36'] Exploring Operation: 36/3=12, Resulting Numbers: [22, 12] Generated Node #0,1,0: 10:[22, 12] Operation: 36/3=12 Exploring Operation: 36-3=33, Resulting Numbers: [22, 33] Generated Node #0,1,1: 10:[22, 33] Operation: 36-3=33 Exploring Operation: 22-3=19, Resulting Numbers: [36, 19] Generated Node #0,1,2: 10:[36, 19] Operation: 22-3=19 Exploring Operation: 36-22=14, Resulting Numbers: [3, 14] Generated Node #0,1,3: 10:[3, 14] Operation: 36-22=14 Moving to Node #0,2 Current State: 10:[3, 28, 42], Operations: ['64-22=42'] Exploring Operation: 42/3=14, Resulting Numbers: [28, 14] Generated Node #0,2,0: 10:[28, 14] Operation: 42/3=14 Exploring Operation: 42-28=14, Resulting Numbers: [3, 14] Generated Node #0,2,1: 10:[3, 14] Operation: 42-28=14 Exploring Operation: 42-3=39, Resulting Numbers: [28, 39] Generated Node #0,2,2: 10:[28, 39] Operation: 42-3=39 Exploring Operation: 28-3=25, Resulting Numbers: [42, 25] Generated Node #0,2,3: 10:[42, 25] Operation: 28-3=25 Moving to Node #0,0 Current State: 10:[64, 3, 6], Operations: ['28-22=6'] Exploring Operation: 64-6=58, Resulting Numbers: [3, 58] Generated Node #0,0,0: 10:[3, 58] Operation: 64-6=58 Exploring Operation: 3+6=9, Resulting Numbers: [64, 9] Generated Node #0,0,1: 10:[64, 9] Operation: 3+6=9 Exploring Operation: 64-3=61, Resulting Numbers: [6, 61] Generated Node #0,0,2: 10:[6, 61] Operation: 64-3=61 Exploring Operation: 6/3=2, Resulting Numbers: [64, 2] Generated Node #0,0,3: 10:[64, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[3, 58], Operations: ['28-22=6', '64-6=58'] Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,10 unequal: No Solution Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 10:[6, 61], Operations: ['28-22=6', '64-3=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,10 unequal: No Solution Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,10 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:[64, 2], Operations: ['28-22=6', '6/3=2'] Exploring Operation: 64*2=128, Resulting Numbers: [128] 128,10 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,10 unequal: No Solution Exploring Operation: 64+2=66, Resulting Numbers: [66] 66,10 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:[64, 9], Operations: ['28-22=6', '3+6=9'] Exploring Operation: 64+9=73, Resulting Numbers: [73] 73,10 unequal: No Solution Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 64*9=576, Resulting Numbers: [576] 576,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 10:[64, 28, 19], Operations: ['22-3=19'] Exploring Operation: 64+28=92, Resulting Numbers: [19, 92] Generated Node #0,3,0: 10:[19, 92] Operation: 64+28=92 Exploring Operation: 64-19=45, Resulting Numbers: [28, 45] Generated Node #0,3,1: 10:[28, 45] Operation: 64-19=45 Exploring Operation: 28-19=9, Resulting Numbers: [64, 9] Generated Node #0,3,2: 10:[64, 9] Operation: 28-19=9 Exploring Operation: 64-28=36, Resulting Numbers: [19, 36] Generated Node #0,3,3: 10:[19, 36] Operation: 64-28=36 Moving to Node #0,1,3 Current State: 10:[3, 14], Operations: ['64-28=36', '36-22=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[3, 14], Operations: ['64-22=42', '42-28=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,10 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,10 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,10 unequal: No Solution Moving to Node #0,1,0 Current State: 10:[22, 12], Operations: ['64-28=36', '36/3=12'] Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,10 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[22, 64, 3, 28], Operations: [] Exploring Operation: 64-28=36, Resulting Numbers: [22, 3, 36] Generated Node #0,1: 10:[22, 3, 36] Operation: 64-28=36 Moving to Node #0,1 Current State: 10:[22, 3, 36], Operations: ['64-28=36'] Exploring Operation: 36/3=12, Resulting Numbers: [22, 12] Generated Node #0,1,0: 10:[22, 12] Operation: 36/3=12 Moving to Node #0,1,0 Current State: 10:[22, 12], Operations: ['64-28=36', '36/3=12'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
