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
[ 8, 97, 69, 81 ]
61
[ "97-8=89", "69+81=150", "150-89=61" ]
Current State: 61:[8, 97, 69, 81], Operations: [] Exploring Operation: 97-8=89, Resulting Numbers: [69, 81, 89] Generated Node #2: [69, 81, 89] from Operation: 97-8=89 Current State: 61:[69, 81, 89], Operations: ['97-8=89'] Exploring Operation: 69+81=150, Resulting Numbers: [89, 150] Generated Node #3: [89, 150] from Operation: 69+81=150 Current State: 61:[89, 150], Operations: ['97-8=89', '69+81=150'] Exploring Operation: 150-89=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[8, 97, 69, 81], Operations: [] Exploring Operation: 69-8=61, Resulting Numbers: [97, 81, 61] Generated Node #0,0: 61:[97, 81, 61] Operation: 69-8=61 Exploring Operation: 81-8=73, Resulting Numbers: [97, 69, 73] Generated Node #0,1: 61:[97, 69, 73] Operation: 81-8=73 Exploring Operation: 8+97=105, Resulting Numbers: [69, 81, 105] Generated Node #0,2: 61:[69, 81, 105] Operation: 8+97=105 Exploring Operation: 8+69=77, Resulting Numbers: [97, 81, 77] Generated Node #0,3: 61:[97, 81, 77] Operation: 8+69=77 Exploring Operation: 97-8=89, Resulting Numbers: [69, 81, 89] Generated Node #0,4: 61:[69, 81, 89] Operation: 97-8=89 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[97, 81, 61], Operations: ['69-8=61'] Exploring Operation: 97+61=158, Resulting Numbers: [81, 158] Generated Node #0,0,0: 61:[81, 158] Operation: 97+61=158 Exploring Operation: 97-81=16, Resulting Numbers: [61, 16] Generated Node #0,0,1: 61:[61, 16] Operation: 97-81=16 Exploring Operation: 81-61=20, Resulting Numbers: [97, 20] Generated Node #0,0,2: 61:[97, 20] Operation: 81-61=20 Exploring Operation: 97-61=36, Resulting Numbers: [81, 36] Generated Node #0,0,3: 61:[81, 36] Operation: 97-61=36 Exploring Operation: 97+81=178, Resulting Numbers: [61, 178] Generated Node #0,0,4: 61:[61, 178] Operation: 97+81=178 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[61, 16], Operations: ['69-8=61', '97-81=16'] Exploring Operation: 61+16=77, Resulting Numbers: [77] 77,61 unequal: No Solution Exploring Operation: 61*16=976, Resulting Numbers: [976] 976,61 unequal: No Solution Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,61 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 #0,0,3 Current State: 61:[81, 36], Operations: ['69-8=61', '97-61=36'] Exploring Operation: 81-36=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 81+36=117, Resulting Numbers: [117] 117,61 unequal: No Solution Exploring Operation: 81*36=2916, Resulting Numbers: [2916] 2916,61 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 #0,0,2 Current State: 61:[97, 20], Operations: ['69-8=61', '81-61=20'] Exploring Operation: 97*20=1940, Resulting Numbers: [1940] 1940,61 unequal: No Solution Exploring Operation: 97+20=117, Resulting Numbers: [117] 117,61 unequal: No Solution Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,61 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 #0,0,0 Current State: 61:[81, 158], Operations: ['69-8=61', '97+61=158'] Exploring Operation: 81*158=12798, Resulting Numbers: [12798] 12798,61 unequal: No Solution Exploring Operation: 158-81=77, Resulting Numbers: [77] 77,61 unequal: No Solution Exploring Operation: 81+158=239, Resulting Numbers: [239] 239,61 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 #0,0,4 Current State: 61:[61, 178], Operations: ['69-8=61', '97+81=178'] Exploring Operation: 178-61=117, Resulting Numbers: [117] 117,61 unequal: No Solution Exploring Operation: 61*178=10858, Resulting Numbers: [10858] 10858,61 unequal: No Solution Exploring Operation: 61+178=239, Resulting Numbers: [239] 239,61 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:[97, 69, 73], Operations: ['81-8=73'] Exploring Operation: 73-69=4, Resulting Numbers: [97, 4] Generated Node #0,1,0: 61:[97, 4] Operation: 73-69=4 Exploring Operation: 97-73=24, Resulting Numbers: [69, 24] Generated Node #0,1,1: 61:[69, 24] Operation: 97-73=24 Exploring Operation: 97-69=28, Resulting Numbers: [73, 28] Generated Node #0,1,2: 61:[73, 28] Operation: 97-69=28 Exploring Operation: 97+69=166, Resulting Numbers: [73, 166] Generated Node #0,1,3: 61:[73, 166] Operation: 97+69=166 Exploring Operation: 97+73=170, Resulting Numbers: [69, 170] Generated Node #0,1,4: 61:[69, 170] Operation: 97+73=170 Moving to Node #0,1,1 Current State: 61:[69, 24], Operations: ['81-8=73', '97-73=24'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,61 unequal: No Solution Exploring Operation: 69*24=1656, Resulting Numbers: [1656] 1656,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[73, 28], Operations: ['81-8=73', '97-69=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,61 unequal: No Solution Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[97, 4], Operations: ['81-8=73', '73-69=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,61 unequal: No Solution Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,61 unequal: No Solution Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[73, 166], Operations: ['81-8=73', '97+69=166'] Exploring Operation: 166-73=93, Resulting Numbers: [93] 93,61 unequal: No Solution Exploring Operation: 73+166=239, Resulting Numbers: [239] 239,61 unequal: No Solution Exploring Operation: 73*166=12118, Resulting Numbers: [12118] 12118,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[69, 170], Operations: ['81-8=73', '97+73=170'] Exploring Operation: 69+170=239, Resulting Numbers: [239] 239,61 unequal: No Solution Exploring Operation: 69*170=11730, Resulting Numbers: [11730] 11730,61 unequal: No Solution Exploring Operation: 170-69=101, Resulting Numbers: [101] 101,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 61:[69, 81, 89], Operations: ['97-8=89'] Exploring Operation: 89-69=20, Resulting Numbers: [81, 20] Generated Node #0,4,0: 61:[81, 20] Operation: 89-69=20 Exploring Operation: 89-81=8, Resulting Numbers: [69, 8] Generated Node #0,4,1: 61:[69, 8] Operation: 89-81=8 Exploring Operation: 69+81=150, Resulting Numbers: [89, 150] Generated Node #0,4,2: 61:[89, 150] Operation: 69+81=150 Exploring Operation: 81-69=12, Resulting Numbers: [89, 12] Generated Node #0,4,3: 61:[89, 12] Operation: 81-69=12 Exploring Operation: 69+89=158, Resulting Numbers: [81, 158] Generated Node #0,4,4: 61:[81, 158] Operation: 69+89=158 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 61:[81, 20], Operations: ['97-8=89', '89-69=20'] Exploring Operation: 81*20=1620, Resulting Numbers: [1620] 1620,61 unequal: No Solution Exploring Operation: 81+20=101, Resulting Numbers: [101] 101,61 unequal: No Solution Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[8, 97, 69, 81], Operations: [] Exploring Operation: 97-8=89, Resulting Numbers: [69, 81, 89] Generated Node #0,4: 61:[69, 81, 89] Operation: 97-8=89 Moving to Node #0,4 Current State: 61:[69, 81, 89], Operations: ['97-8=89'] Exploring Operation: 89-69=20, Resulting Numbers: [81, 20] Generated Node #0,4,0: 61:[81, 20] Operation: 89-69=20 Moving to Node #0,4,0 Current State: 61:[81, 20], Operations: ['97-8=89', '89-69=20'] Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 9, 40, 44, 3 ]
25
[ "40-9=31", "44+31=75", "75/3=25" ]
Current State: 25:[9, 40, 44, 3], Operations: [] Exploring Operation: 40-9=31, Resulting Numbers: [44, 3, 31] Generated Node #2: [44, 3, 31] from Operation: 40-9=31 Current State: 25:[44, 3, 31], Operations: ['40-9=31'] Exploring Operation: 44+31=75, Resulting Numbers: [3, 75] Generated Node #3: [3, 75] from Operation: 44+31=75 Current State: 25:[3, 75], Operations: ['40-9=31', '44+31=75'] Exploring Operation: 75/3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[9, 40, 44, 3], Operations: [] Exploring Operation: 44-40=4, Resulting Numbers: [9, 3, 4] Generated Node #0,0: 25:[9, 3, 4] Operation: 44-40=4 Exploring Operation: 40-9=31, Resulting Numbers: [44, 3, 31] Generated Node #0,1: 25:[44, 3, 31] Operation: 40-9=31 Exploring Operation: 44-9=35, Resulting Numbers: [40, 3, 35] Generated Node #0,2: 25:[40, 3, 35] Operation: 44-9=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[9, 3, 4], Operations: ['44-40=4'] Exploring Operation: 9-4=5, Resulting Numbers: [3, 5] Generated Node #0,0,0: 25:[3, 5] Operation: 9-4=5 Exploring Operation: 9-3=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 25:[4, 6] Operation: 9-3=6 Exploring Operation: 9*3=27, Resulting Numbers: [4, 27] Generated Node #0,0,2: 25:[4, 27] Operation: 9*3=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[3, 5], Operations: ['44-40=4', '9-4=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,25 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,25 unequal: No Solution No 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: 25:[4, 6], Operations: ['44-40=4', '9-3=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,25 unequal: No Solution No 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: 25:[4, 27], Operations: ['44-40=4', '9*3=27'] Exploring Operation: 4*27=108, Resulting Numbers: [108] 108,25 unequal: No Solution Exploring Operation: 27-4=23, Resulting Numbers: [23] 23,25 unequal: No Solution Exploring Operation: 4+27=31, Resulting Numbers: [31] 31,25 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: 25:[44, 3, 31], Operations: ['40-9=31'] Exploring Operation: 44-3=41, Resulting Numbers: [31, 41] Generated Node #0,1,0: 25:[31, 41] Operation: 44-3=41 Exploring Operation: 31-3=28, Resulting Numbers: [44, 28] Generated Node #0,1,1: 25:[44, 28] Operation: 31-3=28 Exploring Operation: 44-31=13, Resulting Numbers: [3, 13] Generated Node #0,1,2: 25:[3, 13] Operation: 44-31=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 25:[3, 13], Operations: ['40-9=31', '44-31=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,25 unequal: No Solution No 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: 25:[31, 41], Operations: ['40-9=31', '44-3=41'] Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 31+41=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 31*41=1271, Resulting Numbers: [1271] 1271,25 unequal: No Solution No 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: 25:[44, 28], Operations: ['40-9=31', '31-3=28'] Exploring Operation: 44*28=1232, Resulting Numbers: [1232] 1232,25 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 44+28=72, Resulting Numbers: [72] 72,25 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: 25:[40, 3, 35], Operations: ['44-9=35'] Exploring Operation: 35-3=32, Resulting Numbers: [40, 32] Generated Node #0,2,0: 25:[40, 32] Operation: 35-3=32 Exploring Operation: 40-3=37, Resulting Numbers: [35, 37] Generated Node #0,2,1: 25:[35, 37] Operation: 40-3=37 Exploring Operation: 40-35=5, Resulting Numbers: [3, 5] Generated Node #0,2,2: 25:[3, 5] Operation: 40-35=5 Moving to Node #0,2,2 Current State: 25:[3, 5], Operations: ['44-9=35', '40-35=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,25 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[40, 32], Operations: ['44-9=35', '35-3=32'] Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 40+32=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 40*32=1280, Resulting Numbers: [1280] 1280,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[35, 37], Operations: ['44-9=35', '40-3=37'] Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,25 unequal: No Solution Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,25 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
[ 82, 3, 33, 65 ]
28
[ "82-65=17", "33/3=11", "17+11=28" ]
Current State: 28:[82, 3, 33, 65], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [3, 33, 17] Generated Node #2: [3, 33, 17] from Operation: 82-65=17 Current State: 28:[3, 33, 17], Operations: ['82-65=17'] Exploring Operation: 33/3=11, Resulting Numbers: [17, 11] Generated Node #3: [17, 11] from Operation: 33/3=11 Current State: 28:[17, 11], Operations: ['82-65=17', '33/3=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[82, 3, 33, 65], Operations: [] Exploring Operation: 65-33=32, Resulting Numbers: [82, 3, 32] Generated Node #0,0: 28:[82, 3, 32] Operation: 65-33=32 Exploring Operation: 82-65=17, Resulting Numbers: [3, 33, 17] Generated Node #0,1: 28:[3, 33, 17] Operation: 82-65=17 Exploring Operation: 82-33=49, Resulting Numbers: [3, 65, 49] Generated Node #0,2: 28:[3, 65, 49] Operation: 82-33=49 Exploring Operation: 33-3=30, Resulting Numbers: [82, 65, 30] Generated Node #0,3: 28:[82, 65, 30] Operation: 33-3=30 Exploring Operation: 82-3=79, Resulting Numbers: [33, 65, 79] Generated Node #0,4: 28:[33, 65, 79] Operation: 82-3=79 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[3, 33, 17], Operations: ['82-65=17'] Exploring Operation: 33-17=16, Resulting Numbers: [3, 16] Generated Node #0,1,0: 28:[3, 16] Operation: 33-17=16 Exploring Operation: 17-3=14, Resulting Numbers: [33, 14] Generated Node #0,1,1: 28:[33, 14] Operation: 17-3=14 Exploring Operation: 33-3=30, Resulting Numbers: [17, 30] Generated Node #0,1,2: 28:[17, 30] Operation: 33-3=30 Exploring Operation: 3+33=36, Resulting Numbers: [17, 36] Generated Node #0,1,3: 28:[17, 36] Operation: 3+33=36 Exploring Operation: 33/3=11, Resulting Numbers: [17, 11] Generated Node #0,1,4: 28:[17, 11] Operation: 33/3=11 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[3, 16], Operations: ['82-65=17', '33-17=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,28 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 #0,1,1 Current State: 28:[33, 14], Operations: ['82-65=17', '17-3=14'] Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,28 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,28 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,28 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 #0,1,2 Current State: 28:[17, 30], Operations: ['82-65=17', '33-3=30'] Exploring Operation: 17+30=47, Resulting Numbers: [47] 47,28 unequal: No Solution Exploring Operation: 17*30=510, Resulting Numbers: [510] 510,28 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,28 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 #0,1,4 Current State: 28:[17, 11], Operations: ['82-65=17', '33/3=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[82, 3, 33, 65], Operations: [] Exploring Operation: 82-65=17, Resulting Numbers: [3, 33, 17] Generated Node #0,1: 28:[3, 33, 17] Operation: 82-65=17 Moving to Node #0,1 Current State: 28:[3, 33, 17], Operations: ['82-65=17'] Exploring Operation: 33/3=11, Resulting Numbers: [17, 11] Generated Node #0,1,4: 28:[17, 11] Operation: 33/3=11 Moving to Node #0,1,4 Current State: 28:[17, 11], Operations: ['82-65=17', '33/3=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_5
sum_heuristic
[ 45, 7, 15, 55 ]
59
[ "45/15=3", "7+55=62", "62-3=59" ]
Current State: 59:[45, 7, 15, 55], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [7, 55, 3] Generated Node #2: [7, 55, 3] from Operation: 45/15=3 Current State: 59:[7, 55, 3], Operations: ['45/15=3'] Exploring Operation: 7+55=62, Resulting Numbers: [3, 62] Generated Node #3: [3, 62] from Operation: 7+55=62 Current State: 59:[3, 62], Operations: ['45/15=3', '7+55=62'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[45, 7, 15, 55], Operations: [] Exploring Operation: 7+15=22, Resulting Numbers: [45, 55, 22] Generated Node #0,0: 59:[45, 55, 22] Operation: 7+15=22 Exploring Operation: 45+7=52, Resulting Numbers: [15, 55, 52] Generated Node #0,1: 59:[15, 55, 52] Operation: 45+7=52 Exploring Operation: 45+15=60, Resulting Numbers: [7, 55, 60] Generated Node #0,2: 59:[7, 55, 60] Operation: 45+15=60 Moving to Node #0,0 Current State: 59:[45, 55, 22], Operations: ['7+15=22'] Exploring Operation: 45+22=67, Resulting Numbers: [55, 67] Generated Node #0,0,0: 59:[55, 67] Operation: 45+22=67 Exploring Operation: 45-22=23, Resulting Numbers: [55, 23] Generated Node #0,0,1: 59:[55, 23] Operation: 45-22=23 Exploring Operation: 55+22=77, Resulting Numbers: [45, 77] Generated Node #0,0,2: 59:[45, 77] Operation: 55+22=77 Moving to Node #0,1 Current State: 59:[15, 55, 52], Operations: ['45+7=52'] Exploring Operation: 15+55=70, Resulting Numbers: [52, 70] Generated Node #0,1,0: 59:[52, 70] Operation: 15+55=70 Exploring Operation: 15+52=67, Resulting Numbers: [55, 67] Generated Node #0,1,1: 59:[55, 67] Operation: 15+52=67 Exploring Operation: 55-15=40, Resulting Numbers: [52, 40] Generated Node #0,1,2: 59:[52, 40] Operation: 55-15=40 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[55, 67], Operations: ['45+7=52', '15+52=67'] Exploring Operation: 67-55=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 55*67=3685, Resulting Numbers: [3685] 3685,59 unequal: No Solution Exploring Operation: 55+67=122, Resulting Numbers: [122] 122,59 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 #0,1,0 Current State: 59:[52, 70], Operations: ['45+7=52', '15+55=70'] Exploring Operation: 52+70=122, Resulting Numbers: [122] 122,59 unequal: No Solution Exploring Operation: 52*70=3640, Resulting Numbers: [3640] 3640,59 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,59 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 #0,1,2 Current State: 59:[52, 40], Operations: ['45+7=52', '55-15=40'] Exploring Operation: 52*40=2080, Resulting Numbers: [2080] 2080,59 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 52+40=92, Resulting Numbers: [92] 92,59 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: 59:[7, 55, 60], Operations: ['45+15=60'] Exploring Operation: 7+55=62, Resulting Numbers: [60, 62] Generated Node #0,2,0: 59:[60, 62] Operation: 7+55=62 Exploring Operation: 60-7=53, Resulting Numbers: [55, 53] Generated Node #0,2,1: 59:[55, 53] Operation: 60-7=53 Exploring Operation: 55-7=48, Resulting Numbers: [60, 48] Generated Node #0,2,2: 59:[60, 48] Operation: 55-7=48 Moving to Node #0,2,0 Current State: 59:[60, 62], Operations: ['45+15=60', '7+55=62'] Exploring Operation: 62-60=2, Resulting Numbers: [2] 2,59 unequal: No Solution Exploring Operation: 60*62=3720, Resulting Numbers: [3720] 3720,59 unequal: No Solution Exploring Operation: 60+62=122, Resulting Numbers: [122] 122,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[55, 53], Operations: ['45+15=60', '60-7=53'] Exploring Operation: 55+53=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 55*53=2915, Resulting Numbers: [2915] 2915,59 unequal: No Solution Exploring Operation: 55-53=2, Resulting Numbers: [2] 2,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[60, 48], Operations: ['45+15=60', '55-7=48'] Exploring Operation: 60*48=2880, Resulting Numbers: [2880] 2880,59 unequal: No Solution Exploring Operation: 60+48=108, Resulting Numbers: [108] 108,59 unequal: No Solution Exploring Operation: 60-48=12, Resulting Numbers: [12] 12,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[55, 67], Operations: ['7+15=22', '45+22=67'] Exploring Operation: 67-55=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 55+67=122, Resulting Numbers: [122] 122,59 unequal: No Solution Exploring Operation: 55*67=3685, Resulting Numbers: [3685] 3685,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[45, 77], Operations: ['7+15=22', '55+22=77'] Exploring Operation: 77-45=32, Resulting Numbers: [32] 32,59 unequal: No Solution Exploring Operation: 45*77=3465, Resulting Numbers: [3465] 3465,59 unequal: No Solution Exploring Operation: 45+77=122, Resulting Numbers: [122] 122,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[55, 23], Operations: ['7+15=22', '45-22=23'] Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,59 unequal: No Solution Exploring Operation: 55*23=1265, Resulting Numbers: [1265] 1265,59 unequal: No Solution Exploring Operation: 55+23=78, Resulting Numbers: [78] 78,59 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 46, 92, 23, 17 ]
68
[ "46-23=23", "92*17=1564", "1564/23=68" ]
Current State: 68:[46, 92, 23, 17], Operations: [] Exploring Operation: 46-23=23, Resulting Numbers: [92, 17, 23] Generated Node #2: [92, 17, 23] from Operation: 46-23=23 Current State: 68:[92, 17, 23], Operations: ['46-23=23'] Exploring Operation: 92*17=1564, Resulting Numbers: [23, 1564] Generated Node #3: [23, 1564] from Operation: 92*17=1564 Current State: 68:[23, 1564], Operations: ['46-23=23', '92*17=1564'] Exploring Operation: 1564/23=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[46, 92, 23, 17], Operations: [] Exploring Operation: 92-23=69, Resulting Numbers: [46, 17, 69] Generated Node #0,0: 68:[46, 17, 69] Operation: 92-23=69 Exploring Operation: 92/46=2, Resulting Numbers: [23, 17, 2] Generated Node #0,1: 68:[23, 17, 2] Operation: 92/46=2 Exploring Operation: 92/23=4, Resulting Numbers: [46, 17, 4] Generated Node #0,2: 68:[46, 17, 4] Operation: 92/23=4 Moving to Node #0,1 Current State: 68:[23, 17, 2], Operations: ['92/46=2'] Exploring Operation: 23-2=21, Resulting Numbers: [17, 21] Generated Node #0,1,0: 68:[17, 21] Operation: 23-2=21 Exploring Operation: 23-17=6, Resulting Numbers: [2, 6] Generated Node #0,1,1: 68:[2, 6] Operation: 23-17=6 Exploring Operation: 23+17=40, Resulting Numbers: [2, 40] Generated Node #0,1,2: 68:[2, 40] Operation: 23+17=40 Moving to Node #0,2 Current State: 68:[46, 17, 4], Operations: ['92/23=4'] Exploring Operation: 46-17=29, Resulting Numbers: [4, 29] Generated Node #0,2,0: 68:[4, 29] Operation: 46-17=29 Exploring Operation: 46+17=63, Resulting Numbers: [4, 63] Generated Node #0,2,1: 68:[4, 63] Operation: 46+17=63 Exploring Operation: 46-4=42, Resulting Numbers: [17, 42] Generated Node #0,2,2: 68:[17, 42] Operation: 46-4=42 Moving to Node #0,0 Current State: 68:[46, 17, 69], Operations: ['92-23=69'] Exploring Operation: 69-46=23, Resulting Numbers: [17, 23] Generated Node #0,0,0: 68:[17, 23] Operation: 69-46=23 Exploring Operation: 46+17=63, Resulting Numbers: [69, 63] Generated Node #0,0,1: 68:[69, 63] Operation: 46+17=63 Exploring Operation: 46-17=29, Resulting Numbers: [69, 29] Generated Node #0,0,2: 68:[69, 29] Operation: 46-17=29 Moving to Node #0,1,1 Current State: 68:[2, 6], Operations: ['92/46=2', '23-17=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,68 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,68 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[17, 21], Operations: ['92/46=2', '23-2=21'] Exploring Operation: 17*21=357, Resulting Numbers: [357] 357,68 unequal: No Solution Exploring Operation: 17+21=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[4, 63], Operations: ['92/23=4', '46+17=63'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 4+63=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 4*63=252, Resulting Numbers: [252] 252,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[4, 29], Operations: ['92/23=4', '46-17=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,68 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[2, 40], Operations: ['92/46=2', '23+17=40'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[69, 29], Operations: ['92-23=69', '46-17=29'] Exploring Operation: 69*29=2001, Resulting Numbers: [2001] 2001,68 unequal: No Solution Exploring Operation: 69-29=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 69+29=98, Resulting Numbers: [98] 98,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[69, 63], Operations: ['92-23=69', '46+17=63'] Exploring Operation: 69+63=132, Resulting Numbers: [132] 132,68 unequal: No Solution Exploring Operation: 69-63=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 69*63=4347, Resulting Numbers: [4347] 4347,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[17, 23], Operations: ['92-23=69', '69-46=23'] Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[17, 42], Operations: ['92/23=4', '46-4=42'] Exploring Operation: 17*42=714, Resulting Numbers: [714] 714,68 unequal: No Solution Exploring Operation: 17+42=59, Resulting Numbers: [59] 59,68 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,68 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 16, 81, 87, 8 ]
18
[ "16+81=97", "87-8=79", "97-79=18" ]
Current State: 18:[16, 81, 87, 8], Operations: [] Exploring Operation: 16+81=97, Resulting Numbers: [87, 8, 97] Generated Node #2: [87, 8, 97] from Operation: 16+81=97 Current State: 18:[87, 8, 97], Operations: ['16+81=97'] Exploring Operation: 87-8=79, Resulting Numbers: [97, 79] Generated Node #3: [97, 79] from Operation: 87-8=79 Current State: 18:[97, 79], Operations: ['16+81=97', '87-8=79'] Exploring Operation: 97-79=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[16, 81, 87, 8], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [16, 8, 6] Generated Node #0,0: 18:[16, 8, 6] Operation: 87-81=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[16, 8, 6], Operations: ['87-81=6'] Exploring Operation: 16/8=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 18:[6, 2] Operation: 16/8=2 Moving to Node #0,0,0 Current State: 18:[6, 2], Operations: ['87-81=6', '16/8=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,18 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
[ 41, 35, 2, 93 ]
46
[ "41*2=82", "35+93=128", "128-82=46" ]
Current State: 46:[41, 35, 2, 93], Operations: [] Exploring Operation: 41*2=82, Resulting Numbers: [35, 93, 82] Generated Node #2: [35, 93, 82] from Operation: 41*2=82 Current State: 46:[35, 93, 82], Operations: ['41*2=82'] Exploring Operation: 35+93=128, Resulting Numbers: [82, 128] Generated Node #3: [82, 128] from Operation: 35+93=128 Current State: 46:[82, 128], Operations: ['41*2=82', '35+93=128'] Exploring Operation: 128-82=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[41, 35, 2, 93], Operations: [] Exploring Operation: 93-41=52, Resulting Numbers: [35, 2, 52] Generated Node #0,0: 46:[35, 2, 52] Operation: 93-41=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[35, 2, 52], Operations: ['93-41=52'] Exploring Operation: 52-35=17, Resulting Numbers: [2, 17] Generated Node #0,0,0: 46:[2, 17] Operation: 52-35=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[2, 17], Operations: ['93-41=52', '52-35=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,46 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
[ 75, 27, 59, 91 ]
29
[ "59+91=150", "150/75=2", "27+2=29" ]
Current State: 29:[75, 27, 59, 91], Operations: [] Exploring Operation: 59+91=150, Resulting Numbers: [75, 27, 150] Generated Node #2: [75, 27, 150] from Operation: 59+91=150 Current State: 29:[75, 27, 150], Operations: ['59+91=150'] Exploring Operation: 150/75=2, Resulting Numbers: [27, 2] Generated Node #3: [27, 2] from Operation: 150/75=2 Current State: 29:[27, 2], Operations: ['59+91=150', '150/75=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[75, 27, 59, 91], Operations: [] Exploring Operation: 91-75=16, Resulting Numbers: [27, 59, 16] Generated Node #0,0: 29:[27, 59, 16] Operation: 91-75=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[27, 59, 16], Operations: ['91-75=16'] Exploring Operation: 59-27=32, Resulting Numbers: [16, 32] Generated Node #0,0,0: 29:[16, 32] Operation: 59-27=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[16, 32], Operations: ['91-75=16', '59-27=32'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,29 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 No solution found.
0
hs_1
mult_heuristic
[ 94, 25, 37, 99 ]
92
[ "99-25=74", "74/37=2", "94-2=92" ]
Current State: 92:[94, 25, 37, 99], Operations: [] Exploring Operation: 99-25=74, Resulting Numbers: [94, 37, 74] Generated Node #2: [94, 37, 74] from Operation: 99-25=74 Current State: 92:[94, 37, 74], Operations: ['99-25=74'] Exploring Operation: 74/37=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 74/37=2 Current State: 92:[94, 2], Operations: ['99-25=74', '74/37=2'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[94, 25, 37, 99], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [25, 37, 5] Generated Node #0,0: 92:[25, 37, 5] Operation: 99-94=5 Exploring Operation: 37-25=12, Resulting Numbers: [94, 99, 12] Generated Node #0,1: 92:[94, 99, 12] Operation: 37-25=12 Moving to Node #0,0 Current State: 92:[25, 37, 5], Operations: ['99-94=5'] Exploring Operation: 37-25=12, Resulting Numbers: [5, 12] Generated Node #0,0,0: 92:[5, 12] Operation: 37-25=12 Exploring Operation: 37+5=42, Resulting Numbers: [25, 42] Generated Node #0,0,1: 92:[25, 42] Operation: 37+5=42 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[25, 42], Operations: ['99-94=5', '37+5=42'] Exploring Operation: 25+42=67, Resulting Numbers: [67] 67,92 unequal: No Solution Exploring Operation: 42-25=17, Resulting Numbers: [17] 17,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[5, 12], Operations: ['99-94=5', '37-25=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 5+12=17, Resulting Numbers: [17] 17,92 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: 92:[94, 99, 12], Operations: ['37-25=12'] Exploring Operation: 99-12=87, Resulting Numbers: [94, 87] Generated Node #0,1,0: 92:[94, 87] Operation: 99-12=87 Exploring Operation: 99-94=5, Resulting Numbers: [12, 5] Generated Node #0,1,1: 92:[12, 5] Operation: 99-94=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 92:[94, 87], Operations: ['37-25=12', '99-12=87'] Exploring Operation: 94-87=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 94+87=181, Resulting Numbers: [181] 181,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 92:[12, 5], Operations: ['37-25=12', '99-94=5'] Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,92 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,92 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
[ 28, 70, 58, 72 ]
32
[ "28+70=98", "58+72=130", "130-98=32" ]
Current State: 32:[28, 70, 58, 72], Operations: [] Exploring Operation: 28+70=98, Resulting Numbers: [58, 72, 98] Generated Node #2: [58, 72, 98] from Operation: 28+70=98 Current State: 32:[58, 72, 98], Operations: ['28+70=98'] Exploring Operation: 58+72=130, Resulting Numbers: [98, 130] Generated Node #3: [98, 130] from Operation: 58+72=130 Current State: 32:[98, 130], Operations: ['28+70=98', '58+72=130'] Exploring Operation: 130-98=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[28, 70, 58, 72], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [28, 58, 2] Generated Node #0,0: 32:[28, 58, 2] Operation: 72-70=2 Exploring Operation: 72-58=14, Resulting Numbers: [28, 70, 14] Generated Node #0,1: 32:[28, 70, 14] Operation: 72-58=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[28, 58, 2], Operations: ['72-70=2'] Exploring Operation: 58-28=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 32:[2, 30] Operation: 58-28=30 Exploring Operation: 58/2=29, Resulting Numbers: [28, 29] Generated Node #0,0,1: 32:[28, 29] Operation: 58/2=29 Moving to Node #0,0,0 Current State: 32:[2, 30], Operations: ['72-70=2', '58-28=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[28, 70, 58, 72], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [28, 58, 2] Generated Node #0,0: 32:[28, 58, 2] Operation: 72-70=2 Moving to Node #0,0 Current State: 32:[28, 58, 2], Operations: ['72-70=2'] Exploring Operation: 58-28=30, Resulting Numbers: [2, 30] Generated Node #0,0,0: 32:[2, 30] Operation: 58-28=30 Moving to Node #0,0,0 Current State: 32:[2, 30], Operations: ['72-70=2', '58-28=30'] Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 51, 8, 31, 12 ]
80
[ "51-31=20", "12-8=4", "20*4=80" ]
Current State: 80:[51, 8, 31, 12], Operations: [] Exploring Operation: 51-31=20, Resulting Numbers: [8, 12, 20] Generated Node #2: [8, 12, 20] from Operation: 51-31=20 Current State: 80:[8, 12, 20], Operations: ['51-31=20'] Exploring Operation: 12-8=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 12-8=4 Current State: 80:[20, 4], Operations: ['51-31=20', '12-8=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[51, 8, 31, 12], Operations: [] Exploring Operation: 51-8=43, Resulting Numbers: [31, 12, 43] Generated Node #0,0: 80:[31, 12, 43] Operation: 51-8=43 Exploring Operation: 51-12=39, Resulting Numbers: [8, 31, 39] Generated Node #0,1: 80:[8, 31, 39] Operation: 51-12=39 Exploring Operation: 31-12=19, Resulting Numbers: [51, 8, 19] Generated Node #0,2: 80:[51, 8, 19] Operation: 31-12=19 Exploring Operation: 51-31=20, Resulting Numbers: [8, 12, 20] Generated Node #0,3: 80:[8, 12, 20] Operation: 51-31=20 Exploring Operation: 51+31=82, Resulting Numbers: [8, 12, 82] Generated Node #0,4: 80:[8, 12, 82] Operation: 51+31=82 Moving to Node #0,3 Current State: 80:[8, 12, 20], Operations: ['51-31=20'] Exploring Operation: 12-8=4, Resulting Numbers: [20, 4] Generated Node #0,3,0: 80:[20, 4] Operation: 12-8=4 Exploring Operation: 20-12=8, Resulting Numbers: [8, 8] Generated Node #0,3,1: 80:[8, 8] Operation: 20-12=8 Exploring Operation: 12+20=32, Resulting Numbers: [8, 32] Generated Node #0,3,2: 80:[8, 32] Operation: 12+20=32 Exploring Operation: 8+12=20, Resulting Numbers: [20, 20] Generated Node #0,3,3: 80:[20, 20] Operation: 8+12=20 Exploring Operation: 20-8=12, Resulting Numbers: [12, 12] Generated Node #0,3,4: 80:[12, 12] Operation: 20-8=12 Moving to Node #0,4 Current State: 80:[8, 12, 82], Operations: ['51+31=82'] Exploring Operation: 8+82=90, Resulting Numbers: [12, 90] Generated Node #0,4,0: 80:[12, 90] Operation: 8+82=90 Exploring Operation: 82-8=74, Resulting Numbers: [12, 74] Generated Node #0,4,1: 80:[12, 74] Operation: 82-8=74 Exploring Operation: 8+12=20, Resulting Numbers: [82, 20] Generated Node #0,4,2: 80:[82, 20] Operation: 8+12=20 Exploring Operation: 82-12=70, Resulting Numbers: [8, 70] Generated Node #0,4,3: 80:[8, 70] Operation: 82-12=70 Exploring Operation: 12-8=4, Resulting Numbers: [82, 4] Generated Node #0,4,4: 80:[82, 4] Operation: 12-8=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 80:[82, 20], Operations: ['51+31=82', '8+12=20'] Exploring Operation: 82*20=1640, Resulting Numbers: [1640] 1640,80 unequal: No Solution Exploring Operation: 82+20=102, Resulting Numbers: [102] 102,80 unequal: No Solution Exploring Operation: 82-20=62, Resulting Numbers: [62] 62,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 80:[82, 4], Operations: ['51+31=82', '12-8=4'] Exploring Operation: 82*4=328, Resulting Numbers: [328] 328,80 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 82+4=86, Resulting Numbers: [86] 86,80 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 #0,4,1 Current State: 80:[12, 74], Operations: ['51+31=82', '82-8=74'] Exploring Operation: 12+74=86, Resulting Numbers: [86] 86,80 unequal: No Solution Exploring Operation: 74-12=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 12*74=888, Resulting Numbers: [888] 888,80 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 #0,4,3 Current State: 80:[8, 70], Operations: ['51+31=82', '82-12=70'] Exploring Operation: 8*70=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 8+70=78, Resulting Numbers: [78] 78,80 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 #0,4,0 Current State: 80:[12, 90], Operations: ['51+31=82', '8+82=90'] Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 12*90=1080, Resulting Numbers: [1080] 1080,80 unequal: No Solution Exploring Operation: 12+90=102, Resulting Numbers: [102] 102,80 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:[8, 31, 39], Operations: ['51-12=39'] Exploring Operation: 8+31=39, Resulting Numbers: [39, 39] Generated Node #0,1,0: 80:[39, 39] Operation: 8+31=39 Exploring Operation: 31-8=23, Resulting Numbers: [39, 23] Generated Node #0,1,1: 80:[39, 23] Operation: 31-8=23 Exploring Operation: 39-31=8, Resulting Numbers: [8, 8] Generated Node #0,1,2: 80:[8, 8] Operation: 39-31=8 Exploring Operation: 8+39=47, Resulting Numbers: [31, 47] Generated Node #0,1,3: 80:[31, 47] Operation: 8+39=47 Exploring Operation: 31+39=70, Resulting Numbers: [8, 70] Generated Node #0,1,4: 80:[8, 70] Operation: 31+39=70 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[8, 8], Operations: ['51-12=39', '39-31=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,80 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,80 unequal: No Solution Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,80 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:[39, 39], Operations: ['51-12=39', '8+31=39'] Exploring Operation: 39+39=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,80 unequal: No Solution Exploring Operation: 39*39=1521, Resulting Numbers: [1521] 1521,80 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,80 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:[39, 23], Operations: ['51-12=39', '31-8=23'] Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,80 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 #0,1,4 Current State: 80:[8, 70], Operations: ['51-12=39', '31+39=70'] Exploring Operation: 8*70=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 8+70=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[31, 47], Operations: ['51-12=39', '8+39=47'] Exploring Operation: 47-31=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 31*47=1457, Resulting Numbers: [1457] 1457,80 unequal: No Solution Exploring Operation: 31+47=78, Resulting Numbers: [78] 78,80 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:[51, 8, 19], Operations: ['31-12=19'] Exploring Operation: 51+19=70, Resulting Numbers: [8, 70] Generated Node #0,2,0: 80:[8, 70] Operation: 51+19=70 Exploring Operation: 51-8=43, Resulting Numbers: [19, 43] Generated Node #0,2,1: 80:[19, 43] Operation: 51-8=43 Exploring Operation: 8+19=27, Resulting Numbers: [51, 27] Generated Node #0,2,2: 80:[51, 27] Operation: 8+19=27 Exploring Operation: 51-19=32, Resulting Numbers: [8, 32] Generated Node #0,2,3: 80:[8, 32] Operation: 51-19=32 Exploring Operation: 19-8=11, Resulting Numbers: [51, 11] Generated Node #0,2,4: 80:[51, 11] Operation: 19-8=11 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[19, 43], Operations: ['31-12=19', '51-8=43'] Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,80 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:[8, 32], Operations: ['31-12=19', '51-19=32'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,80 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 8*32=256, Resulting Numbers: [256] 256,80 unequal: No Solution Exploring Operation: 8+32=40, Resulting Numbers: [40] 40,80 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:[8, 70], Operations: ['31-12=19', '51+19=70'] Exploring Operation: 8+70=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 8*70=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 80:[51, 11], Operations: ['31-12=19', '19-8=11'] Exploring Operation: 51+11=62, Resulting Numbers: [62] 62,80 unequal: No Solution Exploring Operation: 51*11=561, Resulting Numbers: [561] 561,80 unequal: No Solution Exploring Operation: 51-11=40, Resulting Numbers: [40] 40,80 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:[51, 27], Operations: ['31-12=19', '8+19=27'] Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,80 unequal: No Solution Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,80 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,80 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:[31, 12, 43], Operations: ['51-8=43'] Exploring Operation: 31-12=19, Resulting Numbers: [43, 19] Generated Node #0,0,0: 80:[43, 19] Operation: 31-12=19 Exploring Operation: 31+12=43, Resulting Numbers: [43, 43] Generated Node #0,0,1: 80:[43, 43] Operation: 31+12=43 Exploring Operation: 43-31=12, Resulting Numbers: [12, 12] Generated Node #0,0,2: 80:[12, 12] Operation: 43-31=12 Exploring Operation: 43-12=31, Resulting Numbers: [31, 31] Generated Node #0,0,3: 80:[31, 31] Operation: 43-12=31 Exploring Operation: 31+43=74, Resulting Numbers: [12, 74] Generated Node #0,0,4: 80:[12, 74] Operation: 31+43=74 Moving to Node #0,3,0 Current State: 80:[20, 4], Operations: ['51-31=20', '12-8=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,80 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[51, 8, 31, 12], Operations: [] Exploring Operation: 51-31=20, Resulting Numbers: [8, 12, 20] Generated Node #0,3: 80:[8, 12, 20] Operation: 51-31=20 Moving to Node #0,3 Current State: 80:[8, 12, 20], Operations: ['51-31=20'] Exploring Operation: 12-8=4, Resulting Numbers: [20, 4] Generated Node #0,3,0: 80:[20, 4] Operation: 12-8=4 Moving to Node #0,3,0 Current State: 80:[20, 4], Operations: ['51-31=20', '12-8=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.925347
hs_5
mult_heuristic
[ 71, 63, 64, 14 ]
65
[ "71-64=7", "14/7=2", "63+2=65" ]
Current State: 65:[71, 63, 64, 14], Operations: [] Exploring Operation: 71-64=7, Resulting Numbers: [63, 14, 7] Generated Node #2: [63, 14, 7] from Operation: 71-64=7 Current State: 65:[63, 14, 7], Operations: ['71-64=7'] Exploring Operation: 14/7=2, Resulting Numbers: [63, 2] Generated Node #3: [63, 2] from Operation: 14/7=2 Current State: 65:[63, 2], Operations: ['71-64=7', '14/7=2'] Exploring Operation: 63+2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[71, 63, 64, 14], Operations: [] Exploring Operation: 71-64=7, Resulting Numbers: [63, 14, 7] Generated Node #0,0: 65:[63, 14, 7] Operation: 71-64=7 Exploring Operation: 71-63=8, Resulting Numbers: [64, 14, 8] Generated Node #0,1: 65:[64, 14, 8] Operation: 71-63=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[63, 14, 7], Operations: ['71-64=7'] Exploring Operation: 14-7=7, Resulting Numbers: [63, 7] Generated Node #0,0,0: 65:[63, 7] Operation: 14-7=7 Exploring Operation: 63/7=9, Resulting Numbers: [14, 9] Generated Node #0,0,1: 65:[14, 9] Operation: 63/7=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[63, 7], Operations: ['71-64=7', '14-7=7'] Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 65:[14, 9], Operations: ['71-64=7', '63/7=9'] Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,65 unequal: No Solution Exploring Operation: 14+9=23, Resulting Numbers: [23] 23,65 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: 65:[64, 14, 8], Operations: ['71-63=8'] Exploring Operation: 64/8=8, Resulting Numbers: [14, 8] Generated Node #0,1,0: 65:[14, 8] Operation: 64/8=8 Exploring Operation: 14-8=6, Resulting Numbers: [64, 6] Generated Node #0,1,1: 65:[64, 6] Operation: 14-8=6 Moving to Node #0,1,1 Current State: 65:[64, 6], Operations: ['71-63=8', '14-8=6'] Exploring Operation: 64-6=58, Resulting Numbers: [58] 58,65 unequal: No Solution Exploring Operation: 64+6=70, Resulting Numbers: [70] 70,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[14, 8], Operations: ['71-63=8', '64/8=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,65 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
[ 11, 51, 20, 67 ]
69
[ "51-11=40", "40/20=2", "67+2=69" ]
Current State: 69:[11, 51, 20, 67], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [20, 67, 40] Generated Node #2: [20, 67, 40] from Operation: 51-11=40 Current State: 69:[20, 67, 40], Operations: ['51-11=40'] Exploring Operation: 40/20=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 40/20=2 Current State: 69:[67, 2], Operations: ['51-11=40', '40/20=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[11, 51, 20, 67], Operations: [] Exploring Operation: 11+51=62, Resulting Numbers: [20, 67, 62] Generated Node #0,0: 69:[20, 67, 62] Operation: 11+51=62 Exploring Operation: 51+20=71, Resulting Numbers: [11, 67, 71] Generated Node #0,1: 69:[11, 67, 71] Operation: 51+20=71 Exploring Operation: 51-20=31, Resulting Numbers: [11, 67, 31] Generated Node #0,2: 69:[11, 67, 31] Operation: 51-20=31 Moving to Node #0,0 Current State: 69:[20, 67, 62], Operations: ['11+51=62'] Exploring Operation: 62-20=42, Resulting Numbers: [67, 42] Generated Node #0,0,0: 69:[67, 42] Operation: 62-20=42 Exploring Operation: 67-62=5, Resulting Numbers: [20, 5] Generated Node #0,0,1: 69:[20, 5] Operation: 67-62=5 Exploring Operation: 20+62=82, Resulting Numbers: [67, 82] Generated Node #0,0,2: 69:[67, 82] Operation: 20+62=82 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[20, 5], Operations: ['11+51=62', '67-62=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[67, 82], Operations: ['11+51=62', '20+62=82'] Exploring Operation: 67+82=149, Resulting Numbers: [149] 149,69 unequal: No Solution Exploring Operation: 82-67=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 67*82=5494, Resulting Numbers: [5494] 5494,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[67, 42], Operations: ['11+51=62', '62-20=42'] Exploring Operation: 67+42=109, Resulting Numbers: [109] 109,69 unequal: No Solution Exploring Operation: 67-42=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 67*42=2814, Resulting Numbers: [2814] 2814,69 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: 69:[11, 67, 71], Operations: ['51+20=71'] Exploring Operation: 71-11=60, Resulting Numbers: [67, 60] Generated Node #0,1,0: 69:[67, 60] Operation: 71-11=60 Exploring Operation: 71-67=4, Resulting Numbers: [11, 4] Generated Node #0,1,1: 69:[11, 4] Operation: 71-67=4 Exploring Operation: 11+67=78, Resulting Numbers: [71, 78] Generated Node #0,1,2: 69:[71, 78] Operation: 11+67=78 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[11, 4], Operations: ['51+20=71', '71-67=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[67, 60], Operations: ['51+20=71', '71-11=60'] Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 67+60=127, Resulting Numbers: [127] 127,69 unequal: No Solution Exploring Operation: 67*60=4020, Resulting Numbers: [4020] 4020,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[71, 78], Operations: ['51+20=71', '11+67=78'] Exploring Operation: 71*78=5538, Resulting Numbers: [5538] 5538,69 unequal: No Solution Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[11, 67, 31], Operations: ['51-20=31'] Exploring Operation: 31-11=20, Resulting Numbers: [67, 20] Generated Node #0,2,0: 69:[67, 20] Operation: 31-11=20 Exploring Operation: 67-11=56, Resulting Numbers: [31, 56] Generated Node #0,2,1: 69:[31, 56] Operation: 67-11=56 Exploring Operation: 11+67=78, Resulting Numbers: [31, 78] Generated Node #0,2,2: 69:[31, 78] Operation: 11+67=78 Moving to Node #0,2,0 Current State: 69:[67, 20], Operations: ['51-20=31', '31-11=20'] Exploring Operation: 67-20=47, Resulting Numbers: [47] 47,69 unequal: No Solution Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 67*20=1340, Resulting Numbers: [1340] 1340,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[31, 78], Operations: ['51-20=31', '11+67=78'] Exploring Operation: 31*78=2418, Resulting Numbers: [2418] 2418,69 unequal: No Solution Exploring Operation: 31+78=109, Resulting Numbers: [109] 109,69 unequal: No Solution Exploring Operation: 78-31=47, Resulting Numbers: [47] 47,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[31, 56], Operations: ['51-20=31', '67-11=56'] Exploring Operation: 56-31=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 31*56=1736, Resulting Numbers: [1736] 1736,69 unequal: No Solution Exploring Operation: 31+56=87, Resulting Numbers: [87] 87,69 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 58, 69, 44, 71 ]
