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
[ 39, 74, 73, 21 ]
32
[ "74+73=147", "147/21=7", "39-7=32" ]
Current State: 32:[39, 74, 73, 21], Operations: [] Exploring Operation: 74+73=147, Resulting Numbers: [39, 21, 147] Generated Node #2: [39, 21, 147] from Operation: 74+73=147 Current State: 32:[39, 21, 147], Operations: ['74+73=147'] Exploring Operation: 147/21=7, Resulting Numbers: [39, 7] Generated Node #3: [39, 7] from Operation: 147/21=7 Current State: 32:[39, 7], Operations: ['74+73=147', '147/21=7'] Exploring Operation: 39-7=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[39, 74, 73, 21], Operations: [] Exploring Operation: 73-39=34, Resulting Numbers: [74, 21, 34] Generated Node #0,0: 32:[74, 21, 34] Operation: 73-39=34 Exploring Operation: 74-73=1, Resulting Numbers: [39, 21, 1] Generated Node #0,1: 32:[39, 21, 1] Operation: 74-73=1 Exploring Operation: 74-21=53, Resulting Numbers: [39, 73, 53] Generated Node #0,2: 32:[39, 73, 53] Operation: 74-21=53 Exploring Operation: 74-39=35, Resulting Numbers: [73, 21, 35] Generated Node #0,3: 32:[73, 21, 35] Operation: 74-39=35 Exploring Operation: 73-21=52, Resulting Numbers: [39, 74, 52] Generated Node #0,4: 32:[39, 74, 52] Operation: 73-21=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[39, 21, 1], Operations: ['74-73=1'] Exploring Operation: 21-1=20, Resulting Numbers: [39, 20] Generated Node #0,1,0: 32:[39, 20] Operation: 21-1=20 Exploring Operation: 39/1=39, Resulting Numbers: [21, 39] Generated Node #0,1,1: 32:[21, 39] Operation: 39/1=39 Exploring Operation: 39-21=18, Resulting Numbers: [1, 18] Generated Node #0,1,2: 32:[1, 18] Operation: 39-21=18 Exploring Operation: 39*1=39, Resulting Numbers: [21, 39] Generated Node #0,1,3: 32:[21, 39] Operation: 39*1=39 Exploring Operation: 39-1=38, Resulting Numbers: [21, 38] Generated Node #0,1,4: 32:[21, 38] Operation: 39-1=38 Moving to Node #0,1,2 Current State: 32:[1, 18], Operations: ['74-73=1', '39-21=18'] Exploring Operation: 1*18=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 1+18=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 18-1=17, Resulting Numbers: [17] 17,32 unequal: No Solution Moving to Node #0,1,4 Current State: 32:[21, 38], Operations: ['74-73=1', '39-1=38'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,32 unequal: No Solution Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[39, 20], Operations: ['74-73=1', '21-1=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[21, 39], Operations: ['74-73=1', '39/1=39'] Exploring Operation: 21*39=819, Resulting Numbers: [819] 819,32 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 21+39=60, Resulting Numbers: [60] 60,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[21, 39], Operations: ['74-73=1', '39*1=39'] Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,32 unequal: No Solution Exploring Operation: 21+39=60, Resulting Numbers: [60] 60,32 unequal: No Solution Exploring Operation: 21*39=819, Resulting Numbers: [819] 819,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[74, 21, 34], Operations: ['73-39=34'] Exploring Operation: 21+34=55, Resulting Numbers: [74, 55] Generated Node #0,0,0: 32:[74, 55] Operation: 21+34=55 Exploring Operation: 74-21=53, Resulting Numbers: [34, 53] Generated Node #0,0,1: 32:[34, 53] Operation: 74-21=53 Exploring Operation: 34-21=13, Resulting Numbers: [74, 13] Generated Node #0,0,2: 32:[74, 13] Operation: 34-21=13 Exploring Operation: 74+21=95, Resulting Numbers: [34, 95] Generated Node #0,0,3: 32:[34, 95] Operation: 74+21=95 Exploring Operation: 74-34=40, Resulting Numbers: [21, 40] Generated Node #0,0,4: 32:[21, 40] Operation: 74-34=40 Moving to Node #0,0,4 Current State: 32:[21, 40], Operations: ['73-39=34', '74-34=40'] Exploring Operation: 40-21=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 21+40=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 21*40=840, Resulting Numbers: [840] 840,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[34, 53], Operations: ['73-39=34', '74-21=53'] Exploring Operation: 34*53=1802, Resulting Numbers: [1802] 1802,32 unequal: No Solution Exploring Operation: 34+53=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,32 unequal: No Solution Moving to Node #0,0,2 Current State: 32:[74, 13], Operations: ['73-39=34', '34-21=13'] Exploring Operation: 74*13=962, Resulting Numbers: [962] 962,32 unequal: No Solution Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 74+13=87, Resulting Numbers: [87] 87,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[74, 55], Operations: ['73-39=34', '21+34=55'] Exploring Operation: 74*55=4070, Resulting Numbers: [4070] 4070,32 unequal: No Solution Exploring Operation: 74-55=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 74+55=129, Resulting Numbers: [129] 129,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[34, 95], Operations: ['73-39=34', '74+21=95'] Exploring Operation: 34*95=3230, Resulting Numbers: [3230] 3230,32 unequal: No Solution Exploring Operation: 34+95=129, Resulting Numbers: [129] 129,32 unequal: No Solution Exploring Operation: 95-34=61, Resulting Numbers: [61] 61,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[73, 21, 35], Operations: ['74-39=35'] Exploring Operation: 35-21=14, Resulting Numbers: [73, 14] Generated Node #0,3,0: 32:[73, 14] Operation: 35-21=14 Exploring Operation: 73-21=52, Resulting Numbers: [35, 52] Generated Node #0,3,1: 32:[35, 52] Operation: 73-21=52 Exploring Operation: 21+35=56, Resulting Numbers: [73, 56] Generated Node #0,3,2: 32:[73, 56] Operation: 21+35=56 Exploring Operation: 73+21=94, Resulting Numbers: [35, 94] Generated Node #0,3,3: 32:[35, 94] Operation: 73+21=94 Exploring Operation: 73-35=38, Resulting Numbers: [21, 38] Generated Node #0,3,4: 32:[21, 38] Operation: 73-35=38 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 32:[21, 38], Operations: ['74-39=35', '73-35=38'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 21*38=798, Resulting Numbers: [798] 798,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 32:[35, 52], Operations: ['74-39=35', '73-21=52'] Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 32:[73, 14], Operations: ['74-39=35', '35-21=14'] Exploring Operation: 73*14=1022, Resulting Numbers: [1022] 1022,32 unequal: No Solution Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 73+14=87, Resulting Numbers: [87] 87,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 32:[73, 56], Operations: ['74-39=35', '21+35=56'] Exploring Operation: 73+56=129, Resulting Numbers: [129] 129,32 unequal: No Solution Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 73*56=4088, Resulting Numbers: [4088] 4088,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 32:[35, 94], Operations: ['74-39=35', '73+21=94'] Exploring Operation: 35*94=3290, Resulting Numbers: [3290] 3290,32 unequal: No Solution Exploring Operation: 94-35=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 35+94=129, Resulting Numbers: [129] 129,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[39, 73, 53], Operations: ['74-21=53'] Exploring Operation: 39+73=112, Resulting Numbers: [53, 112] Generated Node #0,2,0: 32:[53, 112] Operation: 39+73=112 Exploring Operation: 53-39=14, Resulting Numbers: [73, 14] Generated Node #0,2,1: 32:[73, 14] Operation: 53-39=14 Exploring Operation: 73-53=20, Resulting Numbers: [39, 20] Generated Node #0,2,2: 32:[39, 20] Operation: 73-53=20 Exploring Operation: 39+53=92, Resulting Numbers: [73, 92] Generated Node #0,2,3: 32:[73, 92] Operation: 39+53=92 Exploring Operation: 73-39=34, Resulting Numbers: [53, 34] Generated Node #0,2,4: 32:[53, 34] Operation: 73-39=34 Moving to Node #0,2,2 Current State: 32:[39, 20], Operations: ['74-21=53', '73-53=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,32 unequal: No Solution Moving to Node #0,2,4 Current State: 32:[53, 34], Operations: ['74-21=53', '73-39=34'] Exploring Operation: 53+34=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 53-34=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 53*34=1802, Resulting Numbers: [1802] 1802,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[73, 14], Operations: ['74-21=53', '53-39=14'] Exploring Operation: 73-14=59, Resulting Numbers: [59] 59,32 unequal: No Solution Exploring Operation: 73+14=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 73*14=1022, Resulting Numbers: [1022] 1022,32 unequal: No Solution Moving to Node #0,2,0 Current State: 32:[53, 112], Operations: ['74-21=53', '39+73=112'] Exploring Operation: 53*112=5936, Resulting Numbers: [5936] 5936,32 unequal: No Solution Exploring Operation: 53+112=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 112-53=59, Resulting Numbers: [59] 59,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[73, 92], Operations: ['74-21=53', '39+53=92'] Exploring Operation: 92-73=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 73+92=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 73*92=6716, Resulting Numbers: [6716] 6716,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 32:[39, 74, 52], Operations: ['73-21=52'] Exploring Operation: 74-52=22, Resulting Numbers: [39, 22] Generated Node #0,4,0: 32:[39, 22] Operation: 74-52=22 Exploring Operation: 39+74=113, Resulting Numbers: [52, 113] Generated Node #0,4,1: 32:[52, 113] Operation: 39+74=113 Exploring Operation: 74-39=35, Resulting Numbers: [52, 35] Generated Node #0,4,2: 32:[52, 35] Operation: 74-39=35 Exploring Operation: 39+52=91, Resulting Numbers: [74, 91] Generated Node #0,4,3: 32:[74, 91] Operation: 39+52=91 Exploring Operation: 52-39=13, Resulting Numbers: [74, 13] Generated Node #0,4,4: 32:[74, 13] Operation: 52-39=13 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 32:[39, 22], Operations: ['73-21=52', '74-52=22'] Exploring Operation: 39*22=858, Resulting Numbers: [858] 858,32 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 39+22=61, Resulting Numbers: [61] 61,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 32:[52, 35], Operations: ['73-21=52', '74-39=35'] Exploring Operation: 52+35=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 52*35=1820, Resulting Numbers: [1820] 1820,32 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 32:[74, 13], Operations: ['73-21=52', '52-39=13'] Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 74+13=87, Resulting Numbers: [87] 87,32 unequal: No Solution Exploring Operation: 74*13=962, Resulting Numbers: [962] 962,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 32:[52, 113], Operations: ['73-21=52', '39+74=113'] Exploring Operation: 113-52=61, Resulting Numbers: [61] 61,32 unequal: No Solution Exploring Operation: 52*113=5876, Resulting Numbers: [5876] 5876,32 unequal: No Solution Exploring Operation: 52+113=165, Resulting Numbers: [165] 165,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 32:[74, 91], Operations: ['73-21=52', '39+52=91'] Exploring Operation: 91-74=17, Resulting Numbers: [17] 17,32 unequal: No Solution Exploring Operation: 74+91=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 74*91=6734, Resulting Numbers: [6734] 6734,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 41, 1, 93, 27 ]
79
[ "41*1=41", "93+27=120", "120-41=79" ]
Current State: 79:[41, 1, 93, 27], Operations: [] Exploring Operation: 41*1=41, Resulting Numbers: [93, 27, 41] Generated Node #2: [93, 27, 41] from Operation: 41*1=41 Current State: 79:[93, 27, 41], Operations: ['41*1=41'] Exploring Operation: 93+27=120, Resulting Numbers: [41, 120] Generated Node #3: [41, 120] from Operation: 93+27=120 Current State: 79:[41, 120], Operations: ['41*1=41', '93+27=120'] Exploring Operation: 120-41=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[41, 1, 93, 27], Operations: [] Exploring Operation: 41+1=42, Resulting Numbers: [93, 27, 42] Generated Node #0,0: 79:[93, 27, 42] Operation: 41+1=42 Exploring Operation: 93-1=92, Resulting Numbers: [41, 27, 92] Generated Node #0,1: 79:[41, 27, 92] Operation: 93-1=92 Exploring Operation: 41+27=68, Resulting Numbers: [1, 93, 68] Generated Node #0,2: 79:[1, 93, 68] Operation: 41+27=68 Exploring Operation: 1+27=28, Resulting Numbers: [41, 93, 28] Generated Node #0,3: 79:[41, 93, 28] Operation: 1+27=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[93, 27, 42], Operations: ['41+1=42'] Exploring Operation: 93-27=66, Resulting Numbers: [42, 66] Generated Node #0,0,0: 79:[42, 66] Operation: 93-27=66 Exploring Operation: 93+27=120, Resulting Numbers: [42, 120] Generated Node #0,0,1: 79:[42, 120] Operation: 93+27=120 Exploring Operation: 27+42=69, Resulting Numbers: [93, 69] Generated Node #0,0,2: 79:[93, 69] Operation: 27+42=69 Exploring Operation: 42-27=15, Resulting Numbers: [93, 15] Generated Node #0,0,3: 79:[93, 15] Operation: 42-27=15 Moving to Node #0,0,2 Current State: 79:[93, 69], Operations: ['41+1=42', '27+42=69'] Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,79 unequal: No Solution Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[42, 66], Operations: ['41+1=42', '93-27=66'] Exploring Operation: 42*66=2772, Resulting Numbers: [2772] 2772,79 unequal: No Solution Exploring Operation: 66-42=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 42+66=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[93, 15], Operations: ['41+1=42', '42-27=15'] Exploring Operation: 93-15=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 93*15=1395, Resulting Numbers: [1395] 1395,79 unequal: No Solution Exploring Operation: 93+15=108, Resulting Numbers: [108] 108,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[42, 120], Operations: ['41+1=42', '93+27=120'] Exploring Operation: 120-42=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 42*120=5040, Resulting Numbers: [5040] 5040,79 unequal: No Solution Exploring Operation: 42+120=162, Resulting Numbers: [162] 162,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[41, 27, 92], Operations: ['93-1=92'] Exploring Operation: 41-27=14, Resulting Numbers: [92, 14] Generated Node #0,1,0: 79:[92, 14] Operation: 41-27=14 Exploring Operation: 27+92=119, Resulting Numbers: [41, 119] Generated Node #0,1,1: 79:[41, 119] Operation: 27+92=119 Exploring Operation: 41+27=68, Resulting Numbers: [92, 68] Generated Node #0,1,2: 79:[92, 68] Operation: 41+27=68 Exploring Operation: 92-27=65, Resulting Numbers: [41, 65] Generated Node #0,1,3: 79:[41, 65] Operation: 92-27=65 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[92, 68], Operations: ['93-1=92', '41+27=68'] Exploring Operation: 92*68=6256, Resulting Numbers: [6256] 6256,79 unequal: No Solution Exploring Operation: 92-68=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 92+68=160, Resulting Numbers: [160] 160,79 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 #0,1,3 Current State: 79:[41, 65], Operations: ['93-1=92', '92-27=65'] Exploring Operation: 41+65=106, Resulting Numbers: [106] 106,79 unequal: No Solution Exploring Operation: 41*65=2665, Resulting Numbers: [2665] 2665,79 unequal: No Solution Exploring Operation: 65-41=24, Resulting Numbers: [24] 24,79 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 #0,1,0 Current State: 79:[92, 14], Operations: ['93-1=92', '41-27=14'] Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 92+14=106, Resulting Numbers: [106] 106,79 unequal: No Solution Exploring Operation: 92*14=1288, Resulting Numbers: [1288] 1288,79 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 #0,1,1 Current State: 79:[41, 119], Operations: ['93-1=92', '27+92=119'] Exploring Operation: 119-41=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 41+119=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 41*119=4879, Resulting Numbers: [4879] 4879,79 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 #0,2 Current State: 79:[1, 93, 68], Operations: ['41+27=68'] Exploring Operation: 93-1=92, Resulting Numbers: [68, 92] Generated Node #0,2,0: 79:[68, 92] Operation: 93-1=92 Exploring Operation: 93/1=93, Resulting Numbers: [68, 93] Generated Node #0,2,1: 79:[68, 93] Operation: 93/1=93 Exploring Operation: 1*93=93, Resulting Numbers: [68, 93] Generated Node #0,2,2: 79:[68, 93] Operation: 1*93=93 Exploring Operation: 1+68=69, Resulting Numbers: [93, 69] Generated Node #0,2,3: 79:[93, 69] Operation: 1+68=69 Moving to Node #0,2,0 Current State: 79:[68, 92], Operations: ['41+27=68', '93-1=92'] Exploring Operation: 68+92=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 92-68=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 68*92=6256, Resulting Numbers: [6256] 6256,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[93, 69], Operations: ['41+27=68', '1+68=69'] Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,79 unequal: No Solution Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,79 unequal: No Solution Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[68, 93], Operations: ['41+27=68', '1*93=93'] Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 68*93=6324, Resulting Numbers: [6324] 6324,79 unequal: No Solution Exploring Operation: 68+93=161, Resulting Numbers: [161] 161,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[68, 93], Operations: ['41+27=68', '93/1=93'] Exploring Operation: 93-68=25, Resulting Numbers: [25] 25,79 unequal: No Solution Exploring Operation: 68*93=6324, Resulting Numbers: [6324] 6324,79 unequal: No Solution Exploring Operation: 68+93=161, Resulting Numbers: [161] 161,79 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 #0,3 Current State: 79:[41, 93, 28], Operations: ['1+27=28'] Exploring Operation: 93-28=65, Resulting Numbers: [41, 65] Generated Node #0,3,0: 79:[41, 65] Operation: 93-28=65 Exploring Operation: 41+28=69, Resulting Numbers: [93, 69] Generated Node #0,3,1: 79:[93, 69] Operation: 41+28=69 Exploring Operation: 93-41=52, Resulting Numbers: [28, 52] Generated Node #0,3,2: 79:[28, 52] Operation: 93-41=52 Exploring Operation: 41-28=13, Resulting Numbers: [93, 13] Generated Node #0,3,3: 79:[93, 13] Operation: 41-28=13 Moving to Node #0,3,1 Current State: 79:[93, 69], Operations: ['1+27=28', '41+28=69'] Exploring Operation: 93-69=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 93+69=162, Resulting Numbers: [162] 162,79 unequal: No Solution Exploring Operation: 93*69=6417, Resulting Numbers: [6417] 6417,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[41, 65], Operations: ['1+27=28', '93-28=65'] Exploring Operation: 65-41=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 41*65=2665, Resulting Numbers: [2665] 2665,79 unequal: No Solution Exploring Operation: 41+65=106, Resulting Numbers: [106] 106,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[28, 52], Operations: ['1+27=28', '93-41=52'] Exploring Operation: 28+52=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 28*52=1456, Resulting Numbers: [1456] 1456,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[93, 13], Operations: ['1+27=28', '41-28=13'] Exploring Operation: 93+13=106, Resulting Numbers: [106] 106,79 unequal: No Solution Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 93*13=1209, Resulting Numbers: [1209] 1209,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 90, 45, 27, 48 ]
81
[ "90-45=45", "48-45=3", "27*3=81" ]
Current State: 81:[90, 45, 27, 48], Operations: [] Exploring Operation: 90-45=45, Resulting Numbers: [27, 48, 45] Generated Node #2: [27, 48, 45] from Operation: 90-45=45 Current State: 81:[27, 48, 45], Operations: ['90-45=45'] Exploring Operation: 48-45=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 48-45=3 Current State: 81:[27, 3], Operations: ['90-45=45', '48-45=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[90, 45, 27, 48], Operations: [] Exploring Operation: 45+48=93, Resulting Numbers: [90, 27, 93] Generated Node #0,0: 81:[90, 27, 93] Operation: 45+48=93 Exploring Operation: 90/45=2, Resulting Numbers: [27, 48, 2] Generated Node #0,1: 81:[27, 48, 2] Operation: 90/45=2 Exploring Operation: 48-45=3, Resulting Numbers: [90, 27, 3] Generated Node #0,2: 81:[90, 27, 3] Operation: 48-45=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[90, 27, 3], Operations: ['48-45=3'] Exploring Operation: 90/3=30, Resulting Numbers: [27, 30] Generated Node #0,2,0: 81:[27, 30] Operation: 90/3=30 Exploring Operation: 90-3=87, Resulting Numbers: [27, 87] Generated Node #0,2,1: 81:[27, 87] Operation: 90-3=87 Exploring Operation: 27*3=81, Resulting Numbers: [90, 81] Generated Node #0,2,2: 81:[90, 81] Operation: 27*3=81 Moving to Node #0,2,0 Current State: 81:[27, 30], Operations: ['48-45=3', '90/3=30'] Exploring Operation: 30-27=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 27*30=810, Resulting Numbers: [810] 810,81 unequal: No Solution Exploring Operation: 27+30=57, Resulting Numbers: [57] 57,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[27, 87], Operations: ['48-45=3', '90-3=87'] Exploring Operation: 27*87=2349, Resulting Numbers: [2349] 2349,81 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,81 unequal: No Solution Exploring Operation: 27+87=114, Resulting Numbers: [114] 114,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[90, 81], Operations: ['48-45=3', '27*3=81'] Exploring Operation: 90*81=7290, Resulting Numbers: [7290] 7290,81 unequal: No Solution Exploring Operation: 90-81=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 90+81=171, Resulting Numbers: [171] 171,81 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 Current State: 81:[90, 27, 93], Operations: ['45+48=93'] Exploring Operation: 93-90=3, Resulting Numbers: [27, 3] Generated Node #0,0,0: 81:[27, 3] Operation: 93-90=3 Exploring Operation: 90-27=63, Resulting Numbers: [93, 63] Generated Node #0,0,1: 81:[93, 63] Operation: 90-27=63 Exploring Operation: 93-27=66, Resulting Numbers: [90, 66] Generated Node #0,0,2: 81:[90, 66] Operation: 93-27=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[27, 3], Operations: ['45+48=93', '93-90=3'] Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[90, 45, 27, 48], Operations: [] Exploring Operation: 45+48=93, Resulting Numbers: [90, 27, 93] Generated Node #0,0: 81:[90, 27, 93] Operation: 45+48=93 Moving to Node #0,0 Current State: 81:[90, 27, 93], Operations: ['45+48=93'] Exploring Operation: 93-90=3, Resulting Numbers: [27, 3] Generated Node #0,0,0: 81:[27, 3] Operation: 93-90=3 Moving to Node #0,0,0 Current State: 81:[27, 3], Operations: ['45+48=93', '93-90=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 79, 19, 69, 46 ]
40
[ "79-19=60", "46*60=2760", "2760/69=40" ]
Current State: 40:[79, 19, 69, 46], Operations: [] Exploring Operation: 79-19=60, Resulting Numbers: [69, 46, 60] Generated Node #2: [69, 46, 60] from Operation: 79-19=60 Current State: 40:[69, 46, 60], Operations: ['79-19=60'] Exploring Operation: 46*60=2760, Resulting Numbers: [69, 2760] Generated Node #3: [69, 2760] from Operation: 46*60=2760 Current State: 40:[69, 2760], Operations: ['79-19=60', '46*60=2760'] Exploring Operation: 2760/69=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[79, 19, 69, 46], Operations: [] Exploring Operation: 79-69=10, Resulting Numbers: [19, 46, 10] Generated Node #0,0: 40:[19, 46, 10] Operation: 79-69=10 Moving to Node #0,0 Current State: 40:[19, 46, 10], Operations: ['79-69=10'] Exploring Operation: 46-10=36, Resulting Numbers: [19, 36] Generated Node #0,0,0: 40:[19, 36] Operation: 46-10=36 Moving to Node #0,0,0 Current State: 40:[19, 36], Operations: ['79-69=10', '46-10=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,40 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 32, 64, 66, 66 ]
96
[ "32+64=96", "66-66=0", "96+0=96" ]
Current State: 96:[32, 64, 66, 66], Operations: [] Exploring Operation: 32+64=96, Resulting Numbers: [66, 66, 96] Generated Node #2: [66, 66, 96] from Operation: 32+64=96 Current State: 96:[66, 66, 96], Operations: ['32+64=96'] Exploring Operation: 66-66=0, Resulting Numbers: [96, 0] Generated Node #3: [96, 0] from Operation: 66-66=0 Current State: 96:[96, 0], Operations: ['32+64=96', '66-66=0'] Exploring Operation: 96+0=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[32, 64, 66, 66], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [32, 66, 2] Generated Node #0,0: 96:[32, 66, 2] Operation: 66-64=2 Exploring Operation: 66-64=2, Resulting Numbers: [32, 66, 2] Generated Node #0,1: 96:[32, 66, 2] Operation: 66-64=2 Exploring Operation: 66-66=0, Resulting Numbers: [32, 64, 0] Generated Node #0,2: 96:[32, 64, 0] Operation: 66-66=0 Exploring Operation: 66/66=1, Resulting Numbers: [32, 64, 1] Generated Node #0,3: 96:[32, 64, 1] Operation: 66/66=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 96:[32, 64, 1], Operations: ['66/66=1'] Exploring Operation: 64/32=2, Resulting Numbers: [1, 2] Generated Node #0,3,0: 96:[1, 2] Operation: 64/32=2 Exploring Operation: 64-32=32, Resulting Numbers: [1, 32] Generated Node #0,3,1: 96:[1, 32] Operation: 64-32=32 Exploring Operation: 64-1=63, Resulting Numbers: [32, 63] Generated Node #0,3,2: 96:[32, 63] Operation: 64-1=63 Exploring Operation: 32+64=96, Resulting Numbers: [1, 96] Generated Node #0,3,3: 96:[1, 96] Operation: 32+64=96 Moving to Node #0,3,0 Current State: 96:[1, 2], Operations: ['66/66=1', '64/32=2'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,96 unequal: No Solution Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[1, 96], Operations: ['66/66=1', '32+64=96'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[32, 64, 66, 66], Operations: [] Exploring Operation: 66/66=1, Resulting Numbers: [32, 64, 1] Generated Node #0,3: 96:[32, 64, 1] Operation: 66/66=1 Moving to Node #0,3 Current State: 96:[32, 64, 1], Operations: ['66/66=1'] Exploring Operation: 32+64=96, Resulting Numbers: [1, 96] Generated Node #0,3,3: 96:[1, 96] Operation: 32+64=96 Moving to Node #0,3,3 Current State: 96:[1, 96], Operations: ['66/66=1', '32+64=96'] Exploring Operation: 96/1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 6, 10, 39, 8 ]
78
[ "6+10=16", "39*16=624", "624/8=78" ]
Current State: 78:[6, 10, 39, 8], Operations: [] Exploring Operation: 6+10=16, Resulting Numbers: [39, 8, 16] Generated Node #2: [39, 8, 16] from Operation: 6+10=16 Current State: 78:[39, 8, 16], Operations: ['6+10=16'] Exploring Operation: 39*16=624, Resulting Numbers: [8, 624] Generated Node #3: [8, 624] from Operation: 39*16=624 Current State: 78:[8, 624], Operations: ['6+10=16', '39*16=624'] Exploring Operation: 624/8=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[6, 10, 39, 8], Operations: [] Exploring Operation: 10*8=80, Resulting Numbers: [6, 39, 80] Generated Node #0,0: 78:[6, 39, 80] Operation: 10*8=80 Exploring Operation: 10-8=2, Resulting Numbers: [6, 39, 2] Generated Node #0,1: 78:[6, 39, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 78:[6, 39, 2], Operations: ['10-8=2'] Exploring Operation: 6/2=3, Resulting Numbers: [39, 3] Generated Node #0,1,0: 78:[39, 3] Operation: 6/2=3 Exploring Operation: 39*2=78, Resulting Numbers: [6, 78] Generated Node #0,1,1: 78:[6, 78] Operation: 39*2=78 Moving to Node #0,1,0 Current State: 78:[39, 3], Operations: ['10-8=2', '6/2=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[6, 78], Operations: ['10-8=2', '39*2=78'] Exploring Operation: 6+78=84, Resulting Numbers: [84] 84,78 unequal: No Solution Exploring Operation: 78/6=13, Resulting Numbers: [13] 13,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[6, 39, 80], Operations: ['10*8=80'] Exploring Operation: 80-39=41, Resulting Numbers: [6, 41] Generated Node #0,0,0: 78:[6, 41] Operation: 80-39=41 Exploring Operation: 80-6=74, Resulting Numbers: [39, 74] Generated Node #0,0,1: 78:[39, 74] Operation: 80-6=74 Moving to Node #0,0,0 Current State: 78:[6, 41], Operations: ['10*8=80', '80-39=41'] Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,78 unequal: No Solution Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,78 unequal: No Solution Moving to Node #0,0,1 Current State: 78:[39, 74], Operations: ['10*8=80', '80-6=74'] Exploring Operation: 39+74=113, Resulting Numbers: [113] 113,78 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,78 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
[ 75, 92, 63, 23 ]
69
[ "92-75=17", "63+23=86", "86-17=69" ]
Current State: 69:[75, 92, 63, 23], Operations: [] Exploring Operation: 92-75=17, Resulting Numbers: [63, 23, 17] Generated Node #2: [63, 23, 17] from Operation: 92-75=17 Current State: 69:[63, 23, 17], Operations: ['92-75=17'] Exploring Operation: 63+23=86, Resulting Numbers: [17, 86] Generated Node #3: [17, 86] from Operation: 63+23=86 Current State: 69:[17, 86], Operations: ['92-75=17', '63+23=86'] Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[75, 92, 63, 23], Operations: [] Exploring Operation: 92-75=17, Resulting Numbers: [63, 23, 17] Generated Node #0,0: 69:[63, 23, 17] Operation: 92-75=17 Exploring Operation: 92-63=29, Resulting Numbers: [75, 23, 29] Generated Node #0,1: 69:[75, 23, 29] Operation: 92-63=29 Moving to Node #0,0 Current State: 69:[63, 23, 17], Operations: ['92-75=17'] Exploring Operation: 23-17=6, Resulting Numbers: [63, 6] Generated Node #0,0,0: 69:[63, 6] Operation: 23-17=6 Exploring Operation: 63+17=80, Resulting Numbers: [23, 80] Generated Node #0,0,1: 69:[23, 80] Operation: 63+17=80 Moving to Node #0,1 Current State: 69:[75, 23, 29], Operations: ['92-63=29'] Exploring Operation: 75-23=52, Resulting Numbers: [29, 52] Generated Node #0,1,0: 69:[29, 52] Operation: 75-23=52 Exploring Operation: 29-23=6, Resulting Numbers: [75, 6] Generated Node #0,1,1: 69:[75, 6] Operation: 29-23=6 Moving to Node #0,0,0 Current State: 69:[63, 6], Operations: ['92-75=17', '23-17=6'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[75, 92, 63, 23], Operations: [] Exploring Operation: 92-75=17, Resulting Numbers: [63, 23, 17] Generated Node #0,0: 69:[63, 23, 17] Operation: 92-75=17 Moving to Node #0,0 Current State: 69:[63, 23, 17], Operations: ['92-75=17'] Exploring Operation: 23-17=6, Resulting Numbers: [63, 6] Generated Node #0,0,0: 69:[63, 6] Operation: 23-17=6 Moving to Node #0,0,0 Current State: 69:[63, 6], Operations: ['92-75=17', '23-17=6'] Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.989583
hs_2
sum_heuristic
[ 4, 14, 91, 53 ]
96
[ "91-14=77", "77-53=24", "4*24=96" ]
Current State: 96:[4, 14, 91, 53], Operations: [] Exploring Operation: 91-14=77, Resulting Numbers: [4, 53, 77] Generated Node #2: [4, 53, 77] from Operation: 91-14=77 Current State: 96:[4, 53, 77], Operations: ['91-14=77'] Exploring Operation: 77-53=24, Resulting Numbers: [4, 24] Generated Node #3: [4, 24] from Operation: 77-53=24 Current State: 96:[4, 24], Operations: ['91-14=77', '77-53=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[4, 14, 91, 53], Operations: [] Exploring Operation: 4+91=95, Resulting Numbers: [14, 53, 95] Generated Node #0,0: 96:[14, 53, 95] Operation: 4+91=95 Exploring Operation: 53-4=49, Resulting Numbers: [14, 91, 49] Generated Node #0,1: 96:[14, 91, 49] Operation: 53-4=49 Moving to Node #0,0 Current State: 96:[14, 53, 95], Operations: ['4+91=95'] Exploring Operation: 53-14=39, Resulting Numbers: [95, 39] Generated Node #0,0,0: 96:[95, 39] Operation: 53-14=39 Exploring Operation: 95-53=42, Resulting Numbers: [14, 42] Generated Node #0,0,1: 96:[14, 42] Operation: 95-53=42 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[95, 39], Operations: ['4+91=95', '53-14=39'] Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 95+39=134, Resulting Numbers: [134] 134,96 unequal: No Solution No 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: 96:[14, 42], Operations: ['4+91=95', '95-53=42'] Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,96 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: 96:[14, 91, 49], Operations: ['53-4=49'] Exploring Operation: 49-14=35, Resulting Numbers: [91, 35] Generated Node #0,1,0: 96:[91, 35] Operation: 49-14=35 Exploring Operation: 91-49=42, Resulting Numbers: [14, 42] Generated Node #0,1,1: 96:[14, 42] Operation: 91-49=42 Moving to Node #0,1,0 Current State: 96:[91, 35], Operations: ['53-4=49', '49-14=35'] Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,96 unequal: No Solution Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[14, 42], Operations: ['53-4=49', '91-49=42'] Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,96 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,96 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 28, 47, 2, 13 ]
45
[ "47-28=19", "2*13=26", "19+26=45" ]
Current State: 45:[28, 47, 2, 13], Operations: [] Exploring Operation: 47-28=19, Resulting Numbers: [2, 13, 19] Generated Node #2: [2, 13, 19] from Operation: 47-28=19 Current State: 45:[2, 13, 19], Operations: ['47-28=19'] Exploring Operation: 2*13=26, Resulting Numbers: [19, 26] Generated Node #3: [19, 26] from Operation: 2*13=26 Current State: 45:[19, 26], Operations: ['47-28=19', '2*13=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[28, 47, 2, 13], Operations: [] Exploring Operation: 28-13=15, Resulting Numbers: [47, 2, 15] Generated Node #0,0: 45:[47, 2, 15] Operation: 28-13=15 Exploring Operation: 28*2=56, Resulting Numbers: [47, 13, 56] Generated Node #0,1: 45:[47, 13, 56] Operation: 28*2=56 Exploring Operation: 47-28=19, Resulting Numbers: [2, 13, 19] Generated Node #0,2: 45:[2, 13, 19] Operation: 47-28=19 Exploring Operation: 28+13=41, Resulting Numbers: [47, 2, 41] Generated Node #0,3: 45:[47, 2, 41] Operation: 28+13=41 Exploring Operation: 28/2=14, Resulting Numbers: [47, 13, 14] Generated Node #0,4: 45:[47, 13, 14] Operation: 28/2=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[47, 2, 15], Operations: ['28-13=15'] Exploring Operation: 15-2=13, Resulting Numbers: [47, 13] Generated Node #0,0,0: 45:[47, 13] Operation: 15-2=13 Exploring Operation: 47-2=45, Resulting Numbers: [15, 45] Generated Node #0,0,1: 45:[15, 45] Operation: 47-2=45 Exploring Operation: 2+15=17, Resulting Numbers: [47, 17] Generated Node #0,0,2: 45:[47, 17] Operation: 2+15=17 Exploring Operation: 47-15=32, Resulting Numbers: [2, 32] Generated Node #0,0,3: 45:[2, 32] Operation: 47-15=32 Exploring Operation: 47+2=49, Resulting Numbers: [15, 49] Generated Node #0,0,4: 45:[15, 49] Operation: 47+2=49 Moving to Node #0,0,1 Current State: 45:[15, 45], Operations: ['28-13=15', '47-2=45'] Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 15*45=675, Resulting Numbers: [675] 675,45 unequal: No Solution Moving to Node #0,0,2 Current State: 45:[47, 17], Operations: ['28-13=15', '2+15=17'] Exploring Operation: 47+17=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 47*17=799, Resulting Numbers: [799] 799,45 unequal: No Solution Moving to Node #0,0,0 Current State: 45:[47, 13], Operations: ['28-13=15', '15-2=13'] Exploring Operation: 47*13=611, Resulting Numbers: [611] 611,45 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 47+13=60, Resulting Numbers: [60] 60,45 unequal: No Solution Moving to Node #0,0,4 Current State: 45:[15, 49], Operations: ['28-13=15', '47+2=49'] Exploring Operation: 15+49=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 15*49=735, Resulting Numbers: [735] 735,45 unequal: No Solution Moving to Node #0,0,3 Current State: 45:[2, 32], Operations: ['28-13=15', '47-15=32'] Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,45 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 45:[47, 13, 14], Operations: ['28/2=14'] Exploring Operation: 47-13=34, Resulting Numbers: [14, 34] Generated Node #0,4,0: 45:[14, 34] Operation: 47-13=34 Exploring Operation: 47+13=60, Resulting Numbers: [14, 60] Generated Node #0,4,1: 45:[14, 60] Operation: 47+13=60 Exploring Operation: 14-13=1, Resulting Numbers: [47, 1] Generated Node #0,4,2: 45:[47, 1] Operation: 14-13=1 Exploring Operation: 13+14=27, Resulting Numbers: [47, 27] Generated Node #0,4,3: 45:[47, 27] Operation: 13+14=27 Exploring Operation: 47-14=33, Resulting Numbers: [13, 33] Generated Node #0,4,4: 45:[13, 33] Operation: 47-14=33 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 45:[47, 1], Operations: ['28/2=14', '14-13=1'] Exploring Operation: 47+1=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,45 unequal: No Solution Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,45 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 45:[14, 34], Operations: ['28/2=14', '47-13=34'] Exploring Operation: 14+34=48, Resulting Numbers: [48] 48,45 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 45:[47, 27], Operations: ['28/2=14', '13+14=27'] Exploring Operation: 47-27=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 47+27=74, Resulting Numbers: [74] 74,45 unequal: No Solution Exploring Operation: 47*27=1269, Resulting Numbers: [1269] 1269,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 45:[13, 33], Operations: ['28/2=14', '47-14=33'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,45 unequal: No Solution Exploring Operation: 13*33=429, Resulting Numbers: [429] 429,45 unequal: No Solution Exploring Operation: 13+33=46, Resulting Numbers: [46] 46,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 45:[14, 60], Operations: ['28/2=14', '47+13=60'] Exploring Operation: 60-14=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 14*60=840, Resulting Numbers: [840] 840,45 unequal: No Solution Exploring Operation: 14+60=74, Resulting Numbers: [74] 74,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 45:[2, 13, 19], Operations: ['47-28=19'] Exploring Operation: 2+13=15, Resulting Numbers: [19, 15] Generated Node #0,2,0: 45:[19, 15] Operation: 2+13=15 Exploring Operation: 19-2=17, Resulting Numbers: [13, 17] Generated Node #0,2,1: 45:[13, 17] Operation: 19-2=17 Exploring Operation: 2+19=21, Resulting Numbers: [13, 21] Generated Node #0,2,2: 45:[13, 21] Operation: 2+19=21 Exploring Operation: 19-13=6, Resulting Numbers: [2, 6] Generated Node #0,2,3: 45:[2, 6] Operation: 19-13=6 Exploring Operation: 13-2=11, Resulting Numbers: [19, 11] Generated Node #0,2,4: 45:[19, 11] Operation: 13-2=11 Moving to Node #0,2,3 Current State: 45:[2, 6], Operations: ['47-28=19', '19-13=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[13, 17], Operations: ['47-28=19', '19-2=17'] Exploring Operation: 13*17=221, Resulting Numbers: [221] 221,45 unequal: No Solution Exploring Operation: 13+17=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,2,0 Current State: 45:[19, 15], Operations: ['47-28=19', '2+13=15'] Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,45 unequal: No Solution Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,2,4 Current State: 45:[19, 11], Operations: ['47-28=19', '13-2=11'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[13, 21], Operations: ['47-28=19', '2+19=21'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,45 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 45:[47, 2, 41], Operations: ['28+13=41'] Exploring Operation: 47-2=45, Resulting Numbers: [41, 45] Generated Node #0,3,0: 45:[41, 45] Operation: 47-2=45 Exploring Operation: 2+41=43, Resulting Numbers: [47, 43] Generated Node #0,3,1: 45:[47, 43] Operation: 2+41=43 Exploring Operation: 47+2=49, Resulting Numbers: [41, 49] Generated Node #0,3,2: 45:[41, 49] Operation: 47+2=49 Exploring Operation: 47-41=6, Resulting Numbers: [2, 6] Generated Node #0,3,3: 45:[2, 6] Operation: 47-41=6 Exploring Operation: 41-2=39, Resulting Numbers: [47, 39] Generated Node #0,3,4: 45:[47, 39] Operation: 41-2=39 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 45:[2, 6], Operations: ['28+13=41', '47-41=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,45 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 45:[41, 45], Operations: ['28+13=41', '47-2=45'] Exploring Operation: 41+45=86, Resulting Numbers: [86] 86,45 unequal: No Solution Exploring Operation: 41*45=1845, Resulting Numbers: [1845] 1845,45 unequal: No Solution Exploring Operation: 45-41=4, Resulting Numbers: [4] 4,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 45:[47, 43], Operations: ['28+13=41', '2+41=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,45 unequal: No Solution Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 45:[41, 49], Operations: ['28+13=41', '47+2=49'] Exploring Operation: 41+49=90, Resulting Numbers: [90] 90,45 unequal: No Solution Exploring Operation: 41*49=2009, Resulting Numbers: [2009] 2009,45 unequal: No Solution Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 45:[47, 39], Operations: ['28+13=41', '41-2=39'] Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,45 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,45 unequal: No Solution Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,45 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 45:[47, 13, 56], Operations: ['28*2=56'] Exploring Operation: 47+13=60, Resulting Numbers: [56, 60] Generated Node #0,1,0: 45:[56, 60] Operation: 47+13=60 Exploring Operation: 47-13=34, Resulting Numbers: [56, 34] Generated Node #0,1,1: 45:[56, 34] Operation: 47-13=34 Exploring Operation: 56-47=9, Resulting Numbers: [13, 9] Generated Node #0,1,2: 45:[13, 9] Operation: 56-47=9 Exploring Operation: 13+56=69, Resulting Numbers: [47, 69] Generated Node #0,1,3: 45:[47, 69] Operation: 13+56=69 Exploring Operation: 56-13=43, Resulting Numbers: [47, 43] Generated Node #0,1,4: 45:[47, 43] Operation: 56-13=43 Moving to Node #0,1,2 Current State: 45:[13, 9], Operations: ['28*2=56', '56-47=9'] Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,45 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,1,4 Current State: 45:[47, 43], Operations: ['28*2=56', '56-13=43'] Exploring Operation: 47-43=4, Resulting Numbers: [4] 4,45 unequal: No Solution Exploring Operation: 47*43=2021, Resulting Numbers: [2021] 2021,45 unequal: No Solution Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,45 unequal: No Solution Moving to Node #0,1,1 Current State: 45:[56, 34], Operations: ['28*2=56', '47-13=34'] Exploring Operation: 56*34=1904, Resulting Numbers: [1904] 1904,45 unequal: No Solution Exploring Operation: 56-34=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 56+34=90, Resulting Numbers: [90] 90,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[56, 60], Operations: ['28*2=56', '47+13=60'] Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,45 unequal: No Solution Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,45 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,45 unequal: No Solution Moving to Node #0,1,3 Current State: 45:[47, 69], Operations: ['28*2=56', '13+56=69'] Exploring Operation: 69-47=22, Resulting Numbers: [22] 22,45 unequal: No Solution Exploring Operation: 47+69=116, Resulting Numbers: [116] 116,45 unequal: No Solution Exploring Operation: 47*69=3243, Resulting Numbers: [3243] 3243,45 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
[ 86, 67, 90, 16 ]
63
[ "90-86=4", "16/4=4", "67-4=63" ]
Current State: 63:[86, 67, 90, 16], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [67, 16, 4] Generated Node #2: [67, 16, 4] from Operation: 90-86=4 Current State: 63:[67, 16, 4], Operations: ['90-86=4'] Exploring Operation: 16/4=4, Resulting Numbers: [67, 4] Generated Node #3: [67, 4] from Operation: 16/4=4 Current State: 63:[67, 4], Operations: ['90-86=4', '16/4=4'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[86, 67, 90, 16], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [67, 16, 4] Generated Node #0,0: 63:[67, 16, 4] Operation: 90-86=4 Exploring Operation: 90-67=23, Resulting Numbers: [86, 16, 23] Generated Node #0,1: 63:[86, 16, 23] Operation: 90-67=23 Moving to Node #0,0 Current State: 63:[67, 16, 4], Operations: ['90-86=4'] Exploring Operation: 67-4=63, Resulting Numbers: [16, 63] Generated Node #0,0,0: 63:[16, 63] Operation: 67-4=63 Exploring Operation: 16+4=20, Resulting Numbers: [67, 20] Generated Node #0,0,1: 63:[67, 20] Operation: 16+4=20 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[16, 63], Operations: ['90-86=4', '67-4=63'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 16+63=79, Resulting Numbers: [79] 79,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[67, 20], Operations: ['90-86=4', '16+4=20'] Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,63 unequal: No Solution Exploring Operation: 67-20=47, Resulting Numbers: [47] 47,63 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: 63:[86, 16, 23], Operations: ['90-67=23'] Exploring Operation: 86-23=63, Resulting Numbers: [16, 63] Generated Node #0,1,0: 63:[16, 63] Operation: 86-23=63 Exploring Operation: 86-16=70, Resulting Numbers: [23, 70] Generated Node #0,1,1: 63:[23, 70] Operation: 86-16=70 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 63:[16, 63], Operations: ['90-67=23', '86-23=63'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 16+63=79, Resulting Numbers: [79] 79,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 63:[23, 70], Operations: ['90-67=23', '86-16=70'] Exploring Operation: 70-23=47, Resulting Numbers: [47] 47,63 unequal: No Solution Exploring Operation: 23+70=93, Resulting Numbers: [93] 93,63 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
[ 52, 45, 39, 90 ]
67
[ "45-39=6", "90/6=15", "52+15=67" ]
Current State: 67:[52, 45, 39, 90], Operations: [] Exploring Operation: 45-39=6, Resulting Numbers: [52, 90, 6] Generated Node #2: [52, 90, 6] from Operation: 45-39=6 Current State: 67:[52, 90, 6], Operations: ['45-39=6'] Exploring Operation: 90/6=15, Resulting Numbers: [52, 15] Generated Node #3: [52, 15] from Operation: 90/6=15 Current State: 67:[52, 15], Operations: ['45-39=6', '90/6=15'] Exploring Operation: 52+15=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[52, 45, 39, 90], Operations: [] Exploring Operation: 90-39=51, Resulting Numbers: [52, 45, 51] Generated Node #0,0: 67:[52, 45, 51] Operation: 90-39=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[52, 45, 51], Operations: ['90-39=51'] Exploring Operation: 45+51=96, Resulting Numbers: [52, 96] Generated Node #0,0,0: 67:[52, 96] Operation: 45+51=96 Moving to Node #0,0,0 Current State: 67:[52, 96], Operations: ['90-39=51', '45+51=96'] Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,67 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
[ 62, 17, 99, 2 ]
59
[ "62+17=79", "2*79=158", "158-99=59" ]
Current State: 59:[62, 17, 99, 2], Operations: [] Exploring Operation: 62+17=79, Resulting Numbers: [99, 2, 79] Generated Node #2: [99, 2, 79] from Operation: 62+17=79 Current State: 59:[99, 2, 79], Operations: ['62+17=79'] Exploring Operation: 2*79=158, Resulting Numbers: [99, 158] Generated Node #3: [99, 158] from Operation: 2*79=158 Current State: 59:[99, 158], Operations: ['62+17=79', '2*79=158'] Exploring Operation: 158-99=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[62, 17, 99, 2], Operations: [] Exploring Operation: 17*2=34, Resulting Numbers: [62, 99, 34] Generated Node #0,0: 59:[62, 99, 34] Operation: 17*2=34 Exploring Operation: 62-2=60, Resulting Numbers: [17, 99, 60] Generated Node #0,1: 59:[17, 99, 60] Operation: 62-2=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[62, 99, 34], Operations: ['17*2=34'] Exploring Operation: 99-62=37, Resulting Numbers: [34, 37] Generated Node #0,0,0: 59:[34, 37] Operation: 99-62=37 Exploring Operation: 99-34=65, Resulting Numbers: [62, 65] Generated Node #0,0,1: 59:[62, 65] Operation: 99-34=65 Moving to Node #0,0,1 Current State: 59:[62, 65], Operations: ['17*2=34', '99-34=65'] Exploring Operation: 65-62=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 62+65=127, Resulting Numbers: [127] 127,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[34, 37], Operations: ['17*2=34', '99-62=37'] Exploring Operation: 34+37=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 37-34=3, Resulting Numbers: [3] 3,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[17, 99, 60], Operations: ['62-2=60'] Exploring Operation: 99-17=82, Resulting Numbers: [60, 82] Generated Node #0,1,0: 59:[60, 82] Operation: 99-17=82 Exploring Operation: 60-17=43, Resulting Numbers: [99, 43] Generated Node #0,1,1: 59:[99, 43] Operation: 60-17=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 59:[60, 82], Operations: ['62-2=60', '99-17=82'] Exploring Operation: 60+82=142, Resulting Numbers: [142] 142,59 unequal: No Solution Exploring Operation: 82-60=22, Resulting Numbers: [22] 22,59 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 #0,1,1 Current State: 59:[99, 43], Operations: ['62-2=60', '60-17=43'] Exploring Operation: 99-43=56, Resulting Numbers: [56] 56,59 unequal: No Solution Exploring Operation: 99+43=142, Resulting Numbers: [142] 142,59 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 No solution found.