0.960938
hs_4
sum_heuristic
[ 66, 82, 33, 69 ]
20
[ "82-66=16", "69-33=36", "36-16=20" ]
Current State: 20:[66, 82, 33, 69], Operations: [] Exploring Operation: 82-66=16, Resulting Numbers: [33, 69, 16] Generated Node #2: [33, 69, 16] from Operation: 82-66=16 Current State: 20:[33, 69, 16], Operations: ['82-66=16'] Exploring Operation: 69-33=36, Resulting Numbers: [16, 36] Generated Node #3: [16, 36] from Operation: 69-33=36 Current State: 20:[16, 36], Operations: ['82-66=16', '69-33=36'] Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[66, 82, 33, 69], Operations: [] Exploring Operation: 82-66=16, Resulting Numbers: [33, 69, 16] Generated Node #0,0: 20:[33, 69, 16] Operation: 82-66=16 Exploring Operation: 66/33=2, Resulting Numbers: [82, 69, 2] Generated Node #0,1: 20:[82, 69, 2] Operation: 66/33=2 Exploring Operation: 66-33=33, Resulting Numbers: [82, 69, 33] Generated Node #0,2: 20:[82, 69, 33] Operation: 66-33=33 Exploring Operation: 69-66=3, Resulting Numbers: [82, 33, 3] Generated Node #0,3: 20:[82, 33, 3] Operation: 69-66=3 Exploring Operation: 82-69=13, Resulting Numbers: [66, 33, 13] Generated Node #0,4: 20:[66, 33, 13] Operation: 82-69=13 Start Sub Search at level 1: Moving to Node #0,4 Current State: 20:[66, 33, 13], Operations: ['82-69=13'] Exploring Operation: 66-33=33, Resulting Numbers: [13, 33] Generated Node #0,4,0: 20:[13, 33] Operation: 66-33=33 Exploring Operation: 66/33=2, Resulting Numbers: [13, 2] Generated Node #0,4,1: 20:[13, 2] Operation: 66/33=2 Exploring Operation: 66+13=79, Resulting Numbers: [33, 79] Generated Node #0,4,2: 20:[33, 79] Operation: 66+13=79 Exploring Operation: 33-13=20, Resulting Numbers: [66, 20] Generated Node #0,4,3: 20:[66, 20] Operation: 33-13=20 Exploring Operation: 66-13=53, Resulting Numbers: [33, 53] Generated Node #0,4,4: 20:[33, 53] Operation: 66-13=53 Moving to Node #0,4,1 Current State: 20:[13, 2], Operations: ['82-69=13', '66/33=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,20 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,20 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,20 unequal: No Solution Moving to Node #0,4,0 Current State: 20:[13, 33], Operations: ['82-69=13', '66-33=33'] Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,20 unequal: No Solution Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[66, 82, 33, 69], Operations: [] Exploring Operation: 82-69=13, Resulting Numbers: [66, 33, 13] Generated Node #0,4: 20:[66, 33, 13] Operation: 82-69=13 Moving to Node #0,4 Current State: 20:[66, 33, 13], Operations: ['82-69=13'] Exploring Operation: 66-33=33, Resulting Numbers: [13, 33] Generated Node #0,4,0: 20:[13, 33] Operation: 66-33=33 Moving to Node #0,4,0 Current State: 20:[13, 33], Operations: ['82-69=13', '66-33=33'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 98, 95, 64, 29 ]
38
[ "98-95=3", "64-29=35", "3+35=38" ]
Current State: 38:[98, 95, 64, 29], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [64, 29, 3] Generated Node #2: [64, 29, 3] from Operation: 98-95=3 Current State: 38:[64, 29, 3], Operations: ['98-95=3'] Exploring Operation: 64-29=35, Resulting Numbers: [3, 35] Generated Node #3: [3, 35] from Operation: 64-29=35 Current State: 38:[3, 35], Operations: ['98-95=3', '64-29=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[98, 95, 64, 29], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [64, 29, 3] Generated Node #0,0: 38:[64, 29, 3] Operation: 98-95=3 Moving to Node #0,0 Current State: 38:[64, 29, 3], Operations: ['98-95=3'] Exploring Operation: 64-29=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 38:[3, 35] Operation: 64-29=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[3, 35], Operations: ['98-95=3', '64-29=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[98, 95, 64, 29], Operations: [] Exploring Operation: 98-95=3, Resulting Numbers: [64, 29, 3] Generated Node #0,0: 38:[64, 29, 3] Operation: 98-95=3 Moving to Node #0,0 Current State: 38:[64, 29, 3], Operations: ['98-95=3'] Exploring Operation: 64-29=35, Resulting Numbers: [3, 35] Generated Node #0,0,0: 38:[3, 35] Operation: 64-29=35 Moving to Node #0,0,0 Current State: 38:[3, 35], Operations: ['98-95=3', '64-29=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 3, 21, 86, 3 ]
80
[ "21-3=18", "18/3=6", "86-6=80" ]
Current State: 80:[3, 21, 86, 3], Operations: [] Exploring Operation: 21-3=18, Resulting Numbers: [86, 18] Generated Node #2: [86, 18] from Operation: 21-3=18 Current State: 80:[86, 18], Operations: ['21-3=18'] Exploring Operation: 18/3=6, Resulting Numbers: [86, 6] Generated Node #3: [86, 6] from Operation: 18/3=6 Current State: 80:[86, 6], Operations: ['21-3=18', '18/3=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[3, 21, 86, 3], Operations: [] Exploring Operation: 3+3=6, Resulting Numbers: [21, 86, 6] Generated Node #0,0: 80:[21, 86, 6] Operation: 3+3=6 Exploring Operation: 21/3=7, Resulting Numbers: [86, 3, 7] Generated Node #0,1: 80:[86, 3, 7] Operation: 21/3=7 Exploring Operation: 86-3=83, Resulting Numbers: [21, 3, 83] Generated Node #0,2: 80:[21, 3, 83] Operation: 86-3=83 Exploring Operation: 86-3=83, Resulting Numbers: [3, 21, 83] Generated Node #0,3: 80:[3, 21, 83] Operation: 86-3=83 Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[21, 3, 83], Operations: ['86-3=83'] Exploring Operation: 21+3=24, Resulting Numbers: [83, 24] Generated Node #0,2,0: 80:[83, 24] Operation: 21+3=24 Exploring Operation: 21/3=7, Resulting Numbers: [83, 7] Generated Node #0,2,1: 80:[83, 7] Operation: 21/3=7 Exploring Operation: 83-3=80, Resulting Numbers: [21, 80] Generated Node #0,2,2: 80:[21, 80] Operation: 83-3=80 Exploring Operation: 21-3=18, Resulting Numbers: [83, 18] Generated Node #0,2,3: 80:[83, 18] Operation: 21-3=18 Moving to Node #0,2,2 Current State: 80:[21, 80], Operations: ['86-3=83', '83-3=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[83, 7], Operations: ['86-3=83', '21/3=7'] Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,80 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[83, 18], Operations: ['86-3=83', '21-3=18'] Exploring Operation: 83+18=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 83*18=1494, Resulting Numbers: [1494] 1494,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[83, 24], Operations: ['86-3=83', '21+3=24'] Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,80 unequal: No Solution Exploring Operation: 83*24=1992, Resulting Numbers: [1992] 1992,80 unequal: No Solution Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,80 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 #0,3 Current State: 80:[3, 21, 83], Operations: ['86-3=83'] Exploring Operation: 21/3=7, Resulting Numbers: [83, 7] Generated Node #0,3,0: 80:[83, 7] Operation: 21/3=7 Exploring Operation: 21-3=18, Resulting Numbers: [83, 18] Generated Node #0,3,1: 80:[83, 18] Operation: 21-3=18 Exploring Operation: 3+21=24, Resulting Numbers: [83, 24] Generated Node #0,3,2: 80:[83, 24] Operation: 3+21=24 Exploring Operation: 83-3=80, Resulting Numbers: [21, 80] Generated Node #0,3,3: 80:[21, 80] Operation: 83-3=80 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 80:[21, 80], Operations: ['86-3=83', '83-3=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 