75
[ "69-58=11", "44/11=4", "71+4=75" ]
Current State: 75:[58, 69, 44, 71], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [44, 71, 11] Generated Node #2: [44, 71, 11] from Operation: 69-58=11 Current State: 75:[44, 71, 11], Operations: ['69-58=11'] Exploring Operation: 44/11=4, Resulting Numbers: [71, 4] Generated Node #3: [71, 4] from Operation: 44/11=4 Current State: 75:[71, 4], Operations: ['69-58=11', '44/11=4'] Exploring Operation: 71+4=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[58, 69, 44, 71], Operations: [] Exploring Operation: 71-44=27, Resulting Numbers: [58, 69, 27] Generated Node #0,0: 75:[58, 69, 27] Operation: 71-44=27 Exploring Operation: 58-44=14, Resulting Numbers: [69, 71, 14] Generated Node #0,1: 75:[69, 71, 14] Operation: 58-44=14 Exploring Operation: 69-58=11, Resulting Numbers: [44, 71, 11] Generated Node #0,2: 75:[44, 71, 11] Operation: 69-58=11 Exploring Operation: 69-44=25, Resulting Numbers: [58, 71, 25] Generated Node #0,3: 75:[58, 71, 25] Operation: 69-44=25 Moving to Node #0,1 Current State: 75:[69, 71, 14], Operations: ['58-44=14'] Exploring Operation: 71+14=85, Resulting Numbers: [69, 85] Generated Node #0,1,0: 75:[69, 85] Operation: 71+14=85 Exploring Operation: 69-14=55, Resulting Numbers: [71, 55] Generated Node #0,1,1: 75:[71, 55] Operation: 69-14=55 Exploring Operation: 69+14=83, Resulting Numbers: [71, 83] Generated Node #0,1,2: 75:[71, 83] Operation: 69+14=83 Exploring Operation: 71-69=2, Resulting Numbers: [14, 2] Generated Node #0,1,3: 75:[14, 2] Operation: 71-69=2 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 75:[14, 2], Operations: ['58-44=14', '71-69=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,75 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,75 unequal: No Solution Exploring Operation: 14*2=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 75:[71, 83], Operations: ['58-44=14', '69+14=83'] Exploring Operation: 71+83=154, Resulting Numbers: [154] 154,75 unequal: No Solution Exploring Operation: 71*83=5893, Resulting Numbers: [5893] 5893,75 unequal: No Solution Exploring Operation: 83-71=12, Resulting Numbers: [12] 12,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 75:[69, 85], Operations: ['58-44=14', '71+14=85'] Exploring Operation: 69*85=5865, Resulting Numbers: [5865] 5865,75 unequal: No Solution Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,75 unequal: No Solution Exploring Operation: 69+85=154, Resulting Numbers: [154] 154,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 75:[71, 55], Operations: ['58-44=14', '69-14=55'] Exploring Operation: 71*55=3905, Resulting Numbers: [3905] 3905,75 unequal: No Solution Exploring Operation: 71-55=16, Resulting Numbers: [16] 16,75 unequal: No Solution Exploring Operation: 71+55=126, Resulting Numbers: [126] 126,75 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: 75:[58, 71, 25], Operations: ['69-44=25'] Exploring Operation: 58+25=83, Resulting Numbers: [71, 83] Generated Node #0,3,0: 75:[71, 83] Operation: 58+25=83 Exploring Operation: 71+25=96, Resulting Numbers: [58, 96] Generated Node #0,3,1: 75:[58, 96] Operation: 71+25=96 Exploring Operation: 71-58=13, Resulting Numbers: [25, 13] Generated Node #0,3,2: 75:[25, 13] Operation: 71-58=13 Exploring Operation: 58-25=33, Resulting Numbers: [71, 33] Generated Node #0,3,3: 75:[71, 33] Operation: 58-25=33 Moving to Node #0,0 Current State: 75:[58, 69, 27], Operations: ['71-44=27'] Exploring Operation: 58-27=31, Resulting Numbers: [69, 31] Generated Node #0,0,0: 75:[69, 31] Operation: 58-27=31 Exploring Operation: 58+27=85, Resulting Numbers: [69, 85] Generated Node #0,0,1: 75:[69, 85] Operation: 58+27=85 Exploring Operation: 69-27=42, Resulting Numbers: [58, 42] Generated Node #0,0,2: 75:[58, 42] Operation: 69-27=42 Exploring Operation: 69-58=11, Resulting Numbers: [27, 11] Generated Node #0,0,3: 75:[27, 11] Operation: 69-58=11 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 75:[27, 11], Operations: ['71-44=27', '69-58=11'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,75 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,75 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,75 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:[69, 31], Operations: ['71-44=27', '58-27=31'] Exploring Operation: 69-31=38, Resulting Numbers: [38] 38,75 unequal: No Solution Exploring Operation: 69*31=2139, Resulting Numbers: [2139] 2139,75 unequal: No Solution Exploring Operation: 69+31=100, Resulting Numbers: [100] 100,75 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 #0,0,1 Current State: 75:[69, 85], Operations: ['71-44=27', '58+27=85'] Exploring Operation: 69+85=154, Resulting Numbers: [154] 154,75 unequal: No Solution Exploring Operation: 69*85=5865, Resulting Numbers: [5865] 5865,75 unequal: No Solution Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,75 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 #0,0,2 Current State: 75:[58, 42], Operations: ['71-44=27', '69-27=42'] Exploring Operation: 58*42=2436, Resulting Numbers: [2436] 2436,75 unequal: No Solution Exploring Operation: 58+42=100, Resulting Numbers: [100] 100,75 unequal: No Solution Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,75 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: 75:[44, 71, 11], Operations: ['69-58=11'] Exploring Operation: 44-11=33, Resulting Numbers: [71, 33] Generated Node #0,2,0: 75:[71, 33] Operation: 44-11=33 Exploring Operation: 44/11=4, Resulting Numbers: [71, 4] Generated Node #0,2,1: 75:[71, 4] Operation: 44/11=4 Exploring Operation: 44+11=55, Resulting Numbers: [71, 55] Generated Node #0,2,2: 75:[71, 55] Operation: 44+11=55 Exploring Operation: 71-44=27, Resulting Numbers: [11, 27] Generated Node #0,2,3: 75:[11, 27] Operation: 71-44=27 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 75:[71, 4], Operations: ['69-58=11', '44/11=4'] Exploring Operation: 71-4=67, Resulting Numbers: [67] 67,75 unequal: No Solution Exploring Operation: 71+4=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[58, 69, 44, 71], Operations: [] Exploring Operation: 69-58=11, Resulting Numbers: [44, 71, 11] Generated Node #0,2: 75:[44, 71, 11] Operation: 69-58=11 Moving to Node #0,2 Current State: 75:[44, 71, 11], Operations: ['69-58=11'] Exploring Operation: 44/11=4, Resulting Numbers: [71, 4] Generated Node #0,2,1: 75:[71, 4] Operation: 44/11=4 Moving to Node #0,2,1 Current State: 75:[71, 4], Operations: ['69-58=11', '44/11=4'] Exploring Operation: 71+4=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
mult_heuristic
[ 97, 44, 40, 55 ]
88
[ "97-40=57", "57-55=2", "44*2=88" ]
Current State: 88:[97, 44, 40, 55], Operations: [] Exploring Operation: 97-40=57, Resulting Numbers: [44, 55, 57] Generated Node #2: [44, 55, 57] from Operation: 97-40=57 Current State: 88:[44, 55, 57], Operations: ['97-40=57'] Exploring Operation: 57-55=2, Resulting Numbers: [44, 2] Generated Node #3: [44, 2] from Operation: 57-55=2 Current State: 88:[44, 2], Operations: ['97-40=57', '57-55=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[97, 44, 40, 55], Operations: [] Exploring Operation: 97-55=42, Resulting Numbers: [44, 40, 42] Generated Node #0,0: 88:[44, 40, 42] Operation: 97-55=42 Exploring Operation: 55-44=11, Resulting Numbers: [97, 40, 11] Generated Node #0,1: 88:[97, 40, 11] Operation: 55-44=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[44, 40, 42], Operations: ['97-55=42'] Exploring Operation: 44-40=4, Resulting Numbers: [42, 4] Generated Node #0,0,0: 88:[42, 4] Operation: 44-40=4 Exploring Operation: 42-40=2, Resulting Numbers: [44, 2] Generated Node #0,0,1: 88:[44, 2] Operation: 42-40=2 Moving to Node #0,0,1 Current State: 88:[44, 2], Operations: ['97-55=42', '42-40=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[97, 44, 40, 55], Operations: [] Exploring Operation: 97-55=42, Resulting Numbers: [44, 40, 42] Generated Node #0,0: 88:[44, 40, 42] Operation: 97-55=42 Moving to Node #0,0 Current State: 88:[44, 40, 42], Operations: ['97-55=42'] Exploring Operation: 42-40=2, Resulting Numbers: [44, 2] Generated Node #0,0,1: 88:[44, 2] Operation: 42-40=2 Moving to Node #0,0,1 Current State: 88:[44, 2], Operations: ['97-55=42', '42-40=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 78, 85, 23, 33 ]
17
[ "85-78=7", "33-23=10", "7+10=17" ]
Current State: 17:[78, 85, 23, 33], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [23, 33, 7] Generated Node #2: [23, 33, 7] from Operation: 85-78=7 Current State: 17:[23, 33, 7], Operations: ['85-78=7'] Exploring Operation: 33-23=10, Resulting Numbers: [7, 10] Generated Node #3: [7, 10] from Operation: 33-23=10 Current State: 17:[7, 10], Operations: ['85-78=7', '33-23=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[78, 85, 23, 33], Operations: [] Exploring Operation: 78-23=55, Resulting Numbers: [85, 33, 55] Generated Node #0,0: 17:[85, 33, 55] Operation: 78-23=55 Exploring Operation: 85-23=62, Resulting Numbers: [78, 33, 62] Generated Node #0,1: 17:[78, 33, 62] Operation: 85-23=62 Exploring Operation: 85-78=7, Resulting Numbers: [23, 33, 7] Generated Node #0,2: 17:[23, 33, 7] Operation: 85-78=7 Exploring Operation: 85-33=52, Resulting Numbers: [78, 23, 52] Generated Node #0,3: 17:[78, 23, 52] Operation: 85-33=52 Exploring Operation: 78-33=45, Resulting Numbers: [85, 23, 45] Generated Node #0,4: 17:[85, 23, 45] Operation: 78-33=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[23, 33, 7], Operations: ['85-78=7'] Exploring Operation: 23-7=16, Resulting Numbers: [33, 16] Generated Node #0,2,0: 17:[33, 16] Operation: 23-7=16 Exploring Operation: 33-23=10, Resulting Numbers: [7, 10] Generated Node #0,2,1: 17:[7, 10] Operation: 33-23=10 Exploring Operation: 33-7=26, Resulting Numbers: [23, 26] Generated Node #0,2,2: 17:[23, 26] Operation: 33-7=26 Exploring Operation: 23+7=30, Resulting Numbers: [33, 30] Generated Node #0,2,3: 17:[33, 30] Operation: 23+7=30 Exploring Operation: 33+7=40, Resulting Numbers: [23, 40] Generated Node #0,2,4: 17:[23, 40] Operation: 33+7=40 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[23, 26], Operations: ['85-78=7', '33-7=26'] Exploring Operation: 23+26=49, Resulting Numbers: [49] 49,17 unequal: No Solution Exploring Operation: 23*26=598, Resulting Numbers: [598] 598,17 unequal: No Solution Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,17 unequal: No Solution No 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: 17:[33, 16], Operations: ['85-78=7', '23-7=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[78, 85, 23, 33], Operations: [] Exploring Operation: 85-78=7, Resulting Numbers: [23, 33, 7] Generated Node #0,2: 17:[23, 33, 7] Operation: 85-78=7 Moving to Node #0,2 Current State: 17:[23, 33, 7], Operations: ['85-78=7'] Exploring Operation: 23-7=16, Resulting Numbers: [33, 16] Generated Node #0,2,0: 17:[33, 16] Operation: 23-7=16 Moving to Node #0,2,0 Current State: 17:[33, 16], Operations: ['85-78=7', '23-7=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 27, 95, 47, 3 ]
24
[ "95-27=68", "47-3=44", "68-44=24" ]
Current State: 24:[27, 95, 47, 3], Operations: [] Exploring Operation: 95-27=68, Resulting Numbers: [47, 3, 68] Generated Node #2: [47, 3, 68] from Operation: 95-27=68 Current State: 24:[47, 3, 68], Operations: ['95-27=68'] Exploring Operation: 47-3=44, Resulting Numbers: [68, 44] Generated Node #3: [68, 44] from Operation: 47-3=44 Current State: 24:[68, 44], Operations: ['95-27=68', '47-3=44'] Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[27, 95, 47, 3], Operations: [] Exploring Operation: 95-27=68, Resulting Numbers: [47, 3, 68] Generated Node #0,0: 24:[47, 3, 68] Operation: 95-27=68 Exploring Operation: 47-27=20, Resulting Numbers: [95, 3, 20] Generated Node #0,1: 24:[95, 3, 20] Operation: 47-27=20 Exploring Operation: 95-47=48, Resulting Numbers: [27, 3, 48] Generated Node #0,2: 24:[27, 3, 48] Operation: 95-47=48 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[27, 3, 48], Operations: ['95-47=48'] Exploring Operation: 48-27=21, Resulting Numbers: [3, 21] Generated Node #0,2,0: 24:[3, 21] Operation: 48-27=21 Exploring Operation: 27-3=24, Resulting Numbers: [48, 24] Generated Node #0,2,1: 24:[48, 24] Operation: 27-3=24 Exploring Operation: 48/3=16, Resulting Numbers: [27, 16] Generated Node #0,2,2: 24:[27, 16] Operation: 48/3=16 Moving to Node #0,2,0 Current State: 24:[3, 21], Operations: ['95-47=48', '48-27=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[27, 95, 47, 3], Operations: [] Exploring Operation: 95-47=48, Resulting Numbers: [27, 3, 48] Generated Node #0,2: 24:[27, 3, 48] Operation: 95-47=48 Moving to Node #0,2 Current State: 24:[27, 3, 48], Operations: ['95-47=48'] Exploring Operation: 48-27=21, Resulting Numbers: [3, 21] Generated Node #0,2,0: 24:[3, 21] Operation: 48-27=21 Moving to Node #0,2,0 Current State: 24:[3, 21], Operations: ['95-47=48', '48-27=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 63, 86, 76, 82 ]
17
[ "86-63=23", "82-76=6", "23-6=17" ]
Current State: 17:[63, 86, 76, 82], Operations: [] Exploring Operation: 86-63=23, Resulting Numbers: [76, 82, 23] Generated Node #2: [76, 82, 23] from Operation: 86-63=23 Current State: 17:[76, 82, 23], Operations: ['86-63=23'] Exploring Operation: 82-76=6, Resulting Numbers: [23, 6] Generated Node #3: [23, 6] from Operation: 82-76=6 Current State: 17:[23, 6], Operations: ['86-63=23', '82-76=6'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[63, 86, 76, 82], Operations: [] Exploring Operation: 86-63=23, Resulting Numbers: [76, 82, 23] Generated Node #0,0: 17:[76, 82, 23] Operation: 86-63=23 Exploring Operation: 82-76=6, Resulting Numbers: [63, 86, 6] Generated Node #0,1: 17:[63, 86, 6] Operation: 82-76=6 Exploring Operation: 86-76=10, Resulting Numbers: [63, 82, 10] Generated Node #0,2: 17:[63, 82, 10] Operation: 86-76=10 Exploring Operation: 86-82=4, Resulting Numbers: [63, 76, 4] Generated Node #0,3: 17:[63, 76, 4] Operation: 86-82=4 Moving to Node #0,2 Current State: 17:[63, 82, 10], Operations: ['86-76=10'] Exploring Operation: 63-10=53, Resulting Numbers: [82, 53] Generated Node #0,2,0: 17:[82, 53] Operation: 63-10=53 Exploring Operation: 82-63=19, Resulting Numbers: [10, 19] Generated Node #0,2,1: 17:[10, 19] Operation: 82-63=19 Exploring Operation: 63+10=73, Resulting Numbers: [82, 73] Generated Node #0,2,2: 17:[82, 73] Operation: 63+10=73 Exploring Operation: 82-10=72, Resulting Numbers: [63, 72] Generated Node #0,2,3: 17:[63, 72] Operation: 82-10=72 Moving to Node #0,3 Current State: 17:[63, 76, 4], Operations: ['86-82=4'] Exploring Operation: 63-4=59, Resulting Numbers: [76, 59] Generated Node #0,3,0: 17:[76, 59] Operation: 63-4=59 Exploring Operation: 76/4=19, Resulting Numbers: [63, 19] Generated Node #0,3,1: 17:[63, 19] Operation: 76/4=19 Exploring Operation: 76-63=13, Resulting Numbers: [4, 13] Generated Node #0,3,2: 17:[4, 13] Operation: 76-63=13 Exploring Operation: 76-4=72, Resulting Numbers: [63, 72] Generated Node #0,3,3: 17:[63, 72] Operation: 76-4=72 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[4, 13], Operations: ['86-82=4', '76-63=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,17 unequal: No Solution Exploring Operation: 4*13=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[63, 86, 76, 82], Operations: [] Exploring Operation: 86-82=4, Resulting Numbers: [63, 76, 4] Generated Node #0,3: 17:[63, 76, 4] Operation: 86-82=4 Moving to Node #0,3 Current State: 17:[63, 76, 4], Operations: ['86-82=4'] Exploring Operation: 76-63=13, Resulting Numbers: [4, 13] Generated Node #0,3,2: 17:[4, 13] Operation: 76-63=13 Moving to Node #0,3,2 Current State: 17:[4, 13], Operations: ['86-82=4', '76-63=13'] Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 18, 13, 32, 29 ]
21
[ "32-29=3", "13*3=39", "39-18=21" ]
Current State: 21:[18, 13, 32, 29], Operations: [] Exploring Operation: 32-29=3, Resulting Numbers: [18, 13, 3] Generated Node #2: [18, 13, 3] from Operation: 32-29=3 Current State: 21:[18, 13, 3], Operations: ['32-29=3'] Exploring Operation: 13*3=39, Resulting Numbers: [18, 39] Generated Node #3: [18, 39] from Operation: 13*3=39 Current State: 21:[18, 39], Operations: ['32-29=3', '13*3=39'] Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[18, 13, 32, 29], Operations: [] Exploring Operation: 18-13=5, Resulting Numbers: [32, 29, 5] Generated Node #0,0: 21:[32, 29, 5] Operation: 18-13=5 Exploring Operation: 32-29=3, Resulting Numbers: [18, 13, 3] Generated Node #0,1: 21:[18, 13, 3] Operation: 32-29=3 Exploring Operation: 29-13=16, Resulting Numbers: [18, 32, 16] Generated Node #0,2: 21:[18, 32, 16] Operation: 29-13=16 Exploring Operation: 32-13=19, Resulting Numbers: [18, 29, 19] Generated Node #0,3: 21:[18, 29, 19] Operation: 32-13=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[18, 13, 3], Operations: ['32-29=3'] Exploring Operation: 18+3=21, Resulting Numbers: [13, 21] Generated Node #0,1,0: 21:[13, 21] Operation: 18+3=21 Exploring Operation: 13-3=10, Resulting Numbers: [18, 10] Generated Node #0,1,1: 21:[18, 10] Operation: 13-3=10 Exploring Operation: 18/3=6, Resulting Numbers: [13, 6] Generated Node #0,1,2: 21:[13, 6] Operation: 18/3=6 Exploring Operation: 18-13=5, Resulting Numbers: [3, 5] Generated Node #0,1,3: 21:[3, 5] Operation: 18-13=5 Moving to Node #0,1,3 Current State: 21:[3, 5], Operations: ['32-29=3', '18-13=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[18, 10], Operations: ['32-29=3', '13-3=10'] Exploring Operation: 18*10=180, Resulting Numbers: [180] 180,21 unequal: No Solution Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[13, 21], Operations: ['32-29=3', '18+3=21'] Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,21 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,21 unequal: No Solution Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[13, 6], Operations: ['32-29=3', '18/3=6'] Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,21 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[18, 29, 19], Operations: ['32-13=19'] Exploring Operation: 29-18=11, Resulting Numbers: [19, 11] Generated Node #0,3,0: 21:[19, 11] Operation: 29-18=11 Exploring Operation: 29-19=10, Resulting Numbers: [18, 10] Generated Node #0,3,1: 21:[18, 10] Operation: 29-19=10 Exploring Operation: 18+19=37, Resulting Numbers: [29, 37] Generated Node #0,3,2: 21:[29, 37] Operation: 18+19=37 Exploring Operation: 19-18=1, Resulting Numbers: [29, 1] Generated Node #0,3,3: 21:[29, 1] Operation: 19-18=1 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 21:[19, 11], Operations: ['32-13=19', '29-18=11'] Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,21 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 21:[18, 10], Operations: ['32-13=19', '29-19=10'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 18*10=180, Resulting Numbers: [180] 180,21 unequal: No Solution Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 21:[29, 1], Operations: ['32-13=19', '19-18=1'] Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 21:[29, 37], Operations: ['32-13=19', '18+19=37'] Exploring Operation: 29*37=1073, Resulting Numbers: [1073] 1073,21 unequal: No Solution Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 29+37=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[18, 32, 16], Operations: ['29-13=16'] Exploring Operation: 32-18=14, Resulting Numbers: [16, 14] Generated Node #0,2,0: 21:[16, 14] Operation: 32-18=14 Exploring Operation: 18-16=2, Resulting Numbers: [32, 2] Generated Node #0,2,1: 21:[32, 2] Operation: 18-16=2 Exploring Operation: 32-16=16, Resulting Numbers: [18, 16] Generated Node #0,2,2: 21:[18, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [18, 2] Generated Node #0,2,3: 21:[18, 2] Operation: 32/16=2 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 21:[18, 2], Operations: ['29-13=16', '32/16=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,21 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,21 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,21 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:[18, 16], Operations: ['29-13=16', '32-16=16'] Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,21 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,21 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:[16, 14], Operations: ['29-13=16', '32-18=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,21 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,21 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 #0,2,1 Current State: 21:[32, 2], Operations: ['29-13=16', '18-16=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,21 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,21 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,21 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:[32, 29, 5], Operations: ['18-13=5'] Exploring Operation: 32-5=27, Resulting Numbers: [29, 27] Generated Node #0,0,0: 21:[29, 27] Operation: 32-5=27 Exploring Operation: 32+5=37, Resulting Numbers: [29, 37] Generated Node #0,0,1: 21:[29, 37] Operation: 32+5=37 Exploring Operation: 29-5=24, Resulting Numbers: [32, 24] Generated Node #0,0,2: 21:[32, 24] Operation: 29-5=24 Exploring Operation: 32-29=3, Resulting Numbers: [5, 3] Generated Node #0,0,3: 21:[5, 3] Operation: 32-29=3 Moving to Node #0,0,3 Current State: 21:[5, 3], Operations: ['18-13=5', '32-29=3'] Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[32, 24], Operations: ['18-13=5', '29-5=24'] 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 Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[29, 27], Operations: ['18-13=5', '32-5=27'] Exploring Operation: 29*27=783, Resulting Numbers: [783] 783,21 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[29, 37], Operations: ['18-13=5', '32+5=37'] Exploring Operation: 37-29=8, Resulting Numbers: [8] 8,21 unequal: No Solution Exploring Operation: 29*37=1073, Resulting Numbers: [1073] 1073,21 unequal: No Solution Exploring Operation: 29+37=66, Resulting Numbers: [66] 66,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 72, 82, 80, 12 ]
12
[ "72/12=6", "82-80=2", "6*2=12" ]
Current State: 12:[72, 82, 80, 12], Operations: [] Exploring Operation: 72/12=6, Resulting Numbers: [82, 80, 6] Generated Node #2: [82, 80, 6] from Operation: 72/12=6 Current State: 12:[82, 80, 6], Operations: ['72/12=6'] Exploring Operation: 82-80=2, Resulting Numbers: [6, 2] Generated Node #3: [6, 2] from Operation: 82-80=2 Current State: 12:[6, 2], Operations: ['72/12=6', '82-80=2'] Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[72, 82, 80, 12], Operations: [] Exploring Operation: 82-80=2, Resulting Numbers: [72, 12, 2] Generated Node #0,0: 12:[72, 12, 2] Operation: 82-80=2 Exploring Operation: 80-72=8, Resulting Numbers: [82, 12, 8] Generated Node #0,1: 12:[82, 12, 8] Operation: 80-72=8 Exploring Operation: 82-72=10, Resulting Numbers: [80, 12, 10] Generated Node #0,2: 12:[80, 12, 10] Operation: 82-72=10 Exploring Operation: 72/12=6, Resulting Numbers: [82, 80, 6] Generated Node #0,3: 12:[82, 80, 6] Operation: 72/12=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[72, 12, 2], Operations: ['82-80=2'] Exploring Operation: 72/12=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 12:[2, 6] Operation: 72/12=6 Exploring Operation: 72-2=70, Resulting Numbers: [12, 70] Generated Node #0,0,1: 12:[12, 70] Operation: 72-2=70 Exploring Operation: 72/2=36, Resulting Numbers: [12, 36] Generated Node #0,0,2: 12:[12, 36] Operation: 72/2=36 Exploring Operation: 72-12=60, Resulting Numbers: [2, 60] Generated Node #0,0,3: 12:[2, 60] Operation: 72-12=60 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 12:[2, 6], Operations: ['82-80=2', '72/12=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[72, 82, 80, 12], Operations: [] Exploring Operation: 82-80=2, Resulting Numbers: [72, 12, 2] Generated Node #0,0: 12:[72, 12, 2] Operation: 82-80=2 Moving to Node #0,0 Current State: 12:[72, 12, 2], Operations: ['82-80=2'] Exploring Operation: 72/12=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 12:[2, 6] Operation: 72/12=6 Moving to Node #0,0,0 Current State: 12:[2, 6], Operations: ['82-80=2', '72/12=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 34, 35, 83, 58 ]
26
[ "35-34=1", "83-58=25", "1+25=26" ]
Current State: 26:[34, 35, 83, 58], Operations: [] Exploring Operation: 35-34=1, Resulting Numbers: [83, 58, 1] Generated Node #2: [83, 58, 1] from Operation: 35-34=1 Current State: 26:[83, 58, 1], Operations: ['35-34=1'] Exploring Operation: 83-58=25, Resulting Numbers: [1, 25] Generated Node #3: [1, 25] from Operation: 83-58=25 Current State: 26:[1, 25], Operations: ['35-34=1', '83-58=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[34, 35, 83, 58], Operations: [] Exploring Operation: 58-34=24, Resulting Numbers: [35, 83, 24] Generated Node #0,0: 26:[35, 83, 24] Operation: 58-34=24 Exploring Operation: 83-34=49, Resulting Numbers: [35, 58, 49] Generated Node #0,1: 26:[35, 58, 49] Operation: 83-34=49 Exploring Operation: 83-35=48, Resulting Numbers: [34, 58, 48] Generated Node #0,2: 26:[34, 58, 48] Operation: 83-35=48 Exploring Operation: 83-58=25, Resulting Numbers: [34, 35, 25] Generated Node #0,3: 26:[34, 35, 25] Operation: 83-58=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 26:[34, 35, 25], Operations: ['83-58=25'] Exploring Operation: 34+25=59, Resulting Numbers: [35, 59] Generated Node #0,3,0: 26:[35, 59] Operation: 34+25=59 Exploring Operation: 35-34=1, Resulting Numbers: [25, 1] Generated Node #0,3,1: 26:[25, 1] Operation: 35-34=1 Exploring Operation: 34-25=9, Resulting Numbers: [35, 9] Generated Node #0,3,2: 26:[35, 9] Operation: 34-25=9 Exploring Operation: 35-25=10, Resulting Numbers: [34, 10] Generated Node #0,3,3: 26:[34, 10] Operation: 35-25=10 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 26:[25, 1], Operations: ['83-58=25', '35-34=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,26 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,26 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[34, 35, 83, 58], Operations: [] Exploring Operation: 83-58=25, Resulting Numbers: [34, 35, 25] Generated Node #0,3: 26:[34, 35, 25] Operation: 83-58=25 Moving to Node #0,3 Current State: 26:[34, 35, 25], Operations: ['83-58=25'] Exploring Operation: 35-34=1, Resulting Numbers: [25, 1] Generated Node #0,3,1: 26:[25, 1] Operation: 35-34=1 Moving to Node #0,3,1 Current State: 26:[25, 1], Operations: ['83-58=25', '35-34=1'] Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 35, 53, 20, 3 ]
65
[ "35+53=88", "20+3=23", "88-23=65" ]
Current State: 65:[35, 53, 20, 3], Operations: [] Exploring Operation: 35+53=88, Resulting Numbers: [20, 3, 88] Generated Node #2: [20, 3, 88] from Operation: 35+53=88 Current State: 65:[20, 3, 88], Operations: ['35+53=88'] Exploring Operation: 20+3=23, Resulting Numbers: [88, 23] Generated Node #3: [88, 23] from Operation: 20+3=23 Current State: 65:[88, 23], Operations: ['35+53=88', '20+3=23'] Exploring Operation: 88-23=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[35, 53, 20, 3], Operations: [] Exploring Operation: 53-35=18, Resulting Numbers: [20, 3, 18] Generated Node #0,0: 65:[20, 3, 18] Operation: 53-35=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[20, 3, 18], Operations: ['53-35=18'] Exploring Operation: 20-18=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 65:[3, 2] Operation: 20-18=2 Moving to Node #0,0,0 Current State: 65:[3, 2], Operations: ['53-35=18', '20-18=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,65 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
[ 15, 40, 18, 14 ]
87
[ "15+40=55", "18+14=32", "55+32=87" ]
Current State: 87:[15, 40, 18, 14], Operations: [] Exploring Operation: 15+40=55, Resulting Numbers: [18, 14, 55] Generated Node #2: [18, 14, 55] from Operation: 15+40=55 Current State: 87:[18, 14, 55], Operations: ['15+40=55'] Exploring Operation: 18+14=32, Resulting Numbers: [55, 32] Generated Node #3: [55, 32] from Operation: 18+14=32 Current State: 87:[55, 32], Operations: ['15+40=55', '18+14=32'] Exploring Operation: 55+32=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[15, 40, 18, 14], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [15, 40, 4] Generated Node #0,0: 87:[15, 40, 4] Operation: 18-14=4 Exploring Operation: 15-14=1, Resulting Numbers: [40, 18, 1] Generated Node #0,1: 87:[40, 18, 1] Operation: 15-14=1 Exploring Operation: 18-15=3, Resulting Numbers: [40, 14, 3] Generated Node #0,2: 87:[40, 14, 3] Operation: 18-15=3 Exploring Operation: 15+14=29, Resulting Numbers: [40, 18, 29] Generated Node #0,3: 87:[40, 18, 29] Operation: 15+14=29 Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[40, 14, 3], Operations: ['18-15=3'] Exploring Operation: 14+3=17, Resulting Numbers: [40, 17] Generated Node #0,2,0: 87:[40, 17] Operation: 14+3=17 Exploring Operation: 40-14=26, Resulting Numbers: [3, 26] Generated Node #0,2,1: 87:[3, 26] Operation: 40-14=26 Exploring Operation: 14-3=11, Resulting Numbers: [40, 11] Generated Node #0,2,2: 87:[40, 11] Operation: 14-3=11 Exploring Operation: 40-3=37, Resulting Numbers: [14, 37] Generated Node #0,2,3: 87:[14, 37] Operation: 40-3=37 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[3, 26], Operations: ['18-15=3', '40-14=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,87 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[40, 11], Operations: ['18-15=3', '14-3=11'] Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,87 unequal: No Solution Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 87:[14, 37], Operations: ['18-15=3', '40-3=37'] Exploring Operation: 14*37=518, Resulting Numbers: [518] 518,87 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,87 unequal: No Solution Exploring Operation: 14+37=51, Resulting Numbers: [51] 51,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[40, 17], Operations: ['18-15=3', '14+3=17'] Exploring Operation: 40+17=57, Resulting Numbers: [57] 57,87 unequal: No Solution Exploring Operation: 40*17=680, Resulting Numbers: [680] 680,87 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[40, 18, 29], Operations: ['15+14=29'] Exploring Operation: 29-18=11, Resulting Numbers: [40, 11] Generated Node #0,3,0: 87:[40, 11] Operation: 29-18=11 Exploring Operation: 40-29=11, Resulting Numbers: [18, 11] Generated Node #0,3,1: 87:[18, 11] Operation: 40-29=11 Exploring Operation: 40-18=22, Resulting Numbers: [29, 22] Generated Node #0,3,2: 87:[29, 22] Operation: 40-18=22 Exploring Operation: 40+18=58, Resulting Numbers: [29, 58] Generated Node #0,3,3: 87:[29, 58] Operation: 40+18=58 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[29, 22], Operations: ['15+14=29', '40-18=22'] Exploring Operation: 29*22=638, Resulting Numbers: [638] 638,87 unequal: No Solution Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,87 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[40, 11], Operations: ['15+14=29', '29-18=11'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,87 unequal: No Solution Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[18, 11], Operations: ['15+14=29', '40-29=11'] Exploring Operation: 18-11=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 18+11=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 18*11=198, Resulting Numbers: [198] 198,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[29, 58], Operations: ['15+14=29', '40+18=58'] Exploring Operation: 29*58=1682, Resulting Numbers: [1682] 1682,87 unequal: No Solution Exploring Operation: 58-29=29, Resulting Numbers: [29] 29,87 unequal: No Solution Exploring Operation: 29+58=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[15, 40, 18, 14], Operations: [] Exploring Operation: 15+14=29, Resulting Numbers: [40, 18, 29] Generated Node #0,3: 87:[40, 18, 29] Operation: 15+14=29 Moving to Node #0,3 Current State: 87:[40, 18, 29], Operations: ['15+14=29'] Exploring Operation: 40+18=58, Resulting Numbers: [29, 58] Generated Node #0,3,3: 87:[29, 58] Operation: 40+18=58 Moving to Node #0,3,3 Current State: 87:[29, 58], Operations: ['15+14=29', '40+18=58'] Exploring Operation: 29+58=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_4
mult_heuristic
[ 15, 76, 50, 40 ]
74
[ "40-15=25", "50/25=2", "76-2=74" ]
Current State: 74:[15, 76, 50, 40], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [76, 50, 25] Generated Node #2: [76, 50, 25] from Operation: 40-15=25 Current State: 74:[76, 50, 25], Operations: ['40-15=25'] Exploring Operation: 50/25=2, Resulting Numbers: [76, 2] Generated Node #3: [76, 2] from Operation: 50/25=2 Current State: 74:[76, 2], Operations: ['40-15=25', '50/25=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[15, 76, 50, 40], Operations: [] Exploring Operation: 50-15=35, Resulting Numbers: [76, 40, 35] Generated Node #0,0: 74:[76, 40, 35] Operation: 50-15=35 Exploring Operation: 40-15=25, Resulting Numbers: [76, 50, 25] Generated Node #0,1: 74:[76, 50, 25] Operation: 40-15=25 Exploring Operation: 50-40=10, Resulting Numbers: [15, 76, 10] Generated Node #0,2: 74:[15, 76, 10] Operation: 50-40=10 Exploring Operation: 15+50=65, Resulting Numbers: [76, 40, 65] Generated Node #0,3: 74:[76, 40, 65] Operation: 15+50=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[76, 40, 35], Operations: ['50-15=35'] Exploring Operation: 76-40=36, Resulting Numbers: [35, 36] Generated Node #0,0,0: 74:[35, 36] Operation: 76-40=36 Exploring Operation: 76-35=41, Resulting Numbers: [40, 41] Generated Node #0,0,1: 74:[40, 41] Operation: 76-35=41 Exploring Operation: 40-35=5, Resulting Numbers: [76, 5] Generated Node #0,0,2: 74:[76, 5] Operation: 40-35=5 Exploring Operation: 40+35=75, Resulting Numbers: [76, 75] Generated Node #0,0,3: 74:[76, 75] Operation: 40+35=75 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 74:[35, 36], Operations: ['50-15=35', '76-40=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,74 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,74 unequal: No Solution No 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: 74:[76, 75], Operations: ['50-15=35', '40+35=75'] Exploring Operation: 76+75=151, Resulting Numbers: [151] 151,74 unequal: No Solution Exploring Operation: 76-75=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 76*75=5700, Resulting Numbers: [5700] 5700,74 unequal: No Solution No 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: 74:[76, 5], Operations: ['50-15=35', '40-35=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,74 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,74 unequal: No Solution No 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: 74:[40, 41], Operations: ['50-15=35', '76-35=41'] Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,74 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,74 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: 74:[76, 40, 65], Operations: ['15+50=65'] Exploring Operation: 40+65=105, Resulting Numbers: [76, 105] Generated Node #0,3,0: 74:[76, 105] Operation: 40+65=105 Exploring Operation: 76-40=36, Resulting Numbers: [65, 36] Generated Node #0,3,1: 74:[65, 36] Operation: 76-40=36 Exploring Operation: 76-65=11, Resulting Numbers: [40, 11] Generated Node #0,3,2: 74:[40, 11] Operation: 76-65=11 Exploring Operation: 65-40=25, Resulting Numbers: [76, 25] Generated Node #0,3,3: 74:[76, 25] Operation: 65-40=25 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 74:[65, 36], Operations: ['15+50=65', '76-40=36'] Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,74 unequal: No Solution Exploring Operation: 65*36=2340, Resulting Numbers: [2340] 2340,74 unequal: No Solution Exploring Operation: 65+36=101, Resulting Numbers: [101] 101,74 unequal: No Solution No 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: 74:[40, 11], Operations: ['15+50=65', '76-65=11'] Exploring Operation: 40*11=440, Resulting Numbers: [440] 440,74 unequal: No Solution Exploring Operation: 40+11=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,74 unequal: No Solution No 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: 74:[76, 25], Operations: ['15+50=65', '65-40=25'] Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,74 unequal: No Solution Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,74 unequal: No Solution No 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: 74:[76, 105], Operations: ['15+50=65', '40+65=105'] Exploring Operation: 105-76=29, Resulting Numbers: [29] 29,74 unequal: No Solution Exploring Operation: 76+105=181, Resulting Numbers: [181] 181,74 unequal: No Solution Exploring Operation: 76*105=7980, Resulting Numbers: [7980] 7980,74 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: 74:[15, 76, 10], Operations: ['50-40=10'] Exploring Operation: 76-15=61, Resulting Numbers: [10, 61] Generated Node #0,2,0: 74:[10, 61] Operation: 76-15=61 Exploring Operation: 76-10=66, Resulting Numbers: [15, 66] Generated Node #0,2,1: 74:[15, 66] Operation: 76-10=66 Exploring Operation: 15+10=25, Resulting Numbers: [76, 25] Generated Node #0,2,2: 74:[76, 25] Operation: 15+10=25 Exploring Operation: 15-10=5, Resulting Numbers: [76, 5] Generated Node #0,2,3: 74:[76, 5] Operation: 15-10=5 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 74:[76, 5], Operations: ['50-40=10', '15-10=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,74 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,74 unequal: No Solution No 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: 74:[76, 25], Operations: ['50-40=10', '15+10=25'] Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,74 unequal: No Solution Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,74 unequal: No Solution No 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: 74:[10, 61], Operations: ['50-40=10', '76-15=61'] Exploring Operation: 10+61=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 10*61=610, Resulting Numbers: [610] 610,74 unequal: No Solution Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,74 unequal: No Solution No 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: 74:[15, 66], Operations: ['50-40=10', '76-10=66'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 15+66=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 15*66=990, Resulting Numbers: [990] 990,74 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: 74:[76, 50, 25], Operations: ['40-15=25'] Exploring Operation: 50/25=2, Resulting Numbers: [76, 2] Generated Node #0,1,0: 74:[76, 2] Operation: 50/25=2 Exploring Operation: 50+25=75, Resulting Numbers: [76, 75] Generated Node #0,1,1: 74:[76, 75] Operation: 50+25=75 Exploring Operation: 50-25=25, Resulting Numbers: [76, 25] Generated Node #0,1,2: 74:[76, 25] Operation: 50-25=25 Exploring Operation: 76-50=26, Resulting Numbers: [25, 26] Generated Node #0,1,3: 74:[25, 26] Operation: 76-50=26 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 74:[76, 2], Operations: ['40-15=25', '50/25=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[15, 76, 50, 40], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [76, 50, 25] Generated Node #0,1: 74:[76, 50, 25] Operation: 40-15=25 Moving to Node #0,1 Current State: 74:[76, 50, 25], Operations: ['40-15=25'] Exploring Operation: 50/25=2, Resulting Numbers: [76, 2] Generated Node #0,1,0: 74:[76, 2] Operation: 50/25=2 Moving to Node #0,1,0 Current State: 74:[76, 2], Operations: ['40-15=25', '50/25=2'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.947049
hs_4
mult_heuristic
[ 10, 5, 24, 95 ]
47
[ "10/5=2", "24*2=48", "95-48=47" ]
Current State: 47:[10, 5, 24, 95], Operations: [] Exploring Operation: 10/5=2, Resulting Numbers: [24, 95, 2] Generated Node #2: [24, 95, 2] from Operation: 10/5=2 Current State: 47:[24, 95, 2], Operations: ['10/5=2'] Exploring Operation: 24*2=48, Resulting Numbers: [95, 48] Generated Node #3: [95, 48] from Operation: 24*2=48 Current State: 47:[95, 48], Operations: ['10/5=2', '24*2=48'] Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[10, 5, 24, 95], Operations: [] Exploring Operation: 10*5=50, Resulting Numbers: [24, 95, 50] Generated Node #0,0: 47:[24, 95, 50] Operation: 10*5=50 Moving to Node #0,0 Current State: 47:[24, 95, 50], Operations: ['10*5=50'] Exploring Operation: 95-50=45, Resulting Numbers: [24, 45] Generated Node #0,0,0: 47:[24, 45] Operation: 95-50=45 Moving to Node #0,0,0 Current State: 47:[24, 45], Operations: ['10*5=50', '95-50=45'] Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,47 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 46, 48, 5, 15 ]
91
[ "46+48=94", "15/5=3", "94-3=91" ]
Current State: 91:[46, 48, 5, 15], Operations: [] Exploring Operation: 46+48=94, Resulting Numbers: [5, 15, 94] Generated Node #2: [5, 15, 94] from Operation: 46+48=94 Current State: 91:[5, 15, 94], Operations: ['46+48=94'] Exploring Operation: 15/5=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 15/5=3 Current State: 91:[94, 3], Operations: ['46+48=94', '15/5=3'] Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[46, 48, 5, 15], Operations: [] Exploring Operation: 46+48=94, Resulting Numbers: [5, 15, 94] Generated Node #0,0: 91:[5, 15, 94] Operation: 46+48=94 Moving to Node #0,0 Current State: 91:[5, 15, 94], Operations: ['46+48=94'] Exploring Operation: 94-5=89, Resulting Numbers: [15, 89] Generated Node #0,0,0: 91:[15, 89] Operation: 94-5=89 Moving to Node #0,0,0 Current State: 91:[15, 89], Operations: ['46+48=94', '94-5=89'] Exploring Operation: 15+89=104, Resulting Numbers: [104] 104,91 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 10, 34, 72, 49 ]
48
[ "10*72=720", "49-34=15", "720/15=48" ]
Current State: 48:[10, 34, 72, 49], Operations: [] Exploring Operation: 10*72=720, Resulting Numbers: [34, 49, 720] Generated Node #2: [34, 49, 720] from Operation: 10*72=720 Current State: 48:[34, 49, 720], Operations: ['10*72=720'] Exploring Operation: 49-34=15, Resulting Numbers: [720, 15] Generated Node #3: [720, 15] from Operation: 49-34=15 Current State: 48:[720, 15], Operations: ['10*72=720', '49-34=15'] Exploring Operation: 720/15=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[10, 34, 72, 49], Operations: [] Exploring Operation: 72-49=23, Resulting Numbers: [10, 34, 23] Generated Node #0,0: 48:[10, 34, 23] Operation: 72-49=23 Exploring Operation: 72-34=38, Resulting Numbers: [10, 49, 38] Generated Node #0,1: 48:[10, 49, 38] Operation: 72-34=38 Exploring Operation: 72-10=62, Resulting Numbers: [34, 49, 62] Generated Node #0,2: 48:[34, 49, 62] Operation: 72-10=62 Exploring Operation: 34-10=24, Resulting Numbers: [72, 49, 24] Generated Node #0,3: 48:[72, 49, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 48:[10, 34, 23], Operations: ['72-49=23'] Exploring Operation: 23-10=13, Resulting Numbers: [34, 13] Generated Node #0,0,0: 48:[34, 13] Operation: 23-10=13 Exploring Operation: 34-23=11, Resulting Numbers: [10, 11] Generated Node #0,0,1: 48:[10, 11] Operation: 34-23=11 Exploring Operation: 34-10=24, Resulting Numbers: [23, 24] Generated Node #0,0,2: 48:[23, 24] Operation: 34-10=24 Exploring Operation: 10+34=44, Resulting Numbers: [23, 44] Generated Node #0,0,3: 48:[23, 44] Operation: 10+34=44 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 48:[23, 24], Operations: ['72-49=23', '34-10=24'] Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,48 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 48:[10, 11], Operations: ['72-49=23', '34-23=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 48:[23, 44], Operations: ['72-49=23', '10+34=44'] Exploring Operation: 23+44=67, Resulting Numbers: [67] 67,48 unequal: No Solution Exploring Operation: 23*44=1012, Resulting Numbers: [1012] 1012,48 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 48:[34, 13], Operations: ['72-49=23', '23-10=13'] Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,48 unequal: No Solution Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 48:[10, 49, 38], Operations: ['72-34=38'] Exploring Operation: 10+38=48, Resulting Numbers: [49, 48] Generated Node #0,1,0: 48:[49, 48] Operation: 10+38=48 Exploring Operation: 38-10=28, Resulting Numbers: [49, 28] Generated Node #0,1,1: 48:[49, 28] Operation: 38-10=28 Exploring Operation: 49-38=11, Resulting Numbers: [10, 11] Generated Node #0,1,2: 48:[10, 11] Operation: 49-38=11 Exploring Operation: 49-10=39, Resulting Numbers: [38, 39] Generated Node #0,1,3: 48:[38, 39] Operation: 49-10=39 Moving to Node #0,1,0 Current State: 48:[49, 48], Operations: ['72-34=38', '10+38=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,48 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,48 unequal: No Solution Moving to Node #0,1,2 Current State: 48:[10, 11], Operations: ['72-34=38', '49-38=11'] Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,48 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,48 unequal: No Solution Moving to Node #0,1,1 Current State: 48:[49, 28], Operations: ['72-34=38', '38-10=28'] Exploring Operation: 49+28=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 49*28=1372, Resulting Numbers: [1372] 1372,48 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,48 unequal: No Solution Moving to Node #0,1,3 Current State: 48:[38, 39], Operations: ['72-34=38', '49-10=39'] Exploring Operation: 39-38=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 38+39=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 38*39=1482, Resulting Numbers: [1482] 1482,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 48:[34, 49, 62], Operations: ['72-10=62'] Exploring Operation: 34+49=83, Resulting Numbers: [62, 83] Generated Node #0,2,0: 48:[62, 83] Operation: 34+49=83 Exploring Operation: 49-34=15, Resulting Numbers: [62, 15] Generated Node #0,2,1: 48:[62, 15] Operation: 49-34=15 Exploring Operation: 62-49=13, Resulting Numbers: [34, 13] Generated Node #0,2,2: 48:[34, 13] Operation: 62-49=13 Exploring Operation: 62-34=28, Resulting Numbers: [49, 28] Generated Node #0,2,3: 48:[49, 28] Operation: 62-34=28 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 48:[49, 28], Operations: ['72-10=62', '62-34=28'] Exploring Operation: 49*28=1372, Resulting Numbers: [1372] 1372,48 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 49+28=77, Resulting Numbers: [77] 77,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 48:[34, 13], Operations: ['72-10=62', '62-49=13'] Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,48 unequal: No Solution Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 48:[62, 15], Operations: ['72-10=62', '49-34=15'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 62+15=77, Resulting Numbers: [77] 77,48 unequal: No Solution Exploring Operation: 62*15=930, Resulting Numbers: [930] 930,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 48:[62, 83], Operations: ['72-10=62', '34+49=83'] Exploring Operation: 83-62=21, Resulting Numbers: [21] 21,48 unequal: No Solution Exploring Operation: 62+83=145, Resulting Numbers: [145] 145,48 unequal: No Solution Exploring Operation: 62*83=5146, Resulting Numbers: [5146] 5146,48 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 48:[72, 49, 24], Operations: ['34-10=24'] Exploring Operation: 72-24=48, Resulting Numbers: [49, 48] Generated Node #0,3,0: 48:[49, 48] Operation: 72-24=48 Exploring Operation: 49-24=25, Resulting Numbers: [72, 25] Generated Node #0,3,1: 48:[72, 25] Operation: 49-24=25 Exploring Operation: 72/24=3, Resulting Numbers: [49, 3] Generated Node #0,3,2: 48:[49, 3] Operation: 72/24=3 Exploring Operation: 72-49=23, Resulting Numbers: [24, 23] Generated Node #0,3,3: 48:[24, 23] Operation: 72-49=23 Moving to Node #0,3,0 Current State: 48:[49, 48], Operations: ['34-10=24', '72-24=48'] Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,48 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,48 unequal: No Solution Moving to Node #0,3,3 Current State: 48:[24, 23], Operations: ['34-10=24', '72-49=23'] Exploring Operation: 24*23=552, Resulting Numbers: [552] 552,48 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,48 unequal: No Solution Exploring Operation: 24+23=47, Resulting Numbers: [47] 47,48 unequal: No Solution Moving to Node #0,3,2 Current State: 48:[49, 3], Operations: ['34-10=24', '72/24=3'] Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,48 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,48 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,48 unequal: No Solution Moving to Node #0,3,1 Current State: 48:[72, 25], Operations: ['34-10=24', '49-24=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,48 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,48 unequal: No Solution Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 67, 72, 2, 19 ]
22
[ "72-67=5", "19-2=17", "5+17=22" ]
Current State: 22:[67, 72, 2, 19], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [2, 19, 5] Generated Node #2: [2, 19, 5] from Operation: 72-67=5 Current State: 22:[2, 19, 5], Operations: ['72-67=5'] Exploring Operation: 19-2=17, Resulting Numbers: [5, 17] Generated Node #3: [5, 17] from Operation: 19-2=17 Current State: 22:[5, 17], Operations: ['72-67=5', '19-2=17'] Exploring Operation: 5+17=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[67, 72, 2, 19], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [2, 19, 5] Generated Node #0,0: 22:[2, 19, 5] Operation: 72-67=5 Moving to Node #0,0 Current State: 22:[2, 19, 5], Operations: ['72-67=5'] Exploring Operation: 19+5=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 22:[2, 24] Operation: 19+5=24 Moving to Node #0,0,0 Current State: 22:[2, 24], Operations: ['72-67=5', '19+5=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[67, 72, 2, 19], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [2, 19, 5] Generated Node #0,0: 22:[2, 19, 5] Operation: 72-67=5 Moving to Node #0,0 Current State: 22:[2, 19, 5], Operations: ['72-67=5'] Exploring Operation: 19+5=24, Resulting Numbers: [2, 24] Generated Node #0,0,0: 22:[2, 24] Operation: 19+5=24 Moving to Node #0,0,0 Current State: 22:[2, 24], Operations: ['72-67=5', '19+5=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 45, 45, 37, 36 ]
90
[ "45+45=90", "37-36=1", "90*1=90" ]
Current State: 90:[45, 45, 37, 36], Operations: [] Exploring Operation: 45+45=90, Resulting Numbers: [37, 36, 90] Generated Node #2: [37, 36, 90] from Operation: 45+45=90 Current State: 90:[37, 36, 90], Operations: ['45+45=90'] Exploring Operation: 37-36=1, Resulting Numbers: [90, 1] Generated Node #3: [90, 1] from Operation: 37-36=1 Current State: 90:[90, 1], Operations: ['45+45=90', '37-36=1'] Exploring Operation: 90*1=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[45, 45, 37, 36], Operations: [] Exploring Operation: 45-36=9, Resulting Numbers: [45, 37, 9] Generated Node #0,0: 90:[45, 37, 9] Operation: 45-36=9 Exploring Operation: 45-37=8, Resulting Numbers: [45, 36, 8] Generated Node #0,1: 90:[45, 36, 8] Operation: 45-37=8 Exploring Operation: 37-36=1, Resulting Numbers: [45, 45, 1] Generated Node #0,2: 90:[45, 45, 1] Operation: 37-36=1 Moving to Node #0,2 Current State: 90:[45, 45, 1], Operations: ['37-36=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45, 45] Generated Node #0,2,0: 90:[45, 45] Operation: 45*1=45 Exploring Operation: 45*1=45, Resulting Numbers: [45, 45] Generated Node #0,2,1: 90:[45, 45] Operation: 45*1=45 Exploring Operation: 45/1=45, Resulting Numbers: [45, 45] Generated Node #0,2,2: 90:[45, 45] Operation: 45/1=45 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[45, 45], Operations: ['37-36=1', '45*1=45'] Exploring Operation: 45-45=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 45/45=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[45, 45, 37, 36], Operations: [] Exploring Operation: 37-36=1, Resulting Numbers: [45, 45, 1] Generated Node #0,2: 90:[45, 45, 1] Operation: 37-36=1 Moving to Node #0,2 Current State: 90:[45, 45, 1], Operations: ['37-36=1'] Exploring Operation: 45*1=45, Resulting Numbers: [45, 45] Generated Node #0,2,0: 90:[45, 45] Operation: 45*1=45 Moving to Node #0,2,0 Current State: 90:[45, 45], Operations: ['37-36=1', '45*1=45'] Exploring Operation: 45+45=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 6, 32, 58, 87 ]
85
[ "6+58=64", "64/32=2", "87-2=85" ]
Current State: 85:[6, 32, 58, 87], Operations: [] Exploring Operation: 6+58=64, Resulting Numbers: [32, 87, 64] Generated Node #2: [32, 87, 64] from Operation: 6+58=64 Current State: 85:[32, 87, 64], Operations: ['6+58=64'] Exploring Operation: 64/32=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 64/32=2 Current State: 85:[87, 2], Operations: ['6+58=64', '64/32=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[6, 32, 58, 87], Operations: [] Exploring Operation: 32+58=90, Resulting Numbers: [6, 87, 90] Generated Node #0,0: 85:[6, 87, 90] Operation: 32+58=90 Exploring Operation: 58-32=26, Resulting Numbers: [6, 87, 26] Generated Node #0,1: 85:[6, 87, 26] Operation: 58-32=26 Exploring Operation: 32-6=26, Resulting Numbers: [58, 87, 26] Generated Node #0,2: 85:[58, 87, 26] Operation: 32-6=26 Exploring Operation: 87-58=29, Resulting Numbers: [6, 32, 29] Generated Node #0,3: 85:[6, 32, 29] Operation: 87-58=29 Moving to Node #0,0 Current State: 85:[6, 87, 90], Operations: ['32+58=90'] Exploring Operation: 90/6=15, Resulting Numbers: [87, 15] Generated Node #0,0,0: 85:[87, 15] Operation: 90/6=15 Exploring Operation: 90-87=3, Resulting Numbers: [6, 3] Generated Node #0,0,1: 85:[6, 3] Operation: 90-87=3 Exploring Operation: 87-6=81, Resulting Numbers: [90, 81] Generated Node #0,0,2: 85:[90, 81] Operation: 87-6=81 Exploring Operation: 90-6=84, Resulting Numbers: [87, 84] Generated Node #0,0,3: 85:[87, 84] Operation: 90-6=84 Moving to Node #0,1 Current State: 85:[6, 87, 26], Operations: ['58-32=26'] Exploring Operation: 87-6=81, Resulting Numbers: [26, 81] Generated Node #0,1,0: 85:[26, 81] Operation: 87-6=81 Exploring Operation: 6+26=32, Resulting Numbers: [87, 32] Generated Node #0,1,1: 85:[87, 32] Operation: 6+26=32 Exploring Operation: 26-6=20, Resulting Numbers: [87, 20] Generated Node #0,1,2: 85:[87, 20] Operation: 26-6=20 Exploring Operation: 6+87=93, Resulting Numbers: [26, 93] Generated Node #0,1,3: 85:[26, 93] Operation: 6+87=93 Moving to Node #0,3 Current State: 85:[6, 32, 29], Operations: ['87-58=29'] Exploring Operation: 32-29=3, Resulting Numbers: [6, 3] Generated Node #0,3,0: 85:[6, 3] Operation: 32-29=3 Exploring Operation: 32+29=61, Resulting Numbers: [6, 61] Generated Node #0,3,1: 85:[6, 61] Operation: 32+29=61 Exploring Operation: 32-6=26, Resulting Numbers: [29, 26] Generated Node #0,3,2: 85:[29, 26] Operation: 32-6=26 Exploring Operation: 29-6=23, Resulting Numbers: [32, 23] Generated Node #0,3,3: 85:[32, 23] Operation: 29-6=23 Moving to Node #0,2 Current State: 85:[58, 87, 26], Operations: ['32-6=26'] Exploring Operation: 87-26=61, Resulting Numbers: [58, 61] Generated Node #0,2,0: 85:[58, 61] Operation: 87-26=61 Exploring Operation: 58+26=84, Resulting Numbers: [87, 84] Generated Node #0,2,1: 85:[87, 84] Operation: 58+26=84 Exploring Operation: 87-58=29, Resulting Numbers: [26, 29] Generated Node #0,2,2: 85:[26, 29] Operation: 87-58=29 Exploring Operation: 58-26=32, Resulting Numbers: [87, 32] Generated Node #0,2,3: 85:[87, 32] Operation: 58-26=32 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[87, 84], Operations: ['32-6=26', '58+26=84'] Exploring Operation: 87+84=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 87*84=7308, Resulting Numbers: [7308] 7308,85 unequal: No Solution Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,85 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 #0,2,3 Current State: 85:[87, 32], Operations: ['32-6=26', '58-26=32'] Exploring Operation: 87*32=2784, Resulting Numbers: [2784] 2784,85 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 87+32=119, Resulting Numbers: [119] 119,85 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 #0,2,2 Current State: 85:[26, 29], Operations: ['32-6=26', '87-58=29'] Exploring Operation: 26*29=754, Resulting Numbers: [754] 754,85 unequal: No Solution Exploring Operation: 26+29=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,85 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 #0,2,0 Current State: 85:[58, 61], Operations: ['32-6=26', '87-26=61'] Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,85 unequal: No Solution Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 85:[6, 3], Operations: ['32+58=90', '90-87=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[87, 84], Operations: ['32+58=90', '90-6=84'] Exploring Operation: 87*84=7308, Resulting Numbers: [7308] 7308,85 unequal: No Solution Exploring Operation: 87+84=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 87-84=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[6, 3], Operations: ['87-58=29', '32-29=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,85 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[87, 15], Operations: ['32+58=90', '90/6=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,85 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,85 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[87, 20], Operations: ['58-32=26', '26-6=20'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,85 unequal: No Solution Exploring Operation: 87+20=107, Resulting Numbers: [107] 107,85 unequal: No Solution Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[90, 81], Operations: ['32+58=90', '87-6=81'] Exploring Operation: 90*81=7290, Resulting Numbers: [7290] 7290,85 unequal: No Solution Exploring Operation: 90+81=171, Resulting Numbers: [171] 171,85 unequal: No Solution Exploring Operation: 90-81=9, Resulting Numbers: [9] 9,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[26, 81], Operations: ['58-32=26', '87-6=81'] Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 26*81=2106, Resulting Numbers: [2106] 2106,85 unequal: No Solution Exploring Operation: 26+81=107, Resulting Numbers: [107] 107,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[87, 32], Operations: ['58-32=26', '6+26=32'] Exploring Operation: 87*32=2784, Resulting Numbers: [2784] 2784,85 unequal: No Solution Exploring Operation: 87+32=119, Resulting Numbers: [119] 119,85 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[26, 93], Operations: ['58-32=26', '6+87=93'] Exploring Operation: 26+93=119, Resulting Numbers: [119] 119,85 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,85 unequal: No Solution Exploring Operation: 26*93=2418, Resulting Numbers: [2418] 2418,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[32, 23], Operations: ['87-58=29', '29-6=23'] Exploring Operation: 32+23=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 32*23=736, Resulting Numbers: [736] 736,85 unequal: No Solution Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[29, 26], Operations: ['87-58=29', '32-6=26'] Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,85 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[6, 61], Operations: ['87-58=29', '32+29=61'] Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,85 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,85 unequal: No Solution Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,85 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 22, 40, 69, 25 ]
76
[ "40-22=18", "69+25=94", "94-18=76" ]
Current State: 76:[22, 40, 69, 25], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [69, 25, 18] Generated Node #2: [69, 25, 18] from Operation: 40-22=18 Current State: 76:[69, 25, 18], Operations: ['40-22=18'] Exploring Operation: 69+25=94, Resulting Numbers: [18, 94] Generated Node #3: [18, 94] from Operation: 69+25=94 Current State: 76:[18, 94], Operations: ['40-22=18', '69+25=94'] Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[22, 40, 69, 25], Operations: [] Exploring Operation: 40-25=15, Resulting Numbers: [22, 69, 15] Generated Node #0,0: 76:[22, 69, 15] Operation: 40-25=15 Exploring Operation: 40-22=18, Resulting Numbers: [69, 25, 18] Generated Node #0,1: 76:[69, 25, 18] Operation: 40-22=18 Exploring Operation: 69-25=44, Resulting Numbers: [22, 40, 44] Generated Node #0,2: 76:[22, 40, 44] Operation: 69-25=44 Exploring Operation: 25-22=3, Resulting Numbers: [40, 69, 3] Generated Node #0,3: 76:[40, 69, 3] Operation: 25-22=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[40, 69, 3], Operations: ['25-22=3'] Exploring Operation: 69+3=72, Resulting Numbers: [40, 72] Generated Node #0,3,0: 76:[40, 72] Operation: 69+3=72 Exploring Operation: 40-3=37, Resulting Numbers: [69, 37] Generated Node #0,3,1: 76:[69, 37] Operation: 40-3=37 Exploring Operation: 69-40=29, Resulting Numbers: [3, 29] Generated Node #0,3,2: 76:[3, 29] Operation: 69-40=29 Exploring Operation: 69/3=23, Resulting Numbers: [40, 23] Generated Node #0,3,3: 76:[40, 23] Operation: 69/3=23 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 76:[40, 72], Operations: ['25-22=3', '69+3=72'] Exploring Operation: 40+72=112, Resulting Numbers: [112] 112,76 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 40*72=2880, Resulting Numbers: [2880] 2880,76 unequal: No Solution No 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: 76:[40, 23], Operations: ['25-22=3', '69/3=23'] Exploring Operation: 40-23=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 40*23=920, Resulting Numbers: [920] 920,76 unequal: No Solution Exploring Operation: 40+23=63, Resulting Numbers: [63] 63,76 unequal: No Solution No 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: 76:[69, 37], Operations: ['25-22=3', '40-3=37'] Exploring Operation: 69-37=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 69*37=2553, Resulting Numbers: [2553] 2553,76 unequal: No Solution Exploring Operation: 69+37=106, Resulting Numbers: [106] 106,76 unequal: No Solution No 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: 76:[3, 29], Operations: ['25-22=3', '69-40=29'] Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,76 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,76 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: 76:[22, 40, 44], Operations: ['69-25=44'] Exploring Operation: 44/22=2, Resulting Numbers: [40, 2] Generated Node #0,2,0: 76:[40, 2] Operation: 44/22=2 Exploring Operation: 44-40=4, Resulting Numbers: [22, 4] Generated Node #0,2,1: 76:[22, 4] Operation: 44-40=4 Exploring Operation: 44-22=22, Resulting Numbers: [40, 22] Generated Node #0,2,2: 76:[40, 22] Operation: 44-22=22 Exploring Operation: 40-22=18, Resulting Numbers: [44, 18] Generated Node #0,2,3: 76:[44, 18] Operation: 40-22=18 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[40, 2], Operations: ['69-25=44', '44/22=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,76 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,76 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,76 unequal: No Solution No 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: 76:[22, 4], Operations: ['69-25=44', '44-40=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,76 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,76 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,76 unequal: No Solution No 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: 76:[40, 22], Operations: ['69-25=44', '44-22=22'] Exploring Operation: 40+22=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,76 unequal: No Solution Exploring Operation: 40*22=880, Resulting Numbers: [880] 880,76 unequal: No Solution No 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: 76:[44, 18], Operations: ['69-25=44', '40-22=18'] Exploring Operation: 44*18=792, Resulting Numbers: [792] 792,76 unequal: No Solution Exploring Operation: 44+18=62, Resulting Numbers: [62] 62,76 unequal: No Solution Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,76 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: 76:[22, 69, 15], Operations: ['40-25=15'] Exploring Operation: 69-22=47, Resulting Numbers: [15, 47] Generated Node #0,0,0: 76:[15, 47] Operation: 69-22=47 Exploring Operation: 22+15=37, Resulting Numbers: [69, 37] Generated Node #0,0,1: 76:[69, 37] Operation: 22+15=37 Exploring Operation: 22-15=7, Resulting Numbers: [69, 7] Generated Node #0,0,2: 76:[69, 7] Operation: 22-15=7 Exploring Operation: 69+15=84, Resulting Numbers: [22, 84] Generated Node #0,0,3: 76:[22, 84] Operation: 69+15=84 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[69, 37], Operations: ['40-25=15', '22+15=37'] Exploring Operation: 69+37=106, Resulting Numbers: [106] 106,76 unequal: No Solution Exploring Operation: 69-37=32, Resulting Numbers: [32] 32,76 unequal: No Solution Exploring Operation: 69*37=2553, Resulting Numbers: [2553] 2553,76 unequal: No Solution No 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: 76:[69, 7], Operations: ['40-25=15', '22-15=7'] Exploring Operation: 69+7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[22, 40, 69, 25], Operations: [] Exploring Operation: 40-25=15, Resulting Numbers: [22, 69, 15] Generated Node #0,0: 76:[22, 69, 15] Operation: 40-25=15 Moving to Node #0,0 Current State: 76:[22, 69, 15], Operations: ['40-25=15'] Exploring Operation: 22-15=7, Resulting Numbers: [69, 7] Generated Node #0,0,2: 76:[69, 7] Operation: 22-15=7 Moving to Node #0,0,2 Current State: 76:[69, 7], Operations: ['40-25=15', '22-15=7'] Exploring Operation: 69+7=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 2, 77, 20, 59 ]
75
[ "2*77=154", "20+59=79", "154-79=75" ]
Current State: 75:[2, 77, 20, 59], Operations: [] Exploring Operation: 2*77=154, Resulting Numbers: [20, 59, 154] Generated Node #2: [20, 59, 154] from Operation: 2*77=154 Current State: 75:[20, 59, 154], Operations: ['2*77=154'] Exploring Operation: 20+59=79, Resulting Numbers: [154, 79] Generated Node #3: [154, 79] from Operation: 20+59=79 Current State: 75:[154, 79], Operations: ['2*77=154', '20+59=79'] Exploring Operation: 154-79=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[2, 77, 20, 59], Operations: [] Exploring Operation: 20+59=79, Resulting Numbers: [2, 77, 79] Generated Node #0,0: 75:[2, 77, 79] Operation: 20+59=79 Moving to Node #0,0 Current State: 75:[2, 77, 79], Operations: ['20+59=79'] Exploring Operation: 79-77=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 75:[2, 2] Operation: 79-77=2 Moving to Node #0,0,0 Current State: 75:[2, 2], Operations: ['20+59=79', '79-77=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 81, 27, 38, 2 ]
43
[ "81/27=3", "38+2=40", "3+40=43" ]
Current State: 43:[81, 27, 38, 2], Operations: [] Exploring Operation: 81/27=3, Resulting Numbers: [38, 2, 3] Generated Node #2: [38, 2, 3] from Operation: 81/27=3 Current State: 43:[38, 2, 3], Operations: ['81/27=3'] Exploring Operation: 38+2=40, Resulting Numbers: [3, 40] Generated Node #3: [3, 40] from Operation: 38+2=40 Current State: 43:[3, 40], Operations: ['81/27=3', '38+2=40'] Exploring Operation: 3+40=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[81, 27, 38, 2], Operations: [] Exploring Operation: 81-27=54, Resulting Numbers: [38, 2, 54] Generated Node #0,0: 43:[38, 2, 54] Operation: 81-27=54 Exploring Operation: 81-2=79, Resulting Numbers: [27, 38, 79] Generated Node #0,1: 43:[27, 38, 79] Operation: 81-2=79 Exploring Operation: 81-38=43, Resulting Numbers: [27, 2, 43] Generated Node #0,2: 43:[27, 2, 43] Operation: 81-38=43 Exploring Operation: 27*2=54, Resulting Numbers: [81, 38, 54] Generated Node #0,3: 43:[81, 38, 54] Operation: 27*2=54 Moving to Node #0,3 Current State: 43:[81, 38, 54], Operations: ['27*2=54'] Exploring Operation: 81-38=43, Resulting Numbers: [54, 43] Generated Node #0,3,0: 43:[54, 43] Operation: 81-38=43 Exploring Operation: 81+38=119, Resulting Numbers: [54, 119] Generated Node #0,3,1: 43:[54, 119] Operation: 81+38=119 Exploring Operation: 54-38=16, Resulting Numbers: [81, 16] Generated Node #0,3,2: 43:[81, 16] Operation: 54-38=16 Exploring Operation: 81-54=27, Resulting Numbers: [38, 27] Generated Node #0,3,3: 43:[38, 27] Operation: 81-54=27 Moving to Node #0,1 Current State: 43:[27, 38, 79], Operations: ['81-2=79'] Exploring Operation: 38-27=11, Resulting Numbers: [79, 11] Generated Node #0,1,0: 43:[79, 11] Operation: 38-27=11 Exploring Operation: 79-38=41, Resulting Numbers: [27, 41] Generated Node #0,1,1: 43:[27, 41] Operation: 79-38=41 Exploring Operation: 27+38=65, Resulting Numbers: [79, 65] Generated Node #0,1,2: 43:[79, 65] Operation: 27+38=65 Exploring Operation: 79-27=52, Resulting Numbers: [38, 52] Generated Node #0,1,3: 43:[38, 52] Operation: 79-27=52 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 43:[38, 52], Operations: ['81-2=79', '79-27=52'] Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,43 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[27, 41], Operations: ['81-2=79', '79-38=41'] Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 27+41=68, Resulting Numbers: [68] 68,43 unequal: No Solution Exploring Operation: 27*41=1107, Resulting Numbers: [1107] 1107,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[79, 65], Operations: ['81-2=79', '27+38=65'] Exploring Operation: 79-65=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 79*65=5135, Resulting Numbers: [5135] 5135,43 unequal: No Solution Exploring Operation: 79+65=144, Resulting Numbers: [144] 144,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[79, 11], Operations: ['81-2=79', '38-27=11'] Exploring Operation: 79+11=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 79*11=869, Resulting Numbers: [869] 869,43 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 43:[38, 2, 54], Operations: ['81-27=54'] Exploring Operation: 38-2=36, Resulting Numbers: [54, 36] Generated Node #0,0,0: 43:[54, 36] Operation: 38-2=36 Exploring Operation: 38+2=40, Resulting Numbers: [54, 40] Generated Node #0,0,1: 43:[54, 40] Operation: 38+2=40 Exploring Operation: 2+54=56, Resulting Numbers: [38, 56] Generated Node #0,0,2: 43:[38, 56] Operation: 2+54=56 Exploring Operation: 54-2=52, Resulting Numbers: [38, 52] Generated Node #0,0,3: 43:[38, 52] Operation: 54-2=52 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[54, 40], Operations: ['81-27=54', '38+2=40'] Exploring Operation: 54+40=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 54*40=2160, Resulting Numbers: [2160] 2160,43 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 43:[38, 52], Operations: ['81-27=54', '54-2=52'] Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,43 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[54, 36], Operations: ['81-27=54', '38-2=36'] Exploring Operation: 54-36=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 54+36=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 54*36=1944, Resulting Numbers: [1944] 1944,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 43:[38, 56], Operations: ['81-27=54', '2+54=56'] Exploring Operation: 38*56=2128, Resulting Numbers: [2128] 2128,43 unequal: No Solution Exploring Operation: 38+56=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 56-38=18, Resulting Numbers: [18] 18,43 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: 43:[27, 2, 43], Operations: ['81-38=43'] Exploring Operation: 27*2=54, Resulting Numbers: [43, 54] Generated Node #0,2,0: 43:[43, 54] Operation: 27*2=54 Exploring Operation: 27+2=29, Resulting Numbers: [43, 29] Generated Node #0,2,1: 43:[43, 29] Operation: 27+2=29 Exploring Operation: 2+43=45, Resulting Numbers: [27, 45] Generated Node #0,2,2: 43:[27, 45] Operation: 2+43=45 Exploring Operation: 27-2=25, Resulting Numbers: [43, 25] Generated Node #0,2,3: 43:[43, 25] Operation: 27-2=25 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[43, 54], Operations: ['81-38=43', '27*2=54'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,43 unequal: No Solution Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[43, 29], Operations: ['81-38=43', '27+2=29'] Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,43 unequal: No Solution Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[27, 45], Operations: ['81-38=43', '2+43=45'] Exploring Operation: 27*45=1215, Resulting Numbers: [1215] 1215,43 unequal: No Solution Exploring Operation: 45-27=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 27+45=72, Resulting Numbers: [72] 72,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 43:[43, 25], Operations: ['81-38=43', '27-2=25'] Exploring Operation: 43+25=68, Resulting Numbers: [68] 68,43 unequal: No Solution Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,43 unequal: No Solution Exploring Operation: 43*25=1075, Resulting Numbers: [1075] 1075,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 43:[54, 43], Operations: ['27*2=54', '81-38=43'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[38, 27], Operations: ['27*2=54', '81-54=27'] Exploring Operation: 38-27=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 38*27=1026, Resulting Numbers: [1026] 1026,43 unequal: No Solution Exploring Operation: 38+27=65, Resulting Numbers: [65] 65,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[81, 16], Operations: ['27*2=54', '54-38=16'] Exploring Operation: 81+16=97, Resulting Numbers: [97] 97,43 unequal: No Solution Exploring Operation: 81*16=1296, Resulting Numbers: [1296] 1296,43 unequal: No Solution Exploring Operation: 81-16=65, Resulting Numbers: [65] 65,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[54, 119], Operations: ['27*2=54', '81+38=119'] Exploring Operation: 54*119=6426, Resulting Numbers: [6426] 6426,43 unequal: No Solution Exploring Operation: 119-54=65, Resulting Numbers: [65] 65,43 unequal: No Solution Exploring Operation: 54+119=173, Resulting Numbers: [173] 173,43 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 38, 6, 14, 76 ]
94
[ "38-6=32", "76-14=62", "32+62=94" ]
Current State: 94:[38, 6, 14, 76], Operations: [] Exploring Operation: 38-6=32, Resulting Numbers: [14, 76, 32] Generated Node #2: [14, 76, 32] from Operation: 38-6=32 Current State: 94:[14, 76, 32], Operations: ['38-6=32'] Exploring Operation: 76-14=62, Resulting Numbers: [32, 62] Generated Node #3: [32, 62] from Operation: 76-14=62 Current State: 94:[32, 62], Operations: ['38-6=32', '76-14=62'] Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[38, 6, 14, 76], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [6, 14, 2] Generated Node #0,0: 94:[6, 14, 2] Operation: 76/38=2 Exploring Operation: 76-14=62, Resulting Numbers: [38, 6, 62] Generated Node #0,1: 94:[38, 6, 62] Operation: 76-14=62 Exploring Operation: 76-38=38, Resulting Numbers: [6, 14, 38] Generated Node #0,2: 94:[6, 14, 38] Operation: 76-38=38 Exploring Operation: 14+76=90, Resulting Numbers: [38, 6, 90] Generated Node #0,3: 94:[38, 6, 90] Operation: 14+76=90 Exploring Operation: 38+14=52, Resulting Numbers: [6, 76, 52] Generated Node #0,4: 94:[6, 76, 52] Operation: 38+14=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[6, 14, 2], Operations: ['76/38=2'] Exploring Operation: 14/2=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 94:[6, 7] Operation: 14/2=7 Exploring Operation: 6-2=4, Resulting Numbers: [14, 4] Generated Node #0,0,1: 94:[14, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [14, 3] Generated Node #0,0,2: 94:[14, 3] Operation: 6/2=3 Exploring Operation: 6*14=84, Resulting Numbers: [2, 84] Generated Node #0,0,3: 94:[2, 84] Operation: 6*14=84 Exploring Operation: 14-6=8, Resulting Numbers: [2, 8] Generated Node #0,0,4: 94:[2, 8] Operation: 14-6=8 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 94:[2, 8], Operations: ['76/38=2', '14-6=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,94 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,94 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 #0,0,0 Current State: 94:[6, 7], Operations: ['76/38=2', '14/2=7'] Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,94 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,94 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,94 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 #0,0,3 Current State: 94:[2, 84], Operations: ['76/38=2', '6*14=84'] Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,94 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,94 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,94 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 #0,0,2 Current State: 94:[14, 3], Operations: ['76/38=2', '6/2=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,94 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,94 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 #0,0,1 Current State: 94:[14, 4], Operations: ['76/38=2', '6-2=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,94 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 #0,3 Current State: 94:[38, 6, 90], Operations: ['14+76=90'] Exploring Operation: 90-6=84, Resulting Numbers: [38, 84] Generated Node #0,3,0: 94:[38, 84] Operation: 90-6=84 Exploring Operation: 6+90=96, Resulting Numbers: [38, 96] Generated Node #0,3,1: 94:[38, 96] Operation: 6+90=96 Exploring Operation: 38-6=32, Resulting Numbers: [90, 32] Generated Node #0,3,2: 94:[90, 32] Operation: 38-6=32 Exploring Operation: 90-38=52, Resulting Numbers: [6, 52] Generated Node #0,3,3: 94:[6, 52] Operation: 90-38=52 Exploring Operation: 38+6=44, Resulting Numbers: [90, 44] Generated Node #0,3,4: 94:[90, 44] Operation: 38+6=44 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 94:[90, 44], Operations: ['14+76=90', '38+6=44'] Exploring Operation: 90-44=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 90*44=3960, Resulting Numbers: [3960] 3960,94 unequal: No Solution Exploring Operation: 90+44=134, Resulting Numbers: [134] 134,94 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 #0,3,3 Current State: 94:[6, 52], Operations: ['14+76=90', '90-38=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,94 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 #0,3,1 Current State: 94:[38, 96], Operations: ['14+76=90', '6+90=96'] Exploring Operation: 38*96=3648, Resulting Numbers: [3648] 3648,94 unequal: No Solution Exploring Operation: 96-38=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 38+96=134, Resulting Numbers: [134] 134,94 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 #0,3,0 Current State: 94:[38, 84], Operations: ['14+76=90', '90-6=84'] Exploring Operation: 38*84=3192, Resulting Numbers: [3192] 3192,94 unequal: No Solution Exploring Operation: 38+84=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,94 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 #0,3,2 Current State: 94:[90, 32], Operations: ['14+76=90', '38-6=32'] Exploring Operation: 90+32=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 90*32=2880, Resulting Numbers: [2880] 2880,94 unequal: No Solution Exploring Operation: 90-32=58, Resulting Numbers: [58] 58,94 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 #0,2 Current State: 94:[6, 14, 38], Operations: ['76-38=38'] Exploring Operation: 6+38=44, Resulting Numbers: [14, 44] Generated Node #0,2,0: 94:[14, 44] Operation: 6+38=44 Exploring Operation: 38-14=24, Resulting Numbers: [6, 24] Generated Node #0,2,1: 94:[6, 24] Operation: 38-14=24 Exploring Operation: 6*14=84, Resulting Numbers: [38, 84] Generated Node #0,2,2: 94:[38, 84] Operation: 6*14=84 Exploring Operation: 14+38=52, Resulting Numbers: [6, 52] Generated Node #0,2,3: 94:[6, 52] Operation: 14+38=52 Exploring Operation: 14-6=8, Resulting Numbers: [38, 8] Generated Node #0,2,4: 94:[38, 8] Operation: 14-6=8 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 94:[6, 52], Operations: ['76-38=38', '14+38=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,94 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:[14, 44], Operations: ['76-38=38', '6+38=44'] Exploring Operation: 14+44=58, Resulting Numbers: [58] 58,94 unequal: No Solution Exploring Operation: 14*44=616, Resulting Numbers: [616] 616,94 unequal: No Solution Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,94 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:[38, 8], Operations: ['76-38=38', '14-6=8'] Exploring Operation: 38*8=304, Resulting Numbers: [304] 304,94 unequal: No Solution Exploring Operation: 38+8=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 38-8=30, Resulting Numbers: [30] 30,94 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:[38, 84], Operations: ['76-38=38', '6*14=84'] Exploring Operation: 38*84=3192, Resulting Numbers: [3192] 3192,94 unequal: No Solution Exploring Operation: 38+84=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 84-38=46, Resulting Numbers: [46] 46,94 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 #0,2,1 Current State: 94:[6, 24], Operations: ['76-38=38', '38-14=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,94 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:[6, 76, 52], Operations: ['38+14=52'] Exploring Operation: 6+52=58, Resulting Numbers: [76, 58] Generated Node #0,4,0: 94:[76, 58] Operation: 6+52=58 Exploring Operation: 76-52=24, Resulting Numbers: [6, 24] Generated Node #0,4,1: 94:[6, 24] Operation: 76-52=24 Exploring Operation: 52-6=46, Resulting Numbers: [76, 46] Generated Node #0,4,2: 94:[76, 46] Operation: 52-6=46 Exploring Operation: 6+76=82, Resulting Numbers: [52, 82] Generated Node #0,4,3: 94:[52, 82] Operation: 6+76=82 Exploring Operation: 76-6=70, Resulting Numbers: [52, 70] Generated Node #0,4,4: 94:[52, 70] Operation: 76-6=70 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 94:[52, 82], Operations: ['38+14=52', '6+76=82'] Exploring Operation: 52*82=4264, Resulting Numbers: [4264] 4264,94 unequal: No Solution Exploring Operation: 82-52=30, Resulting Numbers: [30] 30,94 unequal: No Solution Exploring Operation: 52+82=134, Resulting Numbers: [134] 134,94 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:[76, 46], Operations: ['38+14=52', '52-6=46'] Exploring Operation: 76+46=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 76*46=3496, Resulting Numbers: [3496] 3496,94 unequal: No Solution Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,94 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:[6, 24], Operations: ['38+14=52', '76-52=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 6*24=144, Resulting Numbers: [144] 144,94 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,94 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:[52, 70], Operations: ['38+14=52', '76-6=70'] Exploring Operation: 52+70=122, Resulting Numbers: [122] 122,94 unequal: No Solution Exploring Operation: 52*70=3640, Resulting Numbers: [3640] 3640,94 unequal: No Solution Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,94 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:[76, 58], Operations: ['38+14=52', '6+52=58'] Exploring Operation: 76*58=4408, Resulting Numbers: [4408] 4408,94 unequal: No Solution Exploring Operation: 76+58=134, Resulting Numbers: [134] 134,94 unequal: No Solution Exploring Operation: 76-58=18, Resulting Numbers: [18] 18,94 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 #0,1 Current State: 94:[38, 6, 62], Operations: ['76-14=62'] Exploring Operation: 62-38=24, Resulting Numbers: [6, 24] Generated Node #0,1,0: 94:[6, 24] Operation: 62-38=24 Exploring Operation: 38-6=32, Resulting Numbers: [62, 32] Generated Node #0,1,1: 94:[62, 32] Operation: 38-6=32 Exploring Operation: 62-6=56, Resulting Numbers: [38, 56] Generated Node #0,1,2: 94:[38, 56] Operation: 62-6=56 Exploring Operation: 38+62=100, Resulting Numbers: [6, 100] Generated Node #0,1,3: 94:[6, 100] Operation: 38+62=100 Exploring Operation: 38+6=44, Resulting Numbers: [62, 44] Generated Node #0,1,4: 94:[62, 44] Operation: 38+6=44 Moving to Node #0,1,3 Current State: 94:[6, 100], Operations: ['76-14=62', '38+62=100'] Exploring Operation: 6+100=106, Resulting Numbers: [106] 106,94 unequal: No Solution Exploring Operation: 6*100=600, Resulting Numbers: [600] 600,94 unequal: No Solution Exploring Operation: 100-6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[38, 6, 14, 76], Operations: [] Exploring Operation: 76-14=62, Resulting Numbers: [38, 6, 62] Generated Node #0,1: 94:[38, 6, 62] Operation: 76-14=62 Moving to Node #0,1 Current State: 94:[38, 6, 62], Operations: ['76-14=62'] Exploring Operation: 38+62=100, Resulting Numbers: [6, 100] Generated Node #0,1,3: 94:[6, 100] Operation: 38+62=100 Moving to Node #0,1,3 Current State: 94:[6, 100], Operations: ['76-14=62', '38+62=100'] Exploring Operation: 100-6=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.912326
hs_5
mult_heuristic
[ 51, 31, 29, 87 ]
69
[ "51+87=138", "31-29=2", "138/2=69" ]
Current State: 69:[51, 31, 29, 87], Operations: [] Exploring Operation: 51+87=138, Resulting Numbers: [31, 29, 138] Generated Node #2: [31, 29, 138] from Operation: 51+87=138 Current State: 69:[31, 29, 138], Operations: ['51+87=138'] Exploring Operation: 31-29=2, Resulting Numbers: [138, 2] Generated Node #3: [138, 2] from Operation: 31-29=2 Current State: 69:[138, 2], Operations: ['51+87=138', '31-29=2'] Exploring Operation: 138/2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[51, 31, 29, 87], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [51, 31, 3] Generated Node #0,0: 69:[51, 31, 3] Operation: 87/29=3 Exploring Operation: 51-29=22, Resulting Numbers: [31, 87, 22] Generated Node #0,1: 69:[31, 87, 22] Operation: 51-29=22 Exploring Operation: 51-31=20, Resulting Numbers: [29, 87, 20] Generated Node #0,2: 69:[29, 87, 20] Operation: 51-31=20 Moving to Node #0,0 Current State: 69:[51, 31, 3], Operations: ['87/29=3'] Exploring Operation: 51-31=20, Resulting Numbers: [3, 20] Generated Node #0,0,0: 69:[3, 20] Operation: 51-31=20 Exploring Operation: 51/3=17, Resulting Numbers: [31, 17] Generated Node #0,0,1: 69:[31, 17] Operation: 51/3=17 Exploring Operation: 51+31=82, Resulting Numbers: [3, 82] Generated Node #0,0,2: 69:[3, 82] Operation: 51+31=82 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[3, 20], Operations: ['87/29=3', '51-31=20'] Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[3, 82], Operations: ['87/29=3', '51+31=82'] Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,69 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,69 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[31, 17], Operations: ['87/29=3', '51/3=17'] Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 31*17=527, Resulting Numbers: [527] 527,69 unequal: No Solution Exploring Operation: 31+17=48, Resulting Numbers: [48] 48,69 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: 69:[31, 87, 22], Operations: ['51-29=22'] Exploring Operation: 31-22=9, Resulting Numbers: [87, 9] Generated Node #0,1,0: 69:[87, 9] Operation: 31-22=9 Exploring Operation: 87-31=56, Resulting Numbers: [22, 56] Generated Node #0,1,1: 69:[22, 56] Operation: 87-31=56 Exploring Operation: 87-22=65, Resulting Numbers: [31, 65] Generated Node #0,1,2: 69:[31, 65] Operation: 87-22=65 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[31, 65], Operations: ['51-29=22', '87-22=65'] Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,69 unequal: No Solution Exploring Operation: 31*65=2015, Resulting Numbers: [2015] 2015,69 unequal: No Solution Exploring Operation: 31+65=96, Resulting Numbers: [96] 96,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[22, 56], Operations: ['51-29=22', '87-31=56'] Exploring Operation: 22*56=1232, Resulting Numbers: [1232] 1232,69 unequal: No Solution Exploring Operation: 22+56=78, Resulting Numbers: [78] 78,69 unequal: No Solution Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[87, 9], Operations: ['51-29=22', '31-22=9'] Exploring Operation: 87+9=96, Resulting Numbers: [96] 96,69 unequal: No Solution Exploring Operation: 87*9=783, Resulting Numbers: [783] 783,69 unequal: No Solution Exploring Operation: 87-9=78, Resulting Numbers: [78] 78,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 69:[29, 87, 20], Operations: ['51-31=20'] Exploring Operation: 87/29=3, Resulting Numbers: [20, 3] Generated Node #0,2,0: 69:[20, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [20, 58] Generated Node #0,2,1: 69:[20, 58] Operation: 87-29=58 Exploring Operation: 87-20=67, Resulting Numbers: [29, 67] Generated Node #0,2,2: 69:[29, 67] Operation: 87-20=67 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[20, 3], Operations: ['51-31=20', '87/29=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[29, 67], Operations: ['51-31=20', '87-20=67'] Exploring Operation: 29*67=1943, Resulting Numbers: [1943] 1943,69 unequal: No Solution Exploring Operation: 67-29=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 29+67=96, Resulting Numbers: [96] 96,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[20, 58], Operations: ['51-31=20', '87-29=58'] Exploring Operation: 20*58=1160, Resulting Numbers: [1160] 1160,69 unequal: No Solution Exploring Operation: 20+58=78, Resulting Numbers: [78] 78,69 unequal: No Solution Exploring Operation: 58-20=38, Resulting Numbers: [38] 38,69 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
[ 84, 66, 10, 33 ]
47
[ "84+10=94", "66/33=2", "94/2=47" ]
Current State: 47:[84, 66, 10, 33], Operations: [] Exploring Operation: 84+10=94, Resulting Numbers: [66, 33, 94] Generated Node #2: [66, 33, 94] from Operation: 84+10=94 Current State: 47:[66, 33, 94], Operations: ['84+10=94'] Exploring Operation: 66/33=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 66/33=2 Current State: 47:[94, 2], Operations: ['84+10=94', '66/33=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[84, 66, 10, 33], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [66, 33, 74] Generated Node #0,0: 47:[66, 33, 74] Operation: 84-10=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[66, 33, 74], Operations: ['84-10=74'] Exploring Operation: 74-33=41, Resulting Numbers: [66, 41] Generated Node #0,0,0: 47:[66, 41] Operation: 74-33=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[66, 41], Operations: ['84-10=74', '74-33=41'] Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 11, 12, 3, 20 ]
35
[ "11+20=31", "12/3=4", "31+4=35" ]
Current State: 35:[11, 12, 3, 20], Operations: [] Exploring Operation: 11+20=31, Resulting Numbers: [12, 3, 31] Generated Node #2: [12, 3, 31] from Operation: 11+20=31 Current State: 35:[12, 3, 31], Operations: ['11+20=31'] Exploring Operation: 12/3=4, Resulting Numbers: [31, 4] Generated Node #3: [31, 4] from Operation: 12/3=4 Current State: 35:[31, 4], Operations: ['11+20=31', '12/3=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[11, 12, 3, 20], Operations: [] Exploring Operation: 12+20=32, Resulting Numbers: [11, 3, 32] Generated Node #0,0: 35:[11, 3, 32] Operation: 12+20=32 Exploring Operation: 20-11=9, Resulting Numbers: [12, 3, 9] Generated Node #0,1: 35:[12, 3, 9] Operation: 20-11=9 Exploring Operation: 20-12=8, Resulting Numbers: [11, 3, 8] Generated Node #0,2: 35:[11, 3, 8] Operation: 20-12=8 Exploring Operation: 11+20=31, Resulting Numbers: [12, 3, 31] Generated Node #0,3: 35:[12, 3, 31] Operation: 11+20=31 Moving to Node #0,2 Current State: 35:[11, 3, 8], Operations: ['20-12=8'] Exploring Operation: 11*3=33, Resulting Numbers: [8, 33] Generated Node #0,2,0: 35:[8, 33] Operation: 11*3=33 Exploring Operation: 8-3=5, Resulting Numbers: [11, 5] Generated Node #0,2,1: 35:[11, 5] Operation: 8-3=5 Exploring Operation: 11-8=3, Resulting Numbers: [3, 3] Generated Node #0,2,2: 35:[3, 3] Operation: 11-8=3 Exploring Operation: 11-3=8, Resulting Numbers: [8, 8] Generated Node #0,2,3: 35:[8, 8] Operation: 11-3=8 Moving to Node #0,1 Current State: 35:[12, 3, 9], Operations: ['20-11=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3, 3] Generated Node #0,1,0: 35:[3, 3] Operation: 12-9=3 Exploring Operation: 12-3=9, Resulting Numbers: [9, 9] Generated Node #0,1,1: 35:[9, 9] Operation: 12-3=9 Exploring Operation: 12/3=4, Resulting Numbers: [9, 4] Generated Node #0,1,2: 35:[9, 4] Operation: 12/3=4 Exploring Operation: 12*3=36, Resulting Numbers: [9, 36] Generated Node #0,1,3: 35:[9, 36] Operation: 12*3=36 Moving to Node #0,0 Current State: 35:[11, 3, 32], Operations: ['12+20=32'] Exploring Operation: 11*3=33, Resulting Numbers: [32, 33] Generated Node #0,0,0: 35:[32, 33] Operation: 11*3=33 Exploring Operation: 11+3=14, Resulting Numbers: [32, 14] Generated Node #0,0,1: 35:[32, 14] Operation: 11+3=14 Exploring Operation: 3+32=35, Resulting Numbers: [11, 35] Generated Node #0,0,2: 35:[11, 35] Operation: 3+32=35 Exploring Operation: 11-3=8, Resulting Numbers: [32, 8] Generated Node #0,0,3: 35:[32, 8] Operation: 11-3=8 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 35:[11, 35], Operations: ['12+20=32', '3+32=35'] Exploring Operation: 11*35=385, Resulting Numbers: [385] 385,35 unequal: No Solution Exploring Operation: 35-11=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 11+35=46, Resulting Numbers: [46] 46,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 35:[32, 8], Operations: ['12+20=32', '11-3=8'] Exploring Operation: 32*8=256, Resulting Numbers: [256] 256,35 unequal: No Solution Exploring Operation: 32+8=40, Resulting Numbers: [40] 40,35 unequal: No Solution Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,35 unequal: No Solution Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[32, 33], Operations: ['12+20=32', '11*3=33'] Exploring Operation: 32*33=1056, Resulting Numbers: [1056] 1056,35 unequal: No Solution Exploring Operation: 32+33=65, Resulting Numbers: [65] 65,35 unequal: No Solution Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[32, 14], Operations: ['12+20=32', '11+3=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,35 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,35 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,35 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: 35:[12, 3, 31], Operations: ['11+20=31'] Exploring Operation: 12-3=9, Resulting Numbers: [31, 9] Generated Node #0,3,0: 35:[31, 9] Operation: 12-3=9 Exploring Operation: 12/3=4, Resulting Numbers: [31, 4] Generated Node #0,3,1: 35:[31, 4] Operation: 12/3=4 Exploring Operation: 3+31=34, Resulting Numbers: [12, 34] Generated Node #0,3,2: 35:[12, 34] Operation: 3+31=34 Exploring Operation: 12*3=36, Resulting Numbers: [31, 36] Generated Node #0,3,3: 35:[31, 36] Operation: 12*3=36 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 35:[31, 4], Operations: ['11+20=31', '12/3=4'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[11, 12, 3, 20], Operations: [] Exploring Operation: 11+20=31, Resulting Numbers: [12, 3, 31] Generated Node #0,3: 35:[12, 3, 31] Operation: 11+20=31 Moving to Node #0,3 Current State: 35:[12, 3, 31], Operations: ['11+20=31'] Exploring Operation: 12/3=4, Resulting Numbers: [31, 4] Generated Node #0,3,1: 35:[31, 4] Operation: 12/3=4 Moving to Node #0,3,1 Current State: 35:[31, 4], Operations: ['11+20=31', '12/3=4'] Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
sum_heuristic
[ 45, 25, 82, 23 ]
39
[ "45-25=20", "82-23=59", "59-20=39" ]
Current State: 39:[45, 25, 82, 23], Operations: [] Exploring Operation: 45-25=20, Resulting Numbers: [82, 23, 20] Generated Node #2: [82, 23, 20] from Operation: 45-25=20 Current State: 39:[82, 23, 20], Operations: ['45-25=20'] Exploring Operation: 82-23=59, Resulting Numbers: [20, 59] Generated Node #3: [20, 59] from Operation: 82-23=59 Current State: 39:[20, 59], Operations: ['45-25=20', '82-23=59'] Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[45, 25, 82, 23], Operations: [] Exploring Operation: 82-45=37, Resulting Numbers: [25, 23, 37] Generated Node #0,0: 39:[25, 23, 37] Operation: 82-45=37 Exploring Operation: 82-25=57, Resulting Numbers: [45, 23, 57] Generated Node #0,1: 39:[45, 23, 57] Operation: 82-25=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[25, 23, 37], Operations: ['82-45=37'] Exploring Operation: 25-23=2, Resulting Numbers: [37, 2] Generated Node #0,0,0: 39:[37, 2] Operation: 25-23=2 Exploring Operation: 25+23=48, Resulting Numbers: [37, 48] Generated Node #0,0,1: 39:[37, 48] Operation: 25+23=48 Moving to Node #0,0,0 Current State: 39:[37, 2], Operations: ['82-45=37', '25-23=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,39 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[45, 25, 82, 23], Operations: [] Exploring Operation: 82-45=37, Resulting Numbers: [25, 23, 37] Generated Node #0,0: 39:[25, 23, 37] Operation: 82-45=37 Moving to Node #0,0 Current State: 39:[25, 23, 37], Operations: ['82-45=37'] Exploring Operation: 25-23=2, Resulting Numbers: [37, 2] Generated Node #0,0,0: 39:[37, 2] Operation: 25-23=2 Moving to Node #0,0,0 Current State: 39:[37, 2], Operations: ['82-45=37', '25-23=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 20, 78, 75, 35 ]
45
[ "35-20=15", "78-75=3", "15*3=45" ]
Current State: 45:[20, 78, 75, 35], Operations: [] Exploring Operation: 35-20=15, Resulting Numbers: [78, 75, 15] Generated Node #2: [78, 75, 15] from Operation: 35-20=15 Current State: 45:[78, 75, 15], Operations: ['35-20=15'] Exploring Operation: 78-75=3, Resulting Numbers: [15, 3] Generated Node #3: [15, 3] from Operation: 78-75=3 Current State: 45:[15, 3], Operations: ['35-20=15', '78-75=3'] Exploring Operation: 15*3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[20, 78, 75, 35], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [20, 78, 40] Generated Node #0,0: 45:[20, 78, 40] Operation: 75-35=40 Exploring Operation: 78-35=43, Resulting Numbers: [20, 75, 43] Generated Node #0,1: 45:[20, 75, 43] Operation: 78-35=43 Exploring Operation: 78-75=3, Resulting Numbers: [20, 35, 3] Generated Node #0,2: 45:[20, 35, 3] Operation: 78-75=3 Moving to Node #0,2 Current State: 45:[20, 35, 3], Operations: ['78-75=3'] Exploring Operation: 35-20=15, Resulting Numbers: [3, 15] Generated Node #0,2,0: 45:[3, 15] Operation: 35-20=15 Exploring Operation: 20+35=55, Resulting Numbers: [3, 55] Generated Node #0,2,1: 45:[3, 55] Operation: 20+35=55 Exploring Operation: 20-3=17, Resulting Numbers: [35, 17] Generated Node #0,2,2: 45:[35, 17] Operation: 20-3=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 45:[3, 15], Operations: ['78-75=3', '35-20=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,45 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[20, 78, 75, 35], Operations: [] Exploring Operation: 78-75=3, Resulting Numbers: [20, 35, 3] Generated Node #0,2: 45:[20, 35, 3] Operation: 78-75=3 Moving to Node #0,2 Current State: 45:[20, 35, 3], Operations: ['78-75=3'] Exploring Operation: 35-20=15, Resulting Numbers: [3, 15] Generated Node #0,2,0: 45:[3, 15] Operation: 35-20=15 Moving to Node #0,2,0 Current State: 45:[3, 15], Operations: ['78-75=3', '35-20=15'] Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 90, 35, 36, 18 ]
32
[ "90-36=54", "54/18=3", "35-3=32" ]
Current State: 32:[90, 35, 36, 18], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [35, 18, 54] Generated Node #2: [35, 18, 54] from Operation: 90-36=54 Current State: 32:[35, 18, 54], Operations: ['90-36=54'] Exploring Operation: 54/18=3, Resulting Numbers: [35, 3] Generated Node #3: [35, 3] from Operation: 54/18=3 Current State: 32:[35, 3], Operations: ['90-36=54', '54/18=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[90, 35, 36, 18], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [35, 36, 5] Generated Node #0,0: 32:[35, 36, 5] Operation: 90/18=5 Moving to Node #0,0 Current State: 32:[35, 36, 5], Operations: ['90/18=5'] Exploring Operation: 36-35=1, Resulting Numbers: [5, 1] Generated Node #0,0,0: 32:[5, 1] Operation: 36-35=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[5, 1], Operations: ['90/18=5', '36-35=1'] Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,32 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
[ 66, 22, 11, 33 ]
67
[ "22+11=33", "33/33=1", "66+1=67" ]
Current State: 67:[66, 22, 11, 33], Operations: [] Exploring Operation: 22+11=33, Resulting Numbers: [66, 33, 33] Generated Node #2: [66, 33, 33] from Operation: 22+11=33 Current State: 67:[66, 33, 33], Operations: ['22+11=33'] Exploring Operation: 33/33=1, Resulting Numbers: [66, 1] Generated Node #3: [66, 1] from Operation: 33/33=1 Current State: 67:[66, 1], Operations: ['22+11=33', '33/33=1'] Exploring Operation: 66+1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[66, 22, 11, 33], Operations: [] Exploring Operation: 22+11=33, Resulting Numbers: [66, 33, 33] Generated Node #0,0: 67:[66, 33, 33] Operation: 22+11=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[66, 33, 33], Operations: ['22+11=33'] Exploring Operation: 33+33=66, Resulting Numbers: [66, 66] Generated Node #0,0,0: 67:[66, 66] Operation: 33+33=66 Moving to Node #0,0,0 Current State: 67:[66, 66], Operations: ['22+11=33', '33+33=66'] Exploring Operation: 66+66=132, Resulting Numbers: [132] 132,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 4, 51, 42 ]
55
[ "37*4=148", "51+42=93", "148-93=55" ]
Current State: 55:[37, 4, 51, 42], Operations: [] Exploring Operation: 37*4=148, Resulting Numbers: [51, 42, 148] Generated Node #2: [51, 42, 148] from Operation: 37*4=148 Current State: 55:[51, 42, 148], Operations: ['37*4=148'] Exploring Operation: 51+42=93, Resulting Numbers: [148, 93] Generated Node #3: [148, 93] from Operation: 51+42=93 Current State: 55:[148, 93], Operations: ['37*4=148', '51+42=93'] Exploring Operation: 148-93=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[37, 4, 51, 42], Operations: [] Exploring Operation: 42-37=5, Resulting Numbers: [4, 51, 5] Generated Node #0,0: 55:[4, 51, 5] Operation: 42-37=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[4, 51, 5], Operations: ['42-37=5'] Exploring Operation: 4+51=55, Resulting Numbers: [5, 55] Generated Node #0,0,0: 55:[5, 55] Operation: 4+51=55 Moving to Node #0,0,0 Current State: 55:[5, 55], Operations: ['42-37=5', '4+51=55'] Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,55 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
[ 4, 36, 72, 43 ]
69
[ "4+36=40", "72-43=29", "40+29=69" ]
Current State: 69:[4, 36, 72, 43], Operations: [] Exploring Operation: 4+36=40, Resulting Numbers: [72, 43, 40] Generated Node #2: [72, 43, 40] from Operation: 4+36=40 Current State: 69:[72, 43, 40], Operations: ['4+36=40'] Exploring Operation: 72-43=29, Resulting Numbers: [40, 29] Generated Node #3: [40, 29] from Operation: 72-43=29 Current State: 69:[40, 29], Operations: ['4+36=40', '72-43=29'] Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[4, 36, 72, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [4, 72, 7] Generated Node #0,0: 69:[4, 72, 7] Operation: 43-36=7 Exploring Operation: 36+43=79, Resulting Numbers: [4, 72, 79] Generated Node #0,1: 69:[4, 72, 79] Operation: 36+43=79 Exploring Operation: 72-43=29, Resulting Numbers: [4, 36, 29] Generated Node #0,2: 69:[4, 36, 29] Operation: 72-43=29 Moving to Node #0,0 Current State: 69:[4, 72, 7], Operations: ['43-36=7'] Exploring Operation: 72-4=68, Resulting Numbers: [7, 68] Generated Node #0,0,0: 69:[7, 68] Operation: 72-4=68 Exploring Operation: 7-4=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 69:[72, 3] Operation: 7-4=3 Exploring Operation: 72-7=65, Resulting Numbers: [4, 65] Generated Node #0,0,2: 69:[4, 65] Operation: 72-7=65 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[72, 3], Operations: ['43-36=7', '7-4=3'] Exploring Operation: 72+3=75, Resulting Numbers: [75] 75,69 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[4, 36, 72, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [4, 72, 7] Generated Node #0,0: 69:[4, 72, 7] Operation: 43-36=7 Moving to Node #0,0 Current State: 69:[4, 72, 7], Operations: ['43-36=7'] Exploring Operation: 7-4=3, Resulting Numbers: [72, 3] Generated Node #0,0,1: 69:[72, 3] Operation: 7-4=3 Moving to Node #0,0,1 Current State: 69:[72, 3], Operations: ['43-36=7', '7-4=3'] Exploring Operation: 72-3=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 4, 56, 81, 31 ]
14
[ "81-56=25", "31+25=56", "56/4=14" ]
Current State: 14:[4, 56, 81, 31], Operations: [] Exploring Operation: 81-56=25, Resulting Numbers: [4, 31, 25] Generated Node #2: [4, 31, 25] from Operation: 81-56=25 Current State: 14:[4, 31, 25], Operations: ['81-56=25'] Exploring Operation: 31+25=56, Resulting Numbers: [4, 56] Generated Node #3: [4, 56] from Operation: 31+25=56 Current State: 14:[4, 56], Operations: ['81-56=25', '31+25=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[4, 56, 81, 31], Operations: [] Exploring Operation: 81-56=25, Resulting Numbers: [4, 31, 25] Generated Node #0,0: 14:[4, 31, 25] Operation: 81-56=25 Exploring Operation: 56-31=25, Resulting Numbers: [4, 81, 25] Generated Node #0,1: 14:[4, 81, 25] Operation: 56-31=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[4, 31, 25], Operations: ['81-56=25'] Exploring Operation: 31-4=27, Resulting Numbers: [25, 27] Generated Node #0,0,0: 14:[25, 27] Operation: 31-4=27 Exploring Operation: 31-25=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 14:[4, 6] Operation: 31-25=6 Moving to Node #0,0,1 Current State: 14:[4, 6], Operations: ['81-56=25', '31-25=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[25, 27], Operations: ['81-56=25', '31-4=27'] Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 25+27=52, Resulting Numbers: [52] 52,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[4, 81, 25], Operations: ['56-31=25'] Exploring Operation: 81-4=77, Resulting Numbers: [25, 77] Generated Node #0,1,0: 14:[25, 77] Operation: 81-4=77 Exploring Operation: 81-25=56, Resulting Numbers: [4, 56] Generated Node #0,1,1: 14:[4, 56] Operation: 81-25=56 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[4, 56], Operations: ['56-31=25', '81-25=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[4, 56, 81, 31], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [4, 81, 25] Generated Node #0,1: 14:[4, 81, 25] Operation: 56-31=25 Moving to Node #0,1 Current State: 14:[4, 81, 25], Operations: ['56-31=25'] Exploring Operation: 81-25=56, Resulting Numbers: [4, 56] Generated Node #0,1,1: 14:[4, 56] Operation: 81-25=56 Moving to Node #0,1,1 Current State: 14:[4, 56], Operations: ['56-31=25', '81-25=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 73, 95, 49, 14 ]
41
[ "95-73=22", "49+14=63", "63-22=41" ]
Current State: 41:[73, 95, 49, 14], Operations: [] Exploring Operation: 95-73=22, Resulting Numbers: [49, 14, 22] Generated Node #2: [49, 14, 22] from Operation: 95-73=22 Current State: 41:[49, 14, 22], Operations: ['95-73=22'] Exploring Operation: 49+14=63, Resulting Numbers: [22, 63] Generated Node #3: [22, 63] from Operation: 49+14=63 Current State: 41:[22, 63], Operations: ['95-73=22', '49+14=63'] Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[73, 95, 49, 14], Operations: [] Exploring Operation: 95-73=22, Resulting Numbers: [49, 14, 22] Generated Node #0,0: 41:[49, 14, 22] Operation: 95-73=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[49, 14, 22], Operations: ['95-73=22'] Exploring Operation: 14+22=36, Resulting Numbers: [49, 36] Generated Node #0,0,0: 41:[49, 36] Operation: 14+22=36 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[49, 36], Operations: ['95-73=22', '14+22=36'] Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 65, 2, 16, 14 ]
84
[ "65-16=49", "2*49=98", "98-14=84" ]
Current State: 84:[65, 2, 16, 14], Operations: [] Exploring Operation: 65-16=49, Resulting Numbers: [2, 14, 49] Generated Node #2: [2, 14, 49] from Operation: 65-16=49 Current State: 84:[2, 14, 49], Operations: ['65-16=49'] Exploring Operation: 2*49=98, Resulting Numbers: [14, 98] Generated Node #3: [14, 98] from Operation: 2*49=98 Current State: 84:[14, 98], Operations: ['65-16=49', '2*49=98'] Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[65, 2, 16, 14], Operations: [] Exploring Operation: 65+16=81, Resulting Numbers: [2, 14, 81] Generated Node #0,0: 84:[2, 14, 81] Operation: 65+16=81 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[2, 14, 81], Operations: ['65+16=81'] Exploring Operation: 2+81=83, Resulting Numbers: [14, 83] Generated Node #0,0,0: 84:[14, 83] Operation: 2+81=83 Moving to Node #0,0,0 Current State: 84:[14, 83], Operations: ['65+16=81', '2+81=83'] Exploring Operation: 14+83=97, Resulting Numbers: [97] 97,84 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
[ 13, 23, 7, 18 ]
52
[ "23-13=10", "7*10=70", "70-18=52" ]
Current State: 52:[13, 23, 7, 18], Operations: [] Exploring Operation: 23-13=10, Resulting Numbers: [7, 18, 10] Generated Node #2: [7, 18, 10] from Operation: 23-13=10 Current State: 52:[7, 18, 10], Operations: ['23-13=10'] Exploring Operation: 7*10=70, Resulting Numbers: [18, 70] Generated Node #3: [18, 70] from Operation: 7*10=70 Current State: 52:[18, 70], Operations: ['23-13=10', '7*10=70'] Exploring Operation: 70-18=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[13, 23, 7, 18], Operations: [] Exploring Operation: 23-18=5, Resulting Numbers: [13, 7, 5] Generated Node #0,0: 52:[13, 7, 5] Operation: 23-18=5 Moving to Node #0,0 Current State: 52:[13, 7, 5], Operations: ['23-18=5'] Exploring Operation: 7-5=2, Resulting Numbers: [13, 2] Generated Node #0,0,0: 52:[13, 2] Operation: 7-5=2 Moving to Node #0,0,0 Current State: 52:[13, 2], Operations: ['23-18=5', '7-5=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,52 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 87, 35, 81 ]
42
[ "35-31=4", "87+81=168", "168/4=42" ]
Current State: 42:[31, 87, 35, 81], Operations: [] Exploring Operation: 35-31=4, Resulting Numbers: [87, 81, 4] Generated Node #2: [87, 81, 4] from Operation: 35-31=4 Current State: 42:[87, 81, 4], Operations: ['35-31=4'] Exploring Operation: 87+81=168, Resulting Numbers: [4, 168] Generated Node #3: [4, 168] from Operation: 87+81=168 Current State: 42:[4, 168], Operations: ['35-31=4', '87+81=168'] Exploring Operation: 168/4=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[31, 87, 35, 81], Operations: [] Exploring Operation: 81-31=50, Resulting Numbers: [87, 35, 50] Generated Node #0,0: 42:[87, 35, 50] Operation: 81-31=50 Exploring Operation: 87-31=56, Resulting Numbers: [35, 81, 56] Generated Node #0,1: 42:[35, 81, 56] Operation: 87-31=56 Exploring Operation: 87-35=52, Resulting Numbers: [31, 81, 52] Generated Node #0,2: 42:[31, 81, 52] Operation: 87-35=52 Exploring Operation: 87-81=6, Resulting Numbers: [31, 35, 6] Generated Node #0,3: 42:[31, 35, 6] Operation: 87-81=6 Exploring Operation: 81-35=46, Resulting Numbers: [31, 87, 46] Generated Node #0,4: 42:[31, 87, 46] Operation: 81-35=46 Start Sub Search at level 1: Moving to Node #0,3 Current State: 42:[31, 35, 6], Operations: ['87-81=6'] Exploring Operation: 35-31=4, Resulting Numbers: [6, 4] Generated Node #0,3,0: 42:[6, 4] Operation: 35-31=4 Exploring Operation: 31-6=25, Resulting Numbers: [35, 25] Generated Node #0,3,1: 42:[35, 25] Operation: 31-6=25 Exploring Operation: 35-6=29, Resulting Numbers: [31, 29] Generated Node #0,3,2: 42:[31, 29] Operation: 35-6=29 Exploring Operation: 35+6=41, Resulting Numbers: [31, 41] Generated Node #0,3,3: 42:[31, 41] Operation: 35+6=41 Exploring Operation: 31+6=37, Resulting Numbers: [35, 37] Generated Node #0,3,4: 42:[35, 37] Operation: 31+6=37 Moving to Node #0,3,0 Current State: 42:[6, 4], Operations: ['87-81=6', '35-31=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 6*4=24, Resulting Numbers: [24] 24,42 unequal: No Solution Moving to Node #0,3,3 Current State: 42:[31, 41], Operations: ['87-81=6', '35+6=41'] Exploring Operation: 31*41=1271, Resulting Numbers: [1271] 1271,42 unequal: No Solution Exploring Operation: 31+41=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,3,1 Current State: 42:[35, 25], Operations: ['87-81=6', '31-6=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,42 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,3,4 Current State: 42:[35, 37], Operations: ['87-81=6', '31+6=37'] Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,42 unequal: No Solution Moving to Node #0,3,2 Current State: 42:[31, 29], Operations: ['87-81=6', '35-6=29'] Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,42 unequal: No Solution Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,42 unequal: No Solution No 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: 42:[31, 81, 52], Operations: ['87-35=52'] Exploring Operation: 81-52=29, Resulting Numbers: [31, 29] Generated Node #0,2,0: 42:[31, 29] Operation: 81-52=29 Exploring Operation: 31+81=112, Resulting Numbers: [52, 112] Generated Node #0,2,1: 42:[52, 112] Operation: 31+81=112 Exploring Operation: 31+52=83, Resulting Numbers: [81, 83] Generated Node #0,2,2: 42:[81, 83] Operation: 31+52=83 Exploring Operation: 81-31=50, Resulting Numbers: [52, 50] Generated Node #0,2,3: 42:[52, 50] Operation: 81-31=50 Exploring Operation: 52-31=21, Resulting Numbers: [81, 21] Generated Node #0,2,4: 42:[81, 21] Operation: 52-31=21 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 42:[31, 29], Operations: ['87-35=52', '81-52=29'] Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 42:[52, 50], Operations: ['87-35=52', '81-31=50'] Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,42 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 42:[81, 21], Operations: ['87-35=52', '52-31=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,42 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 42:[52, 112], Operations: ['87-35=52', '31+81=112'] Exploring Operation: 52*112=5824, Resulting Numbers: [5824] 5824,42 unequal: No Solution Exploring Operation: 112-52=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 52+112=164, Resulting Numbers: [164] 164,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 42:[81, 83], Operations: ['87-35=52', '31+52=83'] Exploring Operation: 81*83=6723, Resulting Numbers: [6723] 6723,42 unequal: No Solution Exploring Operation: 81+83=164, Resulting Numbers: [164] 164,42 unequal: No Solution Exploring Operation: 83-81=2, Resulting Numbers: [2] 2,42 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: 42:[31, 87, 46], Operations: ['81-35=46'] Exploring Operation: 31+87=118, Resulting Numbers: [46, 118] Generated Node #0,4,0: 42:[46, 118] Operation: 31+87=118 Exploring Operation: 87-31=56, Resulting Numbers: [46, 56] Generated Node #0,4,1: 42:[46, 56] Operation: 87-31=56 Exploring Operation: 31+46=77, Resulting Numbers: [87, 77] Generated Node #0,4,2: 42:[87, 77] Operation: 31+46=77 Exploring Operation: 87-46=41, Resulting Numbers: [31, 41] Generated Node #0,4,3: 42:[31, 41] Operation: 87-46=41 Exploring Operation: 46-31=15, Resulting Numbers: [87, 15] Generated Node #0,4,4: 42:[87, 15] Operation: 46-31=15 Moving to Node #0,4,3 Current State: 42:[31, 41], Operations: ['81-35=46', '87-46=41'] Exploring Operation: 31+41=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 31*41=1271, Resulting Numbers: [1271] 1271,42 unequal: No Solution Exploring Operation: 41-31=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,4,1 Current State: 42:[46, 56], Operations: ['81-35=46', '87-31=56'] Exploring Operation: 46+56=102, Resulting Numbers: [102] 102,42 unequal: No Solution Exploring Operation: 46*56=2576, Resulting Numbers: [2576] 2576,42 unequal: No Solution Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,4,4 Current State: 42:[87, 15], Operations: ['81-35=46', '46-31=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,42 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,42 unequal: No Solution Moving to Node #0,4,0 Current State: 42:[46, 118], Operations: ['81-35=46', '31+87=118'] Exploring Operation: 46*118=5428, Resulting Numbers: [5428] 5428,42 unequal: No Solution Exploring Operation: 118-46=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 46+118=164, Resulting Numbers: [164] 164,42 unequal: No Solution Moving to Node #0,4,2 Current State: 42:[87, 77], Operations: ['81-35=46', '31+46=77'] Exploring Operation: 87*77=6699, Resulting Numbers: [6699] 6699,42 unequal: No Solution Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,42 unequal: No Solution Exploring Operation: 87+77=164, Resulting Numbers: [164] 164,42 unequal: No Solution No 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: 42:[87, 35, 50], Operations: ['81-31=50'] Exploring Operation: 35+50=85, Resulting Numbers: [87, 85] Generated Node #0,0,0: 42:[87, 85] Operation: 35+50=85 Exploring Operation: 87+35=122, Resulting Numbers: [50, 122] Generated Node #0,0,1: 42:[50, 122] Operation: 87+35=122 Exploring Operation: 50-35=15, Resulting Numbers: [87, 15] Generated Node #0,0,2: 42:[87, 15] Operation: 50-35=15 Exploring Operation: 87-50=37, Resulting Numbers: [35, 37] Generated Node #0,0,3: 42:[35, 37] Operation: 87-50=37 Exploring Operation: 87-35=52, Resulting Numbers: [50, 52] Generated Node #0,0,4: 42:[50, 52] Operation: 87-35=52 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 42:[35, 37], Operations: ['81-31=50', '87-50=37'] Exploring Operation: 35*37=1295, Resulting Numbers: [1295] 1295,42 unequal: No Solution Exploring Operation: 35+37=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 37-35=2, Resulting Numbers: [2] 2,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 42:[50, 52], Operations: ['81-31=50', '87-35=52'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,42 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 42:[87, 15], Operations: ['81-31=50', '50-35=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,42 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,42 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[87, 85], Operations: ['81-31=50', '35+50=85'] Exploring Operation: 87*85=7395, Resulting Numbers: [7395] 7395,42 unequal: No Solution Exploring Operation: 87-85=2, Resulting Numbers: [2] 2,42 unequal: No Solution Exploring Operation: 87+85=172, Resulting Numbers: [172] 172,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 42:[50, 122], Operations: ['81-31=50', '87+35=122'] Exploring Operation: 50+122=172, Resulting Numbers: [172] 172,42 unequal: No Solution Exploring Operation: 122-50=72, Resulting Numbers: [72] 72,42 unequal: No Solution Exploring Operation: 50*122=6100, Resulting Numbers: [6100] 6100,42 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: 42:[35, 81, 56], Operations: ['87-31=56'] Exploring Operation: 81-35=46, Resulting Numbers: [56, 46] Generated Node #0,1,0: 42:[56, 46] Operation: 81-35=46 Exploring Operation: 81-56=25, Resulting Numbers: [35, 25] Generated Node #0,1,1: 42:[35, 25] Operation: 81-56=25 Exploring Operation: 56-35=21, Resulting Numbers: [81, 21] Generated Node #0,1,2: 42:[81, 21] Operation: 56-35=21 Exploring Operation: 35+56=91, Resulting Numbers: [81, 91] Generated Node #0,1,3: 42:[81, 91] Operation: 35+56=91 Exploring Operation: 35+81=116, Resulting Numbers: [56, 116] Generated Node #0,1,4: 42:[56, 116] Operation: 35+81=116 Moving to Node #0,1,1 Current State: 42:[35, 25], Operations: ['87-31=56', '81-56=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,42 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[56, 46], Operations: ['87-31=56', '81-35=46'] Exploring Operation: 56+46=102, Resulting Numbers: [102] 102,42 unequal: No Solution Exploring Operation: 56*46=2576, Resulting Numbers: [2576] 2576,42 unequal: No Solution Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,1,2 Current State: 42:[81, 21], Operations: ['87-31=56', '56-35=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,42 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,42 unequal: No Solution Moving to Node #0,1,3 Current State: 42:[81, 91], Operations: ['87-31=56', '35+56=91'] Exploring Operation: 81*91=7371, Resulting Numbers: [7371] 7371,42 unequal: No Solution Exploring Operation: 81+91=172, Resulting Numbers: [172] 172,42 unequal: No Solution Exploring Operation: 91-81=10, Resulting Numbers: [10] 10,42 unequal: No Solution Moving to Node #0,1,4 Current State: 42:[56, 116], Operations: ['87-31=56', '35+81=116'] Exploring Operation: 116-56=60, Resulting Numbers: [60] 60,42 unequal: No Solution Exploring Operation: 56+116=172, Resulting Numbers: [172] 172,42 unequal: No Solution Exploring Operation: 56*116=6496, Resulting Numbers: [6496] 6496,42 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
[ 44, 12, 59, 7 ]
51
[ "44+12=56", "56/7=8", "59-8=51" ]
Current State: 51:[44, 12, 59, 7], Operations: [] Exploring Operation: 44+12=56, Resulting Numbers: [59, 7, 56] Generated Node #2: [59, 7, 56] from Operation: 44+12=56 Current State: 51:[59, 7, 56], Operations: ['44+12=56'] Exploring Operation: 56/7=8, Resulting Numbers: [59, 8] Generated Node #3: [59, 8] from Operation: 56/7=8 Current State: 51:[59, 8], Operations: ['44+12=56', '56/7=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[44, 12, 59, 7], Operations: [] Exploring Operation: 59-12=47, Resulting Numbers: [44, 7, 47] Generated Node #0,0: 51:[44, 7, 47] Operation: 59-12=47 Exploring Operation: 59-7=52, Resulting Numbers: [44, 12, 52] Generated Node #0,1: 51:[44, 12, 52] Operation: 59-7=52 Exploring Operation: 44+7=51, Resulting Numbers: [12, 59, 51] Generated Node #0,2: 51:[12, 59, 51] Operation: 44+7=51 Exploring Operation: 59-44=15, Resulting Numbers: [12, 7, 15] Generated Node #0,3: 51:[12, 7, 15] Operation: 59-44=15 Exploring Operation: 44+12=56, Resulting Numbers: [59, 7, 56] Generated Node #0,4: 51:[59, 7, 56] Operation: 44+12=56 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[12, 7, 15], Operations: ['59-44=15'] Exploring Operation: 15-12=3, Resulting Numbers: [7, 3] Generated Node #0,3,0: 51:[7, 3] Operation: 15-12=3 Exploring Operation: 12+7=19, Resulting Numbers: [15, 19] Generated Node #0,3,1: 51:[15, 19] Operation: 12+7=19 Exploring Operation: 12-7=5, Resulting Numbers: [15, 5] Generated Node #0,3,2: 51:[15, 5] Operation: 12-7=5 Exploring Operation: 7+15=22, Resulting Numbers: [12, 22] Generated Node #0,3,3: 51:[12, 22] Operation: 7+15=22 Exploring Operation: 15-7=8, Resulting Numbers: [12, 8] Generated Node #0,3,4: 51:[12, 8] Operation: 15-7=8 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[7, 3], Operations: ['59-44=15', '15-12=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,51 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:[15, 19], Operations: ['59-44=15', '12+7=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,51 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,51 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:[15, 5], Operations: ['59-44=15', '12-7=5'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,51 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,51 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 51:[12, 22], Operations: ['59-44=15', '7+15=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,51 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,51 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 #0,3,4 Current State: 51:[12, 8], Operations: ['59-44=15', '15-7=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,51 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[44, 12, 52], Operations: ['59-7=52'] Exploring Operation: 44+12=56, Resulting Numbers: [52, 56] Generated Node #0,1,0: 51:[52, 56] Operation: 44+12=56 Exploring Operation: 12+52=64, Resulting Numbers: [44, 64] Generated Node #0,1,1: 51:[44, 64] Operation: 12+52=64 Exploring Operation: 44-12=32, Resulting Numbers: [52, 32] Generated Node #0,1,2: 51:[52, 32] Operation: 44-12=32 Exploring Operation: 52-44=8, Resulting Numbers: [12, 8] Generated Node #0,1,3: 51:[12, 8] Operation: 52-44=8 Exploring Operation: 52-12=40, Resulting Numbers: [44, 40] Generated Node #0,1,4: 51:[44, 40] Operation: 52-12=40 Moving to Node #0,1,0 Current State: 51:[52, 56], Operations: ['59-7=52', '44+12=56'] Exploring Operation: 52*56=2912, Resulting Numbers: [2912] 2912,51 unequal: No Solution Exploring Operation: 56-52=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 52+56=108, Resulting Numbers: [108] 108,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[12, 8], Operations: ['59-7=52', '52-44=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[52, 32], Operations: ['59-7=52', '44-12=32'] Exploring Operation: 52*32=1664, Resulting Numbers: [1664] 1664,51 unequal: No Solution Exploring Operation: 52-32=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 52+32=84, Resulting Numbers: [84] 84,51 unequal: No Solution Moving to Node #0,1,4 Current State: 51:[44, 40], Operations: ['59-7=52', '52-12=40'] Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,51 unequal: No Solution Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,51 unequal: No Solution Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[44, 64], Operations: ['59-7=52', '12+52=64'] Exploring Operation: 44+64=108, Resulting Numbers: [108] 108,51 unequal: No Solution Exploring Operation: 64-44=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 44*64=2816, Resulting Numbers: [2816] 2816,51 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 #0,2 Current State: 51:[12, 59, 51], Operations: ['44+7=51'] Exploring Operation: 12+51=63, Resulting Numbers: [59, 63] Generated Node #0,2,0: 51:[59, 63] Operation: 12+51=63 Exploring Operation: 59-51=8, Resulting Numbers: [12, 8] Generated Node #0,2,1: 51:[12, 8] Operation: 59-51=8 Exploring Operation: 59-12=47, Resulting Numbers: [51, 47] Generated Node #0,2,2: 51:[51, 47] Operation: 59-12=47 Exploring Operation: 12+59=71, Resulting Numbers: [51, 71] Generated Node #0,2,3: 51:[51, 71] Operation: 12+59=71 Exploring Operation: 51-12=39, Resulting Numbers: [59, 39] Generated Node #0,2,4: 51:[59, 39] Operation: 51-12=39 Moving to Node #0,2,2 Current State: 51:[51, 47], Operations: ['44+7=51', '59-12=47'] Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 51*47=2397, Resulting Numbers: [2397] 2397,51 unequal: No Solution Exploring Operation: 51+47=98, Resulting Numbers: [98] 98,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[12, 8], Operations: ['44+7=51', '59-51=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,51 unequal: No Solution Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,51 unequal: No Solution Moving to Node #0,2,0 Current State: 51:[59, 63], Operations: ['44+7=51', '12+51=63'] Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 59+63=122, Resulting Numbers: [122] 122,51 unequal: No Solution Exploring Operation: 59*63=3717, Resulting Numbers: [3717] 3717,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[51, 71], Operations: ['44+7=51', '12+59=71'] Exploring Operation: 71-51=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 51*71=3621, Resulting Numbers: [3621] 3621,51 unequal: No Solution Exploring Operation: 51+71=122, Resulting Numbers: [122] 122,51 unequal: No Solution Moving to Node #0,2,4 Current State: 51:[59, 39], Operations: ['44+7=51', '51-12=39'] Exploring Operation: 59+39=98, Resulting Numbers: [98] 98,51 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,51 unequal: No Solution Exploring Operation: 59*39=2301, Resulting Numbers: [2301] 2301,51 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 #0,0 Current State: 51:[44, 7, 47], Operations: ['59-12=47'] Exploring Operation: 44+7=51, Resulting Numbers: [47, 51] Generated Node #0,0,0: 51:[47, 51] Operation: 44+7=51 Exploring Operation: 7+47=54, Resulting Numbers: [44, 54] Generated Node #0,0,1: 51:[44, 54] Operation: 7+47=54 Exploring Operation: 47-44=3, Resulting Numbers: [7, 3] Generated Node #0,0,2: 51:[7, 3] Operation: 47-44=3 Exploring Operation: 44-7=37, Resulting Numbers: [47, 37] Generated Node #0,0,3: 51:[47, 37] Operation: 44-7=37 Exploring Operation: 47-7=40, Resulting Numbers: [44, 40] Generated Node #0,0,4: 51:[44, 40] Operation: 47-7=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[47, 51], Operations: ['59-12=47', '44+7=51'] Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,51 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 51:[7, 3], Operations: ['59-12=47', '47-44=3'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[44, 54], Operations: ['59-12=47', '7+47=54'] Exploring Operation: 44*54=2376, Resulting Numbers: [2376] 2376,51 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 44+54=98, Resulting Numbers: [98] 98,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 51:[47, 37], Operations: ['59-12=47', '44-7=37'] Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,51 unequal: No Solution Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 51:[44, 40], Operations: ['59-12=47', '47-7=40'] Exploring Operation: 44-40=4, Resulting Numbers: [4] 4,51 unequal: No Solution Exploring Operation: 44*40=1760, Resulting Numbers: [1760] 1760,51 unequal: No Solution Exploring Operation: 44+40=84, Resulting Numbers: [84] 84,51 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 #0,4 Current State: 51:[59, 7, 56], Operations: ['44+12=56'] Exploring Operation: 56-7=49, Resulting Numbers: [59, 49] Generated Node #0,4,0: 51:[59, 49] Operation: 56-7=49 Exploring Operation: 59-7=52, Resulting Numbers: [56, 52] Generated Node #0,4,1: 51:[56, 52] Operation: 59-7=52 Exploring Operation: 59-56=3, Resulting Numbers: [7, 3] Generated Node #0,4,2: 51:[7, 3] Operation: 59-56=3 Exploring Operation: 56/7=8, Resulting Numbers: [59, 8] Generated Node #0,4,3: 51:[59, 8] Operation: 56/7=8 Exploring Operation: 59+7=66, Resulting Numbers: [56, 66] Generated Node #0,4,4: 51:[56, 66] Operation: 59+7=66 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 51:[7, 3], Operations: ['44+12=56', '59-56=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,51 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 #0,4,1 Current State: 51:[56, 52], Operations: ['44+12=56', '59-7=52'] Exploring Operation: 56+52=108, Resulting Numbers: [108] 108,51 unequal: No Solution Exploring Operation: 56*52=2912, Resulting Numbers: [2912] 2912,51 unequal: No Solution Exploring Operation: 56-52=4, Resulting Numbers: [4] 4,51 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 #0,4,0 Current State: 51:[59, 49], Operations: ['44+12=56', '56-7=49'] Exploring Operation: 59+49=108, Resulting Numbers: [108] 108,51 unequal: No Solution Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,51 unequal: No Solution Exploring Operation: 59*49=2891, Resulting Numbers: [2891] 2891,51 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 #0,4,3 Current State: 51:[59, 8], Operations: ['44+12=56', '56/7=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[44, 12, 59, 7], Operations: [] Exploring Operation: 44+12=56, Resulting Numbers: [59, 7, 56] Generated Node #0,4: 51:[59, 7, 56] Operation: 44+12=56 Moving to Node #0,4 Current State: 51:[59, 7, 56], Operations: ['44+12=56'] Exploring Operation: 56/7=8, Resulting Numbers: [59, 8] Generated Node #0,4,3: 51:[59, 8] Operation: 56/7=8 Moving to Node #0,4,3 Current State: 51:[59, 8], Operations: ['44+12=56', '56/7=8'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.908854
hs_5
mult_heuristic
[ 68, 3, 51, 72 ]
50
[ "68+3=71", "72-51=21", "71-21=50" ]
Current State: 50:[68, 3, 51, 72], Operations: [] Exploring Operation: 68+3=71, Resulting Numbers: [51, 72, 71] Generated Node #2: [51, 72, 71] from Operation: 68+3=71 Current State: 50:[51, 72, 71], Operations: ['68+3=71'] Exploring Operation: 72-51=21, Resulting Numbers: [71, 21] Generated Node #3: [71, 21] from Operation: 72-51=21 Current State: 50:[71, 21], Operations: ['68+3=71', '72-51=21'] Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[68, 3, 51, 72], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [3, 51, 4] Generated Node #0,0: 50:[3, 51, 4] Operation: 72-68=4 Exploring Operation: 68-51=17, Resulting Numbers: [3, 72, 17] Generated Node #0,1: 50:[3, 72, 17] Operation: 68-51=17 Exploring Operation: 72/3=24, Resulting Numbers: [68, 51, 24] Generated Node #0,2: 50:[68, 51, 24] Operation: 72/3=24 Exploring Operation: 72-51=21, Resulting Numbers: [68, 3, 21] Generated Node #0,3: 50:[68, 3, 21] Operation: 72-51=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[3, 51, 4], Operations: ['72-68=4'] Exploring Operation: 3*4=12, Resulting Numbers: [51, 12] Generated Node #0,0,0: 50:[51, 12] Operation: 3*4=12 Exploring Operation: 3+4=7, Resulting Numbers: [51, 7] Generated Node #0,0,1: 50:[51, 7] Operation: 3+4=7 Exploring Operation: 4-3=1, Resulting Numbers: [51, 1] Generated Node #0,0,2: 50:[51, 1] Operation: 4-3=1 Exploring Operation: 51-3=48, Resulting Numbers: [4, 48] Generated Node #0,0,3: 50:[4, 48] Operation: 51-3=48 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 50:[51, 1], Operations: ['72-68=4', '4-3=1'] Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,50 unequal: No Solution Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,50 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[68, 3, 51, 72], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [3, 51, 4] Generated Node #0,0: 50:[3, 51, 4] Operation: 72-68=4 Moving to Node #0,0 Current State: 50:[3, 51, 4], Operations: ['72-68=4'] Exploring Operation: 4-3=1, Resulting Numbers: [51, 1] Generated Node #0,0,2: 50:[51, 1] Operation: 4-3=1 Moving to Node #0,0,2 Current State: 50:[51, 1], Operations: ['72-68=4', '4-3=1'] Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 24, 34, 57, 40 ]
87
[ "34-24=10", "57+40=97", "97-10=87" ]
Current State: 87:[24, 34, 57, 40], Operations: [] Exploring Operation: 34-24=10, Resulting Numbers: [57, 40, 10] Generated Node #2: [57, 40, 10] from Operation: 34-24=10 Current State: 87:[57, 40, 10], Operations: ['34-24=10'] Exploring Operation: 57+40=97, Resulting Numbers: [10, 97] Generated Node #3: [10, 97] from Operation: 57+40=97 Current State: 87:[10, 97], Operations: ['34-24=10', '57+40=97'] Exploring Operation: 97-10=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[24, 34, 57, 40], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [34, 40, 33] Generated Node #0,0: 87:[34, 40, 33] Operation: 57-24=33 Moving to Node #0,0 Current State: 87:[34, 40, 33], Operations: ['57-24=33'] Exploring Operation: 40-34=6, Resulting Numbers: [33, 6] Generated Node #0,0,0: 87:[33, 6] Operation: 40-34=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[33, 6], Operations: ['57-24=33', '40-34=6'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 35, 77, 20, 27 ]
65
[ "35+77=112", "20+27=47", "112-47=65" ]
Current State: 65:[35, 77, 20, 27], Operations: [] Exploring Operation: 35+77=112, Resulting Numbers: [20, 27, 112] Generated Node #2: [20, 27, 112] from Operation: 35+77=112 Current State: 65:[20, 27, 112], Operations: ['35+77=112'] Exploring Operation: 20+27=47, Resulting Numbers: [112, 47] Generated Node #3: [112, 47] from Operation: 20+27=47 Current State: 65:[112, 47], Operations: ['35+77=112', '20+27=47'] Exploring Operation: 112-47=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[35, 77, 20, 27], Operations: [] Exploring Operation: 35-20=15, Resulting Numbers: [77, 27, 15] Generated Node #0,0: 65:[77, 27, 15] Operation: 35-20=15 Exploring Operation: 35-27=8, Resulting Numbers: [77, 20, 8] Generated Node #0,1: 65:[77, 20, 8] Operation: 35-27=8 Exploring Operation: 35+27=62, Resulting Numbers: [77, 20, 62] Generated Node #0,2: 65:[77, 20, 62] Operation: 35+27=62 Exploring Operation: 35+20=55, Resulting Numbers: [77, 27, 55] Generated Node #0,3: 65:[77, 27, 55] Operation: 35+20=55 Moving to Node #0,1 Current State: 65:[77, 20, 8], Operations: ['35-27=8'] Exploring Operation: 20-8=12, Resulting Numbers: [77, 12] Generated Node #0,1,0: 65:[77, 12] Operation: 20-8=12 Exploring Operation: 77-8=69, Resulting Numbers: [20, 69] Generated Node #0,1,1: 65:[20, 69] Operation: 77-8=69 Exploring Operation: 77+8=85, Resulting Numbers: [20, 85] Generated Node #0,1,2: 65:[20, 85] Operation: 77+8=85 Exploring Operation: 77-20=57, Resulting Numbers: [8, 57] Generated Node #0,1,3: 65:[8, 57] Operation: 77-20=57 Moving to Node #0,2 Current State: 65:[77, 20, 62], Operations: ['35+27=62'] Exploring Operation: 77-62=15, Resulting Numbers: [20, 15] Generated Node #0,2,0: 65:[20, 15] Operation: 77-62=15 Exploring Operation: 77+20=97, Resulting Numbers: [62, 97] Generated Node #0,2,1: 65:[62, 97] Operation: 77+20=97 Exploring Operation: 77-20=57, Resulting Numbers: [62, 57] Generated Node #0,2,2: 65:[62, 57] Operation: 77-20=57 Exploring Operation: 20+62=82, Resulting Numbers: [77, 82] Generated Node #0,2,3: 65:[77, 82] Operation: 20+62=82 Moving to Node #0,0 Current State: 65:[77, 27, 15], Operations: ['35-20=15'] Exploring Operation: 27-15=12, Resulting Numbers: [77, 12] Generated Node #0,0,0: 65:[77, 12] Operation: 27-15=12 Exploring Operation: 77-15=62, Resulting Numbers: [27, 62] Generated Node #0,0,1: 65:[27, 62] Operation: 77-15=62 Exploring Operation: 27+15=42, Resulting Numbers: [77, 42] Generated Node #0,0,2: 65:[77, 42] Operation: 27+15=42 Exploring Operation: 77-27=50, Resulting Numbers: [15, 50] Generated Node #0,0,3: 65:[15, 50] Operation: 77-27=50 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[77, 12], Operations: ['35-20=15', '27-15=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[35, 77, 20, 27], Operations: [] Exploring Operation: 35-20=15, Resulting Numbers: [77, 27, 15] Generated Node #0,0: 65:[77, 27, 15] Operation: 35-20=15 Moving to Node #0,0 Current State: 65:[77, 27, 15], Operations: ['35-20=15'] Exploring Operation: 27-15=12, Resulting Numbers: [77, 12] Generated Node #0,0,0: 65:[77, 12] Operation: 27-15=12 Moving to Node #0,0,0 Current State: 65:[77, 12], Operations: ['35-20=15', '27-15=12'] Exploring Operation: 77-12=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 55, 59, 72, 48 ]
30
[ "59-55=4", "72+48=120", "120/4=30" ]
Current State: 30:[55, 59, 72, 48], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [72, 48, 4] Generated Node #2: [72, 48, 4] from Operation: 59-55=4 Current State: 30:[72, 48, 4], Operations: ['59-55=4'] Exploring Operation: 72+48=120, Resulting Numbers: [4, 120] Generated Node #3: [4, 120] from Operation: 72+48=120 Current State: 30:[4, 120], Operations: ['59-55=4', '72+48=120'] Exploring Operation: 120/4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[55, 59, 72, 48], Operations: [] Exploring Operation: 72-55=17, Resulting Numbers: [59, 48, 17] Generated Node #0,0: 30:[59, 48, 17] Operation: 72-55=17 Exploring Operation: 72-59=13, Resulting Numbers: [55, 48, 13] Generated Node #0,1: 30:[55, 48, 13] Operation: 72-59=13 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[55, 48, 13], Operations: ['72-59=13'] Exploring Operation: 55-48=7, Resulting Numbers: [13, 7] Generated Node #0,1,0: 30:[13, 7] Operation: 55-48=7 Exploring Operation: 55-13=42, Resulting Numbers: [48, 42] Generated Node #0,1,1: 30:[48, 42] Operation: 55-13=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[13, 7], Operations: ['72-59=13', '55-48=7'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[48, 42], Operations: ['72-59=13', '55-13=42'] Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,30 unequal: No Solution Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[59, 48, 17], Operations: ['72-55=17'] Exploring Operation: 59-48=11, Resulting Numbers: [17, 11] Generated Node #0,0,0: 30:[17, 11] Operation: 59-48=11 Exploring Operation: 59-17=42, Resulting Numbers: [48, 42] Generated Node #0,0,1: 30:[48, 42] Operation: 59-17=42 Moving to Node #0,0,0 Current State: 30:[17, 11], Operations: ['72-55=17', '59-48=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[48, 42], Operations: ['72-55=17', '59-17=42'] Exploring Operation: 48-42=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 48+42=90, Resulting Numbers: [90] 90,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 3, 3, 96, 3 ]
78
[ "3+3=6", "3*6=18", "96-18=78" ]
Current State: 78:[3, 3, 96, 3], Operations: [] Exploring Operation: 3+3=6, Resulting Numbers: [96, 6] Generated Node #2: [96, 6] from Operation: 3+3=6 Current State: 78:[96, 6], Operations: ['3+3=6'] Exploring Operation: 3*6=18, Resulting Numbers: [96, 18] Generated Node #3: [96, 18] from Operation: 3*6=18 Current State: 78:[96, 18], Operations: ['3+3=6', '3*6=18'] Exploring Operation: 96-18=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[3, 3, 96, 3], Operations: [] Exploring Operation: 96-3=93, Resulting Numbers: [3, 3, 93] Generated Node #0,0: 78:[3, 3, 93] Operation: 96-3=93 Exploring Operation: 96/3=32, Resulting Numbers: [3, 3, 32] Generated Node #0,1: 78:[3, 3, 32] Operation: 96/3=32 Exploring Operation: 96/3=32, Resulting Numbers: [3, 3, 32] Generated Node #0,2: 78:[3, 3, 32] Operation: 96/3=32 Exploring Operation: 96/3=32, Resulting Numbers: [3, 3, 32] Generated Node #0,3: 78:[3, 3, 32] Operation: 96/3=32 Moving to Node #0,1 Current State: 78:[3, 3, 32], Operations: ['96/3=32'] Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,1,0: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,1,1: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,1,2: 78:[3, 35] Operation: 3+32=35 Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,1,3: 78:[3, 35] Operation: 3+32=35 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 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 #0,1,1 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 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: 78:[3, 3, 32], Operations: ['96/3=32'] Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,3,0: 78:[3, 35] Operation: 3+32=35 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,3,1: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,3,2: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,3,3: 78:[3, 35] Operation: 3+32=35 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 78:[3, 3, 32], Operations: ['96/3=32'] Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,2,0: 78:[3, 35] Operation: 3+32=35 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,2,1: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 32-3=29, Resulting Numbers: [3, 29] Generated Node #0,2,2: 78:[3, 29] Operation: 32-3=29 Exploring Operation: 3+32=35, Resulting Numbers: [3, 35] Generated Node #0,2,3: 78:[3, 35] Operation: 3+32=35 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 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 #0,2,2 Current State: 78:[3, 29], Operations: ['96/3=32', '32-3=29'] Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 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 #0,2,0 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 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 #0,2,3 Current State: 78:[3, 35], Operations: ['96/3=32', '3+32=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,78 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 78:[3, 3, 93], Operations: ['96-3=93'] Exploring Operation: 93-3=90, Resulting Numbers: [3, 90] Generated Node #0,0,0: 78:[3, 90] Operation: 93-3=90 Exploring Operation: 93/3=31, Resulting Numbers: [3, 31] Generated Node #0,0,1: 78:[3, 31] Operation: 93/3=31 Exploring Operation: 93/3=31, Resulting Numbers: [3, 31] Generated Node #0,0,2: 78:[3, 31] Operation: 93/3=31 Exploring Operation: 93-3=90, Resulting Numbers: [3, 90] Generated Node #0,0,3: 78:[3, 90] Operation: 93-3=90 Moving to Node #0,0,1 Current State: 78:[3, 31], Operations: ['96-3=93', '93/3=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,78 unequal: No Solution Moving to Node #0,0,2 Current State: 78:[3, 31], Operations: ['96-3=93', '93/3=31'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,78 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,78 unequal: No Solution Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,78 unequal: No Solution Moving to Node #0,0,3 Current State: 78:[3, 90], Operations: ['96-3=93', '93-3=90'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,78 unequal: No Solution Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,78 unequal: No Solution Exploring Operation: 3*90=270, Resulting Numbers: [270] 270,78 unequal: No Solution Moving to Node #0,0,0 Current State: 78:[3, 90], Operations: ['96-3=93', '93-3=90'] Exploring Operation: 3*90=270, Resulting Numbers: [270] 270,78 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,78 unequal: No Solution Exploring Operation: 3+90=93, Resulting Numbers: [93] 93,78 unequal: No Solution Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,78 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 72, 15, 23, 23 ]
86
[ "72+15=87", "23/23=1", "87-1=86" ]
Current State: 86:[72, 15, 23, 23], Operations: [] Exploring Operation: 72+15=87, Resulting Numbers: [23, 23, 87] Generated Node #2: [23, 23, 87] from Operation: 72+15=87 Current State: 86:[23, 23, 87], Operations: ['72+15=87'] Exploring Operation: 23/23=1, Resulting Numbers: [87, 1] Generated Node #3: [87, 1] from Operation: 23/23=1 Current State: 86:[87, 1], Operations: ['72+15=87', '23/23=1'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[72, 15, 23, 23], Operations: [] Exploring Operation: 23-23=0, Resulting Numbers: [72, 15, 0] Generated Node #0,0: 86:[72, 15, 0] Operation: 23-23=0 Exploring Operation: 23+23=46, Resulting Numbers: [72, 15, 46] Generated Node #0,1: 86:[72, 15, 46] Operation: 23+23=46 Exploring Operation: 72-23=49, Resulting Numbers: [15, 23, 49] Generated Node #0,2: 86:[15, 23, 49] Operation: 72-23=49 Exploring Operation: 23/23=1, Resulting Numbers: [72, 15, 1] Generated Node #0,3: 86:[72, 15, 1] Operation: 23/23=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[72, 15, 1], Operations: ['23/23=1'] Exploring Operation: 15-1=14, Resulting Numbers: [72, 14] Generated Node #0,3,0: 86:[72, 14] Operation: 15-1=14 Exploring Operation: 72-15=57, Resulting Numbers: [1, 57] Generated Node #0,3,1: 86:[1, 57] Operation: 72-15=57 Exploring Operation: 72+1=73, Resulting Numbers: [15, 73] Generated Node #0,3,2: 86:[15, 73] Operation: 72+1=73 Exploring Operation: 72+15=87, Resulting Numbers: [1, 87] Generated Node #0,3,3: 86:[1, 87] Operation: 72+15=87 Moving to Node #0,3,3 Current State: 86:[1, 87], Operations: ['23/23=1', '72+15=87'] Exploring Operation: 1*87=87, Resulting Numbers: [87] 87,86 unequal: No Solution Exploring Operation: 1+87=88, Resulting Numbers: [88] 88,86 unequal: No Solution Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[72, 15, 23, 23], Operations: [] Exploring Operation: 23/23=1, Resulting Numbers: [72, 15, 1] Generated Node #0,3: 86:[72, 15, 1] Operation: 23/23=1 Moving to Node #0,3 Current State: 86:[72, 15, 1], Operations: ['23/23=1'] Exploring Operation: 72+15=87, Resulting Numbers: [1, 87] Generated Node #0,3,3: 86:[1, 87] Operation: 72+15=87 Moving to Node #0,3,3 Current State: 86:[1, 87], Operations: ['23/23=1', '72+15=87'] Exploring Operation: 87-1=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 95, 32, 7, 7 ]
10
[ "95-32=63", "7+63=70", "70/7=10" ]
Current State: 10:[95, 32, 7, 7], Operations: [] Exploring Operation: 95-32=63, Resulting Numbers: [7, 7, 63] Generated Node #2: [7, 7, 63] from Operation: 95-32=63 Current State: 10:[7, 7, 63], Operations: ['95-32=63'] Exploring Operation: 7+63=70, Resulting Numbers: [70] 70,10 equal: Goal Reached Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[95, 32, 7, 7], Operations: [] Exploring Operation: 95-7=88, Resulting Numbers: [32, 7, 88] Generated Node #0,0: 10:[32, 7, 88] Operation: 95-7=88 Exploring Operation: 95-7=88, Resulting Numbers: [32, 7, 88] Generated Node #0,1: 10:[32, 7, 88] Operation: 95-7=88 Exploring Operation: 95-32=63, Resulting Numbers: [7, 7, 63] Generated Node #0,2: 10:[7, 7, 63] Operation: 95-32=63 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[7, 7, 63], Operations: ['95-32=63'] Exploring Operation: 63/7=9, Resulting Numbers: [7, 9] Generated Node #0,2,0: 10:[7, 9] Operation: 63/7=9 Exploring Operation: 63-7=56, Resulting Numbers: [7, 56] Generated Node #0,2,1: 10:[7, 56] Operation: 63-7=56 Exploring Operation: 63/7=9, Resulting Numbers: [7, 9] Generated Node #0,2,2: 10:[7, 9] Operation: 63/7=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 10:[7, 9], Operations: ['95-32=63', '63/7=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,10 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 10:[7, 9], Operations: ['95-32=63', '63/7=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 10:[7, 56], Operations: ['95-32=63', '63-7=56'] Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[32, 7, 88], Operations: ['95-7=88'] Exploring Operation: 88-7=81, Resulting Numbers: [32, 81] Generated Node #0,0,0: 10:[32, 81] Operation: 88-7=81 Exploring Operation: 88-32=56, Resulting Numbers: [7, 56] Generated Node #0,0,1: 10:[7, 56] Operation: 88-32=56 Exploring Operation: 32-7=25, Resulting Numbers: [88, 25] Generated Node #0,0,2: 10:[88, 25] Operation: 32-7=25 Moving to Node #0,0,1 Current State: 10:[7, 56], Operations: ['95-7=88', '88-32=56'] Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,10 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,10 unequal: No Solution Moving to Node #0,0,0 Current State: 10:[32, 81], Operations: ['95-7=88', '88-7=81'] Exploring Operation: 32*81=2592, Resulting Numbers: [2592] 2592,10 unequal: No Solution Exploring Operation: 32+81=113, Resulting Numbers: [113] 113,10 unequal: No Solution Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,10 unequal: No Solution Moving to Node #0,0,2 Current State: 10:[88, 25], Operations: ['95-7=88', '32-7=25'] Exploring Operation: 88*25=2200, Resulting Numbers: [2200] 2200,10 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 88+25=113, Resulting Numbers: [113] 113,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[32, 7, 88], Operations: ['95-7=88'] Exploring Operation: 88-32=56, Resulting Numbers: [7, 56] Generated Node #0,1,0: 10:[7, 56] Operation: 88-32=56 Exploring Operation: 32-7=25, Resulting Numbers: [88, 25] Generated Node #0,1,1: 10:[88, 25] Operation: 32-7=25 Exploring Operation: 88-7=81, Resulting Numbers: [32, 81] Generated Node #0,1,2: 10:[32, 81] Operation: 88-7=81 Moving to Node #0,1,0 Current State: 10:[7, 56], Operations: ['95-7=88', '88-32=56'] Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 56-7=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 56/7=8, Resulting Numbers: [8] 8,10 unequal: No Solution Moving to Node #0,1,1 Current State: 10:[88, 25], Operations: ['95-7=88', '32-7=25'] Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,10 unequal: No Solution Exploring Operation: 88*25=2200, Resulting Numbers: [2200] 2200,10 unequal: No Solution Exploring Operation: 88+25=113, Resulting Numbers: [113] 113,10 unequal: No Solution Moving to Node #0,1,2 Current State: 10:[32, 81], Operations: ['95-7=88', '88-7=81'] Exploring Operation: 81-32=49, Resulting Numbers: [49] 49,10 unequal: No Solution Exploring Operation: 32+81=113, Resulting Numbers: [113] 113,10 unequal: No Solution Exploring Operation: 32*81=2592, Resulting Numbers: [2592] 2592,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 50, 16, 17, 26 ]
77
[ "50-16=34", "17+26=43", "34+43=77" ]
Current State: 77:[50, 16, 17, 26], Operations: [] Exploring Operation: 50-16=34, Resulting Numbers: [17, 26, 34] Generated Node #2: [17, 26, 34] from Operation: 50-16=34 Current State: 77:[17, 26, 34], Operations: ['50-16=34'] Exploring Operation: 17+26=43, Resulting Numbers: [34, 43] Generated Node #3: [34, 43] from Operation: 17+26=43 Current State: 77:[34, 43], Operations: ['50-16=34', '17+26=43'] Exploring Operation: 34+43=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[50, 16, 17, 26], Operations: [] Exploring Operation: 50+26=76, Resulting Numbers: [16, 17, 76] Generated Node #0,0: 77:[16, 17, 76] Operation: 50+26=76 Moving to Node #0,0 Current State: 77:[16, 17, 76], Operations: ['50+26=76'] Exploring Operation: 17-16=1, Resulting Numbers: [76, 1] Generated Node #0,0,0: 77:[76, 1] Operation: 17-16=1 Moving to Node #0,0,0 Current State: 77:[76, 1], Operations: ['50+26=76', '17-16=1'] Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[50, 16, 17, 26], Operations: [] Exploring Operation: 50+26=76, Resulting Numbers: [16, 17, 76] Generated Node #0,0: 77:[16, 17, 76] Operation: 50+26=76 Moving to Node #0,0 Current State: 77:[16, 17, 76], Operations: ['50+26=76'] Exploring Operation: 17-16=1, Resulting Numbers: [76, 1] Generated Node #0,0,0: 77:[76, 1] Operation: 17-16=1 Moving to Node #0,0,0 Current State: 77:[76, 1], Operations: ['50+26=76', '17-16=1'] Exploring Operation: 76+1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 3, 38, 10, 2 ]
24
[ "10-3=7", "2*7=14", "38-14=24" ]
Current State: 24:[3, 38, 10, 2], Operations: [] Exploring Operation: 10-3=7, Resulting Numbers: [38, 2, 7] Generated Node #2: [38, 2, 7] from Operation: 10-3=7 Current State: 24:[38, 2, 7], Operations: ['10-3=7'] Exploring Operation: 2*7=14, Resulting Numbers: [38, 14] Generated Node #3: [38, 14] from Operation: 2*7=14 Current State: 24:[38, 14], Operations: ['10-3=7', '2*7=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[3, 38, 10, 2], Operations: [] Exploring Operation: 38-10=28, Resulting Numbers: [3, 2, 28] Generated Node #0,0: 24:[3, 2, 28] Operation: 38-10=28 Exploring Operation: 38-2=36, Resulting Numbers: [3, 10, 36] Generated Node #0,1: 24:[3, 10, 36] Operation: 38-2=36 Exploring Operation: 38/2=19, Resulting Numbers: [3, 10, 19] Generated Node #0,2: 24:[3, 10, 19] Operation: 38/2=19 Exploring Operation: 38-3=35, Resulting Numbers: [10, 2, 35] Generated Node #0,3: 24:[10, 2, 35] Operation: 38-3=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[3, 2, 28], Operations: ['38-10=28'] Exploring Operation: 28/2=14, Resulting Numbers: [3, 14] Generated Node #0,0,0: 24:[3, 14] Operation: 28/2=14 Exploring Operation: 3*2=6, Resulting Numbers: [28, 6] Generated Node #0,0,1: 24:[28, 6] Operation: 3*2=6 Exploring Operation: 28-2=26, Resulting Numbers: [3, 26] Generated Node #0,0,2: 24:[3, 26] Operation: 28-2=26 Exploring Operation: 28-3=25, Resulting Numbers: [2, 25] Generated Node #0,0,3: 24:[2, 25] Operation: 28-3=25 Moving to Node #0,0,3 Current State: 24:[2, 25], Operations: ['38-10=28', '28-3=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,24 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[3, 26], Operations: ['38-10=28', '28-2=26'] Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,24 unequal: No Solution Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[3, 14], Operations: ['38-10=28', '28/2=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,24 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[28, 6], Operations: ['38-10=28', '3*2=6'] Exploring Operation: 28*6=168, Resulting Numbers: [168] 168,24 unequal: No Solution Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,24 unequal: No Solution Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[3, 10, 19], Operations: ['38/2=19'] Exploring Operation: 3+10=13, Resulting Numbers: [19, 13] Generated Node #0,2,0: 24:[19, 13] Operation: 3+10=13 Exploring Operation: 10+19=29, Resulting Numbers: [3, 29] Generated Node #0,2,1: 24:[3, 29] Operation: 10+19=29 Exploring Operation: 3+19=22, Resulting Numbers: [10, 22] Generated Node #0,2,2: 24:[10, 22] Operation: 3+19=22 Exploring Operation: 19-10=9, Resulting Numbers: [3, 9] Generated Node #0,2,3: 24:[3, 9] Operation: 19-10=9 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 24:[3, 9], Operations: ['38/2=19', '19-10=9'] Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,24 unequal: No Solution Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,24 unequal: No Solution No 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: 24:[10, 22], Operations: ['38/2=19', '3+19=22'] Exploring Operation: 10*22=220, Resulting Numbers: [220] 220,24 unequal: No Solution Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 10+22=32, Resulting Numbers: [32] 32,24 unequal: No Solution No 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: 24:[3, 29], Operations: ['38/2=19', '10+19=29'] Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,24 unequal: No Solution Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 3*29=87, Resulting Numbers: [87] 87,24 unequal: No Solution No 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: 24:[19, 13], Operations: ['38/2=19', '3+10=13'] Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,24 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,24 unequal: No Solution Exploring Operation: 19*13=247, Resulting Numbers: [247] 247,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[10, 2, 35], Operations: ['38-3=35'] Exploring Operation: 35-10=25, Resulting Numbers: [2, 25] Generated Node #0,3,0: 24:[2, 25] Operation: 35-10=25 Exploring Operation: 35-2=33, Resulting Numbers: [10, 33] Generated Node #0,3,1: 24:[10, 33] Operation: 35-2=33 Exploring Operation: 10-2=8, Resulting Numbers: [35, 8] Generated Node #0,3,2: 24:[35, 8] Operation: 10-2=8 Exploring Operation: 10+2=12, Resulting Numbers: [35, 12] Generated Node #0,3,3: 24:[35, 12] Operation: 10+2=12 Moving to Node #0,3,0 Current State: 24:[2, 25], Operations: ['38-3=35', '35-10=25'] Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,24 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,24 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,24 unequal: No Solution Moving to Node #0,3,2 Current State: 24:[35, 8], Operations: ['38-3=35', '10-2=8'] Exploring Operation: 35*8=280, Resulting Numbers: [280] 280,24 unequal: No Solution Exploring Operation: 35+8=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,24 unequal: No Solution Moving to Node #0,3,1 Current State: 24:[10, 33], Operations: ['38-3=35', '35-2=33'] Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,24 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,24 unequal: No Solution Moving to Node #0,3,3 Current State: 24:[35, 12], Operations: ['38-3=35', '10+2=12'] Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 35*12=420, Resulting Numbers: [420] 420,24 unequal: No Solution Exploring Operation: 35+12=47, Resulting Numbers: [47] 47,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 24:[3, 10, 36], Operations: ['38-2=36'] Exploring Operation: 36-3=33, Resulting Numbers: [10, 33] Generated Node #0,1,0: 24:[10, 33] Operation: 36-3=33 Exploring Operation: 36/3=12, Resulting Numbers: [10, 12] Generated Node #0,1,1: 24:[10, 12] Operation: 36/3=12 Exploring Operation: 36-10=26, Resulting Numbers: [3, 26] Generated Node #0,1,2: 24:[3, 26] Operation: 36-10=26 Exploring Operation: 3+10=13, Resulting Numbers: [36, 13] Generated Node #0,1,3: 24:[36, 13] Operation: 3+10=13 Moving to Node #0,1,1 Current State: 24:[10, 12], Operations: ['38-2=36', '36/3=12'] Exploring Operation: 10*12=120, Resulting Numbers: [120] 120,24 unequal: No Solution Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,24 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[3, 26], Operations: ['38-2=36', '36-10=26'] Exploring Operation: 3+26=29, Resulting Numbers: [29] 29,24 unequal: No Solution Exploring Operation: 3*26=78, Resulting Numbers: [78] 78,24 unequal: No Solution Exploring Operation: 26-3=23, Resulting Numbers: [23] 23,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[10, 33], Operations: ['38-2=36', '36-3=33'] Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,24 unequal: No Solution Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,24 unequal: No Solution Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,24 unequal: No Solution Moving to Node #0,1,3 Current State: 24:[36, 13], Operations: ['38-2=36', '3+10=13'] Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,24 unequal: No Solution Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 3, 6, 72, 7 ]
97
[ "3*6=18", "72+7=79", "18+79=97" ]
Current State: 97:[3, 6, 72, 7], Operations: [] Exploring Operation: 3*6=18, Resulting Numbers: [72, 7, 18] Generated Node #2: [72, 7, 18] from Operation: 3*6=18 Current State: 97:[72, 7, 18], Operations: ['3*6=18'] Exploring Operation: 72+7=79, Resulting Numbers: [18, 79] Generated Node #3: [18, 79] from Operation: 72+7=79 Current State: 97:[18, 79], Operations: ['3*6=18', '72+7=79'] Exploring Operation: 18+79=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[3, 6, 72, 7], Operations: [] Exploring Operation: 6*7=42, Resulting Numbers: [3, 72, 42] Generated Node #0,0: 97:[3, 72, 42] Operation: 6*7=42 Exploring Operation: 3*6=18, Resulting Numbers: [72, 7, 18] Generated Node #0,1: 97:[72, 7, 18] Operation: 3*6=18 Exploring Operation: 3*7=21, Resulting Numbers: [6, 72, 21] Generated Node #0,2: 97:[6, 72, 21] Operation: 3*7=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[3, 72, 42], Operations: ['6*7=42'] Exploring Operation: 3*42=126, Resulting Numbers: [72, 126] Generated Node #0,0,0: 97:[72, 126] Operation: 3*42=126 Exploring Operation: 3+42=45, Resulting Numbers: [72, 45] Generated Node #0,0,1: 97:[72, 45] Operation: 3+42=45 Exploring Operation: 3+72=75, Resulting Numbers: [42, 75] Generated Node #0,0,2: 97:[42, 75] Operation: 3+72=75 Moving to Node #0,0,0 Current State: 97:[72, 126], Operations: ['6*7=42', '3*42=126'] Exploring Operation: 72*126=9072, Resulting Numbers: [9072] 9072,97 unequal: No Solution Exploring Operation: 126-72=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 72+126=198, Resulting Numbers: [198] 198,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[72, 45], Operations: ['6*7=42', '3+42=45'] Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 72*45=3240, Resulting Numbers: [3240] 3240,97 unequal: No Solution Exploring Operation: 72+45=117, Resulting Numbers: [117] 117,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[42, 75], Operations: ['6*7=42', '3+72=75'] Exploring Operation: 42*75=3150, Resulting Numbers: [3150] 3150,97 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,97 unequal: No Solution Exploring Operation: 42+75=117, Resulting Numbers: [117] 117,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[6, 72, 21], Operations: ['3*7=21'] Exploring Operation: 6+72=78, Resulting Numbers: [21, 78] Generated Node #0,2,0: 97:[21, 78] Operation: 6+72=78 Exploring Operation: 6+21=27, Resulting Numbers: [72, 27] Generated Node #0,2,1: 97:[72, 27] Operation: 6+21=27 Exploring Operation: 6*21=126, Resulting Numbers: [72, 126] Generated Node #0,2,2: 97:[72, 126] Operation: 6*21=126 Moving to Node #0,2,2 Current State: 97:[72, 126], Operations: ['3*7=21', '6*21=126'] Exploring Operation: 72+126=198, Resulting Numbers: [198] 198,97 unequal: No Solution Exploring Operation: 126-72=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 72*126=9072, Resulting Numbers: [9072] 9072,97 unequal: No Solution Moving to Node #0,2,0 Current State: 97:[21, 78], Operations: ['3*7=21', '6+72=78'] Exploring Operation: 21+78=99, Resulting Numbers: [99] 99,97 unequal: No Solution Exploring Operation: 21*78=1638, Resulting Numbers: [1638] 1638,97 unequal: No Solution Exploring Operation: 78-21=57, Resulting Numbers: [57] 57,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[72, 27], Operations: ['3*7=21', '6+21=27'] Exploring Operation: 72+27=99, Resulting Numbers: [99] 99,97 unequal: No Solution Exploring Operation: 72*27=1944, Resulting Numbers: [1944] 1944,97 unequal: No Solution Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[72, 7, 18], Operations: ['3*6=18'] Exploring Operation: 72+18=90, Resulting Numbers: [7, 90] Generated Node #0,1,0: 97:[7, 90] Operation: 72+18=90 Exploring Operation: 72+7=79, Resulting Numbers: [18, 79] Generated Node #0,1,1: 97:[18, 79] Operation: 72+7=79 Exploring Operation: 7*18=126, Resulting Numbers: [72, 126] Generated Node #0,1,2: 97:[72, 126] Operation: 7*18=126 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[72, 126], Operations: ['3*6=18', '7*18=126'] Exploring Operation: 126-72=54, Resulting Numbers: [54] 54,97 unequal: No Solution Exploring Operation: 72*126=9072, Resulting Numbers: [9072] 9072,97 unequal: No Solution Exploring Operation: 72+126=198, Resulting Numbers: [198] 198,97 unequal: No Solution No 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: 97:[7, 90], Operations: ['3*6=18', '72+18=90'] Exploring Operation: 7*90=630, Resulting Numbers: [630] 630,97 unequal: No Solution Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[3, 6, 72, 7], Operations: [] Exploring Operation: 3*6=18, Resulting Numbers: [72, 7, 18] Generated Node #0,1: 97:[72, 7, 18] Operation: 3*6=18 Moving to Node #0,1 Current State: 97:[72, 7, 18], Operations: ['3*6=18'] Exploring Operation: 72+18=90, Resulting Numbers: [7, 90] Generated Node #0,1,0: 97:[7, 90] Operation: 72+18=90 Moving to Node #0,1,0 Current State: 97:[7, 90], Operations: ['3*6=18', '72+18=90'] Exploring Operation: 7+90=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.965278
hs_3
sum_heuristic
[ 71, 99, 26, 17 ]
62
[ "99*17=1683", "1683-71=1612", "1612/26=62" ]
Current State: 62:[71, 99, 26, 17], Operations: [] Exploring Operation: 99*17=1683, Resulting Numbers: [71, 26, 1683] Generated Node #2: [71, 26, 1683] from Operation: 99*17=1683 Current State: 62:[71, 26, 1683], Operations: ['99*17=1683'] Exploring Operation: 1683-71=1612, Resulting Numbers: [26, 1612] Generated Node #3: [26, 1612] from Operation: 1683-71=1612 Current State: 62:[26, 1612], Operations: ['99*17=1683', '1683-71=1612'] Exploring Operation: 1612/26=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[71, 99, 26, 17], Operations: [] Exploring Operation: 99-26=73, Resulting Numbers: [71, 17, 73] Generated Node #0,0: 62:[71, 17, 73] Operation: 99-26=73 Exploring Operation: 26-17=9, Resulting Numbers: [71, 99, 9] Generated Node #0,1: 62:[71, 99, 9] Operation: 26-17=9 Exploring Operation: 99-17=82, Resulting Numbers: [71, 26, 82] Generated Node #0,2: 62:[71, 26, 82] Operation: 99-17=82 Exploring Operation: 71-17=54, Resulting Numbers: [99, 26, 54] Generated Node #0,3: 62:[99, 26, 54] Operation: 71-17=54 Exploring Operation: 99-71=28, Resulting Numbers: [26, 17, 28] Generated Node #0,4: 62:[26, 17, 28] Operation: 99-71=28 Start Sub Search at level 1: Moving to Node #0,4 Current State: 62:[26, 17, 28], Operations: ['99-71=28'] Exploring Operation: 17+28=45, Resulting Numbers: [26, 45] Generated Node #0,4,0: 62:[26, 45] Operation: 17+28=45 Exploring Operation: 26-17=9, Resulting Numbers: [28, 9] Generated Node #0,4,1: 62:[28, 9] Operation: 26-17=9 Exploring Operation: 26+17=43, Resulting Numbers: [28, 43] Generated Node #0,4,2: 62:[28, 43] Operation: 26+17=43 Exploring Operation: 28-26=2, Resulting Numbers: [17, 2] Generated Node #0,4,3: 62:[17, 2] Operation: 28-26=2 Exploring Operation: 28-17=11, Resulting Numbers: [26, 11] Generated Node #0,4,4: 62:[26, 11] Operation: 28-17=11 Moving to Node #0,4,1 Current State: 62:[28, 9], Operations: ['99-71=28', '26-17=9'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 28+9=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 28*9=252, Resulting Numbers: [252] 252,62 unequal: No Solution Moving to Node #0,4,4 Current State: 62:[26, 11], Operations: ['99-71=28', '28-17=11'] Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,62 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,62 unequal: No Solution Moving to Node #0,4,3 Current State: 62:[17, 2], Operations: ['99-71=28', '28-26=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,62 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,62 unequal: No Solution Moving to Node #0,4,2 Current State: 62:[28, 43], Operations: ['99-71=28', '26+17=43'] Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 28*43=1204, Resulting Numbers: [1204] 1204,62 unequal: No Solution Exploring Operation: 28+43=71, Resulting Numbers: [71] 71,62 unequal: No Solution Moving to Node #0,4,0 Current State: 62:[26, 45], Operations: ['99-71=28', '17+28=45'] Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,62 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[71, 17, 73], Operations: ['99-26=73'] Exploring Operation: 17+73=90, Resulting Numbers: [71, 90] Generated Node #0,0,0: 62:[71, 90] Operation: 17+73=90 Exploring Operation: 73-17=56, Resulting Numbers: [71, 56] Generated Node #0,0,1: 62:[71, 56] Operation: 73-17=56 Exploring Operation: 71+17=88, Resulting Numbers: [73, 88] Generated Node #0,0,2: 62:[73, 88] Operation: 71+17=88 Exploring Operation: 71-17=54, Resulting Numbers: [73, 54] Generated Node #0,0,3: 62:[73, 54] Operation: 71-17=54 Exploring Operation: 73-71=2, Resulting Numbers: [17, 2] Generated Node #0,0,4: 62:[17, 2] Operation: 73-71=2 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 62:[17, 2], Operations: ['99-26=73', '73-71=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 62:[71, 56], Operations: ['99-26=73', '73-17=56'] Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 62:[73, 54], Operations: ['99-26=73', '71-17=54'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 73*54=3942, Resulting Numbers: [3942] 3942,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[71, 90], Operations: ['99-26=73', '17+73=90'] Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,62 unequal: No Solution Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 62:[73, 88], Operations: ['99-26=73', '71+17=88'] Exploring Operation: 88-73=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 73+88=161, Resulting Numbers: [161] 161,62 unequal: No Solution Exploring Operation: 73*88=6424, Resulting Numbers: [6424] 6424,62 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 #0,2 Current State: 62:[71, 26, 82], Operations: ['99-17=82'] Exploring Operation: 26+82=108, Resulting Numbers: [71, 108] Generated Node #0,2,0: 62:[71, 108] Operation: 26+82=108 Exploring Operation: 71-26=45, Resulting Numbers: [82, 45] Generated Node #0,2,1: 62:[82, 45] Operation: 71-26=45 Exploring Operation: 71+26=97, Resulting Numbers: [82, 97] Generated Node #0,2,2: 62:[82, 97] Operation: 71+26=97 Exploring Operation: 82-26=56, Resulting Numbers: [71, 56] Generated Node #0,2,3: 62:[71, 56] Operation: 82-26=56 Exploring Operation: 82-71=11, Resulting Numbers: [26, 11] Generated Node #0,2,4: 62:[26, 11] Operation: 82-71=11 Moving to Node #0,2,4 Current State: 62:[26, 11], Operations: ['99-17=82', '82-71=11'] Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,62 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,62 unequal: No Solution Moving to Node #0,2,3 Current State: 62:[71, 56], Operations: ['99-17=82', '82-26=56'] Exploring Operation: 71*56=3976, Resulting Numbers: [3976] 3976,62 unequal: No Solution Exploring Operation: 71+56=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 71-56=15, Resulting Numbers: [15] 15,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[82, 45], Operations: ['99-17=82', '71-26=45'] Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 82+45=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 82*45=3690, Resulting Numbers: [3690] 3690,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[71, 108], Operations: ['99-17=82', '26+82=108'] Exploring Operation: 71+108=179, Resulting Numbers: [179] 179,62 unequal: No Solution Exploring Operation: 108-71=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 71*108=7668, Resulting Numbers: [7668] 7668,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[82, 97], Operations: ['99-17=82', '71+26=97'] Exploring Operation: 82+97=179, Resulting Numbers: [179] 179,62 unequal: No Solution Exploring Operation: 97-82=15, Resulting Numbers: [15] 15,62 unequal: No Solution Exploring Operation: 82*97=7954, Resulting Numbers: [7954] 7954,62 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 #0,3 Current State: 62:[99, 26, 54], Operations: ['71-17=54'] Exploring Operation: 99-26=73, Resulting Numbers: [54, 73] Generated Node #0,3,0: 62:[54, 73] Operation: 99-26=73 Exploring Operation: 99+26=125, Resulting Numbers: [54, 125] Generated Node #0,3,1: 62:[54, 125] Operation: 99+26=125 Exploring Operation: 26+54=80, Resulting Numbers: [99, 80] Generated Node #0,3,2: 62:[99, 80] Operation: 26+54=80 Exploring Operation: 99-54=45, Resulting Numbers: [26, 45] Generated Node #0,3,3: 62:[26, 45] Operation: 99-54=45 Exploring Operation: 54-26=28, Resulting Numbers: [99, 28] Generated Node #0,3,4: 62:[99, 28] Operation: 54-26=28 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 62:[54, 73], Operations: ['71-17=54', '99-26=73'] Exploring Operation: 54*73=3942, Resulting Numbers: [3942] 3942,62 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,62 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 #0,3,3 Current State: 62:[26, 45], Operations: ['71-17=54', '99-54=45'] Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,62 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,62 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 #0,3,4 Current State: 62:[99, 28], Operations: ['71-17=54', '54-26=28'] Exploring Operation: 99*28=2772, Resulting Numbers: [2772] 2772,62 unequal: No Solution Exploring Operation: 99+28=127, Resulting Numbers: [127] 127,62 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,62 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 #0,3,2 Current State: 62:[99, 80], Operations: ['71-17=54', '26+54=80'] Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 99+80=179, Resulting Numbers: [179] 179,62 unequal: No Solution Exploring Operation: 99*80=7920, Resulting Numbers: [7920] 7920,62 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 #0,3,1 Current State: 62:[54, 125], Operations: ['71-17=54', '99+26=125'] Exploring Operation: 125-54=71, Resulting Numbers: [71] 71,62 unequal: No Solution Exploring Operation: 54*125=6750, Resulting Numbers: [6750] 6750,62 unequal: No Solution Exploring Operation: 54+125=179, Resulting Numbers: [179] 179,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[71, 99, 9], Operations: ['26-17=9'] Exploring Operation: 99-71=28, Resulting Numbers: [9, 28] Generated Node #0,1,0: 62:[9, 28] Operation: 99-71=28 Exploring Operation: 71+9=80, Resulting Numbers: [99, 80] Generated Node #0,1,1: 62:[99, 80] Operation: 71+9=80 Exploring Operation: 99/9=11, Resulting Numbers: [71, 11] Generated Node #0,1,2: 62:[71, 11] Operation: 99/9=11 Exploring Operation: 71-9=62, Resulting Numbers: [99, 62] Generated Node #0,1,3: 62:[99, 62] Operation: 71-9=62 Exploring Operation: 99-9=90, Resulting Numbers: [71, 90] Generated Node #0,1,4: 62:[71, 90] Operation: 99-9=90 Moving to Node #0,1,0 Current State: 62:[9, 28], Operations: ['26-17=9', '99-71=28'] Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,62 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,62 unequal: No Solution Moving to Node #0,1,2 Current State: 62:[71, 11], Operations: ['26-17=9', '99/9=11'] Exploring Operation: 71*11=781, Resulting Numbers: [781] 781,62 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,62 unequal: No Solution Exploring Operation: 71+11=82, Resulting Numbers: [82] 82,62 unequal: No Solution Moving to Node #0,1,3 Current State: 62:[99, 62], Operations: ['26-17=9', '71-9=62'] Exploring Operation: 99-62=37, Resulting Numbers: [37] 37,62 unequal: No Solution Exploring Operation: 99*62=6138, Resulting Numbers: [6138] 6138,62 unequal: No Solution Exploring Operation: 99+62=161, Resulting Numbers: [161] 161,62 unequal: No Solution Moving to Node #0,1,4 Current State: 62:[71, 90], Operations: ['26-17=9', '99-9=90'] Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,62 unequal: No Solution Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,62 unequal: No Solution Moving to Node #0,1,1 Current State: 62:[99, 80], Operations: ['26-17=9', '71+9=80'] Exploring Operation: 99*80=7920, Resulting Numbers: [7920] 7920,62 unequal: No Solution Exploring Operation: 99-80=19, Resulting Numbers: [19] 19,62 unequal: No Solution Exploring Operation: 99+80=179, Resulting Numbers: [179] 179,62 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
[ 83, 84, 2, 49 ]
49
[ "84-83=1", "2-1=1", "49*1=49" ]
Current State: 49:[83, 84, 2, 49], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [2, 49, 1] Generated Node #2: [2, 49, 1] from Operation: 84-83=1 Current State: 49:[2, 49, 1], Operations: ['84-83=1'] Exploring Operation: 2-1=1, Resulting Numbers: [49, 1] Generated Node #3: [49, 1] from Operation: 2-1=1 Current State: 49:[49, 1], Operations: ['84-83=1', '2-1=1'] Exploring Operation: 49*1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[83, 84, 2, 49], Operations: [] Exploring Operation: 84-83=1, Resulting Numbers: [2, 49, 1] Generated Node #0,0: 49:[2, 49, 1] Operation: 84-83=1 Exploring Operation: 84-49=35, Resulting Numbers: [83, 2, 35] Generated Node #0,1: 49:[83, 2, 35] Operation: 84-49=35 Exploring Operation: 84/2=42, Resulting Numbers: [83, 49, 42] Generated Node #0,2: 49:[83, 49, 42] Operation: 84/2=42 Moving to Node #0,0 Current State: 49:[2, 49, 1], Operations: ['84-83=1'] Exploring Operation: 2+1=3, Resulting Numbers: [49, 3] Generated Node #0,0,0: 49:[49, 3] Operation: 2+1=3 Exploring Operation: 2/1=2, Resulting Numbers: [49, 2] Generated Node #0,0,1: 49:[49, 2] Operation: 2/1=2 Exploring Operation: 2*1=2, Resulting Numbers: [49, 2] Generated Node #0,0,2: 49:[49, 2] Operation: 2*1=2 Moving to Node #0,2 Current State: 49:[83, 49, 42], Operations: ['84/2=42'] Exploring Operation: 49-42=7, Resulting Numbers: [83, 7] Generated Node #0,2,0: 49:[83, 7] Operation: 49-42=7 Exploring Operation: 83-49=34, Resulting Numbers: [42, 34] Generated Node #0,2,1: 49:[42, 34] Operation: 83-49=34 Exploring Operation: 83-42=41, Resulting Numbers: [49, 41] Generated Node #0,2,2: 49:[49, 41] Operation: 83-42=41 Moving to Node #0,1 Current State: 49:[83, 2, 35], Operations: ['84-49=35'] Exploring Operation: 83-2=81, Resulting Numbers: [35, 81] Generated Node #0,1,0: 49:[35, 81] Operation: 83-2=81 Exploring Operation: 83-35=48, Resulting Numbers: [2, 48] Generated Node #0,1,1: 49:[2, 48] Operation: 83-35=48 Exploring Operation: 2+35=37, Resulting Numbers: [83, 37] Generated Node #0,1,2: 49:[83, 37] Operation: 2+35=37 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 49:[2, 48], Operations: ['84-49=35', '83-35=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[35, 81], Operations: ['84-49=35', '83-2=81'] Exploring Operation: 35*81=2835, Resulting Numbers: [2835] 2835,49 unequal: No Solution Exploring Operation: 35+81=116, Resulting Numbers: [116] 116,49 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 49:[83, 37], Operations: ['84-49=35', '2+35=37'] Exploring Operation: 83*37=3071, Resulting Numbers: [3071] 3071,49 unequal: No Solution Exploring Operation: 83+37=120, Resulting Numbers: [120] 120,49 unequal: No Solution Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,49 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: 49:[49, 3], Operations: ['84-83=1', '2+1=3'] Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,49 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,49 unequal: No Solution Moving to Node #0,0,2 Current State: 49:[49, 2], Operations: ['84-83=1', '2*1=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,49 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,49 unequal: No Solution Moving to Node #0,0,1 Current State: 49:[49, 2], Operations: ['84-83=1', '2/1=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,49 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,49 unequal: No Solution Moving to Node #0,2,2 Current State: 49:[49, 41], Operations: ['84/2=42', '83-42=41'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,49 unequal: No Solution Exploring Operation: 49*41=2009, Resulting Numbers: [2009] 2009,49 unequal: No Solution Exploring Operation: 49+41=90, Resulting Numbers: [90] 90,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[42, 34], Operations: ['84/2=42', '83-49=34'] Exploring Operation: 42+34=76, Resulting Numbers: [76] 76,49 unequal: No Solution Exploring Operation: 42*34=1428, Resulting Numbers: [1428] 1428,49 unequal: No Solution Exploring Operation: 42-34=8, Resulting Numbers: [8] 8,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[83, 7], Operations: ['84/2=42', '49-42=7'] Exploring Operation: 83+7=90, Resulting Numbers: [90] 90,49 unequal: No Solution Exploring Operation: 83-7=76, Resulting Numbers: [76] 76,49 unequal: No Solution Exploring Operation: 83*7=581, Resulting Numbers: [581] 581,49 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 44, 12, 20, 16 ]
41
[ "20+16=36", "36/12=3", "44-3=41" ]
Current State: 41:[44, 12, 20, 16], Operations: [] Exploring Operation: 20+16=36, Resulting Numbers: [44, 12, 36] Generated Node #2: [44, 12, 36] from Operation: 20+16=36 Current State: 41:[44, 12, 36], Operations: ['20+16=36'] Exploring Operation: 36/12=3, Resulting Numbers: [44, 3] Generated Node #3: [44, 3] from Operation: 36/12=3 Current State: 41:[44, 3], Operations: ['20+16=36', '36/12=3'] Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[44, 12, 20, 16], Operations: [] Exploring Operation: 12+20=32, Resulting Numbers: [44, 16, 32] Generated Node #0,0: 41:[44, 16, 32] Operation: 12+20=32 Exploring Operation: 12+16=28, Resulting Numbers: [44, 20, 28] Generated Node #0,1: 41:[44, 20, 28] Operation: 12+16=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[44, 16, 32], Operations: ['12+20=32'] Exploring Operation: 16+32=48, Resulting Numbers: [44, 48] Generated Node #0,0,0: 41:[44, 48] Operation: 16+32=48 Exploring Operation: 44-16=28, Resulting Numbers: [32, 28] Generated Node #0,0,1: 41:[32, 28] Operation: 44-16=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[44, 48], Operations: ['12+20=32', '16+32=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[32, 28], Operations: ['12+20=32', '44-16=28'] Exploring Operation: 32-28=4, Resulting Numbers: [4] 4,41 unequal: No Solution Exploring Operation: 32+28=60, Resulting Numbers: [60] 60,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[44, 20, 28], Operations: ['12+16=28'] Exploring Operation: 44-20=24, Resulting Numbers: [28, 24] Generated Node #0,1,0: 41:[28, 24] Operation: 44-20=24 Exploring Operation: 20+28=48, Resulting Numbers: [44, 48] Generated Node #0,1,1: 41:[44, 48] Operation: 20+28=48 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[44, 48], Operations: ['12+16=28', '20+28=48'] Exploring Operation: 44+48=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 48-44=4, Resulting Numbers: [4] 4,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[28, 24], Operations: ['12+16=28', '44-20=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,41 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 88, 76, 33, 99 ]
11
[ "88-76=12", "33+99=132", "132/12=11" ]
Current State: 11:[88, 76, 33, 99], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [33, 99, 12] Generated Node #2: [33, 99, 12] from Operation: 88-76=12 Current State: 11:[33, 99, 12], Operations: ['88-76=12'] Exploring Operation: 33+99=132, Resulting Numbers: [12, 132] Generated Node #3: [12, 132] from Operation: 33+99=132 Current State: 11:[12, 132], Operations: ['88-76=12', '33+99=132'] Exploring Operation: 132/12=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[88, 76, 33, 99], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [33, 99, 12] Generated Node #0,0: 11:[33, 99, 12] Operation: 88-76=12 Exploring Operation: 99-88=11, Resulting Numbers: [76, 33, 11] Generated Node #0,1: 11:[76, 33, 11] Operation: 99-88=11 Moving to Node #0,1 Current State: 11:[76, 33, 11], Operations: ['99-88=11'] Exploring Operation: 76-33=43, Resulting Numbers: [11, 43] Generated Node #0,1,0: 11:[11, 43] Operation: 76-33=43 Exploring Operation: 33/11=3, Resulting Numbers: [76, 3] Generated Node #0,1,1: 11:[76, 3] Operation: 33/11=3 Moving to Node #0,0 Current State: 11:[33, 99, 12], Operations: ['88-76=12'] Exploring Operation: 99/33=3, Resulting Numbers: [12, 3] Generated Node #0,0,0: 11:[12, 3] Operation: 99/33=3 Exploring Operation: 99-33=66, Resulting Numbers: [12, 66] Generated Node #0,0,1: 11:[12, 66] Operation: 99-33=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[12, 3], Operations: ['88-76=12', '99/33=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,11 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,11 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:[12, 66], Operations: ['88-76=12', '99-33=66'] Exploring Operation: 66-12=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 12+66=78, Resulting Numbers: [78] 78,11 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: 11:[11, 43], Operations: ['99-88=11', '76-33=43'] Exploring Operation: 11+43=54, Resulting Numbers: [54] 54,11 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[76, 3], Operations: ['99-88=11', '33/11=3'] Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,11 unequal: No Solution Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,11 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 90, 90, 90, 86 ]
90
[ "90-90=0", "86*0=0", "90+0=90" ]
Current State: 90:[90, 90, 90, 86], Operations: [] Exploring Operation: 90-90=0, Resulting Numbers: [86, 0] Generated Node #2: [86, 0] from Operation: 90-90=0 Current State: 90:[86, 0], Operations: ['90-90=0'] Exploring Operation: 86*0=0, Resulting Numbers: [0] 0,90 equal: Goal Reached Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[90, 90, 90, 86], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [90, 90, 4] Generated Node #0,0: 90:[90, 90, 4] Operation: 90-86=4 Exploring Operation: 90-86=4, Resulting Numbers: [90, 90, 4] Generated Node #0,1: 90:[90, 90, 4] Operation: 90-86=4 Exploring Operation: 90/90=1, Resulting Numbers: [90, 86, 1] Generated Node #0,2: 90:[90, 86, 1] Operation: 90/90=1 Exploring Operation: 90-86=4, Resulting Numbers: [90, 90, 4] Generated Node #0,3: 90:[90, 90, 4] Operation: 90-86=4 Moving to Node #0,0 Current State: 90:[90, 90, 4], Operations: ['90-86=4'] Exploring Operation: 90-90=0, Resulting Numbers: [4, 0] Generated Node #0,0,0: 90:[4, 0] Operation: 90-90=0 Exploring Operation: 90+4=94, Resulting Numbers: [90, 94] Generated Node #0,0,1: 90:[90, 94] Operation: 90+4=94 Exploring Operation: 90-4=86, Resulting Numbers: [90, 86] Generated Node #0,0,2: 90:[90, 86] Operation: 90-4=86 Exploring Operation: 90/90=1, Resulting Numbers: [4, 1] Generated Node #0,0,3: 90:[4, 1] Operation: 90/90=1 Moving to Node #0,3 Current State: 90:[90, 90, 4], Operations: ['90-86=4'] Exploring Operation: 90+4=94, Resulting Numbers: [90, 94] Generated Node #0,3,0: 90:[90, 94] Operation: 90+4=94 Exploring Operation: 90-90=0, Resulting Numbers: [4, 0] Generated Node #0,3,1: 90:[4, 0] Operation: 90-90=0 Exploring Operation: 90/90=1, Resulting Numbers: [4, 1] Generated Node #0,3,2: 90:[4, 1] Operation: 90/90=1 Exploring Operation: 90-4=86, Resulting Numbers: [90, 86] Generated Node #0,3,3: 90:[90, 86] Operation: 90-4=86 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 90:[4, 1], Operations: ['90-86=4', '90/90=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 90:[4, 0], Operations: ['90-86=4', '90-90=0'] Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 90:[90, 94], Operations: ['90-86=4', '90+4=94'] Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,90 unequal: No Solution Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 90:[90, 86], Operations: ['90-86=4', '90-4=86'] Exploring Operation: 90-86=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90+86=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 90*86=7740, Resulting Numbers: [7740] 7740,90 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: 90:[90, 90, 4], Operations: ['90-86=4'] Exploring Operation: 90+4=94, Resulting Numbers: [90, 94] Generated Node #0,1,0: 90:[90, 94] Operation: 90+4=94 Exploring Operation: 90-90=0, Resulting Numbers: [4, 0] Generated Node #0,1,1: 90:[4, 0] Operation: 90-90=0 Exploring Operation: 90-4=86, Resulting Numbers: [90, 86] Generated Node #0,1,2: 90:[90, 86] Operation: 90-4=86 Exploring Operation: 90/90=1, Resulting Numbers: [4, 1] Generated Node #0,1,3: 90:[4, 1] Operation: 90/90=1 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[4, 1], Operations: ['90-86=4', '90/90=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[4, 0], Operations: ['90-86=4', '90-90=0'] Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[90, 94], Operations: ['90-86=4', '90+4=94'] Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,90 unequal: No Solution Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 90:[90, 86], Operations: ['90-86=4', '90-4=86'] Exploring Operation: 90+86=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 90*86=7740, Resulting Numbers: [7740] 7740,90 unequal: No Solution Exploring Operation: 90-86=4, Resulting Numbers: [4] 4,90 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: 90:[90, 86, 1], Operations: ['90/90=1'] Exploring Operation: 90*1=90, Resulting Numbers: [86, 90] Generated Node #0,2,0: 90:[86, 90] Operation: 90*1=90 Exploring Operation: 90-86=4, Resulting Numbers: [1, 4] Generated Node #0,2,1: 90:[1, 4] Operation: 90-86=4 Exploring Operation: 90/1=90, Resulting Numbers: [86, 90] Generated Node #0,2,2: 90:[86, 90] Operation: 90/1=90 Exploring Operation: 86+1=87, Resulting Numbers: [90, 87] Generated Node #0,2,3: 90:[90, 87] Operation: 86+1=87 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 90:[1, 4], Operations: ['90/90=1', '90-86=4'] Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[90, 87], Operations: ['90/90=1', '86+1=87'] Exploring Operation: 90+87=177, Resulting Numbers: [177] 177,90 unequal: No Solution Exploring Operation: 90*87=7830, Resulting Numbers: [7830] 7830,90 unequal: No Solution Exploring Operation: 90-87=3, Resulting Numbers: [3] 3,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 90:[86, 90], Operations: ['90/90=1', '90*1=90'] Exploring Operation: 90-86=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 86*90=7740, Resulting Numbers: [7740] 7740,90 unequal: No Solution Exploring Operation: 86+90=176, Resulting Numbers: [176] 176,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[86, 90], Operations: ['90/90=1', '90/1=90'] Exploring Operation: 86+90=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 86*90=7740, Resulting Numbers: [7740] 7740,90 unequal: No Solution Exploring Operation: 90-86=4, Resulting Numbers: [4] 4,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 90:[4, 1], Operations: ['90-86=4', '90/90=1'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,90 unequal: No Solution Exploring Operation: 4+1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[4, 0], Operations: ['90-86=4', '90-90=0'] Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4+0=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 4*0=0, Resulting Numbers: [0] 0,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[90, 86], Operations: ['90-86=4', '90-4=86'] Exploring Operation: 90-86=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90+86=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 90*86=7740, Resulting Numbers: [7740] 7740,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[90, 94], Operations: ['90-86=4', '90+4=94'] Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,90 unequal: No Solution Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,90 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 98, 38, 89, 82 ]
24
[ "89-82=7", "98/7=14", "38-14=24" ]
Current State: 24:[98, 38, 89, 82], Operations: [] Exploring Operation: 89-82=7, Resulting Numbers: [98, 38, 7] Generated Node #2: [98, 38, 7] from Operation: 89-82=7 Current State: 24:[98, 38, 7], Operations: ['89-82=7'] Exploring Operation: 98/7=14, Resulting Numbers: [38, 14] Generated Node #3: [38, 14] from Operation: 98/7=14 Current State: 24:[38, 14], Operations: ['89-82=7', '98/7=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[98, 38, 89, 82], Operations: [] Exploring Operation: 98-82=16, Resulting Numbers: [38, 89, 16] Generated Node #0,0: 24:[38, 89, 16] Operation: 98-82=16 Exploring Operation: 89-82=7, Resulting Numbers: [98, 38, 7] Generated Node #0,1: 24:[98, 38, 7] Operation: 89-82=7 Exploring Operation: 98-89=9, Resulting Numbers: [38, 82, 9] Generated Node #0,2: 24:[38, 82, 9] Operation: 98-89=9 Moving to Node #0,2 Current State: 24:[38, 82, 9], Operations: ['98-89=9'] Exploring Operation: 82-9=73, Resulting Numbers: [38, 73] Generated Node #0,2,0: 24:[38, 73] Operation: 82-9=73 Exploring Operation: 82-38=44, Resulting Numbers: [9, 44] Generated Node #0,2,1: 24:[9, 44] Operation: 82-38=44 Exploring Operation: 38-9=29, Resulting Numbers: [82, 29] Generated Node #0,2,2: 24:[82, 29] Operation: 38-9=29 Moving to Node #0,0 Current State: 24:[38, 89, 16], Operations: ['98-82=16'] Exploring Operation: 89-16=73, Resulting Numbers: [38, 73] Generated Node #0,0,0: 24:[38, 73] Operation: 89-16=73 Exploring Operation: 89-38=51, Resulting Numbers: [16, 51] Generated Node #0,0,1: 24:[16, 51] Operation: 89-38=51 Exploring Operation: 38-16=22, Resulting Numbers: [89, 22] Generated Node #0,0,2: 24:[89, 22] Operation: 38-16=22 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[16, 51], Operations: ['98-82=16', '89-38=51'] Exploring Operation: 16*51=816, Resulting Numbers: [816] 816,24 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 16+51=67, Resulting Numbers: [67] 67,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[38, 73], Operations: ['98-82=16', '89-16=73'] Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,24 unequal: No Solution Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[89, 22], Operations: ['98-82=16', '38-16=22'] Exploring Operation: 89-22=67, Resulting Numbers: [67] 67,24 unequal: No Solution Exploring Operation: 89+22=111, Resulting Numbers: [111] 111,24 unequal: No Solution Exploring Operation: 89*22=1958, Resulting Numbers: [1958] 1958,24 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: 24:[98, 38, 7], Operations: ['89-82=7'] Exploring Operation: 98-7=91, Resulting Numbers: [38, 91] Generated Node #0,1,0: 24:[38, 91] Operation: 98-7=91 Exploring Operation: 98-38=60, Resulting Numbers: [7, 60] Generated Node #0,1,1: 24:[7, 60] Operation: 98-38=60 Exploring Operation: 98/7=14, Resulting Numbers: [38, 14] Generated Node #0,1,2: 24:[38, 14] Operation: 98/7=14 Moving to Node #0,1,2 Current State: 24:[38, 14], Operations: ['89-82=7', '98/7=14'] Exploring Operation: 38+14=52, Resulting Numbers: [52] 52,24 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[98, 38, 89, 82], Operations: [] Exploring Operation: 89-82=7, Resulting Numbers: [98, 38, 7] Generated Node #0,1: 24:[98, 38, 7] Operation: 89-82=7 Moving to Node #0,1 Current State: 24:[98, 38, 7], Operations: ['89-82=7'] Exploring Operation: 98/7=14, Resulting Numbers: [38, 14] Generated Node #0,1,2: 24:[38, 14] Operation: 98/7=14 Moving to Node #0,1,2 Current State: 24:[38, 14], Operations: ['89-82=7', '98/7=14'] Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.976563
hs_3
sum_heuristic
[ 93, 42, 86, 2 ]
98
[ "93+42=135", "135-86=49", "2*49=98" ]
Current State: 98:[93, 42, 86, 2], Operations: [] Exploring Operation: 93+42=135, Resulting Numbers: [86, 2, 135] Generated Node #2: [86, 2, 135] from Operation: 93+42=135 Current State: 98:[86, 2, 135], Operations: ['93+42=135'] Exploring Operation: 135-86=49, Resulting Numbers: [2, 49] Generated Node #3: [2, 49] from Operation: 135-86=49 Current State: 98:[2, 49], Operations: ['93+42=135', '135-86=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[93, 42, 86, 2], Operations: [] Exploring Operation: 86-42=44, Resulting Numbers: [93, 2, 44] Generated Node #0,0: 98:[93, 2, 44] Operation: 86-42=44 Exploring Operation: 93-86=7, Resulting Numbers: [42, 2, 7] Generated Node #0,1: 98:[42, 2, 7] Operation: 93-86=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[42, 2, 7], Operations: ['93-86=7'] Exploring Operation: 42/7=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 98:[2, 6] Operation: 42/7=6 Exploring Operation: 42+7=49, Resulting Numbers: [2, 49] Generated Node #0,1,1: 98:[2, 49] Operation: 42+7=49 Moving to Node #0,1,1 Current State: 98:[2, 49], Operations: ['93-86=7', '42+7=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,98 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[93, 42, 86, 2], Operations: [] Exploring Operation: 93-86=7, Resulting Numbers: [42, 2, 7] Generated Node #0,1: 98:[42, 2, 7] Operation: 93-86=7 Moving to Node #0,1 Current State: 98:[42, 2, 7], Operations: ['93-86=7'] Exploring Operation: 42+7=49, Resulting Numbers: [2, 49] Generated Node #0,1,1: 98:[2, 49] Operation: 42+7=49 Moving to Node #0,1,1 Current State: 98:[2, 49], Operations: ['93-86=7', '42+7=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 16, 2, 38, 23 ]
85
[ "16+38=54", "2*54=108", "108-23=85" ]
Current State: 85:[16, 2, 38, 23], Operations: [] Exploring Operation: 16+38=54, Resulting Numbers: [2, 23, 54] Generated Node #2: [2, 23, 54] from Operation: 16+38=54 Current State: 85:[2, 23, 54], Operations: ['16+38=54'] Exploring Operation: 2*54=108, Resulting Numbers: [23, 108] Generated Node #3: [23, 108] from Operation: 2*54=108 Current State: 85:[23, 108], Operations: ['16+38=54', '2*54=108'] Exploring Operation: 108-23=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[16, 2, 38, 23], Operations: [] Exploring Operation: 2*38=76, Resulting Numbers: [16, 23, 76] Generated Node #0,0: 85:[16, 23, 76] Operation: 2*38=76 Exploring Operation: 38-23=15, Resulting Numbers: [16, 2, 15] Generated Node #0,1: 85:[16, 2, 15] Operation: 38-23=15 Exploring Operation: 38-16=22, Resulting Numbers: [2, 23, 22] Generated Node #0,2: 85:[2, 23, 22] Operation: 38-16=22 Exploring Operation: 38/2=19, Resulting Numbers: [16, 23, 19] Generated Node #0,3: 85:[16, 23, 19] Operation: 38/2=19 Moving to Node #0,1 Current State: 85:[16, 2, 15], Operations: ['38-23=15'] Exploring Operation: 16-2=14, Resulting Numbers: [15, 14] Generated Node #0,1,0: 85:[15, 14] Operation: 16-2=14 Exploring Operation: 2+15=17, Resulting Numbers: [16, 17] Generated Node #0,1,1: 85:[16, 17] Operation: 2+15=17 Exploring Operation: 16+2=18, Resulting Numbers: [15, 18] Generated Node #0,1,2: 85:[15, 18] Operation: 16+2=18 Exploring Operation: 16/2=8, Resulting Numbers: [15, 8] Generated Node #0,1,3: 85:[15, 8] Operation: 16/2=8 Moving to Node #0,3 Current State: 85:[16, 23, 19], Operations: ['38/2=19'] Exploring Operation: 16+23=39, Resulting Numbers: [19, 39] Generated Node #0,3,0: 85:[19, 39] Operation: 16+23=39 Exploring Operation: 19-16=3, Resulting Numbers: [23, 3] Generated Node #0,3,1: 85:[23, 3] Operation: 19-16=3 Exploring Operation: 23-16=7, Resulting Numbers: [19, 7] Generated Node #0,3,2: 85:[19, 7] Operation: 23-16=7 Exploring Operation: 23-19=4, Resulting Numbers: [16, 4] Generated Node #0,3,3: 85:[16, 4] Operation: 23-19=4 Moving to Node #0,2 Current State: 85:[2, 23, 22], Operations: ['38-16=22'] Exploring Operation: 23-22=1, Resulting Numbers: [2, 1] Generated Node #0,2,0: 85:[2, 1] Operation: 23-22=1 Exploring Operation: 23-2=21, Resulting Numbers: [22, 21] Generated Node #0,2,1: 85:[22, 21] Operation: 23-2=21 Exploring Operation: 22/2=11, Resulting Numbers: [23, 11] Generated Node #0,2,2: 85:[23, 11] Operation: 22/2=11 Exploring Operation: 22-2=20, Resulting Numbers: [23, 20] Generated Node #0,2,3: 85:[23, 20] Operation: 22-2=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 85:[2, 1], Operations: ['38-16=22', '23-22=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,85 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 #0,2,1 Current State: 85:[22, 21], Operations: ['38-16=22', '23-2=21'] Exploring Operation: 22-21=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 22+21=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 22*21=462, Resulting Numbers: [462] 462,85 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 #0,2,3 Current State: 85:[23, 20], Operations: ['38-16=22', '22-2=20'] Exploring Operation: 23*20=460, Resulting Numbers: [460] 460,85 unequal: No Solution Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,85 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 #0,2,2 Current State: 85:[23, 11], Operations: ['38-16=22', '22/2=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,85 unequal: No Solution Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 85:[16, 23, 76], Operations: ['2*38=76'] Exploring Operation: 23+76=99, Resulting Numbers: [16, 99] Generated Node #0,0,0: 85:[16, 99] Operation: 23+76=99 Exploring Operation: 16+23=39, Resulting Numbers: [76, 39] Generated Node #0,0,1: 85:[76, 39] Operation: 16+23=39 Exploring Operation: 23-16=7, Resulting Numbers: [76, 7] Generated Node #0,0,2: 85:[76, 7] Operation: 23-16=7 Exploring Operation: 16+76=92, Resulting Numbers: [23, 92] Generated Node #0,0,3: 85:[23, 92] Operation: 16+76=92 Moving to Node #0,1,1 Current State: 85:[16, 17], Operations: ['38-23=15', '2+15=17'] Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,85 unequal: No Solution Moving to Node #0,3,3 Current State: 85:[16, 4], Operations: ['38/2=19', '23-19=4'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,85 unequal: No Solution Exploring Operation: 16+4=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[15, 18], Operations: ['38-23=15', '16+2=18'] Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,85 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,85 unequal: No Solution Moving to Node #0,3,2 Current State: 85:[19, 7], Operations: ['38/2=19', '23-16=7'] Exploring Operation: 19*7=133, Resulting Numbers: [133] 133,85 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 19+7=26, Resulting Numbers: [26] 26,85 unequal: No Solution Moving to Node #0,1,0 Current State: 85:[15, 14], Operations: ['38-23=15', '16-2=14'] Exploring Operation: 15+14=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 15-14=1, Resulting Numbers: [1] 1,85 unequal: No Solution Exploring Operation: 15*14=210, Resulting Numbers: [210] 210,85 unequal: No Solution Moving to Node #0,1,3 Current State: 85:[15, 8], Operations: ['38-23=15', '16/2=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,85 unequal: No Solution Moving to Node #0,3,1 Current State: 85:[23, 3], Operations: ['38/2=19', '19-16=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,85 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,85 unequal: No Solution Moving to Node #0,0,2 Current State: 85:[76, 7], Operations: ['2*38=76', '23-16=7'] Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 76*7=532, Resulting Numbers: [532] 532,85 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[23, 92], Operations: ['2*38=76', '16+76=92'] Exploring Operation: 23*92=2116, Resulting Numbers: [2116] 2116,85 unequal: No Solution Exploring Operation: 23+92=115, Resulting Numbers: [115] 115,85 unequal: No Solution Exploring Operation: 92/23=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 92-23=69, Resulting Numbers: [69] 69,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[16, 99], Operations: ['2*38=76', '23+76=99'] Exploring Operation: 16*99=1584, Resulting Numbers: [1584] 1584,85 unequal: No Solution Exploring Operation: 99-16=83, Resulting Numbers: [83] 83,85 unequal: No Solution Exploring Operation: 16+99=115, Resulting Numbers: [115] 115,85 unequal: No Solution Moving to Node #0,3,0 Current State: 85:[19, 39], Operations: ['38/2=19', '16+23=39'] Exploring Operation: 19*39=741, Resulting Numbers: [741] 741,85 unequal: No Solution Exploring Operation: 19+39=58, Resulting Numbers: [58] 58,85 unequal: No Solution Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,85 unequal: No Solution Moving to Node #0,0,1 Current State: 85:[76, 39], Operations: ['2*38=76', '16+23=39'] Exploring Operation: 76*39=2964, Resulting Numbers: [2964] 2964,85 unequal: No Solution Exploring Operation: 76-39=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 76+39=115, Resulting Numbers: [115] 115,85 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 2, 54, 47, 60 ]
100
[ "2*47=94", "60-54=6", "94+6=100" ]
Current State: 100:[2, 54, 47, 60], Operations: [] Exploring Operation: 2*47=94, Resulting Numbers: [54, 60, 94] Generated Node #2: [54, 60, 94] from Operation: 2*47=94 Current State: 100:[54, 60, 94], Operations: ['2*47=94'] Exploring Operation: 60-54=6, Resulting Numbers: [94, 6] Generated Node #3: [94, 6] from Operation: 60-54=6 Current State: 100:[94, 6], Operations: ['2*47=94', '60-54=6'] Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[2, 54, 47, 60], Operations: [] Exploring Operation: 60-47=13, Resulting Numbers: [2, 54, 13] Generated Node #0,0: 100:[2, 54, 13] Operation: 60-47=13 Exploring Operation: 60-54=6, Resulting Numbers: [2, 47, 6] Generated Node #0,1: 100:[2, 47, 6] Operation: 60-54=6 Exploring Operation: 54+47=101, Resulting Numbers: [2, 60, 101] Generated Node #0,2: 100:[2, 60, 101] Operation: 54+47=101 Exploring Operation: 47+60=107, Resulting Numbers: [2, 54, 107] Generated Node #0,3: 100:[2, 54, 107] Operation: 47+60=107 Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[2, 47, 6], Operations: ['60-54=6'] Exploring Operation: 6-2=4, Resulting Numbers: [47, 4] Generated Node #0,1,0: 100:[47, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [47, 3] Generated Node #0,1,1: 100:[47, 3] Operation: 6/2=3 Exploring Operation: 2+47=49, Resulting Numbers: [6, 49] Generated Node #0,1,2: 100:[6, 49] Operation: 2+47=49 Exploring Operation: 47+6=53, Resulting Numbers: [2, 53] Generated Node #0,1,3: 100:[2, 53] Operation: 47+6=53 Moving to Node #0,1,2 Current State: 100:[6, 49], Operations: ['60-54=6', '2+47=49'] Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 6*49=294, Resulting Numbers: [294] 294,100 unequal: No Solution Exploring Operation: 49-6=43, Resulting Numbers: [43] 43,100 unequal: No Solution Moving to Node #0,1,3 Current State: 100:[2, 53], Operations: ['60-54=6', '47+6=53'] Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,100 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,100 unequal: No Solution Moving to Node #0,1,0 Current State: 100:[47, 4], Operations: ['60-54=6', '6-2=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,100 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[47, 3], Operations: ['60-54=6', '6/2=3'] Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,100 unequal: No Solution Exploring Operation: 47+3=50, Resulting Numbers: [50] 50,100 unequal: No Solution Exploring Operation: 47*3=141, Resulting Numbers: [141] 141,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[2, 54, 13], Operations: ['60-47=13'] Exploring Operation: 54-2=52, Resulting Numbers: [13, 52] Generated Node #0,0,0: 100:[13, 52] Operation: 54-2=52 Exploring Operation: 2*13=26, Resulting Numbers: [54, 26] Generated Node #0,0,1: 100:[54, 26] Operation: 2*13=26 Exploring Operation: 54/2=27, Resulting Numbers: [13, 27] Generated Node #0,0,2: 100:[13, 27] Operation: 54/2=27 Exploring Operation: 13-2=11, Resulting Numbers: [54, 11] Generated Node #0,0,3: 100:[54, 11] Operation: 13-2=11 Moving to Node #0,0,0 Current State: 100:[13, 52], Operations: ['60-47=13', '54-2=52'] Exploring Operation: 13*52=676, Resulting Numbers: [676] 676,100 unequal: No Solution Exploring Operation: 52-13=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 13+52=65, Resulting Numbers: [65] 65,100 unequal: No Solution Exploring Operation: 52/13=4, Resulting Numbers: [4] 4,100 unequal: No Solution Moving to Node #0,0,2 Current State: 100:[13, 27], Operations: ['60-47=13', '54/2=27'] Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,100 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,100 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[54, 26], Operations: ['60-47=13', '2*13=26'] Exploring Operation: 54-26=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 54+26=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 54*26=1404, Resulting Numbers: [1404] 1404,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[54, 11], Operations: ['60-47=13', '13-2=11'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,100 unequal: No Solution Exploring Operation: 54*11=594, Resulting Numbers: [594] 594,100 unequal: No Solution Exploring Operation: 54+11=65, Resulting Numbers: [65] 65,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 100:[2, 60, 101], Operations: ['54+47=101'] Exploring Operation: 60/2=30, Resulting Numbers: [101, 30] Generated Node #0,2,0: 100:[101, 30] Operation: 60/2=30 Exploring Operation: 101-2=99, Resulting Numbers: [60, 99] Generated Node #0,2,1: 100:[60, 99] Operation: 101-2=99 Exploring Operation: 101-60=41, Resulting Numbers: [2, 41] Generated Node #0,2,2: 100:[2, 41] Operation: 101-60=41 Exploring Operation: 60-2=58, Resulting Numbers: [101, 58] Generated Node #0,2,3: 100:[101, 58] Operation: 60-2=58 Moving to Node #0,2,0 Current State: 100:[101, 30], Operations: ['54+47=101', '60/2=30'] Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,100 unequal: No Solution Exploring Operation: 101+30=131, Resulting Numbers: [131] 131,100 unequal: No Solution Exploring Operation: 101*30=3030, Resulting Numbers: [3030] 3030,100 unequal: No Solution Moving to Node #0,2,3 Current State: 100:[101, 58], Operations: ['54+47=101', '60-2=58'] Exploring Operation: 101+58=159, Resulting Numbers: [159] 159,100 unequal: No Solution Exploring Operation: 101*58=5858, Resulting Numbers: [5858] 5858,100 unequal: No Solution Exploring Operation: 101-58=43, Resulting Numbers: [43] 43,100 unequal: No Solution Moving to Node #0,2,2 Current State: 100:[2, 41], Operations: ['54+47=101', '101-60=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,100 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,100 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,100 unequal: No Solution Moving to Node #0,2,1 Current State: 100:[60, 99], Operations: ['54+47=101', '101-2=99'] Exploring Operation: 60*99=5940, Resulting Numbers: [5940] 5940,100 unequal: No Solution Exploring Operation: 60+99=159, Resulting Numbers: [159] 159,100 unequal: No Solution Exploring Operation: 99-60=39, Resulting Numbers: [39] 39,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[2, 54, 107], Operations: ['47+60=107'] Exploring Operation: 54-2=52, Resulting Numbers: [107, 52] Generated Node #0,3,0: 100:[107, 52] Operation: 54-2=52 Exploring Operation: 54/2=27, Resulting Numbers: [107, 27] Generated Node #0,3,1: 100:[107, 27] Operation: 54/2=27 Exploring Operation: 107-54=53, Resulting Numbers: [2, 53] Generated Node #0,3,2: 100:[2, 53] Operation: 107-54=53 Exploring Operation: 107-2=105, Resulting Numbers: [54, 105] Generated Node #0,3,3: 100:[54, 105] Operation: 107-2=105 Moving to Node #0,3,2 Current State: 100:[2, 53], Operations: ['47+60=107', '107-54=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,100 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,100 unequal: No Solution Moving to Node #0,3,1 Current State: 100:[107, 27], Operations: ['47+60=107', '54/2=27'] Exploring Operation: 107*27=2889, Resulting Numbers: [2889] 2889,100 unequal: No Solution Exploring Operation: 107-27=80, Resulting Numbers: [80] 80,100 unequal: No Solution Exploring Operation: 107+27=134, Resulting Numbers: [134] 134,100 unequal: No Solution Moving to Node #0,3,0 Current State: 100:[107, 52], Operations: ['47+60=107', '54-2=52'] Exploring Operation: 107-52=55, Resulting Numbers: [55] 55,100 unequal: No Solution Exploring Operation: 107*52=5564, Resulting Numbers: [5564] 5564,100 unequal: No Solution Exploring Operation: 107+52=159, Resulting Numbers: [159] 159,100 unequal: No Solution Moving to Node #0,3,3 Current State: 100:[54, 105], Operations: ['47+60=107', '107-2=105'] Exploring Operation: 54*105=5670, Resulting Numbers: [5670] 5670,100 unequal: No Solution Exploring Operation: 105-54=51, Resulting Numbers: [51] 51,100 unequal: No Solution Exploring Operation: 54+105=159, Resulting Numbers: [159] 159,100 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
[ 2, 68, 99, 74 ]
28
[ "68+74=142", "142/2=71", "99-71=28" ]
Current State: 28:[2, 68, 99, 74], Operations: [] Exploring Operation: 68+74=142, Resulting Numbers: [2, 99, 142] Generated Node #2: [2, 99, 142] from Operation: 68+74=142 Current State: 28:[2, 99, 142], Operations: ['68+74=142'] Exploring Operation: 142/2=71, Resulting Numbers: [99, 71] Generated Node #3: [99, 71] from Operation: 142/2=71 Current State: 28:[99, 71], Operations: ['68+74=142', '142/2=71'] Exploring Operation: 99-71=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[2, 68, 99, 74], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [2, 99, 6] Generated Node #0,0: 28:[2, 99, 6] Operation: 74-68=6 Exploring Operation: 99-68=31, Resulting Numbers: [2, 74, 31] Generated Node #0,1: 28:[2, 74, 31] Operation: 99-68=31 Exploring Operation: 68/2=34, Resulting Numbers: [99, 74, 34] Generated Node #0,2: 28:[99, 74, 34] Operation: 68/2=34 Exploring Operation: 99-74=25, Resulting Numbers: [2, 68, 25] Generated Node #0,3: 28:[2, 68, 25] Operation: 99-74=25 Exploring Operation: 74/2=37, Resulting Numbers: [68, 99, 37] Generated Node #0,4: 28:[68, 99, 37] Operation: 74/2=37 Moving to Node #0,3 Current State: 28:[2, 68, 25], Operations: ['99-74=25'] Exploring Operation: 68-25=43, Resulting Numbers: [2, 43] Generated Node #0,3,0: 28:[2, 43] Operation: 68-25=43 Exploring Operation: 2+25=27, Resulting Numbers: [68, 27] Generated Node #0,3,1: 28:[68, 27] Operation: 2+25=27 Exploring Operation: 68-2=66, Resulting Numbers: [25, 66] Generated Node #0,3,2: 28:[25, 66] Operation: 68-2=66 Exploring Operation: 2+68=70, Resulting Numbers: [25, 70] Generated Node #0,3,3: 28:[25, 70] Operation: 2+68=70 Exploring Operation: 68/2=34, Resulting Numbers: [25, 34] Generated Node #0,3,4: 28:[25, 34] Operation: 68/2=34 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 28:[25, 34], Operations: ['99-74=25', '68/2=34'] Exploring Operation: 25*34=850, Resulting Numbers: [850] 850,28 unequal: No Solution Exploring Operation: 25+34=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,28 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 #0,3,0 Current State: 28:[2, 43], Operations: ['99-74=25', '68-25=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,28 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 #0,3,1 Current State: 28:[68, 27], Operations: ['99-74=25', '2+25=27'] Exploring Operation: 68+27=95, Resulting Numbers: [95] 95,28 unequal: No Solution Exploring Operation: 68*27=1836, Resulting Numbers: [1836] 1836,28 unequal: No Solution Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,28 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 #0,3,2 Current State: 28:[25, 66], Operations: ['99-74=25', '68-2=66'] Exploring Operation: 25*66=1650, Resulting Numbers: [1650] 1650,28 unequal: No Solution Exploring Operation: 25+66=91, Resulting Numbers: [91] 91,28 unequal: No Solution Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,28 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 #0,3,3 Current State: 28:[25, 70], Operations: ['99-74=25', '2+68=70'] Exploring Operation: 25+70=95, Resulting Numbers: [95] 95,28 unequal: No Solution Exploring Operation: 70-25=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 25*70=1750, Resulting Numbers: [1750] 1750,28 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: 28:[2, 74, 31], Operations: ['99-68=31'] Exploring Operation: 2+74=76, Resulting Numbers: [31, 76] Generated Node #0,1,0: 28:[31, 76] Operation: 2+74=76 Exploring Operation: 74-31=43, Resulting Numbers: [2, 43] Generated Node #0,1,1: 28:[2, 43] Operation: 74-31=43 Exploring Operation: 74/2=37, Resulting Numbers: [31, 37] Generated Node #0,1,2: 28:[31, 37] Operation: 74/2=37 Exploring Operation: 31-2=29, Resulting Numbers: [74, 29] Generated Node #0,1,3: 28:[74, 29] Operation: 31-2=29 Exploring Operation: 74-2=72, Resulting Numbers: [31, 72] Generated Node #0,1,4: 28:[31, 72] Operation: 74-2=72 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[31, 37], Operations: ['99-68=31', '74/2=37'] Exploring Operation: 31+37=68, Resulting Numbers: [68] 68,28 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 31*37=1147, Resulting Numbers: [1147] 1147,28 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 #0,1,1 Current State: 28:[2, 43], Operations: ['99-68=31', '74-31=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,28 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,28 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 #0,1,3 Current State: 28:[74, 29], Operations: ['99-68=31', '31-2=29'] Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,28 unequal: No Solution Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,28 unequal: No Solution Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,28 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 #0,1,4 Current State: 28:[31, 72], Operations: ['99-68=31', '74-2=72'] Exploring Operation: 31*72=2232, Resulting Numbers: [2232] 2232,28 unequal: No Solution Exploring Operation: 31+72=103, Resulting Numbers: [103] 103,28 unequal: No Solution Exploring Operation: 72-31=41, Resulting Numbers: [41] 41,28 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 #0,1,0 Current State: 28:[31, 76], Operations: ['99-68=31', '2+74=76'] Exploring Operation: 31+76=107, Resulting Numbers: [107] 107,28 unequal: No Solution Exploring Operation: 31*76=2356, Resulting Numbers: [2356] 2356,28 unequal: No Solution Exploring Operation: 76-31=45, Resulting Numbers: [45] 45,28 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: 28:[2, 99, 6], Operations: ['74-68=6'] Exploring Operation: 2+6=8, Resulting Numbers: [99, 8] Generated Node #0,0,0: 28:[99, 8] Operation: 2+6=8 Exploring Operation: 99-6=93, Resulting Numbers: [2, 93] Generated Node #0,0,1: 28:[2, 93] Operation: 99-6=93 Exploring Operation: 99-2=97, Resulting Numbers: [6, 97] Generated Node #0,0,2: 28:[6, 97] Operation: 99-2=97 Exploring Operation: 6-2=4, Resulting Numbers: [99, 4] Generated Node #0,0,3: 28:[99, 4] Operation: 6-2=4 Exploring Operation: 6/2=3, Resulting Numbers: [99, 3] Generated Node #0,0,4: 28:[99, 3] Operation: 6/2=3 Moving to Node #0,4 Current State: 28:[68, 99, 37], Operations: ['74/2=37'] Exploring Operation: 68-37=31, Resulting Numbers: [99, 31] Generated Node #0,4,0: 28:[99, 31] Operation: 68-37=31 Exploring Operation: 99-37=62, Resulting Numbers: [68, 62] Generated Node #0,4,1: 28:[68, 62] Operation: 99-37=62 Exploring Operation: 68+37=105, Resulting Numbers: [99, 105] Generated Node #0,4,2: 28:[99, 105] Operation: 68+37=105 Exploring Operation: 99-68=31, Resulting Numbers: [37, 31] Generated Node #0,4,3: 28:[37, 31] Operation: 99-68=31 Exploring Operation: 68+99=167, Resulting Numbers: [37, 167] Generated Node #0,4,4: 28:[37, 167] Operation: 68+99=167 Moving to Node #0,2 Current State: 28:[99, 74, 34], Operations: ['68/2=34'] Exploring Operation: 99+34=133, Resulting Numbers: [74, 133] Generated Node #0,2,0: 28:[74, 133] Operation: 99+34=133 Exploring Operation: 99-34=65, Resulting Numbers: [74, 65] Generated Node #0,2,1: 28:[74, 65] Operation: 99-34=65 Exploring Operation: 99+74=173, Resulting Numbers: [34, 173] Generated Node #0,2,2: 28:[34, 173] Operation: 99+74=173 Exploring Operation: 99-74=25, Resulting Numbers: [34, 25] Generated Node #0,2,3: 28:[34, 25] Operation: 99-74=25 Exploring Operation: 74-34=40, Resulting Numbers: [99, 40] Generated Node #0,2,4: 28:[99, 40] Operation: 74-34=40 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 28:[34, 25], Operations: ['68/2=34', '99-74=25'] Exploring Operation: 34+25=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 34*25=850, Resulting Numbers: [850] 850,28 unequal: No Solution Exploring Operation: 34-25=9, Resulting Numbers: [9] 9,28 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 #0,2,1 Current State: 28:[74, 65], Operations: ['68/2=34', '99-34=65'] Exploring Operation: 74*65=4810, Resulting Numbers: [4810] 4810,28 unequal: No Solution Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,28 unequal: No Solution Exploring Operation: 74+65=139, Resulting Numbers: [139] 139,28 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 #0,2,4 Current State: 28:[99, 40], Operations: ['68/2=34', '74-34=40'] Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,28 unequal: No Solution Exploring Operation: 99+40=139, Resulting Numbers: [139] 139,28 unequal: No Solution Exploring Operation: 99*40=3960, Resulting Numbers: [3960] 3960,28 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 #0,2,0 Current State: 28:[74, 133], Operations: ['68/2=34', '99+34=133'] Exploring Operation: 74+133=207, Resulting Numbers: [207] 207,28 unequal: No Solution Exploring Operation: 74*133=9842, Resulting Numbers: [9842] 9842,28 unequal: No Solution Exploring Operation: 133-74=59, Resulting Numbers: [59] 59,28 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 #0,2,2 Current State: 28:[34, 173], Operations: ['68/2=34', '99+74=173'] Exploring Operation: 173-34=139, Resulting Numbers: [139] 139,28 unequal: No Solution Exploring Operation: 34*173=5882, Resulting Numbers: [5882] 5882,28 unequal: No Solution Exploring Operation: 34+173=207, Resulting Numbers: [207] 207,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,3 Current State: 28:[37, 31], Operations: ['74/2=37', '99-68=31'] Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,28 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,28 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[2, 93], Operations: ['74-68=6', '99-6=93'] Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,28 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,28 unequal: No Solution Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,28 unequal: No Solution Moving to Node #0,0,2 Current State: 28:[6, 97], Operations: ['74-68=6', '99-2=97'] Exploring Operation: 6*97=582, Resulting Numbers: [582] 582,28 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,28 unequal: No Solution Exploring Operation: 6+97=103, Resulting Numbers: [103] 103,28 unequal: No Solution Moving to Node #0,0,3 Current State: 28:[99, 4], Operations: ['74-68=6', '6-2=4'] Exploring Operation: 99+4=103, Resulting Numbers: [103] 103,28 unequal: No Solution Exploring Operation: 99*4=396, Resulting Numbers: [396] 396,28 unequal: No Solution Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,28 unequal: No Solution Moving to Node #0,0,4 Current State: 28:[99, 3], Operations: ['74-68=6', '6/2=3'] Exploring Operation: 99/3=33, Resulting Numbers: [33] 33,28 unequal: No Solution Exploring Operation: 99-3=96, Resulting Numbers: [96] 96,28 unequal: No Solution Exploring Operation: 99+3=102, Resulting Numbers: [102] 102,28 unequal: No Solution Exploring Operation: 99*3=297, Resulting Numbers: [297] 297,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[99, 8], Operations: ['74-68=6', '2+6=8'] Exploring Operation: 99+8=107, Resulting Numbers: [107] 107,28 unequal: No Solution Exploring Operation: 99*8=792, Resulting Numbers: [792] 792,28 unequal: No Solution Exploring Operation: 99-8=91, Resulting Numbers: [91] 91,28 unequal: No Solution Moving to Node #0,4,0 Current State: 28:[99, 31], Operations: ['74/2=37', '68-37=31'] Exploring Operation: 99*31=3069, Resulting Numbers: [3069] 3069,28 unequal: No Solution Exploring Operation: 99+31=130, Resulting Numbers: [130] 130,28 unequal: No Solution Exploring Operation: 99-31=68, Resulting Numbers: [68] 68,28 unequal: No Solution Moving to Node #0,4,1 Current State: 28:[68, 62], Operations: ['74/2=37', '99-37=62'] Exploring Operation: 68-62=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 68*62=4216, Resulting Numbers: [4216] 4216,28 unequal: No Solution Exploring Operation: 68+62=130, Resulting Numbers: [130] 130,28 unequal: No Solution Moving to Node #0,4,4 Current State: 28:[37, 167], Operations: ['74/2=37', '68+99=167'] Exploring Operation: 37*167=6179, Resulting Numbers: [6179] 6179,28 unequal: No Solution Exploring Operation: 167-37=130, Resulting Numbers: [130] 130,28 unequal: No Solution Exploring Operation: 37+167=204, Resulting Numbers: [204] 204,28 unequal: No Solution Moving to Node #0,4,2 Current State: 28:[99, 105], Operations: ['74/2=37', '68+37=105'] Exploring Operation: 99*105=10395, Resulting Numbers: [10395] 10395,28 unequal: No Solution Exploring Operation: 105-99=6, Resulting Numbers: [6] 6,28 unequal: No Solution Exploring Operation: 99+105=204, Resulting Numbers: [204] 204,28 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 96, 6, 86, 78 ]
23
[ "96-86=10", "78/6=13", "10+13=23" ]
Current State: 23:[96, 6, 86, 78], Operations: [] Exploring Operation: 96-86=10, Resulting Numbers: [6, 78, 10] Generated Node #2: [6, 78, 10] from Operation: 96-86=10 Current State: 23:[6, 78, 10], Operations: ['96-86=10'] Exploring Operation: 78/6=13, Resulting Numbers: [10, 13] Generated Node #3: [10, 13] from Operation: 78/6=13 Current State: 23:[10, 13], Operations: ['96-86=10', '78/6=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[96, 6, 86, 78], Operations: [] Exploring Operation: 78/6=13, Resulting Numbers: [96, 86, 13] Generated Node #0,0: 23:[96, 86, 13] Operation: 78/6=13 Exploring Operation: 96-86=10, Resulting Numbers: [6, 78, 10] Generated Node #0,1: 23:[6, 78, 10] Operation: 96-86=10 Exploring Operation: 86-78=8, Resulting Numbers: [96, 6, 8] Generated Node #0,2: 23:[96, 6, 8] Operation: 86-78=8 Exploring Operation: 96-78=18, Resulting Numbers: [6, 86, 18] Generated Node #0,3: 23:[6, 86, 18] Operation: 96-78=18 Exploring Operation: 96/6=16, Resulting Numbers: [86, 78, 16] Generated Node #0,4: 23:[86, 78, 16] Operation: 96/6=16 Moving to Node #0,1 Current State: 23:[6, 78, 10], Operations: ['96-86=10'] Exploring Operation: 6+78=84, Resulting Numbers: [10, 84] Generated Node #0,1,0: 23:[10, 84] Operation: 6+78=84 Exploring Operation: 78-6=72, Resulting Numbers: [10, 72] Generated Node #0,1,1: 23:[10, 72] Operation: 78-6=72 Exploring Operation: 6+10=16, Resulting Numbers: [78, 16] Generated Node #0,1,2: 23:[78, 16] Operation: 6+10=16 Exploring Operation: 78-10=68, Resulting Numbers: [6, 68] Generated Node #0,1,3: 23:[6, 68] Operation: 78-10=68 Exploring Operation: 78/6=13, Resulting Numbers: [10, 13] Generated Node #0,1,4: 23:[10, 13] Operation: 78/6=13 Moving to Node #0,3 Current State: 23:[6, 86, 18], Operations: ['96-78=18'] Exploring Operation: 86-6=80, Resulting Numbers: [18, 80] Generated Node #0,3,0: 23:[18, 80] Operation: 86-6=80 Exploring Operation: 6+18=24, Resulting Numbers: [86, 24] Generated Node #0,3,1: 23:[86, 24] Operation: 6+18=24 Exploring Operation: 6+86=92, Resulting Numbers: [18, 92] Generated Node #0,3,2: 23:[18, 92] Operation: 6+86=92 Exploring Operation: 18-6=12, Resulting Numbers: [86, 12] Generated Node #0,3,3: 23:[86, 12] Operation: 18-6=12 Exploring Operation: 86-18=68, Resulting Numbers: [6, 68] Generated Node #0,3,4: 23:[6, 68] Operation: 86-18=68 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 23:[18, 80], Operations: ['96-78=18', '86-6=80'] Exploring Operation: 18*80=1440, Resulting Numbers: [1440] 1440,23 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 18+80=98, Resulting Numbers: [98] 98,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 23:[6, 68], Operations: ['96-78=18', '86-18=68'] Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,23 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[86, 24], Operations: ['96-78=18', '6+18=24'] Exploring Operation: 86-24=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 86+24=110, Resulting Numbers: [110] 110,23 unequal: No Solution Exploring Operation: 86*24=2064, Resulting Numbers: [2064] 2064,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[18, 92], Operations: ['96-78=18', '6+86=92'] Exploring Operation: 92-18=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 18*92=1656, Resulting Numbers: [1656] 1656,23 unequal: No Solution Exploring Operation: 18+92=110, Resulting Numbers: [110] 110,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 23:[86, 12], Operations: ['96-78=18', '18-6=12'] Exploring Operation: 86*12=1032, Resulting Numbers: [1032] 1032,23 unequal: No Solution Exploring Operation: 86-12=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 86+12=98, Resulting Numbers: [98] 98,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 23:[96, 6, 8], Operations: ['86-78=8'] Exploring Operation: 6+8=14, Resulting Numbers: [96, 14] Generated Node #0,2,0: 23:[96, 14] Operation: 6+8=14 Exploring Operation: 96-6=90, Resulting Numbers: [8, 90] Generated Node #0,2,1: 23:[8, 90] Operation: 96-6=90 Exploring Operation: 96/6=16, Resulting Numbers: [8, 16] Generated Node #0,2,2: 23:[8, 16] Operation: 96/6=16 Exploring Operation: 96-8=88, Resulting Numbers: [6, 88] Generated Node #0,2,3: 23:[6, 88] Operation: 96-8=88 Exploring Operation: 96/8=12, Resulting Numbers: [6, 12] Generated Node #0,2,4: 23:[6, 12] Operation: 96/8=12 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[8, 16], Operations: ['86-78=8', '96/6=16'] Exploring Operation: 8*16=128, Resulting Numbers: [128] 128,23 unequal: No Solution Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 8+16=24, Resulting Numbers: [24] 24,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 23:[6, 12], Operations: ['86-78=8', '96/8=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,23 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[96, 14], Operations: ['86-78=8', '6+8=14'] Exploring Operation: 96*14=1344, Resulting Numbers: [1344] 1344,23 unequal: No Solution Exploring Operation: 96-14=82, Resulting Numbers: [82] 82,23 unequal: No Solution Exploring Operation: 96+14=110, Resulting Numbers: [110] 110,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[8, 90], Operations: ['86-78=8', '96-6=90'] Exploring Operation: 8*90=720, Resulting Numbers: [720] 720,23 unequal: No Solution Exploring Operation: 8+90=98, Resulting Numbers: [98] 98,23 unequal: No Solution Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[6, 88], Operations: ['86-78=8', '96-8=88'] Exploring Operation: 6*88=528, Resulting Numbers: [528] 528,23 unequal: No Solution Exploring Operation: 88-6=82, Resulting Numbers: [82] 82,23 unequal: No Solution Exploring Operation: 6+88=94, Resulting Numbers: [94] 94,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 23:[86, 78, 16], Operations: ['96/6=16'] Exploring Operation: 86-16=70, Resulting Numbers: [78, 70] Generated Node #0,4,0: 23:[78, 70] Operation: 86-16=70 Exploring Operation: 86+16=102, Resulting Numbers: [78, 102] Generated Node #0,4,1: 23:[78, 102] Operation: 86+16=102 Exploring Operation: 78+16=94, Resulting Numbers: [86, 94] Generated Node #0,4,2: 23:[86, 94] Operation: 78+16=94 Exploring Operation: 78-16=62, Resulting Numbers: [86, 62] Generated Node #0,4,3: 23:[86, 62] Operation: 78-16=62 Exploring Operation: 86-78=8, Resulting Numbers: [16, 8] Generated Node #0,4,4: 23:[16, 8] Operation: 86-78=8 Moving to Node #0,0 Current State: 23:[96, 86, 13], Operations: ['78/6=13'] Exploring Operation: 86-13=73, Resulting Numbers: [96, 73] Generated Node #0,0,0: 23:[96, 73] Operation: 86-13=73 Exploring Operation: 96-86=10, Resulting Numbers: [13, 10] Generated Node #0,0,1: 23:[13, 10] Operation: 96-86=10 Exploring Operation: 96-13=83, Resulting Numbers: [86, 83] Generated Node #0,0,2: 23:[86, 83] Operation: 96-13=83 Exploring Operation: 96+13=109, Resulting Numbers: [86, 109] Generated Node #0,0,3: 23:[86, 109] Operation: 96+13=109 Exploring Operation: 86+13=99, Resulting Numbers: [96, 99] Generated Node #0,0,4: 23:[96, 99] Operation: 86+13=99 Moving to Node #0,4,4 Current State: 23:[16, 8], Operations: ['96/6=16', '86-78=8'] Exploring Operation: 16-8=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 16+8=24, Resulting Numbers: [24] 24,23 unequal: No Solution Exploring Operation: 16*8=128, Resulting Numbers: [128] 128,23 unequal: No Solution Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,1,4 Current State: 23:[10, 13], Operations: ['96-86=10', '78/6=13'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,23 unequal: No Solution Exploring Operation: 10*13=130, Resulting Numbers: [130] 130,23 unequal: No Solution Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[96, 6, 86, 78], Operations: [] Exploring Operation: 96-86=10, Resulting Numbers: [6, 78, 10] Generated Node #0,1: 23:[6, 78, 10] Operation: 96-86=10 Moving to Node #0,1 Current State: 23:[6, 78, 10], Operations: ['96-86=10'] Exploring Operation: 78/6=13, Resulting Numbers: [10, 13] Generated Node #0,1,4: 23:[10, 13] Operation: 78/6=13 Moving to Node #0,1,4 Current State: 23:[10, 13], Operations: ['96-86=10', '78/6=13'] Exploring Operation: 10+13=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.936632
hs_5
sum_heuristic
[ 30, 9, 58, 61 ]
98
[ "30-9=21", "58+61=119", "119-21=98" ]
Current State: 98:[30, 9, 58, 61], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [58, 61, 21] Generated Node #2: [58, 61, 21] from Operation: 30-9=21 Current State: 98:[58, 61, 21], Operations: ['30-9=21'] Exploring Operation: 58+61=119, Resulting Numbers: [21, 119] Generated Node #3: [21, 119] from Operation: 58+61=119 Current State: 98:[21, 119], Operations: ['30-9=21', '58+61=119'] Exploring Operation: 119-21=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[30, 9, 58, 61], Operations: [] Exploring Operation: 30+61=91, Resulting Numbers: [9, 58, 91] Generated Node #0,0: 98:[9, 58, 91] Operation: 30+61=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[9, 58, 91], Operations: ['30+61=91'] Exploring Operation: 58-9=49, Resulting Numbers: [91, 49] Generated Node #0,0,0: 98:[91, 49] Operation: 58-9=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 98:[91, 49], Operations: ['30+61=91', '58-9=49'] Exploring Operation: 91-49=42, Resulting Numbers: [42] 42,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 71, 12, 44, 53 ]
68
[ "71-12=59", "53-44=9", "59+9=68" ]
Current State: 68:[71, 12, 44, 53], Operations: [] Exploring Operation: 71-12=59, Resulting Numbers: [44, 53, 59] Generated Node #2: [44, 53, 59] from Operation: 71-12=59 Current State: 68:[44, 53, 59], Operations: ['71-12=59'] Exploring Operation: 53-44=9, Resulting Numbers: [59, 9] Generated Node #3: [59, 9] from Operation: 53-44=9 Current State: 68:[59, 9], Operations: ['71-12=59', '53-44=9'] Exploring Operation: 59+9=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[71, 12, 44, 53], Operations: [] Exploring Operation: 53-44=9, Resulting Numbers: [71, 12, 9] Generated Node #0,0: 68:[71, 12, 9] Operation: 53-44=9 Exploring Operation: 44-12=32, Resulting Numbers: [71, 53, 32] Generated Node #0,1: 68:[71, 53, 32] Operation: 44-12=32 Exploring Operation: 71-53=18, Resulting Numbers: [12, 44, 18] Generated Node #0,2: 68:[12, 44, 18] Operation: 71-53=18 Exploring Operation: 12+53=65, Resulting Numbers: [71, 44, 65] Generated Node #0,3: 68:[71, 44, 65] Operation: 12+53=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[71, 12, 9], Operations: ['53-44=9'] Exploring Operation: 71-12=59, Resulting Numbers: [9, 59] Generated Node #0,0,0: 68:[9, 59] Operation: 71-12=59 Exploring Operation: 12-9=3, Resulting Numbers: [71, 3] Generated Node #0,0,1: 68:[71, 3] Operation: 12-9=3 Exploring Operation: 12+9=21, Resulting Numbers: [71, 21] Generated Node #0,0,2: 68:[71, 21] Operation: 12+9=21 Exploring Operation: 71-9=62, Resulting Numbers: [12, 62] Generated Node #0,0,3: 68:[12, 62] Operation: 71-9=62 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[71, 3], Operations: ['53-44=9', '12-9=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[71, 12, 44, 53], Operations: [] Exploring Operation: 53-44=9, Resulting Numbers: [71, 12, 9] Generated Node #0,0: 68:[71, 12, 9] Operation: 53-44=9 Moving to Node #0,0 Current State: 68:[71, 12, 9], Operations: ['53-44=9'] Exploring Operation: 12-9=3, Resulting Numbers: [71, 3] Generated Node #0,0,1: 68:[71, 3] Operation: 12-9=3 Moving to Node #0,0,1 Current State: 68:[71, 3], Operations: ['53-44=9', '12-9=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 52, 26, 21, 10 ]
41
[ "52/26=2", "10*2=20", "21+20=41" ]
Current State: 41:[52, 26, 21, 10], Operations: [] Exploring Operation: 52/26=2, Resulting Numbers: [21, 10, 2] Generated Node #2: [21, 10, 2] from Operation: 52/26=2 Current State: 41:[21, 10, 2], Operations: ['52/26=2'] Exploring Operation: 10*2=20, Resulting Numbers: [21, 20] Generated Node #3: [21, 20] from Operation: 10*2=20 Current State: 41:[21, 20], Operations: ['52/26=2', '10*2=20'] Exploring Operation: 21+20=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[52, 26, 21, 10], Operations: [] Exploring Operation: 21+10=31, Resulting Numbers: [52, 26, 31] Generated Node #0,0: 41:[52, 26, 31] Operation: 21+10=31 Exploring Operation: 52-10=42, Resulting Numbers: [26, 21, 42] Generated Node #0,1: 41:[26, 21, 42] Operation: 52-10=42 Exploring Operation: 26+10=36, Resulting Numbers: [52, 21, 36] Generated Node #0,2: 41:[52, 21, 36] Operation: 26+10=36 Moving to Node #0,0 Current State: 41:[52, 26, 31], Operations: ['21+10=31'] Exploring Operation: 26+31=57, Resulting Numbers: [52, 57] Generated Node #0,0,0: 41:[52, 57] Operation: 26+31=57 Exploring Operation: 52-31=21, Resulting Numbers: [26, 21] Generated Node #0,0,1: 41:[26, 21] Operation: 52-31=21 Exploring Operation: 52-26=26, Resulting Numbers: [31, 26] Generated Node #0,0,2: 41:[31, 26] Operation: 52-26=26 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 41:[31, 26], Operations: ['21+10=31', '52-26=26'] Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,41 unequal: No Solution Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,41 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[52, 57], Operations: ['21+10=31', '26+31=57'] Exploring Operation: 52+57=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 52*57=2964, Resulting Numbers: [2964] 2964,41 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[26, 21], Operations: ['21+10=31', '52-31=21'] Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,41 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 41:[26, 21, 42], Operations: ['52-10=42'] Exploring Operation: 26-21=5, Resulting Numbers: [42, 5] Generated Node #0,1,0: 41:[42, 5] Operation: 26-21=5 Exploring Operation: 26+21=47, Resulting Numbers: [42, 47] Generated Node #0,1,1: 41:[42, 47] Operation: 26+21=47 Exploring Operation: 42-21=21, Resulting Numbers: [26, 21] Generated Node #0,1,2: 41:[26, 21] Operation: 42-21=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[42, 47], Operations: ['52-10=42', '26+21=47'] Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,41 unequal: No Solution Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[26, 21], Operations: ['52-10=42', '42-21=21'] Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,41 unequal: No Solution Exploring Operation: 26*21=546, Resulting Numbers: [546] 546,41 unequal: No Solution Exploring Operation: 26+21=47, Resulting Numbers: [47] 47,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[42, 5], Operations: ['52-10=42', '26-21=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 42*5=210, Resulting Numbers: [210] 210,41 unequal: No Solution Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 41:[52, 21, 36], Operations: ['26+10=36'] Exploring Operation: 52-21=31, Resulting Numbers: [36, 31] Generated Node #0,2,0: 41:[36, 31] Operation: 52-21=31 Exploring Operation: 21+36=57, Resulting Numbers: [52, 57] Generated Node #0,2,1: 41:[52, 57] Operation: 21+36=57 Exploring Operation: 52+21=73, Resulting Numbers: [36, 73] Generated Node #0,2,2: 41:[36, 73] Operation: 52+21=73 Moving to Node #0,2,0 Current State: 41:[36, 31], Operations: ['26+10=36', '52-21=31'] Exploring Operation: 36+31=67, Resulting Numbers: [67] 67,41 unequal: No Solution Exploring Operation: 36*31=1116, Resulting Numbers: [1116] 1116,41 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[52, 57], Operations: ['26+10=36', '21+36=57'] Exploring Operation: 52+57=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 52*57=2964, Resulting Numbers: [2964] 2964,41 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[36, 73], Operations: ['26+10=36', '52+21=73'] Exploring Operation: 73-36=37, Resulting Numbers: [37] 37,41 unequal: No Solution Exploring Operation: 36+73=109, Resulting Numbers: [109] 109,41 unequal: No Solution Exploring Operation: 36*73=2628, Resulting Numbers: [2628] 2628,41 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 86, 63, 24, 28 ]
75
[ "86-63=23", "24+28=52", "23+52=75" ]
Current State: 75:[86, 63, 24, 28], Operations: [] Exploring Operation: 86-63=23, Resulting Numbers: [24, 28, 23] Generated Node #2: [24, 28, 23] from Operation: 86-63=23 Current State: 75:[24, 28, 23], Operations: ['86-63=23'] Exploring Operation: 24+28=52, Resulting Numbers: [23, 52] Generated Node #3: [23, 52] from Operation: 24+28=52 Current State: 75:[23, 52], Operations: ['86-63=23', '24+28=52'] Exploring Operation: 23+52=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[86, 63, 24, 28], Operations: [] Exploring Operation: 86-63=23, Resulting Numbers: [24, 28, 23] Generated Node #0,0: 75:[24, 28, 23] Operation: 86-63=23 Exploring Operation: 63-28=35, Resulting Numbers: [86, 24, 35] Generated Node #0,1: 75:[86, 24, 35] Operation: 63-28=35 Moving to Node #0,0 Current State: 75:[24, 28, 23], Operations: ['86-63=23'] Exploring Operation: 28-23=5, Resulting Numbers: [24, 5] Generated Node #0,0,0: 75:[24, 5] Operation: 28-23=5 Exploring Operation: 28-24=4, Resulting Numbers: [23, 4] Generated Node #0,0,1: 75:[23, 4] Operation: 28-24=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[24, 5], Operations: ['86-63=23', '28-23=5'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,75 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 #0,0,1 Current State: 75:[23, 4], Operations: ['86-63=23', '28-24=4'] Exploring Operation: 23+4=27, Resulting Numbers: [27] 27,75 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,75 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: 75:[86, 24, 35], Operations: ['63-28=35'] Exploring Operation: 35-24=11, Resulting Numbers: [86, 11] Generated Node #0,1,0: 75:[86, 11] Operation: 35-24=11 Exploring Operation: 86-24=62, Resulting Numbers: [35, 62] Generated Node #0,1,1: 75:[35, 62] Operation: 86-24=62 Moving to Node #0,1,0 Current State: 75:[86, 11], Operations: ['63-28=35', '35-24=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[86, 63, 24, 28], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [86, 24, 35] Generated Node #0,1: 75:[86, 24, 35] Operation: 63-28=35 Moving to Node #0,1 Current State: 75:[86, 24, 35], Operations: ['63-28=35'] Exploring Operation: 35-24=11, Resulting Numbers: [86, 11] Generated Node #0,1,0: 75:[86, 11] Operation: 35-24=11 Moving to Node #0,1,0 Current State: 75:[86, 11], Operations: ['63-28=35', '35-24=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 58, 80, 94, 47 ]
44
[ "80-58=22", "94/47=2", "22*2=44" ]
Current State: 44:[58, 80, 94, 47], Operations: [] Exploring Operation: 80-58=22, Resulting Numbers: [94, 47, 22] Generated Node #2: [94, 47, 22] from Operation: 80-58=22 Current State: 44:[94, 47, 22], Operations: ['80-58=22'] Exploring Operation: 94/47=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 94/47=2 Current State: 44:[22, 2], Operations: ['80-58=22', '94/47=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[58, 80, 94, 47], Operations: [] Exploring Operation: 94-80=14, Resulting Numbers: [58, 47, 14] Generated Node #0,0: 44:[58, 47, 14] Operation: 94-80=14 Moving to Node #0,0 Current State: 44:[58, 47, 14], Operations: ['94-80=14'] Exploring Operation: 58-47=11, Resulting Numbers: [14, 11] Generated Node #0,0,0: 44:[14, 11] Operation: 58-47=11 Moving to Node #0,0,0 Current State: 44:[14, 11], Operations: ['94-80=14', '58-47=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,44 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 48, 5, 15, 1 ]
37
[ "48+5=53", "15+1=16", "53-16=37" ]
Current State: 37:[48, 5, 15, 1], Operations: [] Exploring Operation: 48+5=53, Resulting Numbers: [15, 1, 53] Generated Node #2: [15, 1, 53] from Operation: 48+5=53 Current State: 37:[15, 1, 53], Operations: ['48+5=53'] Exploring Operation: 15+1=16, Resulting Numbers: [53, 16] Generated Node #3: [53, 16] from Operation: 15+1=16 Current State: 37:[53, 16], Operations: ['48+5=53', '15+1=16'] Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[48, 5, 15, 1], Operations: [] Exploring Operation: 48-5=43, Resulting Numbers: [15, 1, 43] Generated Node #0,0: 37:[15, 1, 43] Operation: 48-5=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[15, 1, 43], Operations: ['48-5=43'] Exploring Operation: 15+1=16, Resulting Numbers: [43, 16] Generated Node #0,0,0: 37:[43, 16] Operation: 15+1=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[43, 16], Operations: ['48-5=43', '15+1=16'] Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,37 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
[ 2, 32, 55, 36 ]
70
[ "55-36=19", "2*19=38", "32+38=70" ]
Current State: 70:[2, 32, 55, 36], Operations: [] Exploring Operation: 55-36=19, Resulting Numbers: [2, 32, 19] Generated Node #2: [2, 32, 19] from Operation: 55-36=19 Current State: 70:[2, 32, 19], Operations: ['55-36=19'] Exploring Operation: 2*19=38, Resulting Numbers: [32, 38] Generated Node #3: [32, 38] from Operation: 2*19=38 Current State: 70:[32, 38], Operations: ['55-36=19', '2*19=38'] Exploring Operation: 32+38=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[2, 32, 55, 36], Operations: [] Exploring Operation: 55-32=23, Resulting Numbers: [2, 36, 23] Generated Node #0,0: 70:[2, 36, 23] Operation: 55-32=23 Exploring Operation: 55-36=19, Resulting Numbers: [2, 32, 19] Generated Node #0,1: 70:[2, 32, 19] Operation: 55-36=19 Moving to Node #0,1 Current State: 70:[2, 32, 19], Operations: ['55-36=19'] Exploring Operation: 32-19=13, Resulting Numbers: [2, 13] Generated Node #0,1,0: 70:[2, 13] Operation: 32-19=13 Exploring Operation: 2+32=34, Resulting Numbers: [19, 34] Generated Node #0,1,1: 70:[19, 34] Operation: 2+32=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 70:[2, 13], Operations: ['55-36=19', '32-19=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,70 unequal: No Solution No 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: 70:[19, 34], Operations: ['55-36=19', '2+32=34'] Exploring Operation: 19+34=53, Resulting Numbers: [53] 53,70 unequal: No Solution Exploring Operation: 34-19=15, Resulting Numbers: [15] 15,70 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: 70:[2, 36, 23], Operations: ['55-32=23'] Exploring Operation: 23-2=21, Resulting Numbers: [36, 21] Generated Node #0,0,0: 70:[36, 21] Operation: 23-2=21 Exploring Operation: 36-23=13, Resulting Numbers: [2, 13] Generated Node #0,0,1: 70:[2, 13] Operation: 36-23=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[2, 13], Operations: ['55-32=23', '36-23=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,70 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,70 unequal: No Solution No 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: 70:[36, 21], Operations: ['55-32=23', '23-2=21'] Exploring Operation: 36+21=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,70 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
[ 45, 60, 68, 46 ]
83
[ "45+60=105", "68-46=22", "105-22=83" ]
Current State: 83:[45, 60, 68, 46], Operations: [] Exploring Operation: 45+60=105, Resulting Numbers: [68, 46, 105] Generated Node #2: [68, 46, 105] from Operation: 45+60=105 Current State: 83:[68, 46, 105], Operations: ['45+60=105'] Exploring Operation: 68-46=22, Resulting Numbers: [105, 22] Generated Node #3: [105, 22] from Operation: 68-46=22 Current State: 83:[105, 22], Operations: ['45+60=105', '68-46=22'] Exploring Operation: 105-22=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[45, 60, 68, 46], Operations: [] Exploring Operation: 60+46=106, Resulting Numbers: [45, 68, 106] Generated Node #0,0: 83:[45, 68, 106] Operation: 60+46=106 Exploring Operation: 45+60=105, Resulting Numbers: [68, 46, 105] Generated Node #0,1: 83:[68, 46, 105] Operation: 45+60=105 Exploring Operation: 45+46=91, Resulting Numbers: [60, 68, 91] Generated Node #0,2: 83:[60, 68, 91] Operation: 45+46=91 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[60, 68, 91], Operations: ['45+46=91'] Exploring Operation: 91-60=31, Resulting Numbers: [68, 31] Generated Node #0,2,0: 83:[68, 31] Operation: 91-60=31 Exploring Operation: 68-60=8, Resulting Numbers: [91, 8] Generated Node #0,2,1: 83:[91, 8] Operation: 68-60=8 Exploring Operation: 60+68=128, Resulting Numbers: [91, 128] Generated Node #0,2,2: 83:[91, 128] Operation: 60+68=128 Moving to Node #0,2,2 Current State: 83:[91, 128], Operations: ['45+46=91', '60+68=128'] Exploring Operation: 128-91=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 91+128=219, Resulting Numbers: [219] 219,83 unequal: No Solution Exploring Operation: 91*128=11648, Resulting Numbers: [11648] 11648,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[68, 31], Operations: ['45+46=91', '91-60=31'] Exploring Operation: 68+31=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 68-31=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 68*31=2108, Resulting Numbers: [2108] 2108,83 unequal: No Solution Moving to Node #0,2,1 Current State: 83:[91, 8], Operations: ['45+46=91', '68-60=8'] Exploring Operation: 91*8=728, Resulting Numbers: [728] 728,83 unequal: No Solution Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[45, 60, 68, 46], Operations: [] Exploring Operation: 45+46=91, Resulting Numbers: [60, 68, 91] Generated Node #0,2: 83:[60, 68, 91] Operation: 45+46=91 Moving to Node #0,2 Current State: 83:[60, 68, 91], Operations: ['45+46=91'] Exploring Operation: 68-60=8, Resulting Numbers: [91, 8] Generated Node #0,2,1: 83:[91, 8] Operation: 68-60=8 Moving to Node #0,2,1 Current State: 83:[91, 8], Operations: ['45+46=91', '68-60=8'] Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 40, 22, 6, 84 ]
72
[ "40-22=18", "6+84=90", "90-18=72" ]
Current State: 72:[40, 22, 6, 84], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [6, 84, 18] Generated Node #2: [6, 84, 18] from Operation: 40-22=18 Current State: 72:[6, 84, 18], Operations: ['40-22=18'] Exploring Operation: 6+84=90, Resulting Numbers: [18, 90] Generated Node #3: [18, 90] from Operation: 6+84=90 Current State: 72:[18, 90], Operations: ['40-22=18', '6+84=90'] Exploring Operation: 90-18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[40, 22, 6, 84], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [6, 84, 18] Generated Node #0,0: 72:[6, 84, 18] Operation: 40-22=18 Exploring Operation: 84/6=14, Resulting Numbers: [40, 22, 14] Generated Node #0,1: 72:[40, 22, 14] Operation: 84/6=14 Exploring Operation: 84-40=44, Resulting Numbers: [22, 6, 44] Generated Node #0,2: 72:[22, 6, 44] Operation: 84-40=44 Moving to Node #0,1 Current State: 72:[40, 22, 14], Operations: ['84/6=14'] Exploring Operation: 40-22=18, Resulting Numbers: [14, 18] Generated Node #0,1,0: 72:[14, 18] Operation: 40-22=18 Exploring Operation: 40-14=26, Resulting Numbers: [22, 26] Generated Node #0,1,1: 72:[22, 26] Operation: 40-14=26 Exploring Operation: 22+14=36, Resulting Numbers: [40, 36] Generated Node #0,1,2: 72:[40, 36] Operation: 22+14=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[14, 18], Operations: ['84/6=14', '40-22=18'] Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,72 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 14*18=252, Resulting Numbers: [252] 252,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 72:[22, 26], Operations: ['84/6=14', '40-14=26'] Exploring Operation: 22*26=572, Resulting Numbers: [572] 572,72 unequal: No Solution Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,72 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 72:[40, 36], Operations: ['84/6=14', '22+14=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 40-36=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 40*36=1440, Resulting Numbers: [1440] 1440,72 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: 72:[22, 6, 44], Operations: ['84-40=44'] Exploring Operation: 44-22=22, Resulting Numbers: [6, 22] Generated Node #0,2,0: 72:[6, 22] Operation: 44-22=22 Exploring Operation: 44/22=2, Resulting Numbers: [6, 2] Generated Node #0,2,1: 72:[6, 2] Operation: 44/22=2 Exploring Operation: 44-6=38, Resulting Numbers: [22, 38] Generated Node #0,2,2: 72:[22, 38] Operation: 44-6=38 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 72:[6, 2], Operations: ['84-40=44', '44/22=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,72 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 72:[6, 22], Operations: ['84-40=44', '44-22=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,72 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,72 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 72:[22, 38], Operations: ['84-40=44', '44-6=38'] Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,72 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 72:[6, 84, 18], Operations: ['40-22=18'] Exploring Operation: 84-6=78, Resulting Numbers: [18, 78] Generated Node #0,0,0: 72:[18, 78] Operation: 84-6=78 Exploring Operation: 84-18=66, Resulting Numbers: [6, 66] Generated Node #0,0,1: 72:[6, 66] Operation: 84-18=66 Exploring Operation: 84/6=14, Resulting Numbers: [18, 14] Generated Node #0,0,2: 72:[18, 14] Operation: 84/6=14 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 72:[18, 14], Operations: ['40-22=18', '84/6=14'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 18+14=32, Resulting Numbers: [32] 32,72 unequal: No Solution Exploring Operation: 18*14=252, Resulting Numbers: [252] 252,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[18, 78], Operations: ['40-22=18', '84-6=78'] Exploring Operation: 78-18=60, Resulting Numbers: [60] 60,72 unequal: No Solution Exploring Operation: 18+78=96, Resulting Numbers: [96] 96,72 unequal: No Solution Exploring Operation: 18*78=1404, Resulting Numbers: [1404] 1404,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[6, 66], Operations: ['40-22=18', '84-18=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,72 unequal: No Solution Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[40, 22, 6, 84], Operations: [] Exploring Operation: 40-22=18, Resulting Numbers: [6, 84, 18] Generated Node #0,0: 72:[6, 84, 18] Operation: 40-22=18 Moving to Node #0,0 Current State: 72:[6, 84, 18], Operations: ['40-22=18'] Exploring Operation: 84-18=66, Resulting Numbers: [6, 66] Generated Node #0,0,1: 72:[6, 66] Operation: 84-18=66 Moving to Node #0,0,1 Current State: 72:[6, 66], Operations: ['40-22=18', '84-18=66'] Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_3
sum_heuristic
[ 42, 87, 74, 83 ]
94
[ "87-83=4", "42*4=168", "168-74=94" ]
Current State: 94:[42, 87, 74, 83], Operations: [] Exploring Operation: 87-83=4, Resulting Numbers: [42, 74, 4] Generated Node #2: [42, 74, 4] from Operation: 87-83=4 Current State: 94:[42, 74, 4], Operations: ['87-83=4'] Exploring Operation: 42*4=168, Resulting Numbers: [74, 168] Generated Node #3: [74, 168] from Operation: 42*4=168 Current State: 94:[74, 168], Operations: ['87-83=4', '42*4=168'] Exploring Operation: 168-74=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[42, 87, 74, 83], Operations: [] Exploring Operation: 83-74=9, Resulting Numbers: [42, 87, 9] Generated Node #0,0: 94:[42, 87, 9] Operation: 83-74=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[42, 87, 9], Operations: ['83-74=9'] Exploring Operation: 87+9=96, Resulting Numbers: [42, 96] Generated Node #0,0,0: 94:[42, 96] Operation: 87+9=96 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[42, 96], Operations: ['83-74=9', '87+9=96'] Exploring Operation: 96-42=54, Resulting Numbers: [54] 54,94 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 No solution found.
0
hs_1
mult_heuristic
[ 51, 68, 61, 30 ]
21
[ "68*30=2040", "2040/51=40", "61-40=21" ]
Current State: 21:[51, 68, 61, 30], Operations: [] Exploring Operation: 68*30=2040, Resulting Numbers: [51, 61, 2040] Generated Node #2: [51, 61, 2040] from Operation: 68*30=2040 Current State: 21:[51, 61, 2040], Operations: ['68*30=2040'] Exploring Operation: 2040/51=40, Resulting Numbers: [61, 40] Generated Node #3: [61, 40] from Operation: 2040/51=40 Current State: 21:[61, 40], Operations: ['68*30=2040', '2040/51=40'] Exploring Operation: 61-40=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[51, 68, 61, 30], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [51, 30, 7] Generated Node #0,0: 21:[51, 30, 7] Operation: 68-61=7 Exploring Operation: 68-30=38, Resulting Numbers: [51, 61, 38] Generated Node #0,1: 21:[51, 61, 38] Operation: 68-30=38 Exploring Operation: 61-51=10, Resulting Numbers: [68, 30, 10] Generated Node #0,2: 21:[68, 30, 10] Operation: 61-51=10 Exploring Operation: 68-51=17, Resulting Numbers: [61, 30, 17] Generated Node #0,3: 21:[61, 30, 17] Operation: 68-51=17 Exploring Operation: 51-30=21, Resulting Numbers: [68, 61, 21] Generated Node #0,4: 21:[68, 61, 21] Operation: 51-30=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[51, 30, 7], Operations: ['68-61=7'] Exploring Operation: 51-7=44, Resulting Numbers: [30, 44] Generated Node #0,0,0: 21:[30, 44] Operation: 51-7=44 Exploring Operation: 51+7=58, Resulting Numbers: [30, 58] Generated Node #0,0,1: 21:[30, 58] Operation: 51+7=58 Exploring Operation: 51-30=21, Resulting Numbers: [7, 21] Generated Node #0,0,2: 21:[7, 21] Operation: 51-30=21 Exploring Operation: 30+7=37, Resulting Numbers: [51, 37] Generated Node #0,0,3: 21:[51, 37] Operation: 30+7=37 Exploring Operation: 30-7=23, Resulting Numbers: [51, 23] Generated Node #0,0,4: 21:[51, 23] Operation: 30-7=23 Moving to Node #0,0,2 Current State: 21:[7, 21], Operations: ['68-61=7', '51-30=21'] Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 7*21=147, Resulting Numbers: [147] 147,21 unequal: No Solution Exploring Operation: 7+21=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,21 unequal: No Solution Moving to Node #0,0,4 Current State: 21:[51, 23], Operations: ['68-61=7', '30-7=23'] Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 51+23=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 51*23=1173, Resulting Numbers: [1173] 1173,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[30, 44], Operations: ['68-61=7', '51-7=44'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[30, 58], Operations: ['68-61=7', '51+7=58'] Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 30*58=1740, Resulting Numbers: [1740] 1740,21 unequal: No Solution Exploring Operation: 30+58=88, Resulting Numbers: [88] 88,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[51, 37], Operations: ['68-61=7', '30+7=37'] Exploring Operation: 51+37=88, Resulting Numbers: [88] 88,21 unequal: No Solution Exploring Operation: 51*37=1887, Resulting Numbers: [1887] 1887,21 unequal: No Solution Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[61, 30, 17], Operations: ['68-51=17'] Exploring Operation: 61+17=78, Resulting Numbers: [30, 78] Generated Node #0,3,0: 21:[30, 78] Operation: 61+17=78 Exploring Operation: 61-17=44, Resulting Numbers: [30, 44] Generated Node #0,3,1: 21:[30, 44] Operation: 61-17=44 Exploring Operation: 30+17=47, Resulting Numbers: [61, 47] Generated Node #0,3,2: 21:[61, 47] Operation: 30+17=47 Exploring Operation: 61-30=31, Resulting Numbers: [17, 31] Generated Node #0,3,3: 21:[17, 31] Operation: 61-30=31 Exploring Operation: 30-17=13, Resulting Numbers: [61, 13] Generated Node #0,3,4: 21:[61, 13] Operation: 30-17=13 Moving to Node #0,3,3 Current State: 21:[17, 31], Operations: ['68-51=17', '61-30=31'] Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 17*31=527, Resulting Numbers: [527] 527,21 unequal: No Solution Moving to Node #0,3,1 Current State: 21:[30, 44], Operations: ['68-51=17', '61-17=44'] Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,21 unequal: No Solution Moving to Node #0,3,4 Current State: 21:[61, 13], Operations: ['68-51=17', '30-17=13'] Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,21 unequal: No Solution Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[30, 78], Operations: ['68-51=17', '61+17=78'] Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,21 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,21 unequal: No Solution Moving to Node #0,3,2 Current State: 21:[61, 47], Operations: ['68-51=17', '30+17=47'] Exploring Operation: 61+47=108, Resulting Numbers: [108] 108,21 unequal: No Solution Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 61*47=2867, Resulting Numbers: [2867] 2867,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[68, 30, 10], Operations: ['61-51=10'] Exploring Operation: 68-10=58, Resulting Numbers: [30, 58] Generated Node #0,2,0: 21:[30, 58] Operation: 68-10=58 Exploring Operation: 68-30=38, Resulting Numbers: [10, 38] Generated Node #0,2,1: 21:[10, 38] Operation: 68-30=38 Exploring Operation: 30-10=20, Resulting Numbers: [68, 20] Generated Node #0,2,2: 21:[68, 20] Operation: 30-10=20 Exploring Operation: 68+10=78, Resulting Numbers: [30, 78] Generated Node #0,2,3: 21:[30, 78] Operation: 68+10=78 Exploring Operation: 30/10=3, Resulting Numbers: [68, 3] Generated Node #0,2,4: 21:[68, 3] Operation: 30/10=3 Moving to Node #0,2,1 Current State: 21:[10, 38], Operations: ['61-51=10', '68-30=38'] Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,21 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[30, 58], Operations: ['61-51=10', '68-10=58'] Exploring Operation: 30*58=1740, Resulting Numbers: [1740] 1740,21 unequal: No Solution Exploring Operation: 58-30=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 30+58=88, Resulting Numbers: [88] 88,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[68, 3], Operations: ['61-51=10', '30/10=3'] Exploring Operation: 68*3=204, Resulting Numbers: [204] 204,21 unequal: No Solution Exploring Operation: 68+3=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[68, 20], Operations: ['61-51=10', '30-10=20'] Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,21 unequal: No Solution Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,21 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,21 unequal: No Solution Moving to Node #0,2,3 Current State: 21:[30, 78], Operations: ['61-51=10', '68+10=78'] Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,21 unequal: No Solution Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[51, 61, 38], Operations: ['68-30=38'] Exploring Operation: 61-38=23, Resulting Numbers: [51, 23] Generated Node #0,1,0: 21:[51, 23] Operation: 61-38=23 Exploring Operation: 51+38=89, Resulting Numbers: [61, 89] Generated Node #0,1,1: 21:[61, 89] Operation: 51+38=89 Exploring Operation: 61-51=10, Resulting Numbers: [38, 10] Generated Node #0,1,2: 21:[38, 10] Operation: 61-51=10 Exploring Operation: 51+61=112, Resulting Numbers: [38, 112] Generated Node #0,1,3: 21:[38, 112] Operation: 51+61=112 Exploring Operation: 51-38=13, Resulting Numbers: [61, 13] Generated Node #0,1,4: 21:[61, 13] Operation: 51-38=13 Moving to Node #0,1,2 Current State: 21:[38, 10], Operations: ['68-30=38', '61-51=10'] Exploring Operation: 38+10=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 38*10=380, Resulting Numbers: [380] 380,21 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[51, 23], Operations: ['68-30=38', '61-38=23'] Exploring Operation: 51*23=1173, Resulting Numbers: [1173] 1173,21 unequal: No Solution Exploring Operation: 51-23=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 51+23=74, Resulting Numbers: [74] 74,21 unequal: No Solution Moving to Node #0,1,4 Current State: 21:[61, 13], Operations: ['68-30=38', '51-38=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[61, 89], Operations: ['68-30=38', '51+38=89'] Exploring Operation: 61+89=150, Resulting Numbers: [150] 150,21 unequal: No Solution Exploring Operation: 89-61=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 61*89=5429, Resulting Numbers: [5429] 5429,21 unequal: No Solution Moving to Node #0,1,3 Current State: 21:[38, 112], Operations: ['68-30=38', '51+61=112'] Exploring Operation: 38*112=4256, Resulting Numbers: [4256] 4256,21 unequal: No Solution Exploring Operation: 112-38=74, Resulting Numbers: [74] 74,21 unequal: No Solution Exploring Operation: 38+112=150, Resulting Numbers: [150] 150,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 21:[68, 61, 21], Operations: ['51-30=21'] Exploring Operation: 61-21=40, Resulting Numbers: [68, 40] Generated Node #0,4,0: 21:[68, 40] Operation: 61-21=40 Exploring Operation: 68+61=129, Resulting Numbers: [21, 129] Generated Node #0,4,1: 21:[21, 129] Operation: 68+61=129 Exploring Operation: 68-61=7, Resulting Numbers: [21, 7] Generated Node #0,4,2: 21:[21, 7] Operation: 68-61=7 Exploring Operation: 68+21=89, Resulting Numbers: [61, 89] Generated Node #0,4,3: 21:[61, 89] Operation: 68+21=89 Exploring Operation: 68-21=47, Resulting Numbers: [61, 47] Generated Node #0,4,4: 21:[61, 47] Operation: 68-21=47 Moving to Node #0,4,2 Current State: 21:[21, 7], Operations: ['51-30=21', '68-61=7'] Exploring Operation: 21+7=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 21-7=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 21/7=3, Resulting Numbers: [3] 3,21 unequal: No Solution Exploring Operation: 21*7=147, Resulting Numbers: [147] 147,21 unequal: No Solution Moving to Node #0,4,4 Current State: 21:[61, 47], Operations: ['51-30=21', '68-21=47'] Exploring Operation: 61*47=2867, Resulting Numbers: [2867] 2867,21 unequal: No Solution Exploring Operation: 61-47=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 61+47=108, Resulting Numbers: [108] 108,21 unequal: No Solution Moving to Node #0,4,0 Current State: 21:[68, 40], Operations: ['51-30=21', '61-21=40'] Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,21 unequal: No Solution Exploring Operation: 68*40=2720, Resulting Numbers: [2720] 2720,21 unequal: No Solution Moving to Node #0,4,1 Current State: 21:[21, 129], Operations: ['51-30=21', '68+61=129'] Exploring Operation: 21+129=150, Resulting Numbers: [150] 150,21 unequal: No Solution Exploring Operation: 129-21=108, Resulting Numbers: [108] 108,21 unequal: No Solution Exploring Operation: 21*129=2709, Resulting Numbers: [2709] 2709,21 unequal: No Solution Moving to Node #0,4,3 Current State: 21:[61, 89], Operations: ['51-30=21', '68+21=89'] Exploring Operation: 89-61=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 61+89=150, Resulting Numbers: [150] 150,21 unequal: No Solution Exploring Operation: 61*89=5429, Resulting Numbers: [5429] 5429,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 70, 6, 8, 49 ]
57
[ "70-6=64", "64/8=8", "49+8=57" ]
Current State: 57:[70, 6, 8, 49], Operations: [] Exploring Operation: 70-6=64, Resulting Numbers: [8, 49, 64] Generated Node #2: [8, 49, 64] from Operation: 70-6=64 Current State: 57:[8, 49, 64], Operations: ['70-6=64'] Exploring Operation: 64/8=8, Resulting Numbers: [49, 8] Generated Node #3: [49, 8] from Operation: 64/8=8 Current State: 57:[49, 8], Operations: ['70-6=64', '64/8=8'] Exploring Operation: 49+8=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[70, 6, 8, 49], Operations: [] Exploring Operation: 70-49=21, Resulting Numbers: [6, 8, 21] Generated Node #0,0: 57:[6, 8, 21] Operation: 70-49=21 Moving to Node #0,0 Current State: 57:[6, 8, 21], Operations: ['70-49=21'] Exploring Operation: 8-6=2, Resulting Numbers: [21, 2] Generated Node #0,0,0: 57:[21, 2] Operation: 8-6=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[21, 2], Operations: ['70-49=21', '8-6=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,57 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
[ 94, 20, 89, 92 ]
77
[ "94-20=74", "92-89=3", "74+3=77" ]
Current State: 77:[94, 20, 89, 92], Operations: [] Exploring Operation: 94-20=74, Resulting Numbers: [89, 92, 74] Generated Node #2: [89, 92, 74] from Operation: 94-20=74 Current State: 77:[89, 92, 74], Operations: ['94-20=74'] Exploring Operation: 92-89=3, Resulting Numbers: [74, 3] Generated Node #3: [74, 3] from Operation: 92-89=3 Current State: 77:[74, 3], Operations: ['94-20=74', '92-89=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[94, 20, 89, 92], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [20, 89, 2] Generated Node #0,0: 77:[20, 89, 2] Operation: 94-92=2 Exploring Operation: 94-89=5, Resulting Numbers: [20, 92, 5] Generated Node #0,1: 77:[20, 92, 5] Operation: 94-89=5 Moving to Node #0,0 Current State: 77:[20, 89, 2], Operations: ['94-92=2'] Exploring Operation: 89-20=69, Resulting Numbers: [2, 69] Generated Node #0,0,0: 77:[2, 69] Operation: 89-20=69 Exploring Operation: 20/2=10, Resulting Numbers: [89, 10] Generated Node #0,0,1: 77:[89, 10] Operation: 20/2=10 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[2, 69], Operations: ['94-92=2', '89-20=69'] Exploring Operation: 2+69=71, Resulting Numbers: [71] 71,77 unequal: No Solution Exploring Operation: 69-2=67, Resulting Numbers: [67] 67,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[89, 10], Operations: ['94-92=2', '20/2=10'] Exploring Operation: 89-10=79, Resulting Numbers: [79] 79,77 unequal: No Solution Exploring Operation: 89+10=99, Resulting Numbers: [99] 99,77 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: 77:[20, 92, 5], Operations: ['94-89=5'] Exploring Operation: 92-20=72, Resulting Numbers: [5, 72] Generated Node #0,1,0: 77:[5, 72] Operation: 92-20=72 Exploring Operation: 20/5=4, Resulting Numbers: [92, 4] Generated Node #0,1,1: 77:[92, 4] Operation: 20/5=4 Moving to Node #0,1,0 Current State: 77:[5, 72], Operations: ['94-89=5', '92-20=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,77 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[94, 20, 89, 92], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [20, 92, 5] Generated Node #0,1: 77:[20, 92, 5] Operation: 94-89=5 Moving to Node #0,1 Current State: 77:[20, 92, 5], Operations: ['94-89=5'] Exploring Operation: 92-20=72, Resulting Numbers: [5, 72] Generated Node #0,1,0: 77:[5, 72] Operation: 92-20=72 Moving to Node #0,1,0 Current State: 77:[5, 72], Operations: ['94-89=5', '92-20=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.986111
hs_2
sum_heuristic
[ 24, 15, 81, 49 ]
45
[ "15+81=96", "96/24=4", "49-4=45" ]
Current State: 45:[24, 15, 81, 49], Operations: [] Exploring Operation: 15+81=96, Resulting Numbers: [24, 49, 96] Generated Node #2: [24, 49, 96] from Operation: 15+81=96 Current State: 45:[24, 49, 96], Operations: ['15+81=96'] Exploring Operation: 96/24=4, Resulting Numbers: [49, 4] Generated Node #3: [49, 4] from Operation: 96/24=4 Current State: 45:[49, 4], Operations: ['15+81=96', '96/24=4'] Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[24, 15, 81, 49], Operations: [] Exploring Operation: 81-24=57, Resulting Numbers: [15, 49, 57] Generated Node #0,0: 45:[15, 49, 57] Operation: 81-24=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[15, 49, 57], Operations: ['81-24=57'] Exploring Operation: 57-49=8, Resulting Numbers: [15, 8] Generated Node #0,0,0: 45:[15, 8] Operation: 57-49=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 45:[15, 8], Operations: ['81-24=57', '57-49=8'] Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,45 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 No solution found.
0
hs_1
sum_heuristic
[ 13, 77, 15, 78 ]
27
[ "13+77=90", "78-15=63", "90-63=27" ]
Current State: 27:[13, 77, 15, 78], Operations: [] Exploring Operation: 13+77=90, Resulting Numbers: [15, 78, 90] Generated Node #2: [15, 78, 90] from Operation: 13+77=90 Current State: 27:[15, 78, 90], Operations: ['13+77=90'] Exploring Operation: 78-15=63, Resulting Numbers: [90, 63] Generated Node #3: [90, 63] from Operation: 78-15=63 Current State: 27:[90, 63], Operations: ['13+77=90', '78-15=63'] Exploring Operation: 90-63=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[13, 77, 15, 78], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [77, 15, 6] Generated Node #0,0: 27:[77, 15, 6] Operation: 78/13=6 Exploring Operation: 78-77=1, Resulting Numbers: [13, 15, 1] Generated Node #0,1: 27:[13, 15, 1] Operation: 78-77=1 Exploring Operation: 78-15=63, Resulting Numbers: [13, 77, 63] Generated Node #0,2: 27:[13, 77, 63] Operation: 78-15=63 Exploring Operation: 77-15=62, Resulting Numbers: [13, 78, 62] Generated Node #0,3: 27:[13, 78, 62] Operation: 77-15=62 Exploring Operation: 77-13=64, Resulting Numbers: [15, 78, 64] Generated Node #0,4: 27:[15, 78, 64] Operation: 77-13=64 Moving to Node #0,1 Current State: 27:[13, 15, 1], Operations: ['78-77=1'] Exploring Operation: 13+15=28, Resulting Numbers: [1, 28] Generated Node #0,1,0: 27:[1, 28] Operation: 13+15=28 Exploring Operation: 15-1=14, Resulting Numbers: [13, 14] Generated Node #0,1,1: 27:[13, 14] Operation: 15-1=14 Exploring Operation: 15-13=2, Resulting Numbers: [1, 2] Generated Node #0,1,2: 27:[1, 2] Operation: 15-13=2 Exploring Operation: 13*1=13, Resulting Numbers: [15, 13] Generated Node #0,1,3: 27:[15, 13] Operation: 13*1=13 Exploring Operation: 13-1=12, Resulting Numbers: [15, 12] Generated Node #0,1,4: 27:[15, 12] Operation: 13-1=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[1, 28], Operations: ['78-77=1', '13+15=28'] Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,27 unequal: No Solution Exploring Operation: 1+28=29, Resulting Numbers: [29] 29,27 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[13, 77, 15, 78], Operations: [] Exploring Operation: 78-77=1, Resulting Numbers: [13, 15, 1] Generated Node #0,1: 27:[13, 15, 1] Operation: 78-77=1 Moving to Node #0,1 Current State: 27:[13, 15, 1], Operations: ['78-77=1'] Exploring Operation: 13+15=28, Resulting Numbers: [1, 28] Generated Node #0,1,0: 27:[1, 28] Operation: 13+15=28 Moving to Node #0,1,0 Current State: 27:[1, 28], Operations: ['78-77=1', '13+15=28'] Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 59, 90, 56, 8 ]
18
[ "59-56=3", "8-3=5", "90/5=18" ]
Current State: 18:[59, 90, 56, 8], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [90, 8, 3] Generated Node #2: [90, 8, 3] from Operation: 59-56=3 Current State: 18:[90, 8, 3], Operations: ['59-56=3'] Exploring Operation: 8-3=5, Resulting Numbers: [90, 5] Generated Node #3: [90, 5] from Operation: 8-3=5 Current State: 18:[90, 5], Operations: ['59-56=3', '8-3=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[59, 90, 56, 8], Operations: [] Exploring Operation: 90-56=34, Resulting Numbers: [59, 8, 34] Generated Node #0,0: 18:[59, 8, 34] Operation: 90-56=34 Exploring Operation: 59-56=3, Resulting Numbers: [90, 8, 3] Generated Node #0,1: 18:[90, 8, 3] Operation: 59-56=3 Exploring Operation: 90-59=31, Resulting Numbers: [56, 8, 31] Generated Node #0,2: 18:[56, 8, 31] Operation: 90-59=31 Moving to Node #0,2 Current State: 18:[56, 8, 31], Operations: ['90-59=31'] Exploring Operation: 56-8=48, Resulting Numbers: [31, 48] Generated Node #0,2,0: 18:[31, 48] Operation: 56-8=48 Exploring Operation: 56/8=7, Resulting Numbers: [31, 7] Generated Node #0,2,1: 18:[31, 7] Operation: 56/8=7 Exploring Operation: 56-31=25, Resulting Numbers: [8, 25] Generated Node #0,2,2: 18:[8, 25] Operation: 56-31=25 Moving to Node #0,0 Current State: 18:[59, 8, 34], Operations: ['90-56=34'] Exploring Operation: 59-8=51, Resulting Numbers: [34, 51] Generated Node #0,0,0: 18:[34, 51] Operation: 59-8=51 Exploring Operation: 59-34=25, Resulting Numbers: [8, 25] Generated Node #0,0,1: 18:[8, 25] Operation: 59-34=25 Exploring Operation: 34-8=26, Resulting Numbers: [59, 26] Generated Node #0,0,2: 18:[59, 26] Operation: 34-8=26 Moving to Node #0,1 Current State: 18:[90, 8, 3], Operations: ['59-56=3'] Exploring Operation: 90-3=87, Resulting Numbers: [8, 87] Generated Node #0,1,0: 18:[8, 87] Operation: 90-3=87 Exploring Operation: 90-8=82, Resulting Numbers: [3, 82] Generated Node #0,1,1: 18:[3, 82] Operation: 90-8=82 Exploring Operation: 90/3=30, Resulting Numbers: [8, 30] Generated Node #0,1,2: 18:[8, 30] Operation: 90/3=30 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[8, 30], Operations: ['59-56=3', '90/3=30'] Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 8*30=240, Resulting Numbers: [240] 240,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[3, 82], Operations: ['59-56=3', '90-8=82'] Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,18 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[8, 87], Operations: ['59-56=3', '90-3=87'] Exploring Operation: 8*87=696, Resulting Numbers: [696] 696,18 unequal: No Solution Exploring Operation: 8+87=95, Resulting Numbers: [95] 95,18 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 18:[8, 25], Operations: ['90-59=31', '56-31=25'] Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,18 unequal: No Solution Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[8, 25], Operations: ['90-56=34', '59-34=25'] Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[31, 7], Operations: ['90-59=31', '56/8=7'] Exploring Operation: 31*7=217, Resulting Numbers: [217] 217,18 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 31+7=38, Resulting Numbers: [38] 38,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[31, 48], Operations: ['90-59=31', '56-8=48'] Exploring Operation: 31+48=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 48-31=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 31*48=1488, Resulting Numbers: [1488] 1488,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[59, 26], Operations: ['90-56=34', '34-8=26'] Exploring Operation: 59+26=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 59-26=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 59*26=1534, Resulting Numbers: [1534] 1534,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[34, 51], Operations: ['90-56=34', '59-8=51'] Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,18 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 24, 56, 28, 56 ]
50
[ "24*56=1344", "56+1344=1400", "1400/28=50" ]
Current State: 50:[24, 56, 28, 56], Operations: [] Exploring Operation: 24*56=1344, Resulting Numbers: [28, 1344] Generated Node #2: [28, 1344] from Operation: 24*56=1344 Current State: 50:[28, 1344], Operations: ['24*56=1344'] Exploring Operation: 56+1344=1400, Resulting Numbers: [28, 1400] Generated Node #3: [28, 1400] from Operation: 56+1344=1400 Current State: 50:[28, 1400], Operations: ['24*56=1344', '56+1344=1400'] Exploring Operation: 1400/28=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[24, 56, 28, 56], Operations: [] Exploring Operation: 56-56=0, Resulting Numbers: [24, 28, 0] Generated Node #0,0: 50:[24, 28, 0] Operation: 56-56=0 Exploring Operation: 56/56=1, Resulting Numbers: [24, 28, 1] Generated Node #0,1: 50:[24, 28, 1] Operation: 56/56=1 Exploring Operation: 56/28=2, Resulting Numbers: [24, 56, 2] Generated Node #0,2: 50:[24, 56, 2] Operation: 56/28=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[24, 28, 1], Operations: ['56/56=1'] Exploring Operation: 28-24=4, Resulting Numbers: [1, 4] Generated Node #0,1,0: 50:[1, 4] Operation: 28-24=4 Exploring Operation: 24+1=25, Resulting Numbers: [28, 25] Generated Node #0,1,1: 50:[28, 25] Operation: 24+1=25 Exploring Operation: 24+28=52, Resulting Numbers: [1, 52] Generated Node #0,1,2: 50:[1, 52] Operation: 24+28=52 Moving to Node #0,1,0 Current State: 50:[1, 4], Operations: ['56/56=1', '28-24=4'] Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[28, 25], Operations: ['56/56=1', '24+1=25'] Exploring Operation: 28*25=700, Resulting Numbers: [700] 700,50 unequal: No Solution Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,50 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,50 unequal: No Solution Moving to Node #0,1,2 Current State: 50:[1, 52], Operations: ['56/56=1', '24+28=52'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,50 unequal: No Solution Exploring Operation: 1*52=52, Resulting Numbers: [52] 52,50 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:[24, 28, 0], Operations: ['56-56=0'] Exploring Operation: 24+28=52, Resulting Numbers: [0, 52] Generated Node #0,0,0: 50:[0, 52] Operation: 24+28=52 Exploring Operation: 28*0=0, Resulting Numbers: [24, 0] Generated Node #0,0,1: 50:[24, 0] Operation: 28*0=0 Exploring Operation: 28-24=4, Resulting Numbers: [0, 4] Generated Node #0,0,2: 50:[0, 4] Operation: 28-24=4 Moving to Node #0,0,1 Current State: 50:[24, 0], Operations: ['56-56=0', '28*0=0'] Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,50 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,50 unequal: No Solution Moving to Node #0,0,2 Current State: 50:[0, 4], Operations: ['56-56=0', '28-24=4'] Exploring Operation: 0*4=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 0+4=4, Resulting Numbers: [4] 4,50 unequal: No Solution Exploring Operation: 4-0=4, Resulting Numbers: [4] 4,50 unequal: No Solution Moving to Node #0,0,0 Current State: 50:[0, 52], Operations: ['56-56=0', '24+28=52'] Exploring Operation: 0*52=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 52-0=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 0+52=52, Resulting Numbers: [52] 52,50 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 #0,2 Current State: 50:[24, 56, 2], Operations: ['56/28=2'] Exploring Operation: 56-24=32, Resulting Numbers: [2, 32] Generated Node #0,2,0: 50:[2, 32] Operation: 56-24=32 Exploring Operation: 56/2=28, Resulting Numbers: [24, 28] Generated Node #0,2,1: 50:[24, 28] Operation: 56/2=28 Exploring Operation: 56-2=54, Resulting Numbers: [24, 54] Generated Node #0,2,2: 50:[24, 54] Operation: 56-2=54 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 50:[24, 28], Operations: ['56/28=2', '56/2=28'] Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,50 unequal: No Solution Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,50 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,50 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 #0,2,2 Current State: 50:[24, 54], Operations: ['56/28=2', '56-2=54'] Exploring Operation: 24+54=78, Resulting Numbers: [78] 78,50 unequal: No Solution Exploring Operation: 54-24=30, Resulting Numbers: [30] 30,50 unequal: No Solution Exploring Operation: 24*54=1296, Resulting Numbers: [1296] 1296,50 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 #0,2,0 Current State: 50:[2, 32], Operations: ['56/28=2', '56-24=32'] Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,50 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,50 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,50 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_3
sum_heuristic
[ 8, 32, 21, 72 ]
11
[ "8+32=40", "72-21=51", "51-40=11" ]
Current State: 11:[8, 32, 21, 72], Operations: [] Exploring Operation: 8+32=40, Resulting Numbers: [21, 72, 40] Generated Node #2: [21, 72, 40] from Operation: 8+32=40 Current State: 11:[21, 72, 40], Operations: ['8+32=40'] Exploring Operation: 72-21=51, Resulting Numbers: [40, 51] Generated Node #3: [40, 51] from Operation: 72-21=51 Current State: 11:[40, 51], Operations: ['8+32=40', '72-21=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[8, 32, 21, 72], Operations: [] Exploring Operation: 72/8=9, Resulting Numbers: [32, 21, 9] Generated Node #0,0: 11:[32, 21, 9] Operation: 72/8=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[32, 21, 9], Operations: ['72/8=9'] Exploring Operation: 32-21=11, Resulting Numbers: [9, 11] Generated Node #0,0,0: 11:[9, 11] Operation: 32-21=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[9, 11], Operations: ['72/8=9', '32-21=11'] Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,11 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
[ 10, 31, 77, 93 ]
64
[ "77-10=67", "93/31=3", "67-3=64" ]
Current State: 64:[10, 31, 77, 93], Operations: [] Exploring Operation: 77-10=67, Resulting Numbers: [31, 93, 67] Generated Node #2: [31, 93, 67] from Operation: 77-10=67 Current State: 64:[31, 93, 67], Operations: ['77-10=67'] Exploring Operation: 93/31=3, Resulting Numbers: [67, 3] Generated Node #3: [67, 3] from Operation: 93/31=3 Current State: 64:[67, 3], Operations: ['77-10=67', '93/31=3'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[10, 31, 77, 93], Operations: [] Exploring Operation: 77-10=67, Resulting Numbers: [31, 93, 67] Generated Node #0,0: 64:[31, 93, 67] Operation: 77-10=67 Exploring Operation: 93/31=3, Resulting Numbers: [10, 77, 3] Generated Node #0,1: 64:[10, 77, 3] Operation: 93/31=3 Exploring Operation: 93-31=62, Resulting Numbers: [10, 77, 62] Generated Node #0,2: 64:[10, 77, 62] Operation: 93-31=62 Exploring Operation: 93-77=16, Resulting Numbers: [10, 31, 16] Generated Node #0,3: 64:[10, 31, 16] Operation: 93-77=16 Start Sub Search at level 1: Moving to Node #0,3 Current State: 64:[10, 31, 16], Operations: ['93-77=16'] Exploring Operation: 31-16=15, Resulting Numbers: [10, 15] Generated Node #0,3,0: 64:[10, 15] Operation: 31-16=15 Exploring Operation: 31-10=21, Resulting Numbers: [16, 21] Generated Node #0,3,1: 64:[16, 21] Operation: 31-10=21 Exploring Operation: 16-10=6, Resulting Numbers: [31, 6] Generated Node #0,3,2: 64:[31, 6] Operation: 16-10=6 Exploring Operation: 10+16=26, Resulting Numbers: [31, 26] Generated Node #0,3,3: 64:[31, 26] Operation: 10+16=26 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 64:[10, 15], Operations: ['93-77=16', '31-16=15'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 10*15=150, Resulting Numbers: [150] 150,64 unequal: No Solution Exploring Operation: 10+15=25, Resulting Numbers: [25] 25,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 64:[31, 6], Operations: ['93-77=16', '16-10=6'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,64 unequal: No Solution Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 64:[16, 21], Operations: ['93-77=16', '31-10=21'] Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,64 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,64 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 64:[31, 26], Operations: ['93-77=16', '10+16=26'] Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,64 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,64 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[10, 77, 3], Operations: ['93/31=3'] Exploring Operation: 77-10=67, Resulting Numbers: [3, 67] Generated Node #0,1,0: 64:[3, 67] Operation: 77-10=67 Exploring Operation: 10-3=7, Resulting Numbers: [77, 7] Generated Node #0,1,1: 64:[77, 7] Operation: 10-3=7 Exploring Operation: 10*3=30, Resulting Numbers: [77, 30] Generated Node #0,1,2: 64:[77, 30] Operation: 10*3=30 Exploring Operation: 77-3=74, Resulting Numbers: [10, 74] Generated Node #0,1,3: 64:[10, 74] Operation: 77-3=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 64:[3, 67], Operations: ['93/31=3', '77-10=67'] Exploring Operation: 3+67=70, Resulting Numbers: [70] 70,64 unequal: No Solution Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[10, 31, 77, 93], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [10, 77, 3] Generated Node #0,1: 64:[10, 77, 3] Operation: 93/31=3 Moving to Node #0,1 Current State: 64:[10, 77, 3], Operations: ['93/31=3'] Exploring Operation: 77-10=67, Resulting Numbers: [3, 67] Generated Node #0,1,0: 64:[3, 67] Operation: 77-10=67 Moving to Node #0,1,0 Current State: 64:[3, 67], Operations: ['93/31=3', '77-10=67'] Exploring Operation: 67-3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 48, 94, 23, 33 ]
35
[ "94-48=46", "46/23=2", "33+2=35" ]
Current State: 35:[48, 94, 23, 33], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [23, 33, 46] Generated Node #2: [23, 33, 46] from Operation: 94-48=46 Current State: 35:[23, 33, 46], Operations: ['94-48=46'] Exploring Operation: 46/23=2, Resulting Numbers: [33, 2] Generated Node #3: [33, 2] from Operation: 46/23=2 Current State: 35:[33, 2], Operations: ['94-48=46', '46/23=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[48, 94, 23, 33], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [23, 33, 46] Generated Node #0,0: 35:[23, 33, 46] Operation: 94-48=46 Moving to Node #0,0 Current State: 35:[23, 33, 46], Operations: ['94-48=46'] Exploring Operation: 46/23=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 35:[33, 2] Operation: 46/23=2 Moving to Node #0,0,0 Current State: 35:[33, 2], Operations: ['94-48=46', '46/23=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[48, 94, 23, 33], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [23, 33, 46] Generated Node #0,0: 35:[23, 33, 46] Operation: 94-48=46 Moving to Node #0,0 Current State: 35:[23, 33, 46], Operations: ['94-48=46'] Exploring Operation: 46/23=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 35:[33, 2] Operation: 46/23=2 Moving to Node #0,0,0 Current State: 35:[33, 2], Operations: ['94-48=46', '46/23=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 82, 71, 78, 17 ]
92
[ "82+71=153", "78-17=61", "153-61=92" ]
Current State: 92:[82, 71, 78, 17], Operations: [] Exploring Operation: 82+71=153, Resulting Numbers: [78, 17, 153] Generated Node #2: [78, 17, 153] from Operation: 82+71=153 Current State: 92:[78, 17, 153], Operations: ['82+71=153'] Exploring Operation: 78-17=61, Resulting Numbers: [153, 61] Generated Node #3: [153, 61] from Operation: 78-17=61 Current State: 92:[153, 61], Operations: ['82+71=153', '78-17=61'] Exploring Operation: 153-61=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[82, 71, 78, 17], Operations: [] Exploring Operation: 78-71=7, Resulting Numbers: [82, 17, 7] Generated Node #0,0: 92:[82, 17, 7] Operation: 78-71=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[82, 17, 7], Operations: ['78-71=7'] Exploring Operation: 82+7=89, Resulting Numbers: [17, 89] Generated Node #0,0,0: 92:[17, 89] Operation: 82+7=89 Moving to Node #0,0,0 Current State: 92:[17, 89], Operations: ['78-71=7', '82+7=89'] Exploring Operation: 17+89=106, Resulting Numbers: [106] 106,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 57, 66, 84, 15 ]
14
[ "66-57=9", "15-9=6", "84/6=14" ]
Current State: 14:[57, 66, 84, 15], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [84, 15, 9] Generated Node #2: [84, 15, 9] from Operation: 66-57=9 Current State: 14:[84, 15, 9], Operations: ['66-57=9'] Exploring Operation: 15-9=6, Resulting Numbers: [84, 6] Generated Node #3: [84, 6] from Operation: 15-9=6 Current State: 14:[84, 6], Operations: ['66-57=9', '15-9=6'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[57, 66, 84, 15], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [57, 15, 18] Generated Node #0,0: 14:[57, 15, 18] Operation: 84-66=18 Exploring Operation: 84-57=27, Resulting Numbers: [66, 15, 27] Generated Node #0,1: 14:[66, 15, 27] Operation: 84-57=27 Exploring Operation: 57-15=42, Resulting Numbers: [66, 84, 42] Generated Node #0,2: 14:[66, 84, 42] Operation: 57-15=42 Exploring Operation: 66-57=9, Resulting Numbers: [84, 15, 9] Generated Node #0,3: 14:[84, 15, 9] Operation: 66-57=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[57, 15, 18], Operations: ['84-66=18'] Exploring Operation: 57-15=42, Resulting Numbers: [18, 42] Generated Node #0,0,0: 14:[18, 42] Operation: 57-15=42 Exploring Operation: 57+15=72, Resulting Numbers: [18, 72] Generated Node #0,0,1: 14:[18, 72] Operation: 57+15=72 Exploring Operation: 57-18=39, Resulting Numbers: [15, 39] Generated Node #0,0,2: 14:[15, 39] Operation: 57-18=39 Exploring Operation: 18-15=3, Resulting Numbers: [57, 3] Generated Node #0,0,3: 14:[57, 3] Operation: 18-15=3 Moving to Node #0,0,2 Current State: 14:[15, 39], Operations: ['84-66=18', '57-18=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[18, 42], Operations: ['84-66=18', '57-15=42'] Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 18*42=756, Resulting Numbers: [756] 756,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[57, 3], Operations: ['84-66=18', '18-15=3'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,14 unequal: No Solution Exploring Operation: 57+3=60, Resulting Numbers: [60] 60,14 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 57*3=171, Resulting Numbers: [171] 171,14 unequal: No Solution Moving to Node #0,0,1 Current State: 14:[18, 72], Operations: ['84-66=18', '57+15=72'] Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 18*72=1296, Resulting Numbers: [1296] 1296,14 unequal: No Solution Exploring Operation: 72/18=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 18+72=90, Resulting Numbers: [90] 90,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[66, 15, 27], Operations: ['84-57=27'] Exploring Operation: 66-15=51, Resulting Numbers: [27, 51] Generated Node #0,1,0: 14:[27, 51] Operation: 66-15=51 Exploring Operation: 66+15=81, Resulting Numbers: [27, 81] Generated Node #0,1,1: 14:[27, 81] Operation: 66+15=81 Exploring Operation: 66-27=39, Resulting Numbers: [15, 39] Generated Node #0,1,2: 14:[15, 39] Operation: 66-27=39 Exploring Operation: 27-15=12, Resulting Numbers: [66, 12] Generated Node #0,1,3: 14:[66, 12] Operation: 27-15=12 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 14:[15, 39], Operations: ['84-57=27', '66-27=39'] Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,14 unequal: No Solution Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[27, 51], Operations: ['84-57=27', '66-15=51'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 14:[66, 12], Operations: ['84-57=27', '27-15=12'] Exploring Operation: 66-12=54, Resulting Numbers: [54] 54,14 unequal: No Solution Exploring Operation: 66+12=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 66*12=792, Resulting Numbers: [792] 792,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[27, 81], Operations: ['84-57=27', '66+15=81'] Exploring Operation: 81/27=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 27+81=108, Resulting Numbers: [108] 108,14 unequal: No Solution Exploring Operation: 27*81=2187, Resulting Numbers: [2187] 2187,14 unequal: No Solution Exploring Operation: 81-27=54, Resulting Numbers: [54] 54,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[84, 15, 9], Operations: ['66-57=9'] Exploring Operation: 84-15=69, Resulting Numbers: [9, 69] Generated Node #0,3,0: 14:[9, 69] Operation: 84-15=69 Exploring Operation: 84-9=75, Resulting Numbers: [15, 75] Generated Node #0,3,1: 14:[15, 75] Operation: 84-9=75 Exploring Operation: 84+9=93, Resulting Numbers: [15, 93] Generated Node #0,3,2: 14:[15, 93] Operation: 84+9=93 Exploring Operation: 15-9=6, Resulting Numbers: [84, 6] Generated Node #0,3,3: 14:[84, 6] Operation: 15-9=6 Moving to Node #0,3,0 Current State: 14:[9, 69], Operations: ['66-57=9', '84-15=69'] Exploring Operation: 9+69=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 9*69=621, Resulting Numbers: [621] 621,14 unequal: No Solution Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,14 unequal: No Solution Moving to Node #0,3,1 Current State: 14:[15, 75], Operations: ['66-57=9', '84-9=75'] Exploring Operation: 75/15=5, Resulting Numbers: [5] 5,14 unequal: No Solution Exploring Operation: 15+75=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 15*75=1125, Resulting Numbers: [1125] 1125,14 unequal: No Solution Exploring Operation: 75-15=60, Resulting Numbers: [60] 60,14 unequal: No Solution Moving to Node #0,3,3 Current State: 14:[84, 6], Operations: ['66-57=9', '15-9=6'] Exploring Operation: 84-6=78, Resulting Numbers: [78] 78,14 unequal: No Solution Exploring Operation: 84+6=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[57, 66, 84, 15], Operations: [] Exploring Operation: 66-57=9, Resulting Numbers: [84, 15, 9] Generated Node #0,3: 14:[84, 15, 9] Operation: 66-57=9 Moving to Node #0,3 Current State: 14:[84, 15, 9], Operations: ['66-57=9'] Exploring Operation: 15-9=6, Resulting Numbers: [84, 6] Generated Node #0,3,3: 14:[84, 6] Operation: 15-9=6 Moving to Node #0,3,3 Current State: 14:[84, 6], Operations: ['66-57=9', '15-9=6'] Exploring Operation: 84/6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.950521
hs_4
mult_heuristic
[ 92, 14, 79, 61 ]
34
[ "92+14=106", "79+61=140", "140-106=34" ]
Current State: 34:[92, 14, 79, 61], Operations: [] Exploring Operation: 92+14=106, Resulting Numbers: [79, 61, 106] Generated Node #2: [79, 61, 106] from Operation: 92+14=106 Current State: 34:[79, 61, 106], Operations: ['92+14=106'] Exploring Operation: 79+61=140, Resulting Numbers: [106, 140] Generated Node #3: [106, 140] from Operation: 79+61=140 Current State: 34:[106, 140], Operations: ['92+14=106', '79+61=140'] Exploring Operation: 140-106=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[92, 14, 79, 61], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [14, 61, 13] Generated Node #0,0: 34:[14, 61, 13] Operation: 92-79=13 Exploring Operation: 92-61=31, Resulting Numbers: [14, 79, 31] Generated Node #0,1: 34:[14, 79, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 34:[14, 61, 13], Operations: ['92-79=13'] Exploring Operation: 61-13=48, Resulting Numbers: [14, 48] Generated Node #0,0,0: 34:[14, 48] Operation: 61-13=48 Exploring Operation: 61-14=47, Resulting Numbers: [13, 47] Generated Node #0,0,1: 34:[13, 47] Operation: 61-14=47 Moving to Node #0,1 Current State: 34:[14, 79, 31], Operations: ['92-61=31'] Exploring Operation: 79-31=48, Resulting Numbers: [14, 48] Generated Node #0,1,0: 34:[14, 48] Operation: 79-31=48 Exploring Operation: 79-14=65, Resulting Numbers: [31, 65] Generated Node #0,1,1: 34:[31, 65] Operation: 79-14=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 34:[14, 48], Operations: ['92-61=31', '79-31=48'] Exploring Operation: 14+48=62, Resulting Numbers: [62] 62,34 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[92, 14, 79, 61], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [14, 79, 31] Generated Node #0,1: 34:[14, 79, 31] Operation: 92-61=31 Moving to Node #0,1 Current State: 34:[14, 79, 31], Operations: ['92-61=31'] Exploring Operation: 79-31=48, Resulting Numbers: [14, 48] Generated Node #0,1,0: 34:[14, 48] Operation: 79-31=48 Moving to Node #0,1,0 Current State: 34:[14, 48], Operations: ['92-61=31', '79-31=48'] Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
sum_heuristic
[ 8, 75, 7, 25 ]
77
[ "75/25=3", "8+3=11", "7*11=77" ]
Current State: 77:[8, 75, 7, 25], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [8, 7, 3] Generated Node #2: [8, 7, 3] from Operation: 75/25=3 Current State: 77:[8, 7, 3], Operations: ['75/25=3'] Exploring Operation: 8+3=11, Resulting Numbers: [7, 11] Generated Node #3: [7, 11] from Operation: 8+3=11 Current State: 77:[7, 11], Operations: ['75/25=3', '8+3=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[8, 75, 7, 25], Operations: [] Exploring Operation: 25-7=18, Resulting Numbers: [8, 75, 18] Generated Node #0,0: 77:[8, 75, 18] Operation: 25-7=18 Exploring Operation: 75/25=3, Resulting Numbers: [8, 7, 3] Generated Node #0,1: 77:[8, 7, 3] Operation: 75/25=3 Exploring Operation: 8+75=83, Resulting Numbers: [7, 25, 83] Generated Node #0,2: 77:[7, 25, 83] Operation: 8+75=83 Exploring Operation: 25-8=17, Resulting Numbers: [75, 7, 17] Generated Node #0,3: 77:[75, 7, 17] Operation: 25-8=17 Moving to Node #0,1 Current State: 77:[8, 7, 3], Operations: ['75/25=3'] Exploring Operation: 8+3=11, Resulting Numbers: [7, 11] Generated Node #0,1,0: 77:[7, 11] Operation: 8+3=11 Exploring Operation: 8-3=5, Resulting Numbers: [7, 5] Generated Node #0,1,1: 77:[7, 5] Operation: 8-3=5 Exploring Operation: 7-3=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 77:[8, 4] Operation: 7-3=4 Exploring Operation: 7+3=10, Resulting Numbers: [8, 10] Generated Node #0,1,3: 77:[8, 10] Operation: 7+3=10 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[7, 11], Operations: ['75/25=3', '8+3=11'] Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[8, 75, 7, 25], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [8, 7, 3] Generated Node #0,1: 77:[8, 7, 3] Operation: 75/25=3 Moving to Node #0,1 Current State: 77:[8, 7, 3], Operations: ['75/25=3'] Exploring Operation: 8+3=11, Resulting Numbers: [7, 11] Generated Node #0,1,0: 77:[7, 11] Operation: 8+3=11 Moving to Node #0,1,0 Current State: 77:[7, 11], Operations: ['75/25=3', '8+3=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 24, 82, 17, 92 ]
17
[ "82-24=58", "92-17=75", "75-58=17" ]
Current State: 17:[24, 82, 17, 92], Operations: [] Exploring Operation: 82-24=58, Resulting Numbers: [17, 92, 58] Generated Node #2: [17, 92, 58] from Operation: 82-24=58 Current State: 17:[17, 92, 58], Operations: ['82-24=58'] Exploring Operation: 92-17=75, Resulting Numbers: [58, 75] Generated Node #3: [58, 75] from Operation: 92-17=75 Current State: 17:[58, 75], Operations: ['82-24=58', '92-17=75'] Exploring Operation: 75-58=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[24, 82, 17, 92], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [24, 17, 10] Generated Node #0,0: 17:[24, 17, 10] Operation: 92-82=10 Exploring Operation: 92-24=68, Resulting Numbers: [82, 17, 68] Generated Node #0,1: 17:[82, 17, 68] Operation: 92-24=68 Exploring Operation: 82-24=58, Resulting Numbers: [17, 92, 58] Generated Node #0,2: 17:[17, 92, 58] Operation: 82-24=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[24, 17, 10], Operations: ['92-82=10'] Exploring Operation: 24-17=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 17:[10, 7] Operation: 24-17=7 Exploring Operation: 24+10=34, Resulting Numbers: [17, 34] Generated Node #0,0,1: 17:[17, 34] Operation: 24+10=34 Exploring Operation: 24-10=14, Resulting Numbers: [17, 14] Generated Node #0,0,2: 17:[17, 14] Operation: 24-10=14 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 17:[17, 14], Operations: ['92-82=10', '24-10=14'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 17*14=238, Resulting Numbers: [238] 238,17 unequal: No Solution No 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: 17:[10, 7], Operations: ['92-82=10', '24-17=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[24, 82, 17, 92], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [24, 17, 10] Generated Node #0,0: 17:[24, 17, 10] Operation: 92-82=10 Moving to Node #0,0 Current State: 17:[24, 17, 10], Operations: ['92-82=10'] Exploring Operation: 24-17=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 17:[10, 7] Operation: 24-17=7 Moving to Node #0,0,0 Current State: 17:[10, 7], Operations: ['92-82=10', '24-17=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 22, 12, 18, 54 ]
13
[ "22-12=10", "54/18=3", "10+3=13" ]
Current State: 13:[22, 12, 18, 54], Operations: [] Exploring Operation: 22-12=10, Resulting Numbers: [18, 54, 10] Generated Node #2: [18, 54, 10] from Operation: 22-12=10 Current State: 13:[18, 54, 10], Operations: ['22-12=10'] Exploring Operation: 54/18=3, Resulting Numbers: [10, 3] Generated Node #3: [10, 3] from Operation: 54/18=3 Current State: 13:[10, 3], Operations: ['22-12=10', '54/18=3'] Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[22, 12, 18, 54], Operations: [] Exploring Operation: 54-22=32, Resulting Numbers: [12, 18, 32] Generated Node #0,0: 13:[12, 18, 32] Operation: 54-22=32 Exploring Operation: 54/18=3, Resulting Numbers: [22, 12, 3] Generated Node #0,1: 13:[22, 12, 3] Operation: 54/18=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[22, 12, 3], Operations: ['54/18=3'] Exploring Operation: 22-3=19, Resulting Numbers: [12, 19] Generated Node #0,1,0: 13:[12, 19] Operation: 22-3=19 Exploring Operation: 12+3=15, Resulting Numbers: [22, 15] Generated Node #0,1,1: 13:[22, 15] Operation: 12+3=15 Moving to Node #0,1,0 Current State: 13:[12, 19], Operations: ['54/18=3', '22-3=19'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[22, 15], Operations: ['54/18=3', '12+3=15'] Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,13 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,13 unequal: No Solution No 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: 13:[12, 18, 32], Operations: ['54-22=32'] Exploring Operation: 32-12=20, Resulting Numbers: [18, 20] Generated Node #0,0,0: 13:[18, 20] Operation: 32-12=20 Exploring Operation: 32-18=14, Resulting Numbers: [12, 14] Generated Node #0,0,1: 13:[12, 14] Operation: 32-18=14 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[12, 14], Operations: ['54-22=32', '32-18=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,13 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[18, 20], Operations: ['54-22=32', '32-12=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,13 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_2
sum_heuristic
[ 72, 70, 11, 5 ]
21
[ "72-70=2", "5*2=10", "11+10=21" ]
Current State: 21:[72, 70, 11, 5], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [11, 5, 2] Generated Node #2: [11, 5, 2] from Operation: 72-70=2 Current State: 21:[11, 5, 2], Operations: ['72-70=2'] Exploring Operation: 5*2=10, Resulting Numbers: [11, 10] Generated Node #3: [11, 10] from Operation: 5*2=10 Current State: 21:[11, 10], Operations: ['72-70=2', '5*2=10'] Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[72, 70, 11, 5], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [11, 5, 2] Generated Node #0,0: 21:[11, 5, 2] Operation: 72-70=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[11, 5, 2], Operations: ['72-70=2'] Exploring Operation: 11-5=6, Resulting Numbers: [2, 6] Generated Node #0,0,0: 21:[2, 6] Operation: 11-5=6 Moving to Node #0,0,0 Current State: 21:[2, 6], Operations: ['72-70=2', '11-5=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,21 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
[ 90, 16, 82, 2 ]
18
[ "90*16=1440", "82-2=80", "1440/80=18" ]
Current State: 18:[90, 16, 82, 2], Operations: [] Exploring Operation: 90*16=1440, Resulting Numbers: [82, 2, 1440] Generated Node #2: [82, 2, 1440] from Operation: 90*16=1440 Current State: 18:[82, 2, 1440], Operations: ['90*16=1440'] Exploring Operation: 82-2=80, Resulting Numbers: [1440, 80] Generated Node #3: [1440, 80] from Operation: 82-2=80 Current State: 18:[1440, 80], Operations: ['90*16=1440', '82-2=80'] Exploring Operation: 1440/80=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 16, 82, 2], Operations: [] Exploring Operation: 90-82=8, Resulting Numbers: [16, 2, 8] Generated Node #0,0: 18:[16, 2, 8] Operation: 90-82=8 Moving to Node #0,0 Current State: 18:[16, 2, 8], Operations: ['90-82=8'] Exploring Operation: 16/8=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 18:[2, 2] Operation: 16/8=2 Moving to Node #0,0,0 Current State: 18:[2, 2], Operations: ['90-82=8', '16/8=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 73, 40, 46, 18 ]
97
[ "73-40=33", "46+18=64", "33+64=97" ]
Current State: 97:[73, 40, 46, 18], Operations: [] Exploring Operation: 73-40=33, Resulting Numbers: [46, 18, 33] Generated Node #2: [46, 18, 33] from Operation: 73-40=33 Current State: 97:[46, 18, 33], Operations: ['73-40=33'] Exploring Operation: 46+18=64, Resulting Numbers: [33, 64] Generated Node #3: [33, 64] from Operation: 46+18=64 Current State: 97:[33, 64], Operations: ['73-40=33', '46+18=64'] Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[73, 40, 46, 18], Operations: [] Exploring Operation: 73+18=91, Resulting Numbers: [40, 46, 91] Generated Node #0,0: 97:[40, 46, 91] Operation: 73+18=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[40, 46, 91], Operations: ['73+18=91'] Exploring Operation: 40+46=86, Resulting Numbers: [91, 86] Generated Node #0,0,0: 97:[91, 86] Operation: 40+46=86 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[91, 86], Operations: ['73+18=91', '40+46=86'] Exploring Operation: 91+86=177, Resulting Numbers: [177] 177,97 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
[ 52, 55, 88, 15 ]
93
[ "55-52=3", "15/3=5", "88+5=93" ]
Current State: 93:[52, 55, 88, 15], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [88, 15, 3] Generated Node #2: [88, 15, 3] from Operation: 55-52=3 Current State: 93:[88, 15, 3], Operations: ['55-52=3'] Exploring Operation: 15/3=5, Resulting Numbers: [88, 5] Generated Node #3: [88, 5] from Operation: 15/3=5 Current State: 93:[88, 5], Operations: ['55-52=3', '15/3=5'] Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[52, 55, 88, 15], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [88, 15, 3] Generated Node #0,0: 93:[88, 15, 3] Operation: 55-52=3 Moving to Node #0,0 Current State: 93:[88, 15, 3], Operations: ['55-52=3'] Exploring Operation: 15/3=5, Resulting Numbers: [88, 5] Generated Node #0,0,0: 93:[88, 5] Operation: 15/3=5 Moving to Node #0,0,0 Current State: 93:[88, 5], Operations: ['55-52=3', '15/3=5'] Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[52, 55, 88, 15], Operations: [] Exploring Operation: 55-52=3, Resulting Numbers: [88, 15, 3] Generated Node #0,0: 93:[88, 15, 3] Operation: 55-52=3 Moving to Node #0,0 Current State: 93:[88, 15, 3], Operations: ['55-52=3'] Exploring Operation: 15/3=5, Resulting Numbers: [88, 5] Generated Node #0,0,0: 93:[88, 5] Operation: 15/3=5 Moving to Node #0,0,0 Current State: 93:[88, 5], Operations: ['55-52=3', '15/3=5'] Exploring Operation: 88+5=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.993924
hs_1
sum_heuristic