0
hs_2
mult_heuristic
[ 19, 5, 82, 3 ]
60
[ "5-3=2", "82/2=41", "19+41=60" ]
Current State: 60:[19, 5, 82, 3], Operations: [] Exploring Operation: 5-3=2, Resulting Numbers: [19, 82, 2] Generated Node #2: [19, 82, 2] from Operation: 5-3=2 Current State: 60:[19, 82, 2], Operations: ['5-3=2'] Exploring Operation: 82/2=41, Resulting Numbers: [19, 41] Generated Node #3: [19, 41] from Operation: 82/2=41 Current State: 60:[19, 41], Operations: ['5-3=2', '82/2=41'] Exploring Operation: 19+41=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[19, 5, 82, 3], Operations: [] Exploring Operation: 82-19=63, Resulting Numbers: [5, 3, 63] Generated Node #0,0: 60:[5, 3, 63] Operation: 82-19=63 Moving to Node #0,0 Current State: 60:[5, 3, 63], Operations: ['82-19=63'] Exploring Operation: 63-3=60, Resulting Numbers: [5, 60] Generated Node #0,0,0: 60:[5, 60] Operation: 63-3=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[5, 60], Operations: ['82-19=63', '63-3=60'] Exploring Operation: 60/5=12, Resulting Numbers: [12] 12,60 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
[ 78, 3, 20, 67 ]
13
[ "78-67=11", "3*11=33", "33-20=13" ]
Current State: 13:[78, 3, 20, 67], Operations: [] Exploring Operation: 78-67=11, Resulting Numbers: [3, 20, 11] Generated Node #2: [3, 20, 11] from Operation: 78-67=11 Current State: 13:[3, 20, 11], Operations: ['78-67=11'] Exploring Operation: 3*11=33, Resulting Numbers: [20, 33] Generated Node #3: [20, 33] from Operation: 3*11=33 Current State: 13:[20, 33], Operations: ['78-67=11', '3*11=33'] Exploring Operation: 33-20=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[78, 3, 20, 67], Operations: [] Exploring Operation: 78-67=11, Resulting Numbers: [3, 20, 11] Generated Node #0,0: 13:[3, 20, 11] Operation: 78-67=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[3, 20, 11], Operations: ['78-67=11'] Exploring Operation: 20-3=17, Resulting Numbers: [11, 17] Generated Node #0,0,0: 13:[11, 17] Operation: 20-3=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[11, 17], Operations: ['78-67=11', '20-3=17'] Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 30, 87, 44, 39 ]
62
[ "87-30=57", "44-39=5", "57+5=62" ]
Current State: 62:[30, 87, 44, 39], Operations: [] Exploring Operation: 87-30=57, Resulting Numbers: [44, 39, 57] Generated Node #2: [44, 39, 57] from Operation: 87-30=57 Current State: 62:[44, 39, 57], Operations: ['87-30=57'] Exploring Operation: 44-39=5, Resulting Numbers: [57, 5] Generated Node #3: [57, 5] from Operation: 44-39=5 Current State: 62:[57, 5], Operations: ['87-30=57', '44-39=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[30, 87, 44, 39], Operations: [] Exploring Operation: 87-30=57, Resulting Numbers: [44, 39, 57] Generated Node #0,0: 62:[44, 39, 57] Operation: 87-30=57 Exploring Operation: 87-39=48, Resulting Numbers: [30, 44, 48] Generated Node #0,1: 62:[30, 44, 48] Operation: 87-39=48 Exploring Operation: 87-44=43, Resulting Numbers: [30, 39, 43] Generated Node #0,2: 62:[30, 39, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[30, 39, 43], Operations: ['87-44=43'] Exploring Operation: 43-39=4, Resulting Numbers: [30, 4] Generated Node #0,2,0: 62:[30, 4] Operation: 43-39=4 Exploring Operation: 30+39=69, Resulting Numbers: [43, 69] Generated Node #0,2,1: 62:[43, 69] Operation: 30+39=69 Exploring Operation: 39-30=9, Resulting Numbers: [43, 9] Generated Node #0,2,2: 62:[43, 9] Operation: 39-30=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[30, 4], Operations: ['87-44=43', '43-39=4'] Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 62:[43, 69], Operations: ['87-44=43', '30+39=69'] Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,62 unequal: No Solution Exploring Operation: 43+69=112, Resulting Numbers: [112] 112,62 unequal: No Solution Exploring Operation: 43*69=2967, Resulting Numbers: [2967] 2967,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 62:[43, 9], Operations: ['87-44=43', '39-30=9'] Exploring Operation: 43*9=387, Resulting Numbers: [387] 387,62 unequal: No Solution Exploring Operation: 43+9=52, Resulting Numbers: [52] 52,62 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[44, 39, 57], Operations: ['87-30=57'] Exploring Operation: 44+39=83, Resulting Numbers: [57, 83] Generated Node #0,0,0: 62:[57, 83] Operation: 44+39=83 Exploring Operation: 57-44=13, Resulting Numbers: [39, 13] Generated Node #0,0,1: 62:[39, 13] Operation: 57-44=13 Exploring Operation: 44-39=5, Resulting Numbers: [57, 5] Generated Node #0,0,2: 62:[57, 5] Operation: 44-39=5 Moving to Node #0,0,2 Current State: 62:[57, 5], Operations: ['87-30=57', '44-39=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[30, 87, 44, 39], Operations: [] Exploring Operation: 87-30=57, Resulting Numbers: [44, 39, 57] Generated Node #0,0: 62:[44, 39, 57] Operation: 87-30=57 Moving to Node #0,0 Current State: 62:[44, 39, 57], Operations: ['87-30=57'] Exploring Operation: 44-39=5, Resulting Numbers: [57, 5] Generated Node #0,0,2: 62:[57, 5] Operation: 44-39=5 Moving to Node #0,0,2 Current State: 62:[57, 5], Operations: ['87-30=57', '44-39=5'] Exploring Operation: 57+5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 20, 9, 26, 49 ]
64
[ "20-9=11", "26+49=75", "75-11=64" ]
Current State: 64:[20, 9, 26, 49], Operations: [] Exploring Operation: 20-9=11, Resulting Numbers: [26, 49, 11] Generated Node #2: [26, 49, 11] from Operation: 20-9=11 Current State: 64:[26, 49, 11], Operations: ['20-9=11'] Exploring Operation: 26+49=75, Resulting Numbers: [11, 75] Generated Node #3: [11, 75] from Operation: 26+49=75 Current State: 64:[11, 75], Operations: ['20-9=11', '26+49=75'] Exploring Operation: 75-11=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[20, 9, 26, 49], Operations: [] Exploring Operation: 49-26=23, Resulting Numbers: [20, 9, 23] Generated Node #0,0: 64:[20, 9, 23] Operation: 49-26=23 Exploring Operation: 49-20=29, Resulting Numbers: [9, 26, 29] Generated Node #0,1: 64:[9, 26, 29] Operation: 49-20=29 Exploring Operation: 20+49=69, Resulting Numbers: [9, 26, 69] Generated Node #0,2: 64:[9, 26, 69] Operation: 20+49=69 Exploring Operation: 26+49=75, Resulting Numbers: [20, 9, 75] Generated Node #0,3: 64:[20, 9, 75] Operation: 26+49=75 Exploring Operation: 9+49=58, Resulting Numbers: [20, 26, 58] Generated Node #0,4: 64:[20, 26, 58] Operation: 9+49=58 Moving to Node #0,1 Current State: 64:[9, 26, 29], Operations: ['49-20=29'] Exploring Operation: 26+29=55, Resulting Numbers: [9, 55] Generated Node #0,1,0: 64:[9, 55] Operation: 26+29=55 Exploring Operation: 26-9=17, Resulting Numbers: [29, 17] Generated Node #0,1,1: 64:[29, 17] Operation: 26-9=17 Exploring Operation: 9+26=35, Resulting Numbers: [29, 35] Generated Node #0,1,2: 64:[29, 35] Operation: 9+26=35 Exploring Operation: 29-26=3, Resulting Numbers: [9, 3] Generated Node #0,1,3: 64:[9, 3] Operation: 29-26=3 Exploring Operation: 29-9=20, Resulting Numbers: [26, 20] Generated Node #0,1,4: 64:[26, 20] Operation: 29-9=20 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 64:[9, 3], Operations: ['49-20=29', '29-26=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,64 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,64 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[29, 17], Operations: ['49-20=29', '26-9=17'] Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,64 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,64 unequal: No Solution Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 64:[29, 35], Operations: ['49-20=29', '9+26=35'] Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[20, 9, 26, 49], Operations: [] Exploring Operation: 49-20=29, Resulting Numbers: [9, 26, 29] Generated Node #0,1: 64:[9, 26, 29] Operation: 49-20=29 Moving to Node #0,1 Current State: 64:[9, 26, 29], Operations: ['49-20=29'] Exploring Operation: 9+26=35, Resulting Numbers: [29, 35] Generated Node #0,1,2: 64:[29, 35] Operation: 9+26=35 Moving to Node #0,1,2 Current State: 64:[29, 35], Operations: ['49-20=29', '9+26=35'] Exploring Operation: 29+35=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 39, 70, 37, 62 ]
78
[ "39-37=2", "70*2=140", "140-62=78" ]
Current State: 78:[39, 70, 37, 62], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [70, 62, 2] Generated Node #2: [70, 62, 2] from Operation: 39-37=2 Current State: 78:[70, 62, 2], Operations: ['39-37=2'] Exploring Operation: 70*2=140, Resulting Numbers: [62, 140] Generated Node #3: [62, 140] from Operation: 70*2=140 Current State: 78:[62, 140], Operations: ['39-37=2', '70*2=140'] Exploring Operation: 140-62=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[39, 70, 37, 62], Operations: [] Exploring Operation: 70-62=8, Resulting Numbers: [39, 37, 8] Generated Node #0,0: 78:[39, 37, 8] Operation: 70-62=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[39, 37, 8], Operations: ['70-62=8'] Exploring Operation: 39-37=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 78:[8, 2] Operation: 39-37=2 Moving to Node #0,0,0 Current State: 78:[8, 2], Operations: ['70-62=8', '39-37=2'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 70, 15, 7 ]
29
[ "70/35=2", "7*2=14", "15+14=29" ]
Current State: 29:[35, 70, 15, 7], Operations: [] Exploring Operation: 70/35=2, Resulting Numbers: [15, 7, 2] Generated Node #2: [15, 7, 2] from Operation: 70/35=2 Current State: 29:[15, 7, 2], Operations: ['70/35=2'] Exploring Operation: 7*2=14, Resulting Numbers: [15, 14] Generated Node #3: [15, 14] from Operation: 7*2=14 Current State: 29:[15, 14], Operations: ['70/35=2', '7*2=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[35, 70, 15, 7], Operations: [] Exploring Operation: 70-35=35, Resulting Numbers: [15, 7, 35] Generated Node #0,0: 29:[15, 7, 35] Operation: 70-35=35 Exploring Operation: 70-7=63, Resulting Numbers: [35, 15, 63] Generated Node #0,1: 29:[35, 15, 63] Operation: 70-7=63 Exploring Operation: 70/7=10, Resulting Numbers: [35, 15, 10] Generated Node #0,2: 29:[35, 15, 10] Operation: 70/7=10 Exploring Operation: 70-15=55, Resulting Numbers: [35, 7, 55] Generated Node #0,3: 29:[35, 7, 55] Operation: 70-15=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[35, 15, 10], Operations: ['70/7=10'] Exploring Operation: 35-10=25, Resulting Numbers: [15, 25] Generated Node #0,2,0: 29:[15, 25] Operation: 35-10=25 Exploring Operation: 35+10=45, Resulting Numbers: [15, 45] Generated Node #0,2,1: 29:[15, 45] Operation: 35+10=45 Exploring Operation: 35-15=20, Resulting Numbers: [10, 20] Generated Node #0,2,2: 29:[10, 20] Operation: 35-15=20 Exploring Operation: 15+10=25, Resulting Numbers: [35, 25] Generated Node #0,2,3: 29:[35, 25] Operation: 15+10=25 Moving to Node #0,2,3 Current State: 29:[35, 25], Operations: ['70/7=10', '15+10=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,29 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[15, 25], Operations: ['70/7=10', '35-10=25'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,29 unequal: No Solution Moving to Node #0,2,2 Current State: 29:[10, 20], Operations: ['70/7=10', '35-15=20'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,29 unequal: No Solution Exploring Operation: 10*20=200, Resulting Numbers: [200] 200,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[15, 45], Operations: ['70/7=10', '35+10=45'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,29 unequal: No Solution Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 15*45=675, Resulting Numbers: [675] 675,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[15, 7, 35], Operations: ['70-35=35'] Exploring Operation: 35-7=28, Resulting Numbers: [15, 28] Generated Node #0,0,0: 29:[15, 28] Operation: 35-7=28 Exploring Operation: 15+7=22, Resulting Numbers: [35, 22] Generated Node #0,0,1: 29:[35, 22] Operation: 15+7=22 Exploring Operation: 15-7=8, Resulting Numbers: [35, 8] Generated Node #0,0,2: 29:[35, 8] Operation: 15-7=8 Exploring Operation: 7+35=42, Resulting Numbers: [15, 42] Generated Node #0,0,3: 29:[15, 42] Operation: 7+35=42 Moving to Node #0,0,1 Current State: 29:[35, 22], Operations: ['70-35=35', '15+7=22'] Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,29 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,29 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[15, 28], Operations: ['70-35=35', '35-7=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,29 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,29 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[15, 42], Operations: ['70-35=35', '7+35=42'] Exploring Operation: 15+42=57, Resulting Numbers: [57] 57,29 unequal: No Solution Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 15*42=630, Resulting Numbers: [630] 630,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[35, 8], Operations: ['70-35=35', '15-7=8'] Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,29 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,29 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[35, 15, 63], Operations: ['70-7=63'] Exploring Operation: 63-15=48, Resulting Numbers: [35, 48] Generated Node #0,1,0: 29:[35, 48] Operation: 63-15=48 Exploring Operation: 35+15=50, Resulting Numbers: [63, 50] Generated Node #0,1,1: 29:[63, 50] Operation: 35+15=50 Exploring Operation: 35-15=20, Resulting Numbers: [63, 20] Generated Node #0,1,2: 29:[63, 20] Operation: 35-15=20 Exploring Operation: 63-35=28, Resulting Numbers: [15, 28] Generated Node #0,1,3: 29:[15, 28] Operation: 63-35=28 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 29:[15, 28], Operations: ['70-7=63', '63-35=28'] Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,29 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,29 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,29 unequal: No Solution No 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: 29:[35, 48], Operations: ['70-7=63', '63-15=48'] Exploring Operation: 35*48=1680, Resulting Numbers: [1680] 1680,29 unequal: No Solution Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,29 unequal: No Solution No 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: 29:[63, 20], Operations: ['70-7=63', '35-15=20'] Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,29 unequal: No Solution Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,29 unequal: No Solution Exploring Operation: 63*20=1260, Resulting Numbers: [1260] 1260,29 unequal: No Solution No 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: 29:[63, 50], Operations: ['70-7=63', '35+15=50'] Exploring Operation: 63*50=3150, Resulting Numbers: [3150] 3150,29 unequal: No Solution Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 63+50=113, Resulting Numbers: [113] 113,29 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: 29:[35, 7, 55], Operations: ['70-15=55'] Exploring Operation: 55-7=48, Resulting Numbers: [35, 48] Generated Node #0,3,0: 29:[35, 48] Operation: 55-7=48 Exploring Operation: 35+7=42, Resulting Numbers: [55, 42] Generated Node #0,3,1: 29:[55, 42] Operation: 35+7=42 Exploring Operation: 35-7=28, Resulting Numbers: [55, 28] Generated Node #0,3,2: 29:[55, 28] Operation: 35-7=28 Exploring Operation: 55-35=20, Resulting Numbers: [7, 20] Generated Node #0,3,3: 29:[7, 20] Operation: 55-35=20 Moving to Node #0,3,0 Current State: 29:[35, 48], Operations: ['70-15=55', '55-7=48'] Exploring Operation: 48-35=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 35+48=83, Resulting Numbers: [83] 83,29 unequal: No Solution Exploring Operation: 35*48=1680, Resulting Numbers: [1680] 1680,29 unequal: No Solution Moving to Node #0,3,2 Current State: 29:[55, 28], Operations: ['70-15=55', '35-7=28'] Exploring Operation: 55+28=83, Resulting Numbers: [83] 83,29 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 55*28=1540, Resulting Numbers: [1540] 1540,29 unequal: No Solution Moving to Node #0,3,3 Current State: 29:[7, 20], Operations: ['70-15=55', '55-35=20'] Exploring Operation: 7*20=140, Resulting Numbers: [140] 140,29 unequal: No Solution Exploring Operation: 20-7=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 7+20=27, Resulting Numbers: [27] 27,29 unequal: No Solution Moving to Node #0,3,1 Current State: 29:[55, 42], Operations: ['70-15=55', '35+7=42'] Exploring Operation: 55+42=97, Resulting Numbers: [97] 97,29 unequal: No Solution Exploring Operation: 55-42=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 55*42=2310, Resulting Numbers: [2310] 2310,29 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
[ 5, 5, 27, 78 ]
51
[ "5-5=0", "78-27=51", "0+51=51" ]
Current State: 51:[5, 5, 27, 78], Operations: [] Exploring Operation: 5-5=0, Resulting Numbers: [27, 78, 0] Generated Node #2: [27, 78, 0] from Operation: 5-5=0 Current State: 51:[27, 78, 0], Operations: ['5-5=0'] Exploring Operation: 78-27=51, Resulting Numbers: [0, 51] Generated Node #3: [0, 51] from Operation: 78-27=51 Current State: 51:[0, 51], Operations: ['5-5=0', '78-27=51'] Exploring Operation: 0+51=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[5, 5, 27, 78], Operations: [] Exploring Operation: 27-5=22, Resulting Numbers: [5, 78, 22] Generated Node #0,0: 51:[5, 78, 22] Operation: 27-5=22 Exploring Operation: 78-27=51, Resulting Numbers: [5, 5, 51] Generated Node #0,1: 51:[5, 5, 51] Operation: 78-27=51 Moving to Node #0,1 Current State: 51:[5, 5, 51], Operations: ['78-27=51'] Exploring Operation: 5/5=1, Resulting Numbers: [51, 1] Generated Node #0,1,0: 51:[51, 1] Operation: 5/5=1 Exploring Operation: 5-5=0, Resulting Numbers: [51, 0] Generated Node #0,1,1: 51:[51, 0] Operation: 5-5=0 Moving to Node #0,0 Current State: 51:[5, 78, 22], Operations: ['27-5=22'] Exploring Operation: 78-5=73, Resulting Numbers: [22, 73] Generated Node #0,0,0: 51:[22, 73] Operation: 78-5=73 Exploring Operation: 78-22=56, Resulting Numbers: [5, 56] Generated Node #0,0,1: 51:[5, 56] Operation: 78-22=56 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[5, 56], Operations: ['27-5=22', '78-22=56'] Exploring Operation: 5+56=61, Resulting Numbers: [61] 61,51 unequal: No Solution Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[5, 5, 27, 78], Operations: [] Exploring Operation: 27-5=22, Resulting Numbers: [5, 78, 22] Generated Node #0,0: 51:[5, 78, 22] Operation: 27-5=22 Moving to Node #0,0 Current State: 51:[5, 78, 22], Operations: ['27-5=22'] Exploring Operation: 78-22=56, Resulting Numbers: [5, 56] Generated Node #0,0,1: 51:[5, 56] Operation: 78-22=56 Moving to Node #0,0,1 Current State: 51:[5, 56], Operations: ['27-5=22', '78-22=56'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 26, 55, 98, 99 ]
82
[ "26+55=81", "99-98=1", "81+1=82" ]
Current State: 82:[26, 55, 98, 99], Operations: [] Exploring Operation: 26+55=81, Resulting Numbers: [98, 99, 81] Generated Node #2: [98, 99, 81] from Operation: 26+55=81 Current State: 82:[98, 99, 81], Operations: ['26+55=81'] Exploring Operation: 99-98=1, Resulting Numbers: [81, 1] Generated Node #3: [81, 1] from Operation: 99-98=1 Current State: 82:[81, 1], Operations: ['26+55=81', '99-98=1'] Exploring Operation: 81+1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[26, 55, 98, 99], Operations: [] Exploring Operation: 99-55=44, Resulting Numbers: [26, 98, 44] Generated Node #0,0: 82:[26, 98, 44] Operation: 99-55=44 Exploring Operation: 98-55=43, Resulting Numbers: [26, 99, 43] Generated Node #0,1: 82:[26, 99, 43] Operation: 98-55=43 Exploring Operation: 26+55=81, Resulting Numbers: [98, 99, 81] Generated Node #0,2: 82:[98, 99, 81] Operation: 26+55=81 Exploring Operation: 99-98=1, Resulting Numbers: [26, 55, 1] Generated Node #0,3: 82:[26, 55, 1] Operation: 99-98=1 Exploring Operation: 99-26=73, Resulting Numbers: [55, 98, 73] Generated Node #0,4: 82:[55, 98, 73] Operation: 99-26=73 Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[26, 55, 1], Operations: ['99-98=1'] Exploring Operation: 26+55=81, Resulting Numbers: [1, 81] Generated Node #0,3,0: 82:[1, 81] Operation: 26+55=81 Exploring Operation: 55-26=29, Resulting Numbers: [1, 29] Generated Node #0,3,1: 82:[1, 29] Operation: 55-26=29 Exploring Operation: 26*1=26, Resulting Numbers: [55, 26] Generated Node #0,3,2: 82:[55, 26] Operation: 26*1=26 Exploring Operation: 55-1=54, Resulting Numbers: [26, 54] Generated Node #0,3,3: 82:[26, 54] Operation: 55-1=54 Exploring Operation: 26+1=27, Resulting Numbers: [55, 27] Generated Node #0,3,4: 82:[55, 27] Operation: 26+1=27 Moving to Node #0,3,0 Current State: 82:[1, 81], Operations: ['99-98=1', '26+55=81'] Exploring Operation: 81/1=81, Resulting Numbers: [81] 81,82 unequal: No Solution Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,82 unequal: No Solution Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[26, 55, 98, 99], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [26, 55, 1] Generated Node #0,3: 82:[26, 55, 1] Operation: 99-98=1 Moving to Node #0,3 Current State: 82:[26, 55, 1], Operations: ['99-98=1'] Exploring Operation: 26+55=81, Resulting Numbers: [1, 81] Generated Node #0,3,0: 82:[1, 81] Operation: 26+55=81 Moving to Node #0,3,0 Current State: 82:[1, 81], Operations: ['99-98=1', '26+55=81'] Exploring Operation: 1+81=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 52, 18, 57, 51 ]
74
[ "52-18=34", "57+51=108", "108-34=74" ]
Current State: 74:[52, 18, 57, 51], Operations: [] Exploring Operation: 52-18=34, Resulting Numbers: [57, 51, 34] Generated Node #2: [57, 51, 34] from Operation: 52-18=34 Current State: 74:[57, 51, 34], Operations: ['52-18=34'] Exploring Operation: 57+51=108, Resulting Numbers: [34, 108] Generated Node #3: [34, 108] from Operation: 57+51=108 Current State: 74:[34, 108], Operations: ['52-18=34', '57+51=108'] Exploring Operation: 108-34=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[52, 18, 57, 51], Operations: [] Exploring Operation: 57-52=5, Resulting Numbers: [18, 51, 5] Generated Node #0,0: 74:[18, 51, 5] Operation: 57-52=5 Exploring Operation: 18+57=75, Resulting Numbers: [52, 51, 75] Generated Node #0,1: 74:[52, 51, 75] Operation: 18+57=75 Exploring Operation: 57-18=39, Resulting Numbers: [52, 51, 39] Generated Node #0,2: 74:[52, 51, 39] Operation: 57-18=39 Exploring Operation: 52-18=34, Resulting Numbers: [57, 51, 34] Generated Node #0,3: 74:[57, 51, 34] Operation: 52-18=34 Moving to Node #0,1 Current State: 74:[52, 51, 75], Operations: ['18+57=75'] Exploring Operation: 52-51=1, Resulting Numbers: [75, 1] Generated Node #0,1,0: 74:[75, 1] Operation: 52-51=1 Exploring Operation: 75-52=23, Resulting Numbers: [51, 23] Generated Node #0,1,1: 74:[51, 23] Operation: 75-52=23 Exploring Operation: 52+51=103, Resulting Numbers: [75, 103] Generated Node #0,1,2: 74:[75, 103] Operation: 52+51=103 Exploring Operation: 75-51=24, Resulting Numbers: [52, 24] Generated Node #0,1,3: 74:[52, 24] Operation: 75-51=24 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[75, 1], Operations: ['18+57=75', '52-51=1'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[52, 18, 57, 51], Operations: [] Exploring Operation: 18+57=75, Resulting Numbers: [52, 51, 75] Generated Node #0,1: 74:[52, 51, 75] Operation: 18+57=75 Moving to Node #0,1 Current State: 74:[52, 51, 75], Operations: ['18+57=75'] Exploring Operation: 52-51=1, Resulting Numbers: [75, 1] Generated Node #0,1,0: 74:[75, 1] Operation: 52-51=1 Moving to Node #0,1,0 Current State: 74:[75, 1], Operations: ['18+57=75', '52-51=1'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 41, 93, 97, 26 ]
60
[ "41-26=15", "97-93=4", "15*4=60" ]
Current State: 60:[41, 93, 97, 26], Operations: [] Exploring Operation: 41-26=15, Resulting Numbers: [93, 97, 15] Generated Node #2: [93, 97, 15] from Operation: 41-26=15 Current State: 60:[93, 97, 15], Operations: ['41-26=15'] Exploring Operation: 97-93=4, Resulting Numbers: [15, 4] Generated Node #3: [15, 4] from Operation: 97-93=4 Current State: 60:[15, 4], Operations: ['41-26=15', '97-93=4'] Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[41, 93, 97, 26], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [41, 26, 4] Generated Node #0,0: 60:[41, 26, 4] Operation: 97-93=4 Moving to Node #0,0 Current State: 60:[41, 26, 4], Operations: ['97-93=4'] Exploring Operation: 41-26=15, Resulting Numbers: [4, 15] Generated Node #0,0,0: 60:[4, 15] Operation: 41-26=15 Moving to Node #0,0,0 Current State: 60:[4, 15], Operations: ['97-93=4', '41-26=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[41, 93, 97, 26], Operations: [] Exploring Operation: 97-93=4, Resulting Numbers: [41, 26, 4] Generated Node #0,0: 60:[41, 26, 4] Operation: 97-93=4 Moving to Node #0,0 Current State: 60:[41, 26, 4], Operations: ['97-93=4'] Exploring Operation: 41-26=15, Resulting Numbers: [4, 15] Generated Node #0,0,0: 60:[4, 15] Operation: 41-26=15 Moving to Node #0,0,0 Current State: 60:[4, 15], Operations: ['97-93=4', '41-26=15'] Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 86, 21, 3, 6 ]
81
[ "21-6=15", "15/3=5", "86-5=81" ]
Current State: 81:[86, 21, 3, 6], Operations: [] Exploring Operation: 21-6=15, Resulting Numbers: [86, 3, 15] Generated Node #2: [86, 3, 15] from Operation: 21-6=15 Current State: 81:[86, 3, 15], Operations: ['21-6=15'] Exploring Operation: 15/3=5, Resulting Numbers: [86, 5] Generated Node #3: [86, 5] from Operation: 15/3=5 Current State: 81:[86, 5], Operations: ['21-6=15', '15/3=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[86, 21, 3, 6], Operations: [] Exploring Operation: 86-3=83, Resulting Numbers: [21, 6, 83] Generated Node #0,0: 81:[21, 6, 83] Operation: 86-3=83 Exploring Operation: 21+6=27, Resulting Numbers: [86, 3, 27] Generated Node #0,1: 81:[86, 3, 27] Operation: 21+6=27 Exploring Operation: 86-6=80, Resulting Numbers: [21, 3, 80] Generated Node #0,2: 81:[21, 3, 80] Operation: 86-6=80 Exploring Operation: 21/3=7, Resulting Numbers: [86, 6, 7] Generated Node #0,3: 81:[86, 6, 7] Operation: 21/3=7 Moving to Node #0,1 Current State: 81:[86, 3, 27], Operations: ['21+6=27'] Exploring Operation: 27/3=9, Resulting Numbers: [86, 9] Generated Node #0,1,0: 81:[86, 9] Operation: 27/3=9 Exploring Operation: 86-3=83, Resulting Numbers: [27, 83] Generated Node #0,1,1: 81:[27, 83] Operation: 86-3=83 Exploring Operation: 3*27=81, Resulting Numbers: [86, 81] Generated Node #0,1,2: 81:[86, 81] Operation: 3*27=81 Exploring Operation: 86+3=89, Resulting Numbers: [27, 89] Generated Node #0,1,3: 81:[27, 89] Operation: 86+3=89 Moving to Node #0,2 Current State: 81:[21, 3, 80], Operations: ['86-6=80'] Exploring Operation: 21-3=18, Resulting Numbers: [80, 18] Generated Node #0,2,0: 81:[80, 18] Operation: 21-3=18 Exploring Operation: 21+3=24, Resulting Numbers: [80, 24] Generated Node #0,2,1: 81:[80, 24] Operation: 21+3=24 Exploring Operation: 21/3=7, Resulting Numbers: [80, 7] Generated Node #0,2,2: 81:[80, 7] Operation: 21/3=7 Exploring Operation: 3+80=83, Resulting Numbers: [21, 83] Generated Node #0,2,3: 81:[21, 83] Operation: 3+80=83 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[80, 7], Operations: ['86-6=80', '21/3=7'] Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,81 unequal: No Solution Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,81 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 #0,2,1 Current State: 81:[80, 24], Operations: ['86-6=80', '21+3=24'] Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,81 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,81 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 #0,2,3 Current State: 81:[21, 83], Operations: ['86-6=80', '3+80=83'] Exploring Operation: 83-21=62, Resulting Numbers: [62] 62,81 unequal: No Solution Exploring Operation: 21*83=1743, Resulting Numbers: [1743] 1743,81 unequal: No Solution Exploring Operation: 21+83=104, Resulting Numbers: [104] 104,81 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 #0,2,0 Current State: 81:[80, 18], Operations: ['86-6=80', '21-3=18'] Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,81 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,81 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: 81:[86, 6, 7], Operations: ['21/3=7'] Exploring Operation: 86-7=79, Resulting Numbers: [6, 79] Generated Node #0,3,0: 81:[6, 79] Operation: 86-7=79 Exploring Operation: 6+7=13, Resulting Numbers: [86, 13] Generated Node #0,3,1: 81:[86, 13] Operation: 6+7=13 Exploring Operation: 7-6=1, Resulting Numbers: [86, 1] Generated Node #0,3,2: 81:[86, 1] Operation: 7-6=1 Exploring Operation: 86-6=80, Resulting Numbers: [7, 80] Generated Node #0,3,3: 81:[7, 80] Operation: 86-6=80 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 81:[7, 80], Operations: ['21/3=7', '86-6=80'] Exploring Operation: 7*80=560, Resulting Numbers: [560] 560,81 unequal: No Solution Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 7+80=87, Resulting Numbers: [87] 87,81 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 #0,3,0 Current State: 81:[6, 79], Operations: ['21/3=7', '86-7=79'] Exploring Operation: 6*79=474, Resulting Numbers: [474] 474,81 unequal: No Solution Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,81 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 #0,3,2 Current State: 81:[86, 1], Operations: ['21/3=7', '7-6=1'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,81 unequal: No Solution Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,81 unequal: No Solution Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,81 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 #0,3,1 Current State: 81:[86, 13], Operations: ['21/3=7', '6+7=13'] Exploring Operation: 86*13=1118, Resulting Numbers: [1118] 1118,81 unequal: No Solution Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 86+13=99, Resulting Numbers: [99] 99,81 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: 81:[21, 6, 83], Operations: ['86-3=83'] Exploring Operation: 21-6=15, Resulting Numbers: [83, 15] Generated Node #0,0,0: 81:[83, 15] Operation: 21-6=15 Exploring Operation: 21+6=27, Resulting Numbers: [83, 27] Generated Node #0,0,1: 81:[83, 27] Operation: 21+6=27 Exploring Operation: 6+83=89, Resulting Numbers: [21, 89] Generated Node #0,0,2: 81:[21, 89] Operation: 6+83=89 Exploring Operation: 83-6=77, Resulting Numbers: [21, 77] Generated Node #0,0,3: 81:[21, 77] Operation: 83-6=77 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[83, 27], Operations: ['86-3=83', '21+6=27'] Exploring Operation: 83*27=2241, Resulting Numbers: [2241] 2241,81 unequal: No Solution Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 83+27=110, Resulting Numbers: [110] 110,81 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 #0,0,0 Current State: 81:[83, 15], Operations: ['86-3=83', '21-6=15'] Exploring Operation: 83*15=1245, Resulting Numbers: [1245] 1245,81 unequal: No Solution Exploring Operation: 83+15=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 83-15=68, Resulting Numbers: [68] 68,81 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 #0,0,3 Current State: 81:[21, 77], Operations: ['86-3=83', '83-6=77'] Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 21+77=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 21*77=1617, Resulting Numbers: [1617] 1617,81 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 #0,0,2 Current State: 81:[21, 89], Operations: ['86-3=83', '6+83=89'] Exploring Operation: 21*89=1869, Resulting Numbers: [1869] 1869,81 unequal: No Solution Exploring Operation: 89-21=68, Resulting Numbers: [68] 68,81 unequal: No Solution Exploring Operation: 21+89=110, Resulting Numbers: [110] 110,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 81:[27, 83], Operations: ['21+6=27', '86-3=83'] Exploring Operation: 27*83=2241, Resulting Numbers: [2241] 2241,81 unequal: No Solution Exploring Operation: 83-27=56, Resulting Numbers: [56] 56,81 unequal: No Solution Exploring Operation: 27+83=110, Resulting Numbers: [110] 110,81 unequal: No Solution Moving to Node #0,1,2 Current State: 81:[86, 81], Operations: ['21+6=27', '3*27=81'] Exploring Operation: 86+81=167, Resulting Numbers: [167] 167,81 unequal: No Solution Exploring Operation: 86-81=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 86*81=6966, Resulting Numbers: [6966] 6966,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[86, 9], Operations: ['21+6=27', '27/3=9'] Exploring Operation: 86-9=77, Resulting Numbers: [77] 77,81 unequal: No Solution Exploring Operation: 86+9=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 86*9=774, Resulting Numbers: [774] 774,81 unequal: No Solution Moving to Node #0,1,3 Current State: 81:[27, 89], Operations: ['21+6=27', '86+3=89'] Exploring Operation: 27*89=2403, Resulting Numbers: [2403] 2403,81 unequal: No Solution Exploring Operation: 27+89=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 89-27=62, Resulting Numbers: [62] 62,81 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 69, 80, 8, 4 ]
52
[ "80-69=11", "4*11=44", "8+44=52" ]
Current State: 52:[69, 80, 8, 4], Operations: [] Exploring Operation: 80-69=11, Resulting Numbers: [8, 4, 11] Generated Node #2: [8, 4, 11] from Operation: 80-69=11 Current State: 52:[8, 4, 11], Operations: ['80-69=11'] Exploring Operation: 4*11=44, Resulting Numbers: [8, 44] Generated Node #3: [8, 44] from Operation: 4*11=44 Current State: 52:[8, 44], Operations: ['80-69=11', '4*11=44'] Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[69, 80, 8, 4], Operations: [] Exploring Operation: 80-69=11, Resulting Numbers: [8, 4, 11] Generated Node #0,0: 52:[8, 4, 11] Operation: 80-69=11 Exploring Operation: 69-8=61, Resulting Numbers: [80, 4, 61] Generated Node #0,1: 52:[80, 4, 61] Operation: 69-8=61 Exploring Operation: 80/8=10, Resulting Numbers: [69, 4, 10] Generated Node #0,2: 52:[69, 4, 10] Operation: 80/8=10 Exploring Operation: 80/4=20, Resulting Numbers: [69, 8, 20] Generated Node #0,3: 52:[69, 8, 20] Operation: 80/4=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[8, 4, 11], Operations: ['80-69=11'] Exploring Operation: 8/4=2, Resulting Numbers: [11, 2] Generated Node #0,0,0: 52:[11, 2] Operation: 8/4=2 Exploring Operation: 8+4=12, Resulting Numbers: [11, 12] Generated Node #0,0,1: 52:[11, 12] Operation: 8+4=12 Exploring Operation: 11-8=3, Resulting Numbers: [4, 3] Generated Node #0,0,2: 52:[4, 3] Operation: 11-8=3 Exploring Operation: 8-4=4, Resulting Numbers: [11, 4] Generated Node #0,0,3: 52:[11, 4] Operation: 8-4=4 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[4, 3], Operations: ['80-69=11', '11-8=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[11, 2], Operations: ['80-69=11', '8/4=2'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,52 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 52:[11, 4], Operations: ['80-69=11', '8-4=4'] Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,52 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[11, 12], Operations: ['80-69=11', '8+4=12'] Exploring Operation: 11*12=132, Resulting Numbers: [132] 132,52 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 11+12=23, Resulting Numbers: [23] 23,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[69, 4, 10], Operations: ['80/8=10'] Exploring Operation: 10-4=6, Resulting Numbers: [69, 6] Generated Node #0,2,0: 52:[69, 6] Operation: 10-4=6 Exploring Operation: 69-4=65, Resulting Numbers: [10, 65] Generated Node #0,2,1: 52:[10, 65] Operation: 69-4=65 Exploring Operation: 4+10=14, Resulting Numbers: [69, 14] Generated Node #0,2,2: 52:[69, 14] Operation: 4+10=14 Exploring Operation: 69-10=59, Resulting Numbers: [4, 59] Generated Node #0,2,3: 52:[4, 59] Operation: 69-10=59 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[4, 59], Operations: ['80/8=10', '69-10=59'] Exploring Operation: 4+59=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 4*59=236, Resulting Numbers: [236] 236,52 unequal: No Solution Exploring Operation: 59-4=55, Resulting Numbers: [55] 55,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[10, 65], Operations: ['80/8=10', '69-4=65'] Exploring Operation: 10+65=75, Resulting Numbers: [75] 75,52 unequal: No Solution Exploring Operation: 10*65=650, Resulting Numbers: [650] 650,52 unequal: No Solution Exploring Operation: 65-10=55, Resulting Numbers: [55] 55,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[69, 14], Operations: ['80/8=10', '4+10=14'] Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,52 unequal: No Solution Exploring Operation: 69-14=55, Resulting Numbers: [55] 55,52 unequal: No Solution Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[69, 6], Operations: ['80/8=10', '10-4=6'] Exploring Operation: 69*6=414, Resulting Numbers: [414] 414,52 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,52 unequal: No Solution Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[69, 8, 20], Operations: ['80/4=20'] Exploring Operation: 69-20=49, Resulting Numbers: [8, 49] Generated Node #0,3,0: 52:[8, 49] Operation: 69-20=49 Exploring Operation: 69-8=61, Resulting Numbers: [20, 61] Generated Node #0,3,1: 52:[20, 61] Operation: 69-8=61 Exploring Operation: 8+20=28, Resulting Numbers: [69, 28] Generated Node #0,3,2: 52:[69, 28] Operation: 8+20=28 Exploring Operation: 20-8=12, Resulting Numbers: [69, 12] Generated Node #0,3,3: 52:[69, 12] Operation: 20-8=12 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 52:[8, 49], Operations: ['80/4=20', '69-20=49'] Exploring Operation: 8*49=392, Resulting Numbers: [392] 392,52 unequal: No Solution Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 52:[20, 61], Operations: ['80/4=20', '69-8=61'] Exploring Operation: 20*61=1220, Resulting Numbers: [1220] 1220,52 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,52 unequal: No Solution Exploring Operation: 20+61=81, Resulting Numbers: [81] 81,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 52:[69, 12], Operations: ['80/4=20', '20-8=12'] Exploring Operation: 69+12=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,52 unequal: No Solution Exploring Operation: 69*12=828, Resulting Numbers: [828] 828,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[69, 28], Operations: ['80/4=20', '8+20=28'] Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,52 unequal: No Solution Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,52 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[80, 4, 61], Operations: ['69-8=61'] Exploring Operation: 61-4=57, Resulting Numbers: [80, 57] Generated Node #0,1,0: 52:[80, 57] Operation: 61-4=57 Exploring Operation: 80-61=19, Resulting Numbers: [4, 19] Generated Node #0,1,1: 52:[4, 19] Operation: 80-61=19 Exploring Operation: 80-4=76, Resulting Numbers: [61, 76] Generated Node #0,1,2: 52:[61, 76] Operation: 80-4=76 Exploring Operation: 80/4=20, Resulting Numbers: [61, 20] Generated Node #0,1,3: 52:[61, 20] Operation: 80/4=20 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[4, 19], Operations: ['69-8=61', '80-61=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[61, 20], Operations: ['69-8=61', '80/4=20'] Exploring Operation: 61*20=1220, Resulting Numbers: [1220] 1220,52 unequal: No Solution Exploring Operation: 61+20=81, Resulting Numbers: [81] 81,52 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[80, 57], Operations: ['69-8=61', '61-4=57'] Exploring Operation: 80*57=4560, Resulting Numbers: [4560] 4560,52 unequal: No Solution Exploring Operation: 80-57=23, Resulting Numbers: [23] 23,52 unequal: No Solution Exploring Operation: 80+57=137, Resulting Numbers: [137] 137,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[61, 76], Operations: ['69-8=61', '80-4=76'] Exploring Operation: 76-61=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 61*76=4636, Resulting Numbers: [4636] 4636,52 unequal: No Solution Exploring Operation: 61+76=137, Resulting Numbers: [137] 137,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 75, 10, 84, 75 ]
73
[ "75/75=1", "84-10=74", "74-1=73" ]
Current State: 73:[75, 10, 84, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [10, 84, 1] Generated Node #2: [10, 84, 1] from Operation: 75/75=1 Current State: 73:[10, 84, 1], Operations: ['75/75=1'] Exploring Operation: 84-10=74, Resulting Numbers: [1, 74] Generated Node #3: [1, 74] from Operation: 84-10=74 Current State: 73:[1, 74], Operations: ['75/75=1', '84-10=74'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[75, 10, 84, 75], Operations: [] Exploring Operation: 75-10=65, Resulting Numbers: [84, 75, 65] Generated Node #0,0: 73:[84, 75, 65] Operation: 75-10=65 Exploring Operation: 75-10=65, Resulting Numbers: [75, 84, 65] Generated Node #0,1: 73:[75, 84, 65] Operation: 75-10=65 Exploring Operation: 75+10=85, Resulting Numbers: [84, 75, 85] Generated Node #0,2: 73:[84, 75, 85] Operation: 75+10=85 Exploring Operation: 84-10=74, Resulting Numbers: [75, 75, 74] Generated Node #0,3: 73:[75, 75, 74] Operation: 84-10=74 Moving to Node #0,3 Current State: 73:[75, 75, 74], Operations: ['84-10=74'] Exploring Operation: 75-74=1, Resulting Numbers: [75, 1] Generated Node #0,3,0: 73:[75, 1] Operation: 75-74=1 Exploring Operation: 75-75=0, Resulting Numbers: [74, 0] Generated Node #0,3,1: 73:[74, 0] Operation: 75-75=0 Exploring Operation: 75-74=1, Resulting Numbers: [75, 1] Generated Node #0,3,2: 73:[75, 1] Operation: 75-74=1 Exploring Operation: 75/75=1, Resulting Numbers: [74, 1] Generated Node #0,3,3: 73:[74, 1] Operation: 75/75=1 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 73:[74, 1], Operations: ['84-10=74', '75/75=1'] Exploring Operation: 74*1=74, Resulting Numbers: [74] 74,73 unequal: No Solution Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[75, 10, 84, 75], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [75, 75, 74] Generated Node #0,3: 73:[75, 75, 74] Operation: 84-10=74 Moving to Node #0,3 Current State: 73:[75, 75, 74], Operations: ['84-10=74'] Exploring Operation: 75/75=1, Resulting Numbers: [74, 1] Generated Node #0,3,3: 73:[74, 1] Operation: 75/75=1 Moving to Node #0,3,3 Current State: 73:[74, 1], Operations: ['84-10=74', '75/75=1'] Exploring Operation: 74-1=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 94, 16, 78, 20 ]
21
[ "94-16=78", "78/78=1", "20+1=21" ]
Current State: 21:[94, 16, 78, 20], Operations: [] Exploring Operation: 94-16=78, Resulting Numbers: [78, 20, 78] Generated Node #2: [78, 20, 78] from Operation: 94-16=78 Current State: 21:[78, 20, 78], Operations: ['94-16=78'] Exploring Operation: 78/78=1, Resulting Numbers: [20, 1] Generated Node #3: [20, 1] from Operation: 78/78=1 Current State: 21:[20, 1], Operations: ['94-16=78', '78/78=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[94, 16, 78, 20], Operations: [] Exploring Operation: 94-78=16, Resulting Numbers: [16, 20, 16] Generated Node #0,0: 21:[16, 20, 16] Operation: 94-78=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[16, 20, 16], Operations: ['94-78=16'] Exploring Operation: 16/16=1, Resulting Numbers: [20, 1] Generated Node #0,0,0: 21:[20, 1] Operation: 16/16=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[20, 1], Operations: ['94-78=16', '16/16=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[94, 16, 78, 20], Operations: [] Exploring Operation: 94-78=16, Resulting Numbers: [16, 20, 16] Generated Node #0,0: 21:[16, 20, 16] Operation: 94-78=16 Moving to Node #0,0 Current State: 21:[16, 20, 16], Operations: ['94-78=16'] Exploring Operation: 16/16=1, Resulting Numbers: [20, 1] Generated Node #0,0,0: 21:[20, 1] Operation: 16/16=1 Moving to Node #0,0,0 Current State: 21:[20, 1], Operations: ['94-78=16', '16/16=1'] Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 37, 6, 43, 11 ]
75
[ "37+6=43", "43-11=32", "43+32=75" ]