80:[83, 7], Operations: ['86-3=83', '21/3=7'] Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,80 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 80:[83, 18], Operations: ['86-3=83', '21-3=18'] Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 83*18=1494, Resulting Numbers: [1494] 1494,80 unequal: No Solution Exploring Operation: 83+18=101, Resulting Numbers: [101] 101,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 80:[83, 24], Operations: ['86-3=83', '3+21=24'] Exploring Operation: 83*24=1992, Resulting Numbers: [1992] 1992,80 unequal: No Solution Exploring Operation: 83+24=107, Resulting Numbers: [107] 107,80 unequal: No Solution Exploring Operation: 83-24=59, Resulting Numbers: [59] 59,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[21, 86, 6], Operations: ['3+3=6'] Exploring Operation: 21+6=27, Resulting Numbers: [86, 27] Generated Node #0,0,0: 80:[86, 27] Operation: 21+6=27 Exploring Operation: 21-6=15, Resulting Numbers: [86, 15] Generated Node #0,0,1: 80:[86, 15] Operation: 21-6=15 Exploring Operation: 86+6=92, Resulting Numbers: [21, 92] Generated Node #0,0,2: 80:[21, 92] Operation: 86+6=92 Exploring Operation: 86-6=80, Resulting Numbers: [21, 80] Generated Node #0,0,3: 80:[21, 80] Operation: 86-6=80 Moving to Node #0,0,3 Current State: 80:[21, 80], Operations: ['3+3=6', '86-6=80'] Exploring Operation: 80-21=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 21+80=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 21*80=1680, Resulting Numbers: [1680] 1680,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[86, 15], Operations: ['3+3=6', '21-6=15'] Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,80 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[21, 92], Operations: ['3+3=6', '86+6=92'] Exploring Operation: 21*92=1932, Resulting Numbers: [1932] 1932,80 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,80 unequal: No Solution Exploring Operation: 21+92=113, Resulting Numbers: [113] 113,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[86, 27], Operations: ['3+3=6', '21+6=27'] Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,80 unequal: No Solution Exploring Operation: 86*27=2322, Resulting Numbers: [2322] 2322,80 unequal: No Solution Exploring Operation: 86+27=113, Resulting Numbers: [113] 113,80 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:[86, 3, 7], Operations: ['21/3=7'] Exploring Operation: 86-3=83, Resulting Numbers: [7, 83] Generated Node #0,1,0: 80:[7, 83] Operation: 86-3=83 Exploring Operation: 86-7=79, Resulting Numbers: [3, 79] Generated Node #0,1,1: 80:[3, 79] Operation: 86-7=79 Exploring Operation: 3+7=10, Resulting Numbers: [86, 10] Generated Node #0,1,2: 80:[86, 10] Operation: 3+7=10 Exploring Operation: 7-3=4, Resulting Numbers: [86, 4] Generated Node #0,1,3: 80:[86, 4] Operation: 7-3=4 Moving to Node #0,1,1 Current State: 80:[3, 79], Operations: ['21/3=7', '86-7=79'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[7, 83], Operations: ['21/3=7', '86-3=83'] Exploring Operation: 7*83=581, Resulting Numbers: [581] 581,80 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 7+83=90, Resulting Numbers: [90] 90,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[86, 4], Operations: ['21/3=7', '7-3=4'] Exploring Operation: 86-4=82, Resulting Numbers: [82] 82,80 unequal: No Solution Exploring Operation: 86+4=90, Resulting Numbers: [90] 90,80 unequal: No Solution Exploring Operation: 86*4=344, Resulting Numbers: [344] 344,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[86, 10], Operations: ['21/3=7', '3+7=10'] Exploring Operation: 86-10=76, Resulting Numbers: [76] 76,80 unequal: No Solution Exploring Operation: 86*10=860, Resulting Numbers: [860] 860,80 unequal: No Solution Exploring Operation: 86+10=96, Resulting Numbers: [96] 96,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 61, 24, 70, 7 ]
12
[ "70-61=9", "9-7=2", "24/2=12" ]
Current State: 12:[61, 24, 70, 7], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [24, 7, 9] Generated Node #2: [24, 7, 9] from Operation: 70-61=9 Current State: 12:[24, 7, 9], Operations: ['70-61=9'] Exploring Operation: 9-7=2, Resulting Numbers: [24, 2] Generated Node #3: [24, 2] from Operation: 9-7=2 Current State: 12:[24, 2], Operations: ['70-61=9', '9-7=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[61, 24, 70, 7], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [24, 7, 9] Generated Node #0,0: 12:[24, 7, 9] Operation: 70-61=9 Exploring Operation: 61-24=37, Resulting Numbers: [70, 7, 37] Generated Node #0,1: 12:[70, 7, 37] Operation: 61-24=37 Exploring Operation: 70-24=46, Resulting Numbers: [61, 7, 46] Generated Node #0,2: 12:[61, 7, 46] Operation: 70-24=46 Exploring Operation: 61-7=54, Resulting Numbers: [24, 70, 54] Generated Node #0,3: 12:[24, 70, 54] Operation: 61-7=54 Exploring Operation: 70/7=10, Resulting Numbers: [61, 24, 10] Generated Node #0,4: 12:[61, 24, 10] Operation: 70/7=10 Moving to Node #0,0 Current State: 12:[24, 7, 9], Operations: ['70-61=9'] Exploring Operation: 24+7=31, Resulting Numbers: [9, 31] Generated Node #0,0,0: 12:[9, 31] Operation: 24+7=31 Exploring Operation: 24-9=15, Resulting Numbers: [7, 15] Generated Node #0,0,1: 12:[7, 15] Operation: 24-9=15 Exploring Operation: 9-7=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 12:[24, 2] Operation: 9-7=2 Exploring Operation: 7+9=16, Resulting Numbers: [24, 16] Generated Node #0,0,3: 12:[24, 16] Operation: 7+9=16 Exploring Operation: 24-7=17, Resulting Numbers: [9, 17] Generated Node #0,0,4: 12:[9, 17] Operation: 24-7=17 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[7, 15], Operations: ['70-61=9', '24-9=15'] Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,12 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 #0,0,4 Current State: 12:[9, 17], Operations: ['70-61=9', '24-7=17'] Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,12 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,12 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 #0,0,2 Current State: 12:[24, 2], Operations: ['70-61=9', '9-7=2'] Exploring Operation: 24+2=26, Resulting Numbers: [26] 26,12 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,12 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[61, 24, 70, 7], Operations: [] Exploring Operation: 70-61=9, Resulting Numbers: [24, 7, 9] Generated Node #0,0: 12:[24, 7, 9] Operation: 70-61=9 Moving to Node #0,0 Current State: 12:[24, 7, 9], Operations: ['70-61=9'] Exploring Operation: 9-7=2, Resulting Numbers: [24, 2] Generated Node #0,0,2: 12:[24, 2] Operation: 9-7=2 Moving to Node #0,0,2 Current State: 12:[24, 2], Operations: ['70-61=9', '9-7=2'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 77, 90, 42, 22 ]
83
[ "90+42=132", "132/22=6", "77+6=83" ]
Current State: 83:[77, 90, 42, 22], Operations: [] Exploring Operation: 90+42=132, Resulting Numbers: [77, 22, 132] Generated Node #2: [77, 22, 132] from Operation: 90+42=132 Current State: 83:[77, 22, 132], Operations: ['90+42=132'] Exploring Operation: 132/22=6, Resulting Numbers: [77, 6] Generated Node #3: [77, 6] from Operation: 132/22=6 Current State: 83:[77, 6], Operations: ['90+42=132', '132/22=6'] Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[77, 90, 42, 22], Operations: [] Exploring Operation: 42+22=64, Resulting Numbers: [77, 90, 64] Generated Node #0,0: 83:[77, 90, 64] Operation: 42+22=64 Exploring Operation: 90-22=68, Resulting Numbers: [77, 42, 68] Generated Node #0,1: 83:[77, 42, 68] Operation: 90-22=68 Moving to Node #0,0 Current State: 83:[77, 90, 64], Operations: ['42+22=64'] Exploring Operation: 77+64=141, Resulting Numbers: [90, 141] Generated Node #0,0,0: 83:[90, 141] Operation: 77+64=141 Exploring Operation: 90-64=26, Resulting Numbers: [77, 26] Generated Node #0,0,1: 83:[77, 26] Operation: 90-64=26 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 83:[77, 26], Operations: ['42+22=64', '90-64=26'] Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 83:[90, 141], Operations: ['42+22=64', '77+64=141'] Exploring Operation: 90+141=231, Resulting Numbers: [231] 231,83 unequal: No Solution Exploring Operation: 141-90=51, Resulting Numbers: [51] 51,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 83:[77, 42, 68], Operations: ['90-22=68'] Exploring Operation: 77+42=119, Resulting Numbers: [68, 119] Generated Node #0,1,0: 83:[68, 119] Operation: 77+42=119 Exploring Operation: 42+68=110, Resulting Numbers: [77, 110] Generated Node #0,1,1: 83:[77, 110] Operation: 42+68=110 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[77, 110], Operations: ['90-22=68', '42+68=110'] Exploring Operation: 110-77=33, Resulting Numbers: [33] 33,83 unequal: No Solution Exploring Operation: 77+110=187, Resulting Numbers: [187] 187,83 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:[68, 119], Operations: ['90-22=68', '77+42=119'] Exploring Operation: 119-68=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 68+119=187, Resulting Numbers: [187] 187,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 65, 87, 60, 2 ]
52
[ "87-65=22", "60/2=30", "22+30=52" ]
Current State: 52:[65, 87, 60, 2], Operations: [] Exploring Operation: 87-65=22, Resulting Numbers: [60, 2, 22] Generated Node #2: [60, 2, 22] from Operation: 87-65=22 Current State: 52:[60, 2, 22], Operations: ['87-65=22'] Exploring Operation: 60/2=30, Resulting Numbers: [22, 30] Generated Node #3: [22, 30] from Operation: 60/2=30 Current State: 52:[22, 30], Operations: ['87-65=22', '60/2=30'] Exploring Operation: 22+30=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[65, 87, 60, 2], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [65, 87, 30] Generated Node #0,0: 52:[65, 87, 30] Operation: 60/2=30 Exploring Operation: 65-60=5, Resulting Numbers: [87, 2, 5] Generated Node #0,1: 52:[87, 2, 5] Operation: 65-60=5 Exploring Operation: 87-65=22, Resulting Numbers: [60, 2, 22] Generated Node #0,2: 52:[60, 2, 22] Operation: 87-65=22 Exploring Operation: 87-60=27, Resulting Numbers: [65, 2, 27] Generated Node #0,3: 52:[65, 2, 27] Operation: 87-60=27 Moving to Node #0,2 Current State: 52:[60, 2, 22], Operations: ['87-65=22'] Exploring Operation: 22/2=11, Resulting Numbers: [60, 11] Generated Node #0,2,0: 52:[60, 11] Operation: 22/2=11 Exploring Operation: 2+22=24, Resulting Numbers: [60, 24] Generated Node #0,2,1: 52:[60, 24] Operation: 2+22=24 Exploring Operation: 60/2=30, Resulting Numbers: [22, 30] Generated Node #0,2,2: 52:[22, 30] Operation: 60/2=30 Exploring Operation: 60-2=58, Resulting Numbers: [22, 58] Generated Node #0,2,3: 52:[22, 58] Operation: 60-2=58 Moving to Node #0,3 Current State: 52:[65, 2, 27], Operations: ['87-60=27'] Exploring Operation: 2*27=54, Resulting Numbers: [65, 54] Generated Node #0,3,0: 52:[65, 54] Operation: 2*27=54 Exploring Operation: 65-2=63, Resulting Numbers: [27, 63] Generated Node #0,3,1: 52:[27, 63] Operation: 65-2=63 Exploring Operation: 65-27=38, Resulting Numbers: [2, 38] Generated Node #0,3,2: 52:[2, 38] Operation: 65-27=38 Exploring Operation: 27-2=25, Resulting Numbers: [65, 25] Generated Node #0,3,3: 52:[65, 25] Operation: 27-2=25 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 52:[27, 63], Operations: ['87-60=27', '65-2=63'] Exploring