Current State: 75:[37, 6, 43, 11], Operations: [] Exploring Operation: 37+6=43, Resulting Numbers: [43, 11, 43] Generated Node #2: [43, 11, 43] from Operation: 37+6=43 Current State: 75:[43, 11, 43], Operations: ['37+6=43'] Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,75 equal: Goal Reached Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[37, 6, 43, 11], Operations: [] Exploring Operation: 37+43=80, Resulting Numbers: [6, 11, 80] Generated Node #0,0: 75:[6, 11, 80] Operation: 37+43=80 Exploring Operation: 43-37=6, Resulting Numbers: [6, 11, 6] Generated Node #0,1: 75:[6, 11, 6] Operation: 43-37=6 Exploring Operation: 43-11=32, Resulting Numbers: [37, 6, 32] Generated Node #0,2: 75:[37, 6, 32] Operation: 43-11=32 Exploring Operation: 37-11=26, Resulting Numbers: [6, 43, 26] Generated Node #0,3: 75:[6, 43, 26] Operation: 37-11=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[6, 11, 6], Operations: ['43-37=6'] Exploring Operation: 11-6=5, Resulting Numbers: [6, 5] Generated Node #0,1,0: 75:[6, 5] Operation: 11-6=5 Exploring Operation: 11+6=17, Resulting Numbers: [6, 17] Generated Node #0,1,1: 75:[6, 17] Operation: 11+6=17 Exploring Operation: 6+11=17, Resulting Numbers: [6, 17] Generated Node #0,1,2: 75:[6, 17] Operation: 6+11=17 Exploring Operation: 11-6=5, Resulting Numbers: [6, 5] Generated Node #0,1,3: 75:[6, 5] Operation: 11-6=5 Moving to Node #0,1,0 Current State: 75:[6, 5], Operations: ['43-37=6', '11-6=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[6, 5], Operations: ['43-37=6', '11-6=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,75 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,75 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[6, 17], Operations: ['43-37=6', '6+11=17'] Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[6, 17], Operations: ['43-37=6', '11+6=17'] Exploring Operation: 6*17=102, Resulting Numbers: [102] 102,75 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,75 unequal: No Solution Exploring Operation: 6+17=23, Resulting Numbers: [23] 23,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[6, 11, 80], Operations: ['37+43=80'] Exploring Operation: 6+11=17, Resulting Numbers: [80, 17] Generated Node #0,0,0: 75:[80, 17] Operation: 6+11=17 Exploring Operation: 11-6=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 75:[80, 5] Operation: 11-6=5 Exploring Operation: 80-11=69, Resulting Numbers: [6, 69] Generated Node #0,0,2: 75:[6, 69] Operation: 80-11=69 Exploring Operation: 80-6=74, Resulting Numbers: [11, 74] Generated Node #0,0,3: 75:[11, 74] Operation: 80-6=74 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 75:[80, 5], Operations: ['37+43=80', '11-6=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[37, 6, 43, 11], Operations: [] Exploring Operation: 37+43=80, Resulting Numbers: [6, 11, 80] Generated Node #0,0: 75:[6, 11, 80] Operation: 37+43=80 Moving to Node #0,0 Current State: 75:[6, 11, 80], Operations: ['37+43=80'] Exploring Operation: 11-6=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 75:[80, 5] Operation: 11-6=5 Moving to Node #0,0,1 Current State: 75:[80, 5], Operations: ['37+43=80', '11-6=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 92, 77, 3, 11 ]
50
[ "92-11=81", "81/3=27", "77-27=50" ]
Current State: 50:[92, 77, 3, 11], Operations: [] Exploring Operation: 92-11=81, Resulting Numbers: [77, 3, 81] Generated Node #2: [77, 3, 81] from Operation: 92-11=81 Current State: 50:[77, 3, 81], Operations: ['92-11=81'] Exploring Operation: 81/3=27, Resulting Numbers: [77, 27] Generated Node #3: [77, 27] from Operation: 81/3=27 Current State: 50:[77, 27], Operations: ['92-11=81', '81/3=27'] Exploring Operation: 77-27=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[92, 77, 3, 11], Operations: [] Exploring Operation: 77/11=7, Resulting Numbers: [92, 3, 7] Generated Node #0,0: 50:[92, 3, 7] Operation: 77/11=7 Exploring Operation: 92-77=15, Resulting Numbers: [3, 11, 15] Generated Node #0,1: 50:[3, 11, 15] Operation: 92-77=15 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[3, 11, 15], Operations: ['92-77=15'] Exploring Operation: 11+15=26, Resulting Numbers: [3, 26] Generated Node #0,1,0: 50:[3, 26] Operation: 11+15=26 Exploring Operation: 15/3=5, Resulting Numbers: [11, 5] Generated Node #0,1,1: 50:[11, 5] Operation: 15/3=5 Moving to Node #0,1,1 Current State: 50:[11, 5], Operations: ['92-77=15', '15/3=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,50 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[3, 26], Operations: ['92-77=15', '11+15=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,50 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[92, 3, 7], Operations: ['77/11=7'] Exploring Operation: 92-7=85, Resulting Numbers: [3, 85] Generated Node #0,0,0: 50:[3, 85] Operation: 92-7=85 Exploring Operation: 92-3=89, Resulting Numbers: [7, 89] Generated Node #0,0,1: 50:[7, 89] Operation: 92-3=89 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[3, 85], Operations: ['77/11=7', '92-7=85'] Exploring Operation: 3+85=88, Resulting Numbers: [88] 88,50 unequal: No Solution Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,50 unequal: No Solution No 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: 50:[7, 89], Operations: ['77/11=7', '92-3=89'] Exploring Operation: 89-7=82, Resulting Numbers: [82] 82,50 unequal: No Solution Exploring Operation: 7+89=96, Resulting Numbers: [96] 96,50 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
[ 60, 70, 86, 22 ]
54
[ "70-60=10", "86-22=64", "64-10=54" ]
Current State: 54:[60, 70, 86, 22], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [86, 22, 10] Generated Node #2: [86, 22, 10] from Operation: 70-60=10 Current State: 54:[86, 22, 10], Operations: ['70-60=10'] Exploring Operation: 86-22=64, Resulting Numbers: [10, 64] Generated Node #3: [10, 64] from Operation: 86-22=64 Current State: 54:[10, 64], Operations: ['70-60=10', '86-22=64'] Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[60, 70, 86, 22], Operations: [] Exploring Operation: 70-60=10, Resulting Numbers: [86, 22, 10] Generated Node #0,0: 54:[86, 22, 10] Operation: 70-60=10 Exploring Operation: 86-22=64, Resulting Numbers: [60, 70, 64] Generated Node #0,1: 54:[60, 70, 64] Operation: 86-22=64 Exploring Operation: 86-60=26, Resulting Numbers: [70, 22, 26] Generated Node #0,2: 54:[70, 22, 26] Operation: 86-60=26 Exploring Operation: 86-70=16, Resulting Numbers: [60, 22, 16] Generated Node #0,3: 54:[60, 22, 16] Operation: 86-70=16 Moving to Node #0,3 Current State: 54:[60, 22, 16], Operations: ['86-70=16'] Exploring Operation: 22-16=6, Resulting Numbers: [60, 6] Generated Node #0,3,0: 54:[60, 6] Operation: 22-16=6 Exploring Operation: 60-16=44, Resulting Numbers: [22, 44] Generated Node #0,3,1: 54:[22, 44] Operation: 60-16=44 Exploring Operation: 60-22=38, Resulting Numbers: [16, 38] Generated Node #0,3,2: 54:[16, 38] Operation: 60-22=38 Exploring Operation: 22+16=38, Resulting Numbers: [60, 38] Generated Node #0,3,3: 54:[60, 38] Operation: 22+16=38 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 54:[60, 6], Operations: ['86-70=16', '22-16=6'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[60, 70, 86, 22], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [60, 22, 16] Generated Node #0,3: 54:[60, 22, 16] Operation: 86-70=16 Moving to Node #0,3 Current State: 54:[60, 22, 16], Operations: ['86-70=16'] Exploring Operation: 22-16=6, Resulting Numbers: [60, 6] Generated Node #0,3,0: 54:[60, 6] Operation: 22-16=6 Moving to Node #0,3,0 Current State: 54:[60, 6], Operations: ['86-70=16', '22-16=6'] Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 99, 25, 81, 12 ]
55
[ "99+25=124", "81-12=69", "124-69=55" ]
Current State: 55:[99, 25, 81, 12], Operations: [] Exploring Operation: 99+25=124, Resulting Numbers: [81, 12, 124] Generated Node #2: [81, 12, 124] from Operation: 99+25=124 Current State: 55:[81, 12, 124], Operations: ['99+25=124'] Exploring Operation: 81-12=69, Resulting Numbers: [124, 69] Generated Node #3: [124, 69] from Operation: 81-12=69 Current State: 55:[124, 69], Operations: ['99+25=124', '81-12=69'] Exploring Operation: 124-69=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[99, 25, 81, 12], Operations: [] Exploring Operation: 99-25=74, Resulting Numbers: [81, 12, 74] Generated Node #0,0: 55:[81, 12, 74] Operation: 99-25=74 Exploring Operation: 99-81=18, Resulting Numbers: [25, 12, 18] Generated Node #0,1: 55:[25, 12, 18] Operation: 99-81=18 Exploring Operation: 81-25=56, Resulting Numbers: [99, 12, 56] Generated Node #0,2: 55:[99, 12, 56] Operation: 81-25=56 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[25, 12, 18], Operations: ['99-81=18'] Exploring Operation: 25-18=7, Resulting Numbers: [12, 7] Generated Node #0,1,0: 55:[12, 7] Operation: 25-18=7 Exploring Operation: 25+18=43, Resulting Numbers: [12, 43] Generated Node #0,1,1: 55:[12, 43] Operation: 25+18=43 Exploring Operation: 25-12=13, Resulting Numbers: [18, 13] Generated Node #0,1,2: 55:[18, 13] Operation: 25-12=13 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[12, 7], Operations: ['99-81=18', '25-18=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[18, 13], Operations: ['99-81=18', '25-12=13'] Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,55 unequal: No Solution Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[12, 43], Operations: ['99-81=18', '25+18=43'] Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[99, 25, 81, 12], Operations: [] Exploring Operation: 99-81=18, Resulting Numbers: [25, 12, 18] Generated Node #0,1: 55:[25, 12, 18] Operation: 99-81=18 Moving to Node #0,1 Current State: 55:[25, 12, 18], Operations: ['99-81=18'] Exploring Operation: 25+18=43, Resulting Numbers: [12, 43] Generated Node #0,1,1: 55:[12, 43] Operation: 25+18=43 Moving to Node #0,1,1 Current State: 55:[12, 43], Operations: ['99-81=18', '25+18=43'] Exploring Operation: 12+43=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 87, 57, 1, 70 ]
74
[ "87+57=144", "1*70=70", "144-70=74" ]
Current State: 74:[87, 57, 1, 70], Operations: [] Exploring Operation: 87+57=144, Resulting Numbers: [1, 70, 144] Generated Node #2: [1, 70, 144] from Operation: 87+57=144 Current State: 74:[1, 70, 144], Operations: ['87+57=144'] Exploring Operation: 1*70=70, Resulting Numbers: [144, 70] Generated Node #3: [144, 70] from Operation: 1*70=70 Current State: 74:[144, 70], Operations: ['87+57=144', '1*70=70'] Exploring Operation: 144-70=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[87, 57, 1, 70], Operations: [] Exploring Operation: 87-1=86, Resulting Numbers: [57, 70, 86] Generated Node #0,0: 74:[57, 70, 86] Operation: 87-1=86 Exploring Operation: 87-70=17, Resulting Numbers: [57, 1, 17] Generated Node #0,1: 74:[57, 1, 17] Operation: 87-70=17 Exploring Operation: 70-57=13, Resulting Numbers: [87, 1, 13] Generated Node #0,2: 74:[87, 1, 13] Operation: 70-57=13 Exploring Operation: 87-57=30, Resulting Numbers: [1, 70, 30] Generated Node #0,3: 74:[1, 70, 30] Operation: 87-57=30 Moving to Node #0,3 Current State: 74:[1, 70, 30], Operations: ['87-57=30'] Exploring Operation: 1+30=31, Resulting Numbers: [70, 31] Generated Node #0,3,0: 74:[70, 31] Operation: 1+30=31 Exploring Operation: 1*70=70, Resulting Numbers: [30, 70] Generated Node #0,3,1: 74:[30, 70] Operation: 1*70=70 Exploring Operation: 70-30=40, Resulting Numbers: [1, 40] Generated Node #0,3,2: 74:[1, 40] Operation: 70-30=40 Exploring Operation: 1+70=71, Resulting Numbers: [30, 71] Generated Node #0,3,3: 74:[30, 71] Operation: 1+70=71 Moving to Node #0,2 Current State: 74:[87, 1, 13], Operations: ['70-57=13'] Exploring Operation: 87*1=87, Resulting Numbers: [13, 87] Generated Node #0,2,0: 74:[13, 87] Operation: 87*1=87 Exploring Operation: 87-13=74, Resulting Numbers: [1, 74] Generated Node #0,2,1: 74:[1, 74] Operation: 87-13=74 Exploring Operation: 13-1=12, Resulting Numbers: [87, 12] Generated Node #0,2,2: 74:[87, 12] Operation: 13-1=12 Exploring Operation: 87-1=86, Resulting Numbers: [13, 86] Generated Node #0,2,3: 74:[13, 86] Operation: 87-1=86 Moving to Node #0,1 Current State: 74:[57, 1, 17], Operations: ['87-70=17'] Exploring Operation: 57+17=74, Resulting Numbers: [1, 74] Generated Node #0,1,0: 74:[1, 74] Operation: 57+17=74 Exploring Operation: 57+1=58, Resulting Numbers: [17, 58] Generated Node #0,1,1: 74:[17, 58] Operation: 57+1=58 Exploring Operation: 57-17=40, Resulting Numbers: [1, 40] Generated Node #0,1,2: 74:[1, 40] Operation: 57-17=40 Exploring Operation: 17-1=16, Resulting Numbers: [57, 16] Generated Node #0,1,3: 74:[57, 16] Operation: 17-1=16 Moving to Node #0,0 Current State: 74:[57, 70, 86], Operations: ['87-1=86'] Exploring Operation: 70-57=13, Resulting Numbers: [86, 13] Generated Node #0,0,0: 74:[86, 13] Operation: 70-57=13 Exploring Operation: 86-57=29, Resulting Numbers: [70, 29] Generated Node #0,0,1: 74:[70, 29] Operation: 86-57=29 Exploring Operation: 86-70=16, Resulting Numbers: [57, 16] Generated Node #0,0,2: 74:[57, 16] Operation: 86-70=16 Exploring Operation: 57+70=127, Resulting Numbers: [86, 127] Generated Node #0,0,3: 74:[86, 127] Operation: 57+70=127 Moving to Node #0,2,1 Current State: 74:[1, 74], Operations: ['70-57=13', '87-13=74'] Exploring Operation: 1*74=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[87, 57, 1, 70], Operations: [] Exploring Operation: 70-57=13, Resulting Numbers: [87, 1, 13] Generated Node #0,2: 74:[87, 1, 13] Operation: 70-57=13 Moving to Node #0,2 Current State: 74:[87, 1, 13], Operations: ['70-57=13'] Exploring Operation: 87-13=74, Resulting Numbers: [1, 74] Generated Node #0,2,1: 74:[1, 74] Operation: 87-13=74 Moving to Node #0,2,1 Current State: 74:[1, 74], Operations: ['70-57=13', '87-13=74'] Exploring Operation: 1*74=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
0.978299
hs_4
sum_heuristic
[ 28, 76, 56, 61 ]
64
[ "61-56=5", "28*5=140", "140-76=64" ]
Current State: 64:[28, 76, 56, 61], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [28, 76, 5] Generated Node #2: [28, 76, 5] from Operation: 61-56=5 Current State: 64:[28, 76, 5], Operations: ['61-56=5'] Exploring Operation: 28*5=140, Resulting Numbers: [76, 140] Generated Node #3: [76, 140] from Operation: 28*5=140 Current State: 64:[76, 140], Operations: ['61-56=5', '28*5=140'] Exploring Operation: 140-76=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[28, 76, 56, 61], Operations: [] Exploring Operation: 76-56=20, Resulting Numbers: [28, 61, 20] Generated Node #0,0: 64:[28, 61, 20] Operation: 76-56=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[28, 61, 20], Operations: ['76-56=20'] Exploring Operation: 28-20=8, Resulting Numbers: [61, 8] Generated Node #0,0,0: 64:[61, 8] Operation: 28-20=8 Moving to Node #0,0,0 Current State: 64:[61, 8], Operations: ['76-56=20', '28-20=8'] Exploring Operation: 61+8=69, Resulting Numbers: [69] 69,64 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
[ 22, 25, 84, 65 ]
37
[ "25-22=3", "84/3=28", "65-28=37" ]
Current State: 37:[22, 25, 84, 65], Operations: [] Exploring Operation: 25-22=3, Resulting Numbers: [84, 65, 3] Generated Node #2: [84, 65, 3] from Operation: 25-22=3 Current State: 37:[84, 65, 3], Operations: ['25-22=3'] Exploring Operation: 84/3=28, Resulting Numbers: [65, 28] Generated Node #3: [65, 28] from Operation: 84/3=28 Current State: 37:[65, 28], Operations: ['25-22=3', '84/3=28'] Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[22, 25, 84, 65], Operations: [] Exploring Operation: 84-22=62, Resulting Numbers: [25, 65, 62] Generated Node #0,0: 37:[25, 65, 62] Operation: 84-22=62 Exploring Operation: 84-65=19, Resulting Numbers: [22, 25, 19] Generated Node #0,1: 37:[22, 25, 19] Operation: 84-65=19 Moving to Node #0,1 Current State: 37:[22, 25, 19], Operations: ['84-65=19'] Exploring Operation: 25+19=44, Resulting Numbers: [22, 44] Generated Node #0,1,0: 37:[22, 44] Operation: 25+19=44 Exploring Operation: 22+19=41, Resulting Numbers: [25, 41] Generated Node #0,1,1: 37:[25, 41] Operation: 22+19=41 Moving to Node #0,0 Current State: 37:[25, 65, 62], Operations: ['84-22=62'] Exploring Operation: 62-25=37, Resulting Numbers: [65, 37] Generated Node #0,0,0: 37:[65, 37] Operation: 62-25=37 Exploring Operation: 65-25=40, Resulting Numbers: [62, 40] Generated Node #0,0,1: 37:[62, 40] Operation: 65-25=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[65, 37], Operations: ['84-22=62', '62-25=37'] Exploring Operation: 65+37=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 65-37=28, Resulting Numbers: [28] 28,37 unequal: No Solution No 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: 37:[62, 40], Operations: ['84-22=62', '65-25=40'] Exploring Operation: 62+40=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 37:[25, 41], Operations: ['84-65=19', '22+19=41'] Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,37 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[22, 44], Operations: ['84-65=19', '25+19=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,37 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 72, 15, 20 ]
80
[ "72-12=60", "60/15=4", "20*4=80" ]
Current State: 80:[12, 72, 15, 20], Operations: [] Exploring Operation: 72-12=60, Resulting Numbers: [15, 20, 60] Generated Node #2: [15, 20, 60] from Operation: 72-12=60 Current State: 80:[15, 20, 60], Operations: ['72-12=60'] Exploring Operation: 60/15=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 60/15=4 Current State: 80:[20, 4], Operations: ['72-12=60', '60/15=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[12, 72, 15, 20], Operations: [] Exploring Operation: 15-12=3, Resulting Numbers: [72, 20, 3] Generated Node #0,0: 80:[72, 20, 3] Operation: 15-12=3 Exploring Operation: 12+72=84, Resulting Numbers: [15, 20, 84] Generated Node #0,1: 80:[15, 20, 84] Operation: 12+72=84 Exploring Operation: 20-12=8, Resulting Numbers: [72, 15, 8] Generated Node #0,2: 80:[72, 15, 8] Operation: 20-12=8 Exploring Operation: 72/12=6, Resulting Numbers: [15, 20, 6] Generated Node #0,3: 80:[15, 20, 6] Operation: 72/12=6 Moving to Node #0,3 Current State: 80:[15, 20, 6], Operations: ['72/12=6'] Exploring Operation: 15+6=21, Resulting Numbers: [20, 21] Generated Node #0,3,0: 80:[20, 21] Operation: 15+6=21 Exploring Operation: 20-15=5, Resulting Numbers: [6, 5] Generated Node #0,3,1: 80:[6, 5] Operation: 20-15=5 Exploring Operation: 15-6=9, Resulting Numbers: [20, 9] Generated Node #0,3,2: 80:[20, 9] Operation: 15-6=9 Exploring Operation: 20-6=14, Resulting Numbers: [15, 14] Generated Node #0,3,3: 80:[15, 14] Operation: 20-6=14 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[20, 21], Operations: ['72/12=6', '15+6=21'] Exploring Operation: 20+21=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 21-20=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 20*21=420, Resulting Numbers: [420] 420,80 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 #0,3,1 Current State: 80:[6, 5], Operations: ['72/12=6', '20-15=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,80 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 #0,3,2 Current State: 80:[20, 9], Operations: ['72/12=6', '15-6=9'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,80 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,80 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 #0,3,3 Current State: 80:[15, 14], Operations: ['72/12=6', '20-6=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,80 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 80:[15, 20, 84], Operations: ['12+72=84'] Exploring Operation: 15+20=35, Resulting Numbers: [84, 35] Generated Node #0,1,0: 80:[84, 35] Operation: 15+20=35 Exploring Operation: 84-20=64, Resulting Numbers: [15, 64] Generated Node #0,1,1: 80:[15, 64] Operation: 84-20=64 Exploring Operation: 84-15=69, Resulting Numbers: [20, 69] Generated Node #0,1,2: 80:[20, 69] Operation: 84-15=69 Exploring Operation: 20-15=5, Resulting Numbers: [84, 5] Generated Node #0,1,3: 80:[84, 5] Operation: 20-15=5 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[84, 5], Operations: ['12+72=84', '20-15=5'] Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,80 unequal: No Solution Exploring Operation: 84*5=420, Resulting Numbers: [420] 420,80 unequal: No Solution Exploring Operation: 84+5=89, Resulting Numbers: [89] 89,80 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 #0,1,0 Current State: 80:[84, 35], Operations: ['12+72=84', '15+20=35'] Exploring Operation: 84*35=2940, Resulting Numbers: [2940] 2940,80 unequal: No Solution Exploring Operation: 84+35=119, Resulting Numbers: [119] 119,80 unequal: No Solution Exploring Operation: 84-35=49, Resulting Numbers: [49] 49,80 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 #0,1,2 Current State: 80:[20, 69], Operations: ['12+72=84', '84-15=69'] Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 20*69=1380, Resulting Numbers: [1380] 1380,80 unequal: No Solution Exploring Operation: 20+69=89, Resulting Numbers: [89] 89,80 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 #0,1,1 Current State: 80:[15, 64], Operations: ['12+72=84', '84-20=64'] Exploring Operation: 15*64=960, Resulting Numbers: [960] 960,80 unequal: No Solution Exploring Operation: 64-15=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 15+64=79, Resulting Numbers: [79] 79,80 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: 80:[72, 15, 8], Operations: ['20-12=8'] Exploring Operation: 72+8=80, Resulting Numbers: [15, 80] Generated Node #0,2,0: 80:[15, 80] Operation: 72+8=80 Exploring Operation: 72/8=9, Resulting Numbers: [15, 9] Generated Node #0,2,1: 80:[15, 9] Operation: 72/8=9 Exploring Operation: 72+15=87, Resulting Numbers: [8, 87] Generated Node #0,2,2: 80:[8, 87] Operation: 72+15=87 Exploring Operation: 15-8=7, Resulting Numbers: [72, 7] Generated Node #0,2,3: 80:[72, 7] Operation: 15-8=7 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[15, 80], Operations: ['20-12=8', '72+8=80'] Exploring Operation: 15+80=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 80-15=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 15*80=1200, Resulting Numbers: [1200] 1200,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[15, 9], Operations: ['20-12=8', '72/8=9'] Exploring Operation: 15*9=135, Resulting Numbers: [135] 135,80 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 15+9=24, Resulting Numbers: [24] 24,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[8, 87], Operations: ['20-12=8', '72+15=87'] Exploring Operation: 8*87=696, Resulting Numbers: [696] 696,80 unequal: No Solution Exploring Operation: 8+87=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[72, 7], Operations: ['20-12=8', '15-8=7'] Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,80 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,80 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: 80:[72, 20, 3], Operations: ['15-12=3'] Exploring Operation: 72/3=24, Resulting Numbers: [20, 24] Generated Node #0,0,0: 80:[20, 24] Operation: 72/3=24 Exploring Operation: 72+3=75, Resulting Numbers: [20, 75] Generated Node #0,0,1: 80:[20, 75] Operation: 72+3=75 Exploring Operation: 20-3=17, Resulting Numbers: [72, 17] Generated Node #0,0,2: 80:[72, 17] Operation: 20-3=17 Exploring Operation: 72-3=69, Resulting Numbers: [20, 69] Generated Node #0,0,3: 80:[20, 69] Operation: 72-3=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[20, 24], Operations: ['15-12=3', '72/3=24'] Exploring Operation: 20+24=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 24-20=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 20*24=480, Resulting Numbers: [480] 480,80 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:[20, 75], Operations: ['15-12=3', '72+3=75'] Exploring Operation: 20*75=1500, Resulting Numbers: [1500] 1500,80 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 20+75=95, Resulting Numbers: [95] 95,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[72, 17], Operations: ['15-12=3', '20-3=17'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 72*17=1224, Resulting Numbers: [1224] 1224,80 unequal: No Solution Exploring Operation: 72+17=89, Resulting Numbers: [89] 89,80 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 #0,0,3 Current State: 80:[20, 69], Operations: ['15-12=3', '72-3=69'] Exploring Operation: 20+69=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 20*69=1380, Resulting Numbers: [1380] 1380,80 unequal: No Solution Exploring Operation: 69-20=49, Resulting Numbers: [49] 49,80 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
[ 81, 88, 3, 44 ]
81
[ "88/44=2", "3-2=1", "81*1=81" ]
Current State: 81:[81, 88, 3, 44], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [81, 3, 2] Generated Node #2: [81, 3, 2] from Operation: 88/44=2 Current State: 81:[81, 3, 2], Operations: ['88/44=2'] Exploring Operation: 3-2=1, Resulting Numbers: [81, 1] Generated Node #3: [81, 1] from Operation: 3-2=1 Current State: 81:[81, 1], Operations: ['88/44=2', '3-2=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[81, 88, 3, 44], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [81, 3, 2] Generated Node #0,0: 81:[81, 3, 2] Operation: 88/44=2 Exploring Operation: 88-44=44, Resulting Numbers: [81, 3, 44] Generated Node #0,1: 81:[81, 3, 44] Operation: 88-44=44 Exploring Operation: 81-44=37, Resulting Numbers: [88, 3, 37] Generated Node #0,2: 81:[88, 3, 37] Operation: 81-44=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[81, 3, 2], Operations: ['88/44=2'] Exploring Operation: 81-2=79, Resulting Numbers: [3, 79] Generated Node #0,0,0: 81:[3, 79] Operation: 81-2=79 Exploring Operation: 81+2=83, Resulting Numbers: [3, 83] Generated Node #0,0,1: 81:[3, 83] Operation: 81+2=83 Exploring Operation: 81/3=27, Resulting Numbers: [2, 27] Generated Node #0,0,2: 81:[2, 27] Operation: 81/3=27 Moving to Node #0,0,2 Current State: 81:[2, 27], Operations: ['88/44=2', '81/3=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,81 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,81 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[3, 79], Operations: ['88/44=2', '81-2=79'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[3, 83], Operations: ['88/44=2', '81+2=83'] Exploring Operation: 3+83=86, Resulting Numbers: [86] 86,81 unequal: No Solution Exploring Operation: 3*83=249, Resulting Numbers: [249] 249,81 unequal: No Solution Exploring Operation: 83-3=80, Resulting Numbers: [80] 80,81 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 #0,1 Current State: 81:[81, 3, 44], Operations: ['88-44=44'] Exploring Operation: 81/3=27, Resulting Numbers: [44, 27] Generated Node #0,1,0: 81:[44, 27] Operation: 81/3=27 Exploring Operation: 81-44=37, Resulting Numbers: [3, 37] Generated Node #0,1,1: 81:[3, 37] Operation: 81-44=37 Exploring Operation: 44-3=41, Resulting Numbers: [81, 41] Generated Node #0,1,2: 81:[81, 41] Operation: 44-3=41 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[3, 37], Operations: ['88-44=44', '81-44=37'] Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,81 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,81 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,81 unequal: No Solution No 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: 81:[81, 41], Operations: ['88-44=44', '44-3=41'] Exploring Operation: 81+41=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 81*41=3321, Resulting Numbers: [3321] 3321,81 unequal: No Solution Exploring Operation: 81-41=40, Resulting Numbers: [40] 40,81 unequal: No Solution No 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: 81:[44, 27], Operations: ['88-44=44', '81/3=27'] Exploring Operation: 44+27=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 44-27=17, Resulting Numbers: [17] 17,81 unequal: No Solution Exploring Operation: 44*27=1188, Resulting Numbers: [1188] 1188,81 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: 81:[88, 3, 37], Operations: ['81-44=37'] Exploring Operation: 37-3=34, Resulting Numbers: [88, 34] Generated Node #0,2,0: 81:[88, 34] Operation: 37-3=34 Exploring Operation: 88-3=85, Resulting Numbers: [37, 85] Generated Node #0,2,1: 81:[37, 85] Operation: 88-3=85 Exploring Operation: 88+3=91, Resulting Numbers: [37, 91] Generated Node #0,2,2: 81:[37, 91] Operation: 88+3=91 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[88, 34], Operations: ['81-44=37', '37-3=34'] Exploring Operation: 88+34=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 88*34=2992, Resulting Numbers: [2992] 2992,81 unequal: No Solution Exploring Operation: 88-34=54, Resulting Numbers: [54] 54,81 unequal: No Solution No 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: 81:[37, 85], Operations: ['81-44=37', '88-3=85'] Exploring Operation: 37+85=122, Resulting Numbers: [122] 122,81 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,81 unequal: No Solution Exploring Operation: 37*85=3145, Resulting Numbers: [3145] 3145,81 unequal: No Solution No 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: 81:[37, 91], Operations: ['81-44=37', '88+3=91'] Exploring Operation: 37+91=128, Resulting Numbers: [128] 128,81 unequal: No Solution Exploring Operation: 91-37=54, Resulting Numbers: [54] 54,81 unequal: No Solution Exploring Operation: 37*91=3367, Resulting Numbers: [3367] 3367,81 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
[ 27, 49, 59, 25 ]
21
[ "49+59=108", "108/27=4", "25-4=21" ]
Current State: 21:[27, 49, 59, 25], Operations: [] Exploring Operation: 49+59=108, Resulting Numbers: [27, 25, 108] Generated Node #2: [27, 25, 108] from Operation: 49+59=108 Current State: 21:[27, 25, 108], Operations: ['49+59=108'] Exploring Operation: 108/27=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 108/27=4 Current State: 21:[25, 4], Operations: ['49+59=108', '108/27=4'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[27, 49, 59, 25], Operations: [] Exploring Operation: 49-27=22, Resulting Numbers: [59, 25, 22] Generated Node #0,0: 21:[59, 25, 22] Operation: 49-27=22 Exploring Operation: 59-27=32, Resulting Numbers: [49, 25, 32] Generated Node #0,1: 21:[49, 25, 32] Operation: 59-27=32 Exploring Operation: 59-49=10, Resulting Numbers: [27, 25, 10] Generated Node #0,2: 21:[27, 25, 10] Operation: 59-49=10 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[27, 25, 10], Operations: ['59-49=10'] Exploring Operation: 25-10=15, Resulting Numbers: [27, 15] Generated Node #0,2,0: 21:[27, 15] Operation: 25-10=15 Exploring Operation: 27-25=2, Resulting Numbers: [10, 2] Generated Node #0,2,1: 21:[10, 2] Operation: 27-25=2 Exploring Operation: 27-10=17, Resulting Numbers: [25, 17] Generated Node #0,2,2: 21:[25, 17] Operation: 27-10=17 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[10, 2], Operations: ['59-49=10', '27-25=2'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,21 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 #0,2,2 Current State: 21:[25, 17], Operations: ['59-49=10', '27-10=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,21 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,21 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 #0,2,0 Current State: 21:[27, 15], Operations: ['59-49=10', '25-10=15'] Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,21 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 #0,0 Current State: 21:[59, 25, 22], Operations: ['49-27=22'] Exploring Operation: 25-22=3, Resulting Numbers: [59, 3] Generated Node #0,0,0: 21:[59, 3] Operation: 25-22=3 Exploring Operation: 59-25=34, Resulting Numbers: [22, 34] Generated Node #0,0,1: 21:[22, 34] Operation: 59-25=34 Exploring Operation: 59-22=37, Resulting Numbers: [25, 37] Generated Node #0,0,2: 21:[25, 37] Operation: 59-22=37 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[22, 34], Operations: ['49-27=22', '59-25=34'] Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 22+34=56, Resulting Numbers: [56] 56,21 unequal: No Solution Exploring Operation: 22*34=748, Resulting Numbers: [748] 748,21 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:[25, 37], Operations: ['49-27=22', '59-22=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,21 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,21 unequal: No Solution Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,21 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:[59, 3], Operations: ['49-27=22', '25-22=3'] Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,21 unequal: No Solution Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,21 unequal: No Solution Exploring Operation: 59-3=56, Resulting Numbers: [56] 56,21 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 #0,1 Current State: 21:[49, 25, 32], Operations: ['59-27=32'] Exploring Operation: 49-32=17, Resulting Numbers: [25, 17] Generated Node #0,1,0: 21:[25, 17] Operation: 49-32=17 Exploring Operation: 49-25=24, Resulting Numbers: [32, 24] Generated Node #0,1,1: 21:[32, 24] Operation: 49-25=24 Exploring Operation: 32-25=7, Resulting Numbers: [49, 7] Generated Node #0,1,2: 21:[49, 7] Operation: 32-25=7 Moving to Node #0,1,0 Current State: 21:[25, 17], Operations: ['59-27=32', '49-32=17'] Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[32, 24], Operations: ['59-27=32', '49-25=24'] Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,21 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[49, 7], Operations: ['59-27=32', '32-25=7'] Exploring Operation: 49+7=56, Resulting Numbers: [56] 56,21 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,21 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
[ 21, 98, 96, 89 ]
95
[ "96-89=7", "21/7=3", "98-3=95" ]
Current State: 95:[21, 98, 96, 89], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [21, 98, 7] Generated Node #2: [21, 98, 7] from Operation: 96-89=7 Current State: 95:[21, 98, 7], Operations: ['96-89=7'] Exploring Operation: 21/7=3, Resulting Numbers: [98, 3] Generated Node #3: [98, 3] from Operation: 21/7=3 Current State: 95:[98, 3], Operations: ['96-89=7', '21/7=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[21, 98, 96, 89], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [21, 89, 2] Generated Node #0,0: 95:[21, 89, 2] Operation: 98-96=2 Exploring Operation: 96-89=7, Resulting Numbers: [21, 98, 7] Generated Node #0,1: 95:[21, 98, 7] Operation: 96-89=7 Exploring Operation: 21+89=110, Resulting Numbers: [98, 96, 110] Generated Node #0,2: 95:[98, 96, 110] Operation: 21+89=110 Exploring Operation: 98-21=77, Resulting Numbers: [96, 89, 77] Generated Node #0,3: 95:[96, 89, 77] Operation: 98-21=77 Exploring Operation: 98-89=9, Resulting Numbers: [21, 96, 9] Generated Node #0,4: 95:[21, 96, 9] Operation: 98-89=9 Moving to Node #0,1 Current State: 95:[21, 98, 7], Operations: ['96-89=7'] Exploring Operation: 98/7=14, Resulting Numbers: [21, 14] Generated Node #0,1,0: 95:[21, 14] Operation: 98/7=14 Exploring Operation: 21-7=14, Resulting Numbers: [98, 14] Generated Node #0,1,1: 95:[98, 14] Operation: 21-7=14 Exploring Operation: 21/7=3, Resulting Numbers: [98, 3] Generated Node #0,1,2: 95:[98, 3] Operation: 21/7=3 Exploring Operation: 21+7=28, Resulting Numbers: [98, 28] Generated Node #0,1,3: 95:[98, 28] Operation: 21+7=28 Exploring Operation: 98-7=91, Resulting Numbers: [21, 91] Generated Node #0,1,4: 95:[21, 91] Operation: 98-7=91 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[98, 3], Operations: ['96-89=7', '21/7=3'] Exploring Operation: 98+3=101, Resulting Numbers: [101] 101,95 unequal: No Solution Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[21, 98, 96, 89], Operations: [] Exploring Operation: 96-89=7, Resulting Numbers: [21, 98, 7] Generated Node #0,1: 95:[21, 98, 7] Operation: 96-89=7 Moving to Node #0,1 Current State: 95:[21, 98, 7], Operations: ['96-89=7'] Exploring Operation: 21/7=3, Resulting Numbers: [98, 3] Generated Node #0,1,2: 95:[98, 3] Operation: 21/7=3 Moving to Node #0,1,2 Current State: 95:[98, 3], Operations: ['96-89=7', '21/7=3'] Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 14, 65, 56, 26 ]
95
[ "56/14=4", "65+26=91", "4+91=95" ]
Current State: 95:[14, 65, 56, 26], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [65, 26, 4] Generated Node #2: [65, 26, 4] from Operation: 56/14=4 Current State: 95:[65, 26, 4], Operations: ['56/14=4'] Exploring Operation: 65+26=91, Resulting Numbers: [4, 91] Generated Node #3: [4, 91] from Operation: 65+26=91 Current State: 95:[4, 91], Operations: ['56/14=4', '65+26=91'] Exploring Operation: 4+91=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[14, 65, 56, 26], Operations: [] Exploring Operation: 65-56=9, Resulting Numbers: [14, 26, 9] Generated Node #0,0: 95:[14, 26, 9] Operation: 65-56=9 Exploring Operation: 56/14=4, Resulting Numbers: [65, 26, 4] Generated Node #0,1: 95:[65, 26, 4] Operation: 56/14=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[14, 26, 9], Operations: ['65-56=9'] Exploring Operation: 26-9=17, Resulting Numbers: [14, 17] Generated Node #0,0,0: 95:[14, 17] Operation: 26-9=17 Exploring Operation: 14-9=5, Resulting Numbers: [26, 5] Generated Node #0,0,1: 95:[26, 5] Operation: 14-9=5 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[14, 17], Operations: ['65-56=9', '26-9=17'] Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,95 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,95 unequal: No Solution No 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: 95:[26, 5], Operations: ['65-56=9', '14-9=5'] Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,95 unequal: No Solution Exploring Operation: 26+5=31, Resulting Numbers: [31] 31,95 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: 95:[65, 26, 4], Operations: ['56/14=4'] Exploring Operation: 65+26=91, Resulting Numbers: [4, 91] Generated Node #0,1,0: 95:[4, 91] Operation: 65+26=91 Exploring Operation: 65-26=39, Resulting Numbers: [4, 39] Generated Node #0,1,1: 95:[4, 39] Operation: 65-26=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[4, 91], Operations: ['56/14=4', '65+26=91'] Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 4+91=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[14, 65, 56, 26], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [65, 26, 4] Generated Node #0,1: 95:[65, 26, 4] Operation: 56/14=4 Moving to Node #0,1 Current State: 95:[65, 26, 4], Operations: ['56/14=4'] Exploring Operation: 65+26=91, Resulting Numbers: [4, 91] Generated Node #0,1,0: 95:[4, 91] Operation: 65+26=91 Moving to Node #0,1,0 Current State: 95:[4, 91], Operations: ['56/14=4', '65+26=91'] Exploring Operation: 4+91=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
sum_heuristic
[ 87, 2, 88, 35 ]
62
[ "87-35=52", "52/2=26", "88-26=62" ]
Current State: 62:[87, 2, 88, 35], Operations: [] Exploring Operation: 87-35=52, Resulting Numbers: [2, 88, 52] Generated Node #2: [2, 88, 52] from Operation: 87-35=52 Current State: 62:[2, 88, 52], Operations: ['87-35=52'] Exploring Operation: 52/2=26, Resulting Numbers: [88, 26] Generated Node #3: [88, 26] from Operation: 52/2=26 Current State: 62:[88, 26], Operations: ['87-35=52', '52/2=26'] Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[87, 2, 88, 35], Operations: [] Exploring Operation: 88-35=53, Resulting Numbers: [87, 2, 53] Generated Node #0,0: 62:[87, 2, 53] Operation: 88-35=53 Exploring Operation: 87-35=52, Resulting Numbers: [2, 88, 52] Generated Node #0,1: 62:[2, 88, 52] Operation: 87-35=52 Exploring Operation: 88-87=1, Resulting Numbers: [2, 35, 1] Generated Node #0,2: 62:[2, 35, 1] Operation: 88-87=1 Exploring Operation: 88/2=44, Resulting Numbers: [87, 35, 44] Generated Node #0,3: 62:[87, 35, 44] Operation: 88/2=44 Moving to Node #0,2 Current State: 62:[2, 35, 1], Operations: ['88-87=1'] Exploring Operation: 35-1=34, Resulting Numbers: [2, 34] Generated Node #0,2,0: 62:[2, 34] Operation: 35-1=34 Exploring Operation: 35-2=33, Resulting Numbers: [1, 33] Generated Node #0,2,1: 62:[1, 33] Operation: 35-2=33 Exploring Operation: 2/1=2, Resulting Numbers: [35, 2] Generated Node #0,2,2: 62:[35, 2] Operation: 2/1=2 Exploring Operation: 2*1=2, Resulting Numbers: [35, 2] Generated Node #0,2,3: 62:[35, 2] Operation: 2*1=2 Moving to Node #0,0 Current State: 62:[87, 2, 53], Operations: ['88-35=53'] Exploring Operation: 87-53=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 62:[2, 34] Operation: 87-53=34 Exploring Operation: 87+2=89, Resulting Numbers: [53, 89] Generated Node #0,0,1: 62:[53, 89] Operation: 87+2=89 Exploring Operation: 2+53=55, Resulting Numbers: [87, 55] Generated Node #0,0,2: 62:[87, 55] Operation: 2+53=55 Exploring Operation: 87-2=85, Resulting Numbers: [53, 85] Generated Node #0,0,3: 62:[53, 85] Operation: 87-2=85 Moving to Node #0,1 Current State: 62:[2, 88, 52], Operations: ['87-35=52'] Exploring Operation: 88-52=36, Resulting Numbers: [2, 36] Generated Node #0,1,0: 62:[2, 36] Operation: 88-52=36 Exploring Operation: 52/2=26, Resulting Numbers: [88, 26] Generated Node #0,1,1: 62:[88, 26] Operation: 52/2=26 Exploring Operation: 88-2=86, Resulting Numbers: [52, 86] Generated Node #0,1,2: 62:[52, 86] Operation: 88-2=86 Exploring Operation: 88/2=44, Resulting Numbers: [52, 44] Generated Node #0,1,3: 62:[52, 44] Operation: 88/2=44 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[2, 36], Operations: ['87-35=52', '88-52=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,62 unequal: No Solution Exploring Operation: 2*36=72, Resulting Numbers: [72] 72,62 unequal: No Solution Exploring Operation: 2+36=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 #0,1,3 Current State: 62:[52, 44], Operations: ['87-35=52', '88/2=44'] Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,62 unequal: No Solution Exploring Operation: 52+44=96, Resulting Numbers: [96] 96,62 unequal: No Solution Exploring Operation: 52*44=2288, Resulting Numbers: [2288] 2288,62 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:[88, 26], Operations: ['87-35=52', '52/2=26'] Exploring Operation: 88*26=2288, Resulting Numbers: [2288] 2288,62 unequal: No Solution Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[87, 2, 88, 35], Operations: [] Exploring Operation: 87-35=52, Resulting Numbers: [2, 88, 52] Generated Node #0,1: 62:[2, 88, 52] Operation: 87-35=52 Moving to Node #0,1 Current State: 62:[2, 88, 52], Operations: ['87-35=52'] Exploring Operation: 52/2=26, Resulting Numbers: [88, 26] Generated Node #0,1,1: 62:[88, 26] Operation: 52/2=26 Moving to Node #0,1,1 Current State: 62:[88, 26], Operations: ['87-35=52', '52/2=26'] Exploring Operation: 88-26=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
sum_heuristic
[ 61, 97, 93, 9 ]
89
[ "97-61=36", "36/9=4", "93-4=89" ]
Current State: 89:[61, 97, 93, 9], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [93, 9, 36] Generated Node #2: [93, 9, 36] from Operation: 97-61=36 Current State: 89:[93, 9, 36], Operations: ['97-61=36'] Exploring Operation: 36/9=4, Resulting Numbers: [93, 4] Generated Node #3: [93, 4] from Operation: 36/9=4 Current State: 89:[93, 4], Operations: ['97-61=36', '36/9=4'] Exploring Operation: 93-4=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[61, 97, 93, 9], Operations: [] Exploring Operation: 61-9=52, Resulting Numbers: [97, 93, 52] Generated Node #0,0: 89:[97, 93, 52] Operation: 61-9=52 Exploring Operation: 97-9=88, Resulting Numbers: [61, 93, 88] Generated Node #0,1: 89:[61, 93, 88] Operation: 97-9=88 Exploring Operation: 97+9=106, Resulting Numbers: [61, 93, 106] Generated Node #0,2: 89:[61, 93, 106] Operation: 97+9=106 Exploring Operation: 93-9=84, Resulting Numbers: [61, 97, 84] Generated Node #0,3: 89:[61, 97, 84] Operation: 93-9=84 Exploring Operation: 61+9=70, Resulting Numbers: [97, 93, 70] Generated Node #0,4: 89:[97, 93, 70] Operation: 61+9=70 Start Sub Search at level 1: Moving to Node #0,4 Current State: 89:[97, 93, 70], Operations: ['61+9=70'] Exploring Operation: 93-70=23, Resulting Numbers: [97, 23] Generated Node #0,4,0: 89:[97, 23] Operation: 93-70=23 Exploring Operation: 97-93=4, Resulting Numbers: [70, 4] Generated Node #0,4,1: 89:[70, 4] Operation: 97-93=4 Exploring Operation: 97-70=27, Resulting Numbers: [93, 27] Generated Node #0,4,2: 89:[93, 27] Operation: 97-70=27 Exploring Operation: 93+70=163, Resulting Numbers: [97, 163] Generated Node #0,4,3: 89:[97, 163] Operation: 93+70=163 Exploring Operation: 97+70=167, Resulting Numbers: [93, 167] Generated Node #0,4,4: 89:[93, 167] Operation: 97+70=167 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 89:[93, 27], Operations: ['61+9=70', '97-70=27'] Exploring Operation: 93+27=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 93-27=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 93*27=2511, Resulting Numbers: [2511] 2511,89 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 #0,4,0 Current State: 89:[97, 23], Operations: ['61+9=70', '93-70=23'] Exploring Operation: 97-23=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 97+23=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 97*23=2231, Resulting Numbers: [2231] 2231,89 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 #0,4,3 Current State: 89:[97, 163], Operations: ['61+9=70', '93+70=163'] Exploring Operation: 97+163=260, Resulting Numbers: [260] 260,89 unequal: No Solution Exploring Operation: 97*163=15811, Resulting Numbers: [15811] 15811,89 unequal: No Solution Exploring Operation: 163-97=66, Resulting Numbers: [66] 66,89 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 #0,4,4 Current State: 89:[93, 167], Operations: ['61+9=70', '97+70=167'] Exploring Operation: 93+167=260, Resulting Numbers: [260] 260,89 unequal: No Solution Exploring Operation: 93*167=15531, Resulting Numbers: [15531] 15531,89 unequal: No Solution Exploring Operation: 167-93=74, Resulting Numbers: [74] 74,89 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 #0,4,1 Current State: 89:[70, 4], Operations: ['61+9=70', '97-93=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,89 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[61, 93, 88], Operations: ['97-9=88'] Exploring Operation: 88-61=27, Resulting Numbers: [93, 27] Generated Node #0,1,0: 89:[93, 27] Operation: 88-61=27 Exploring Operation: 93-61=32, Resulting Numbers: [88, 32] Generated Node #0,1,1: 89:[88, 32] Operation: 93-61=32 Exploring Operation: 61+88=149, Resulting Numbers: [93, 149] Generated Node #0,1,2: 89:[93, 149] Operation: 61+88=149 Exploring Operation: 93-88=5, Resulting Numbers: [61, 5] Generated Node #0,1,3: 89:[61, 5] Operation: 93-88=5 Exploring Operation: 61+93=154, Resulting Numbers: [88, 154] Generated Node #0,1,4: 89:[88, 154] Operation: 61+93=154 Moving to Node #0,1,1 Current State: 89:[88, 32], Operations: ['97-9=88', '93-61=32'] Exploring Operation: 88*32=2816, Resulting Numbers: [2816] 2816,89 unequal: No Solution Exploring Operation: 88-32=56, Resulting Numbers: [56] 56,89 unequal: No Solution Exploring Operation: 88+32=120, Resulting Numbers: [120] 120,89 unequal: No Solution Moving to Node #0,1,2 Current State: 89:[93, 149], Operations: ['97-9=88', '61+88=149'] Exploring Operation: 93+149=242, Resulting Numbers: [242] 242,89 unequal: No Solution Exploring Operation: 149-93=56, Resulting Numbers: [56] 56,89 unequal: No Solution Exploring Operation: 93*149=13857, Resulting Numbers: [13857] 13857,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[93, 27], Operations: ['97-9=88', '88-61=27'] Exploring Operation: 93+27=120, Resulting Numbers: [120] 120,89 unequal: No Solution Exploring Operation: 93-27=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 93*27=2511, Resulting Numbers: [2511] 2511,89 unequal: No Solution Moving to Node #0,1,4 Current State: 89:[88, 154], Operations: ['97-9=88', '61+93=154'] Exploring Operation: 154-88=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 88*154=13552, Resulting Numbers: [13552] 13552,89 unequal: No Solution Exploring Operation: 88+154=242, Resulting Numbers: [242] 242,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[61, 5], Operations: ['97-9=88', '93-88=5'] Exploring Operation: 61*5=305, Resulting Numbers: [305] 305,89 unequal: No Solution Exploring Operation: 61+5=66, Resulting Numbers: [66] 66,89 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 89:[61, 97, 84], Operations: ['93-9=84'] Exploring Operation: 97-84=13, Resulting Numbers: [61, 13] Generated Node #0,3,0: 89:[61, 13] Operation: 97-84=13 Exploring Operation: 97-61=36, Resulting Numbers: [84, 36] Generated Node #0,3,1: 89:[84, 36] Operation: 97-61=36 Exploring Operation: 84-61=23, Resulting Numbers: [97, 23] Generated Node #0,3,2: 89:[97, 23] Operation: 84-61=23 Exploring Operation: 61+84=145, Resulting Numbers: [97, 145] Generated Node #0,3,3: 89:[97, 145] Operation: 61+84=145 Exploring Operation: 61+97=158, Resulting Numbers: [84, 158] Generated Node #0,3,4: 89:[84, 158] Operation: 61+97=158 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 89:[84, 36], Operations: ['93-9=84', '97-61=36'] Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,89 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,89 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 #0,3,3 Current State: 89:[97, 145], Operations: ['93-9=84', '61+84=145'] Exploring Operation: 145-97=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 97*145=14065, Resulting Numbers: [14065] 14065,89 unequal: No Solution Exploring Operation: 97+145=242, Resulting Numbers: [242] 242,89 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 #0,3,2 Current State: 89:[97, 23], Operations: ['93-9=84', '84-61=23'] Exploring Operation: 97*23=2231, Resulting Numbers: [2231] 2231,89 unequal: No Solution Exploring Operation: 97-23=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 97+23=120, Resulting Numbers: [120] 120,89 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 #0,3,4 Current State: 89:[84, 158], Operations: ['93-9=84', '61+97=158'] Exploring Operation: 84+158=242, Resulting Numbers: [242] 242,89 unequal: No Solution Exploring Operation: 84*158=13272, Resulting Numbers: [13272] 13272,89 unequal: No Solution Exploring Operation: 158-84=74, Resulting Numbers: [74] 74,89 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 #0,3,0 Current State: 89:[61, 13], Operations: ['93-9=84', '97-84=13'] Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,89 unequal: No Solution Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[97, 93, 52], Operations: ['61-9=52'] Exploring Operation: 97-52=45, Resulting Numbers: [93, 45] Generated Node #0,0,0: 89:[93, 45] Operation: 97-52=45 Exploring Operation: 97+52=149, Resulting Numbers: [93, 149] Generated Node #0,0,1: 89:[93, 149] Operation: 97+52=149 Exploring Operation: 97-93=4, Resulting Numbers: [52, 4] Generated Node #0,0,2: 89:[52, 4] Operation: 97-93=4 Exploring Operation: 93-52=41, Resulting Numbers: [97, 41] Generated Node #0,0,3: 89:[97, 41] Operation: 93-52=41 Exploring Operation: 93+52=145, Resulting Numbers: [97, 145] Generated Node #0,0,4: 89:[97, 145] Operation: 93+52=145 Moving to Node #0,0,0 Current State: 89:[93, 45], Operations: ['61-9=52', '97-52=45'] Exploring Operation: 93*45=4185, Resulting Numbers: [4185] 4185,89 unequal: No Solution Exploring Operation: 93-45=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 93+45=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,0,3 Current State: 89:[97, 41], Operations: ['61-9=52', '93-52=41'] Exploring Operation: 97-41=56, Resulting Numbers: [56] 56,89 unequal: No Solution Exploring Operation: 97*41=3977, Resulting Numbers: [3977] 3977,89 unequal: No Solution Exploring Operation: 97+41=138, Resulting Numbers: [138] 138,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[93, 149], Operations: ['61-9=52', '97+52=149'] Exploring Operation: 93*149=13857, Resulting Numbers: [13857] 13857,89 unequal: No Solution Exploring Operation: 93+149=242, Resulting Numbers: [242] 242,89 unequal: No Solution Exploring Operation: 149-93=56, Resulting Numbers: [56] 56,89 unequal: No Solution Moving to Node #0,0,4 Current State: 89:[97, 145], Operations: ['61-9=52', '93+52=145'] Exploring Operation: 97+145=242, Resulting Numbers: [242] 242,89 unequal: No Solution Exploring Operation: 97*145=14065, Resulting Numbers: [14065] 14065,89 unequal: No Solution Exploring Operation: 145-97=48, Resulting Numbers: [48] 48,89 unequal: No Solution Moving to Node #0,0,2 Current State: 89:[52, 4], Operations: ['61-9=52', '97-93=4'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,89 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,89 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[61, 93, 106], Operations: ['97+9=106'] Exploring Operation: 93-61=32, Resulting Numbers: [106, 32] Generated Node #0,2,0: 89:[106, 32] Operation: 93-61=32 Exploring Operation: 106-93=13, Resulting Numbers: [61, 13] Generated Node #0,2,1: 89:[61, 13] Operation: 106-93=13 Exploring Operation: 106-61=45, Resulting Numbers: [93, 45] Generated Node #0,2,2: 89:[93, 45] Operation: 106-61=45 Exploring Operation: 61+106=167, Resulting Numbers: [93, 167] Generated Node #0,2,3: 89:[93, 167] Operation: 61+106=167 Exploring Operation: 61+93=154, Resulting Numbers: [106, 154] Generated Node #0,2,4: 89:[106, 154] Operation: 61+93=154 Moving to Node #0,2,2 Current State: 89:[93, 45], Operations: ['97+9=106', '106-61=45'] Exploring Operation: 93*45=4185, Resulting Numbers: [4185] 4185,89 unequal: No Solution Exploring Operation: 93+45=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 93-45=48, Resulting Numbers: [48] 48,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[106, 32], Operations: ['97+9=106', '93-61=32'] Exploring Operation: 106*32=3392, Resulting Numbers: [3392] 3392,89 unequal: No Solution Exploring Operation: 106+32=138, Resulting Numbers: [138] 138,89 unequal: No Solution Exploring Operation: 106-32=74, Resulting Numbers: [74] 74,89 unequal: No Solution Moving to Node #0,2,3 Current State: 89:[93, 167], Operations: ['97+9=106', '61+106=167'] Exploring Operation: 93+167=260, Resulting Numbers: [260] 260,89 unequal: No Solution Exploring Operation: 167-93=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 93*167=15531, Resulting Numbers: [15531] 15531,89 unequal: No Solution Moving to Node #0,2,4 Current State: 89:[106, 154], Operations: ['97+9=106', '61+93=154'] Exploring Operation: 154-106=48, Resulting Numbers: [48] 48,89 unequal: No Solution Exploring Operation: 106*154=16324, Resulting Numbers: [16324] 16324,89 unequal: No Solution Exploring Operation: 106+154=260, Resulting Numbers: [260] 260,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[61, 13], Operations: ['97+9=106', '106-93=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,89 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,89 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 27, 55, 31, 57 ]
85
[ "57-55=2", "27*2=54", "31+54=85" ]
Current State: 85:[27, 55, 31, 57], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [27, 31, 2] Generated Node #2: [27, 31, 2] from Operation: 57-55=2 Current State: 85:[27, 31, 2], Operations: ['57-55=2'] Exploring Operation: 27*2=54, Resulting Numbers: [31, 54] Generated Node #3: [31, 54] from Operation: 27*2=54 Current State: 85:[31, 54], Operations: ['57-55=2', '27*2=54'] Exploring Operation: 31+54=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[27, 55, 31, 57], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [27, 31, 2] Generated Node #0,0: 85:[27, 31, 2] Operation: 57-55=2 Exploring Operation: 55+31=86, Resulting Numbers: [27, 57, 86] Generated Node #0,1: 85:[27, 57, 86] Operation: 55+31=86 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[27, 31, 2], Operations: ['57-55=2'] Exploring Operation: 31-27=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 85:[2, 4] Operation: 31-27=4 Exploring Operation: 27-2=25, Resulting Numbers: [31, 25] Generated Node #0,0,1: 85:[31, 25] Operation: 27-2=25 Moving to Node #0,0,0 Current State: 85:[2, 4], Operations: ['57-55=2', '31-27=4'] Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[31, 25], Operations: ['57-55=2', '27-2=25'] Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,85 unequal: No Solution Exploring Operation: 31+25=56, Resulting Numbers: [56] 56,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[27, 57, 86], Operations: ['55+31=86'] Exploring Operation: 57-27=30, Resulting Numbers: [86, 30] Generated Node #0,1,0: 85:[86, 30] Operation: 57-27=30 Exploring Operation: 27+57=84, Resulting Numbers: [86, 84] Generated Node #0,1,1: 85:[86, 84] Operation: 27+57=84 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[86, 84], Operations: ['55+31=86', '27+57=84'] Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 86+84=170, Resulting Numbers: [170] 170,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[86, 30], Operations: ['55+31=86', '57-27=30'] Exploring Operation: 86+30=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 86-30=56, Resulting Numbers: [56] 56,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 66, 17, 87, 43 ]
47
[ "66+17=83", "87+43=130", "130-83=47" ]
Current State: 47:[66, 17, 87, 43], Operations: [] Exploring Operation: 66+17=83, Resulting Numbers: [87, 43, 83] Generated Node #2: [87, 43, 83] from Operation: 66+17=83 Current State: 47:[87, 43, 83], Operations: ['66+17=83'] Exploring Operation: 87+43=130, Resulting Numbers: [83, 130] Generated Node #3: [83, 130] from Operation: 87+43=130 Current State: 47:[83, 130], Operations: ['66+17=83', '87+43=130'] Exploring Operation: 130-83=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[66, 17, 87, 43], Operations: [] Exploring Operation: 87-43=44, Resulting Numbers: [66, 17, 44] Generated Node #0,0: 47:[66, 17, 44] Operation: 87-43=44 Exploring Operation: 87-17=70, Resulting Numbers: [66, 43, 70] Generated Node #0,1: 47:[66, 43, 70] Operation: 87-17=70 Exploring Operation: 87-66=21, Resulting Numbers: [17, 43, 21] Generated Node #0,2: 47:[17, 43, 21] Operation: 87-66=21 Exploring Operation: 66-17=49, Resulting Numbers: [87, 43, 49] Generated Node #0,3: 47:[87, 43, 49] Operation: 66-17=49 Exploring Operation: 17+43=60, Resulting Numbers: [66, 87, 60] Generated Node #0,4: 47:[66, 87, 60] Operation: 17+43=60 Moving to Node #0,1 Current State: 47:[66, 43, 70], Operations: ['87-17=70'] Exploring Operation: 43+70=113, Resulting Numbers: [66, 113] Generated Node #0,1,0: 47:[66, 113] Operation: 43+70=113 Exploring Operation: 70-43=27, Resulting Numbers: [66, 27] Generated Node #0,1,1: 47:[66, 27] Operation: 70-43=27 Exploring Operation: 70-66=4, Resulting Numbers: [43, 4] Generated Node #0,1,2: 47:[43, 4] Operation: 70-66=4 Exploring Operation: 66+43=109, Resulting Numbers: [70, 109] Generated Node #0,1,3: 47:[70, 109] Operation: 66+43=109 Exploring Operation: 66-43=23, Resulting Numbers: [70, 23] Generated Node #0,1,4: 47:[70, 23] Operation: 66-43=23 Moving to Node #0,3 Current State: 47:[87, 43, 49], Operations: ['66-17=49'] Exploring Operation: 87+43=130, Resulting Numbers: [49, 130] Generated Node #0,3,0: 47:[49, 130] Operation: 87+43=130 Exploring Operation: 49-43=6, Resulting Numbers: [87, 6] Generated Node #0,3,1: 47:[87, 6] Operation: 49-43=6 Exploring Operation: 87-43=44, Resulting Numbers: [49, 44] Generated Node #0,3,2: 47:[49, 44] Operation: 87-43=44 Exploring Operation: 87-49=38, Resulting Numbers: [43, 38] Generated Node #0,3,3: 47:[43, 38] Operation: 87-49=38 Exploring Operation: 43+49=92, Resulting Numbers: [87, 92] Generated Node #0,3,4: 47:[87, 92] Operation: 43+49=92 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 47:[49, 44], Operations: ['66-17=49', '87-43=44'] Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,47 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 47:[43, 38], Operations: ['66-17=49', '87-49=38'] Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 43+38=81, Resulting Numbers: [81] 81,47 unequal: No Solution Exploring Operation: 43*38=1634, Resulting Numbers: [1634] 1634,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 47:[87, 6], Operations: ['66-17=49', '49-43=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,47 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 47:[49, 130], Operations: ['66-17=49', '87+43=130'] Exploring Operation: 130-49=81, Resulting Numbers: [81] 81,47 unequal: No Solution Exploring Operation: 49+130=179, Resulting Numbers: [179] 179,47 unequal: No Solution Exploring Operation: 49*130=6370, Resulting Numbers: [6370] 6370,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 47:[87, 92], Operations: ['66-17=49', '43+49=92'] Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,47 unequal: No Solution Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,47 unequal: No Solution Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,47 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: 47:[66, 17, 44], Operations: ['87-43=44'] Exploring Operation: 66-17=49, Resulting Numbers: [44, 49] Generated Node #0,0,0: 47:[44, 49] Operation: 66-17=49 Exploring Operation: 66+17=83, Resulting Numbers: [44, 83] Generated Node #0,0,1: 47:[44, 83] Operation: 66+17=83 Exploring Operation: 17+44=61, Resulting Numbers: [66, 61] Generated Node #0,0,2: 47:[66, 61] Operation: 17+44=61 Exploring Operation: 44-17=27, Resulting Numbers: [66, 27] Generated Node #0,0,3: 47:[66, 27] Operation: 44-17=27 Exploring Operation: 66-44=22, Resulting Numbers: [17, 22] Generated Node #0,0,4: 47:[17, 22] Operation: 66-44=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[44, 49], Operations: ['87-43=44', '66-17=49'] Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,47 unequal: No Solution Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[66, 61], Operations: ['87-43=44', '17+44=61'] Exploring Operation: 66-61=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 66+61=127, Resulting Numbers: [127] 127,47 unequal: No Solution Exploring Operation: 66*61=4026, Resulting Numbers: [4026] 4026,47 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 #0,0,1 Current State: 47:[44, 83], Operations: ['87-43=44', '66+17=83'] Exploring Operation: 44+83=127, Resulting Numbers: [127] 127,47 unequal: No Solution Exploring Operation: 44*83=3652, Resulting Numbers: [3652] 3652,47 unequal: No Solution Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 47:[66, 27], Operations: ['87-43=44', '44-17=27'] Exploring Operation: 66*27=1782, Resulting Numbers: [1782] 1782,47 unequal: No Solution Exploring Operation: 66+27=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,47 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 #0,0,4 Current State: 47:[17, 22], Operations: ['87-43=44', '66-44=22'] Exploring Operation: 17*22=374, Resulting Numbers: [374] 374,47 unequal: No Solution Exploring Operation: 17+22=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 47:[17, 43, 21], Operations: ['87-66=21'] Exploring Operation: 17+43=60, Resulting Numbers: [21, 60] Generated Node #0,2,0: 47:[21, 60] Operation: 17+43=60 Exploring Operation: 21-17=4, Resulting Numbers: [43, 4] Generated Node #0,2,1: 47:[43, 4] Operation: 21-17=4 Exploring Operation: 17+21=38, Resulting Numbers: [43, 38] Generated Node #0,2,2: 47:[43, 38] Operation: 17+21=38 Exploring Operation: 43-17=26, Resulting Numbers: [21, 26] Generated Node #0,2,3: 47:[21, 26] Operation: 43-17=26 Exploring Operation: 43+21=64, Resulting Numbers: [17, 64] Generated Node #0,2,4: 47:[17, 64] Operation: 43+21=64 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 47:[43, 38], Operations: ['87-66=21', '17+21=38'] Exploring Operation: 43*38=1634, Resulting Numbers: [1634] 1634,47 unequal: No Solution Exploring Operation: 43+38=81, Resulting Numbers: [81] 81,47 unequal: No Solution Exploring Operation: 43-38=5, Resulting Numbers: [5] 5,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 47:[21, 60], Operations: ['87-66=21', '17+43=60'] Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 21*60=1260, Resulting Numbers: [1260] 1260,47 unequal: No Solution Exploring Operation: 21+60=81, Resulting Numbers: [81] 81,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 47:[43, 4], Operations: ['87-66=21', '21-17=4'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,47 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,47 unequal: No Solution Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[66, 17, 87, 43], Operations: [] Exploring Operation: 87-66=21, Resulting Numbers: [17, 43, 21] Generated Node #0,2: 47:[17, 43, 21] Operation: 87-66=21 Moving to Node #0,2 Current State: 47:[17, 43, 21], Operations: ['87-66=21'] Exploring Operation: 21-17=4, Resulting Numbers: [43, 4] Generated Node #0,2,1: 47:[43, 4] Operation: 21-17=4 Moving to Node #0,2,1 Current State: 47:[43, 4], Operations: ['87-66=21', '21-17=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_5
sum_heuristic
[ 22, 87, 51, 28 ]
84
[ "51-22=29", "87*28=2436", "2436/29=84" ]
Current State: 84:[22, 87, 51, 28], Operations: [] Exploring Operation: 51-22=29, Resulting Numbers: [87, 28, 29] Generated Node #2: [87, 28, 29] from Operation: 51-22=29 Current State: 84:[87, 28, 29], Operations: ['51-22=29'] Exploring Operation: 87*28=2436, Resulting Numbers: [29, 2436] Generated Node #3: [29, 2436] from Operation: 87*28=2436 Current State: 84:[29, 2436], Operations: ['51-22=29', '87*28=2436'] Exploring Operation: 2436/29=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[22, 87, 51, 28], Operations: [] Exploring Operation: 51-22=29, Resulting Numbers: [87, 28, 29] Generated Node #0,0: 84:[87, 28, 29] Operation: 51-22=29 Exploring Operation: 51-28=23, Resulting Numbers: [22, 87, 23] Generated Node #0,1: 84:[22, 87, 23] Operation: 51-28=23 Exploring Operation: 87-51=36, Resulting Numbers: [22, 28, 36] Generated Node #0,2: 84:[22, 28, 36] Operation: 87-51=36 Exploring Operation: 51+28=79, Resulting Numbers: [22, 87, 79] Generated Node #0,3: 84:[22, 87, 79] Operation: 51+28=79 Moving to Node #0,0 Current State: 84:[87, 28, 29], Operations: ['51-22=29'] Exploring Operation: 29-28=1, Resulting Numbers: [87, 1] Generated Node #0,0,0: 84:[87, 1] Operation: 29-28=1 Exploring Operation: 87-29=58, Resulting Numbers: [28, 58] Generated Node #0,0,1: 84:[28, 58] Operation: 87-29=58 Exploring Operation: 87-28=59, Resulting Numbers: [29, 59] Generated Node #0,0,2: 84:[29, 59] Operation: 87-28=59 Exploring Operation: 87/29=3, Resulting Numbers: [28, 3] Generated Node #0,0,3: 84:[28, 3] Operation: 87/29=3 Moving to Node #0,1 Current State: 84:[22, 87, 23], Operations: ['51-28=23'] Exploring Operation: 87-23=64, Resulting Numbers: [22, 64] Generated Node #0,1,0: 84:[22, 64] Operation: 87-23=64 Exploring Operation: 22+23=45, Resulting Numbers: [87, 45] Generated Node #0,1,1: 84:[87, 45] Operation: 22+23=45 Exploring Operation: 87-22=65, Resulting Numbers: [23, 65] Generated Node #0,1,2: 84:[23, 65] Operation: 87-22=65 Exploring Operation: 23-22=1, Resulting Numbers: [87, 1] Generated Node #0,1,3: 84:[87, 1] Operation: 23-22=1 Moving to Node #0,2 Current State: 84:[22, 28, 36], Operations: ['87-51=36'] Exploring Operation: 22+28=50, Resulting Numbers: [36, 50] Generated Node #0,2,0: 84:[36, 50] Operation: 22+28=50 Exploring Operation: 36-28=8, Resulting Numbers: [22, 8] Generated Node #0,2,1: 84:[22, 8] Operation: 36-28=8 Exploring Operation: 36-22=14, Resulting Numbers: [28, 14] Generated Node #0,2,2: 84:[28, 14] Operation: 36-22=14 Exploring Operation: 28-22=6, Resulting Numbers: [36, 6] Generated Node #0,2,3: 84:[36, 6] Operation: 28-22=6 Moving to Node #0,3 Current State: 84:[22, 87, 79], Operations: ['51+28=79'] Exploring Operation: 87-22=65, Resulting Numbers: [79, 65] Generated Node #0,3,0: 84:[79, 65] Operation: 87-22=65 Exploring Operation: 87-79=8, Resulting Numbers: [22, 8] Generated Node #0,3,1: 84:[22, 8] Operation: 87-79=8 Exploring Operation: 22+79=101, Resulting Numbers: [87, 101] Generated Node #0,3,2: 84:[87, 101] Operation: 22+79=101 Exploring Operation: 79-22=57, Resulting Numbers: [87, 57] Generated Node #0,3,3: 84:[87, 57] Operation: 79-22=57 Moving to Node #0,0,3 Current State: 84:[28, 3], Operations: ['51-22=29', '87/29=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[22, 87, 51, 28], Operations: [] Exploring Operation: 51-22=29, Resulting Numbers: [87, 28, 29] Generated Node #0,0: 84:[87, 28, 29] Operation: 51-22=29 Moving to Node #0,0 Current State: 84:[87, 28, 29], Operations: ['51-22=29'] Exploring Operation: 87/29=3, Resulting Numbers: [28, 3] Generated Node #0,0,3: 84:[28, 3] Operation: 87/29=3 Moving to Node #0,0,3 Current State: 84:[28, 3], Operations: ['51-22=29', '87/29=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
0.976563
hs_4
mult_heuristic
[ 3, 77, 43, 40 ]
77
[ "3+77=80", "43-40=3", "80-3=77" ]
Current State: 77:[3, 77, 43, 40], Operations: [] Exploring Operation: 3+77=80, Resulting Numbers: [43, 40, 80] Generated Node #2: [43, 40, 80] from Operation: 3+77=80 Current State: 77:[43, 40, 80], Operations: ['3+77=80'] Exploring Operation: 43-40=3, Resulting Numbers: [80, 3] Generated Node #3: [80, 3] from Operation: 43-40=3 Current State: 77:[80, 3], Operations: ['3+77=80', '43-40=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[3, 77, 43, 40], Operations: [] Exploring Operation: 43+40=83, Resulting Numbers: [3, 77, 83] Generated Node #0,0: 77:[3, 77, 83] Operation: 43+40=83 Exploring Operation: 43-40=3, Resulting Numbers: [3, 77, 3] Generated Node #0,1: 77:[3, 77, 3] Operation: 43-40=3 Moving to Node #0,1 Current State: 77:[3, 77, 3], Operations: ['43-40=3'] Exploring Operation: 3*3=9, Resulting Numbers: [77, 9] Generated Node #0,1,0: 77:[77, 9] Operation: 3*3=9 Exploring Operation: 3+3=6, Resulting Numbers: [77, 6] Generated Node #0,1,1: 77:[77, 6] Operation: 3+3=6 Moving to Node #0,0 Current State: 77:[3, 77, 83], Operations: ['43+40=83'] Exploring Operation: 83-77=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 77:[3, 6] Operation: 83-77=6 Exploring Operation: 83-3=80, Resulting Numbers: [77, 80] Generated Node #0,0,1: 77:[77, 80] Operation: 83-3=80 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[77, 80], Operations: ['43+40=83', '83-3=80'] Exploring Operation: 77+80=157, Resulting Numbers: [157] 157,77 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[3, 6], Operations: ['43+40=83', '83-77=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 77:[77, 6], Operations: ['43-40=3', '3+3=6'] Exploring Operation: 77+6=83, Resulting Numbers: [83] 83,77 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[77, 9], Operations: ['43-40=3', '3*3=9'] Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,77 unequal: No Solution Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,77 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 58, 71, 56, 34 ]
39
[ "58+71=129", "56+34=90", "129-90=39" ]
Current State: 39:[58, 71, 56, 34], Operations: [] Exploring Operation: 58+71=129, Resulting Numbers: [56, 34, 129] Generated Node #2: [56, 34, 129] from Operation: 58+71=129 Current State: 39:[56, 34, 129], Operations: ['58+71=129'] Exploring Operation: 56+34=90, Resulting Numbers: [129, 90] Generated Node #3: [129, 90] from Operation: 56+34=90 Current State: 39:[129, 90], Operations: ['58+71=129', '56+34=90'] Exploring Operation: 129-90=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[58, 71, 56, 34], Operations: [] Exploring Operation: 71-58=13, Resulting Numbers: [56, 34, 13] Generated Node #0,0: 39:[56, 34, 13] Operation: 71-58=13 Exploring Operation: 71-56=15, Resulting Numbers: [58, 34, 15] Generated Node #0,1: 39:[58, 34, 15] Operation: 71-56=15 Exploring Operation: 58-34=24, Resulting Numbers: [71, 56, 24] Generated Node #0,2: 39:[71, 56, 24] Operation: 58-34=24 Exploring Operation: 58-56=2, Resulting Numbers: [71, 34, 2] Generated Node #0,3: 39:[71, 34, 2] Operation: 58-56=2 Exploring Operation: 71-34=37, Resulting Numbers: [58, 56, 37] Generated Node #0,4: 39:[58, 56, 37] Operation: 71-34=37 Moving to Node #0,0 Current State: 39:[56, 34, 13], Operations: ['71-58=13'] Exploring Operation: 56+13=69, Resulting Numbers: [34, 69] Generated Node #0,0,0: 39:[34, 69] Operation: 56+13=69 Exploring Operation: 34-13=21, Resulting Numbers: [56, 21] Generated Node #0,0,1: 39:[56, 21] Operation: 34-13=21 Exploring Operation: 56-13=43, Resulting Numbers: [34, 43] Generated Node #0,0,2: 39:[34, 43] Operation: 56-13=43 Exploring Operation: 56-34=22, Resulting Numbers: [13, 22] Generated Node #0,0,3: 39:[13, 22] Operation: 56-34=22 Exploring Operation: 34+13=47, Resulting Numbers: [56, 47] Generated Node #0,0,4: 39:[56, 47] Operation: 34+13=47 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[34, 43], Operations: ['71-58=13', '56-13=43'] Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,39 unequal: No Solution Exploring Operation: 43-34=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 34*43=1462, Resulting Numbers: [1462] 1462,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 39:[13, 22], Operations: ['71-58=13', '56-34=22'] Exploring Operation: 13*22=286, Resulting Numbers: [286] 286,39 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[56, 21], Operations: ['71-58=13', '34-13=21'] Exploring Operation: 56-21=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 56+21=77, Resulting Numbers: [77] 77,39 unequal: No Solution Exploring Operation: 56*21=1176, Resulting Numbers: [1176] 1176,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 39:[56, 47], Operations: ['71-58=13', '34+13=47'] Exploring Operation: 56+47=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,39 unequal: No Solution Exploring Operation: 56*47=2632, Resulting Numbers: [2632] 2632,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[34, 69], Operations: ['71-58=13', '56+13=69'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 34+69=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 34*69=2346, Resulting Numbers: [2346] 2346,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 39:[58, 34, 15], Operations: ['71-56=15'] Exploring Operation: 58-15=43, Resulting Numbers: [34, 43] Generated Node #0,1,0: 39:[34, 43] Operation: 58-15=43 Exploring Operation: 34-15=19, Resulting Numbers: [58, 19] Generated Node #0,1,1: 39:[58, 19] Operation: 34-15=19 Exploring Operation: 34+15=49, Resulting Numbers: [58, 49] Generated Node #0,1,2: 39:[58, 49] Operation: 34+15=49 Exploring Operation: 58-34=24, Resulting Numbers: [15, 24] Generated Node #0,1,3: 39:[15, 24] Operation: 58-34=24 Exploring Operation: 58+15=73, Resulting Numbers: [34, 73] Generated Node #0,1,4: 39:[34, 73] Operation: 58+15=73 Moving to Node #0,3 Current State: 39:[71, 34, 2], Operations: ['58-56=2'] Exploring Operation: 34+2=36, Resulting Numbers: [71, 36] Generated Node #0,3,0: 39:[71, 36] Operation: 34+2=36 Exploring Operation: 71-2=69, Resulting Numbers: [34, 69] Generated Node #0,3,1: 39:[34, 69] Operation: 71-2=69 Exploring Operation: 71+2=73, Resulting Numbers: [34, 73] Generated Node #0,3,2: 39:[34, 73] Operation: 71+2=73 Exploring Operation: 34/2=17, Resulting Numbers: [71, 17] Generated Node #0,3,3: 39:[71, 17] Operation: 34/2=17 Exploring Operation: 71-34=37, Resulting Numbers: [2, 37] Generated Node #0,3,4: 39:[2, 37] Operation: 71-34=37 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 39:[2, 37], Operations: ['58-56=2', '71-34=37'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[58, 71, 56, 34], Operations: [] Exploring Operation: 58-56=2, Resulting Numbers: [71, 34, 2] Generated Node #0,3: 39:[71, 34, 2] Operation: 58-56=2 Moving to Node #0,3 Current State: 39:[71, 34, 2], Operations: ['58-56=2'] Exploring Operation: 71-34=37, Resulting Numbers: [2, 37] Generated Node #0,3,4: 39:[2, 37] Operation: 71-34=37 Moving to Node #0,3,4 Current State: 39:[2, 37], Operations: ['58-56=2', '71-34=37'] Exploring Operation: 2+37=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 21, 6, 22, 9 ]
17
[ "21+9=30", "30/6=5", "22-5=17" ]
Current State: 17:[21, 6, 22, 9], Operations: [] Exploring Operation: 21+9=30, Resulting Numbers: [6, 22, 30] Generated Node #2: [6, 22, 30] from Operation: 21+9=30 Current State: 17:[6, 22, 30], Operations: ['21+9=30'] Exploring Operation: 30/6=5, Resulting Numbers: [22, 5] Generated Node #3: [22, 5] from Operation: 30/6=5 Current State: 17:[22, 5], Operations: ['21+9=30', '30/6=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[21, 6, 22, 9], Operations: [] Exploring Operation: 6+9=15, Resulting Numbers: [21, 22, 15] Generated Node #0,0: 17:[21, 22, 15] Operation: 6+9=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[21, 22, 15], Operations: ['6+9=15'] Exploring Operation: 22-15=7, Resulting Numbers: [21, 7] Generated Node #0,0,0: 17:[21, 7] Operation: 22-15=7 Moving to Node #0,0,0 Current State: 17:[21, 7], Operations: ['6+9=15', '22-15=7'] Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,17 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
[ 90, 94, 15, 62 ]
51
[ "94-90=4", "62-15=47", "4+47=51" ]
Current State: 51:[90, 94, 15, 62], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [15, 62, 4] Generated Node #2: [15, 62, 4] from Operation: 94-90=4 Current State: 51:[15, 62, 4], Operations: ['94-90=4'] Exploring Operation: 62-15=47, Resulting Numbers: [4, 47] Generated Node #3: [4, 47] from Operation: 62-15=47 Current State: 51:[4, 47], Operations: ['94-90=4', '62-15=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[90, 94, 15, 62], Operations: [] Exploring Operation: 90-62=28, Resulting Numbers: [94, 15, 28] Generated Node #0,0: 51:[94, 15, 28] Operation: 90-62=28 Exploring Operation: 94-90=4, Resulting Numbers: [15, 62, 4] Generated Node #0,1: 51:[15, 62, 4] Operation: 94-90=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[15, 62, 4], Operations: ['94-90=4'] Exploring Operation: 62-4=58, Resulting Numbers: [15, 58] Generated Node #0,1,0: 51:[15, 58] Operation: 62-4=58 Exploring Operation: 62-15=47, Resulting Numbers: [4, 47] Generated Node #0,1,1: 51:[4, 47] Operation: 62-15=47 Moving to Node #0,1,1 Current State: 51:[4, 47], Operations: ['94-90=4', '62-15=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[90, 94, 15, 62], Operations: [] Exploring Operation: 94-90=4, Resulting Numbers: [15, 62, 4] Generated Node #0,1: 51:[15, 62, 4] Operation: 94-90=4 Moving to Node #0,1 Current State: 51:[15, 62, 4], Operations: ['94-90=4'] Exploring Operation: 62-15=47, Resulting Numbers: [4, 47] Generated Node #0,1,1: 51:[4, 47] Operation: 62-15=47 Moving to Node #0,1,1 Current State: 51:[4, 47], Operations: ['94-90=4', '62-15=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 12, 25, 2, 23 ]
20
[ "25-12=13", "23-13=10", "2*10=20" ]
Current State: 20:[12, 25, 2, 23], Operations: [] Exploring Operation: 25-12=13, Resulting Numbers: [2, 23, 13] Generated Node #2: [2, 23, 13] from Operation: 25-12=13 Current State: 20:[2, 23, 13], Operations: ['25-12=13'] Exploring Operation: 23-13=10, Resulting Numbers: [2, 10] Generated Node #3: [2, 10] from Operation: 23-13=10 Current State: 20:[2, 10], Operations: ['25-12=13', '23-13=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[12, 25, 2, 23], Operations: [] Exploring Operation: 12-2=10, Resulting Numbers: [25, 23, 10] Generated Node #0,0: 20:[25, 23, 10] Operation: 12-2=10 Exploring Operation: 25-12=13, Resulting Numbers: [2, 23, 13] Generated Node #0,1: 20:[2, 23, 13] Operation: 25-12=13 Exploring Operation: 23-12=11, Resulting Numbers: [25, 2, 11] Generated Node #0,2: 20:[25, 2, 11] Operation: 23-12=11 Exploring Operation: 25-23=2, Resulting Numbers: [12, 2, 2] Generated Node #0,3: 20:[12, 2, 2] Operation: 25-23=2 Moving to Node #0,3 Current State: 20:[12, 2, 2], Operations: ['25-23=2'] Exploring Operation: 12-2=10, Resulting Numbers: [2, 10] Generated Node #0,3,0: 20:[2, 10] Operation: 12-2=10 Exploring Operation: 12-2=10, Resulting Numbers: [2, 10] Generated Node #0,3,1: 20:[2, 10] Operation: 12-2=10 Exploring Operation: 12/2=6, Resulting Numbers: [2, 6] Generated Node #0,3,2: 20:[2, 6] Operation: 12/2=6 Exploring Operation: 12/2=6, Resulting Numbers: [2, 6] Generated Node #0,3,3: 20:[2, 6] Operation: 12/2=6 Moving to Node #0,2 Current State: 20:[25, 2, 11], Operations: ['23-12=11'] Exploring Operation: 2*11=22, Resulting Numbers: [25, 22] Generated Node #0,2,0: 20:[25, 22] Operation: 2*11=22 Exploring Operation: 25-2=23, Resulting Numbers: [11, 23] Generated Node #0,2,1: 20:[11, 23] Operation: 25-2=23 Exploring Operation: 25-11=14, Resulting Numbers: [2, 14] Generated Node #0,2,2: 20:[2, 14] Operation: 25-11=14 Exploring Operation: 11-2=9, Resulting Numbers: [25, 9] Generated Node #0,2,3: 20:[25, 9] Operation: 11-2=9 Moving to Node #0,1 Current State: 20:[2, 23, 13], Operations: ['25-12=13'] Exploring Operation: 13-2=11, Resulting Numbers: [23, 11] Generated Node #0,1,0: 20:[23, 11] Operation: 13-2=11 Exploring Operation: 2+23=25, Resulting Numbers: [13, 25] Generated Node #0,1,1: 20:[13, 25] Operation: 2+23=25 Exploring Operation: 23-13=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 20:[2, 10] Operation: 23-13=10 Exploring Operation: 23-2=21, Resulting Numbers: [13, 21] Generated Node #0,1,3: 20:[13, 21] Operation: 23-2=21 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[2, 10], Operations: ['25-12=13', '23-13=10'] Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[12, 25, 2, 23], Operations: [] Exploring Operation: 25-12=13, Resulting Numbers: [2, 23, 13] Generated Node #0,1: 20:[2, 23, 13] Operation: 25-12=13 Moving to Node #0,1 Current State: 20:[2, 23, 13], Operations: ['25-12=13'] Exploring Operation: 23-13=10, Resulting Numbers: [2, 10] Generated Node #0,1,2: 20:[2, 10] Operation: 23-13=10 Moving to Node #0,1,2 Current State: 20:[2, 10], Operations: ['25-12=13', '23-13=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
sum_heuristic
[ 70, 84, 12, 25 ]
50
[ "84-70=14", "14-12=2", "25*2=50" ]
Current State: 50:[70, 84, 12, 25], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [12, 25, 14] Generated Node #2: [12, 25, 14] from Operation: 84-70=14 Current State: 50:[12, 25, 14], Operations: ['84-70=14'] Exploring Operation: 14-12=2, Resulting Numbers: [25, 2] Generated Node #3: [25, 2] from Operation: 14-12=2 Current State: 50:[25, 2], Operations: ['84-70=14', '14-12=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[70, 84, 12, 25], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [12, 25, 14] Generated Node #0,0: 50:[12, 25, 14] Operation: 84-70=14 Moving to Node #0,0 Current State: 50:[12, 25, 14], Operations: ['84-70=14'] Exploring Operation: 14-12=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 50:[25, 2] Operation: 14-12=2 Moving to Node #0,0,0 Current State: 50:[25, 2], Operations: ['84-70=14', '14-12=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[70, 84, 12, 25], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [12, 25, 14] Generated Node #0,0: 50:[12, 25, 14] Operation: 84-70=14 Moving to Node #0,0 Current State: 50:[12, 25, 14], Operations: ['84-70=14'] Exploring Operation: 14-12=2, Resulting Numbers: [25, 2] Generated Node #0,0,0: 50:[25, 2] Operation: 14-12=2 Moving to Node #0,0,0 Current State: 50:[25, 2], Operations: ['84-70=14', '14-12=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 56, 68, 78, 23 ]
23
[ "56+68=124", "78+23=101", "124-101=23" ]
Current State: 23:[56, 68, 78, 23], Operations: [] Exploring Operation: 56+68=124, Resulting Numbers: [78, 23, 124] Generated Node #2: [78, 23, 124] from Operation: 56+68=124 Current State: 23:[78, 23, 124], Operations: ['56+68=124'] Exploring Operation: 78+23=101, Resulting Numbers: [124, 101] Generated Node #3: [124, 101] from Operation: 78+23=101 Current State: 23:[124, 101], Operations: ['56+68=124', '78+23=101'] Exploring Operation: 124-101=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[56, 68, 78, 23], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [78, 23, 12] Generated Node #0,0: 23:[78, 23, 12] Operation: 68-56=12 Exploring Operation: 56-23=33, Resulting Numbers: [68, 78, 33] Generated Node #0,1: 23:[68, 78, 33] Operation: 56-23=33 Exploring Operation: 78-56=22, Resulting Numbers: [68, 23, 22] Generated Node #0,2: 23:[68, 23, 22] Operation: 78-56=22 Exploring Operation: 78-68=10, Resulting Numbers: [56, 23, 10] Generated Node #0,3: 23:[56, 23, 10] Operation: 78-68=10 Moving to Node #0,2 Current State: 23:[68, 23, 22], Operations: ['78-56=22'] Exploring Operation: 23+22=45, Resulting Numbers: [68, 45] Generated Node #0,2,0: 23:[68, 45] Operation: 23+22=45 Exploring Operation: 68-23=45, Resulting Numbers: [22, 45] Generated Node #0,2,1: 23:[22, 45] Operation: 68-23=45 Exploring Operation: 68-22=46, Resulting Numbers: [23, 46] Generated Node #0,2,2: 23:[23, 46] Operation: 68-22=46 Exploring Operation: 68+22=90, Resulting Numbers: [23, 90] Generated Node #0,2,3: 23:[23, 90] Operation: 68+22=90 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[22, 45], Operations: ['78-56=22', '68-23=45'] Exploring Operation: 22+45=67, Resulting Numbers: [67] 67,23 unequal: No Solution Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[56, 68, 78, 23], Operations: [] Exploring Operation: 78-56=22, Resulting Numbers: [68, 23, 22] Generated Node #0,2: 23:[68, 23, 22] Operation: 78-56=22 Moving to Node #0,2 Current State: 23:[68, 23, 22], Operations: ['78-56=22'] Exploring Operation: 68-23=45, Resulting Numbers: [22, 45] Generated Node #0,2,1: 23:[22, 45] Operation: 68-23=45 Moving to Node #0,2,1 Current State: 23:[22, 45], Operations: ['78-56=22', '68-23=45'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 38, 10, 17, 33 ]
32
[ "38+10=48", "33-17=16", "48-16=32" ]
Current State: 32:[38, 10, 17, 33], Operations: [] Exploring Operation: 38+10=48, Resulting Numbers: [17, 33, 48] Generated Node #2: [17, 33, 48] from Operation: 38+10=48 Current State: 32:[17, 33, 48], Operations: ['38+10=48'] Exploring Operation: 33-17=16, Resulting Numbers: [48, 16] Generated Node #3: [48, 16] from Operation: 33-17=16 Current State: 32:[48, 16], Operations: ['38+10=48', '33-17=16'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[38, 10, 17, 33], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [10, 17, 5] Generated Node #0,0: 32:[10, 17, 5] Operation: 38-33=5 Exploring Operation: 17-10=7, Resulting Numbers: [38, 33, 7] Generated Node #0,1: 32:[38, 33, 7] Operation: 17-10=7 Exploring Operation: 38-17=21, Resulting Numbers: [10, 33, 21] Generated Node #0,2: 32:[10, 33, 21] Operation: 38-17=21 Exploring Operation: 38-10=28, Resulting Numbers: [17, 33, 28] Generated Node #0,3: 32:[17, 33, 28] Operation: 38-10=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[10, 17, 5], Operations: ['38-33=5'] Exploring Operation: 10-5=5, Resulting Numbers: [17, 5] Generated Node #0,0,0: 32:[17, 5] Operation: 10-5=5 Exploring Operation: 10/5=2, Resulting Numbers: [17, 2] Generated Node #0,0,1: 32:[17, 2] Operation: 10/5=2 Exploring Operation: 17-10=7, Resulting Numbers: [5, 7] Generated Node #0,0,2: 32:[5, 7] Operation: 17-10=7 Exploring Operation: 10+5=15, Resulting Numbers: [17, 15] Generated Node #0,0,3: 32:[17, 15] Operation: 10+5=15 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 32:[17, 2], Operations: ['38-33=5', '10/5=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,32 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,32 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[17, 5], Operations: ['38-33=5', '10-5=5'] Exploring Operation: 17-5=12, Resulting Numbers: [12] 12,32 unequal: No Solution Exploring Operation: 17*5=85, Resulting Numbers: [85] 85,32 unequal: No Solution Exploring Operation: 17+5=22, Resulting Numbers: [22] 22,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 32:[5, 7], Operations: ['38-33=5', '17-10=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 32:[17, 15], Operations: ['38-33=5', '10+5=15'] Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[38, 10, 17, 33], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [10, 17, 5] Generated Node #0,0: 32:[10, 17, 5] Operation: 38-33=5 Moving to Node #0,0 Current State: 32:[10, 17, 5], Operations: ['38-33=5'] Exploring Operation: 10+5=15, Resulting Numbers: [17, 15] Generated Node #0,0,3: 32:[17, 15] Operation: 10+5=15 Moving to Node #0,0,3 Current State: 32:[17, 15], Operations: ['38-33=5', '10+5=15'] Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 28, 33, 15, 60 ]
40
[ "33-28=5", "60-15=45", "45-5=40" ]
Current State: 40:[28, 33, 15, 60], Operations: [] Exploring Operation: 33-28=5, Resulting Numbers: [15, 60, 5] Generated Node #2: [15, 60, 5] from Operation: 33-28=5 Current State: 40:[15, 60, 5], Operations: ['33-28=5'] Exploring Operation: 60-15=45, Resulting Numbers: [5, 45] Generated Node #3: [5, 45] from Operation: 60-15=45 Current State: 40:[5, 45], Operations: ['33-28=5', '60-15=45'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[28, 33, 15, 60], Operations: [] Exploring Operation: 33-28=5, Resulting Numbers: [15, 60, 5] Generated Node #0,0: 40:[15, 60, 5] Operation: 33-28=5 Exploring Operation: 60/15=4, Resulting Numbers: [28, 33, 4] Generated Node #0,1: 40:[28, 33, 4] Operation: 60/15=4 Exploring Operation: 60-28=32, Resulting Numbers: [33, 15, 32] Generated Node #0,2: 40:[33, 15, 32] Operation: 60-28=32 Exploring Operation: 60-15=45, Resulting Numbers: [28, 33, 45] Generated Node #0,3: 40:[28, 33, 45] Operation: 60-15=45 Exploring Operation: 60-33=27, Resulting Numbers: [28, 15, 27] Generated Node #0,4: 40:[28, 15, 27] Operation: 60-33=27 Moving to Node #0,1 Current State: 40:[28, 33, 4], Operations: ['60/15=4'] Exploring Operation: 33+4=37, Resulting Numbers: [28, 37] Generated Node #0,1,0: 40:[28, 37] Operation: 33+4=37 Exploring Operation: 33-28=5, Resulting Numbers: [4, 5] Generated Node #0,1,1: 40:[4, 5] Operation: 33-28=5 Exploring Operation: 28/4=7, Resulting Numbers: [33, 7] Generated Node #0,1,2: 40:[33, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [33, 24] Generated Node #0,1,3: 40:[33, 24] Operation: 28-4=24 Exploring Operation: 28+4=32, Resulting Numbers: [33, 32] Generated Node #0,1,4: 40:[33, 32] Operation: 28+4=32 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 40:[4, 5], Operations: ['60/15=4', '33-28=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,40 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,40 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 40:[33, 7], Operations: ['60/15=4', '28/4=7'] Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,40 unequal: No Solution Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[28, 33, 15, 60], Operations: [] Exploring Operation: 60/15=4, Resulting Numbers: [28, 33, 4] Generated Node #0,1: 40:[28, 33, 4] Operation: 60/15=4 Moving to Node #0,1 Current State: 40:[28, 33, 4], Operations: ['60/15=4'] Exploring Operation: 28/4=7, Resulting Numbers: [33, 7] Generated Node #0,1,2: 40:[33, 7] Operation: 28/4=7 Moving to Node #0,1,2 Current State: 40:[33, 7], Operations: ['60/15=4', '28/4=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 15, 14, 46, 97 ]
22
[ "15+14=29", "97-46=51", "51-29=22" ]
Current State: 22:[15, 14, 46, 97], Operations: [] Exploring Operation: 15+14=29, Resulting Numbers: [46, 97, 29] Generated Node #2: [46, 97, 29] from Operation: 15+14=29 Current State: 22:[46, 97, 29], Operations: ['15+14=29'] Exploring Operation: 97-46=51, Resulting Numbers: [29, 51] Generated Node #3: [29, 51] from Operation: 97-46=51 Current State: 22:[29, 51], Operations: ['15+14=29', '97-46=51'] Exploring Operation: 51-29=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[15, 14, 46, 97], Operations: [] Exploring Operation: 46-14=32, Resulting Numbers: [15, 97, 32] Generated Node #0,0: 22:[15, 97, 32] Operation: 46-14=32 Exploring Operation: 46-15=31, Resulting Numbers: [14, 97, 31] Generated Node #0,1: 22:[14, 97, 31] Operation: 46-15=31 Exploring Operation: 97-15=82, Resulting Numbers: [14, 46, 82] Generated Node #0,2: 22:[14, 46, 82] Operation: 97-15=82 Exploring Operation: 97-46=51, Resulting Numbers: [15, 14, 51] Generated Node #0,3: 22:[15, 14, 51] Operation: 97-46=51 Exploring Operation: 97-14=83, Resulting Numbers: [15, 46, 83] Generated Node #0,4: 22:[15, 46, 83] Operation: 97-14=83 Moving to Node #0,3 Current State: 22:[15, 14, 51], Operations: ['97-46=51'] Exploring Operation: 51-14=37, Resulting Numbers: [15, 37] Generated Node #0,3,0: 22:[15, 37] Operation: 51-14=37 Exploring Operation: 15+14=29, Resulting Numbers: [51, 29] Generated Node #0,3,1: 22:[51, 29] Operation: 15+14=29 Exploring Operation: 51-15=36, Resulting Numbers: [14, 36] Generated Node #0,3,2: 22:[14, 36] Operation: 51-15=36 Exploring Operation: 15-14=1, Resulting Numbers: [51, 1] Generated Node #0,3,3: 22:[51, 1] Operation: 15-14=1 Exploring Operation: 15+51=66, Resulting Numbers: [14, 66] Generated Node #0,3,4: 22:[14, 66] Operation: 15+51=66 Moving to Node #0,2 Current State: 22:[14, 46, 82], Operations: ['97-15=82'] Exploring Operation: 82-14=68, Resulting Numbers: [46, 68] Generated Node #0,2,0: 22:[46, 68] Operation: 82-14=68 Exploring Operation: 14+46=60, Resulting Numbers: [82, 60] Generated Node #0,2,1: 22:[82, 60] Operation: 14+46=60 Exploring Operation: 46-14=32, Resulting Numbers: [82, 32] Generated Node #0,2,2: 22:[82, 32] Operation: 46-14=32 Exploring Operation: 82-46=36, Resulting Numbers: [14, 36] Generated Node #0,2,3: 22:[14, 36] Operation: 82-46=36 Exploring Operation: 14+82=96, Resulting Numbers: [46, 96] Generated Node #0,2,4: 22:[46, 96] Operation: 14+82=96 Moving to Node #0,1 Current State: 22:[14, 97, 31], Operations: ['46-15=31'] Exploring Operation: 97-14=83, Resulting Numbers: [31, 83] Generated Node #0,1,0: 22:[31, 83] Operation: 97-14=83 Exploring Operation: 14+97=111, Resulting Numbers: [31, 111] Generated Node #0,1,1: 22:[31, 111] Operation: 14+97=111 Exploring Operation: 14+31=45, Resulting Numbers: [97, 45] Generated Node #0,1,2: 22:[97, 45] Operation: 14+31=45 Exploring Operation: 31-14=17, Resulting Numbers: [97, 17] Generated Node #0,1,3: 22:[97, 17] Operation: 31-14=17 Exploring Operation: 97-31=66, Resulting Numbers: [14, 66] Generated Node #0,1,4: 22:[14, 66] Operation: 97-31=66 Moving to Node #0,0 Current State: 22:[15, 97, 32], Operations: ['46-14=32'] Exploring Operation: 97-15=82, Resulting Numbers: [32, 82] Generated Node #0,0,0: 22:[32, 82] Operation: 97-15=82 Exploring Operation: 97-32=65, Resulting Numbers: [15, 65] Generated Node #0,0,1: 22:[15, 65] Operation: 97-32=65 Exploring Operation: 15+32=47, Resulting Numbers: [97, 47] Generated Node #0,0,2: 22:[97, 47] Operation: 15+32=47 Exploring Operation: 32-15=17, Resulting Numbers: [97, 17] Generated Node #0,0,3: 22:[97, 17] Operation: 32-15=17 Exploring Operation: 15+97=112, Resulting Numbers: [32, 112] Generated Node #0,0,4: 22:[32, 112] Operation: 15+97=112 Moving to Node #0,4 Current State: 22:[15, 46, 83], Operations: ['97-14=83'] Exploring Operation: 46-15=31, Resulting Numbers: [83, 31] Generated Node #0,4,0: 22:[83, 31] Operation: 46-15=31 Exploring Operation: 15+46=61, Resulting Numbers: [83, 61] Generated Node #0,4,1: 22:[83, 61] Operation: 15+46=61 Exploring Operation: 15+83=98, Resulting Numbers: [46, 98] Generated Node #0,4,2: 22:[46, 98] Operation: 15+83=98 Exploring Operation: 83-15=68, Resulting Numbers: [46, 68] Generated Node #0,4,3: 22:[46, 68] Operation: 83-15=68 Exploring Operation: 83-46=37, Resulting Numbers: [15, 37] Generated Node #0,4,4: 22:[15, 37] Operation: 83-46=37 Moving to Node #0,3,2 Current State: 22:[14, 36], Operations: ['97-46=51', '51-15=36'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[15, 14, 46, 97], Operations: [] Exploring Operation: 97-46=51, Resulting Numbers: [15, 14, 51] Generated Node #0,3: 22:[15, 14, 51] Operation: 97-46=51 Moving to Node #0,3 Current State: 22:[15, 14, 51], Operations: ['97-46=51'] Exploring Operation: 51-15=36, Resulting Numbers: [14, 36] Generated Node #0,3,2: 22:[14, 36] Operation: 51-15=36 Moving to Node #0,3,2 Current State: 22:[14, 36], Operations: ['97-46=51', '51-15=36'] Exploring Operation: 36-14=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.969618
hs_5
mult_heuristic
[ 3, 81, 16, 67 ]
26
[ "81-67=14", "3*14=42", "42-16=26" ]
Current State: 26:[3, 81, 16, 67], Operations: [] Exploring Operation: 81-67=14, Resulting Numbers: [3, 16, 14] Generated Node #2: [3, 16, 14] from Operation: 81-67=14 Current State: 26:[3, 16, 14], Operations: ['81-67=14'] Exploring Operation: 3*14=42, Resulting Numbers: [16, 42] Generated Node #3: [16, 42] from Operation: 3*14=42 Current State: 26:[16, 42], Operations: ['81-67=14', '3*14=42'] Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[3, 81, 16, 67], Operations: [] Exploring Operation: 81-67=14, Resulting Numbers: [3, 16, 14] Generated Node #0,0: 26:[3, 16, 14] Operation: 81-67=14 Moving to Node #0,0 Current State: 26:[3, 16, 14], Operations: ['81-67=14'] Exploring Operation: 16-3=13, Resulting Numbers: [14, 13] Generated Node #0,0,0: 26:[14, 13] Operation: 16-3=13 Moving to Node #0,0,0 Current State: 26:[14, 13], Operations: ['81-67=14', '16-3=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,26 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 4, 66, 84, 85 ]
61
[ "66-4=62", "85-84=1", "62-1=61" ]
Current State: 61:[4, 66, 84, 85], Operations: [] Exploring Operation: 66-4=62, Resulting Numbers: [84, 85, 62] Generated Node #2: [84, 85, 62] from Operation: 66-4=62 Current State: 61:[84, 85, 62], Operations: ['66-4=62'] Exploring Operation: 85-84=1, Resulting Numbers: [62, 1] Generated Node #3: [62, 1] from Operation: 85-84=1 Current State: 61:[62, 1], Operations: ['66-4=62', '85-84=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[4, 66, 84, 85], Operations: [] Exploring Operation: 66-4=62, Resulting Numbers: [84, 85, 62] Generated Node #0,0: 61:[84, 85, 62] Operation: 66-4=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[84, 85, 62], Operations: ['66-4=62'] Exploring Operation: 85-84=1, Resulting Numbers: [62, 1] Generated Node #0,0,0: 61:[62, 1] Operation: 85-84=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[62, 1], Operations: ['66-4=62', '85-84=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[4, 66, 84, 85], Operations: [] Exploring Operation: 66-4=62, Resulting Numbers: [84, 85, 62] Generated Node #0,0: 61:[84, 85, 62] Operation: 66-4=62 Moving to Node #0,0 Current State: 61:[84, 85, 62], Operations: ['66-4=62'] Exploring Operation: 85-84=1, Resulting Numbers: [62, 1] Generated Node #0,0,0: 61:[62, 1] Operation: 85-84=1 Moving to Node #0,0,0 Current State: 61:[62, 1], Operations: ['66-4=62', '85-84=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 16, 9, 65, 29 ]
11
[ "16+9=25", "65-29=36", "36-25=11" ]
Current State: 11:[16, 9, 65, 29], Operations: [] Exploring Operation: 16+9=25, Resulting Numbers: [65, 29, 25] Generated Node #2: [65, 29, 25] from Operation: 16+9=25 Current State: 11:[65, 29, 25], Operations: ['16+9=25'] Exploring Operation: 65-29=36, Resulting Numbers: [25, 36] Generated Node #3: [25, 36] from Operation: 65-29=36 Current State: 11:[25, 36], Operations: ['16+9=25', '65-29=36'] Exploring Operation: 36-25=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[16, 9, 65, 29], Operations: [] Exploring Operation: 29-16=13, Resulting Numbers: [9, 65, 13] Generated Node #0,0: 11:[9, 65, 13] Operation: 29-16=13 Exploring Operation: 65-16=49, Resulting Numbers: [9, 29, 49] Generated Node #0,1: 11:[9, 29, 49] Operation: 65-16=49 Exploring Operation: 65-29=36, Resulting Numbers: [16, 9, 36] Generated Node #0,2: 11:[16, 9, 36] Operation: 65-29=36 Exploring Operation: 65-9=56, Resulting Numbers: [16, 29, 56] Generated Node #0,3: 11:[16, 29, 56] Operation: 65-9=56 Moving to Node #0,2 Current State: 11:[16, 9, 36], Operations: ['65-29=36'] Exploring Operation: 36/9=4, Resulting Numbers: [16, 4] Generated Node #0,2,0: 11:[16, 4] Operation: 36/9=4 Exploring Operation: 36-9=27, Resulting Numbers: [16, 27] Generated Node #0,2,1: 11:[16, 27] Operation: 36-9=27 Exploring Operation: 16-9=7, Resulting Numbers: [36, 7] Generated Node #0,2,2: 11:[36, 7] Operation: 16-9=7 Exploring Operation: 36-16=20, Resulting Numbers: [9, 20] Generated Node #0,2,3: 11:[9, 20] Operation: 36-16=20 Moving to Node #0,1 Current State: 11:[9, 29, 49], Operations: ['65-16=49'] Exploring Operation: 49-9=40, Resulting Numbers: [29, 40] Generated Node #0,1,0: 11:[29, 40] Operation: 49-9=40 Exploring Operation: 49-29=20, Resulting Numbers: [9, 20] Generated Node #0,1,1: 11:[9, 20] Operation: 49-29=20 Exploring Operation: 9+29=38, Resulting Numbers: [49, 38] Generated Node #0,1,2: 11:[49, 38] Operation: 9+29=38 Exploring Operation: 29-9=20, Resulting Numbers: [49, 20] Generated Node #0,1,3: 11:[49, 20] Operation: 29-9=20 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[9, 20], Operations: ['65-16=49', '49-29=20'] Exploring Operation: 9*20=180, Resulting Numbers: [180] 180,11 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[16, 9, 65, 29], Operations: [] Exploring Operation: 65-16=49, Resulting Numbers: [9, 29, 49] Generated Node #0,1: 11:[9, 29, 49] Operation: 65-16=49 Moving to Node #0,1 Current State: 11:[9, 29, 49], Operations: ['65-16=49'] Exploring Operation: 49-29=20, Resulting Numbers: [9, 20] Generated Node #0,1,1: 11:[9, 20] Operation: 49-29=20 Moving to Node #0,1,1 Current State: 11:[9, 20], Operations: ['65-16=49', '49-29=20'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 35, 98, 53, 13 ]
23
[ "98-35=63", "53-13=40", "63-40=23" ]
Current State: 23:[35, 98, 53, 13], Operations: [] Exploring Operation: 98-35=63, Resulting Numbers: [53, 13, 63] Generated Node #2: [53, 13, 63] from Operation: 98-35=63 Current State: 23:[53, 13, 63], Operations: ['98-35=63'] Exploring Operation: 53-13=40, Resulting Numbers: [63, 40] Generated Node #3: [63, 40] from Operation: 53-13=40 Current State: 23:[63, 40], Operations: ['98-35=63', '53-13=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[35, 98, 53, 13], Operations: [] Exploring Operation: 98-53=45, Resulting Numbers: [35, 13, 45] Generated Node #0,0: 23:[35, 13, 45] Operation: 98-53=45 Exploring Operation: 98-35=63, Resulting Numbers: [53, 13, 63] Generated Node #0,1: 23:[53, 13, 63] Operation: 98-35=63 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[35, 13, 45], Operations: ['98-53=45'] Exploring Operation: 45-13=32, Resulting Numbers: [35, 32] Generated Node #0,0,0: 23:[35, 32] Operation: 45-13=32 Exploring Operation: 35-13=22, Resulting Numbers: [45, 22] Generated Node #0,0,1: 23:[45, 22] Operation: 35-13=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[35, 32], Operations: ['98-53=45', '45-13=32'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,23 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 #0,0,1 Current State: 23:[45, 22], Operations: ['98-53=45', '35-13=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[35, 98, 53, 13], Operations: [] Exploring Operation: 98-53=45, Resulting Numbers: [35, 13, 45] Generated Node #0,0: 23:[35, 13, 45] Operation: 98-53=45 Moving to Node #0,0 Current State: 23:[35, 13, 45], Operations: ['98-53=45'] Exploring Operation: 35-13=22, Resulting Numbers: [45, 22] Generated Node #0,0,1: 23:[45, 22] Operation: 35-13=22 Moving to Node #0,0,1 Current State: 23:[45, 22], Operations: ['98-53=45', '35-13=22'] Exploring Operation: 45-22=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 17, 27, 10, 93 ]
29
[ "27+93=120", "120/10=12", "17+12=29" ]
Current State: 29:[17, 27, 10, 93], Operations: [] Exploring Operation: 27+93=120, Resulting Numbers: [17, 10, 120] Generated Node #2: [17, 10, 120] from Operation: 27+93=120 Current State: 29:[17, 10, 120], Operations: ['27+93=120'] Exploring Operation: 120/10=12, Resulting Numbers: [17, 12] Generated Node #3: [17, 12] from Operation: 120/10=12 Current State: 29:[17, 12], Operations: ['27+93=120', '120/10=12'] Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[17, 27, 10, 93], Operations: [] Exploring Operation: 93-17=76, Resulting Numbers: [27, 10, 76] Generated Node #0,0: 29:[27, 10, 76] Operation: 93-17=76 Exploring Operation: 27+10=37, Resulting Numbers: [17, 93, 37] Generated Node #0,1: 29:[17, 93, 37] Operation: 27+10=37 Exploring Operation: 17+10=27, Resulting Numbers: [27, 93, 27] Generated Node #0,2: 29:[27, 93, 27] Operation: 17+10=27 Exploring Operation: 93-10=83, Resulting Numbers: [17, 27, 83] Generated Node #0,3: 29:[17, 27, 83] Operation: 93-10=83 Exploring Operation: 93-27=66, Resulting Numbers: [17, 10, 66] Generated Node #0,4: 29:[17, 10, 66] Operation: 93-27=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[27, 10, 76], Operations: ['93-17=76'] Exploring Operation: 76-10=66, Resulting Numbers: [27, 66] Generated Node #0,0,0: 29:[27, 66] Operation: 76-10=66 Exploring Operation: 76-27=49, Resulting Numbers: [10, 49] Generated Node #0,0,1: 29:[10, 49] Operation: 76-27=49 Exploring Operation: 27+10=37, Resulting Numbers: [76, 37] Generated Node #0,0,2: 29:[76, 37] Operation: 27+10=37 Exploring Operation: 27-10=17, Resulting Numbers: [76, 17] Generated Node #0,0,3: 29:[76, 17] Operation: 27-10=17 Exploring Operation: 10+76=86, Resulting Numbers: [27, 86] Generated Node #0,0,4: 29:[27, 86] Operation: 10+76=86 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[27, 66], Operations: ['93-17=76', '76-10=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,29 unequal: No Solution No 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: 29:[10, 49], Operations: ['93-17=76', '76-27=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,29 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,29 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,29 unequal: No Solution No 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: 29:[76, 37], Operations: ['93-17=76', '27+10=37'] Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 76*37=2812, Resulting Numbers: [2812] 2812,29 unequal: No Solution Exploring Operation: 76+37=113, Resulting Numbers: [113] 113,29 unequal: No Solution No 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: 29:[76, 17], Operations: ['93-17=76', '27-10=17'] Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,29 unequal: No Solution Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,29 unequal: No Solution No 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: 29:[27, 86], Operations: ['93-17=76', '10+76=86'] Exploring Operation: 27+86=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 27*86=2322, Resulting Numbers: [2322] 2322,29 unequal: No Solution Exploring Operation: 86-27=59, Resulting Numbers: [59] 59,29 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: 29:[27, 93, 27], Operations: ['17+10=27'] Exploring Operation: 27/27=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 29:[93, 1] Operation: 27/27=1 Exploring Operation: 27+93=120, Resulting Numbers: [27, 120] Generated Node #0,2,1: 29:[27, 120] Operation: 27+93=120 Exploring Operation: 93-27=66, Resulting Numbers: [27, 66] Generated Node #0,2,2: 29:[27, 66] Operation: 93-27=66 Exploring Operation: 27+27=54, Resulting Numbers: [93, 54] Generated Node #0,2,3: 29:[93, 54] Operation: 27+27=54 Exploring Operation: 93-27=66, Resulting Numbers: [27, 66] Generated Node #0,2,4: 29:[27, 66] Operation: 93-27=66 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 29:[27, 66], Operations: ['17+10=27', '93-27=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,29 unequal: No Solution No 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: 29:[27, 66], Operations: ['17+10=27', '93-27=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,29 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,29 unequal: No Solution No 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: 29:[93, 54], Operations: ['17+10=27', '27+27=54'] Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 93+54=147, Resulting Numbers: [147] 147,29 unequal: No Solution Exploring Operation: 93*54=5022, Resulting Numbers: [5022] 5022,29 unequal: No Solution No 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: 29:[93, 1], Operations: ['17+10=27', '27/27=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,29 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,29 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,29 unequal: No Solution No 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: 29:[27, 120], Operations: ['17+10=27', '27+93=120'] Exploring Operation: 120-27=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 27+120=147, Resulting Numbers: [147] 147,29 unequal: No Solution Exploring Operation: 27*120=3240, Resulting Numbers: [3240] 3240,29 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: 29:[17, 27, 83], Operations: ['93-10=83'] Exploring Operation: 83-17=66, Resulting Numbers: [27, 66] Generated Node #0,3,0: 29:[27, 66] Operation: 83-17=66 Exploring Operation: 83-27=56, Resulting Numbers: [17, 56] Generated Node #0,3,1: 29:[17, 56] Operation: 83-27=56 Exploring Operation: 17+83=100, Resulting Numbers: [27, 100] Generated Node #0,3,2: 29:[27, 100] Operation: 17+83=100 Exploring Operation: 17+27=44, Resulting Numbers: [83, 44] Generated Node #0,3,3: 29:[83, 44] Operation: 17+27=44 Exploring Operation: 27-17=10, Resulting Numbers: [83, 10] Generated Node #0,3,4: 29:[83, 10] Operation: 27-17=10 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 29:[27, 66], Operations: ['93-10=83', '83-17=66'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 27*66=1782, Resulting Numbers: [1782] 1782,29 unequal: No Solution No 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: 29:[17, 56], Operations: ['93-10=83', '83-27=56'] Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,29 unequal: No Solution No 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: 29:[83, 44], Operations: ['93-10=83', '17+27=44'] Exploring Operation: 83-44=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 83+44=127, Resulting Numbers: [127] 127,29 unequal: No Solution Exploring Operation: 83*44=3652, Resulting Numbers: [3652] 3652,29 unequal: No Solution No 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: 29:[27, 100], Operations: ['93-10=83', '17+83=100'] Exploring Operation: 27+100=127, Resulting Numbers: [127] 127,29 unequal: No Solution Exploring Operation: 27*100=2700, Resulting Numbers: [2700] 2700,29 unequal: No Solution Exploring Operation: 100-27=73, Resulting Numbers: [73] 73,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 29:[83, 10], Operations: ['93-10=83', '27-17=10'] Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,29 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 83*10=830, Resulting Numbers: [830] 830,29 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: 29:[17, 10, 66], Operations: ['93-27=66'] Exploring Operation: 17-10=7, Resulting Numbers: [66, 7] Generated Node #0,4,0: 29:[66, 7] Operation: 17-10=7 Exploring Operation: 17+10=27, Resulting Numbers: [66, 27] Generated Node #0,4,1: 29:[66, 27] Operation: 17+10=27 Exploring Operation: 10+66=76, Resulting Numbers: [17, 76] Generated Node #0,4,2: 29:[17, 76] Operation: 10+66=76 Exploring Operation: 66-10=56, Resulting Numbers: [17, 56] Generated Node #0,4,3: 29:[17, 56] Operation: 66-10=56 Exploring Operation: 66-17=49, Resulting Numbers: [10, 49] Generated Node #0,4,4: 29:[10, 49] Operation: 66-17=49 Moving to Node #0,4,1 Current State: 29:[66, 27], Operations: ['93-27=66', '17+10=27'] Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 66*27=1782, Resulting Numbers: [1782] 1782,29 unequal: No Solution Exploring Operation: 66+27=93, Resulting Numbers: [93] 93,29 unequal: No Solution Moving to Node #0,4,4 Current State: 29:[10, 49], Operations: ['93-27=66', '66-17=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,29 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,29 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,29 unequal: No Solution Moving to Node #0,4,3 Current State: 29:[17, 56], Operations: ['93-27=66', '66-10=56'] Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,29 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,29 unequal: No Solution Moving to Node #0,4,0 Current State: 29:[66, 7], Operations: ['93-27=66', '17-10=7'] Exploring Operation: 66+7=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 66-7=59, Resulting Numbers: [59] 59,29 unequal: No Solution Exploring Operation: 66*7=462, Resulting Numbers: [462] 462,29 unequal: No Solution Moving to Node #0,4,2 Current State: 29:[17, 76], Operations: ['93-27=66', '10+66=76'] Exploring Operation: 17*76=1292, Resulting Numbers: [1292] 1292,29 unequal: No Solution Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,29 unequal: No Solution Exploring Operation: 17+76=93, Resulting Numbers: [93] 93,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[17, 93, 37], Operations: ['27+10=37'] Exploring Operation: 93-17=76, Resulting Numbers: [37, 76] Generated Node #0,1,0: 29:[37, 76] Operation: 93-17=76 Exploring Operation: 37-17=20, Resulting Numbers: [93, 20] Generated Node #0,1,1: 29:[93, 20] Operation: 37-17=20 Exploring Operation: 93-37=56, Resulting Numbers: [17, 56] Generated Node #0,1,2: 29:[17, 56] Operation: 93-37=56 Exploring Operation: 17+93=110, Resulting Numbers: [37, 110] Generated Node #0,1,3: 29:[37, 110] Operation: 17+93=110 Exploring Operation: 17+37=54, Resulting Numbers: [93, 54] Generated Node #0,1,4: 29:[93, 54] Operation: 17+37=54 Moving to Node #0,1,2 Current State: 29:[17, 56], Operations: ['27+10=37', '93-37=56'] Exploring Operation: 17*56=952, Resulting Numbers: [952] 952,29 unequal: No Solution Exploring Operation: 17+56=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[37, 76], Operations: ['27+10=37', '93-17=76'] Exploring Operation: 76-37=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 37+76=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 37*76=2812, Resulting Numbers: [2812] 2812,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[93, 20], Operations: ['27+10=37', '37-17=20'] Exploring Operation: 93+20=113, Resulting Numbers: [113] 113,29 unequal: No Solution Exploring Operation: 93-20=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 93*20=1860, Resulting Numbers: [1860] 1860,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[37, 110], Operations: ['27+10=37', '17+93=110'] Exploring Operation: 37+110=147, Resulting Numbers: [147] 147,29 unequal: No Solution Exploring Operation: 110-37=73, Resulting Numbers: [73] 73,29 unequal: No Solution Exploring Operation: 37*110=4070, Resulting Numbers: [4070] 4070,29 unequal: No Solution Moving to Node #0,1,4 Current State: 29:[93, 54], Operations: ['27+10=37', '17+37=54'] Exploring Operation: 93+54=147, Resulting Numbers: [147] 147,29 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,29 unequal: No Solution Exploring Operation: 93*54=5022, Resulting Numbers: [5022] 5022,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 17, 62, 3, 54 ]
96
[ "62-17=45", "54-3=51", "45+51=96" ]
Current State: 96:[17, 62, 3, 54], Operations: [] Exploring Operation: 62-17=45, Resulting Numbers: [3, 54, 45] Generated Node #2: [3, 54, 45] from Operation: 62-17=45 Current State: 96:[3, 54, 45], Operations: ['62-17=45'] Exploring Operation: 54-3=51, Resulting Numbers: [45, 51] Generated Node #3: [45, 51] from Operation: 54-3=51 Current State: 96:[45, 51], Operations: ['62-17=45', '54-3=51'] Exploring Operation: 45+51=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[17, 62, 3, 54], Operations: [] Exploring Operation: 62-17=45, Resulting Numbers: [3, 54, 45] Generated Node #0,0: 96:[3, 54, 45] Operation: 62-17=45 Exploring Operation: 62-54=8, Resulting Numbers: [17, 3, 8] Generated Node #0,1: 96:[17, 3, 8] Operation: 62-54=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[17, 3, 8], Operations: ['62-54=8'] Exploring Operation: 17+8=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 96:[3, 25] Operation: 17+8=25 Exploring Operation: 17-8=9, Resulting Numbers: [3, 9] Generated Node #0,1,1: 96:[3, 9] Operation: 17-8=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 96:[3, 25], Operations: ['62-54=8', '17+8=25'] Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,96 unequal: No Solution Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,96 unequal: No Solution No 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: 96:[3, 9], Operations: ['62-54=8', '17-8=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,96 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: 96:[3, 54, 45], Operations: ['62-17=45'] Exploring Operation: 54-45=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 96:[3, 9] Operation: 54-45=9 Exploring Operation: 54+45=99, Resulting Numbers: [3, 99] Generated Node #0,0,1: 96:[3, 99] Operation: 54+45=99 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[3, 9], Operations: ['62-17=45', '54-45=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,96 unequal: No Solution No 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: 96:[3, 99], Operations: ['62-17=45', '54+45=99'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[17, 62, 3, 54], Operations: [] Exploring Operation: 62-17=45, Resulting Numbers: [3, 54, 45] Generated Node #0,0: 96:[3, 54, 45] Operation: 62-17=45 Moving to Node #0,0 Current State: 96:[3, 54, 45], Operations: ['62-17=45'] Exploring Operation: 54+45=99, Resulting Numbers: [3, 99] Generated Node #0,0,1: 96:[3, 99] Operation: 54+45=99 Moving to Node #0,0,1 Current State: 96:[3, 99], Operations: ['62-17=45', '54+45=99'] Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 43, 68, 61, 19 ]
16
[ "68+61=129", "129/43=3", "19-3=16" ]
Current State: 16:[43, 68, 61, 19], Operations: [] Exploring Operation: 68+61=129, Resulting Numbers: [43, 19, 129] Generated Node #2: [43, 19, 129] from Operation: 68+61=129 Current State: 16:[43, 19, 129], Operations: ['68+61=129'] Exploring Operation: 129/43=3, Resulting Numbers: [19, 3] Generated Node #3: [19, 3] from Operation: 129/43=3 Current State: 16:[19, 3], Operations: ['68+61=129', '129/43=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[43, 68, 61, 19], Operations: [] Exploring Operation: 68-43=25, Resulting Numbers: [61, 19, 25] Generated Node #0,0: 16:[61, 19, 25] Operation: 68-43=25 Exploring Operation: 61-43=18, Resulting Numbers: [68, 19, 18] Generated Node #0,1: 16:[68, 19, 18] Operation: 61-43=18 Exploring Operation: 68-61=7, Resulting Numbers: [43, 19, 7] Generated Node #0,2: 16:[43, 19, 7] Operation: 68-61=7 Exploring Operation: 68-19=49, Resulting Numbers: [43, 61, 49] Generated Node #0,3: 16:[43, 61, 49] Operation: 68-19=49 Exploring Operation: 43-19=24, Resulting Numbers: [68, 61, 24] Generated Node #0,4: 16:[68, 61, 24] Operation: 43-19=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[43, 19, 7], Operations: ['68-61=7'] Exploring Operation: 19-7=12, Resulting Numbers: [43, 12] Generated Node #0,2,0: 16:[43, 12] Operation: 19-7=12 Exploring Operation: 19+7=26, Resulting Numbers: [43, 26] Generated Node #0,2,1: 16:[43, 26] Operation: 19+7=26 Exploring Operation: 43-19=24, Resulting Numbers: [7, 24] Generated Node #0,2,2: 16:[7, 24] Operation: 43-19=24 Exploring Operation: 43-7=36, Resulting Numbers: [19, 36] Generated Node #0,2,3: 16:[19, 36] Operation: 43-7=36 Exploring Operation: 43+7=50, Resulting Numbers: [19, 50] Generated Node #0,2,4: 16:[19, 50] Operation: 43+7=50 Moving to Node #0,2,2 Current State: 16:[7, 24], Operations: ['68-61=7', '43-19=24'] Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[19, 36], Operations: ['68-61=7', '43-7=36'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[43, 12], Operations: ['68-61=7', '19-7=12'] Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,16 unequal: No Solution Moving to Node #0,2,1 Current State: 16:[43, 26], Operations: ['68-61=7', '19+7=26'] Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,16 unequal: No Solution Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,16 unequal: No Solution Moving to Node #0,2,4 Current State: 16:[19, 50], Operations: ['68-61=7', '43+7=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,16 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[61, 19, 25], Operations: ['68-43=25'] Exploring Operation: 25-19=6, Resulting Numbers: [61, 6] Generated Node #0,0,0: 16:[61, 6] Operation: 25-19=6 Exploring Operation: 61+19=80, Resulting Numbers: [25, 80] Generated Node #0,0,1: 16:[25, 80] Operation: 61+19=80 Exploring Operation: 61-25=36, Resulting Numbers: [19, 36] Generated Node #0,0,2: 16:[19, 36] Operation: 61-25=36 Exploring Operation: 61+25=86, Resulting Numbers: [19, 86] Generated Node #0,0,3: 16:[19, 86] Operation: 61+25=86 Exploring Operation: 61-19=42, Resulting Numbers: [25, 42] Generated Node #0,0,4: 16:[25, 42] Operation: 61-19=42 Moving to Node #0,0,2 Current State: 16:[19, 36], Operations: ['68-43=25', '61-25=36'] Exploring Operation: 19*36=684, Resulting Numbers: [684] 684,16 unequal: No Solution Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 19+36=55, Resulting Numbers: [55] 55,16 unequal: No Solution Moving to Node #0,0,4 Current State: 16:[25, 42], Operations: ['68-43=25', '61-19=42'] Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 25*42=1050, Resulting Numbers: [1050] 1050,16 unequal: No Solution Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[61, 6], Operations: ['68-43=25', '25-19=6'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,16 unequal: No Solution Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[25, 80], Operations: ['68-43=25', '61+19=80'] Exploring Operation: 25+80=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 25*80=2000, Resulting Numbers: [2000] 2000,16 unequal: No Solution Exploring Operation: 80-25=55, Resulting Numbers: [55] 55,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[19, 86], Operations: ['68-43=25', '61+25=86'] Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,16 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[68, 19, 18], Operations: ['61-43=18'] Exploring Operation: 68-18=50, Resulting Numbers: [19, 50] Generated Node #0,1,0: 16:[19, 50] Operation: 68-18=50 Exploring Operation: 19-18=1, Resulting Numbers: [68, 1] Generated Node #0,1,1: 16:[68, 1] Operation: 19-18=1 Exploring Operation: 68-19=49, Resulting Numbers: [18, 49] Generated Node #0,1,2: 16:[18, 49] Operation: 68-19=49 Exploring Operation: 68+18=86, Resulting Numbers: [19, 86] Generated Node #0,1,3: 16:[19, 86] Operation: 68+18=86 Exploring Operation: 68+19=87, Resulting Numbers: [18, 87] Generated Node #0,1,4: 16:[18, 87] Operation: 68+19=87 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[18, 49], Operations: ['61-43=18', '68-19=49'] Exploring Operation: 18+49=67, Resulting Numbers: [67] 67,16 unequal: No Solution Exploring Operation: 18*49=882, Resulting Numbers: [882] 882,16 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,16 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:[19, 50], Operations: ['61-43=18', '68-18=50'] Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,16 unequal: No Solution Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[68, 1], Operations: ['61-43=18', '19-18=1'] Exploring Operation: 68*1=68, Resulting Numbers: [68] 68,16 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,16 unequal: No Solution Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,16 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 #0,1,3 Current State: 16:[19, 86], Operations: ['61-43=18', '68+18=86'] Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,16 unequal: No Solution Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,16 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,16 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 #0,1,4 Current State: 16:[18, 87], Operations: ['61-43=18', '68+19=87'] Exploring Operation: 87-18=69, Resulting Numbers: [69] 69,16 unequal: No Solution Exploring Operation: 18+87=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 18*87=1566, Resulting Numbers: [1566] 1566,16 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 #0,3 Current State: 16:[43, 61, 49], Operations: ['68-19=49'] Exploring Operation: 49-43=6, Resulting Numbers: [61, 6] Generated Node #0,3,0: 16:[61, 6] Operation: 49-43=6 Exploring Operation: 43+61=104, Resulting Numbers: [49, 104] Generated Node #0,3,1: 16:[49, 104] Operation: 43+61=104 Exploring Operation: 61-49=12, Resulting Numbers: [43, 12] Generated Node #0,3,2: 16:[43, 12] Operation: 61-49=12 Exploring Operation: 61-43=18, Resulting Numbers: [49, 18] Generated Node #0,3,3: 16:[49, 18] Operation: 61-43=18 Exploring Operation: 43+49=92, Resulting Numbers: [61, 92] Generated Node #0,3,4: 16:[61, 92] Operation: 43+49=92 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 16:[43, 12], Operations: ['68-19=49', '61-49=12'] Exploring Operation: 43+12=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 43*12=516, Resulting Numbers: [516] 516,16 unequal: No Solution Exploring Operation: 43-12=31, Resulting Numbers: [31] 31,16 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 #0,3,3 Current State: 16:[49, 18], Operations: ['68-19=49', '61-43=18'] Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,16 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,16 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 #0,3,0 Current State: 16:[61, 6], Operations: ['68-19=49', '49-43=6'] Exploring Operation: 61*6=366, Resulting Numbers: [366] 366,16 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 61+6=67, Resulting Numbers: [67] 67,16 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 #0,3,1 Current State: 16:[49, 104], Operations: ['68-19=49', '43+61=104'] Exploring Operation: 104-49=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 49+104=153, Resulting Numbers: [153] 153,16 unequal: No Solution Exploring Operation: 49*104=5096, Resulting Numbers: [5096] 5096,16 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 #0,3,4 Current State: 16:[61, 92], Operations: ['68-19=49', '43+49=92'] Exploring Operation: 61+92=153, Resulting Numbers: [153] 153,16 unequal: No Solution Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 61*92=5612, Resulting Numbers: [5612] 5612,16 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 #0,4 Current State: 16:[68, 61, 24], Operations: ['43-19=24'] Exploring Operation: 68+24=92, Resulting Numbers: [61, 92] Generated Node #0,4,0: 16:[61, 92] Operation: 68+24=92 Exploring Operation: 68+61=129, Resulting Numbers: [24, 129] Generated Node #0,4,1: 16:[24, 129] Operation: 68+61=129 Exploring Operation: 68-61=7, Resulting Numbers: [24, 7] Generated Node #0,4,2: 16:[24, 7] Operation: 68-61=7 Exploring Operation: 68-24=44, Resulting Numbers: [61, 44] Generated Node #0,4,3: 16:[61, 44] Operation: 68-24=44 Exploring Operation: 61-24=37, Resulting Numbers: [68, 37] Generated Node #0,4,4: 16:[68, 37] Operation: 61-24=37 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 16:[24, 7], Operations: ['43-19=24', '68-61=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,16 unequal: No Solution Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,16 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 #0,4,3 Current State: 16:[61, 44], Operations: ['43-19=24', '68-24=44'] Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 61*44=2684, Resulting Numbers: [2684] 2684,16 unequal: No Solution Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,16 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 #0,4,4 Current State: 16:[68, 37], Operations: ['43-19=24', '61-24=37'] Exploring Operation: 68-37=31, Resulting Numbers: [31] 31,16 unequal: No Solution Exploring Operation: 68+37=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 68*37=2516, Resulting Numbers: [2516] 2516,16 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 #0,4,0 Current State: 16:[61, 92], Operations: ['43-19=24', '68+24=92'] Exploring Operation: 61*92=5612, Resulting Numbers: [5612] 5612,16 unequal: No Solution Exploring Operation: 61+92=153, Resulting Numbers: [153] 153,16 unequal: No Solution Exploring Operation: 92-61=31, Resulting Numbers: [31] 31,16 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 #0,4,1 Current State: 16:[24, 129], Operations: ['43-19=24', '68+61=129'] Exploring Operation: 24+129=153, Resulting Numbers: [153] 153,16 unequal: No Solution Exploring Operation: 129-24=105, Resulting Numbers: [105] 105,16 unequal: No Solution Exploring Operation: 24*129=3096, Resulting Numbers: [3096] 3096,16 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_5
mult_heuristic
[ 40, 21, 19, 14 ]
94
[ "40+21=61", "19+14=33", "61+33=94" ]
Current State: 94:[40, 21, 19, 14], Operations: [] Exploring Operation: 40+21=61, Resulting Numbers: [19, 14, 61] Generated Node #2: [19, 14, 61] from Operation: 40+21=61 Current State: 94:[19, 14, 61], Operations: ['40+21=61'] Exploring Operation: 19+14=33, Resulting Numbers: [61, 33] Generated Node #3: [61, 33] from Operation: 19+14=33 Current State: 94:[61, 33], Operations: ['40+21=61', '19+14=33'] Exploring Operation: 61+33=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[40, 21, 19, 14], Operations: [] Exploring Operation: 21-19=2, Resulting Numbers: [40, 14, 2] Generated Node #0,0: 94:[40, 14, 2] Operation: 21-19=2 Exploring Operation: 19-14=5, Resulting Numbers: [40, 21, 5] Generated Node #0,1: 94:[40, 21, 5] Operation: 19-14=5 Exploring Operation: 21-14=7, Resulting Numbers: [40, 19, 7] Generated Node #0,2: 94:[40, 19, 7] Operation: 21-14=7 Exploring Operation: 21+14=35, Resulting Numbers: [40, 19, 35] Generated Node #0,3: 94:[40, 19, 35] Operation: 21+14=35 Exploring Operation: 21+19=40, Resulting Numbers: [40, 14, 40] Generated Node #0,4: 94:[40, 14, 40] Operation: 21+19=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[40, 14, 2], Operations: ['21-19=2'] Exploring Operation: 40+2=42, Resulting Numbers: [14, 42] Generated Node #0,0,0: 94:[14, 42] Operation: 40+2=42 Exploring Operation: 40+14=54, Resulting Numbers: [2, 54] Generated Node #0,0,1: 94:[2, 54] Operation: 40+14=54 Exploring Operation: 40-14=26, Resulting Numbers: [2, 26] Generated Node #0,0,2: 94:[2, 26] Operation: 40-14=26 Exploring Operation: 14/2=7, Resulting Numbers: [40, 7] Generated Node #0,0,3: 94:[40, 7] Operation: 14/2=7 Exploring Operation: 14-2=12, Resulting Numbers: [40, 12] Generated Node #0,0,4: 94:[40, 12] Operation: 14-2=12 Moving to Node #0,0,1 Current State: 94:[2, 54], Operations: ['21-19=2', '40+14=54'] Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 2*54=108, Resulting Numbers: [108] 108,94 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[40, 7], Operations: ['21-19=2', '14/2=7'] Exploring Operation: 40+7=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 40*7=280, Resulting Numbers: [280] 280,94 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[14, 42], Operations: ['21-19=2', '40+2=42'] Exploring Operation: 14+42=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 14*42=588, Resulting Numbers: [588] 588,94 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[40, 12], Operations: ['21-19=2', '14-2=12'] Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,94 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[2, 26], Operations: ['21-19=2', '40-14=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,94 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,94 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,94 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,94 unequal: No Solution No 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: 94:[40, 14, 40], Operations: ['21+19=40'] Exploring Operation: 14+40=54, Resulting Numbers: [40, 54] Generated Node #0,4,0: 94:[40, 54] Operation: 14+40=54 Exploring Operation: 40/40=1, Resulting Numbers: [14, 1] Generated Node #0,4,1: 94:[14, 1] Operation: 40/40=1 Exploring Operation: 40-40=0, Resulting Numbers: [14, 0] Generated Node #0,4,2: 94:[14, 0] Operation: 40-40=0 Exploring Operation: 40+14=54, Resulting Numbers: [40, 54] Generated Node #0,4,3: 94:[40, 54] Operation: 40+14=54 Exploring Operation: 40+40=80, Resulting Numbers: [14, 80] Generated Node #0,4,4: 94:[14, 80] Operation: 40+40=80 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 94:[14, 1], Operations: ['21+19=40', '40/40=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,94 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,94 unequal: No Solution No 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: 94:[40, 54], Operations: ['21+19=40', '14+40=54'] Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,94 unequal: No Solution Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,94 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[40, 21, 19, 14], Operations: [] Exploring Operation: 21+19=40, Resulting Numbers: [40, 14, 40] Generated Node #0,4: 94:[40, 14, 40] Operation: 21+19=40 Moving to Node #0,4 Current State: 94:[40, 14, 40], Operations: ['21+19=40'] Exploring Operation: 14+40=54, Resulting Numbers: [40, 54] Generated Node #0,4,0: 94:[40, 54] Operation: 14+40=54 Moving to Node #0,4,0 Current State: 94:[40, 54], Operations: ['21+19=40', '14+40=54'] Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.961806
hs_5
sum_heuristic
[ 2, 6, 12, 82 ]
90
[ "6-2=4", "12+82=94", "94-4=90" ]
Current State: 90:[2, 6, 12, 82], Operations: [] Exploring Operation: 6-2=4, Resulting Numbers: [12, 82, 4] Generated Node #2: [12, 82, 4] from Operation: 6-2=4 Current State: 90:[12, 82, 4], Operations: ['6-2=4'] Exploring Operation: 12+82=94, Resulting Numbers: [4, 94] Generated Node #3: [4, 94] from Operation: 12+82=94 Current State: 90:[4, 94], Operations: ['6-2=4', '12+82=94'] Exploring Operation: 94-4=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[2, 6, 12, 82], Operations: [] Exploring Operation: 12/2=6, Resulting Numbers: [6, 82, 6] Generated Node #0,0: 90:[6, 82, 6] Operation: 12/2=6 Exploring Operation: 12-2=10, Resulting Numbers: [6, 82, 10] Generated Node #0,1: 90:[6, 82, 10] Operation: 12-2=10 Exploring Operation: 12+82=94, Resulting Numbers: [2, 6, 94] Generated Node #0,2: 90:[2, 6, 94] Operation: 12+82=94 Exploring Operation: 82/2=41, Resulting Numbers: [6, 12, 41] Generated Node #0,3: 90:[6, 12, 41] Operation: 82/2=41 Exploring Operation: 6+82=88, Resulting Numbers: [2, 12, 88] Generated Node #0,4: 90:[2, 12, 88] Operation: 6+82=88 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[2, 6, 94], Operations: ['12+82=94'] Exploring Operation: 94/2=47, Resulting Numbers: [6, 47] Generated Node #0,2,0: 90:[6, 47] Operation: 94/2=47 Exploring Operation: 6/2=3, Resulting Numbers: [94, 3] Generated Node #0,2,1: 90:[94, 3] Operation: 6/2=3 Exploring Operation: 94-6=88, Resulting Numbers: [2, 88] Generated Node #0,2,2: 90:[2, 88] Operation: 94-6=88 Exploring Operation: 94-2=92, Resulting Numbers: [6, 92] Generated Node #0,2,3: 90:[6, 92] Operation: 94-2=92 Exploring Operation: 2+6=8, Resulting Numbers: [94, 8] Generated Node #0,2,4: 90:[94, 8] Operation: 2+6=8 Moving to Node #0,2,0 Current State: 90:[6, 47], Operations: ['12+82=94', '94/2=47'] Exploring Operation: 6*47=282, Resulting Numbers: [282] 282,90 unequal: No Solution Exploring Operation: 6+47=53, Resulting Numbers: [53] 53,90 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[6, 92], Operations: ['12+82=94', '94-2=92'] Exploring Operation: 92-6=86, Resulting Numbers: [86] 86,90 unequal: No Solution Exploring Operation: 6+92=98, Resulting Numbers: [98] 98,90 unequal: No Solution Exploring Operation: 6*92=552, Resulting Numbers: [552] 552,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[2, 88], Operations: ['12+82=94', '94-6=88'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,90 unequal: No Solution Exploring Operation: 2*88=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,90 unequal: No Solution Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[2, 6, 12, 82], Operations: [] Exploring Operation: 12+82=94, Resulting Numbers: [2, 6, 94] Generated Node #0,2: 90:[2, 6, 94] Operation: 12+82=94 Moving to Node #0,2 Current State: 90:[2, 6, 94], Operations: ['12+82=94'] Exploring Operation: 94-6=88, Resulting Numbers: [2, 88] Generated Node #0,2,2: 90:[2, 88] Operation: 94-6=88 Moving to Node #0,2,2 Current State: 90:[2, 88], Operations: ['12+82=94', '94-6=88'] Exploring Operation: 2+88=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_5
mult_heuristic
[ 99, 32, 29, 87 ]
64
[ "99-32=67", "87/29=3", "67-3=64" ]
Current State: 64:[99, 32, 29, 87], Operations: [] Exploring Operation: 99-32=67, Resulting Numbers: [29, 87, 67] Generated Node #2: [29, 87, 67] from Operation: 99-32=67 Current State: 64:[29, 87, 67], Operations: ['99-32=67'] Exploring Operation: 87/29=3, Resulting Numbers: [67, 3] Generated Node #3: [67, 3] from Operation: 87/29=3 Current State: 64:[67, 3], Operations: ['99-32=67', '87/29=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[99, 32, 29, 87], Operations: [] Exploring Operation: 99-87=12, Resulting Numbers: [32, 29, 12] Generated Node #0,0: 64:[32, 29, 12] Operation: 99-87=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[32, 29, 12], Operations: ['99-87=12'] Exploring Operation: 29-12=17, Resulting Numbers: [32, 17] Generated Node #0,0,0: 64:[32, 17] Operation: 29-12=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[32, 17], Operations: ['99-87=12', '29-12=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 19, 18, 2, 56 ]
36
[ "19*2=38", "18+56=74", "74-38=36" ]
Current State: 36:[19, 18, 2, 56], Operations: [] Exploring Operation: 19*2=38, Resulting Numbers: [18, 56, 38] Generated Node #2: [18, 56, 38] from Operation: 19*2=38 Current State: 36:[18, 56, 38], Operations: ['19*2=38'] Exploring Operation: 18+56=74, Resulting Numbers: [38, 74] Generated Node #3: [38, 74] from Operation: 18+56=74 Current State: 36:[38, 74], Operations: ['19*2=38', '18+56=74'] Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[19, 18, 2, 56], Operations: [] Exploring Operation: 56-18=38, Resulting Numbers: [19, 2, 38] Generated Node #0,0: 36:[19, 2, 38] Operation: 56-18=38 Exploring Operation: 56-19=37, Resulting Numbers: [18, 2, 37] Generated Node #0,1: 36:[18, 2, 37] Operation: 56-19=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[18, 2, 37], Operations: ['56-19=37'] Exploring Operation: 18*2=36, Resulting Numbers: [37, 36] Generated Node #0,1,0: 36:[37, 36] Operation: 18*2=36 Exploring Operation: 18/2=9, Resulting Numbers: [37, 9] Generated Node #0,1,1: 36:[37, 9] Operation: 18/2=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 36:[37, 36], Operations: ['56-19=37', '18*2=36'] Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,36 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 36:[37, 9], Operations: ['56-19=37', '18/2=9'] Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,36 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[19, 2, 38], Operations: ['56-18=38'] Exploring Operation: 38-19=19, Resulting Numbers: [2, 19] Generated Node #0,0,0: 36:[2, 19] Operation: 38-19=19 Exploring Operation: 38/19=2, Resulting Numbers: [2, 2] Generated Node #0,0,1: 36:[2, 2] Operation: 38/19=2 Moving to Node #0,0,1 Current State: 36:[2, 2], Operations: ['56-18=38', '38/19=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,36 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[2, 19], Operations: ['56-18=38', '38-19=19'] Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,36 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,36 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
[ 64, 27, 33, 9 ]
34
[ "64-33=31", "27/9=3", "31+3=34" ]
Current State: 34:[64, 27, 33, 9], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [27, 9, 31] Generated Node #2: [27, 9, 31] from Operation: 64-33=31 Current State: 34:[27, 9, 31], Operations: ['64-33=31'] Exploring Operation: 27/9=3, Resulting Numbers: [31, 3] Generated Node #3: [31, 3] from Operation: 27/9=3 Current State: 34:[31, 3], Operations: ['64-33=31', '27/9=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[64, 27, 33, 9], Operations: [] Exploring Operation: 27-9=18, Resulting Numbers: [64, 33, 18] Generated Node #0,0: 34:[64, 33, 18] Operation: 27-9=18 Exploring Operation: 64-27=37, Resulting Numbers: [33, 9, 37] Generated Node #0,1: 34:[33, 9, 37] Operation: 64-27=37 Exploring Operation: 64-33=31, Resulting Numbers: [27, 9, 31] Generated Node #0,2: 34:[27, 9, 31] Operation: 64-33=31 Exploring Operation: 64-9=55, Resulting Numbers: [27, 33, 55] Generated Node #0,3: 34:[27, 33, 55] Operation: 64-9=55 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[33, 9, 37], Operations: ['64-27=37'] Exploring Operation: 33+9=42, Resulting Numbers: [37, 42] Generated Node #0,1,0: 34:[37, 42] Operation: 33+9=42 Exploring Operation: 33-9=24, Resulting Numbers: [37, 24] Generated Node #0,1,1: 34:[37, 24] Operation: 33-9=24 Exploring Operation: 37-9=28, Resulting Numbers: [33, 28] Generated Node #0,1,2: 34:[33, 28] Operation: 37-9=28 Exploring Operation: 37-33=4, Resulting Numbers: [9, 4] Generated Node #0,1,3: 34:[9, 4] Operation: 37-33=4 Moving to Node #0,1,2 Current State: 34:[33, 28], Operations: ['64-27=37', '37-9=28'] Exploring Operation: 33*28=924, Resulting Numbers: [924] 924,34 unequal: No Solution Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 33+28=61, Resulting Numbers: [61] 61,34 unequal: No Solution Moving to Node #0,1,3 Current State: 34:[9, 4], Operations: ['64-27=37', '37-33=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,34 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,34 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[37, 24], Operations: ['64-27=37', '33-9=24'] Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,34 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,34 unequal: No Solution Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[37, 42], Operations: ['64-27=37', '33+9=42'] Exploring Operation: 37+42=79, Resulting Numbers: [79] 79,34 unequal: No Solution Exploring Operation: 42-37=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 37*42=1554, Resulting Numbers: [1554] 1554,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 34:[27, 9, 31], Operations: ['64-33=31'] Exploring Operation: 27-9=18, Resulting Numbers: [31, 18] Generated Node #0,2,0: 34:[31, 18] Operation: 27-9=18 Exploring Operation: 31-27=4, Resulting Numbers: [9, 4] Generated Node #0,2,1: 34:[9, 4] Operation: 31-27=4 Exploring Operation: 27+9=36, Resulting Numbers: [31, 36] Generated Node #0,2,2: 34:[31, 36] Operation: 27+9=36 Exploring Operation: 27/9=3, Resulting Numbers: [31, 3] Generated Node #0,2,3: 34:[31, 3] Operation: 27/9=3 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 34:[31, 18], Operations: ['64-33=31', '27-9=18'] Exploring Operation: 31*18=558, Resulting Numbers: [558] 558,34 unequal: No Solution Exploring Operation: 31+18=49, Resulting Numbers: [49] 49,34 unequal: No Solution Exploring Operation: 31-18=13, Resulting Numbers: [13] 13,34 unequal: No Solution No 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: 34:[31, 3], Operations: ['64-33=31', '27/9=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,34 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,34 unequal: No Solution Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[64, 27, 33, 9], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [27, 9, 31] Generated Node #0,2: 34:[27, 9, 31] Operation: 64-33=31 Moving to Node #0,2 Current State: 34:[27, 9, 31], Operations: ['64-33=31'] Exploring Operation: 27/9=3, Resulting Numbers: [31, 3] Generated Node #0,2,3: 34:[31, 3] Operation: 27/9=3 Moving to Node #0,2,3 Current State: 34:[31, 3], Operations: ['64-33=31', '27/9=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 15, 98, 14, 37 ]
28
[ "14*37=518", "518-98=420", "420/15=28" ]
Current State: 28:[15, 98, 14, 37], Operations: [] Exploring Operation: 14*37=518, Resulting Numbers: [15, 98, 518] Generated Node #2: [15, 98, 518] from Operation: 14*37=518 Current State: 28:[15, 98, 518], Operations: ['14*37=518'] Exploring Operation: 518-98=420, Resulting Numbers: [15, 420] Generated Node #3: [15, 420] from Operation: 518-98=420 Current State: 28:[15, 420], Operations: ['14*37=518', '518-98=420'] Exploring Operation: 420/15=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[15, 98, 14, 37], Operations: [] Exploring Operation: 98-37=61, Resulting Numbers: [15, 14, 61] Generated Node #0,0: 28:[15, 14, 61] Operation: 98-37=61 Exploring Operation: 98/14=7, Resulting Numbers: [15, 37, 7] Generated Node #0,1: 28:[15, 37, 7] Operation: 98/14=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[15, 37, 7], Operations: ['98/14=7'] Exploring Operation: 37-15=22, Resulting Numbers: [7, 22] Generated Node #0,1,0: 28:[7, 22] Operation: 37-15=22 Exploring Operation: 37-7=30, Resulting Numbers: [15, 30] Generated Node #0,1,1: 28:[15, 30] Operation: 37-7=30 Moving to Node #0,1,1 Current State: 28:[15, 30], Operations: ['98/14=7', '37-7=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,28 unequal: No Solution Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,28 unequal: No Solution Moving to Node #0,1,0 Current State: 28:[7, 22], Operations: ['98/14=7', '37-15=22'] Exploring Operation: 7+22=29, Resulting Numbers: [29] 29,28 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,28 unequal: No Solution No 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: 28:[15, 14, 61], Operations: ['98-37=61'] Exploring Operation: 61-14=47, Resulting Numbers: [15, 47] Generated Node #0,0,0: 28:[15, 47] Operation: 61-14=47 Exploring Operation: 61-15=46, Resulting Numbers: [14, 46] Generated Node #0,0,1: 28:[14, 46] Operation: 61-15=46 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[14, 46], Operations: ['98-37=61', '61-15=46'] Exploring Operation: 14+46=60, Resulting Numbers: [60] 60,28 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,28 unequal: No Solution No 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: 28:[15, 47], Operations: ['98-37=61', '61-14=47'] Exploring Operation: 47-15=32, Resulting Numbers: [32] 32,28 unequal: No Solution Exploring Operation: 15+47=62, Resulting Numbers: [62] 62,28 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
[ 76, 47, 80, 37 ]
80
[ "76+47=123", "80-37=43", "123-43=80" ]
Current State: 80:[76, 47, 80, 37], Operations: [] Exploring Operation: 76+47=123, Resulting Numbers: [80, 37, 123] Generated Node #2: [80, 37, 123] from Operation: 76+47=123 Current State: 80:[80, 37, 123], Operations: ['76+47=123'] Exploring Operation: 80-37=43, Resulting Numbers: [123, 43] Generated Node #3: [123, 43] from Operation: 80-37=43 Current State: 80:[123, 43], Operations: ['76+47=123', '80-37=43'] Exploring Operation: 123-43=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[76, 47, 80, 37], Operations: [] Exploring Operation: 47+37=84, Resulting Numbers: [76, 80, 84] Generated Node #0,0: 80:[76, 80, 84] Operation: 47+37=84 Exploring Operation: 80-76=4, Resulting Numbers: [47, 37, 4] Generated Node #0,1: 80:[47, 37, 4] Operation: 80-76=4 Exploring Operation: 76-37=39, Resulting Numbers: [47, 80, 39] Generated Node #0,2: 80:[47, 80, 39] Operation: 76-37=39 Exploring Operation: 47-37=10, Resulting Numbers: [76, 80, 10] Generated Node #0,3: 80:[76, 80, 10] Operation: 47-37=10 Start Sub Search at level 1: Moving to Node #0,3 Current State: 80:[76, 80, 10], Operations: ['47-37=10'] Exploring Operation: 76-10=66, Resulting Numbers: [80, 66] Generated Node #0,3,0: 80:[80, 66] Operation: 76-10=66 Exploring Operation: 80-76=4, Resulting Numbers: [10, 4] Generated Node #0,3,1: 80:[10, 4] Operation: 80-76=4 Exploring Operation: 80/10=8, Resulting Numbers: [76, 8] Generated Node #0,3,2: 80:[76, 8] Operation: 80/10=8 Exploring Operation: 76+10=86, Resulting Numbers: [80, 86] Generated Node #0,3,3: 80:[80, 86] Operation: 76+10=86 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 80:[10, 4], Operations: ['47-37=10', '80-76=4'] Exploring Operation: 10*4=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,80 unequal: No Solution Exploring Operation: 10+4=14, Resulting Numbers: [14] 14,80 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:[76, 8], Operations: ['47-37=10', '80/10=8'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,80 unequal: No Solution Exploring Operation: 76+8=84, Resulting Numbers: [84] 84,80 unequal: No Solution Exploring Operation: 76*8=608, Resulting Numbers: [608] 608,80 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 #0,3,3 Current State: 80:[80, 86], Operations: ['47-37=10', '76+10=86'] Exploring Operation: 80*86=6880, Resulting Numbers: [6880] 6880,80 unequal: No Solution Exploring Operation: 80+86=166, Resulting Numbers: [166] 166,80 unequal: No Solution Exploring Operation: 86-80=6, Resulting Numbers: [6] 6,80 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:[80, 66], Operations: ['47-37=10', '76-10=66'] Exploring Operation: 80+66=146, Resulting Numbers: [146] 146,80 unequal: No Solution Exploring Operation: 80*66=5280, Resulting Numbers: [5280] 5280,80 unequal: No Solution Exploring Operation: 80-66=14, Resulting Numbers: [14] 14,80 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:[76, 80, 84], Operations: ['47+37=84'] Exploring Operation: 84-80=4, Resulting Numbers: [76, 4] Generated Node #0,0,0: 80:[76, 4] Operation: 84-80=4 Exploring Operation: 84-76=8, Resulting Numbers: [80, 8] Generated Node #0,0,1: 80:[80, 8] Operation: 84-76=8 Exploring Operation: 80-76=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 80:[84, 4] Operation: 80-76=4 Exploring Operation: 76+80=156, Resulting Numbers: [84, 156] Generated Node #0,0,3: 80:[84, 156] Operation: 76+80=156 Moving to Node #0,0,1 Current State: 80:[80, 8], Operations: ['47+37=84', '84-76=8'] Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,80 unequal: No Solution Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,80 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[84, 4], Operations: ['47+37=84', '80-76=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[76, 47, 80, 37], Operations: [] Exploring Operation: 47+37=84, Resulting Numbers: [76, 80, 84] Generated Node #0,0: 80:[76, 80, 84] Operation: 47+37=84 Moving to Node #0,0 Current State: 80:[76, 80, 84], Operations: ['47+37=84'] Exploring Operation: 80-76=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 80:[84, 4] Operation: 80-76=4 Moving to Node #0,0,2 Current State: 80:[84, 4], Operations: ['47+37=84', '80-76=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 14, 69, 50, 65 ]
68
[ "14+69=83", "65-50=15", "83-15=68" ]
Current State: 68:[14, 69, 50, 65], Operations: [] Exploring Operation: 14+69=83, Resulting Numbers: [50, 65, 83] Generated Node #2: [50, 65, 83] from Operation: 14+69=83 Current State: 68:[50, 65, 83], Operations: ['14+69=83'] Exploring Operation: 65-50=15, Resulting Numbers: [83, 15] Generated Node #3: [83, 15] from Operation: 65-50=15 Current State: 68:[83, 15], Operations: ['14+69=83', '65-50=15'] Exploring Operation: 83-15=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[14, 69, 50, 65], Operations: [] Exploring Operation: 50-14=36, Resulting Numbers: [69, 65, 36] Generated Node #0,0: 68:[69, 65, 36] Operation: 50-14=36 Exploring Operation: 14+50=64, Resulting Numbers: [69, 65, 64] Generated Node #0,1: 68:[69, 65, 64] Operation: 14+50=64 Exploring Operation: 65-50=15, Resulting Numbers: [14, 69, 15] Generated Node #0,2: 68:[14, 69, 15] Operation: 65-50=15 Moving to Node #0,0 Current State: 68:[69, 65, 36], Operations: ['50-14=36'] Exploring Operation: 69-36=33, Resulting Numbers: [65, 33] Generated Node #0,0,0: 68:[65, 33] Operation: 69-36=33 Exploring Operation: 65-36=29, Resulting Numbers: [69, 29] Generated Node #0,0,1: 68:[69, 29] Operation: 65-36=29 Exploring Operation: 69-65=4, Resulting Numbers: [36, 4] Generated Node #0,0,2: 68:[36, 4] Operation: 69-65=4 Moving to Node #0,2 Current State: 68:[14, 69, 15], Operations: ['65-50=15'] Exploring Operation: 14+15=29, Resulting Numbers: [69, 29] Generated Node #0,2,0: 68:[69, 29] Operation: 14+15=29 Exploring Operation: 15-14=1, Resulting Numbers: [69, 1] Generated Node #0,2,1: 68:[69, 1] Operation: 15-14=1 Exploring Operation: 69-14=55, Resulting Numbers: [15, 55] Generated Node #0,2,2: 68:[15, 55] Operation: 69-14=55 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[69, 1], Operations: ['65-50=15', '15-14=1'] Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[14, 69, 50, 65], Operations: [] Exploring Operation: 65-50=15, Resulting Numbers: [14, 69, 15] Generated Node #0,2: 68:[14, 69, 15] Operation: 65-50=15 Moving to Node #0,2 Current State: 68:[14, 69, 15], Operations: ['65-50=15'] Exploring Operation: 15-14=1, Resulting Numbers: [69, 1] Generated Node #0,2,1: 68:[69, 1] Operation: 15-14=1 Moving to Node #0,2,1 Current State: 68:[69, 1], Operations: ['65-50=15', '15-14=1'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 94, 47, 61, 88 ]
84
[ "94-88=6", "61-47=14", "6*14=84" ]
Current State: 84:[94, 47, 61, 88], Operations: [] Exploring Operation: 94-88=6, Resulting Numbers: [47, 61, 6] Generated Node #2: [47, 61, 6] from Operation: 94-88=6 Current State: 84:[47, 61, 6], Operations: ['94-88=6'] Exploring Operation: 61-47=14, Resulting Numbers: [6, 14] Generated Node #3: [6, 14] from Operation: 61-47=14 Current State: 84:[6, 14], Operations: ['94-88=6', '61-47=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[94, 47, 61, 88], Operations: [] Exploring Operation: 94-61=33, Resulting Numbers: [47, 88, 33] Generated Node #0,0: 84:[47, 88, 33] Operation: 94-61=33 Moving to Node #0,0 Current State: 84:[47, 88, 33], Operations: ['94-61=33'] Exploring Operation: 47-33=14, Resulting Numbers: [88, 14] Generated Node #0,0,0: 84:[88, 14] Operation: 47-33=14 Moving to Node #0,0,0 Current State: 84:[88, 14], Operations: ['94-61=33', '47-33=14'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,84 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 81, 29, 69, 33 ]
74
[ "81+29=110", "69-33=36", "110-36=74" ]
Current State: 74:[81, 29, 69, 33], Operations: [] Exploring Operation: 81+29=110, Resulting Numbers: [69, 33, 110] Generated Node #2: [69, 33, 110] from Operation: 81+29=110 Current State: 74:[69, 33, 110], Operations: ['81+29=110'] Exploring Operation: 69-33=36, Resulting Numbers: [110, 36] Generated Node #3: [110, 36] from Operation: 69-33=36 Current State: 74:[110, 36], Operations: ['81+29=110', '69-33=36'] Exploring Operation: 110-36=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[81, 29, 69, 33], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [81, 29, 36] Generated Node #0,0: 74:[81, 29, 36] Operation: 69-33=36 Exploring Operation: 69-29=40, Resulting Numbers: [81, 33, 40] Generated Node #0,1: 74:[81, 33, 40] Operation: 69-29=40 Exploring Operation: 33-29=4, Resulting Numbers: [81, 69, 4] Generated Node #0,2: 74:[81, 69, 4] Operation: 33-29=4 Moving to Node #0,1 Current State: 74:[81, 33, 40], Operations: ['69-29=40'] Exploring Operation: 33+40=73, Resulting Numbers: [81, 73] Generated Node #0,1,0: 74:[81, 73] Operation: 33+40=73 Exploring Operation: 40-33=7, Resulting Numbers: [81, 7] Generated Node #0,1,1: 74:[81, 7] Operation: 40-33=7 Exploring Operation: 81-40=41, Resulting Numbers: [33, 41] Generated Node #0,1,2: 74:[33, 41] Operation: 81-40=41 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[81, 73], Operations: ['69-29=40', '33+40=73'] Exploring Operation: 81*73=5913, Resulting Numbers: [5913] 5913,74 unequal: No Solution Exploring Operation: 81+73=154, Resulting Numbers: [154] 154,74 unequal: No Solution Exploring Operation: 81-73=8, Resulting Numbers: [8] 8,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[33, 41], Operations: ['69-29=40', '81-40=41'] Exploring Operation: 33*41=1353, Resulting Numbers: [1353] 1353,74 unequal: No Solution Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[81, 29, 69, 33], Operations: [] Exploring Operation: 69-29=40, Resulting Numbers: [81, 33, 40] Generated Node #0,1: 74:[81, 33, 40] Operation: 69-29=40 Moving to Node #0,1 Current State: 74:[81, 33, 40], Operations: ['69-29=40'] Exploring Operation: 81-40=41, Resulting Numbers: [33, 41] Generated Node #0,1,2: 74:[33, 41] Operation: 81-40=41 Moving to Node #0,1,2 Current State: 74:[33, 41], Operations: ['69-29=40', '81-40=41'] Exploring Operation: 33+41=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 54, 17, 51, 5 ]
38
[ "54+51=105", "105/5=21", "17+21=38" ]
Current State: 38:[54, 17, 51, 5], Operations: [] Exploring Operation: 54+51=105, Resulting Numbers: [17, 5, 105] Generated Node #2: [17, 5, 105] from Operation: 54+51=105 Current State: 38:[17, 5, 105], Operations: ['54+51=105'] Exploring Operation: 105/5=21, Resulting Numbers: [17, 21] Generated Node #3: [17, 21] from Operation: 105/5=21 Current State: 38:[17, 21], Operations: ['54+51=105', '105/5=21'] Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[54, 17, 51, 5], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [17, 5, 3] Generated Node #0,0: 38:[17, 5, 3] Operation: 54-51=3 Exploring Operation: 54-17=37, Resulting Numbers: [51, 5, 37] Generated Node #0,1: 38:[51, 5, 37] Operation: 54-17=37 Exploring Operation: 51-17=34, Resulting Numbers: [54, 5, 34] Generated Node #0,2: 38:[54, 5, 34] Operation: 51-17=34 Exploring Operation: 51/17=3, Resulting Numbers: [54, 5, 3] Generated Node #0,3: 38:[54, 5, 3] Operation: 51/17=3 Moving to Node #0,0 Current State: 38:[17, 5, 3], Operations: ['54-51=3'] Exploring Operation: 17+3=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 38:[5, 20] Operation: 17+3=20 Exploring Operation: 17+5=22, Resulting Numbers: [3, 22] Generated Node #0,0,1: 38:[3, 22] Operation: 17+5=22 Exploring Operation: 5*3=15, Resulting Numbers: [17, 15] Generated Node #0,0,2: 38:[17, 15] Operation: 5*3=15 Exploring Operation: 5-3=2, Resulting Numbers: [17, 2] Generated Node #0,0,3: 38:[17, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 38:[17, 2], Operations: ['54-51=3', '5-3=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,38 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 38:[5, 20], Operations: ['54-51=3', '17+3=20'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 38:[3, 22], Operations: ['54-51=3', '17+5=22'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 3+22=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 3*22=66, Resulting Numbers: [66] 66,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 38:[17, 15], Operations: ['54-51=3', '5*3=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,38 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,38 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: 38:[51, 5, 37], Operations: ['54-17=37'] Exploring Operation: 51-5=46, Resulting Numbers: [37, 46] Generated Node #0,1,0: 38:[37, 46] Operation: 51-5=46 Exploring Operation: 51+5=56, Resulting Numbers: [37, 56] Generated Node #0,1,1: 38:[37, 56] Operation: 51+5=56 Exploring Operation: 5+37=42, Resulting Numbers: [51, 42] Generated Node #0,1,2: 38:[51, 42] Operation: 5+37=42 Exploring Operation: 51-37=14, Resulting Numbers: [5, 14] Generated Node #0,1,3: 38:[5, 14] Operation: 51-37=14 Moving to Node #0,3 Current State: 38:[54, 5, 3], Operations: ['51/17=3'] Exploring Operation: 54/3=18, Resulting Numbers: [5, 18] Generated Node #0,3,0: 38:[5, 18] Operation: 54/3=18 Exploring Operation: 54-5=49, Resulting Numbers: [3, 49] Generated Node #0,3,1: 38:[3, 49] Operation: 54-5=49 Exploring Operation: 54-3=51, Resulting Numbers: [5, 51] Generated Node #0,3,2: 38:[5, 51] Operation: 54-3=51 Exploring Operation: 5-3=2, Resulting Numbers: [54, 2] Generated Node #0,3,3: 38:[54, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 38:[5, 18], Operations: ['51/17=3', '54/3=18'] Exploring Operation: 18-5=13, Resulting Numbers: [13] 13,38 unequal: No Solution Exploring Operation: 5+18=23, Resulting Numbers: [23] 23,38 unequal: No Solution Exploring Operation: 5*18=90, Resulting Numbers: [90] 90,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 38:[3, 49], Operations: ['51/17=3', '54-5=49'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 3*49=147, Resulting Numbers: [147] 147,38 unequal: No Solution Exploring Operation: 3+49=52, Resulting Numbers: [52] 52,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 38:[5, 51], Operations: ['51/17=3', '54-3=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,38 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,38 unequal: No Solution Exploring Operation: 5*51=255, Resulting Numbers: [255] 255,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 38:[54, 2], Operations: ['51/17=3', '5-3=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,38 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,38 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,38 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,38 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: 38:[54, 5, 34], Operations: ['51-17=34'] Exploring Operation: 54-34=20, Resulting Numbers: [5, 20] Generated Node #0,2,0: 38:[5, 20] Operation: 54-34=20 Exploring Operation: 5+34=39, Resulting Numbers: [54, 39] Generated Node #0,2,1: 38:[54, 39] Operation: 5+34=39 Exploring Operation: 54+5=59, Resulting Numbers: [34, 59] Generated Node #0,2,2: 38:[34, 59] Operation: 54+5=59 Exploring Operation: 54-5=49, Resulting Numbers: [34, 49] Generated Node #0,2,3: 38:[34, 49] Operation: 54-5=49 Moving to Node #0,2,0 Current State: 38:[5, 20], Operations: ['51-17=34', '54-34=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,38 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,38 unequal: No Solution Moving to Node #0,1,3 Current State: 38:[5, 14], Operations: ['54-17=37', '51-37=14'] Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,38 unequal: No Solution Moving to Node #0,1,0 Current State: 38:[37, 46], Operations: ['54-17=37', '51-5=46'] Exploring Operation: 37*46=1702, Resulting Numbers: [1702] 1702,38 unequal: No Solution Exploring Operation: 37+46=83, Resulting Numbers: [83] 83,38 unequal: No Solution Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[34, 49], Operations: ['51-17=34', '54-5=49'] Exploring Operation: 34+49=83, Resulting Numbers: [83] 83,38 unequal: No Solution Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,38 unequal: No Solution Exploring Operation: 34*49=1666, Resulting Numbers: [1666] 1666,38 unequal: No Solution Moving to Node #0,1,2 Current State: 38:[51, 42], Operations: ['54-17=37', '5+37=42'] Exploring Operation: 51+42=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,38 unequal: No Solution Exploring Operation: 51*42=2142, Resulting Numbers: [2142] 2142,38 unequal: No Solution Moving to Node #0,2,1 Current State: 38:[54, 39], Operations: ['51-17=34', '5+34=39'] Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 54*39=2106, Resulting Numbers: [2106] 2106,38 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,38 unequal: No Solution Moving to Node #0,1,1 Current State: 38:[37, 56], Operations: ['54-17=37', '51+5=56'] Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,38 unequal: No Solution Exploring Operation: 37*56=2072, Resulting Numbers: [2072] 2072,38 unequal: No Solution Exploring Operation: 37+56=93, Resulting Numbers: [93] 93,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[34, 59], Operations: ['51-17=34', '54+5=59'] Exploring Operation: 59-34=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 34+59=93, Resulting Numbers: [93] 93,38 unequal: No Solution Exploring Operation: 34*59=2006, Resulting Numbers: [2006] 2006,38 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 56, 9, 26, 85 ]
51
[ "26-9=17", "85/17=5", "56-5=51" ]
Current State: 51:[56, 9, 26, 85], Operations: [] Exploring Operation: 26-9=17, Resulting Numbers: [56, 85, 17] Generated Node #2: [56, 85, 17] from Operation: 26-9=17 Current State: 51:[56, 85, 17], Operations: ['26-9=17'] Exploring Operation: 85/17=5, Resulting Numbers: [56, 5] Generated Node #3: [56, 5] from Operation: 85/17=5 Current State: 51:[56, 5], Operations: ['26-9=17', '85/17=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[56, 9, 26, 85], Operations: [] Exploring Operation: 85-56=29, Resulting Numbers: [9, 26, 29] Generated Node #0,0: 51:[9, 26, 29] Operation: 85-56=29 Exploring Operation: 26-9=17, Resulting Numbers: [56, 85, 17] Generated Node #0,1: 51:[56, 85, 17] Operation: 26-9=17 Exploring Operation: 85-9=76, Resulting Numbers: [56, 26, 76] Generated Node #0,2: 51:[56, 26, 76] Operation: 85-9=76 Exploring Operation: 85-26=59, Resulting Numbers: [56, 9, 59] Generated Node #0,3: 51:[56, 9, 59] Operation: 85-26=59 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[56, 9, 59], Operations: ['85-26=59'] Exploring Operation: 59-56=3, Resulting Numbers: [9, 3] Generated Node #0,3,0: 51:[9, 3] Operation: 59-56=3 Exploring Operation: 56-9=47, Resulting Numbers: [59, 47] Generated Node #0,3,1: 51:[59, 47] Operation: 56-9=47 Exploring Operation: 59-9=50, Resulting Numbers: [56, 50] Generated Node #0,3,2: 51:[56, 50] Operation: 59-9=50 Exploring Operation: 56+9=65, Resulting Numbers: [59, 65] Generated Node #0,3,3: 51:[59, 65] Operation: 56+9=65 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[9, 3], Operations: ['85-26=59', '59-56=3'] Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,51 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,51 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 #0,3,2 Current State: 51:[56, 50], Operations: ['85-26=59', '59-9=50'] Exploring Operation: 56+50=106, Resulting Numbers: [106] 106,51 unequal: No Solution Exploring Operation: 56*50=2800, Resulting Numbers: [2800] 2800,51 unequal: No Solution Exploring Operation: 56-50=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 #0,3,1 Current State: 51:[59, 47], Operations: ['85-26=59', '56-9=47'] Exploring Operation: 59*47=2773, Resulting Numbers: [2773] 2773,51 unequal: No Solution Exploring Operation: 59-47=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 59+47=106, Resulting Numbers: [106] 106,51 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 #0,3,3 Current State: 51:[59, 65], Operations: ['85-26=59', '56+9=65'] Exploring Operation: 59*65=3835, Resulting Numbers: [3835] 3835,51 unequal: No Solution Exploring Operation: 59+65=124, Resulting Numbers: [124] 124,51 unequal: No Solution Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,51 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:[9, 26, 29], Operations: ['85-56=29'] Exploring Operation: 26-9=17, Resulting Numbers: [29, 17] Generated Node #0,0,0: 51:[29, 17] Operation: 26-9=17 Exploring Operation: 26+29=55, Resulting Numbers: [9, 55] Generated Node #0,0,1: 51:[9, 55] Operation: 26+29=55 Exploring Operation: 29-9=20, Resulting Numbers: [26, 20] Generated Node #0,0,2: 51:[26, 20] Operation: 29-9=20 Exploring Operation: 29-26=3, Resulting Numbers: [9, 3] Generated Node #0,0,3: 51:[9, 3] Operation: 29-26=3 Moving to Node #0,0,3 Current State: 51:[9, 3], Operations: ['85-56=29', '29-26=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,51 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,51 unequal: No Solution Moving to Node #0,0,1 Current State: 51:[9, 55], Operations: ['85-56=29', '26+29=55'] Exploring Operation: 9+55=64, Resulting Numbers: [64] 64,51 unequal: No Solution Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 9*55=495, Resulting Numbers: [495] 495,51 unequal: No Solution Moving to Node #0,0,2 Current State: 51:[26, 20], Operations: ['85-56=29', '29-9=20'] Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,51 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,51 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[29, 17], Operations: ['85-56=29', '26-9=17'] Exploring Operation: 29-17=12, Resulting Numbers: [12] 12,51 unequal: No Solution Exploring Operation: 29*17=493, Resulting Numbers: [493] 493,51 unequal: No Solution Exploring Operation: 29+17=46, Resulting Numbers: [46] 46,51 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[56, 85, 17], Operations: ['26-9=17'] Exploring Operation: 85-56=29, Resulting Numbers: [17, 29] Generated Node #0,1,0: 51:[17, 29] Operation: 85-56=29 Exploring Operation: 85-17=68, Resulting Numbers: [56, 68] Generated Node #0,1,1: 51:[56, 68] Operation: 85-17=68 Exploring Operation: 56-17=39, Resulting Numbers: [85, 39] Generated Node #0,1,2: 51:[85, 39] Operation: 56-17=39 Exploring Operation: 85/17=5, Resulting Numbers: [56, 5] Generated Node #0,1,3: 51:[56, 5] Operation: 85/17=5 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 51:[56, 5], Operations: ['26-9=17', '85/17=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[56, 9, 26, 85], Operations: [] Exploring Operation: 26-9=17, Resulting Numbers: [56, 85, 17] Generated Node #0,1: 51:[56, 85, 17] Operation: 26-9=17 Moving to Node #0,1 Current State: 51:[56, 85, 17], Operations: ['26-9=17'] Exploring Operation: 85/17=5, Resulting Numbers: [56, 5] Generated Node #0,1,3: 51:[56, 5] Operation: 85/17=5 Moving to Node #0,1,3 Current State: 51:[56, 5], Operations: ['26-9=17', '85/17=5'] Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.959201
hs_4
sum_heuristic
[ 11, 83, 91, 93 ]
36
[ "83-11=72", "93-91=2", "72/2=36" ]
Current State: 36:[11, 83, 91, 93], Operations: [] Exploring Operation: 83-11=72, Resulting Numbers: [91, 93, 72] Generated Node #2: [91, 93, 72] from Operation: 83-11=72 Current State: 36:[91, 93, 72], Operations: ['83-11=72'] Exploring Operation: 93-91=2, Resulting Numbers: [72, 2] Generated Node #3: [72, 2] from Operation: 93-91=2 Current State: 36:[72, 2], Operations: ['83-11=72', '93-91=2'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[11, 83, 91, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [11, 83, 2] Generated Node #0,0: 36:[11, 83, 2] Operation: 93-91=2 Exploring Operation: 91-83=8, Resulting Numbers: [11, 93, 8] Generated Node #0,1: 36:[11, 93, 8] Operation: 91-83=8 Exploring Operation: 83-11=72, Resulting Numbers: [91, 93, 72] Generated Node #0,2: 36:[91, 93, 72] Operation: 83-11=72 Exploring Operation: 93-83=10, Resulting Numbers: [11, 91, 10] Generated Node #0,3: 36:[11, 91, 10] Operation: 93-83=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[11, 83, 2], Operations: ['93-91=2'] Exploring Operation: 11-2=9, Resulting Numbers: [83, 9] Generated Node #0,0,0: 36:[83, 9] Operation: 11-2=9 Exploring Operation: 83-11=72, Resulting Numbers: [2, 72] Generated Node #0,0,1: 36:[2, 72] Operation: 83-11=72 Exploring Operation: 11+2=13, Resulting Numbers: [83, 13] Generated Node #0,0,2: 36:[83, 13] Operation: 11+2=13 Exploring Operation: 83-2=81, Resulting Numbers: [11, 81] Generated Node #0,0,3: 36:[11, 81] Operation: 83-2=81 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[2, 72], Operations: ['93-91=2', '83-11=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,36 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[11, 83, 91, 93], Operations: [] Exploring Operation: 93-91=2, Resulting Numbers: [11, 83, 2] Generated Node #0,0: 36:[11, 83, 2] Operation: 93-91=2 Moving to Node #0,0 Current State: 36:[11, 83, 2], Operations: ['93-91=2'] Exploring Operation: 83-11=72, Resulting Numbers: [2, 72] Generated Node #0,0,1: 36:[2, 72] Operation: 83-11=72 Moving to Node #0,0,1 Current State: 36:[2, 72], Operations: ['93-91=2', '83-11=72'] Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 33, 12, 37, 80 ]
88
[ "33+12=45", "80-37=43", "45+43=88" ]
Current State: 88:[33, 12, 37, 80], Operations: [] Exploring Operation: 33+12=45, Resulting Numbers: [37, 80, 45] Generated Node #2: [37, 80, 45] from Operation: 33+12=45 Current State: 88:[37, 80, 45], Operations: ['33+12=45'] Exploring Operation: 80-37=43, Resulting Numbers: [45, 43] Generated Node #3: [45, 43] from Operation: 80-37=43 Current State: 88:[45, 43], Operations: ['33+12=45', '80-37=43'] Exploring Operation: 45+43=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[33, 12, 37, 80], Operations: [] Exploring Operation: 80-33=47, Resulting Numbers: [12, 37, 47] Generated Node #0,0: 88:[12, 37, 47] Operation: 80-33=47 Exploring Operation: 33-12=21, Resulting Numbers: [37, 80, 21] Generated Node #0,1: 88:[37, 80, 21] Operation: 33-12=21 Exploring Operation: 80-37=43, Resulting Numbers: [33, 12, 43] Generated Node #0,2: 88:[33, 12, 43] Operation: 80-37=43 Exploring Operation: 33+12=45, Resulting Numbers: [37, 80, 45] Generated Node #0,3: 88:[37, 80, 45] Operation: 33+12=45 Exploring Operation: 37-33=4, Resulting Numbers: [12, 80, 4] Generated Node #0,4: 88:[12, 80, 4] Operation: 37-33=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 88:[12, 80, 4], Operations: ['37-33=4'] Exploring Operation: 12/4=3, Resulting Numbers: [80, 3] Generated Node #0,4,0: 88:[80, 3] Operation: 12/4=3 Exploring Operation: 12+80=92, Resulting Numbers: [4, 92] Generated Node #0,4,1: 88:[4, 92] Operation: 12+80=92 Exploring Operation: 80/4=20, Resulting Numbers: [12, 20] Generated Node #0,4,2: 88:[12, 20] Operation: 80/4=20 Exploring Operation: 80+4=84, Resulting Numbers: [12, 84] Generated Node #0,4,3: 88:[12, 84] Operation: 80+4=84 Exploring Operation: 12-4=8, Resulting Numbers: [80, 8] Generated Node #0,4,4: 88:[80, 8] Operation: 12-4=8 Moving to Node #0,4,2 Current State: 88:[12, 20], Operations: ['37-33=4', '80/4=20'] Exploring Operation: 12+20=32, Resulting Numbers: [32] 32,88 unequal: No Solution Exploring Operation: 12*20=240, Resulting Numbers: [240] 240,88 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[4, 92], Operations: ['37-33=4', '12+80=92'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[33, 12, 37, 80], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [12, 80, 4] Generated Node #0,4: 88:[12, 80, 4] Operation: 37-33=4 Moving to Node #0,4 Current State: 88:[12, 80, 4], Operations: ['37-33=4'] Exploring Operation: 12+80=92, Resulting Numbers: [4, 92] Generated Node #0,4,1: 88:[4, 92] Operation: 12+80=92 Moving to Node #0,4,1 Current State: 88:[4, 92], Operations: ['37-33=4', '12+80=92'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 56, 27, 51, 66 ]
73
[ "56*66=3696", "27+3696=3723", "3723/51=73" ]
Current State: 73:[56, 27, 51, 66], Operations: [] Exploring Operation: 56*66=3696, Resulting Numbers: [27, 51, 3696] Generated Node #2: [27, 51, 3696] from Operation: 56*66=3696 Current State: 73:[27, 51, 3696], Operations: ['56*66=3696'] Exploring Operation: 27+3696=3723, Resulting Numbers: [51, 3723] Generated Node #3: [51, 3723] from Operation: 27+3696=3723 Current State: 73:[51, 3723], Operations: ['56*66=3696', '27+3696=3723'] Exploring Operation: 3723/51=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[56, 27, 51, 66], Operations: [] Exploring Operation: 27+51=78, Resulting Numbers: [56, 66, 78] Generated Node #0,0: 73:[56, 66, 78] Operation: 27+51=78 Exploring Operation: 56+27=83, Resulting Numbers: [51, 66, 83] Generated Node #0,1: 73:[51, 66, 83] Operation: 56+27=83 Moving to Node #0,0 Current State: 73:[56, 66, 78], Operations: ['27+51=78'] Exploring Operation: 78-56=22, Resulting Numbers: [66, 22] Generated Node #0,0,0: 73:[66, 22] Operation: 78-56=22 Exploring Operation: 56+66=122, Resulting Numbers: [78, 122] Generated Node #0,0,1: 73:[78, 122] Operation: 56+66=122 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[78, 122], Operations: ['27+51=78', '56+66=122'] Exploring Operation: 122-78=44, Resulting Numbers: [44] 44,73 unequal: No Solution Exploring Operation: 78+122=200, Resulting Numbers: [200] 200,73 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 #0,0,0 Current State: 73:[66, 22], Operations: ['27+51=78', '78-56=22'] Exploring Operation: 66+22=88, Resulting Numbers: [88] 88,73 unequal: No Solution Exploring Operation: 66-22=44, Resulting Numbers: [44] 44,73 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: 73:[51, 66, 83], Operations: ['56+27=83'] Exploring Operation: 83-51=32, Resulting Numbers: [66, 32] Generated Node #0,1,0: 73:[66, 32] Operation: 83-51=32 Exploring Operation: 51+66=117, Resulting Numbers: [83, 117] Generated Node #0,1,1: 73:[83, 117] Operation: 51+66=117 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[66, 32], Operations: ['56+27=83', '83-51=32'] Exploring Operation: 66+32=98, Resulting Numbers: [98] 98,73 unequal: No Solution Exploring Operation: 66-32=34, Resulting Numbers: [34] 34,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[83, 117], Operations: ['56+27=83', '51+66=117'] Exploring Operation: 83+117=200, Resulting Numbers: [200] 200,73 unequal: No Solution Exploring Operation: 117-83=34, Resulting Numbers: [34] 34,73 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
[ 78, 3, 2, 8 ]
80
[ "78+8=86", "3*2=6", "86-6=80" ]
Current State: 80:[78, 3, 2, 8], Operations: [] Exploring Operation: 78+8=86, Resulting Numbers: [3, 2, 86] Generated Node #2: [3, 2, 86] from Operation: 78+8=86 Current State: 80:[3, 2, 86], Operations: ['78+8=86'] Exploring Operation: 3*2=6, Resulting Numbers: [86, 6] Generated Node #3: [86, 6] from Operation: 3*2=6 Current State: 80:[86, 6], Operations: ['78+8=86', '3*2=6'] Exploring Operation: 86-6=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[78, 3, 2, 8], Operations: [] Exploring Operation: 78/2=39, Resulting Numbers: [3, 8, 39] Generated Node #0,0: 80:[3, 8, 39] Operation: 78/2=39 Exploring Operation: 78+3=81, Resulting Numbers: [2, 8, 81] Generated Node #0,1: 80:[2, 8, 81] Operation: 78+3=81 Exploring Operation: 78+2=80, Resulting Numbers: [3, 8, 80] Generated Node #0,2: 80:[3, 8, 80] Operation: 78+2=80 Moving to Node #0,1 Current State: 80:[2, 8, 81], Operations: ['78+3=81'] Exploring Operation: 2*8=16, Resulting Numbers: [81, 16] Generated Node #0,1,0: 80:[81, 16] Operation: 2*8=16 Exploring Operation: 2+8=10, Resulting Numbers: [81, 10] Generated Node #0,1,1: 80:[81, 10] Operation: 2+8=10 Exploring Operation: 8/2=4, Resulting Numbers: [81, 4] Generated Node #0,1,2: 80:[81, 4] Operation: 8/2=4 Moving to Node #0,2 Current State: 80:[3, 8, 80], Operations: ['78+2=80'] Exploring Operation: 80/8=10, Resulting Numbers: [3, 10] Generated Node #0,2,0: 80:[3, 10] Operation: 80/8=10 Exploring Operation: 3+8=11, Resulting Numbers: [80, 11] Generated Node #0,2,1: 80:[80, 11] Operation: 3+8=11 Exploring Operation: 8-3=5, Resulting Numbers: [80, 5] Generated Node #0,2,2: 80:[80, 5] Operation: 8-3=5 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[80, 5], Operations: ['78+2=80', '8-3=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,80 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[3, 10], Operations: ['78+2=80', '80/8=10'] Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,80 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[80, 11], Operations: ['78+2=80', '3+8=11'] Exploring Operation: 80*11=880, Resulting Numbers: [880] 880,80 unequal: No Solution Exploring Operation: 80+11=91, Resulting Numbers: [91] 91,80 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,80 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: 80:[3, 8, 39], Operations: ['78/2=39'] Exploring Operation: 3+39=42, Resulting Numbers: [8, 42] Generated Node #0,0,0: 80:[8, 42] Operation: 3+39=42 Exploring Operation: 3+8=11, Resulting Numbers: [39, 11] Generated Node #0,0,1: 80:[39, 11] Operation: 3+8=11 Exploring Operation: 8-3=5, Resulting Numbers: [39, 5] Generated Node #0,0,2: 80:[39, 5] Operation: 8-3=5 Moving to Node #0,1,0 Current State: 80:[81, 16], Operations: ['78+3=81', '2*8=16'] Exploring Operation: 81*16=1296, Resulting Numbers: [1296] 1296,80 unequal: No Solution Exploring Operation: 81+16=97, Resulting Numbers: [97] 97,80 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[81, 4], Operations: ['78+3=81', '8/2=4'] Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,80 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[81, 10], Operations: ['78+3=81', '2+8=10'] Exploring Operation: 81*10=810, Resulting Numbers: [810] 810,80 unequal: No Solution Exploring Operation: 81+10=91, Resulting Numbers: [91] 91,80 unequal: No Solution Exploring Operation: 81-10=71, Resulting Numbers: [71] 71,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[39, 5], Operations: ['78/2=39', '8-3=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,80 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[8, 42], Operations: ['78/2=39', '3+39=42'] Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 8+42=50, Resulting Numbers: [50] 50,80 unequal: No Solution Exploring Operation: 8*42=336, Resulting Numbers: [336] 336,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[39, 11], Operations: ['78/2=39', '3+8=11'] Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,80 unequal: No Solution Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,80 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,80 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 9, 50, 25, 47 ]
75
[ "9*25=225", "50-47=3", "225/3=75" ]
Current State: 75:[9, 50, 25, 47], Operations: [] Exploring Operation: 9*25=225, Resulting Numbers: [50, 47, 225] Generated Node #2: [50, 47, 225] from Operation: 9*25=225 Current State: 75:[50, 47, 225], Operations: ['9*25=225'] Exploring Operation: 50-47=3, Resulting Numbers: [225, 3] Generated Node #3: [225, 3] from Operation: 50-47=3 Current State: 75:[225, 3], Operations: ['9*25=225', '50-47=3'] Exploring Operation: 225/3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[9, 50, 25, 47], Operations: [] Exploring Operation: 50+25=75, Resulting Numbers: [9, 47, 75] Generated Node #0,0: 75:[9, 47, 75] Operation: 50+25=75 Exploring Operation: 50-47=3, Resulting Numbers: [9, 25, 3] Generated Node #0,1: 75:[9, 25, 3] Operation: 50-47=3 Moving to Node #0,1 Current State: 75:[9, 25, 3], Operations: ['50-47=3'] Exploring Operation: 9/3=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 75:[25, 3] Operation: 9/3=3 Exploring Operation: 25-9=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 75:[3, 16] Operation: 25-9=16 Moving to Node #0,0 Current State: 75:[9, 47, 75], Operations: ['50+25=75'] Exploring Operation: 47-9=38, Resulting Numbers: [75, 38] Generated Node #0,0,0: 75:[75, 38] Operation: 47-9=38 Exploring Operation: 75-47=28, Resulting Numbers: [9, 28] Generated Node #0,0,1: 75:[9, 28] Operation: 75-47=28 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 75:[9, 28], Operations: ['50+25=75', '75-47=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[75, 38], Operations: ['50+25=75', '47-9=38'] Exploring Operation: 75-38=37, Resulting Numbers: [37] 37,75 unequal: No Solution Exploring Operation: 75+38=113, Resulting Numbers: [113] 113,75 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: 75:[25, 3], Operations: ['50-47=3', '9/3=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[9, 50, 25, 47], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [9, 25, 3] Generated Node #0,1: 75:[9, 25, 3] Operation: 50-47=3 Moving to Node #0,1 Current State: 75:[9, 25, 3], Operations: ['50-47=3'] Exploring Operation: 9/3=3, Resulting Numbers: [25, 3] Generated Node #0,1,0: 75:[25, 3] Operation: 9/3=3 Moving to Node #0,1,0 Current State: 75:[25, 3], Operations: ['50-47=3', '9/3=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 43, 4, 33, 87 ]
22
[ "87-43=44", "44/4=11", "33-11=22" ]
Current State: 22:[43, 4, 33, 87], Operations: [] Exploring Operation: 87-43=44, Resulting Numbers: [4, 33, 44] Generated Node #2: [4, 33, 44] from Operation: 87-43=44 Current State: 22:[4, 33, 44], Operations: ['87-43=44'] Exploring Operation: 44/4=11, Resulting Numbers: [33, 11] Generated Node #3: [33, 11] from Operation: 44/4=11 Current State: 22:[33, 11], Operations: ['87-43=44', '44/4=11'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[43, 4, 33, 87], Operations: [] Exploring Operation: 87-33=54, Resulting Numbers: [43, 4, 54] Generated Node #0,0: 22:[43, 4, 54] Operation: 87-33=54 Exploring Operation: 87-43=44, Resulting Numbers: [4, 33, 44] Generated Node #0,1: 22:[4, 33, 44] Operation: 87-43=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 22:[4, 33, 44], Operations: ['87-43=44'] Exploring Operation: 44-33=11, Resulting Numbers: [4, 11] Generated Node #0,1,0: 22:[4, 11] Operation: 44-33=11 Exploring Operation: 44/4=11, Resulting Numbers: [33, 11] Generated Node #0,1,1: 22:[33, 11] Operation: 44/4=11 Moving to Node #0,1,0 Current State: 22:[4, 11], Operations: ['87-43=44', '44-33=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,22 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[33, 11], Operations: ['87-43=44', '44/4=11'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[43, 4, 33, 87], Operations: [] Exploring Operation: 87-43=44, Resulting Numbers: [4, 33, 44] Generated Node #0,1: 22:[4, 33, 44] Operation: 87-43=44 Moving to Node #0,1 Current State: 22:[4, 33, 44], Operations: ['87-43=44'] Exploring Operation: 44/4=11, Resulting Numbers: [33, 11] Generated Node #0,1,1: 22:[33, 11] Operation: 44/4=11 Moving to Node #0,1,1 Current State: 22:[33, 11], Operations: ['87-43=44', '44/4=11'] Exploring Operation: 33-11=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 10, 11, 2, 82 ]
94
[ "82-10=72", "11*2=22", "72+22=94" ]
Current State: 94:[10, 11, 2, 82], Operations: [] Exploring Operation: 82-10=72, Resulting Numbers: [11, 2, 72] Generated Node #2: [11, 2, 72] from Operation: 82-10=72 Current State: 94:[11, 2, 72], Operations: ['82-10=72'] Exploring Operation: 11*2=22, Resulting Numbers: [72, 22] Generated Node #3: [72, 22] from Operation: 11*2=22 Current State: 94:[72, 22], Operations: ['82-10=72', '11*2=22'] Exploring Operation: 72+22=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[10, 11, 2, 82], Operations: [] Exploring Operation: 82/2=41, Resulting Numbers: [10, 11, 41] Generated Node #0,0: 94:[10, 11, 41] Operation: 82/2=41 Exploring Operation: 10/2=5, Resulting Numbers: [11, 82, 5] Generated Node #0,1: 94:[11, 82, 5] Operation: 10/2=5 Exploring Operation: 10+82=92, Resulting Numbers: [11, 2, 92] Generated Node #0,2: 94:[11, 2, 92] Operation: 10+82=92 Exploring Operation: 11+82=93, Resulting Numbers: [10, 2, 93] Generated Node #0,3: 94:[10, 2, 93] Operation: 11+82=93 Exploring Operation: 11-10=1, Resulting Numbers: [2, 82, 1] Generated Node #0,4: 94:[2, 82, 1] Operation: 11-10=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[10, 2, 93], Operations: ['11+82=93'] Exploring Operation: 10+93=103, Resulting Numbers: [2, 103] Generated Node #0,3,0: 94:[2, 103] Operation: 10+93=103 Exploring Operation: 10+2=12, Resulting Numbers: [93, 12] Generated Node #0,3,1: 94:[93, 12] Operation: 10+2=12 Exploring Operation: 10/2=5, Resulting Numbers: [93, 5] Generated Node #0,3,2: 94:[93, 5] Operation: 10/2=5 Exploring Operation: 2+93=95, Resulting Numbers: [10, 95] Generated Node #0,3,3: 94:[10, 95] Operation: 2+93=95 Exploring Operation: 10-2=8, Resulting Numbers: [93, 8] Generated Node #0,3,4: 94:[93, 8] Operation: 10-2=8 Moving to Node #0,3,2 Current State: 94:[93, 5], Operations: ['11+82=93', '10/2=5'] Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 93*5=465, Resulting Numbers: [465] 465,94 unequal: No Solution Moving to Node #0,3,4 Current State: 94:[93, 8], Operations: ['11+82=93', '10-2=8'] Exploring Operation: 93*8=744, Resulting Numbers: [744] 744,94 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,94 unequal: No Solution Exploring Operation: 93+8=101, Resulting Numbers: [101] 101,94 unequal: No Solution Moving to Node #0,3,0 Current State: 94:[2, 103], Operations: ['11+82=93', '10+93=103'] Exploring Operation: 2*103=206, Resulting Numbers: [206] 206,94 unequal: No Solution Exploring Operation: 2+103=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,94 unequal: No Solution Moving to Node #0,3,3 Current State: 94:[10, 95], Operations: ['11+82=93', '2+93=95'] Exploring Operation: 10*95=950, Resulting Numbers: [950] 950,94 unequal: No Solution Exploring Operation: 95-10=85, Resulting Numbers: [85] 85,94 unequal: No Solution Exploring Operation: 10+95=105, Resulting Numbers: [105] 105,94 unequal: No Solution Moving to Node #0,3,1 Current State: 94:[93, 12], Operations: ['11+82=93', '10+2=12'] Exploring Operation: 93+12=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 93*12=1116, Resulting Numbers: [1116] 1116,94 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,94 unequal: No Solution No 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: 94:[11, 2, 92], Operations: ['10+82=92'] Exploring Operation: 92/2=46, Resulting Numbers: [11, 46] Generated Node #0,2,0: 94:[11, 46] Operation: 92/2=46 Exploring Operation: 2+92=94, Resulting Numbers: [11, 94] Generated Node #0,2,1: 94:[11, 94] Operation: 2+92=94 Exploring Operation: 11+92=103, Resulting Numbers: [2, 103] Generated Node #0,2,2: 94:[2, 103] Operation: 11+92=103 Exploring Operation: 11-2=9, Resulting Numbers: [92, 9] Generated Node #0,2,3: 94:[92, 9] Operation: 11-2=9 Exploring Operation: 11+2=13, Resulting Numbers: [92, 13] Generated Node #0,2,4: 94:[92, 13] Operation: 11+2=13 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[11, 94], Operations: ['10+82=92', '2+92=94'] Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,94 unequal: No Solution Exploring Operation: 11+94=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 11*94=1034, Resulting Numbers: [1034] 1034,94 unequal: No Solution No 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: 94:[2, 103], Operations: ['10+82=92', '11+92=103'] Exploring Operation: 2+103=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 103-2=101, Resulting Numbers: [101] 101,94 unequal: No Solution Exploring Operation: 2*103=206, Resulting Numbers: [206] 206,94 unequal: No Solution No 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: 94:[92, 9], Operations: ['10+82=92', '11-2=9'] Exploring Operation: 92+9=101, Resulting Numbers: [101] 101,94 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,94 unequal: No Solution Exploring Operation: 92*9=828, Resulting Numbers: [828] 828,94 unequal: No Solution No 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: 94:[11, 46], Operations: ['10+82=92', '92/2=46'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,94 unequal: No Solution Exploring Operation: 11*46=506, Resulting Numbers: [506] 506,94 unequal: No Solution Exploring Operation: 11+46=57, Resulting Numbers: [57] 57,94 unequal: No Solution No 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: 94:[92, 13], Operations: ['10+82=92', '11+2=13'] Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,94 unequal: No Solution Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,94 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: 94:[2, 82, 1], Operations: ['11-10=1'] Exploring Operation: 82/2=41, Resulting Numbers: [1, 41] Generated Node #0,4,0: 94:[1, 41] Operation: 82/2=41 Exploring Operation: 2*1=2, Resulting Numbers: [82, 2] Generated Node #0,4,1: 94:[82, 2] Operation: 2*1=2 Exploring Operation: 2+82=84, Resulting Numbers: [1, 84] Generated Node #0,4,2: 94:[1, 84] Operation: 2+82=84 Exploring Operation: 82+1=83, Resulting Numbers: [2, 83] Generated Node #0,4,3: 94:[2, 83] Operation: 82+1=83 Exploring Operation: 2/1=2, Resulting Numbers: [82, 2] Generated Node #0,4,4: 94:[82, 2] Operation: 2/1=2 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 94:[1, 41], Operations: ['11-10=1', '82/2=41'] Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 1+41=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,94 unequal: No Solution Exploring Operation: 1*41=41, Resulting Numbers: [41] 41,94 unequal: No Solution No 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: 94:[1, 84], Operations: ['11-10=1', '2+82=84'] Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,94 unequal: No Solution Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,94 unequal: No Solution No 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: 94:[2, 83], Operations: ['11-10=1', '82+1=83'] Exploring Operation: 2+83=85, Resulting Numbers: [85] 85,94 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,94 unequal: No Solution Exploring Operation: 2*83=166, Resulting Numbers: [166] 166,94 unequal: No Solution No 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: 94:[82, 2], Operations: ['11-10=1', '2*1=2'] Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 82*2=164, Resulting Numbers: [164] 164,94 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,94 unequal: No Solution No 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: 94:[82, 2], Operations: ['11-10=1', '2/1=2'] Exploring Operation: 82+2=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 82*2=164, Resulting Numbers: [164] 164,94 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,94 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: 94:[10, 11, 41], Operations: ['82/2=41'] Exploring Operation: 11+41=52, Resulting Numbers: [10, 52] Generated Node #0,0,0: 94:[10, 52] Operation: 11+41=52 Exploring Operation: 10+11=21, Resulting Numbers: [41, 21] Generated Node #0,0,1: 94:[41, 21] Operation: 10+11=21 Exploring Operation: 10*11=110, Resulting Numbers: [41, 110] Generated Node #0,0,2: 94:[41, 110] Operation: 10*11=110 Exploring Operation: 10+41=51, Resulting Numbers: [11, 51] Generated Node #0,0,3: 94:[11, 51] Operation: 10+41=51 Exploring Operation: 11-10=1, Resulting Numbers: [41, 1] Generated Node #0,0,4: 94:[41, 1] Operation: 11-10=1 Moving to Node #0,0,4 Current State: 94:[41, 1], Operations: ['82/2=41', '11-10=1'] Exploring Operation: 41-1=40, Resulting Numbers: [40] 40,94 unequal: No Solution Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 41/1=41, Resulting Numbers: [41] 41,94 unequal: No Solution Exploring Operation: 41*1=41, Resulting Numbers: [41] 41,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[11, 51], Operations: ['82/2=41', '10+41=51'] Exploring Operation: 11*51=561, Resulting Numbers: [561] 561,94 unequal: No Solution Exploring Operation: 11+51=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[10, 52], Operations: ['82/2=41', '11+41=52'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 10*52=520, Resulting Numbers: [520] 520,94 unequal: No Solution Exploring Operation: 10+52=62, Resulting Numbers: [62] 62,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[41, 110], Operations: ['82/2=41', '10*11=110'] Exploring Operation: 41*110=4510, Resulting Numbers: [4510] 4510,94 unequal: No Solution Exploring Operation: 110-41=69, Resulting Numbers: [69] 69,94 unequal: No Solution Exploring Operation: 41+110=151, Resulting Numbers: [151] 151,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[41, 21], Operations: ['82/2=41', '10+11=21'] Exploring Operation: 41*21=861, Resulting Numbers: [861] 861,94 unequal: No Solution Exploring Operation: 41+21=62, Resulting Numbers: [62] 62,94 unequal: No Solution Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,94 unequal: No Solution No solution 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: 94:[11, 82, 5], Operations: ['10/2=5'] Exploring Operation: 11-5=6, Resulting Numbers: [82, 6] Generated Node #0,1,0: 94:[82, 6] Operation: 11-5=6 Exploring Operation: 11+82=93, Resulting Numbers: [5, 93] Generated Node #0,1,1: 94:[5, 93] Operation: 11+82=93 Exploring Operation: 11*5=55, Resulting Numbers: [82, 55] Generated Node #0,1,2: 94:[82, 55] Operation: 11*5=55 Exploring Operation: 82+5=87, Resulting Numbers: [11, 87] Generated Node #0,1,3: 94:[11, 87] Operation: 82+5=87 Exploring Operation: 82-11=71, Resulting Numbers: [5, 71] Generated Node #0,1,4: 94:[5, 71] Operation: 82-11=71 Moving to Node #0,1,1 Current State: 94:[5, 93], Operations: ['10/2=5', '11+82=93'] Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 5*93=465, Resulting Numbers: [465] 465,94 unequal: No Solution Exploring Operation: 5+93=98, Resulting Numbers: [98] 98,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[11, 87], Operations: ['10/2=5', '82+5=87'] Exploring Operation: 11+87=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 11*87=957, Resulting Numbers: [957] 957,94 unequal: No Solution Exploring Operation: 87-11=76, Resulting Numbers: [76] 76,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[82, 6], Operations: ['10/2=5', '11-5=6'] Exploring Operation: 82*6=492, Resulting Numbers: [492] 492,94 unequal: No Solution Exploring Operation: 82-6=76, Resulting Numbers: [76] 76,94 unequal: No Solution Exploring Operation: 82+6=88, Resulting Numbers: [88] 88,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[82, 55], Operations: ['10/2=5', '11*5=55'] Exploring Operation: 82-55=27, Resulting Numbers: [27] 27,94 unequal: No Solution Exploring Operation: 82*55=4510, Resulting Numbers: [4510] 4510,94 unequal: No Solution Exploring Operation: 82+55=137, Resulting Numbers: [137] 137,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[5, 71], Operations: ['10/2=5', '82-11=71'] Exploring Operation: 5*71=355, Resulting Numbers: [355] 355,94 unequal: No Solution Exploring Operation: 5+71=76, Resulting Numbers: [76] 76,94 unequal: No Solution Exploring Operation: 71-5=66, Resulting Numbers: [66] 66,94 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
[ 4, 65, 31, 5 ]
95
[ "4+65=69", "31-5=26", "69+26=95" ]
Current State: 95:[4, 65, 31, 5], Operations: [] Exploring Operation: 4+65=69, Resulting Numbers: [31, 5, 69] Generated Node #2: [31, 5, 69] from Operation: 4+65=69 Current State: 95:[31, 5, 69], Operations: ['4+65=69'] Exploring Operation: 31-5=26, Resulting Numbers: [69, 26] Generated Node #3: [69, 26] from Operation: 31-5=26 Current State: 95:[69, 26], Operations: ['4+65=69', '31-5=26'] Exploring Operation: 69+26=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[4, 65, 31, 5], Operations: [] Exploring Operation: 65-31=34, Resulting Numbers: [4, 5, 34] Generated Node #0,0: 95:[4, 5, 34] Operation: 65-31=34 Exploring Operation: 65+31=96, Resulting Numbers: [4, 5, 96] Generated Node #0,1: 95:[4, 5, 96] Operation: 65+31=96 Exploring Operation: 4+65=69, Resulting Numbers: [31, 5, 69] Generated Node #0,2: 95:[31, 5, 69] Operation: 4+65=69 Exploring Operation: 31-4=27, Resulting Numbers: [65, 5, 27] Generated Node #0,3: 95:[65, 5, 27] Operation: 31-4=27 Exploring Operation: 65/5=13, Resulting Numbers: [4, 31, 13] Generated Node #0,4: 95:[4, 31, 13] Operation: 65/5=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[4, 5, 96], Operations: ['65+31=96'] Exploring Operation: 4*5=20, Resulting Numbers: [96, 20] Generated Node #0,1,0: 95:[96, 20] Operation: 4*5=20 Exploring Operation: 5-4=1, Resulting Numbers: [96, 1] Generated Node #0,1,1: 95:[96, 1] Operation: 5-4=1 Exploring Operation: 4+5=9, Resulting Numbers: [96, 9] Generated Node #0,1,2: 95:[96, 9] Operation: 4+5=9 Exploring Operation: 4+96=100, Resulting Numbers: [5, 100] Generated Node #0,1,3: 95:[5, 100] Operation: 4+96=100 Exploring Operation: 96-4=92, Resulting Numbers: [5, 92] Generated Node #0,1,4: 95:[5, 92] Operation: 96-4=92 Moving to Node #0,1,0 Current State: 95:[96, 20], Operations: ['65+31=96', '4*5=20'] Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,95 unequal: No Solution Exploring Operation: 96*20=1920, Resulting Numbers: [1920] 1920,95 unequal: No Solution Exploring Operation: 96+20=116, Resulting Numbers: [116] 116,95 unequal: No Solution Moving to Node #0,1,4 Current State: 95:[5, 92], Operations: ['65+31=96', '96-4=92'] Exploring Operation: 92-5=87, Resulting Numbers: [87] 87,95 unequal: No Solution Exploring Operation: 5+92=97, Resulting Numbers: [97] 97,95 unequal: No Solution Exploring Operation: 5*92=460, Resulting Numbers: [460] 460,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[96, 1], Operations: ['65+31=96', '5-4=1'] Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[4, 65, 31, 5], Operations: [] Exploring Operation: 65+31=96, Resulting Numbers: [4, 5, 96] Generated Node #0,1: 95:[4, 5, 96] Operation: 65+31=96 Moving to Node #0,1 Current State: 95:[4, 5, 96], Operations: ['65+31=96'] Exploring Operation: 5-4=1, Resulting Numbers: [96, 1] Generated Node #0,1,1: 95:[96, 1] Operation: 5-4=1 Moving to Node #0,1,1 Current State: 95:[96, 1], Operations: ['65+31=96', '5-4=1'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 88, 1, 87, 94 ]
94
[ "88*1=88", "88-87=1", "94*1=94" ]
Current State: 94:[88, 1, 87, 94], Operations: [] Exploring Operation: 88*1=88, Resulting Numbers: [87, 94, 88] Generated Node #2: [87, 94, 88] from Operation: 88*1=88 Current State: 94:[87, 94, 88], Operations: ['88*1=88'] Exploring Operation: 88-87=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 88-87=1 Current State: 94:[94, 1], Operations: ['88*1=88', '88-87=1'] Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[88, 1, 87, 94], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [88, 1, 7] Generated Node #0,0: 94:[88, 1, 7] Operation: 94-87=7 Exploring Operation: 94-88=6, Resulting Numbers: [1, 87, 6] Generated Node #0,1: 94:[1, 87, 6] Operation: 94-88=6 Exploring Operation: 88+1=89, Resulting Numbers: [87, 94, 89] Generated Node #0,2: 94:[87, 94, 89] Operation: 88+1=89 Exploring Operation: 88-87=1, Resulting Numbers: [1, 94, 1] Generated Node #0,3: 94:[1, 94, 1] Operation: 88-87=1 Exploring Operation: 1+87=88, Resulting Numbers: [88, 94, 88] Generated Node #0,4: 94:[88, 94, 88] Operation: 1+87=88 Moving to Node #0,3 Current State: 94:[1, 94, 1], Operations: ['88-87=1'] Exploring Operation: 1*94=94, Resulting Numbers: [1, 94] Generated Node #0,3,0: 94:[1, 94] Operation: 1*94=94 Exploring Operation: 1+1=2, Resulting Numbers: [94, 2] Generated Node #0,3,1: 94:[94, 2] Operation: 1+1=2 Exploring Operation: 94/1=94, Resulting Numbers: [1, 94] Generated Node #0,3,2: 94:[1, 94] Operation: 94/1=94 Exploring Operation: 1/1=1, Resulting Numbers: [94, 1] Generated Node #0,3,3: 94:[94, 1] Operation: 1/1=1 Exploring Operation: 1*1=1, Resulting Numbers: [94, 1] Generated Node #0,3,4: 94:[94, 1] Operation: 1*1=1 Moving to Node #0,1 Current State: 94:[1, 87, 6], Operations: ['94-88=6'] Exploring Operation: 87+6=93, Resulting Numbers: [1, 93] Generated Node #0,1,0: 94:[1, 93] Operation: 87+6=93 Exploring Operation: 1*87=87, Resulting Numbers: [6, 87] Generated Node #0,1,1: 94:[6, 87] Operation: 1*87=87 Exploring Operation: 87/1=87, Resulting Numbers: [6, 87] Generated Node #0,1,2: 94:[6, 87] Operation: 87/1=87 Exploring Operation: 1+87=88, Resulting Numbers: [6, 88] Generated Node #0,1,3: 94:[6, 88] Operation: 1+87=88 Exploring Operation: 6-1=5, Resulting Numbers: [87, 5] Generated Node #0,1,4: 94:[87, 5] Operation: 6-1=5 Moving to Node #0,4 Current State: 94:[88, 94, 88], Operations: ['1+87=88'] Exploring Operation: 94-88=6, Resulting Numbers: [88, 6] Generated Node #0,4,0: 94:[88, 6] Operation: 94-88=6 Exploring Operation: 94-88=6, Resulting Numbers: [88, 6] Generated Node #0,4,1: 94:[88, 6] Operation: 94-88=6 Exploring Operation: 88+88=176, Resulting Numbers: [94, 176] Generated Node #0,4,2: 94:[94, 176] Operation: 88+88=176 Exploring Operation: 88/88=1, Resulting Numbers: [94, 1] Generated Node #0,4,3: 94:[94, 1] Operation: 88/88=1 Exploring Operation: 88-88=0, Resulting Numbers: [94, 0] Generated Node #0,4,4: 94:[94, 0] Operation: 88-88=0 Moving to Node #0,0 Current State: 94:[88, 1, 7], Operations: ['94-87=7'] Exploring Operation: 88/1=88, Resulting Numbers: [7, 88] Generated Node #0,0,0: 94:[7, 88] Operation: 88/1=88 Exploring Operation: 88+1=89, Resulting Numbers: [7, 89] Generated Node #0,0,1: 94:[7, 89] Operation: 88+1=89 Exploring Operation: 7-1=6, Resulting Numbers: [88, 6] Generated Node #0,0,2: 94:[88, 6] Operation: 7-1=6 Exploring Operation: 88*1=88, Resulting Numbers: [7, 88] Generated Node #0,0,3: 94:[7, 88] Operation: 88*1=88 Exploring Operation: 88+7=95, Resulting Numbers: [1, 95] Generated Node #0,0,4: 94:[1, 95] Operation: 88+7=95 Moving to Node #0,2 Current State: 94:[87, 94, 89], Operations: ['88+1=89'] Exploring Operation: 94-89=5, Resulting Numbers: [87, 5] Generated Node #0,2,0: 94:[87, 5] Operation: 94-89=5 Exploring Operation: 87+94=181, Resulting Numbers: [89, 181] Generated Node #0,2,1: 94:[89, 181] Operation: 87+94=181 Exploring Operation: 87+89=176, Resulting Numbers: [94, 176] Generated Node #0,2,2: 94:[94, 176] Operation: 87+89=176 Exploring Operation: 94-87=7, Resulting Numbers: [89, 7] Generated Node #0,2,3: 94:[89, 7] Operation: 94-87=7 Exploring Operation: 89-87=2, Resulting Numbers: [94, 2] Generated Node #0,2,4: 94:[94, 2] Operation: 89-87=2 Moving to Node #0,3,1 Current State: 94:[94, 2], Operations: ['88-87=1', '1+1=2'] Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,94 unequal: No Solution Moving to Node #0,2,4 Current State: 94:[94, 2], Operations: ['88+1=89', '89-87=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,94 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,94 unequal: No Solution Exploring Operation: 94+2=96, Resulting Numbers: [96] 96,94 unequal: No Solution Exploring Operation: 94*2=188, Resulting Numbers: [188] 188,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[1, 94], Operations: ['88-87=1', '94/1=94'] Exploring Operation: 1+94=95, Resulting Numbers: [95] 95,94 unequal: No Solution Exploring Operation: 1*94=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[88, 1, 87, 94], Operations: [] Exploring Operation: 88-87=1, Resulting Numbers: [1, 94, 1] Generated Node #0,3: 94:[1, 94, 1] Operation: 88-87=1 Moving to Node #0,3 Current State: 94:[1, 94, 1], Operations: ['88-87=1'] Exploring Operation: 94/1=94, Resulting Numbers: [1, 94] Generated Node #0,3,2: 94:[1, 94] Operation: 94/1=94 Moving to Node #0,3,2 Current State: 94:[1, 94], Operations: ['88-87=1', '94/1=94'] Exploring Operation: 1*94=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.961806
hs_5
mult_heuristic
[ 29, 24, 74, 35 ]
78
[ "35-29=6", "24/6=4", "74+4=78" ]
Current State: 78:[29, 24, 74, 35], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [24, 74, 6] Generated Node #2: [24, 74, 6] from Operation: 35-29=6 Current State: 78:[24, 74, 6], Operations: ['35-29=6'] Exploring Operation: 24/6=4, Resulting Numbers: [74, 4] Generated Node #3: [74, 4] from Operation: 24/6=4 Current State: 78:[74, 4], Operations: ['35-29=6', '24/6=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[29, 24, 74, 35], Operations: [] Exploring Operation: 74-35=39, Resulting Numbers: [29, 24, 39] Generated Node #0,0: 78:[29, 24, 39] Operation: 74-35=39 Exploring Operation: 35-29=6, Resulting Numbers: [24, 74, 6] Generated Node #0,1: 78:[24, 74, 6] Operation: 35-29=6 Moving to Node #0,0 Current State: 78:[29, 24, 39], Operations: ['74-35=39'] Exploring Operation: 29-24=5, Resulting Numbers: [39, 5] Generated Node #0,0,0: 78:[39, 5] Operation: 29-24=5 Exploring Operation: 39-29=10, Resulting Numbers: [24, 10] Generated Node #0,0,1: 78:[24, 10] Operation: 39-29=10 Moving to Node #0,1 Current State: 78:[24, 74, 6], Operations: ['35-29=6'] Exploring Operation: 24/6=4, Resulting Numbers: [74, 4] Generated Node #0,1,0: 78:[74, 4] Operation: 24/6=4 Exploring Operation: 74+6=80, Resulting Numbers: [24, 80] Generated Node #0,1,1: 78:[24, 80] Operation: 74+6=80 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[24, 80], Operations: ['35-29=6', '74+6=80'] Exploring Operation: 24+80=104, Resulting Numbers: [104] 104,78 unequal: No Solution Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[74, 4], Operations: ['35-29=6', '24/6=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[29, 24, 74, 35], Operations: [] Exploring Operation: 35-29=6, Resulting Numbers: [24, 74, 6] Generated Node #0,1: 78:[24, 74, 6] Operation: 35-29=6 Moving to Node #0,1 Current State: 78:[24, 74, 6], Operations: ['35-29=6'] Exploring Operation: 24/6=4, Resulting Numbers: [74, 4] Generated Node #0,1,0: 78:[74, 4] Operation: 24/6=4 Moving to Node #0,1,0 Current State: 78:[74, 4], Operations: ['35-29=6', '24/6=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_2
sum_heuristic
[ 20, 10, 48, 68 ]
11
[ "20+48=68", "68/68=1", "10+1=11" ]
Current State: 11:[20, 10, 48, 68], Operations: [] Exploring Operation: 20+48=68, Resulting Numbers: [10, 68, 68] Generated Node #2: [10, 68, 68] from Operation: 20+48=68 Current State: 11:[10, 68, 68], Operations: ['20+48=68'] Exploring Operation: 68/68=1, Resulting Numbers: [10, 1] Generated Node #3: [10, 1] from Operation: 68/68=1 Current State: 11:[10, 1], Operations: ['20+48=68', '68/68=1'] Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[20, 10, 48, 68], Operations: [] Exploring Operation: 48-20=28, Resulting Numbers: [10, 68, 28] Generated Node #0,0: 11:[10, 68, 28] Operation: 48-20=28 Exploring Operation: 68-48=20, Resulting Numbers: [20, 10, 20] Generated Node #0,1: 11:[20, 10, 20] Operation: 68-48=20 Moving to Node #0,1 Current State: 11:[20, 10, 20], Operations: ['68-48=20'] Exploring Operation: 20-10=10, Resulting Numbers: [20, 10] Generated Node #0,1,0: 11:[20, 10] Operation: 20-10=10 Exploring Operation: 20-10=10, Resulting Numbers: [20, 10] Generated Node #0,1,1: 11:[20, 10] Operation: 20-10=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[20, 10], Operations: ['68-48=20', '20-10=10'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,11 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 #0,1,1 Current State: 11:[20, 10], Operations: ['68-48=20', '20-10=10'] Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,11 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,11 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: 11:[10, 68, 28], Operations: ['48-20=28'] Exploring Operation: 68-28=40, Resulting Numbers: [10, 40] Generated Node #0,0,0: 11:[10, 40] Operation: 68-28=40 Exploring Operation: 68-10=58, Resulting Numbers: [28, 58] Generated Node #0,0,1: 11:[28, 58] Operation: 68-10=58 Moving to Node #0,0,0 Current State: 11:[10, 40], Operations: ['48-20=28', '68-28=40'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[28, 58], Operations: ['48-20=28', '68-10=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,11 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,11 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 69, 12, 80, 68 ]
91
[ "69-12=57", "80+68=148", "148-57=91" ]
Current State: 91:[69, 12, 80, 68], Operations: [] Exploring Operation: 69-12=57, Resulting Numbers: [80, 68, 57] Generated Node #2: [80, 68, 57] from Operation: 69-12=57 Current State: 91:[80, 68, 57], Operations: ['69-12=57'] Exploring Operation: 80+68=148, Resulting Numbers: [57, 148] Generated Node #3: [57, 148] from Operation: 80+68=148 Current State: 91:[57, 148], Operations: ['69-12=57', '80+68=148'] Exploring Operation: 148-57=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[69, 12, 80, 68], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [12, 80, 1] Generated Node #0,0: 91:[12, 80, 1] Operation: 69-68=1 Exploring Operation: 80-68=12, Resulting Numbers: [69, 12, 12] Generated Node #0,1: 91:[69, 12, 12] Operation: 80-68=12 Moving to Node #0,0 Current State: 91:[12, 80, 1], Operations: ['69-68=1'] Exploring Operation: 12+80=92, Resulting Numbers: [1, 92] Generated Node #0,0,0: 91:[1, 92] Operation: 12+80=92 Exploring Operation: 12+1=13, Resulting Numbers: [80, 13] Generated Node #0,0,1: 91:[80, 13] Operation: 12+1=13 Moving to Node #0,1 Current State: 91:[69, 12, 12], Operations: ['80-68=12'] Exploring Operation: 69+12=81, Resulting Numbers: [12, 81] Generated Node #0,1,0: 91:[12, 81] Operation: 69+12=81 Exploring Operation: 69+12=81, Resulting Numbers: [12, 81] Generated Node #0,1,1: 91:[12, 81] Operation: 69+12=81 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 91:[12, 81], Operations: ['80-68=12', '69+12=81'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,91 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 91:[12, 81], Operations: ['80-68=12', '69+12=81'] Exploring Operation: 81-12=69, Resulting Numbers: [69] 69,91 unequal: No Solution Exploring Operation: 12+81=93, Resulting Numbers: [93] 93,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 91:[1, 92], Operations: ['69-68=1', '12+80=92'] Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,91 unequal: No Solution Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[69, 12, 80, 68], Operations: [] Exploring Operation: 69-68=1, Resulting Numbers: [12, 80, 1] Generated Node #0,0: 91:[12, 80, 1] Operation: 69-68=1 Moving to Node #0,0 Current State: 91:[12, 80, 1], Operations: ['69-68=1'] Exploring Operation: 12+80=92, Resulting Numbers: [1, 92] Generated Node #0,0,0: 91:[1, 92] Operation: 12+80=92 Moving to Node #0,0,0 Current State: 91:[1, 92], Operations: ['69-68=1', '12+80=92'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 53, 82, 41, 75 ]
97
[ "82/41=2", "75*2=150", "150-53=97" ]
Current State: 97:[53, 82, 41, 75], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [53, 75, 2] Generated Node #2: [53, 75, 2] from Operation: 82/41=2 Current State: 97:[53, 75, 2], Operations: ['82/41=2'] Exploring Operation: 75*2=150, Resulting Numbers: [53, 150] Generated Node #3: [53, 150] from Operation: 75*2=150 Current State: 97:[53, 150], Operations: ['82/41=2', '75*2=150'] Exploring Operation: 150-53=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[53, 82, 41, 75], Operations: [] Exploring Operation: 53+41=94, Resulting Numbers: [82, 75, 94] Generated Node #0,0: 97:[82, 75, 94] Operation: 53+41=94 Moving to Node #0,0 Current State: 97:[82, 75, 94], Operations: ['53+41=94'] Exploring Operation: 82+75=157, Resulting Numbers: [94, 157] Generated Node #0,0,0: 97:[94, 157] Operation: 82+75=157 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[94, 157], Operations: ['53+41=94', '82+75=157'] Exploring Operation: 157-94=63, Resulting Numbers: [63] 63,97 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
[ 20, 78, 6, 81 ]
23
[ "20+78=98", "81-6=75", "98-75=23" ]
Current State: 23:[20, 78, 6, 81], Operations: [] Exploring Operation: 20+78=98, Resulting Numbers: [6, 81, 98] Generated Node #2: [6, 81, 98] from Operation: 20+78=98 Current State: 23:[6, 81, 98], Operations: ['20+78=98'] Exploring Operation: 81-6=75, Resulting Numbers: [98, 75] Generated Node #3: [98, 75] from Operation: 81-6=75 Current State: 23:[98, 75], Operations: ['20+78=98', '81-6=75'] Exploring Operation: 98-75=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[20, 78, 6, 81], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [20, 81, 13] Generated Node #0,0: 23:[20, 81, 13] Operation: 78/6=13 Exploring Operation: 81-78=3, Resulting Numbers: [20, 6, 3] Generated Node #0,1: 23:[20, 6, 3] Operation: 81-78=3 Exploring Operation: 78-6=72, Resulting Numbers: [20, 81, 72] Generated Node #0,2: 23:[20, 81, 72] Operation: 78-6=72 Exploring Operation: 81-20=61, Resulting Numbers: [78, 6, 61] Generated Node #0,3: 23:[78, 6, 61] Operation: 81-20=61 Exploring Operation: 78-20=58, Resulting Numbers: [6, 81, 58] Generated Node #0,4: 23:[6, 81, 58] Operation: 78-20=58 Moving to Node #0,1 Current State: 23:[20, 6, 3], Operations: ['81-78=3'] Exploring Operation: 20+6=26, Resulting Numbers: [3, 26] Generated Node #0,1,0: 23:[3, 26] Operation: 20+6=26 Exploring Operation: 6+3=9, Resulting Numbers: [20, 9] Generated Node #0,1,1: 23:[20, 9] Operation: 6+3=9 Exploring Operation: 20+3=23, Resulting Numbers: [6, 23] Generated Node #0,1,2: 23:[6, 23] Operation: 20+3=23 Exploring Operation: 6*3=18, Resulting Numbers: [20, 18] Generated Node #0,1,3: 23:[20, 18] Operation: 6*3=18 Exploring Operation: 20-3=17, Resulting Numbers: [6, 17] Generated Node #0,1,4: 23:[6, 17] Operation: 20-3=17 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[20, 18], Operations: ['81-78=3', '6*3=18'] Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,23 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[20, 9], Operations: ['81-78=3', '6+3=9'] Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,23 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[6, 23], Operations: ['81-78=3', '20+3=23'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,23 unequal: No Solution Exploring Operation: 6+23=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 6*23=138, Resulting Numbers: [138] 138,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[3, 26], Operations: ['81-78=3', '20+6=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,23 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[20, 78, 6, 81], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [20, 6, 3] Generated Node #0,1: 23:[20, 6, 3] Operation: 81-78=3 Moving to Node #0,1 Current State: 23:[20, 6, 3], Operations: ['81-78=3'] Exploring Operation: 20+6=26, Resulting Numbers: [3, 26] Generated Node #0,1,0: 23:[3, 26] Operation: 20+6=26 Moving to Node #0,1,0 Current State: 23:[3, 26], Operations: ['81-78=3', '20+6=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 63, 36, 98, 61 ]
63
[ "98-36=62", "62-61=1", "63*1=63" ]
Current State: 63:[63, 36, 98, 61], Operations: [] Exploring Operation: 98-36=62, Resulting Numbers: [63, 61, 62] Generated Node #2: [63, 61, 62] from Operation: 98-36=62 Current State: 63:[63, 61, 62], Operations: ['98-36=62'] Exploring Operation: 62-61=1, Resulting Numbers: [63, 1] Generated Node #3: [63, 1] from Operation: 62-61=1 Current State: 63:[63, 1], Operations: ['98-36=62', '62-61=1'] Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[63, 36, 98, 61], Operations: [] Exploring Operation: 98-61=37, Resulting Numbers: [63, 36, 37] Generated Node #0,0: 63:[63, 36, 37] Operation: 98-61=37 Exploring Operation: 61-36=25, Resulting Numbers: [63, 98, 25] Generated Node #0,1: 63:[63, 98, 25] Operation: 61-36=25 Exploring Operation: 98-63=35, Resulting Numbers: [36, 61, 35] Generated Node #0,2: 63:[36, 61, 35] Operation: 98-63=35 Exploring Operation: 98-36=62, Resulting Numbers: [63, 61, 62] Generated Node #0,3: 63:[63, 61, 62] Operation: 98-36=62 Moving to Node #0,3 Current State: 63:[63, 61, 62], Operations: ['98-36=62'] Exploring Operation: 61+62=123, Resulting Numbers: [63, 123] Generated Node #0,3,0: 63:[63, 123] Operation: 61+62=123 Exploring Operation: 63-62=1, Resulting Numbers: [61, 1] Generated Node #0,3,1: 63:[61, 1] Operation: 63-62=1 Exploring Operation: 62-61=1, Resulting Numbers: [63, 1] Generated Node #0,3,2: 63:[63, 1] Operation: 62-61=1 Exploring Operation: 63-61=2, Resulting Numbers: [62, 2] Generated Node #0,3,3: 63:[62, 2] Operation: 63-61=2 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[63, 1], Operations: ['98-36=62', '62-61=1'] Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,63 unequal: No Solution Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,63 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[63, 36, 98, 61], Operations: [] Exploring Operation: 98-36=62, Resulting Numbers: [63, 61, 62] Generated Node #0,3: 63:[63, 61, 62] Operation: 98-36=62 Moving to Node #0,3 Current State: 63:[63, 61, 62], Operations: ['98-36=62'] Exploring Operation: 62-61=1, Resulting Numbers: [63, 1] Generated Node #0,3,2: 63:[63, 1] Operation: 62-61=1 Moving to Node #0,3,2 Current State: 63:[63, 1], Operations: ['98-36=62', '62-61=1'] Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 66, 11, 22, 13 ]
88
[ "66-22=44", "13-11=2", "44*2=88" ]
Current State: 88:[66, 11, 22, 13], Operations: [] Exploring Operation: 66-22=44, Resulting Numbers: [11, 13, 44] Generated Node #2: [11, 13, 44] from Operation: 66-22=44 Current State: 88:[11, 13, 44], Operations: ['66-22=44'] Exploring Operation: 13-11=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 13-11=2 Current State: 88:[44, 2], Operations: ['66-22=44', '13-11=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[66, 11, 22, 13], Operations: [] Exploring Operation: 66+22=88, Resulting Numbers: [11, 13, 88] Generated Node #0,0: 88:[11, 13, 88] Operation: 66+22=88 Moving to Node #0,0 Current State: 88:[11, 13, 88], Operations: ['66+22=88'] Exploring Operation: 13-11=2, Resulting Numbers: [88, 2] Generated Node #0,0,0: 88:[88, 2] Operation: 13-11=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[88, 2], Operations: ['66+22=88', '13-11=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 33, 78, 3, 53 ]
46
[ "53-33=20", "78/3=26", "20+26=46" ]
Current State: 46:[33, 78, 3, 53], Operations: [] Exploring Operation: 53-33=20, Resulting Numbers: [78, 3, 20] Generated Node #2: [78, 3, 20] from Operation: 53-33=20 Current State: 46:[78, 3, 20], Operations: ['53-33=20'] Exploring Operation: 78/3=26, Resulting Numbers: [20, 26] Generated Node #3: [20, 26] from Operation: 78/3=26 Current State: 46:[20, 26], Operations: ['53-33=20', '78/3=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[33, 78, 3, 53], Operations: [] Exploring Operation: 78/3=26, Resulting Numbers: [33, 53, 26] Generated Node #0,0: 46:[33, 53, 26] Operation: 78/3=26 Exploring Operation: 53-33=20, Resulting Numbers: [78, 3, 20] Generated Node #0,1: 46:[78, 3, 20] Operation: 53-33=20 Exploring Operation: 33-3=30, Resulting Numbers: [78, 53, 30] Generated Node #0,2: 46:[78, 53, 30] Operation: 33-3=30 Exploring Operation: 78-33=45, Resulting Numbers: [3, 53, 45] Generated Node #0,3: 46:[3, 53, 45] Operation: 78-33=45 Exploring Operation: 78-53=25, Resulting Numbers: [33, 3, 25] Generated Node #0,4: 46:[33, 3, 25] Operation: 78-53=25 Moving to Node #0,3 Current State: 46:[3, 53, 45], Operations: ['78-33=45'] Exploring Operation: 3+53=56, Resulting Numbers: [45, 56] Generated Node #0,3,0: 46:[45, 56] Operation: 3+53=56 Exploring Operation: 45-3=42, Resulting Numbers: [53, 42] Generated Node #0,3,1: 46:[53, 42] Operation: 45-3=42 Exploring Operation: 53-3=50, Resulting Numbers: [45, 50] Generated Node #0,3,2: 46:[45, 50] Operation: 53-3=50 Exploring Operation: 53-45=8, Resulting Numbers: [3, 8] Generated Node #0,3,3: 46:[3, 8] Operation: 53-45=8 Exploring Operation: 3+45=48, Resulting Numbers: [53, 48] Generated Node #0,3,4: 46:[53, 48] Operation: 3+45=48 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 46:[45, 50], Operations: ['78-33=45', '53-3=50'] Exploring Operation: 45+50=95, Resulting Numbers: [95] 95,46 unequal: No Solution Exploring Operation: 50-45=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 45*50=2250, Resulting Numbers: [2250] 2250,46 unequal: No Solution No 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: 46:[3, 8], Operations: ['78-33=45', '53-45=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,46 unequal: No Solution No 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: 46:[53, 48], Operations: ['78-33=45', '3+45=48'] Exploring Operation: 53+48=101, Resulting Numbers: [101] 101,46 unequal: No Solution Exploring Operation: 53-48=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 53*48=2544, Resulting Numbers: [2544] 2544,46 unequal: No Solution No 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: 46:[45, 56], Operations: ['78-33=45', '3+53=56'] Exploring Operation: 45*56=2520, Resulting Numbers: [2520] 2520,46 unequal: No Solution Exploring Operation: 45+56=101, Resulting Numbers: [101] 101,46 unequal: No Solution Exploring Operation: 56-45=11, Resulting Numbers: [11] 11,46 unequal: No Solution No 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: 46:[53, 42], Operations: ['78-33=45', '45-3=42'] Exploring Operation: 53+42=95, Resulting Numbers: [95] 95,46 unequal: No Solution Exploring Operation: 53-42=11, Resulting Numbers: [11] 11,46 unequal: No Solution Exploring Operation: 53*42=2226, Resulting Numbers: [2226] 2226,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 46:[33, 3, 25], Operations: ['78-53=25'] Exploring Operation: 33-25=8, Resulting Numbers: [3, 8] Generated Node #0,4,0: 46:[3, 8] Operation: 33-25=8 Exploring Operation: 25-3=22, Resulting Numbers: [33, 22] Generated Node #0,4,1: 46:[33, 22] Operation: 25-3=22 Exploring Operation: 33-3=30, Resulting Numbers: [25, 30] Generated Node #0,4,2: 46:[25, 30] Operation: 33-3=30 Exploring Operation: 33+3=36, Resulting Numbers: [25, 36] Generated Node #0,4,3: 46:[25, 36] Operation: 33+3=36 Exploring Operation: 33/3=11, Resulting Numbers: [25, 11] Generated Node #0,4,4: 46:[25, 11] Operation: 33/3=11 Moving to Node #0,0 Current State: 46:[33, 53, 26], Operations: ['78/3=26'] Exploring Operation: 33+26=59, Resulting Numbers: [53, 59] Generated Node #0,0,0: 46:[53, 59] Operation: 33+26=59 Exploring Operation: 53-26=27, Resulting Numbers: [33, 27] Generated Node #0,0,1: 46:[33, 27] Operation: 53-26=27 Exploring Operation: 53-33=20, Resulting Numbers: [26, 20] Generated Node #0,0,2: 46:[26, 20] Operation: 53-33=20 Exploring Operation: 33-26=7, Resulting Numbers: [53, 7] Generated Node #0,0,3: 46:[53, 7] Operation: 33-26=7 Exploring Operation: 33+53=86, Resulting Numbers: [26, 86] Generated Node #0,0,4: 46:[26, 86] Operation: 33+53=86 Moving to Node #0,1 Current State: 46:[78, 3, 20], Operations: ['53-33=20'] Exploring Operation: 78/3=26, Resulting Numbers: [20, 26] Generated Node #0,1,0: 46:[20, 26] Operation: 78/3=26 Exploring Operation: 78-3=75, Resulting Numbers: [20, 75] Generated Node #0,1,1: 46:[20, 75] Operation: 78-3=75 Exploring Operation: 78+3=81, Resulting Numbers: [20, 81] Generated Node #0,1,2: 46:[20, 81] Operation: 78+3=81 Exploring Operation: 3+20=23, Resulting Numbers: [78, 23] Generated Node #0,1,3: 46:[78, 23] Operation: 3+20=23 Exploring Operation: 78-20=58, Resulting Numbers: [3, 58] Generated Node #0,1,4: 46:[3, 58] Operation: 78-20=58 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[20, 26], Operations: ['53-33=20', '78/3=26'] Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,46 unequal: No Solution Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[33, 78, 3, 53], Operations: [] Exploring Operation: 53-33=20, Resulting Numbers: [78, 3, 20] Generated Node #0,1: 46:[78, 3, 20] Operation: 53-33=20 Moving to Node #0,1 Current State: 46:[78, 3, 20], Operations: ['53-33=20'] Exploring Operation: 78/3=26, Resulting Numbers: [20, 26] Generated Node #0,1,0: 46:[20, 26] Operation: 78/3=26 Moving to Node #0,1,0 Current State: 46:[20, 26], Operations: ['53-33=20', '78/3=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.960069
hs_5
sum_heuristic
[ 3, 14, 62, 42 ]
68
[ "3+62=65", "42/14=3", "65+3=68" ]
Current State: 68:[3, 14, 62, 42], Operations: [] Exploring Operation: 3+62=65, Resulting Numbers: [14, 42, 65] Generated Node #2: [14, 42, 65] from Operation: 3+62=65 Current State: 68:[14, 42, 65], Operations: ['3+62=65'] Exploring Operation: 42/14=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 42/14=3 Current State: 68:[65, 3], Operations: ['3+62=65', '42/14=3'] Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[3, 14, 62, 42], Operations: [] Exploring Operation: 3+14=17, Resulting Numbers: [62, 42, 17] Generated Node #0,0: 68:[62, 42, 17] Operation: 3+14=17 Exploring Operation: 42/3=14, Resulting Numbers: [14, 62, 14] Generated Node #0,1: 68:[14, 62, 14] Operation: 42/3=14 Exploring Operation: 42-14=28, Resulting Numbers: [3, 62, 28] Generated Node #0,2: 68:[3, 62, 28] Operation: 42-14=28 Exploring Operation: 62-42=20, Resulting Numbers: [3, 14, 20] Generated Node #0,3: 68:[3, 14, 20] Operation: 62-42=20 Exploring Operation: 42/14=3, Resulting Numbers: [3, 62, 3] Generated Node #0,4: 68:[3, 62, 3] Operation: 42/14=3 Moving to Node #0,3 Current State: 68:[3, 14, 20], Operations: ['62-42=20'] Exploring Operation: 20-14=6, Resulting Numbers: [3, 6] Generated Node #0,3,0: 68:[3, 6] Operation: 20-14=6 Exploring Operation: 20-3=17, Resulting Numbers: [14, 17] Generated Node #0,3,1: 68:[14, 17] Operation: 20-3=17 Exploring Operation: 14-3=11, Resulting Numbers: [20, 11] Generated Node #0,3,2: 68:[20, 11] Operation: 14-3=11 Exploring Operation: 14+20=34, Resulting Numbers: [3, 34] Generated Node #0,3,3: 68:[3, 34] Operation: 14+20=34 Exploring Operation: 3+14=17, Resulting Numbers: [20, 17] Generated Node #0,3,4: 68:[20, 17] Operation: 3+14=17 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 68:[3, 34], Operations: ['62-42=20', '14+20=34'] Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,68 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,68 unequal: No Solution No 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: 68:[3, 6], Operations: ['62-42=20', '20-14=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,68 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,68 unequal: No Solution No 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: 68:[14, 17], Operations: ['62-42=20', '20-3=17'] Exploring Operation: 14*17=238, Resulting Numbers: [238] 238,68 unequal: No Solution Exploring Operation: 14+17=31, Resulting Numbers: [31] 31,68 unequal: No Solution Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,68 unequal: No Solution No 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: 68:[20, 17], Operations: ['62-42=20', '3+14=17'] Exploring Operation: 20*17=340, Resulting Numbers: [340] 340,68 unequal: No Solution Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,68 unequal: No Solution No 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: 68:[20, 11], Operations: ['62-42=20', '14-3=11'] Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,68 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 68:[3, 62, 3], Operations: ['42/14=3'] Exploring Operation: 3/3=1, Resulting Numbers: [62, 1] Generated Node #0,4,0: 68:[62, 1] Operation: 3/3=1 Exploring Operation: 3-3=0, Resulting Numbers: [62, 0] Generated Node #0,4,1: 68:[62, 0] Operation: 3-3=0 Exploring Operation: 3+62=65, Resulting Numbers: [3, 65] Generated Node #0,4,2: 68:[3, 65] Operation: 3+62=65 Exploring Operation: 3+3=6, Resulting Numbers: [62, 6] Generated Node #0,4,3: 68:[62, 6] Operation: 3+3=6 Exploring Operation: 62+3=65, Resulting Numbers: [3, 65] Generated Node #0,4,4: 68:[3, 65] Operation: 62+3=65 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 68:[3, 65], Operations: ['42/14=3', '3+62=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,68 unequal: No Solution Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[3, 14, 62, 42], Operations: [] Exploring Operation: 42/14=3, Resulting Numbers: [3, 62, 3] Generated Node #0,4: 68:[3, 62, 3] Operation: 42/14=3 Moving to Node #0,4 Current State: 68:[3, 62, 3], Operations: ['42/14=3'] Exploring Operation: 3+62=65, Resulting Numbers: [3, 65] Generated Node #0,4,2: 68:[3, 65] Operation: 3+62=65 Moving to Node #0,4,2 Current State: 68:[3, 65], Operations: ['42/14=3', '3+62=65'] Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 18, 45, 58, 81 ]
61
[ "45-18=27", "81/27=3", "58+3=61" ]
Current State: 61:[18, 45, 58, 81], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [58, 81, 27] Generated Node #2: [58, 81, 27] from Operation: 45-18=27 Current State: 61:[58, 81, 27], Operations: ['45-18=27'] Exploring Operation: 81/27=3, Resulting Numbers: [58, 3] Generated Node #3: [58, 3] from Operation: 81/27=3 Current State: 61:[58, 3], Operations: ['45-18=27', '81/27=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[18, 45, 58, 81], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [58, 81, 27] Generated Node #0,0: 61:[58, 81, 27] Operation: 45-18=27 Exploring Operation: 18+58=76, Resulting Numbers: [45, 81, 76] Generated Node #0,1: 61:[45, 81, 76] Operation: 18+58=76 Exploring Operation: 81-18=63, Resulting Numbers: [45, 58, 63] Generated Node #0,2: 61:[45, 58, 63] Operation: 81-18=63 Exploring Operation: 58-18=40, Resulting Numbers: [45, 81, 40] Generated Node #0,3: 61:[45, 81, 40] Operation: 58-18=40 Exploring Operation: 18+45=63, Resulting Numbers: [58, 81, 63] Generated Node #0,4: 61:[58, 81, 63] Operation: 18+45=63 Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[45, 58, 63], Operations: ['81-18=63'] Exploring Operation: 45+63=108, Resulting Numbers: [58, 108] Generated Node #0,2,0: 61:[58, 108] Operation: 45+63=108 Exploring Operation: 58-45=13, Resulting Numbers: [63, 13] Generated Node #0,2,1: 61:[63, 13] Operation: 58-45=13 Exploring Operation: 45+58=103, Resulting Numbers: [63, 103] Generated Node #0,2,2: 61:[63, 103] Operation: 45+58=103 Exploring Operation: 63-58=5, Resulting Numbers: [45, 5] Generated Node #0,2,3: 61:[45, 5] Operation: 63-58=5 Exploring Operation: 63-45=18, Resulting Numbers: [58, 18] Generated Node #0,2,4: 61:[58, 18] Operation: 63-45=18 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 61:[63, 103], Operations: ['81-18=63', '45+58=103'] Exploring Operation: 63*103=6489, Resulting Numbers: [6489] 6489,61 unequal: No Solution Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 63+103=166, Resulting Numbers: [166] 166,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 61:[58, 18], Operations: ['81-18=63', '63-45=18'] Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 58*18=1044, Resulting Numbers: [1044] 1044,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[58, 108], Operations: ['81-18=63', '45+63=108'] Exploring Operation: 58+108=166, Resulting Numbers: [166] 166,61 unequal: No Solution Exploring Operation: 108-58=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 58*108=6264, Resulting Numbers: [6264] 6264,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 61:[63, 13], Operations: ['81-18=63', '58-45=13'] Exploring Operation: 63-13=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 63+13=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 63*13=819, Resulting Numbers: [819] 819,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 61:[45, 5], Operations: ['81-18=63', '63-58=5'] Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[58, 81, 63], Operations: ['18+45=63'] Exploring Operation: 58+81=139, Resulting Numbers: [63, 139] Generated Node #0,4,0: 61:[63, 139] Operation: 58+81=139 Exploring Operation: 63-58=5, Resulting Numbers: [81, 5] Generated Node #0,4,1: 61:[81, 5] Operation: 63-58=5 Exploring Operation: 58+63=121, Resulting Numbers: [81, 121] Generated Node #0,4,2: 61:[81, 121] Operation: 58+63=121 Exploring Operation: 81-58=23, Resulting Numbers: [63, 23] Generated Node #0,4,3: 61:[63, 23] Operation: 81-58=23 Exploring Operation: 81-63=18, Resulting Numbers: [58, 18] Generated Node #0,4,4: 61:[58, 18] Operation: 81-63=18 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 61:[63, 23], Operations: ['18+45=63', '81-58=23'] Exploring Operation: 63+23=86, Resulting Numbers: [86] 86,61 unequal: No Solution Exploring Operation: 63*23=1449, Resulting Numbers: [1449] 1449,61 unequal: No Solution Exploring Operation: 63-23=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 61:[58, 18], Operations: ['18+45=63', '81-63=18'] Exploring Operation: 58*18=1044, Resulting Numbers: [1044] 1044,61 unequal: No Solution Exploring Operation: 58+18=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 58-18=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 61:[81, 5], Operations: ['18+45=63', '63-58=5'] Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,61 unequal: No Solution Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,61 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 61:[63, 139], Operations: ['18+45=63', '58+81=139'] Exploring Operation: 139-63=76, Resulting Numbers: [76] 76,61 unequal: No Solution Exploring Operation: 63+139=202, Resulting Numbers: [202] 202,61 unequal: No Solution Exploring Operation: 63*139=8757, Resulting Numbers: [8757] 8757,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 61:[81, 121], Operations: ['18+45=63', '58+63=121'] Exploring Operation: 121-81=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 81+121=202, Resulting Numbers: [202] 202,61 unequal: No Solution Exploring Operation: 81*121=9801, Resulting Numbers: [9801] 9801,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 61:[45, 81, 76], Operations: ['18+58=76'] Exploring Operation: 45+76=121, Resulting Numbers: [81, 121] Generated Node #0,1,0: 61:[81, 121] Operation: 45+76=121 Exploring Operation: 81-76=5, Resulting Numbers: [45, 5] Generated Node #0,1,1: 61:[45, 5] Operation: 81-76=5 Exploring Operation: 76-45=31, Resulting Numbers: [81, 31] Generated Node #0,1,2: 61:[81, 31] Operation: 76-45=31 Exploring Operation: 81-45=36, Resulting Numbers: [76, 36] Generated Node #0,1,3: 61:[76, 36] Operation: 81-45=36 Exploring Operation: 45+81=126, Resulting Numbers: [76, 126] Generated Node #0,1,4: 61:[76, 126] Operation: 45+81=126 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 61:[76, 36], Operations: ['18+58=76', '81-45=36'] Exploring Operation: 76-36=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 76*36=2736, Resulting Numbers: [2736] 2736,61 unequal: No Solution Exploring Operation: 76+36=112, Resulting Numbers: [112] 112,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 61:[81, 31], Operations: ['18+58=76', '76-45=31'] Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,61 unequal: No Solution Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 61:[45, 5], Operations: ['18+58=76', '81-76=5'] Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,61 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 61:[81, 121], Operations: ['18+58=76', '45+76=121'] Exploring Operation: 81+121=202, Resulting Numbers: [202] 202,61 unequal: No Solution Exploring Operation: 121-81=40, Resulting Numbers: [40] 40,61 unequal: No Solution Exploring Operation: 81*121=9801, Resulting Numbers: [9801] 9801,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 61:[76, 126], Operations: ['18+58=76', '45+81=126'] Exploring Operation: 76*126=9576, Resulting Numbers: [9576] 9576,61 unequal: No Solution Exploring Operation: 126-76=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 76+126=202, Resulting Numbers: [202] 202,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[58, 81, 27], Operations: ['45-18=27'] Exploring Operation: 81+27=108, Resulting Numbers: [58, 108] Generated Node #0,0,0: 61:[58, 108] Operation: 81+27=108 Exploring Operation: 81/27=3, Resulting Numbers: [58, 3] Generated Node #0,0,1: 61:[58, 3] Operation: 81/27=3 Exploring Operation: 58+27=85, Resulting Numbers: [81, 85] Generated Node #0,0,2: 61:[81, 85] Operation: 58+27=85 Exploring Operation: 58-27=31, Resulting Numbers: [81, 31] Generated Node #0,0,3: 61:[81, 31] Operation: 58-27=31 Exploring Operation: 81-27=54, Resulting Numbers: [58, 54] Generated Node #0,0,4: 61:[58, 54] Operation: 81-27=54 Moving to Node #0,0,4 Current State: 61:[58, 54], Operations: ['45-18=27', '81-27=54'] Exploring Operation: 58+54=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 58*54=3132, Resulting Numbers: [3132] 3132,61 unequal: No Solution Exploring Operation: 58-54=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[81, 85], Operations: ['45-18=27', '58+27=85'] Exploring Operation: 85-81=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 81*85=6885, Resulting Numbers: [6885] 6885,61 unequal: No Solution Exploring Operation: 81+85=166, Resulting Numbers: [166] 166,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[58, 108], Operations: ['45-18=27', '81+27=108'] Exploring Operation: 58*108=6264, Resulting Numbers: [6264] 6264,61 unequal: No Solution Exploring Operation: 108-58=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 58+108=166, Resulting Numbers: [166] 166,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[81, 31], Operations: ['45-18=27', '58-27=31'] Exploring Operation: 81-31=50, Resulting Numbers: [50] 50,61 unequal: No Solution Exploring Operation: 81+31=112, Resulting Numbers: [112] 112,61 unequal: No Solution Exploring Operation: 81*31=2511, Resulting Numbers: [2511] 2511,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[58, 3], Operations: ['45-18=27', '81/27=3'] Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,61 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[18, 45, 58, 81], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [58, 81, 27] Generated Node #0,0: 61:[58, 81, 27] Operation: 45-18=27 Moving to Node #0,0 Current State: 61:[58, 81, 27], Operations: ['45-18=27'] Exploring Operation: 81/27=3, Resulting Numbers: [58, 3] Generated Node #0,0,1: 61:[58, 3] Operation: 81/27=3 Moving to Node #0,0,1 Current State: 61:[58, 3], Operations: ['45-18=27', '81/27=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.921007
hs_5
sum_heuristic
[ 45, 5, 92, 95 ]
27
[ "45/5=9", "95-92=3", "9*3=27" ]
Current State: 27:[45, 5, 92, 95], Operations: [] Exploring Operation: 45/5=9, Resulting Numbers: [92, 95, 9] Generated Node #2: [92, 95, 9] from Operation: 45/5=9 Current State: 27:[92, 95, 9], Operations: ['45/5=9'] Exploring Operation: 95-92=3, Resulting Numbers: [9, 3] Generated Node #3: [9, 3] from Operation: 95-92=3 Current State: 27:[9, 3], Operations: ['45/5=9', '95-92=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[45, 5, 92, 95], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [45, 5, 3] Generated Node #0,0: 27:[45, 5, 3] Operation: 95-92=3 Exploring Operation: 95-45=50, Resulting Numbers: [5, 92, 50] Generated Node #0,1: 27:[5, 92, 50] Operation: 95-45=50 Exploring Operation: 95/5=19, Resulting Numbers: [45, 92, 19] Generated Node #0,2: 27:[45, 92, 19] Operation: 95/5=19 Exploring Operation: 92-45=47, Resulting Numbers: [5, 95, 47] Generated Node #0,3: 27:[5, 95, 47] Operation: 92-45=47 Moving to Node #0,0 Current State: 27:[45, 5, 3], Operations: ['95-92=3'] Exploring Operation: 45/5=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 27:[3, 9] Operation: 45/5=9 Exploring Operation: 45-5=40, Resulting Numbers: [3, 40] Generated Node #0,0,1: 27:[3, 40] Operation: 45-5=40 Exploring Operation: 45-3=42, Resulting Numbers: [5, 42] Generated Node #0,0,2: 27:[5, 42] Operation: 45-3=42 Exploring Operation: 45/3=15, Resulting Numbers: [5, 15] Generated Node #0,0,3: 27:[5, 15] Operation: 45/3=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[3, 9], Operations: ['95-92=3', '45/5=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,27 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,27 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[45, 5, 92, 95], Operations: [] Exploring Operation: 95-92=3, Resulting Numbers: [45, 5, 3] Generated Node #0,0: 27:[45, 5, 3] Operation: 95-92=3 Moving to Node #0,0 Current State: 27:[45, 5, 3], Operations: ['95-92=3'] Exploring Operation: 45/5=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 27:[3, 9] Operation: 45/5=9 Moving to Node #0,0,0 Current State: 27:[3, 9], Operations: ['95-92=3', '45/5=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 14, 84, 57, 34 ]
98
[ "84-57=27", "34-27=7", "14*7=98" ]
Current State: 98:[14, 84, 57, 34], Operations: [] Exploring Operation: 84-57=27, Resulting Numbers: [14, 34, 27] Generated Node #2: [14, 34, 27] from Operation: 84-57=27 Current State: 98:[14, 34, 27], Operations: ['84-57=27'] Exploring Operation: 34-27=7, Resulting Numbers: [14, 7] Generated Node #3: [14, 7] from Operation: 34-27=7 Current State: 98:[14, 7], Operations: ['84-57=27', '34-27=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[14, 84, 57, 34], Operations: [] Exploring Operation: 84-34=50, Resulting Numbers: [14, 57, 50] Generated Node #0,0: 98:[14, 57, 50] Operation: 84-34=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[14, 57, 50], Operations: ['84-34=50'] Exploring Operation: 57-50=7, Resulting Numbers: [14, 7] Generated Node #0,0,0: 98:[14, 7] Operation: 57-50=7 Moving to Node #0,0,0 Current State: 98:[14, 7], Operations: ['84-34=50', '57-50=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[14, 84, 57, 34], Operations: [] Exploring Operation: 84-34=50, Resulting Numbers: [14, 57, 50] Generated Node #0,0: 98:[14, 57, 50] Operation: 84-34=50 Moving to Node #0,0 Current State: 98:[14, 57, 50], Operations: ['84-34=50'] Exploring Operation: 57-50=7, Resulting Numbers: [14, 7] Generated Node #0,0,0: 98:[14, 7] Operation: 57-50=7 Moving to Node #0,0,0 Current State: 98:[14, 7], Operations: ['84-34=50', '57-50=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 90, 75, 63, 61 ]
20
[ "75-61=14", "90*14=1260", "1260/63=20" ]
Current State: 20:[90, 75, 63, 61], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [90, 63, 14] Generated Node #2: [90, 63, 14] from Operation: 75-61=14 Current State: 20:[90, 63, 14], Operations: ['75-61=14'] Exploring Operation: 90*14=1260, Resulting Numbers: [63, 1260] Generated Node #3: [63, 1260] from Operation: 90*14=1260 Current State: 20:[63, 1260], Operations: ['75-61=14', '90*14=1260'] Exploring Operation: 1260/63=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[90, 75, 63, 61], Operations: [] Exploring Operation: 90-75=15, Resulting Numbers: [63, 61, 15] Generated Node #0,0: 20:[63, 61, 15] Operation: 90-75=15 Moving to Node #0,0 Current State: 20:[63, 61, 15], Operations: ['90-75=15'] Exploring Operation: 63-61=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 20:[15, 2] Operation: 63-61=2 Moving to Node #0,0,0 Current State: 20:[15, 2], Operations: ['90-75=15', '63-61=2'] Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,20 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 94, 15, 2, 18 ]
59
[ "94-15=79", "2+18=20", "79-20=59" ]
Current State: 59:[94, 15, 2, 18], Operations: [] Exploring Operation: 94-15=79, Resulting Numbers: [2, 18, 79] Generated Node #2: [2, 18, 79] from Operation: 94-15=79 Current State: 59:[2, 18, 79], Operations: ['94-15=79'] Exploring Operation: 2+18=20, Resulting Numbers: [79, 20] Generated Node #3: [79, 20] from Operation: 2+18=20 Current State: 59:[79, 20], Operations: ['94-15=79', '2+18=20'] Exploring Operation: 79-20=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[94, 15, 2, 18], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [94, 15, 36] Generated Node #0,0: 59:[94, 15, 36] Operation: 2*18=36 Exploring Operation: 94-15=79, Resulting Numbers: [2, 18, 79] Generated Node #0,1: 59:[2, 18, 79] Operation: 94-15=79 Exploring Operation: 94/2=47, Resulting Numbers: [15, 18, 47] Generated Node #0,2: 59:[15, 18, 47] Operation: 94/2=47 Exploring Operation: 15*2=30, Resulting Numbers: [94, 18, 30] Generated Node #0,3: 59:[94, 18, 30] Operation: 15*2=30 Exploring Operation: 94-2=92, Resulting Numbers: [15, 18, 92] Generated Node #0,4: 59:[15, 18, 92] Operation: 94-2=92 Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[15, 18, 47], Operations: ['94/2=47'] Exploring Operation: 18-15=3, Resulting Numbers: [47, 3] Generated Node #0,2,0: 59:[47, 3] Operation: 18-15=3 Exploring Operation: 15+47=62, Resulting Numbers: [18, 62] Generated Node #0,2,1: 59:[18, 62] Operation: 15+47=62 Exploring Operation: 15+18=33, Resulting Numbers: [47, 33] Generated Node #0,2,2: 59:[47, 33] Operation: 15+18=33 Exploring Operation: 18+47=65, Resulting Numbers: [15, 65] Generated Node #0,2,3: 59:[15, 65] Operation: 18+47=65 Exploring Operation: 47-15=32, Resulting Numbers: [18, 32] Generated Node #0,2,4: 59:[18, 32] Operation: 47-15=32 Moving to Node #0,2,2 Current State: 59:[47, 33], Operations: ['94/2=47', '15+18=33'] Exploring Operation: 47*33=1551, Resulting Numbers: [1551] 1551,59 unequal: No Solution Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,59 unequal: No Solution Exploring Operation: 47+33=80, Resulting Numbers: [80] 80,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[18, 62], Operations: ['94/2=47', '15+47=62'] Exploring Operation: 62-18=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 18+62=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 18*62=1116, Resulting Numbers: [1116] 1116,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[15, 65], Operations: ['94/2=47', '18+47=65'] Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,59 unequal: No Solution Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[47, 3], Operations: ['94/2=47', '18-15=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,59 unequal: No Solution Exploring Operation: 47*3=141, Resulting Numbers: [141] 141,59 unequal: No Solution Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,59 unequal: No Solution Moving to Node #0,2,4 Current State: 59:[18, 32], Operations: ['94/2=47', '47-15=32'] Exploring Operation: 18+32=50, Resulting Numbers: [50] 50,59 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,59 unequal: No Solution Exploring Operation: 18*32=576, Resulting Numbers: [576] 576,59 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 #0,0 Current State: 59:[94, 15, 36], Operations: ['2*18=36'] Exploring Operation: 94-36=58, Resulting Numbers: [15, 58] Generated Node #0,0,0: 59:[15, 58] Operation: 94-36=58 Exploring Operation: 94-15=79, Resulting Numbers: [36, 79] Generated Node #0,0,1: 59:[36, 79] Operation: 94-15=79 Exploring Operation: 36-15=21, Resulting Numbers: [94, 21] Generated Node #0,0,2: 59:[94, 21] Operation: 36-15=21 Exploring Operation: 94+15=109, Resulting Numbers: [36, 109] Generated Node #0,0,3: 59:[36, 109] Operation: 94+15=109 Exploring Operation: 15+36=51, Resulting Numbers: [94, 51] Generated Node #0,0,4: 59:[94, 51] Operation: 15+36=51 Moving to Node #0,0,1 Current State: 59:[36, 79], Operations: ['2*18=36', '94-15=79'] Exploring Operation: 36+79=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 36*79=2844, Resulting Numbers: [2844] 2844,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[94, 51], Operations: ['2*18=36', '15+36=51'] Exploring Operation: 94-51=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 94*51=4794, Resulting Numbers: [4794] 4794,59 unequal: No Solution Exploring Operation: 94+51=145, Resulting Numbers: [145] 145,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[15, 58], Operations: ['2*18=36', '94-36=58'] Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,59 unequal: No Solution Exploring Operation: 15+58=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 15*58=870, Resulting Numbers: [870] 870,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[94, 21], Operations: ['2*18=36', '36-15=21'] Exploring Operation: 94*21=1974, Resulting Numbers: [1974] 1974,59 unequal: No Solution Exploring Operation: 94+21=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 94-21=73, Resulting Numbers: [73] 73,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[36, 109], Operations: ['2*18=36', '94+15=109'] Exploring Operation: 109-36=73, Resulting Numbers: [73] 73,59 unequal: No Solution Exploring Operation: 36*109=3924, Resulting Numbers: [3924] 3924,59 unequal: No Solution Exploring Operation: 36+109=145, Resulting Numbers: [145] 145,59 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:[94, 18, 30], Operations: ['15*2=30'] Exploring Operation: 30-18=12, Resulting Numbers: [94, 12] Generated Node #0,3,0: 59:[94, 12] Operation: 30-18=12 Exploring Operation: 18+30=48, Resulting Numbers: [94, 48] Generated Node #0,3,1: 59:[94, 48] Operation: 18+30=48 Exploring Operation: 94-30=64, Resulting Numbers: [18, 64] Generated Node #0,3,2: 59:[18, 64] Operation: 94-30=64 Exploring Operation: 94+18=112, Resulting Numbers: [30, 112] Generated Node #0,3,3: 59:[30, 112] Operation: 94+18=112 Exploring Operation: 94-18=76, Resulting Numbers: [30, 76] Generated Node #0,3,4: 59:[30, 76] Operation: 94-18=76 Moving to Node #0,3,1 Current State: 59:[94, 48], Operations: ['15*2=30', '18+30=48'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 94*48=4512, Resulting Numbers: [4512] 4512,59 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[30, 76], Operations: ['15*2=30', '94-18=76'] Exploring Operation: 30*76=2280, Resulting Numbers: [2280] 2280,59 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 30+76=106, Resulting Numbers: [106] 106,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[18, 64], Operations: ['15*2=30', '94-30=64'] Exploring Operation: 64-18=46, Resulting Numbers: [46] 46,59 unequal: No Solution Exploring Operation: 18*64=1152, Resulting Numbers: [1152] 1152,59 unequal: No Solution Exploring Operation: 18+64=82, Resulting Numbers: [82] 82,59 unequal: No Solution Moving to Node #0,3,0 Current State: 59:[94, 12], Operations: ['15*2=30', '30-18=12'] Exploring Operation: 94+12=106, Resulting Numbers: [106] 106,59 unequal: No Solution Exploring Operation: 94*12=1128, Resulting Numbers: [1128] 1128,59 unequal: No Solution Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[30, 112], Operations: ['15*2=30', '94+18=112'] Exploring Operation: 112-30=82, Resulting Numbers: [82] 82,59 unequal: No Solution Exploring Operation: 30+112=142, Resulting Numbers: [142] 142,59 unequal: No Solution Exploring Operation: 30*112=3360, Resulting Numbers: [3360] 3360,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[2, 18, 79], Operations: ['94-15=79'] Exploring Operation: 2*18=36, Resulting Numbers: [79, 36] Generated Node #0,1,0: 59:[79, 36] Operation: 2*18=36 Exploring Operation: 18-2=16, Resulting Numbers: [79, 16] Generated Node #0,1,1: 59:[79, 16] Operation: 18-2=16 Exploring Operation: 79-18=61, Resulting Numbers: [2, 61] Generated Node #0,1,2: 59:[2, 61] Operation: 79-18=61 Exploring Operation: 79-2=77, Resulting Numbers: [18, 77] Generated Node #0,1,3: 59:[18, 77] Operation: 79-2=77 Exploring Operation: 2+18=20, Resulting Numbers: [79, 20] Generated Node #0,1,4: 59:[79, 20] Operation: 2+18=20 Moving to Node #0,1,0 Current State: 59:[79, 36], Operations: ['94-15=79', '2*18=36'] Exploring Operation: 79+36=115, Resulting Numbers: [115] 115,59 unequal: No Solution Exploring Operation: 79*36=2844, Resulting Numbers: [2844] 2844,59 unequal: No Solution Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[18, 77], Operations: ['94-15=79', '79-2=77'] Exploring Operation: 18*77=1386, Resulting Numbers: [1386] 1386,59 unequal: No Solution Exploring Operation: 18+77=95, Resulting Numbers: [95] 95,59 unequal: No Solution Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[94, 15, 2, 18], Operations: [] Exploring Operation: 94-15=79, Resulting Numbers: [2, 18, 79] Generated Node #0,1: 59:[2, 18, 79] Operation: 94-15=79 Moving to Node #0,1 Current State: 59:[2, 18, 79], Operations: ['94-15=79'] Exploring Operation: 79-2=77, Resulting Numbers: [18, 77] Generated Node #0,1,3: 59:[18, 77] Operation: 79-2=77 Moving to Node #0,1,3 Current State: 59:[18, 77], Operations: ['94-15=79', '79-2=77'] Exploring Operation: 77-18=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 1
0.930556
hs_5
sum_heuristic
[ 3, 17, 67, 64 ]
23
[ "3+17=20", "67-64=3", "20+3=23" ]
Current State: 23:[3, 17, 67, 64], Operations: [] Exploring Operation: 3+17=20, Resulting Numbers: [67, 64, 20] Generated Node #2: [67, 64, 20] from Operation: 3+17=20 Current State: 23:[67, 64, 20], Operations: ['3+17=20'] Exploring Operation: 67-64=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 67-64=3 Current State: 23:[20, 3], Operations: ['3+17=20', '67-64=3'] Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[3, 17, 67, 64], Operations: [] Exploring Operation: 3+17=20, Resulting Numbers: [67, 64, 20] Generated Node #0,0: 23:[67, 64, 20] Operation: 3+17=20 Exploring Operation: 67-64=3, Resulting Numbers: [3, 17, 3] Generated Node #0,1: 23:[3, 17, 3] Operation: 67-64=3 Exploring Operation: 67-3=64, Resulting Numbers: [17, 64, 64] Generated Node #0,2: 23:[17, 64, 64] Operation: 67-3=64 Moving to Node #0,1 Current State: 23:[3, 17, 3], Operations: ['67-64=3'] Exploring Operation: 3+3=6, Resulting Numbers: [17, 6] Generated Node #0,1,0: 23:[17, 6] Operation: 3+3=6 Exploring Operation: 3+17=20, Resulting Numbers: [3, 20] Generated Node #0,1,1: 23:[3, 20] Operation: 3+17=20 Exploring Operation: 3*3=9, Resulting Numbers: [17, 9] Generated Node #0,1,2: 23:[17, 9] Operation: 3*3=9 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[17, 9], Operations: ['67-64=3', '3*3=9'] Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 17+9=26, Resulting Numbers: [26] 26,23 unequal: No Solution Exploring Operation: 17*9=153, Resulting Numbers: [153] 153,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[17, 6], Operations: ['67-64=3', '3+3=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[3, 17, 67, 64], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [3, 17, 3] Generated Node #0,1: 23:[3, 17, 3] Operation: 67-64=3 Moving to Node #0,1 Current State: 23:[3, 17, 3], Operations: ['67-64=3'] Exploring Operation: 3+3=6, Resulting Numbers: [17, 6] Generated Node #0,1,0: 23:[17, 6] Operation: 3+3=6 Moving to Node #0,1,0 Current State: 23:[17, 6], Operations: ['67-64=3', '3+3=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 48, 37, 79, 3 ]
58
[ "48/3=16", "79-37=42", "16+42=58" ]
Current State: 58:[48, 37, 79, 3], Operations: [] Exploring Operation: 48/3=16, Resulting Numbers: [37, 79, 16] Generated Node #2: [37, 79, 16] from Operation: 48/3=16 Current State: 58:[37, 79, 16], Operations: ['48/3=16'] Exploring Operation: 79-37=42, Resulting Numbers: [16, 42] Generated Node #3: [16, 42] from Operation: 79-37=42 Current State: 58:[16, 42], Operations: ['48/3=16', '79-37=42'] Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[48, 37, 79, 3], Operations: [] Exploring Operation: 79-37=42, Resulting Numbers: [48, 3, 42] Generated Node #0,0: 58:[48, 3, 42] Operation: 79-37=42 Exploring Operation: 48-37=11, Resulting Numbers: [79, 3, 11] Generated Node #0,1: 58:[79, 3, 11] Operation: 48-37=11 Exploring Operation: 79-48=31, Resulting Numbers: [37, 3, 31] Generated Node #0,2: 58:[37, 3, 31] Operation: 79-48=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[37, 3, 31], Operations: ['79-48=31'] Exploring Operation: 31-3=28, Resulting Numbers: [37, 28] Generated Node #0,2,0: 58:[37, 28] Operation: 31-3=28 Exploring Operation: 37-3=34, Resulting Numbers: [31, 34] Generated Node #0,2,1: 58:[31, 34] Operation: 37-3=34 Exploring Operation: 37-31=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 58:[3, 6] Operation: 37-31=6 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 58:[3, 6], Operations: ['79-48=31', '37-31=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 58:[31, 34], Operations: ['79-48=31', '37-3=34'] Exploring Operation: 31+34=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 34-31=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 31*34=1054, Resulting Numbers: [1054] 1054,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[37, 28], Operations: ['79-48=31', '31-3=28'] Exploring Operation: 37-28=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 37+28=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 37*28=1036, Resulting Numbers: [1036] 1036,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[48, 3, 42], Operations: ['79-37=42'] Exploring Operation: 42-3=39, Resulting Numbers: [48, 39] Generated Node #0,0,0: 58:[48, 39] Operation: 42-3=39 Exploring Operation: 48-42=6, Resulting Numbers: [3, 6] Generated Node #0,0,1: 58:[3, 6] Operation: 48-42=6 Exploring Operation: 48+3=51, Resulting Numbers: [42, 51] Generated Node #0,0,2: 58:[42, 51] Operation: 48+3=51 Moving to Node #0,0,1 Current State: 58:[3, 6], Operations: ['79-37=42', '48-42=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,58 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[48, 39], Operations: ['79-37=42', '42-3=39'] Exploring Operation: 48+39=87, Resulting Numbers: [87] 87,58 unequal: No Solution Exploring Operation: 48*39=1872, Resulting Numbers: [1872] 1872,58 unequal: No Solution Exploring Operation: 48-39=9, Resulting Numbers: [9] 9,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[42, 51], Operations: ['79-37=42', '48+3=51'] Exploring Operation: 42+51=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 42*51=2142, Resulting Numbers: [2142] 2142,58 unequal: No Solution Exploring Operation: 51-42=9, Resulting Numbers: [9] 9,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[79, 3, 11], Operations: ['48-37=11'] Exploring Operation: 79-3=76, Resulting Numbers: [11, 76] Generated Node #0,1,0: 58:[11, 76] Operation: 79-3=76 Exploring Operation: 3*11=33, Resulting Numbers: [79, 33] Generated Node #0,1,1: 58:[79, 33] Operation: 3*11=33 Exploring Operation: 79-11=68, Resulting Numbers: [3, 68] Generated Node #0,1,2: 58:[3, 68] Operation: 79-11=68 Moving to Node #0,1,2 Current State: 58:[3, 68], Operations: ['48-37=11', '79-11=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,58 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[79, 33], Operations: ['48-37=11', '3*11=33'] Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,58 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,58 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[11, 76], Operations: ['48-37=11', '79-3=76'] Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,58 unequal: No Solution Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,58 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
[ 6, 72, 41, 31 ]
68
[ "6+72=78", "41-31=10", "78-10=68" ]
Current State: 68:[6, 72, 41, 31], Operations: [] Exploring Operation: 6+72=78, Resulting Numbers: [41, 31, 78] Generated Node #2: [41, 31, 78] from Operation: 6+72=78 Current State: 68:[41, 31, 78], Operations: ['6+72=78'] Exploring Operation: 41-31=10, Resulting Numbers: [78, 10] Generated Node #3: [78, 10] from Operation: 41-31=10 Current State: 68:[78, 10], Operations: ['6+72=78', '41-31=10'] Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[6, 72, 41, 31], Operations: [] Exploring Operation: 41-6=35, Resulting Numbers: [72, 31, 35] Generated Node #0,0: 68:[72, 31, 35] Operation: 41-6=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[72, 31, 35], Operations: ['41-6=35'] Exploring Operation: 35-31=4, Resulting Numbers: [72, 4] Generated Node #0,0,0: 68:[72, 4] Operation: 35-31=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 68:[72, 4], Operations: ['41-6=35', '35-31=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[6, 72, 41, 31], Operations: [] Exploring Operation: 41-6=35, Resulting Numbers: [72, 31, 35] Generated Node #0,0: 68:[72, 31, 35] Operation: 41-6=35 Moving to Node #0,0 Current State: 68:[72, 31, 35], Operations: ['41-6=35'] Exploring Operation: 35-31=4, Resulting Numbers: [72, 4] Generated Node #0,0,0: 68:[72, 4] Operation: 35-31=4 Moving to Node #0,0,0 Current State: 68:[72, 4], Operations: ['41-6=35', '35-31=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 27, 89, 46, 35 ]
19
[ "89-27=62", "46+35=81", "81-62=19" ]
Current State: 19:[27, 89, 46, 35], Operations: [] Exploring Operation: 89-27=62, Resulting Numbers: [46, 35, 62] Generated Node #2: [46, 35, 62] from Operation: 89-27=62 Current State: 19:[46, 35, 62], Operations: ['89-27=62'] Exploring Operation: 46+35=81, Resulting Numbers: [62, 81] Generated Node #3: [62, 81] from Operation: 46+35=81 Current State: 19:[62, 81], Operations: ['89-27=62', '46+35=81'] Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[27, 89, 46, 35], Operations: [] Exploring Operation: 89-35=54, Resulting Numbers: [27, 46, 54] Generated Node #0,0: 19:[27, 46, 54] Operation: 89-35=54 Exploring Operation: 89-46=43, Resulting Numbers: [27, 35, 43] Generated Node #0,1: 19:[27, 35, 43] Operation: 89-46=43 Exploring Operation: 89-27=62, Resulting Numbers: [46, 35, 62] Generated Node #0,2: 19:[46, 35, 62] Operation: 89-27=62 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[27, 35, 43], Operations: ['89-46=43'] Exploring Operation: 43-35=8, Resulting Numbers: [27, 8] Generated Node #0,1,0: 19:[27, 8] Operation: 43-35=8 Exploring Operation: 43-27=16, Resulting Numbers: [35, 16] Generated Node #0,1,1: 19:[35, 16] Operation: 43-27=16 Exploring Operation: 35-27=8, Resulting Numbers: [43, 8] Generated Node #0,1,2: 19:[43, 8] Operation: 35-27=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[27, 8], Operations: ['89-46=43', '43-35=8'] Exploring Operation: 27*8=216, Resulting Numbers: [216] 216,19 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[27, 89, 46, 35], Operations: [] Exploring Operation: 89-46=43, Resulting Numbers: [27, 35, 43] Generated Node #0,1: 19:[27, 35, 43] Operation: 89-46=43 Moving to Node #0,1 Current State: 19:[27, 35, 43], Operations: ['89-46=43'] Exploring Operation: 43-35=8, Resulting Numbers: [27, 8] Generated Node #0,1,0: 19:[27, 8] Operation: 43-35=8 Moving to Node #0,1,0 Current State: 19:[27, 8], Operations: ['89-46=43', '43-35=8'] Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 61, 15, 2, 51 ]
11
[ "51-15=36", "2*36=72", "72-61=11" ]
Current State: 11:[61, 15, 2, 51], Operations: [] Exploring Operation: 51-15=36, Resulting Numbers: [61, 2, 36] Generated Node #2: [61, 2, 36] from Operation: 51-15=36 Current State: 11:[61, 2, 36], Operations: ['51-15=36'] Exploring Operation: 2*36=72, Resulting Numbers: [61, 72] Generated Node #3: [61, 72] from Operation: 2*36=72 Current State: 11:[61, 72], Operations: ['51-15=36', '2*36=72'] Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[61, 15, 2, 51], Operations: [] Exploring Operation: 61-15=46, Resulting Numbers: [2, 51, 46] Generated Node #0,0: 11:[2, 51, 46] Operation: 61-15=46 Exploring Operation: 51-15=36, Resulting Numbers: [61, 2, 36] Generated Node #0,1: 11:[61, 2, 36] Operation: 51-15=36 Exploring Operation: 61-51=10, Resulting Numbers: [15, 2, 10] Generated Node #0,2: 11:[15, 2, 10] Operation: 61-51=10 Exploring Operation: 61-2=59, Resulting Numbers: [15, 51, 59] Generated Node #0,3: 11:[15, 51, 59] Operation: 61-2=59 Moving to Node #0,2 Current State: 11:[15, 2, 10], Operations: ['61-51=10'] Exploring Operation: 10-2=8, Resulting Numbers: [15, 8] Generated Node #0,2,0: 11:[15, 8] Operation: 10-2=8 Exploring Operation: 2+10=12, Resulting Numbers: [15, 12] Generated Node #0,2,1: 11:[15, 12] Operation: 2+10=12 Exploring Operation: 15+2=17, Resulting Numbers: [10, 17] Generated Node #0,2,2: 11:[10, 17] Operation: 15+2=17 Exploring Operation: 15-2=13, Resulting Numbers: [10, 13] Generated Node #0,2,3: 11:[10, 13] Operation: 15-2=13 Moving to Node #0,1 Current State: 11:[61, 2, 36], Operations: ['51-15=36'] Exploring Operation: 61-2=59, Resulting Numbers: [36, 59] Generated Node #0,1,0: 11:[36, 59] Operation: 61-2=59 Exploring Operation: 36/2=18, Resulting Numbers: [61, 18] Generated Node #0,1,1: 11:[61, 18] Operation: 36/2=18 Exploring Operation: 36-2=34, Resulting Numbers: [61, 34] Generated Node #0,1,2: 11:[61, 34] Operation: 36-2=34 Exploring Operation: 61-36=25, Resulting Numbers: [2, 25] Generated Node #0,1,3: 11:[2, 25] Operation: 61-36=25 Moving to Node #0,0 Current State: 11:[2, 51, 46], Operations: ['61-15=46'] Exploring Operation: 51-2=49, Resulting Numbers: [46, 49] Generated Node #0,0,0: 11:[46, 49] Operation: 51-2=49 Exploring Operation: 46-2=44, Resulting Numbers: [51, 44] Generated Node #0,0,1: 11:[51, 44] Operation: 46-2=44 Exploring Operation: 51-46=5, Resulting Numbers: [2, 5] Generated Node #0,0,2: 11:[2, 5] Operation: 51-46=5 Exploring Operation: 46/2=23, Resulting Numbers: [51, 23] Generated Node #0,0,3: 11:[51, 23] Operation: 46/2=23 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 11:[2, 5], Operations: ['61-15=46', '51-46=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,11 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 #0,0,3 Current State: 11:[51, 23], Operations: ['61-15=46', '46/2=23'] Exploring Operation: 51+23=74, Resulting Numbers: [74] 74,11 unequal: No Solution Exploring Operation: 51*23=1173, Resulting Numbers: [1173] 1173,11 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,11 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 #0,0,0 Current State: 11:[46, 49], Operations: ['61-15=46', '51-2=49'] Exploring Operation: 49-46=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 46+49=95, Resulting Numbers: [95] 95,11 unequal: No Solution Exploring Operation: 46*49=2254, Resulting Numbers: [2254] 2254,11 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 #0,0,1 Current State: 11:[51, 44], Operations: ['61-15=46', '46-2=44'] Exploring Operation: 51*44=2244, Resulting Numbers: [2244] 2244,11 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 51+44=95, Resulting Numbers: [95] 95,11 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: 11:[15, 51, 59], Operations: ['61-2=59'] Exploring Operation: 51-15=36, Resulting Numbers: [59, 36] Generated Node #0,3,0: 11:[59, 36] Operation: 51-15=36 Exploring Operation: 15+51=66, Resulting Numbers: [59, 66] Generated Node #0,3,1: 11:[59, 66] Operation: 15+51=66 Exploring Operation: 59-15=44, Resulting Numbers: [51, 44] Generated Node #0,3,2: 11:[51, 44] Operation: 59-15=44 Exploring Operation: 59-51=8, Resulting Numbers: [15, 8] Generated Node #0,3,3: 11:[15, 8] Operation: 59-51=8 Moving to Node #0,2,3 Current State: 11:[10, 13], Operations: ['61-51=10', '15-2=13'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,11 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,11 unequal: No Solution Moving to Node #0,2,1 Current State: 11:[15, 12], Operations: ['61-51=10', '2+10=12'] Exploring Operation: 15-12=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 15*12=180, Resulting Numbers: [180] 180,11 unequal: No Solution Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,11 unequal: No Solution Moving to Node #0,2,0 Current State: 11:[15, 8], Operations: ['61-51=10', '10-2=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,11 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,11 unequal: No Solution Moving to Node #0,2,2 Current State: 11:[10, 17], Operations: ['61-51=10', '15+2=17'] Exploring Operation: 17-10=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,11 unequal: No Solution Exploring Operation: 10*17=170, Resulting Numbers: [170] 170,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[15, 8], Operations: ['61-2=59', '59-51=8'] Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,11 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[2, 25], Operations: ['51-15=36', '61-36=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,11 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,11 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[61, 18], Operations: ['51-15=36', '36/2=18'] Exploring Operation: 61*18=1098, Resulting Numbers: [1098] 1098,11 unequal: No Solution Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,11 unequal: No Solution Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[51, 44], Operations: ['61-2=59', '59-15=44'] Exploring Operation: 51*44=2244, Resulting Numbers: [2244] 2244,11 unequal: No Solution Exploring Operation: 51+44=95, Resulting Numbers: [95] 95,11 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[36, 59], Operations: ['51-15=36', '61-2=59'] Exploring Operation: 36*59=2124, Resulting Numbers: [2124] 2124,11 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,11 unequal: No Solution Exploring Operation: 36+59=95, Resulting Numbers: [95] 95,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[61, 34], Operations: ['51-15=36', '36-2=34'] Exploring Operation: 61*34=2074, Resulting Numbers: [2074] 2074,11 unequal: No Solution Exploring Operation: 61-34=27, Resulting Numbers: [27] 27,11 unequal: No Solution Exploring Operation: 61+34=95, Resulting Numbers: [95] 95,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[59, 36], Operations: ['61-2=59', '51-15=36'] Exploring Operation: 59+36=95, Resulting Numbers: [95] 95,11 unequal: No Solution Exploring Operation: 59*36=2124, Resulting Numbers: [2124] 2124,11 unequal: No Solution Exploring Operation: 59-36=23, Resulting Numbers: [23] 23,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[59, 66], Operations: ['61-2=59', '15+51=66'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,11 unequal: No Solution Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,11 unequal: No Solution No solution found.
0
hs_4
mult_heuristic