Operation: 27+63=90, Resulting Numbers: [90] 90,52 unequal: No Solution Exploring Operation: 27*63=1701, Resulting Numbers: [1701] 1701,52 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 52:[2, 38], Operations: ['87-60=27', '65-27=38'] Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,52 unequal: No Solution Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,52 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 52:[65, 25], Operations: ['87-60=27', '27-2=25'] Exploring Operation: 65*25=1625, Resulting Numbers: [1625] 1625,52 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,52 unequal: No Solution Exploring Operation: 65+25=90, Resulting Numbers: [90] 90,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 52:[65, 54], Operations: ['87-60=27', '2*27=54'] Exploring Operation: 65*54=3510, Resulting Numbers: [3510] 3510,52 unequal: No Solution Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,52 unequal: No Solution Exploring Operation: 65+54=119, Resulting Numbers: [119] 119,52 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: 52:[87, 2, 5], Operations: ['65-60=5'] Exploring Operation: 87-5=82, Resulting Numbers: [2, 82] Generated Node #0,1,0: 52:[2, 82] Operation: 87-5=82 Exploring Operation: 5-2=3, Resulting Numbers: [87, 3] Generated Node #0,1,1: 52:[87, 3] Operation: 5-2=3 Exploring Operation: 87-2=85, Resulting Numbers: [5, 85] Generated Node #0,1,2: 52:[5, 85] Operation: 87-2=85 Exploring Operation: 87+2=89, Resulting Numbers: [5, 89] Generated Node #0,1,3: 52:[5, 89] Operation: 87+2=89 Moving to Node #0,0 Current State: 52:[65, 87, 30], Operations: ['60/2=30'] Exploring Operation: 87-30=57, Resulting Numbers: [65, 57] Generated Node #0,0,0: 52:[65, 57] Operation: 87-30=57 Exploring Operation: 87-65=22, Resulting Numbers: [30, 22] Generated Node #0,0,1: 52:[30, 22] Operation: 87-65=22 Exploring Operation: 65-30=35, Resulting Numbers: [87, 35] Generated Node #0,0,2: 52:[87, 35] Operation: 65-30=35 Exploring Operation: 65+30=95, Resulting Numbers: [87, 95] Generated Node #0,0,3: 52:[87, 95] Operation: 65+30=95 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 52:[30, 22], Operations: ['60/2=30', '87-65=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[65, 87, 60, 2], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [65, 87, 30] Generated Node #0,0: 52:[65, 87, 30] Operation: 60/2=30 Moving to Node #0,0 Current State: 52:[65, 87, 30], Operations: ['60/2=30'] Exploring Operation: 87-65=22, Resulting Numbers: [30, 22] Generated Node #0,0,1: 52:[30, 22] Operation: 87-65=22 Moving to Node #0,0,1 Current State: 52:[30, 22], Operations: ['60/2=30', '87-65=22'] Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
mult_heuristic
[ 77, 98, 79, 38 ]
87
[ "79-77=2", "98/2=49", "38+49=87" ]
Current State: 87:[77, 98, 79, 38], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [98, 38, 2] Generated Node #2: [98, 38, 2] from Operation: 79-77=2 Current State: 87:[98, 38, 2], Operations: ['79-77=2'] Exploring Operation: 98/2=49, Resulting Numbers: [38, 49] Generated Node #3: [38, 49] from Operation: 98/2=49 Current State: 87:[38, 49], Operations: ['79-77=2', '98/2=49'] Exploring Operation: 38+49=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[77, 98, 79, 38], Operations: [] Exploring Operation: 79-77=2, Resulting Numbers: [98, 38, 2] Generated Node #0,0: 87:[98, 38, 2] Operation: 79-77=2 Moving to Node #0,0 Current State: 87:[98, 38, 2], Operations: ['79-77=2'] Exploring Operation: 98-2=96, Resulting Numbers: [38, 96] Generated Node #0,0,0: 87:[38, 96] Operation: 98-2=96 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[38, 96], Operations: ['79-77=2', '98-2=96'] Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic