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
[ 15, 22, 75, 14 ]
31
[ "75/15=5", "22+14=36", "36-5=31" ]
Current State: 31:[15, 22, 75, 14], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [22, 14, 5] Generated Node #2: [22, 14, 5] from Operation: 75/15=5 Current State: 31:[22, 14, 5], Operations: ['75/15=5'] Exploring Operation: 22+14=36, Resulting Numbers: [5, 36] Generated Node #3: [5, 36] from Operation: 22+14=36 Current State: 31:[5, 36], Operations: ['75/15=5', '22+14=36'] Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[15, 22, 75, 14], Operations: [] Exploring Operation: 75-15=60, Resulting Numbers: [22, 14, 60] Generated Node #0,0: 31:[22, 14, 60] Operation: 75-15=60 Exploring Operation: 75/15=5, Resulting Numbers: [22, 14, 5] Generated Node #0,1: 31:[22, 14, 5] Operation: 75/15=5 Exploring Operation: 75-22=53, Resulting Numbers: [15, 14, 53] Generated Node #0,2: 31:[15, 14, 53] Operation: 75-22=53 Exploring Operation: 75-14=61, Resulting Numbers: [15, 22, 61] Generated Node #0,3: 31:[15, 22, 61] Operation: 75-14=61 Exploring Operation: 15+14=29, Resulting Numbers: [22, 75, 29] Generated Node #0,4: 31:[22, 75, 29] Operation: 15+14=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 31:[22, 14, 5], Operations: ['75/15=5'] Exploring Operation: 22+5=27, Resulting Numbers: [14, 27] Generated Node #0,1,0: 31:[14, 27] Operation: 22+5=27 Exploring Operation: 14-5=9, Resulting Numbers: [22, 9] Generated Node #0,1,1: 31:[22, 9] Operation: 14-5=9 Exploring Operation: 22-5=17, Resulting Numbers: [14, 17] Generated Node #0,1,2: 31:[14, 17] Operation: 22-5=17 Exploring Operation: 14+5=19, Resulting Numbers: [22, 19] Generated Node #0,1,3: 31:[22, 19] Operation: 14+5=19 Exploring Operation: 22+14=36, Resulting Numbers: [5, 36] Generated Node #0,1,4: 31:[5, 36] Operation: 22+14=36 Moving to Node #0,1,0 Current State: 31:[14, 27], Operations: ['75/15=5', '22+5=27'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 14*27=378, Resulting Numbers: [378] 378,31 unequal: No Solution Exploring Operation: 14+27=41, Resulting Numbers: [41] 41,31 unequal: No Solution Moving to Node #0,1,3 Current State: 31:[22, 19], Operations: ['75/15=5', '14+5=19'] Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,31 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,31 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[22, 9], Operations: ['75/15=5', '14-5=9'] Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[15, 22, 75, 14], Operations: [] Exploring Operation: 75/15=5, Resulting Numbers: [22, 14, 5] Generated Node #0,1: 31:[22, 14, 5] Operation: 75/15=5 Moving to Node #0,1 Current State: 31:[22, 14, 5], Operations: ['75/15=5'] Exploring Operation: 14-5=9, Resulting Numbers: [22, 9] Generated Node #0,1,1: 31:[22, 9] Operation: 14-5=9 Moving to Node #0,1,1 Current State: 31:[22, 9], Operations: ['75/15=5', '14-5=9'] Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 84, 66, 36, 46 ]
23
[ "84-66=18", "36/18=2", "46/2=23" ]
Current State: 23:[84, 66, 36, 46], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [36, 46, 18] Generated Node #2: [36, 46, 18] from Operation: 84-66=18 Current State: 23:[36, 46, 18], Operations: ['84-66=18'] Exploring Operation: 36/18=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 36/18=2 Current State: 23:[46, 2], Operations: ['84-66=18', '36/18=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[84, 66, 36, 46], Operations: [] Exploring Operation: 84-66=18, Resulting Numbers: [36, 46, 18] Generated Node #0,0: 23:[36, 46, 18] Operation: 84-66=18 Moving to Node #0,0 Current State: 23:[36, 46, 18], Operations: ['84-66=18'] Exploring Operation: 46-36=10, Resulting Numbers: [18, 10] Generated Node #0,0,0: 23:[18, 10] Operation: 46-36=10 Moving to Node #0,0,0 Current State: 23:[18, 10], Operations: ['84-66=18', '46-36=10'] Exploring Operation: 18+10=28, Resulting Numbers: [28] 28,23 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 80, 7, 43, 3 ]
35
[ "7+3=10", "80/10=8", "43-8=35" ]
Current State: 35:[80, 7, 43, 3], Operations: [] Exploring Operation: 7+3=10, Resulting Numbers: [80, 43, 10] Generated Node #2: [80, 43, 10] from Operation: 7+3=10 Current State: 35:[80, 43, 10], Operations: ['7+3=10'] Exploring Operation: 80/10=8, Resulting Numbers: [43, 8] Generated Node #3: [43, 8] from Operation: 80/10=8 Current State: 35:[43, 8], Operations: ['7+3=10', '80/10=8'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[80, 7, 43, 3], Operations: [] Exploring Operation: 80-43=37, Resulting Numbers: [7, 3, 37] Generated Node #0,0: 35:[7, 3, 37] Operation: 80-43=37 Exploring Operation: 43-7=36, Resulting Numbers: [80, 3, 36] Generated Node #0,1: 35:[80, 3, 36] Operation: 43-7=36 Exploring Operation: 43-3=40, Resulting Numbers: [80, 7, 40] Generated Node #0,2: 35:[80, 7, 40] Operation: 43-3=40 Exploring Operation: 80-7=73, Resulting Numbers: [43, 3, 73] Generated Node #0,3: 35:[43, 3, 73] Operation: 80-7=73 Exploring Operation: 80-3=77, Resulting Numbers: [7, 43, 77] Generated Node #0,4: 35:[7, 43, 77] Operation: 80-3=77 Moving to Node #0,0 Current State: 35:[7, 3, 37], Operations: ['80-43=37'] Exploring Operation: 3+37=40, Resulting Numbers: [7, 40] Generated Node #0,0,0: 35:[7, 40] Operation: 3+37=40 Exploring Operation: 37-3=34, Resulting Numbers: [7, 34] Generated Node #0,0,1: 35:[7, 34] Operation: 37-3=34 Exploring Operation: 7+3=10, Resulting Numbers: [37, 10] Generated Node #0,0,2: 35:[37, 10] Operation: 7+3=10 Exploring Operation: 7-3=4, Resulting Numbers: [37, 4] Generated Node #0,0,3: 35:[37, 4] Operation: 7-3=4 Exploring Operation: 37-7=30, Resulting Numbers: [3, 30] Generated Node #0,0,4: 35:[3, 30] Operation: 37-7=30 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 35:[7, 34], Operations: ['80-43=37', '37-3=34'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,35 unequal: No Solution Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,35 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:[37, 4], Operations: ['80-43=37', '7-3=4'] Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,35 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,35 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:[7, 40], Operations: ['80-43=37', '3+37=40'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,35 unequal: No Solution Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,35 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 #0,0,2 Current State: 35:[37, 10], Operations: ['80-43=37', '7+3=10'] Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,35 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,35 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 #0,0,4 Current State: 35:[3, 30], Operations: ['80-43=37', '37-7=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,35 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,35 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:[43, 3, 73], Operations: ['80-7=73'] Exploring Operation: 43-3=40, Resulting Numbers: [73, 40] Generated Node #0,3,0: 35:[73, 40] Operation: 43-3=40 Exploring Operation: 73-3=70, Resulting Numbers: [43, 70] Generated Node #0,3,1: 35:[43, 70] Operation: 73-3=70 Exploring Operation: 43+3=46, Resulting Numbers: [73, 46] Generated Node #0,3,2: 35:[73, 46] Operation: 43+3=46 Exploring Operation: 3+73=76, Resulting Numbers: [43, 76] Generated Node #0,3,3: 35:[43, 76] Operation: 3+73=76 Exploring Operation: 73-43=30, Resulting Numbers: [3, 30] Generated Node #0,3,4: 35:[3, 30] Operation: 73-43=30 Moving to Node #0,1 Current State: 35:[80, 3, 36], Operations: ['43-7=36'] Exploring Operation: 80-36=44, Resulting Numbers: [3, 44] Generated Node #0,1,0: 35:[3, 44] Operation: 80-36=44 Exploring Operation: 80+3=83, Resulting Numbers: [36, 83] Generated Node #0,1,1: 35:[36, 83] Operation: 80+3=83 Exploring Operation: 36-3=33, Resulting Numbers: [80, 33] Generated Node #0,1,2: 35:[80, 33] Operation: 36-3=33 Exploring Operation: 80-3=77, Resulting Numbers: [36, 77] Generated Node #0,1,3: 35:[36, 77] Operation: 80-3=77 Exploring Operation: 3+36=39, Resulting Numbers: [80, 39] Generated Node #0,1,4: 35:[80, 39] Operation: 3+36=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 35:[3, 44], Operations: ['43-7=36', '80-36=44'] Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,35 unequal: No Solution Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 35:[36, 77], Operations: ['43-7=36', '80-3=77'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 36*77=2772, Resulting Numbers: [2772] 2772,35 unequal: No Solution Exploring Operation: 36+77=113, Resulting Numbers: [113] 113,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 35:[80, 33], Operations: ['43-7=36', '36-3=33'] Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 80+33=113, Resulting Numbers: [113] 113,35 unequal: No Solution Exploring Operation: 80*33=2640, Resulting Numbers: [2640] 2640,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 35:[36, 83], Operations: ['43-7=36', '80+3=83'] Exploring Operation: 36*83=2988, Resulting Numbers: [2988] 2988,35 unequal: No Solution Exploring Operation: 36+83=119, Resulting Numbers: [119] 119,35 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,35 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 35:[80, 39], Operations: ['43-7=36', '3+36=39'] Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,35 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,35 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: 35:[80, 7, 40], Operations: ['43-3=40'] Exploring Operation: 80+7=87, Resulting Numbers: [40, 87] Generated Node #0,2,0: 35:[40, 87] Operation: 80+7=87 Exploring Operation: 80-40=40, Resulting Numbers: [7, 40] Generated Node #0,2,1: 35:[7, 40] Operation: 80-40=40 Exploring Operation: 80-7=73, Resulting Numbers: [40, 73] Generated Node #0,2,2: 35:[40, 73] Operation: 80-7=73 Exploring Operation: 40-7=33, Resulting Numbers: [80, 33] Generated Node #0,2,3: 35:[80, 33] Operation: 40-7=33 Exploring Operation: 80/40=2, Resulting Numbers: [7, 2] Generated Node #0,2,4: 35:[7, 2] Operation: 80/40=2 Moving to Node #0,4 Current State: 35:[7, 43, 77], Operations: ['80-3=77'] Exploring Operation: 43-7=36, Resulting Numbers: [77, 36] Generated Node #0,4,0: 35:[77, 36] Operation: 43-7=36 Exploring Operation: 77-43=34, Resulting Numbers: [7, 34] Generated Node #0,4,1: 35:[7, 34] Operation: 77-43=34 Exploring Operation: 77/7=11, Resulting Numbers: [43, 11] Generated Node #0,4,2: 35:[43, 11] Operation: 77/7=11 Exploring Operation: 77-7=70, Resulting Numbers: [43, 70] Generated Node #0,4,3: 35:[43, 70] Operation: 77-7=70 Exploring Operation: 7+43=50, Resulting Numbers: [77, 50] Generated Node #0,4,4: 35:[77, 50] Operation: 7+43=50 Moving to Node #0,4,1 Current State: 35:[7, 34], Operations: ['80-3=77', '77-43=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,35 unequal: No Solution Moving to Node #0,2,4 Current State: 35:[7, 2], Operations: ['43-3=40', '80/40=2'] Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,35 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[7, 40], Operations: ['43-3=40', '80-40=40'] Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,35 unequal: No Solution Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,35 unequal: No Solution Moving to Node #0,3,4 Current State: 35:[3, 30], Operations: ['80-7=73', '73-43=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,35 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,35 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,35 unequal: No Solution Moving to Node #0,4,2 Current State: 35:[43, 11], Operations: ['80-3=77', '77/7=11'] Exploring Operation: 43+11=54, Resulting Numbers: [54] 54,35 unequal: No Solution Exploring Operation: 43*11=473, Resulting Numbers: [473] 473,35 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,35 unequal: No Solution Moving to Node #0,4,3 Current State: 35:[43, 70], Operations: ['80-3=77', '77-7=70'] Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,35 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,35 unequal: No Solution Moving to Node #0,4,0 Current State: 35:[77, 36], Operations: ['80-3=77', '43-7=36'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,35 unequal: No Solution Exploring Operation: 77*36=2772, Resulting Numbers: [2772] 2772,35 unequal: No Solution Exploring Operation: 77+36=113, Resulting Numbers: [113] 113,35 unequal: No Solution Moving to Node #0,3,1 Current State: 35:[43, 70], Operations: ['80-7=73', '73-3=70'] Exploring Operation: 43*70=3010, Resulting Numbers: [3010] 3010,35 unequal: No Solution Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,35 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,35 unequal: No Solution Moving to Node #0,3,0 Current State: 35:[73, 40], Operations: ['80-7=73', '43-3=40'] Exploring Operation: 73*40=2920, Resulting Numbers: [2920] 2920,35 unequal: No Solution Exploring Operation: 73+40=113, Resulting Numbers: [113] 113,35 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[40, 73], Operations: ['43-3=40', '80-7=73'] Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 40+73=113, Resulting Numbers: [113] 113,35 unequal: No Solution Exploring Operation: 40*73=2920, Resulting Numbers: [2920] 2920,35 unequal: No Solution Moving to Node #0,2,3 Current State: 35:[80, 33], Operations: ['43-3=40', '40-7=33'] Exploring Operation: 80*33=2640, Resulting Numbers: [2640] 2640,35 unequal: No Solution Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 80+33=113, Resulting Numbers: [113] 113,35 unequal: No Solution Moving to Node #0,3,3 Current State: 35:[43, 76], Operations: ['80-7=73', '3+73=76'] Exploring Operation: 43*76=3268, Resulting Numbers: [3268] 3268,35 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 43+76=119, Resulting Numbers: [119] 119,35 unequal: No Solution Moving to Node #0,3,2 Current State: 35:[73, 46], Operations: ['80-7=73', '43+3=46'] Exploring Operation: 73-46=27, Resulting Numbers: [27] 27,35 unequal: No Solution Exploring Operation: 73*46=3358, Resulting Numbers: [3358] 3358,35 unequal: No Solution Exploring Operation: 73+46=119, Resulting Numbers: [119] 119,35 unequal: No Solution Moving to Node #0,4,4 Current State: 35:[77, 50], Operations: ['80-3=77', '7+43=50'] Exploring Operation: 77+50=127, Resulting Numbers: [127] 127,35 unequal: No Solution Exploring Operation: 77*50=3850, Resulting Numbers: [3850] 3850,35 unequal: No Solution Exploring Operation: 77-50=27, Resulting Numbers: [27] 27,35 unequal: No Solution Moving to Node #0,2,0 Current State: 35:[40, 87], Operations: ['43-3=40', '80+7=87'] Exploring Operation: 87-40=47, Resulting Numbers: [47] 47,35 unequal: No Solution Exploring Operation: 40*87=3480, Resulting Numbers: [3480] 3480,35 unequal: No Solution Exploring Operation: 40+87=127, Resulting Numbers: [127] 127,35 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 13, 44, 33, 54 ]
56
[ "44-13=31", "33+54=87", "87-31=56" ]
Current State: 56:[13, 44, 33, 54], Operations: [] Exploring Operation: 44-13=31, Resulting Numbers: [33, 54, 31] Generated Node #2: [33, 54, 31] from Operation: 44-13=31 Current State: 56:[33, 54, 31], Operations: ['44-13=31'] Exploring Operation: 33+54=87, Resulting Numbers: [31, 87] Generated Node #3: [31, 87] from Operation: 33+54=87 Current State: 56:[31, 87], Operations: ['44-13=31', '33+54=87'] Exploring Operation: 87-31=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[13, 44, 33, 54], Operations: [] Exploring Operation: 44-33=11, Resulting Numbers: [13, 54, 11] Generated Node #0,0: 56:[13, 54, 11] Operation: 44-33=11 Exploring Operation: 13+44=57, Resulting Numbers: [33, 54, 57] Generated Node #0,1: 56:[33, 54, 57] Operation: 13+44=57 Exploring Operation: 54-44=10, Resulting Numbers: [13, 33, 10] Generated Node #0,2: 56:[13, 33, 10] Operation: 54-44=10 Moving to Node #0,0 Current State: 56:[13, 54, 11], Operations: ['44-33=11'] Exploring Operation: 54+11=65, Resulting Numbers: [13, 65] Generated Node #0,0,0: 56:[13, 65] Operation: 54+11=65 Exploring Operation: 13-11=2, Resulting Numbers: [54, 2] Generated Node #0,0,1: 56:[54, 2] Operation: 13-11=2 Exploring Operation: 13+11=24, Resulting Numbers: [54, 24] Generated Node #0,0,2: 56:[54, 24] Operation: 13+11=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 56:[54, 2], Operations: ['44-33=11', '13-11=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,56 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[13, 44, 33, 54], Operations: [] Exploring Operation: 44-33=11, Resulting Numbers: [13, 54, 11] Generated Node #0,0: 56:[13, 54, 11] Operation: 44-33=11 Moving to Node #0,0 Current State: 56:[13, 54, 11], Operations: ['44-33=11'] Exploring Operation: 13-11=2, Resulting Numbers: [54, 2] Generated Node #0,0,1: 56:[54, 2] Operation: 13-11=2 Moving to Node #0,0,1 Current State: 56:[54, 2], Operations: ['44-33=11', '13-11=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 90, 79, 2, 45 ]
80
[ "90/2=45", "45/45=1", "79+1=80" ]
Current State: 80:[90, 79, 2, 45], Operations: [] Exploring Operation: 90/2=45, Resulting Numbers: [79, 45, 45] Generated Node #2: [79, 45, 45] from Operation: 90/2=45 Current State: 80:[79, 45, 45], Operations: ['90/2=45'] Exploring Operation: 45/45=1, Resulting Numbers: [79, 1] Generated Node #3: [79, 1] from Operation: 45/45=1 Current State: 80:[79, 1], Operations: ['90/2=45', '45/45=1'] Exploring Operation: 79+1=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[90, 79, 2, 45], Operations: [] Exploring Operation: 90-79=11, Resulting Numbers: [2, 45, 11] Generated Node #0,0: 80:[2, 45, 11] Operation: 90-79=11 Exploring Operation: 90/45=2, Resulting Numbers: [79, 2, 2] Generated Node #0,1: 80:[79, 2, 2] Operation: 90/45=2 Exploring Operation: 90-45=45, Resulting Numbers: [79, 2, 45] Generated Node #0,2: 80:[79, 2, 45] Operation: 90-45=45 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[79, 2, 2], Operations: ['90/45=2'] Exploring Operation: 79+2=81, Resulting Numbers: [2, 81] Generated Node #0,1,0: 80:[2, 81] Operation: 79+2=81 Exploring Operation: 2+2=4, Resulting Numbers: [79, 4] Generated Node #0,1,1: 80:[79, 4] Operation: 2+2=4 Exploring Operation: 79+2=81, Resulting Numbers: [2, 81] Generated Node #0,1,2: 80:[2, 81] Operation: 79+2=81 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 80:[2, 81], Operations: ['90/45=2', '79+2=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,80 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[79, 4], Operations: ['90/45=2', '2+2=4'] Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,80 unequal: No Solution Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 80:[2, 81], Operations: ['90/45=2', '79+2=81'] Exploring Operation: 2+81=83, Resulting Numbers: [83] 83,80 unequal: No Solution Exploring Operation: 2*81=162, Resulting Numbers: [162] 162,80 unequal: No Solution Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[2, 45, 11], Operations: ['90-79=11'] Exploring Operation: 45-2=43, Resulting Numbers: [11, 43] Generated Node #0,0,0: 80:[11, 43] Operation: 45-2=43 Exploring Operation: 11-2=9, Resulting Numbers: [45, 9] Generated Node #0,0,1: 80:[45, 9] Operation: 11-2=9 Exploring Operation: 45-11=34, Resulting Numbers: [2, 34] Generated Node #0,0,2: 80:[2, 34] Operation: 45-11=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[11, 43], Operations: ['90-79=11', '45-2=43'] Exploring Operation: 11*43=473, Resulting Numbers: [473] 473,80 unequal: No Solution Exploring Operation: 11+43=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 80:[45, 9], Operations: ['90-79=11', '11-2=9'] Exploring Operation: 45+9=54, Resulting Numbers: [54] 54,80 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,80 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 80:[2, 34], Operations: ['90-79=11', '45-11=34'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,80 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 80:[79, 2, 45], Operations: ['90-45=45'] Exploring Operation: 79+2=81, Resulting Numbers: [45, 81] Generated Node #0,2,0: 80:[45, 81] Operation: 79+2=81 Exploring Operation: 45-2=43, Resulting Numbers: [79, 43] Generated Node #0,2,1: 80:[79, 43] Operation: 45-2=43 Exploring Operation: 79-45=34, Resulting Numbers: [2, 34] Generated Node #0,2,2: 80:[2, 34] Operation: 79-45=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 80:[79, 43], Operations: ['90-45=45', '45-2=43'] Exploring Operation: 79-43=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 79+43=122, Resulting Numbers: [122] 122,80 unequal: No Solution Exploring Operation: 79*43=3397, Resulting Numbers: [3397] 3397,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 80:[45, 81], Operations: ['90-45=45', '79+2=81'] Exploring Operation: 45*81=3645, Resulting Numbers: [3645] 3645,80 unequal: No Solution Exploring Operation: 45+81=126, Resulting Numbers: [126] 126,80 unequal: No Solution Exploring Operation: 81-45=36, Resulting Numbers: [36] 36,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 80:[2, 34], Operations: ['90-45=45', '79-45=34'] Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,80 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,80 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,80 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 28, 68, 24, 95 ]
84
[ "68+24=92", "95-92=3", "28*3=84" ]
Current State: 84:[28, 68, 24, 95], Operations: [] Exploring Operation: 68+24=92, Resulting Numbers: [28, 95, 92] Generated Node #2: [28, 95, 92] from Operation: 68+24=92 Current State: 84:[28, 95, 92], Operations: ['68+24=92'] Exploring Operation: 95-92=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 95-92=3 Current State: 84:[28, 3], Operations: ['68+24=92', '95-92=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[28, 68, 24, 95], Operations: [] Exploring Operation: 95-68=27, Resulting Numbers: [28, 24, 27] Generated Node #0,0: 84:[28, 24, 27] Operation: 95-68=27 Exploring Operation: 68+24=92, Resulting Numbers: [28, 95, 92] Generated Node #0,1: 84:[28, 95, 92] Operation: 68+24=92 Exploring Operation: 68-28=40, Resulting Numbers: [24, 95, 40] Generated Node #0,2: 84:[24, 95, 40] Operation: 68-28=40 Exploring Operation: 68-24=44, Resulting Numbers: [28, 95, 44] Generated Node #0,3: 84:[28, 95, 44] Operation: 68-24=44 Exploring Operation: 28+68=96, Resulting Numbers: [24, 95, 96] Generated Node #0,4: 84:[24, 95, 96] Operation: 28+68=96 Moving to Node #0,0 Current State: 84:[28, 24, 27], Operations: ['95-68=27'] Exploring Operation: 28-27=1, Resulting Numbers: [24, 1] Generated Node #0,0,0: 84:[24, 1] Operation: 28-27=1 Exploring Operation: 28-24=4, Resulting Numbers: [27, 4] Generated Node #0,0,1: 84:[27, 4] Operation: 28-24=4 Exploring Operation: 27-24=3, Resulting Numbers: [28, 3] Generated Node #0,0,2: 84:[28, 3] Operation: 27-24=3 Exploring Operation: 24+27=51, Resulting Numbers: [28, 51] Generated Node #0,0,3: 84:[28, 51] Operation: 24+27=51 Exploring Operation: 28+24=52, Resulting Numbers: [27, 52] Generated Node #0,0,4: 84:[27, 52] Operation: 28+24=52 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[28, 3], Operations: ['95-68=27', '27-24=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[28, 68, 24, 95], Operations: [] Exploring Operation: 95-68=27, Resulting Numbers: [28, 24, 27] Generated Node #0,0: 84:[28, 24, 27] Operation: 95-68=27 Moving to Node #0,0 Current State: 84:[28, 24, 27], Operations: ['95-68=27'] Exploring Operation: 27-24=3, Resulting Numbers: [28, 3] Generated Node #0,0,2: 84:[28, 3] Operation: 27-24=3 Moving to Node #0,0,2 Current State: 84:[28, 3], Operations: ['95-68=27', '27-24=3'] Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 27, 12, 16, 87 ]
32
[ "27+12=39", "87-16=71", "71-39=32" ]
Current State: 32:[27, 12, 16, 87], Operations: [] Exploring Operation: 27+12=39, Resulting Numbers: [16, 87, 39] Generated Node #2: [16, 87, 39] from Operation: 27+12=39 Current State: 32:[16, 87, 39], Operations: ['27+12=39'] Exploring Operation: 87-16=71, Resulting Numbers: [39, 71] Generated Node #3: [39, 71] from Operation: 87-16=71 Current State: 32:[39, 71], Operations: ['27+12=39', '87-16=71'] Exploring Operation: 71-39=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[27, 12, 16, 87], Operations: [] Exploring Operation: 87-12=75, Resulting Numbers: [27, 16, 75] Generated Node #0,0: 32:[27, 16, 75] Operation: 87-12=75 Exploring Operation: 87-16=71, Resulting Numbers: [27, 12, 71] Generated Node #0,1: 32:[27, 12, 71] Operation: 87-16=71 Exploring Operation: 87-27=60, Resulting Numbers: [12, 16, 60] Generated Node #0,2: 32:[12, 16, 60] Operation: 87-27=60 Moving to Node #0,2 Current State: 32:[12, 16, 60], Operations: ['87-27=60'] Exploring Operation: 60/12=5, Resulting Numbers: [16, 5] Generated Node #0,2,0: 32:[16, 5] Operation: 60/12=5 Exploring Operation: 60-16=44, Resulting Numbers: [12, 44] Generated Node #0,2,1: 32:[12, 44] Operation: 60-16=44 Exploring Operation: 60-12=48, Resulting Numbers: [16, 48] Generated Node #0,2,2: 32:[16, 48] Operation: 60-12=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[16, 5], Operations: ['87-27=60', '60/12=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,32 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[12, 44], Operations: ['87-27=60', '60-16=44'] Exploring Operation: 12+44=56, Resulting Numbers: [56] 56,32 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[27, 12, 16, 87], Operations: [] Exploring Operation: 87-27=60, Resulting Numbers: [12, 16, 60] Generated Node #0,2: 32:[12, 16, 60] Operation: 87-27=60 Moving to Node #0,2 Current State: 32:[12, 16, 60], Operations: ['87-27=60'] Exploring Operation: 60-16=44, Resulting Numbers: [12, 44] Generated Node #0,2,1: 32:[12, 44] Operation: 60-16=44 Moving to Node #0,2,1 Current State: 32:[12, 44], Operations: ['87-27=60', '60-16=44'] Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 24, 80, 16, 10 ]
35
[ "80-24=56", "10*56=560", "560/16=35" ]
Current State: 35:[24, 80, 16, 10], Operations: [] Exploring Operation: 80-24=56, Resulting Numbers: [16, 10, 56] Generated Node #2: [16, 10, 56] from Operation: 80-24=56 Current State: 35:[16, 10, 56], Operations: ['80-24=56'] Exploring Operation: 10*56=560, Resulting Numbers: [16, 560] Generated Node #3: [16, 560] from Operation: 10*56=560 Current State: 35:[16, 560], Operations: ['80-24=56', '10*56=560'] Exploring Operation: 560/16=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[24, 80, 16, 10], Operations: [] Exploring Operation: 80/16=5, Resulting Numbers: [24, 10, 5] Generated Node #0,0: 35:[24, 10, 5] Operation: 80/16=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[24, 10, 5], Operations: ['80/16=5'] Exploring Operation: 24+10=34, Resulting Numbers: [5, 34] Generated Node #0,0,0: 35:[5, 34] Operation: 24+10=34 Moving to Node #0,0,0 Current State: 35:[5, 34], Operations: ['80/16=5', '24+10=34'] Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,35 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
[ 58, 98, 82, 24 ]
97
[ "82-58=24", "24/24=1", "98-1=97" ]
Current State: 97:[58, 98, 82, 24], Operations: [] Exploring Operation: 82-58=24, Resulting Numbers: [98, 24, 24] Generated Node #2: [98, 24, 24] from Operation: 82-58=24 Current State: 97:[98, 24, 24], Operations: ['82-58=24'] Exploring Operation: 24/24=1, Resulting Numbers: [98, 1] Generated Node #3: [98, 1] from Operation: 24/24=1 Current State: 97:[98, 1], Operations: ['82-58=24', '24/24=1'] Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[58, 98, 82, 24], Operations: [] Exploring Operation: 82+24=106, Resulting Numbers: [58, 98, 106] Generated Node #0,0: 97:[58, 98, 106] Operation: 82+24=106 Exploring Operation: 98-24=74, Resulting Numbers: [58, 82, 74] Generated Node #0,1: 97:[58, 82, 74] Operation: 98-24=74 Exploring Operation: 58+24=82, Resulting Numbers: [98, 82, 82] Generated Node #0,2: 97:[98, 82, 82] Operation: 58+24=82 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[98, 82, 82], Operations: ['58+24=82'] Exploring Operation: 98-82=16, Resulting Numbers: [82, 16] Generated Node #0,2,0: 97:[82, 16] Operation: 98-82=16 Exploring Operation: 98-82=16, Resulting Numbers: [82, 16] Generated Node #0,2,1: 97:[82, 16] Operation: 98-82=16 Exploring Operation: 82+82=164, Resulting Numbers: [98, 164] Generated Node #0,2,2: 97:[98, 164] Operation: 82+82=164 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[98, 164], Operations: ['58+24=82', '82+82=164'] Exploring Operation: 98*164=16072, Resulting Numbers: [16072] 16072,97 unequal: No Solution Exploring Operation: 98+164=262, Resulting Numbers: [262] 262,97 unequal: No Solution Exploring Operation: 164-98=66, Resulting Numbers: [66] 66,97 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 #0,2,0 Current State: 97:[82, 16], Operations: ['58+24=82', '98-82=16'] Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 82*16=1312, Resulting Numbers: [1312] 1312,97 unequal: No Solution Exploring Operation: 82+16=98, Resulting Numbers: [98] 98,97 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 #0,2,1 Current State: 97:[82, 16], Operations: ['58+24=82', '98-82=16'] Exploring Operation: 82-16=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 82+16=98, Resulting Numbers: [98] 98,97 unequal: No Solution Exploring Operation: 82*16=1312, Resulting Numbers: [1312] 1312,97 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[58, 98, 106], Operations: ['82+24=106'] Exploring Operation: 58+98=156, Resulting Numbers: [106, 156] Generated Node #0,0,0: 97:[106, 156] Operation: 58+98=156 Exploring Operation: 106-58=48, Resulting Numbers: [98, 48] Generated Node #0,0,1: 97:[98, 48] Operation: 106-58=48 Exploring Operation: 98-58=40, Resulting Numbers: [106, 40] Generated Node #0,0,2: 97:[106, 40] Operation: 98-58=40 Moving to Node #0,0,1 Current State: 97:[98, 48], Operations: ['82+24=106', '106-58=48'] Exploring Operation: 98-48=50, Resulting Numbers: [50] 50,97 unequal: No Solution Exploring Operation: 98*48=4704, Resulting Numbers: [4704] 4704,97 unequal: No Solution Exploring Operation: 98+48=146, Resulting Numbers: [146] 146,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[106, 40], Operations: ['82+24=106', '98-58=40'] Exploring Operation: 106*40=4240, Resulting Numbers: [4240] 4240,97 unequal: No Solution Exploring Operation: 106+40=146, Resulting Numbers: [146] 146,97 unequal: No Solution Exploring Operation: 106-40=66, Resulting Numbers: [66] 66,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[106, 156], Operations: ['82+24=106', '58+98=156'] Exploring Operation: 156-106=50, Resulting Numbers: [50] 50,97 unequal: No Solution Exploring Operation: 106*156=16536, Resulting Numbers: [16536] 16536,97 unequal: No Solution Exploring Operation: 106+156=262, Resulting Numbers: [262] 262,97 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:[58, 82, 74], Operations: ['98-24=74'] Exploring Operation: 58+74=132, Resulting Numbers: [82, 132] Generated Node #0,1,0: 97:[82, 132] Operation: 58+74=132 Exploring Operation: 82-58=24, Resulting Numbers: [74, 24] Generated Node #0,1,1: 97:[74, 24] Operation: 82-58=24 Exploring Operation: 58+82=140, Resulting Numbers: [74, 140] Generated Node #0,1,2: 97:[74, 140] Operation: 58+82=140 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[82, 132], Operations: ['98-24=74', '58+74=132'] Exploring Operation: 132-82=50, Resulting Numbers: [50] 50,97 unequal: No Solution Exploring Operation: 82+132=214, Resulting Numbers: [214] 214,97 unequal: No Solution Exploring Operation: 82*132=10824, Resulting Numbers: [10824] 10824,97 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 #0,1,2 Current State: 97:[74, 140], Operations: ['98-24=74', '58+82=140'] Exploring Operation: 74+140=214, Resulting Numbers: [214] 214,97 unequal: No Solution Exploring Operation: 140-74=66, Resulting Numbers: [66] 66,97 unequal: No Solution Exploring Operation: 74*140=10360, Resulting Numbers: [10360] 10360,97 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 #0,1,1 Current State: 97:[74, 24], Operations: ['98-24=74', '82-58=24'] Exploring Operation: 74*24=1776, Resulting Numbers: [1776] 1776,97 unequal: No Solution Exploring Operation: 74+24=98, Resulting Numbers: [98] 98,97 unequal: No Solution Exploring Operation: 74-24=50, Resulting Numbers: [50] 50,97 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_3
sum_heuristic
[ 6, 64, 46, 11 ]
35
[ "6+64=70", "46-11=35", "70-35=35" ]
Current State: 35:[6, 64, 46, 11], Operations: [] Exploring Operation: 6+64=70, Resulting Numbers: [46, 11, 70] Generated Node #2: [46, 11, 70] from Operation: 6+64=70 Current State: 35:[46, 11, 70], Operations: ['6+64=70'] Exploring Operation: 46-11=35, Resulting Numbers: [70, 35] Generated Node #3: [70, 35] from Operation: 46-11=35 Current State: 35:[70, 35], Operations: ['6+64=70', '46-11=35'] Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 64, 46, 11], Operations: [] Exploring Operation: 46-11=35, Resulting Numbers: [6, 64, 35] Generated Node #0,0: 35:[6, 64, 35] Operation: 46-11=35 Exploring Operation: 64-46=18, Resulting Numbers: [6, 11, 18] Generated Node #0,1: 35:[6, 11, 18] Operation: 64-46=18 Exploring Operation: 64-11=53, Resulting Numbers: [6, 46, 53] Generated Node #0,2: 35:[6, 46, 53] Operation: 64-11=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[6, 11, 18], Operations: ['64-46=18'] Exploring Operation: 18-11=7, Resulting Numbers: [6, 7] Generated Node #0,1,0: 35:[6, 7] Operation: 18-11=7 Exploring Operation: 11+18=29, Resulting Numbers: [6, 29] Generated Node #0,1,1: 35:[6, 29] Operation: 11+18=29 Exploring Operation: 18/6=3, Resulting Numbers: [11, 3] Generated Node #0,1,2: 35:[11, 3] Operation: 18/6=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 35:[6, 7], Operations: ['64-46=18', '18-11=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,35 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,35 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,35 unequal: No Solution No 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: 35:[11, 3], Operations: ['64-46=18', '18/6=3'] Exploring Operation: 11*3=33, Resulting Numbers: [33] 33,35 unequal: No Solution Exploring Operation: 11+3=14, Resulting Numbers: [14] 14,35 unequal: No Solution Exploring Operation: 11-3=8, Resulting Numbers: [8] 8,35 unequal: No Solution No 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: 35:[6, 29], Operations: ['64-46=18', '11+18=29'] Exploring Operation: 6*29=174, Resulting Numbers: [174] 174,35 unequal: No Solution Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[6, 64, 46, 11], Operations: [] Exploring Operation: 64-46=18, Resulting Numbers: [6, 11, 18] Generated Node #0,1: 35:[6, 11, 18] Operation: 64-46=18 Moving to Node #0,1 Current State: 35:[6, 11, 18], Operations: ['64-46=18'] Exploring Operation: 11+18=29, Resulting Numbers: [6, 29] Generated Node #0,1,1: 35:[6, 29] Operation: 11+18=29 Moving to Node #0,1,1 Current State: 35:[6, 29], Operations: ['64-46=18', '11+18=29'] Exploring Operation: 6+29=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 1, 33, 4, 92 ]
73
[ "1+4=5", "33*5=165", "165-92=73" ]
Current State: 73:[1, 33, 4, 92], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [33, 92, 5] Generated Node #2: [33, 92, 5] from Operation: 1+4=5 Current State: 73:[33, 92, 5], Operations: ['1+4=5'] Exploring Operation: 33*5=165, Resulting Numbers: [92, 165] Generated Node #3: [92, 165] from Operation: 33*5=165 Current State: 73:[92, 165], Operations: ['1+4=5', '33*5=165'] Exploring Operation: 165-92=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[1, 33, 4, 92], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [33, 92, 5] Generated Node #0,0: 73:[33, 92, 5] Operation: 1+4=5 Exploring Operation: 1+33=34, Resulting Numbers: [4, 92, 34] Generated Node #0,1: 73:[4, 92, 34] Operation: 1+33=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[33, 92, 5], Operations: ['1+4=5'] Exploring Operation: 92-5=87, Resulting Numbers: [33, 87] Generated Node #0,0,0: 73:[33, 87] Operation: 92-5=87 Exploring Operation: 33+5=38, Resulting Numbers: [92, 38] Generated Node #0,0,1: 73:[92, 38] Operation: 33+5=38 Moving to Node #0,0,0 Current State: 73:[33, 87], Operations: ['1+4=5', '92-5=87'] Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,73 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[92, 38], Operations: ['1+4=5', '33+5=38'] Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,73 unequal: No Solution Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[4, 92, 34], Operations: ['1+33=34'] Exploring Operation: 4+34=38, Resulting Numbers: [92, 38] Generated Node #0,1,0: 73:[92, 38] Operation: 4+34=38 Exploring Operation: 92-4=88, Resulting Numbers: [34, 88] Generated Node #0,1,1: 73:[34, 88] Operation: 92-4=88 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[92, 38], Operations: ['1+33=34', '4+34=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,73 unequal: No Solution Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[34, 88], Operations: ['1+33=34', '92-4=88'] Exploring Operation: 34+88=122, Resulting Numbers: [122] 122,73 unequal: No Solution Exploring Operation: 88-34=54, Resulting Numbers: [54] 54,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 46, 24, 54, 80 ]
77
[ "54-46=8", "24/8=3", "80-3=77" ]
Current State: 77:[46, 24, 54, 80], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [24, 80, 8] Generated Node #2: [24, 80, 8] from Operation: 54-46=8 Current State: 77:[24, 80, 8], Operations: ['54-46=8'] Exploring Operation: 24/8=3, Resulting Numbers: [80, 3] Generated Node #3: [80, 3] from Operation: 24/8=3 Current State: 77:[80, 3], Operations: ['54-46=8', '24/8=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[46, 24, 54, 80], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [24, 80, 8] Generated Node #0,0: 77:[24, 80, 8] Operation: 54-46=8 Moving to Node #0,0 Current State: 77:[24, 80, 8], Operations: ['54-46=8'] Exploring Operation: 24/8=3, Resulting Numbers: [80, 3] Generated Node #0,0,0: 77:[80, 3] Operation: 24/8=3 Moving to Node #0,0,0 Current State: 77:[80, 3], Operations: ['54-46=8', '24/8=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[46, 24, 54, 80], Operations: [] Exploring Operation: 54-46=8, Resulting Numbers: [24, 80, 8] Generated Node #0,0: 77:[24, 80, 8] Operation: 54-46=8 Moving to Node #0,0 Current State: 77:[24, 80, 8], Operations: ['54-46=8'] Exploring Operation: 24/8=3, Resulting Numbers: [80, 3] Generated Node #0,0,0: 77:[80, 3] Operation: 24/8=3 Moving to Node #0,0,0 Current State: 77:[80, 3], Operations: ['54-46=8', '24/8=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 98, 99, 47, 63 ]
17
[ "99-98=1", "63-47=16", "1+16=17" ]
Current State: 17:[98, 99, 47, 63], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [47, 63, 1] Generated Node #2: [47, 63, 1] from Operation: 99-98=1 Current State: 17:[47, 63, 1], Operations: ['99-98=1'] Exploring Operation: 63-47=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 63-47=16 Current State: 17:[1, 16], Operations: ['99-98=1', '63-47=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[98, 99, 47, 63], Operations: [] Exploring Operation: 99-63=36, Resulting Numbers: [98, 47, 36] Generated Node #0,0: 17:[98, 47, 36] Operation: 99-63=36 Exploring Operation: 98-63=35, Resulting Numbers: [99, 47, 35] Generated Node #0,1: 17:[99, 47, 35] Operation: 98-63=35 Exploring Operation: 99-98=1, Resulting Numbers: [47, 63, 1] Generated Node #0,2: 17:[47, 63, 1] Operation: 99-98=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[47, 63, 1], Operations: ['99-98=1'] Exploring Operation: 47-1=46, Resulting Numbers: [63, 46] Generated Node #0,2,0: 17:[63, 46] Operation: 47-1=46 Exploring Operation: 63-1=62, Resulting Numbers: [47, 62] Generated Node #0,2,1: 17:[47, 62] Operation: 63-1=62 Exploring Operation: 63-47=16, Resulting Numbers: [1, 16] Generated Node #0,2,2: 17:[1, 16] Operation: 63-47=16 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 17:[1, 16], Operations: ['99-98=1', '63-47=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[98, 99, 47, 63], Operations: [] Exploring Operation: 99-98=1, Resulting Numbers: [47, 63, 1] Generated Node #0,2: 17:[47, 63, 1] Operation: 99-98=1 Moving to Node #0,2 Current State: 17:[47, 63, 1], Operations: ['99-98=1'] Exploring Operation: 63-47=16, Resulting Numbers: [1, 16] Generated Node #0,2,2: 17:[1, 16] Operation: 63-47=16 Moving to Node #0,2,2 Current State: 17:[1, 16], Operations: ['99-98=1', '63-47=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 16, 27, 15, 2 ]
73
[ "16+27=43", "15*2=30", "43+30=73" ]
Current State: 73:[16, 27, 15, 2], Operations: [] Exploring Operation: 16+27=43, Resulting Numbers: [15, 2, 43] Generated Node #2: [15, 2, 43] from Operation: 16+27=43 Current State: 73:[15, 2, 43], Operations: ['16+27=43'] Exploring Operation: 15*2=30, Resulting Numbers: [43, 30] Generated Node #3: [43, 30] from Operation: 15*2=30 Current State: 73:[43, 30], Operations: ['16+27=43', '15*2=30'] Exploring Operation: 43+30=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[16, 27, 15, 2], Operations: [] Exploring Operation: 27*2=54, Resulting Numbers: [16, 15, 54] Generated Node #0,0: 73:[16, 15, 54] Operation: 27*2=54 Moving to Node #0,0 Current State: 73:[16, 15, 54], Operations: ['27*2=54'] Exploring Operation: 16+15=31, Resulting Numbers: [54, 31] Generated Node #0,0,0: 73:[54, 31] Operation: 16+15=31 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[54, 31], Operations: ['27*2=54', '16+15=31'] Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,73 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
[ 65, 14, 18, 40 ]
73
[ "65-14=51", "40-18=22", "51+22=73" ]
Current State: 73:[65, 14, 18, 40], Operations: [] Exploring Operation: 65-14=51, Resulting Numbers: [18, 40, 51] Generated Node #2: [18, 40, 51] from Operation: 65-14=51 Current State: 73:[18, 40, 51], Operations: ['65-14=51'] Exploring Operation: 40-18=22, Resulting Numbers: [51, 22] Generated Node #3: [51, 22] from Operation: 40-18=22 Current State: 73:[51, 22], Operations: ['65-14=51', '40-18=22'] Exploring Operation: 51+22=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[65, 14, 18, 40], Operations: [] Exploring Operation: 14+18=32, Resulting Numbers: [65, 40, 32] Generated Node #0,0: 73:[65, 40, 32] Operation: 14+18=32 Exploring Operation: 14+40=54, Resulting Numbers: [65, 18, 54] Generated Node #0,1: 73:[65, 18, 54] Operation: 14+40=54 Moving to Node #0,0 Current State: 73:[65, 40, 32], Operations: ['14+18=32'] Exploring Operation: 40+32=72, Resulting Numbers: [65, 72] Generated Node #0,0,0: 73:[65, 72] Operation: 40+32=72 Exploring Operation: 65+32=97, Resulting Numbers: [40, 97] Generated Node #0,0,1: 73:[40, 97] Operation: 65+32=97 Moving to Node #0,1 Current State: 73:[65, 18, 54], Operations: ['14+40=54'] Exploring Operation: 18+54=72, Resulting Numbers: [65, 72] Generated Node #0,1,0: 73:[65, 72] Operation: 18+54=72 Exploring Operation: 65+18=83, Resulting Numbers: [54, 83] Generated Node #0,1,1: 73:[54, 83] Operation: 65+18=83 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[65, 72], Operations: ['14+40=54', '18+54=72'] Exploring Operation: 65+72=137, Resulting Numbers: [137] 137,73 unequal: No Solution Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[54, 83], Operations: ['14+40=54', '65+18=83'] Exploring Operation: 54+83=137, Resulting Numbers: [137] 137,73 unequal: No Solution Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,73 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: 73:[65, 72], Operations: ['14+18=32', '40+32=72'] Exploring Operation: 65+72=137, Resulting Numbers: [137] 137,73 unequal: No Solution Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,73 unequal: No Solution Moving to Node #0,0,1 Current State: 73:[40, 97], Operations: ['14+18=32', '65+32=97'] Exploring Operation: 40+97=137, Resulting Numbers: [137] 137,73 unequal: No Solution Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,73 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 22, 51, 37, 3 ]
22
[ "51-22=29", "37+29=66", "66/3=22" ]
Current State: 22:[22, 51, 37, 3], Operations: [] Exploring Operation: 51-22=29, Resulting Numbers: [37, 3, 29] Generated Node #2: [37, 3, 29] from Operation: 51-22=29 Current State: 22:[37, 3, 29], Operations: ['51-22=29'] Exploring Operation: 37+29=66, Resulting Numbers: [3, 66] Generated Node #3: [3, 66] from Operation: 37+29=66 Current State: 22:[3, 66], Operations: ['51-22=29', '37+29=66'] Exploring Operation: 66/3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[22, 51, 37, 3], Operations: [] Exploring Operation: 37-22=15, Resulting Numbers: [51, 3, 15] Generated Node #0,0: 22:[51, 3, 15] Operation: 37-22=15 Exploring Operation: 51/3=17, Resulting Numbers: [22, 37, 17] Generated Node #0,1: 22:[22, 37, 17] Operation: 51/3=17 Exploring Operation: 51-37=14, Resulting Numbers: [22, 3, 14] Generated Node #0,2: 22:[22, 3, 14] Operation: 51-37=14 Exploring Operation: 51-22=29, Resulting Numbers: [37, 3, 29] Generated Node #0,3: 22:[37, 3, 29] Operation: 51-22=29 Moving to Node #0,2 Current State: 22:[22, 3, 14], Operations: ['51-37=14'] Exploring Operation: 22+3=25, Resulting Numbers: [14, 25] Generated Node #0,2,0: 22:[14, 25] Operation: 22+3=25 Exploring Operation: 14-3=11, Resulting Numbers: [22, 11] Generated Node #0,2,1: 22:[22, 11] Operation: 14-3=11 Exploring Operation: 3+14=17, Resulting Numbers: [22, 17] Generated Node #0,2,2: 22:[22, 17] Operation: 3+14=17 Exploring Operation: 22-14=8, Resulting Numbers: [3, 8] Generated Node #0,2,3: 22:[3, 8] Operation: 22-14=8 Moving to Node #0,1 Current State: 22:[22, 37, 17], Operations: ['51/3=17'] Exploring Operation: 22+17=39, Resulting Numbers: [37, 39] Generated Node #0,1,0: 22:[37, 39] Operation: 22+17=39 Exploring Operation: 37-17=20, Resulting Numbers: [22, 20] Generated Node #0,1,1: 22:[22, 20] Operation: 37-17=20 Exploring Operation: 37-22=15, Resulting Numbers: [17, 15] Generated Node #0,1,2: 22:[17, 15] Operation: 37-22=15 Exploring Operation: 22-17=5, Resulting Numbers: [37, 5] Generated Node #0,1,3: 22:[37, 5] Operation: 22-17=5 Moving to Node #0,3 Current State: 22:[37, 3, 29], Operations: ['51-22=29'] Exploring Operation: 37-3=34, Resulting Numbers: [29, 34] Generated Node #0,3,0: 22:[29, 34] Operation: 37-3=34 Exploring Operation: 37+3=40, Resulting Numbers: [29, 40] Generated Node #0,3,1: 22:[29, 40] Operation: 37+3=40 Exploring Operation: 37-29=8, Resulting Numbers: [3, 8] Generated Node #0,3,2: 22:[3, 8] Operation: 37-29=8 Exploring Operation: 29-3=26, Resulting Numbers: [37, 26] Generated Node #0,3,3: 22:[37, 26] Operation: 29-3=26 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 22:[3, 8], Operations: ['51-22=29', '37-29=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 22:[29, 34], Operations: ['51-22=29', '37-3=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 29*34=986, Resulting Numbers: [986] 986,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 22:[37, 26], Operations: ['51-22=29', '29-3=26'] Exploring Operation: 37*26=962, Resulting Numbers: [962] 962,22 unequal: No Solution Exploring Operation: 37+26=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 37-26=11, Resulting Numbers: [11] 11,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 22:[29, 40], Operations: ['51-22=29', '37+3=40'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 29+40=69, Resulting Numbers: [69] 69,22 unequal: No Solution Exploring Operation: 29*40=1160, Resulting Numbers: [1160] 1160,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 22:[51, 3, 15], Operations: ['37-22=15'] Exploring Operation: 15-3=12, Resulting Numbers: [51, 12] Generated Node #0,0,0: 22:[51, 12] Operation: 15-3=12 Exploring Operation: 51-15=36, Resulting Numbers: [3, 36] Generated Node #0,0,1: 22:[3, 36] Operation: 51-15=36 Exploring Operation: 51/3=17, Resulting Numbers: [15, 17] Generated Node #0,0,2: 22:[15, 17] Operation: 51/3=17 Exploring Operation: 51-3=48, Resulting Numbers: [15, 48] Generated Node #0,0,3: 22:[15, 48] Operation: 51-3=48 Moving to Node #0,2,1 Current State: 22:[22, 11], Operations: ['51-37=14', '14-3=11'] Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,22 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[22, 20], Operations: ['51/3=17', '37-17=20'] Exploring Operation: 22+20=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 22*20=440, Resulting Numbers: [440] 440,22 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,22 unequal: No Solution Moving to Node #0,2,3 Current State: 22:[3, 8], Operations: ['51-37=14', '22-14=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,22 unequal: No Solution Moving to Node #0,2,2 Current State: 22:[22, 17], Operations: ['51-37=14', '3+14=17'] Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,22 unequal: No Solution Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,22 unequal: No Solution Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,22 unequal: No Solution Moving to Node #0,2,0 Current State: 22:[14, 25], Operations: ['51-37=14', '22+3=25'] Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,22 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,22 unequal: No Solution Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,22 unequal: No Solution Moving to Node #0,1,2 Current State: 22:[17, 15], Operations: ['51/3=17', '37-22=15'] Exploring Operation: 17*15=255, Resulting Numbers: [255] 255,22 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 17+15=32, Resulting Numbers: [32] 32,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[15, 17], Operations: ['37-22=15', '51/3=17'] Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,22 unequal: No Solution Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,22 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[3, 36], Operations: ['37-22=15', '51-15=36'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,22 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,22 unequal: No Solution Moving to Node #0,1,3 Current State: 22:[37, 5], Operations: ['51/3=17', '22-17=5'] Exploring Operation: 37*5=185, Resulting Numbers: [185] 185,22 unequal: No Solution Exploring Operation: 37+5=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[51, 12], Operations: ['37-22=15', '15-3=12'] Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,22 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[15, 48], Operations: ['37-22=15', '51-3=48'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,22 unequal: No Solution Exploring Operation: 15*48=720, Resulting Numbers: [720] 720,22 unequal: No Solution Exploring Operation: 15+48=63, Resulting Numbers: [63] 63,22 unequal: No Solution Moving to Node #0,1,0 Current State: 22:[37, 39], Operations: ['51/3=17', '22+17=39'] Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,22 unequal: No Solution Exploring Operation: 37+39=76, Resulting Numbers: [76] 76,22 unequal: No Solution Exploring Operation: 37*39=1443, Resulting Numbers: [1443] 1443,22 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 34, 31, 84, 42 ]
99
[ "34*84=2856", "2856/42=68", "31+68=99" ]
Current State: 99:[34, 31, 84, 42], Operations: [] Exploring Operation: 34*84=2856, Resulting Numbers: [31, 42, 2856] Generated Node #2: [31, 42, 2856] from Operation: 34*84=2856 Current State: 99:[31, 42, 2856], Operations: ['34*84=2856'] Exploring Operation: 2856/42=68, Resulting Numbers: [31, 68] Generated Node #3: [31, 68] from Operation: 2856/42=68 Current State: 99:[31, 68], Operations: ['34*84=2856', '2856/42=68'] Exploring Operation: 31+68=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[34, 31, 84, 42], Operations: [] Exploring Operation: 42-31=11, Resulting Numbers: [34, 84, 11] Generated Node #0,0: 99:[34, 84, 11] Operation: 42-31=11 Exploring Operation: 84-42=42, Resulting Numbers: [34, 31, 42] Generated Node #0,1: 99:[34, 31, 42] Operation: 84-42=42 Exploring Operation: 84/42=2, Resulting Numbers: [34, 31, 2] Generated Node #0,2: 99:[34, 31, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[34, 31, 2], Operations: ['84/42=2'] Exploring Operation: 34-31=3, Resulting Numbers: [2, 3] Generated Node #0,2,0: 99:[2, 3] Operation: 34-31=3 Exploring Operation: 34-2=32, Resulting Numbers: [31, 32] Generated Node #0,2,1: 99:[31, 32] Operation: 34-2=32 Exploring Operation: 31+2=33, Resulting Numbers: [34, 33] Generated Node #0,2,2: 99:[34, 33] Operation: 31+2=33 Moving to Node #0,2,0 Current State: 99:[2, 3], Operations: ['84/42=2', '34-31=3'] Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,99 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[34, 33], Operations: ['84/42=2', '31+2=33'] Exploring Operation: 34-33=1, Resulting Numbers: [1] 1,99 unequal: No Solution Exploring Operation: 34*33=1122, Resulting Numbers: [1122] 1122,99 unequal: No Solution Exploring Operation: 34+33=67, Resulting Numbers: [67] 67,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[31, 32], Operations: ['84/42=2', '34-2=32'] Exploring Operation: 31+32=63, Resulting Numbers: [63] 63,99 unequal: No Solution Exploring Operation: 31*32=992, Resulting Numbers: [992] 992,99 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[34, 31, 42], Operations: ['84-42=42'] Exploring Operation: 42-34=8, Resulting Numbers: [31, 8] Generated Node #0,1,0: 99:[31, 8] Operation: 42-34=8 Exploring Operation: 42-31=11, Resulting Numbers: [34, 11] Generated Node #0,1,1: 99:[34, 11] Operation: 42-31=11 Exploring Operation: 34-31=3, Resulting Numbers: [42, 3] Generated Node #0,1,2: 99:[42, 3] Operation: 34-31=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[34, 11], Operations: ['84-42=42', '42-31=11'] Exploring Operation: 34+11=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 34*11=374, Resulting Numbers: [374] 374,99 unequal: No Solution Exploring Operation: 34-11=23, Resulting Numbers: [23] 23,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[31, 8], Operations: ['84-42=42', '42-34=8'] Exploring Operation: 31*8=248, Resulting Numbers: [248] 248,99 unequal: No Solution Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 99:[42, 3], Operations: ['84-42=42', '34-31=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,99 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,99 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[34, 84, 11], Operations: ['42-31=11'] Exploring Operation: 84-34=50, Resulting Numbers: [11, 50] Generated Node #0,0,0: 99:[11, 50] Operation: 84-34=50 Exploring Operation: 84+11=95, Resulting Numbers: [34, 95] Generated Node #0,0,1: 99:[34, 95] Operation: 84+11=95 Exploring Operation: 34+84=118, Resulting Numbers: [11, 118] Generated Node #0,0,2: 99:[11, 118] Operation: 34+84=118 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[34, 95], Operations: ['42-31=11', '84+11=95'] Exploring Operation: 95-34=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 34+95=129, Resulting Numbers: [129] 129,99 unequal: No Solution Exploring Operation: 34*95=3230, Resulting Numbers: [3230] 3230,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[11, 50], Operations: ['42-31=11', '84-34=50'] Exploring Operation: 50-11=39, Resulting Numbers: [39] 39,99 unequal: No Solution Exploring Operation: 11+50=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 11*50=550, Resulting Numbers: [550] 550,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 99:[11, 118], Operations: ['42-31=11', '34+84=118'] Exploring Operation: 118-11=107, Resulting Numbers: [107] 107,99 unequal: No Solution Exploring Operation: 11*118=1298, Resulting Numbers: [1298] 1298,99 unequal: No Solution Exploring Operation: 11+118=129, Resulting Numbers: [129] 129,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 8, 11, 32, 38 ]
59
[ "38-32=6", "8*6=48", "11+48=59" ]
Current State: 59:[8, 11, 32, 38], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [8, 11, 6] Generated Node #2: [8, 11, 6] from Operation: 38-32=6 Current State: 59:[8, 11, 6], Operations: ['38-32=6'] Exploring Operation: 8*6=48, Resulting Numbers: [11, 48] Generated Node #3: [11, 48] from Operation: 8*6=48 Current State: 59:[11, 48], Operations: ['38-32=6', '8*6=48'] Exploring Operation: 11+48=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[8, 11, 32, 38], Operations: [] Exploring Operation: 8*11=88, Resulting Numbers: [32, 38, 88] Generated Node #0,0: 59:[32, 38, 88] Operation: 8*11=88 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[32, 38, 88], Operations: ['8*11=88'] Exploring Operation: 88-32=56, Resulting Numbers: [38, 56] Generated Node #0,0,0: 59:[38, 56] Operation: 88-32=56 Moving to Node #0,0,0 Current State: 59:[38, 56], Operations: ['8*11=88', '88-32=56'] Exploring Operation: 38+56=94, Resulting Numbers: [94] 94,59 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, 20, 2, 73 ]
30
[ "66+20=86", "86/2=43", "73-43=30" ]
Current State: 30:[66, 20, 2, 73], Operations: [] Exploring Operation: 66+20=86, Resulting Numbers: [2, 73, 86] Generated Node #2: [2, 73, 86] from Operation: 66+20=86 Current State: 30:[2, 73, 86], Operations: ['66+20=86'] Exploring Operation: 86/2=43, Resulting Numbers: [73, 43] Generated Node #3: [73, 43] from Operation: 86/2=43 Current State: 30:[73, 43], Operations: ['66+20=86', '86/2=43'] Exploring Operation: 73-43=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[66, 20, 2, 73], Operations: [] Exploring Operation: 73-20=53, Resulting Numbers: [66, 2, 53] Generated Node #0,0: 30:[66, 2, 53] Operation: 73-20=53 Exploring Operation: 66-20=46, Resulting Numbers: [2, 73, 46] Generated Node #0,1: 30:[2, 73, 46] Operation: 66-20=46 Exploring Operation: 20/2=10, Resulting Numbers: [66, 73, 10] Generated Node #0,2: 30:[66, 73, 10] Operation: 20/2=10 Exploring Operation: 73-66=7, Resulting Numbers: [20, 2, 7] Generated Node #0,3: 30:[20, 2, 7] Operation: 73-66=7 Exploring Operation: 66/2=33, Resulting Numbers: [20, 73, 33] Generated Node #0,4: 30:[20, 73, 33] Operation: 66/2=33 Moving to Node #0,3 Current State: 30:[20, 2, 7], Operations: ['73-66=7'] Exploring Operation: 20-7=13, Resulting Numbers: [2, 13] Generated Node #0,3,0: 30:[2, 13] Operation: 20-7=13 Exploring Operation: 7-2=5, Resulting Numbers: [20, 5] Generated Node #0,3,1: 30:[20, 5] Operation: 7-2=5 Exploring Operation: 20-2=18, Resulting Numbers: [7, 18] Generated Node #0,3,2: 30:[7, 18] Operation: 20-2=18 Exploring Operation: 20/2=10, Resulting Numbers: [7, 10] Generated Node #0,3,3: 30:[7, 10] Operation: 20/2=10 Exploring Operation: 20+7=27, Resulting Numbers: [2, 27] Generated Node #0,3,4: 30:[2, 27] Operation: 20+7=27 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[7, 10], Operations: ['73-66=7', '20/2=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 30:[2, 13], Operations: ['73-66=7', '20-7=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 30:[2, 27], Operations: ['73-66=7', '20+7=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 30:[7, 18], Operations: ['73-66=7', '20-2=18'] Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,30 unequal: No Solution Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 30:[20, 5], Operations: ['73-66=7', '7-2=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,30 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,30 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,30 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: 30:[20, 73, 33], Operations: ['66/2=33'] Exploring Operation: 20+33=53, Resulting Numbers: [73, 53] Generated Node #0,4,0: 30:[73, 53] Operation: 20+33=53 Exploring Operation: 33-20=13, Resulting Numbers: [73, 13] Generated Node #0,4,1: 30:[73, 13] Operation: 33-20=13 Exploring Operation: 73-33=40, Resulting Numbers: [20, 40] Generated Node #0,4,2: 30:[20, 40] Operation: 73-33=40 Exploring Operation: 73-20=53, Resulting Numbers: [33, 53] Generated Node #0,4,3: 30:[33, 53] Operation: 73-20=53 Exploring Operation: 20+73=93, Resulting Numbers: [33, 93] Generated Node #0,4,4: 30:[33, 93] Operation: 20+73=93 Moving to Node #0,0 Current State: 30:[66, 2, 53], Operations: ['73-20=53'] Exploring Operation: 66+2=68, Resulting Numbers: [53, 68] Generated Node #0,0,0: 30:[53, 68] Operation: 66+2=68 Exploring Operation: 66-53=13, Resulting Numbers: [2, 13] Generated Node #0,0,1: 30:[2, 13] Operation: 66-53=13 Exploring Operation: 66-2=64, Resulting Numbers: [53, 64] Generated Node #0,0,2: 30:[53, 64] Operation: 66-2=64 Exploring Operation: 66/2=33, Resulting Numbers: [53, 33] Generated Node #0,0,3: 30:[53, 33] Operation: 66/2=33 Exploring Operation: 53-2=51, Resulting Numbers: [66, 51] Generated Node #0,0,4: 30:[66, 51] Operation: 53-2=51 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[2, 13], Operations: ['73-20=53', '66-53=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,30 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 30:[53, 33], Operations: ['73-20=53', '66/2=33'] Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,30 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,30 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 30:[53, 64], Operations: ['73-20=53', '66-2=64'] Exploring Operation: 53+64=117, Resulting Numbers: [117] 117,30 unequal: No Solution Exploring Operation: 64-53=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 53*64=3392, Resulting Numbers: [3392] 3392,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 30:[66, 51], Operations: ['73-20=53', '53-2=51'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 66+51=117, Resulting Numbers: [117] 117,30 unequal: No Solution Exploring Operation: 66*51=3366, Resulting Numbers: [3366] 3366,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[53, 68], Operations: ['73-20=53', '66+2=68'] Exploring Operation: 53+68=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 68-53=15, Resulting Numbers: [15] 15,30 unequal: No Solution Exploring Operation: 53*68=3604, Resulting Numbers: [3604] 3604,30 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: 30:[2, 73, 46], Operations: ['66-20=46'] Exploring Operation: 73-2=71, Resulting Numbers: [46, 71] Generated Node #0,1,0: 30:[46, 71] Operation: 73-2=71 Exploring Operation: 73-46=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 30:[2, 27] Operation: 73-46=27 Exploring Operation: 46-2=44, Resulting Numbers: [73, 44] Generated Node #0,1,2: 30:[73, 44] Operation: 46-2=44 Exploring Operation: 2+73=75, Resulting Numbers: [46, 75] Generated Node #0,1,3: 30:[46, 75] Operation: 2+73=75 Exploring Operation: 46/2=23, Resulting Numbers: [73, 23] Generated Node #0,1,4: 30:[73, 23] Operation: 46/2=23 Moving to Node #0,2 Current State: 30:[66, 73, 10], Operations: ['20/2=10'] Exploring Operation: 66+10=76, Resulting Numbers: [73, 76] Generated Node #0,2,0: 30:[73, 76] Operation: 66+10=76 Exploring Operation: 73-66=7, Resulting Numbers: [10, 7] Generated Node #0,2,1: 30:[10, 7] Operation: 73-66=7 Exploring Operation: 66-10=56, Resulting Numbers: [73, 56] Generated Node #0,2,2: 30:[73, 56] Operation: 66-10=56 Exploring Operation: 73+10=83, Resulting Numbers: [66, 83] Generated Node #0,2,3: 30:[66, 83] Operation: 73+10=83 Exploring Operation: 73-10=63, Resulting Numbers: [66, 63] Generated Node #0,2,4: 30:[66, 63] Operation: 73-10=63 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[10, 7], Operations: ['20/2=10', '73-66=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,30 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 30:[73, 56], Operations: ['20/2=10', '66-10=56'] Exploring Operation: 73*56=4088, Resulting Numbers: [4088] 4088,30 unequal: No Solution Exploring Operation: 73+56=129, Resulting Numbers: [129] 129,30 unequal: No Solution Exploring Operation: 73-56=17, Resulting Numbers: [17] 17,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 30:[66, 63], Operations: ['20/2=10', '73-10=63'] Exploring Operation: 66+63=129, Resulting Numbers: [129] 129,30 unequal: No Solution Exploring Operation: 66-63=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 66*63=4158, Resulting Numbers: [4158] 4158,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[73, 76], Operations: ['20/2=10', '66+10=76'] Exploring Operation: 73+76=149, Resulting Numbers: [149] 149,30 unequal: No Solution Exploring Operation: 76-73=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 73*76=5548, Resulting Numbers: [5548] 5548,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 30:[66, 83], Operations: ['20/2=10', '73+10=83'] Exploring Operation: 66+83=149, Resulting Numbers: [149] 149,30 unequal: No Solution Exploring Operation: 66*83=5478, Resulting Numbers: [5478] 5478,30 unequal: No Solution Exploring Operation: 83-66=17, Resulting Numbers: [17] 17,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 30:[2, 27], Operations: ['66-20=46', '73-46=27'] Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,30 unequal: No Solution Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,4,2 Current State: 30:[20, 40], Operations: ['66/2=33', '73-33=40'] Exploring Operation: 40-20=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 20+40=60, Resulting Numbers: [60] 60,30 unequal: No Solution Exploring Operation: 40/20=2, Resulting Numbers: [2] 2,30 unequal: No Solution Exploring Operation: 20*40=800, Resulting Numbers: [800] 800,30 unequal: No Solution Moving to Node #0,4,3 Current State: 30:[33, 53], Operations: ['66/2=33', '73-20=53'] Exploring Operation: 33+53=86, Resulting Numbers: [86] 86,30 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 33*53=1749, Resulting Numbers: [1749] 1749,30 unequal: No Solution Moving to Node #0,4,1 Current State: 30:[73, 13], Operations: ['66/2=33', '33-20=13'] Exploring Operation: 73*13=949, Resulting Numbers: [949] 949,30 unequal: No Solution Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,30 unequal: No Solution Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,30 unequal: No Solution Moving to Node #0,1,4 Current State: 30:[73, 23], Operations: ['66-20=46', '46/2=23'] Exploring Operation: 73+23=96, Resulting Numbers: [96] 96,30 unequal: No Solution Exploring Operation: 73*23=1679, Resulting Numbers: [1679] 1679,30 unequal: No Solution Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,30 unequal: No Solution Moving to Node #0,1,0 Current State: 30:[46, 71], Operations: ['66-20=46', '73-2=71'] Exploring Operation: 46+71=117, Resulting Numbers: [117] 117,30 unequal: No Solution Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,30 unequal: No Solution Exploring Operation: 46*71=3266, Resulting Numbers: [3266] 3266,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[73, 44], Operations: ['66-20=46', '46-2=44'] Exploring Operation: 73-44=29, Resulting Numbers: [29] 29,30 unequal: No Solution Exploring Operation: 73+44=117, Resulting Numbers: [117] 117,30 unequal: No Solution Exploring Operation: 73*44=3212, Resulting Numbers: [3212] 3212,30 unequal: No Solution Moving to Node #0,1,3 Current State: 30:[46, 75], Operations: ['66-20=46', '2+73=75'] Exploring Operation: 46*75=3450, Resulting Numbers: [3450] 3450,30 unequal: No Solution Exploring Operation: 46+75=121, Resulting Numbers: [121] 121,30 unequal: No Solution Exploring Operation: 75-46=29, Resulting Numbers: [29] 29,30 unequal: No Solution Moving to Node #0,4,0 Current State: 30:[73, 53], Operations: ['66/2=33', '20+33=53'] Exploring Operation: 73-53=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 73+53=126, Resulting Numbers: [126] 126,30 unequal: No Solution Exploring Operation: 73*53=3869, Resulting Numbers: [3869] 3869,30 unequal: No Solution Moving to Node #0,4,4 Current State: 30:[33, 93], Operations: ['66/2=33', '20+73=93'] Exploring Operation: 33*93=3069, Resulting Numbers: [3069] 3069,30 unequal: No Solution Exploring Operation: 33+93=126, Resulting Numbers: [126] 126,30 unequal: No Solution Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,30 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 7, 7, 21, 42 ]
35
[ "7+7=14", "42-21=21", "14+21=35" ]
Current State: 35:[7, 7, 21, 42], Operations: [] Exploring Operation: 7+7=14, Resulting Numbers: [21, 42, 14] Generated Node #2: [21, 42, 14] from Operation: 7+7=14 Current State: 35:[21, 42, 14], Operations: ['7+7=14'] Exploring Operation: 42-21=21, Resulting Numbers: [14, 21] Generated Node #3: [14, 21] from Operation: 42-21=21 Current State: 35:[14, 21], Operations: ['7+7=14', '42-21=21'] Exploring Operation: 14+21=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[7, 7, 21, 42], Operations: [] Exploring Operation: 21/7=3, Resulting Numbers: [7, 42, 3] Generated Node #0,0: 35:[7, 42, 3] Operation: 21/7=3 Exploring Operation: 42/21=2, Resulting Numbers: [7, 7, 2] Generated Node #0,1: 35:[7, 7, 2] Operation: 42/21=2 Exploring Operation: 21/7=3, Resulting Numbers: [7, 42, 3] Generated Node #0,2: 35:[7, 42, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 35:[7, 7, 2], Operations: ['42/21=2'] Exploring Operation: 7+2=9, Resulting Numbers: [7, 9] Generated Node #0,1,0: 35:[7, 9] Operation: 7+2=9 Exploring Operation: 7-2=5, Resulting Numbers: [7, 5] Generated Node #0,1,1: 35:[7, 5] Operation: 7-2=5 Exploring Operation: 7-2=5, Resulting Numbers: [7, 5] Generated Node #0,1,2: 35:[7, 5] Operation: 7-2=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 35:[7, 5], Operations: ['42/21=2', '7-2=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[7, 7, 21, 42], Operations: [] Exploring Operation: 42/21=2, Resulting Numbers: [7, 7, 2] Generated Node #0,1: 35:[7, 7, 2] Operation: 42/21=2 Moving to Node #0,1 Current State: 35:[7, 7, 2], Operations: ['42/21=2'] Exploring Operation: 7-2=5, Resulting Numbers: [7, 5] Generated Node #0,1,1: 35:[7, 5] Operation: 7-2=5 Moving to Node #0,1,1 Current State: 35:[7, 5], Operations: ['42/21=2', '7-2=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 39, 48, 47, 24 ]
32
[ "48-39=9", "47-24=23", "9+23=32" ]
Current State: 32:[39, 48, 47, 24], Operations: [] Exploring Operation: 48-39=9, Resulting Numbers: [47, 24, 9] Generated Node #2: [47, 24, 9] from Operation: 48-39=9 Current State: 32:[47, 24, 9], Operations: ['48-39=9'] Exploring Operation: 47-24=23, Resulting Numbers: [9, 23] Generated Node #3: [9, 23] from Operation: 47-24=23 Current State: 32:[9, 23], Operations: ['48-39=9', '47-24=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[39, 48, 47, 24], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [39, 24, 1] Generated Node #0,0: 32:[39, 24, 1] Operation: 48-47=1 Exploring Operation: 47-39=8, Resulting Numbers: [48, 24, 8] Generated Node #0,1: 32:[48, 24, 8] Operation: 47-39=8 Exploring Operation: 48-39=9, Resulting Numbers: [47, 24, 9] Generated Node #0,2: 32:[47, 24, 9] Operation: 48-39=9 Exploring Operation: 48/24=2, Resulting Numbers: [39, 47, 2] Generated Node #0,3: 32:[39, 47, 2] Operation: 48/24=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[39, 24, 1], Operations: ['48-47=1'] Exploring Operation: 24+1=25, Resulting Numbers: [39, 25] Generated Node #0,0,0: 32:[39, 25] Operation: 24+1=25 Exploring Operation: 39-1=38, Resulting Numbers: [24, 38] Generated Node #0,0,1: 32:[24, 38] Operation: 39-1=38 Exploring Operation: 39-24=15, Resulting Numbers: [1, 15] Generated Node #0,0,2: 32:[1, 15] Operation: 39-24=15 Exploring Operation: 24-1=23, Resulting Numbers: [39, 23] Generated Node #0,0,3: 32:[39, 23] Operation: 24-1=23 Moving to Node #0,0,2 Current State: 32:[1, 15], Operations: ['48-47=1', '39-24=15'] Exploring Operation: 1+15=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[24, 38], Operations: ['48-47=1', '39-1=38'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,32 unequal: No Solution Exploring Operation: 24*38=912, Resulting Numbers: [912] 912,32 unequal: No Solution Exploring Operation: 24+38=62, Resulting Numbers: [62] 62,32 unequal: No Solution Moving to Node #0,0,0 Current State: 32:[39, 25], Operations: ['48-47=1', '24+1=25'] Exploring Operation: 39+25=64, Resulting Numbers: [64] 64,32 unequal: No Solution Exploring Operation: 39*25=975, Resulting Numbers: [975] 975,32 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,32 unequal: No Solution Moving to Node #0,0,3 Current State: 32:[39, 23], Operations: ['48-47=1', '24-1=23'] Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,32 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 32:[39, 47, 2], Operations: ['48/24=2'] Exploring Operation: 47-2=45, Resulting Numbers: [39, 45] Generated Node #0,3,0: 32:[39, 45] Operation: 47-2=45 Exploring Operation: 47-39=8, Resulting Numbers: [2, 8] Generated Node #0,3,1: 32:[2, 8] Operation: 47-39=8 Exploring Operation: 39-2=37, Resulting Numbers: [47, 37] Generated Node #0,3,2: 32:[47, 37] Operation: 39-2=37 Exploring Operation: 39+2=41, Resulting Numbers: [47, 41] Generated Node #0,3,3: 32:[47, 41] Operation: 39+2=41 Moving to Node #0,3,1 Current State: 32:[2, 8], Operations: ['48/24=2', '47-39=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,32 unequal: No Solution Moving to Node #0,3,2 Current State: 32:[47, 37], Operations: ['48/24=2', '39-2=37'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 47+37=84, Resulting Numbers: [84] 84,32 unequal: No Solution Exploring Operation: 47*37=1739, Resulting Numbers: [1739] 1739,32 unequal: No Solution Moving to Node #0,3,0 Current State: 32:[39, 45], Operations: ['48/24=2', '47-2=45'] Exploring Operation: 39+45=84, Resulting Numbers: [84] 84,32 unequal: No Solution Exploring Operation: 45-39=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 39*45=1755, Resulting Numbers: [1755] 1755,32 unequal: No Solution Moving to Node #0,3,3 Current State: 32:[47, 41], Operations: ['48/24=2', '39+2=41'] Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,32 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,32 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[48, 24, 8], Operations: ['47-39=8'] Exploring Operation: 48/8=6, Resulting Numbers: [24, 6] Generated Node #0,1,0: 32:[24, 6] Operation: 48/8=6 Exploring Operation: 48-24=24, Resulting Numbers: [8, 24] Generated Node #0,1,1: 32:[8, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [8, 2] Generated Node #0,1,2: 32:[8, 2] Operation: 48/24=2 Exploring Operation: 48-8=40, Resulting Numbers: [24, 40] Generated Node #0,1,3: 32:[24, 40] Operation: 48-8=40 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 32:[8, 2], Operations: ['47-39=8', '48/24=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,32 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,32 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 32:[8, 24], Operations: ['47-39=8', '48-24=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[39, 48, 47, 24], Operations: [] Exploring Operation: 47-39=8, Resulting Numbers: [48, 24, 8] Generated Node #0,1: 32:[48, 24, 8] Operation: 47-39=8 Moving to Node #0,1 Current State: 32:[48, 24, 8], Operations: ['47-39=8'] Exploring Operation: 48-24=24, Resulting Numbers: [8, 24] Generated Node #0,1,1: 32:[8, 24] Operation: 48-24=24 Moving to Node #0,1,1 Current State: 32:[8, 24], Operations: ['47-39=8', '48-24=24'] Exploring Operation: 8+24=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.955729
hs_4
sum_heuristic
[ 30, 55, 68, 60 ]
26
[ "60/30=2", "68-55=13", "2*13=26" ]
Current State: 26:[30, 55, 68, 60], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [55, 68, 2] Generated Node #2: [55, 68, 2] from Operation: 60/30=2 Current State: 26:[55, 68, 2], Operations: ['60/30=2'] Exploring Operation: 68-55=13, Resulting Numbers: [2, 13] Generated Node #3: [2, 13] from Operation: 68-55=13 Current State: 26:[2, 13], Operations: ['60/30=2', '68-55=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[30, 55, 68, 60], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [30, 55, 8] Generated Node #0,0: 26:[30, 55, 8] Operation: 68-60=8 Exploring Operation: 60/30=2, Resulting Numbers: [55, 68, 2] Generated Node #0,1: 26:[55, 68, 2] Operation: 60/30=2 Exploring Operation: 60-55=5, Resulting Numbers: [30, 68, 5] Generated Node #0,2: 26:[30, 68, 5] Operation: 60-55=5 Exploring Operation: 68-55=13, Resulting Numbers: [30, 60, 13] Generated Node #0,3: 26:[30, 60, 13] Operation: 68-55=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[30, 55, 8], Operations: ['68-60=8'] Exploring Operation: 30-8=22, Resulting Numbers: [55, 22] Generated Node #0,0,0: 26:[55, 22] Operation: 30-8=22 Exploring Operation: 55-8=47, Resulting Numbers: [30, 47] Generated Node #0,0,1: 26:[30, 47] Operation: 55-8=47 Exploring Operation: 55-30=25, Resulting Numbers: [8, 25] Generated Node #0,0,2: 26:[8, 25] Operation: 55-30=25 Exploring Operation: 30+8=38, Resulting Numbers: [55, 38] Generated Node #0,0,3: 26:[55, 38] Operation: 30+8=38 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 26:[8, 25], Operations: ['68-60=8', '55-30=25'] Exploring Operation: 8*25=200, Resulting Numbers: [200] 200,26 unequal: No Solution Exploring Operation: 8+25=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,26 unequal: No Solution No 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: 26:[30, 47], Operations: ['68-60=8', '55-8=47'] Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,26 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,26 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,26 unequal: No Solution No 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: 26:[55, 22], Operations: ['68-60=8', '30-8=22'] Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,26 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,26 unequal: No Solution Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,26 unequal: No Solution No 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: 26:[55, 38], Operations: ['68-60=8', '30+8=38'] Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,26 unequal: No Solution Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,26 unequal: No Solution Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,26 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: 26:[30, 60, 13], Operations: ['68-55=13'] Exploring Operation: 30-13=17, Resulting Numbers: [60, 17] Generated Node #0,3,0: 26:[60, 17] Operation: 30-13=17 Exploring Operation: 60/30=2, Resulting Numbers: [13, 2] Generated Node #0,3,1: 26:[13, 2] Operation: 60/30=2 Exploring Operation: 60-30=30, Resulting Numbers: [13, 30] Generated Node #0,3,2: 26:[13, 30] Operation: 60-30=30 Exploring Operation: 60-13=47, Resulting Numbers: [30, 47] Generated Node #0,3,3: 26:[30, 47] Operation: 60-13=47 Moving to Node #0,3,1 Current State: 26:[13, 2], Operations: ['68-55=13', '60/30=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,26 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,26 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[30, 55, 68, 60], Operations: [] Exploring Operation: 68-55=13, Resulting Numbers: [30, 60, 13] Generated Node #0,3: 26:[30, 60, 13] Operation: 68-55=13 Moving to Node #0,3 Current State: 26:[30, 60, 13], Operations: ['68-55=13'] Exploring Operation: 60/30=2, Resulting Numbers: [13, 2] Generated Node #0,3,1: 26:[13, 2] Operation: 60/30=2 Moving to Node #0,3,1 Current State: 26:[13, 2], Operations: ['68-55=13', '60/30=2'] Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 10, 68, 28, 2 ]
44
[ "68-10=58", "28/2=14", "58-14=44" ]
Current State: 44:[10, 68, 28, 2], Operations: [] Exploring Operation: 68-10=58, Resulting Numbers: [28, 2, 58] Generated Node #2: [28, 2, 58] from Operation: 68-10=58 Current State: 44:[28, 2, 58], Operations: ['68-10=58'] Exploring Operation: 28/2=14, Resulting Numbers: [58, 14] Generated Node #3: [58, 14] from Operation: 28/2=14 Current State: 44:[58, 14], Operations: ['68-10=58', '28/2=14'] Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[10, 68, 28, 2], Operations: [] Exploring Operation: 28-10=18, Resulting Numbers: [68, 2, 18] Generated Node #0,0: 44:[68, 2, 18] Operation: 28-10=18 Exploring Operation: 68/2=34, Resulting Numbers: [10, 28, 34] Generated Node #0,1: 44:[10, 28, 34] Operation: 68/2=34 Exploring Operation: 68-10=58, Resulting Numbers: [28, 2, 58] Generated Node #0,2: 44:[28, 2, 58] Operation: 68-10=58 Exploring Operation: 68-28=40, Resulting Numbers: [10, 2, 40] Generated Node #0,3: 44:[10, 2, 40] Operation: 68-28=40 Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[10, 2, 40], Operations: ['68-28=40'] Exploring Operation: 40/10=4, Resulting Numbers: [2, 4] Generated Node #0,3,0: 44:[2, 4] Operation: 40/10=4 Exploring Operation: 10+2=12, Resulting Numbers: [40, 12] Generated Node #0,3,1: 44:[40, 12] Operation: 10+2=12 Exploring Operation: 40/2=20, Resulting Numbers: [10, 20] Generated Node #0,3,2: 44:[10, 20] Operation: 40/2=20 Exploring Operation: 2+40=42, Resulting Numbers: [10, 42] Generated Node #0,3,3: 44:[10, 42] Operation: 2+40=42 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 44:[2, 4], Operations: ['68-28=40', '40/10=4'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,44 unequal: No Solution Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,44 unequal: No Solution No 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: 44:[10, 20], Operations: ['68-28=40', '40/2=20'] Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,44 unequal: No Solution Exploring Operation: 10+20=30, Resulting Numbers: [30] 30,44 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 10*20=200, Resulting Numbers: [200] 200,44 unequal: No Solution No 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: 44:[10, 42], Operations: ['68-28=40', '2+40=42'] Exploring Operation: 42-10=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 10*42=420, Resulting Numbers: [420] 420,44 unequal: No Solution Exploring Operation: 10+42=52, Resulting Numbers: [52] 52,44 unequal: No Solution No 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: 44:[40, 12], Operations: ['68-28=40', '10+2=12'] Exploring Operation: 40+12=52, Resulting Numbers: [52] 52,44 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,44 unequal: No Solution Exploring Operation: 40*12=480, Resulting Numbers: [480] 480,44 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: 44:[10, 28, 34], Operations: ['68/2=34'] Exploring Operation: 34-10=24, Resulting Numbers: [28, 24] Generated Node #0,1,0: 44:[28, 24] Operation: 34-10=24 Exploring Operation: 28-10=18, Resulting Numbers: [34, 18] Generated Node #0,1,1: 44:[34, 18] Operation: 28-10=18 Exploring Operation: 34-28=6, Resulting Numbers: [10, 6] Generated Node #0,1,2: 44:[10, 6] Operation: 34-28=6 Exploring Operation: 10+34=44, Resulting Numbers: [28, 44] Generated Node #0,1,3: 44:[28, 44] Operation: 10+34=44 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 44:[10, 6], Operations: ['68/2=34', '34-28=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,44 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,44 unequal: No Solution No 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: 44:[28, 44], Operations: ['68/2=34', '10+34=44'] Exploring Operation: 28+44=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 44-28=16, Resulting Numbers: [16] 16,44 unequal: No Solution Exploring Operation: 28*44=1232, Resulting Numbers: [1232] 1232,44 unequal: No Solution No 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: 44:[28, 24], Operations: ['68/2=34', '34-10=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,44 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,44 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,44 unequal: No Solution No 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: 44:[34, 18], Operations: ['68/2=34', '28-10=18'] Exploring Operation: 34*18=612, Resulting Numbers: [612] 612,44 unequal: No Solution Exploring Operation: 34+18=52, Resulting Numbers: [52] 52,44 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,44 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: 44:[28, 2, 58], Operations: ['68-10=58'] Exploring Operation: 28-2=26, Resulting Numbers: [58, 26] Generated Node #0,2,0: 44:[58, 26] Operation: 28-2=26 Exploring Operation: 58/2=29, Resulting Numbers: [28, 29] Generated Node #0,2,1: 44:[28, 29] Operation: 58/2=29 Exploring Operation: 58-28=30, Resulting Numbers: [2, 30] Generated Node #0,2,2: 44:[2, 30] Operation: 58-28=30 Exploring Operation: 28/2=14, Resulting Numbers: [58, 14] Generated Node #0,2,3: 44:[58, 14] Operation: 28/2=14 Moving to Node #0,2,2 Current State: 44:[2, 30], Operations: ['68-10=58', '58-28=30'] Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,44 unequal: No Solution Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,44 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,44 unequal: No Solution Moving to Node #0,2,1 Current State: 44:[28, 29], Operations: ['68-10=58', '58/2=29'] Exploring Operation: 28*29=812, Resulting Numbers: [812] 812,44 unequal: No Solution Exploring Operation: 28+29=57, Resulting Numbers: [57] 57,44 unequal: No Solution Exploring Operation: 29-28=1, Resulting Numbers: [1] 1,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[58, 14], Operations: ['68-10=58', '28/2=14'] Exploring Operation: 58+14=72, Resulting Numbers: [72] 72,44 unequal: No Solution Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[10, 68, 28, 2], Operations: [] Exploring Operation: 68-10=58, Resulting Numbers: [28, 2, 58] Generated Node #0,2: 44:[28, 2, 58] Operation: 68-10=58 Moving to Node #0,2 Current State: 44:[28, 2, 58], Operations: ['68-10=58'] Exploring Operation: 28/2=14, Resulting Numbers: [58, 14] Generated Node #0,2,3: 44:[58, 14] Operation: 28/2=14 Moving to Node #0,2,3 Current State: 44:[58, 14], Operations: ['68-10=58', '28/2=14'] Exploring Operation: 58-14=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.952257
hs_4
sum_heuristic
[ 8, 31, 97, 94 ]
42
[ "8+31=39", "97-94=3", "39+3=42" ]
Current State: 42:[8, 31, 97, 94], Operations: [] Exploring Operation: 8+31=39, Resulting Numbers: [97, 94, 39] Generated Node #2: [97, 94, 39] from Operation: 8+31=39 Current State: 42:[97, 94, 39], Operations: ['8+31=39'] Exploring Operation: 97-94=3, Resulting Numbers: [39, 3] Generated Node #3: [39, 3] from Operation: 97-94=3 Current State: 42:[39, 3], Operations: ['8+31=39', '97-94=3'] Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[8, 31, 97, 94], Operations: [] Exploring Operation: 97-31=66, Resulting Numbers: [8, 94, 66] Generated Node #0,0: 42:[8, 94, 66] Operation: 97-31=66 Exploring Operation: 94-31=63, Resulting Numbers: [8, 97, 63] Generated Node #0,1: 42:[8, 97, 63] Operation: 94-31=63 Exploring Operation: 97-8=89, Resulting Numbers: [31, 94, 89] Generated Node #0,2: 42:[31, 94, 89] Operation: 97-8=89 Exploring Operation: 97-94=3, Resulting Numbers: [8, 31, 3] Generated Node #0,3: 42:[8, 31, 3] Operation: 97-94=3 Exploring Operation: 31-8=23, Resulting Numbers: [97, 94, 23] Generated Node #0,4: 42:[97, 94, 23] Operation: 31-8=23 Moving to Node #0,3 Current State: 42:[8, 31, 3], Operations: ['97-94=3'] Exploring Operation: 31+3=34, Resulting Numbers: [8, 34] Generated Node #0,3,0: 42:[8, 34] Operation: 31+3=34 Exploring Operation: 8+31=39, Resulting Numbers: [3, 39] Generated Node #0,3,1: 42:[3, 39] Operation: 8+31=39 Exploring Operation: 31-3=28, Resulting Numbers: [8, 28] Generated Node #0,3,2: 42:[8, 28] Operation: 31-3=28 Exploring Operation: 8-3=5, Resulting Numbers: [31, 5] Generated Node #0,3,3: 42:[31, 5] Operation: 8-3=5 Exploring Operation: 31-8=23, Resulting Numbers: [3, 23] Generated Node #0,3,4: 42:[3, 23] Operation: 31-8=23 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 42:[3, 23], Operations: ['97-94=3', '31-8=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,42 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,42 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 #0,3,1 Current State: 42:[3, 39], Operations: ['97-94=3', '8+31=39'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,42 unequal: No Solution Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[8, 31, 97, 94], Operations: [] Exploring Operation: 97-94=3, Resulting Numbers: [8, 31, 3] Generated Node #0,3: 42:[8, 31, 3] Operation: 97-94=3 Moving to Node #0,3 Current State: 42:[8, 31, 3], Operations: ['97-94=3'] Exploring Operation: 8+31=39, Resulting Numbers: [3, 39] Generated Node #0,3,1: 42:[3, 39] Operation: 8+31=39 Moving to Node #0,3,1 Current State: 42:[3, 39], Operations: ['97-94=3', '8+31=39'] Exploring Operation: 3+39=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 83, 90, 5, 2 ]
92
[ "83+5=88", "90*2=180", "180-88=92" ]
Current State: 92:[83, 90, 5, 2], Operations: [] Exploring Operation: 83+5=88, Resulting Numbers: [90, 2, 88] Generated Node #2: [90, 2, 88] from Operation: 83+5=88 Current State: 92:[90, 2, 88], Operations: ['83+5=88'] Exploring Operation: 90*2=180, Resulting Numbers: [88, 180] Generated Node #3: [88, 180] from Operation: 90*2=180 Current State: 92:[88, 180], Operations: ['83+5=88', '90*2=180'] Exploring Operation: 180-88=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[83, 90, 5, 2], Operations: [] Exploring Operation: 90-83=7, Resulting Numbers: [5, 2, 7] Generated Node #0,0: 92:[5, 2, 7] Operation: 90-83=7 Exploring Operation: 83+5=88, Resulting Numbers: [90, 2, 88] Generated Node #0,1: 92:[90, 2, 88] Operation: 83+5=88 Moving to Node #0,0 Current State: 92:[5, 2, 7], Operations: ['90-83=7'] Exploring Operation: 7-5=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 92:[2, 2] Operation: 7-5=2 Exploring Operation: 7-2=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 92:[5, 5] Operation: 7-2=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[2, 2], Operations: ['90-83=7', '7-5=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 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 #0,0,1 Current State: 92:[5, 5], Operations: ['90-83=7', '7-2=5'] Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,92 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,92 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:[90, 2, 88], Operations: ['83+5=88'] Exploring Operation: 90+2=92, Resulting Numbers: [88, 92] Generated Node #0,1,0: 92:[88, 92] Operation: 90+2=92 Exploring Operation: 90-88=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 92:[2, 2] Operation: 90-88=2 Moving to Node #0,1,1 Current State: 92:[2, 2], Operations: ['83+5=88', '90-88=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[88, 92], Operations: ['83+5=88', '90+2=92'] Exploring Operation: 92-88=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 88+92=180, Resulting Numbers: [180] 180,92 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 82, 92, 84, 40 ]
87
[ "92-84=8", "40/8=5", "82+5=87" ]
Current State: 87:[82, 92, 84, 40], Operations: [] Exploring Operation: 92-84=8, Resulting Numbers: [82, 40, 8] Generated Node #2: [82, 40, 8] from Operation: 92-84=8 Current State: 87:[82, 40, 8], Operations: ['92-84=8'] Exploring Operation: 40/8=5, Resulting Numbers: [82, 5] Generated Node #3: [82, 5] from Operation: 40/8=5 Current State: 87:[82, 5], Operations: ['92-84=8', '40/8=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[82, 92, 84, 40], Operations: [] Exploring Operation: 92-82=10, Resulting Numbers: [84, 40, 10] Generated Node #0,0: 87:[84, 40, 10] Operation: 92-82=10 Exploring Operation: 92-84=8, Resulting Numbers: [82, 40, 8] Generated Node #0,1: 87:[82, 40, 8] Operation: 92-84=8 Exploring Operation: 82-40=42, Resulting Numbers: [92, 84, 42] Generated Node #0,2: 87:[92, 84, 42] Operation: 82-40=42 Exploring Operation: 84-82=2, Resulting Numbers: [92, 40, 2] Generated Node #0,3: 87:[92, 40, 2] Operation: 84-82=2 Exploring Operation: 84-40=44, Resulting Numbers: [82, 92, 44] Generated Node #0,4: 87:[82, 92, 44] Operation: 84-40=44 Moving to Node #0,3 Current State: 87:[92, 40, 2], Operations: ['84-82=2'] Exploring Operation: 40/2=20, Resulting Numbers: [92, 20] Generated Node #0,3,0: 87:[92, 20] Operation: 40/2=20 Exploring Operation: 40-2=38, Resulting Numbers: [92, 38] Generated Node #0,3,1: 87:[92, 38] Operation: 40-2=38 Exploring Operation: 40*2=80, Resulting Numbers: [92, 80] Generated Node #0,3,2: 87:[92, 80] Operation: 40*2=80 Exploring Operation: 92-2=90, Resulting Numbers: [40, 90] Generated Node #0,3,3: 87:[40, 90] Operation: 92-2=90 Exploring Operation: 92+2=94, Resulting Numbers: [40, 94] Generated Node #0,3,4: 87:[40, 94] Operation: 92+2=94 Moving to Node #0,1 Current State: 87:[82, 40, 8], Operations: ['92-84=8'] Exploring Operation: 82-8=74, Resulting Numbers: [40, 74] Generated Node #0,1,0: 87:[40, 74] Operation: 82-8=74 Exploring Operation: 40-8=32, Resulting Numbers: [82, 32] Generated Node #0,1,1: 87:[82, 32] Operation: 40-8=32 Exploring Operation: 40/8=5, Resulting Numbers: [82, 5] Generated Node #0,1,2: 87:[82, 5] Operation: 40/8=5 Exploring Operation: 82-40=42, Resulting Numbers: [8, 42] Generated Node #0,1,3: 87:[8, 42] Operation: 82-40=42 Exploring Operation: 82+8=90, Resulting Numbers: [40, 90] Generated Node #0,1,4: 87:[40, 90] Operation: 82+8=90 Moving to Node #0,0 Current State: 87:[84, 40, 10], Operations: ['92-82=10'] Exploring Operation: 40/10=4, Resulting Numbers: [84, 4] Generated Node #0,0,0: 87:[84, 4] Operation: 40/10=4 Exploring Operation: 84-40=44, Resulting Numbers: [10, 44] Generated Node #0,0,1: 87:[10, 44] Operation: 84-40=44 Exploring Operation: 84+10=94, Resulting Numbers: [40, 94] Generated Node #0,0,2: 87:[40, 94] Operation: 84+10=94 Exploring Operation: 84-10=74, Resulting Numbers: [40, 74] Generated Node #0,0,3: 87:[40, 74] Operation: 84-10=74 Exploring Operation: 40-10=30, Resulting Numbers: [84, 30] Generated Node #0,0,4: 87:[84, 30] Operation: 40-10=30 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[84, 4], Operations: ['92-82=10', '40/10=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,87 unequal: No Solution Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,87 unequal: No Solution Exploring Operation: 84*4=336, Resulting Numbers: [336] 336,87 unequal: No Solution Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 87:[84, 30], Operations: ['92-82=10', '40-10=30'] Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,87 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[40, 94], Operations: ['92-82=10', '84+10=94'] Exploring Operation: 40*94=3760, Resulting Numbers: [3760] 3760,87 unequal: No Solution Exploring Operation: 40+94=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[10, 44], Operations: ['92-82=10', '84-40=44'] Exploring Operation: 10+44=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 10*44=440, Resulting Numbers: [440] 440,87 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 87:[40, 74], Operations: ['92-82=10', '84-10=74'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 40+74=114, Resulting Numbers: [114] 114,87 unequal: No Solution Exploring Operation: 40*74=2960, Resulting Numbers: [2960] 2960,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 87:[92, 84, 42], Operations: ['82-40=42'] Exploring Operation: 84-42=42, Resulting Numbers: [92, 42] Generated Node #0,2,0: 87:[92, 42] Operation: 84-42=42 Exploring Operation: 92-42=50, Resulting Numbers: [84, 50] Generated Node #0,2,1: 87:[84, 50] Operation: 92-42=50 Exploring Operation: 84+42=126, Resulting Numbers: [92, 126] Generated Node #0,2,2: 87:[92, 126] Operation: 84+42=126 Exploring Operation: 92-84=8, Resulting Numbers: [42, 8] Generated Node #0,2,3: 87:[42, 8] Operation: 92-84=8 Exploring Operation: 84/42=2, Resulting Numbers: [92, 2] Generated Node #0,2,4: 87:[92, 2] Operation: 84/42=2 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 87:[92, 2], Operations: ['82-40=42', '84/42=2'] Exploring Operation: 92+2=94, Resulting Numbers: [94] 94,87 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,87 unequal: No Solution Exploring Operation: 92*2=184, Resulting Numbers: [184] 184,87 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 87:[92, 42], Operations: ['82-40=42', '84-42=42'] Exploring Operation: 92*42=3864, Resulting Numbers: [3864] 3864,87 unequal: No Solution Exploring Operation: 92+42=134, Resulting Numbers: [134] 134,87 unequal: No Solution Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 87:[42, 8], Operations: ['82-40=42', '92-84=8'] Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,87 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,87 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 87:[84, 50], Operations: ['82-40=42', '92-42=50'] Exploring Operation: 84*50=4200, Resulting Numbers: [4200] 4200,87 unequal: No Solution Exploring Operation: 84-50=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 84+50=134, Resulting Numbers: [134] 134,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 87:[92, 126], Operations: ['82-40=42', '84+42=126'] Exploring Operation: 92+126=218, Resulting Numbers: [218] 218,87 unequal: No Solution Exploring Operation: 126-92=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 92*126=11592, Resulting Numbers: [11592] 11592,87 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: 87:[82, 92, 44], Operations: ['84-40=44'] Exploring Operation: 82-44=38, Resulting Numbers: [92, 38] Generated Node #0,4,0: 87:[92, 38] Operation: 82-44=38 Exploring Operation: 92+44=136, Resulting Numbers: [82, 136] Generated Node #0,4,1: 87:[82, 136] Operation: 92+44=136 Exploring Operation: 82+44=126, Resulting Numbers: [92, 126] Generated Node #0,4,2: 87:[92, 126] Operation: 82+44=126 Exploring Operation: 92-44=48, Resulting Numbers: [82, 48] Generated Node #0,4,3: 87:[82, 48] Operation: 92-44=48 Exploring Operation: 92-82=10, Resulting Numbers: [44, 10] Generated Node #0,4,4: 87:[44, 10] Operation: 92-82=10 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 87:[92, 38], Operations: ['84-40=44', '82-44=38'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 92+38=130, Resulting Numbers: [130] 130,87 unequal: No Solution Exploring Operation: 92*38=3496, Resulting Numbers: [3496] 3496,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 87:[44, 10], Operations: ['84-40=44', '92-82=10'] Exploring Operation: 44+10=54, Resulting Numbers: [54] 54,87 unequal: No Solution Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 44*10=440, Resulting Numbers: [440] 440,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 87:[82, 48], Operations: ['84-40=44', '92-44=48'] Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,87 unequal: No Solution Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,87 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 87:[92, 126], Operations: ['84-40=44', '82+44=126'] Exploring Operation: 92*126=11592, Resulting Numbers: [11592] 11592,87 unequal: No Solution Exploring Operation: 126-92=34, Resulting Numbers: [34] 34,87 unequal: No Solution Exploring Operation: 92+126=218, Resulting Numbers: [218] 218,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 87:[82, 136], Operations: ['84-40=44', '92+44=136'] Exploring Operation: 82*136=11152, Resulting Numbers: [11152] 11152,87 unequal: No Solution Exploring Operation: 82+136=218, Resulting Numbers: [218] 218,87 unequal: No Solution Exploring Operation: 136-82=54, Resulting Numbers: [54] 54,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 87:[82, 5], Operations: ['92-84=8', '40/8=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[82, 92, 84, 40], Operations: [] Exploring Operation: 92-84=8, Resulting Numbers: [82, 40, 8] Generated Node #0,1: 87:[82, 40, 8] Operation: 92-84=8 Moving to Node #0,1 Current State: 87:[82, 40, 8], Operations: ['92-84=8'] Exploring Operation: 40/8=5, Resulting Numbers: [82, 5] Generated Node #0,1,2: 87:[82, 5] Operation: 40/8=5 Moving to Node #0,1,2 Current State: 87:[82, 5], Operations: ['92-84=8', '40/8=5'] Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
0.928819
hs_5
sum_heuristic
[ 82, 92, 14, 22 ]
14
[ "82+92=174", "22+174=196", "196/14=14" ]
Current State: 14:[82, 92, 14, 22], Operations: [] Exploring Operation: 82+92=174, Resulting Numbers: [14, 22, 174] Generated Node #2: [14, 22, 174] from Operation: 82+92=174 Current State: 14:[14, 22, 174], Operations: ['82+92=174'] Exploring Operation: 22+174=196, Resulting Numbers: [14, 196] Generated Node #3: [14, 196] from Operation: 22+174=196 Current State: 14:[14, 196], Operations: ['82+92=174', '22+174=196'] Exploring Operation: 196/14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[82, 92, 14, 22], Operations: [] Exploring Operation: 92-14=78, Resulting Numbers: [82, 22, 78] Generated Node #0,0: 14:[82, 22, 78] Operation: 92-14=78 Exploring Operation: 82-14=68, Resulting Numbers: [92, 22, 68] Generated Node #0,1: 14:[92, 22, 68] Operation: 82-14=68 Exploring Operation: 82-22=60, Resulting Numbers: [92, 14, 60] Generated Node #0,2: 14:[92, 14, 60] Operation: 82-22=60 Exploring Operation: 92-82=10, Resulting Numbers: [14, 22, 10] Generated Node #0,3: 14:[14, 22, 10] Operation: 92-82=10 Exploring Operation: 92-22=70, Resulting Numbers: [82, 14, 70] Generated Node #0,4: 14:[82, 14, 70] Operation: 92-22=70 Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[14, 22, 10], Operations: ['92-82=10'] Exploring Operation: 14-10=4, Resulting Numbers: [22, 4] Generated Node #0,3,0: 14:[22, 4] Operation: 14-10=4 Exploring Operation: 22-14=8, Resulting Numbers: [10, 8] Generated Node #0,3,1: 14:[10, 8] Operation: 22-14=8 Exploring Operation: 14+10=24, Resulting Numbers: [22, 24] Generated Node #0,3,2: 14:[22, 24] Operation: 14+10=24 Exploring Operation: 22-10=12, Resulting Numbers: [14, 12] Generated Node #0,3,3: 14:[14, 12] Operation: 22-10=12 Exploring Operation: 22+10=32, Resulting Numbers: [14, 32] Generated Node #0,3,4: 14:[14, 32] Operation: 22+10=32 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 14:[14, 12], Operations: ['92-82=10', '22-10=12'] Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,14 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 #0,3,1 Current State: 14:[10, 8], Operations: ['92-82=10', '22-14=8'] Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,14 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 #0,3,0 Current State: 14:[22, 4], Operations: ['92-82=10', '14-10=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,14 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 #0,3,2 Current State: 14:[22, 24], Operations: ['92-82=10', '14+10=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,14 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,14 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 #0,3,4 Current State: 14:[14, 32], Operations: ['92-82=10', '22+10=32'] Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 14*32=448, Resulting Numbers: [448] 448,14 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 #0,2 Current State: 14:[92, 14, 60], Operations: ['82-22=60'] Exploring Operation: 92+60=152, Resulting Numbers: [14, 152] Generated Node #0,2,0: 14:[14, 152] Operation: 92+60=152 Exploring Operation: 92+14=106, Resulting Numbers: [60, 106] Generated Node #0,2,1: 14:[60, 106] Operation: 92+14=106 Exploring Operation: 92-14=78, Resulting Numbers: [60, 78] Generated Node #0,2,2: 14:[60, 78] Operation: 92-14=78 Exploring Operation: 92-60=32, Resulting Numbers: [14, 32] Generated Node #0,2,3: 14:[14, 32] Operation: 92-60=32 Exploring Operation: 60-14=46, Resulting Numbers: [92, 46] Generated Node #0,2,4: 14:[92, 46] Operation: 60-14=46 Moving to Node #0,2,3 Current State: 14:[14, 32], Operations: ['82-22=60', '92-60=32'] Exploring Operation: 14+32=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 14*32=448, Resulting Numbers: [448] 448,14 unequal: No Solution Moving to Node #0,2,4 Current State: 14:[92, 46], Operations: ['82-22=60', '60-14=46'] Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 92*46=4232, Resulting Numbers: [4232] 4232,14 unequal: No Solution Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 92+46=138, Resulting Numbers: [138] 138,14 unequal: No Solution Moving to Node #0,2,2 Current State: 14:[60, 78], Operations: ['82-22=60', '92-14=78'] Exploring Operation: 60+78=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 60*78=4680, Resulting Numbers: [4680] 4680,14 unequal: No Solution Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[14, 152], Operations: ['82-22=60', '92+60=152'] Exploring Operation: 152-14=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 14*152=2128, Resulting Numbers: [2128] 2128,14 unequal: No Solution Exploring Operation: 14+152=166, Resulting Numbers: [166] 166,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[60, 106], Operations: ['82-22=60', '92+14=106'] Exploring Operation: 60*106=6360, Resulting Numbers: [6360] 6360,14 unequal: No Solution Exploring Operation: 60+106=166, Resulting Numbers: [166] 166,14 unequal: No Solution Exploring Operation: 106-60=46, Resulting Numbers: [46] 46,14 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 #0,4 Current State: 14:[82, 14, 70], Operations: ['92-22=70'] Exploring Operation: 82+14=96, Resulting Numbers: [70, 96] Generated Node #0,4,0: 14:[70, 96] Operation: 82+14=96 Exploring Operation: 70/14=5, Resulting Numbers: [82, 5] Generated Node #0,4,1: 14:[82, 5] Operation: 70/14=5 Exploring Operation: 70-14=56, Resulting Numbers: [82, 56] Generated Node #0,4,2: 14:[82, 56] Operation: 70-14=56 Exploring Operation: 82-14=68, Resulting Numbers: [70, 68] Generated Node #0,4,3: 14:[70, 68] Operation: 82-14=68 Exploring Operation: 82-70=12, Resulting Numbers: [14, 12] Generated Node #0,4,4: 14:[14, 12] Operation: 82-70=12 Moving to Node #0,4,4 Current State: 14:[14, 12], Operations: ['92-22=70', '82-70=12'] Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,14 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,14 unequal: No Solution Moving to Node #0,4,1 Current State: 14:[82, 5], Operations: ['92-22=70', '70/14=5'] Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,14 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,14 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,14 unequal: No Solution Moving to Node #0,4,2 Current State: 14:[82, 56], Operations: ['92-22=70', '70-14=56'] Exploring Operation: 82*56=4592, Resulting Numbers: [4592] 4592,14 unequal: No Solution Exploring Operation: 82+56=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 82-56=26, Resulting Numbers: [26] 26,14 unequal: No Solution Moving to Node #0,4,3 Current State: 14:[70, 68], Operations: ['92-22=70', '82-14=68'] Exploring Operation: 70*68=4760, Resulting Numbers: [4760] 4760,14 unequal: No Solution Exploring Operation: 70-68=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 70+68=138, Resulting Numbers: [138] 138,14 unequal: No Solution Moving to Node #0,4,0 Current State: 14:[70, 96], Operations: ['92-22=70', '82+14=96'] Exploring Operation: 70*96=6720, Resulting Numbers: [6720] 6720,14 unequal: No Solution Exploring Operation: 70+96=166, Resulting Numbers: [166] 166,14 unequal: No Solution Exploring Operation: 96-70=26, Resulting Numbers: [26] 26,14 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 #0,0 Current State: 14:[82, 22, 78], Operations: ['92-14=78'] Exploring Operation: 82+78=160, Resulting Numbers: [22, 160] Generated Node #0,0,0: 14:[22, 160] Operation: 82+78=160 Exploring Operation: 82-22=60, Resulting Numbers: [78, 60] Generated Node #0,0,1: 14:[78, 60] Operation: 82-22=60 Exploring Operation: 82-78=4, Resulting Numbers: [22, 4] Generated Node #0,0,2: 14:[22, 4] Operation: 82-78=4 Exploring Operation: 78-22=56, Resulting Numbers: [82, 56] Generated Node #0,0,3: 14:[82, 56] Operation: 78-22=56 Exploring Operation: 82+22=104, Resulting Numbers: [78, 104] Generated Node #0,0,4: 14:[78, 104] Operation: 82+22=104 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 14:[22, 4], Operations: ['92-14=78', '82-78=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,14 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,14 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[78, 60], Operations: ['92-14=78', '82-22=60'] Exploring Operation: 78-60=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 78+60=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 78*60=4680, Resulting Numbers: [4680] 4680,14 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 #0,0,3 Current State: 14:[82, 56], Operations: ['92-14=78', '78-22=56'] Exploring Operation: 82*56=4592, Resulting Numbers: [4592] 4592,14 unequal: No Solution Exploring Operation: 82+56=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 82-56=26, Resulting Numbers: [26] 26,14 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 #0,0,0 Current State: 14:[22, 160], Operations: ['92-14=78', '82+78=160'] Exploring Operation: 22+160=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 160-22=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 22*160=3520, Resulting Numbers: [3520] 3520,14 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 #0,0,4 Current State: 14:[78, 104], Operations: ['92-14=78', '82+22=104'] Exploring Operation: 78+104=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 78*104=8112, Resulting Numbers: [8112] 8112,14 unequal: No Solution Exploring Operation: 104-78=26, Resulting Numbers: [26] 26,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[92, 22, 68], Operations: ['82-14=68'] Exploring Operation: 92+68=160, Resulting Numbers: [22, 160] Generated Node #0,1,0: 14:[22, 160] Operation: 92+68=160 Exploring Operation: 92+22=114, Resulting Numbers: [68, 114] Generated Node #0,1,1: 14:[68, 114] Operation: 92+22=114 Exploring Operation: 92-22=70, Resulting Numbers: [68, 70] Generated Node #0,1,2: 14:[68, 70] Operation: 92-22=70 Exploring Operation: 92-68=24, Resulting Numbers: [22, 24] Generated Node #0,1,3: 14:[22, 24] Operation: 92-68=24 Exploring Operation: 68-22=46, Resulting Numbers: [92, 46] Generated Node #0,1,4: 14:[92, 46] Operation: 68-22=46 Moving to Node #0,1,3 Current State: 14:[22, 24], Operations: ['82-14=68', '92-68=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,14 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,1,4 Current State: 14:[92, 46], Operations: ['82-14=68', '68-22=46'] Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,14 unequal: No Solution Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 92*46=4232, Resulting Numbers: [4232] 4232,14 unequal: No Solution Exploring Operation: 92+46=138, Resulting Numbers: [138] 138,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[68, 70], Operations: ['82-14=68', '92-22=70'] Exploring Operation: 68*70=4760, Resulting Numbers: [4760] 4760,14 unequal: No Solution Exploring Operation: 70-68=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 68+70=138, Resulting Numbers: [138] 138,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[22, 160], Operations: ['82-14=68', '92+68=160'] Exploring Operation: 22+160=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 160-22=138, Resulting Numbers: [138] 138,14 unequal: No Solution Exploring Operation: 22*160=3520, Resulting Numbers: [3520] 3520,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[68, 114], Operations: ['82-14=68', '92+22=114'] Exploring Operation: 68+114=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 68*114=7752, Resulting Numbers: [7752] 7752,14 unequal: No Solution Exploring Operation: 114-68=46, Resulting Numbers: [46] 46,14 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
[ 39, 33, 36, 11 ]
24
[ "36-33=3", "39/3=13", "11+13=24" ]
Current State: 24:[39, 33, 36, 11], Operations: [] Exploring Operation: 36-33=3, Resulting Numbers: [39, 11, 3] Generated Node #2: [39, 11, 3] from Operation: 36-33=3 Current State: 24:[39, 11, 3], Operations: ['36-33=3'] Exploring Operation: 39/3=13, Resulting Numbers: [11, 13] Generated Node #3: [11, 13] from Operation: 39/3=13 Current State: 24:[11, 13], Operations: ['36-33=3', '39/3=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[39, 33, 36, 11], Operations: [] Exploring Operation: 39-36=3, Resulting Numbers: [33, 11, 3] Generated Node #0,0: 24:[33, 11, 3] Operation: 39-36=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[33, 11, 3], Operations: ['39-36=3'] Exploring Operation: 33/11=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 24:[3, 3] Operation: 33/11=3 Moving to Node #0,0,0 Current State: 24:[3, 3], Operations: ['39-36=3', '33/11=3'] Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,24 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
[ 11, 85, 76, 28 ]
48
[ "11+85=96", "76-28=48", "96-48=48" ]
Current State: 48:[11, 85, 76, 28], Operations: [] Exploring Operation: 11+85=96, Resulting Numbers: [76, 28, 96] Generated Node #2: [76, 28, 96] from Operation: 11+85=96 Current State: 48:[76, 28, 96], Operations: ['11+85=96'] Exploring Operation: 76-28=48, Resulting Numbers: [96, 48] Generated Node #3: [96, 48] from Operation: 76-28=48 Current State: 48:[96, 48], Operations: ['11+85=96', '76-28=48'] Exploring Operation: 96-48=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[11, 85, 76, 28], Operations: [] Exploring Operation: 85-28=57, Resulting Numbers: [11, 76, 57] Generated Node #0,0: 48:[11, 76, 57] Operation: 85-28=57 Exploring Operation: 76-28=48, Resulting Numbers: [11, 85, 48] Generated Node #0,1: 48:[11, 85, 48] Operation: 76-28=48 Exploring Operation: 85-76=9, Resulting Numbers: [11, 28, 9] Generated Node #0,2: 48:[11, 28, 9] Operation: 85-76=9 Moving to Node #0,2 Current State: 48:[11, 28, 9], Operations: ['85-76=9'] Exploring Operation: 28-9=19, Resulting Numbers: [11, 19] Generated Node #0,2,0: 48:[11, 19] Operation: 28-9=19 Exploring Operation: 11-9=2, Resulting Numbers: [28, 2] Generated Node #0,2,1: 48:[28, 2] Operation: 11-9=2 Exploring Operation: 28-11=17, Resulting Numbers: [9, 17] Generated Node #0,2,2: 48:[9, 17] Operation: 28-11=17 Moving to Node #0,0 Current State: 48:[11, 76, 57], Operations: ['85-28=57'] Exploring Operation: 76-11=65, Resulting Numbers: [57, 65] Generated Node #0,0,0: 48:[57, 65] Operation: 76-11=65 Exploring Operation: 76-57=19, Resulting Numbers: [11, 19] Generated Node #0,0,1: 48:[11, 19] Operation: 76-57=19 Exploring Operation: 57-11=46, Resulting Numbers: [76, 46] Generated Node #0,0,2: 48:[76, 46] Operation: 57-11=46 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[11, 19], Operations: ['85-28=57', '76-57=19'] Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,48 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,48 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 #0,0,0 Current State: 48:[57, 65], Operations: ['85-28=57', '76-11=65'] Exploring Operation: 57*65=3705, Resulting Numbers: [3705] 3705,48 unequal: No Solution Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 57+65=122, Resulting Numbers: [122] 122,48 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 #0,0,2 Current State: 48:[76, 46], Operations: ['85-28=57', '57-11=46'] Exploring Operation: 76*46=3496, Resulting Numbers: [3496] 3496,48 unequal: No Solution Exploring Operation: 76+46=122, Resulting Numbers: [122] 122,48 unequal: No Solution Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,48 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: 48:[11, 85, 48], Operations: ['76-28=48'] Exploring Operation: 85-48=37, Resulting Numbers: [11, 37] Generated Node #0,1,0: 48:[11, 37] Operation: 85-48=37 Exploring Operation: 11+85=96, Resulting Numbers: [48, 96] Generated Node #0,1,1: 48:[48, 96] Operation: 11+85=96 Exploring Operation: 85-11=74, Resulting Numbers: [48, 74] Generated Node #0,1,2: 48:[48, 74] Operation: 85-11=74 Moving to Node #0,2,2 Current State: 48:[9, 17], Operations: ['85-76=9', '28-11=17'] Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,48 unequal: No Solution Moving to Node #0,2,1 Current State: 48:[28, 2], Operations: ['85-76=9', '11-9=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,48 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,48 unequal: No Solution Moving to Node #0,2,0 Current State: 48:[11, 19], Operations: ['85-76=9', '28-9=19'] Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,48 unequal: No Solution Exploring Operation: 11+19=30, Resulting Numbers: [30] 30,48 unequal: No Solution Exploring Operation: 11*19=209, Resulting Numbers: [209] 209,48 unequal: No Solution Moving to Node #0,1,0 Current State: 48:[11, 37], Operations: ['76-28=48', '85-48=37'] Exploring Operation: 37-11=26, Resulting Numbers: [26] 26,48 unequal: No Solution Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[11, 85, 76, 28], Operations: [] Exploring Operation: 76-28=48, Resulting Numbers: [11, 85, 48] Generated Node #0,1: 48:[11, 85, 48] Operation: 76-28=48 Moving to Node #0,1 Current State: 48:[11, 85, 48], Operations: ['76-28=48'] Exploring Operation: 85-48=37, Resulting Numbers: [11, 37] Generated Node #0,1,0: 48:[11, 37] Operation: 85-48=37 Moving to Node #0,1,0 Current State: 48:[11, 37], Operations: ['76-28=48', '85-48=37'] Exploring Operation: 11+37=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
0.96875
hs_3
mult_heuristic
[ 64, 73, 60, 66 ]
47
[ "66-64=2", "60*2=120", "120-73=47" ]
Current State: 47:[64, 73, 60, 66], Operations: [] Exploring Operation: 66-64=2, Resulting Numbers: [73, 60, 2] Generated Node #2: [73, 60, 2] from Operation: 66-64=2 Current State: 47:[73, 60, 2], Operations: ['66-64=2'] Exploring Operation: 60*2=120, Resulting Numbers: [73, 120] Generated Node #3: [73, 120] from Operation: 60*2=120 Current State: 47:[73, 120], Operations: ['66-64=2', '60*2=120'] Exploring Operation: 120-73=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[64, 73, 60, 66], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [60, 66, 9] Generated Node #0,0: 47:[60, 66, 9] Operation: 73-64=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[60, 66, 9], Operations: ['73-64=9'] Exploring Operation: 60-9=51, Resulting Numbers: [66, 51] Generated Node #0,0,0: 47:[66, 51] Operation: 60-9=51 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[66, 51], Operations: ['73-64=9', '60-9=51'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,47 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
[ 21, 50, 1, 81 ]
11
[ "21+50=71", "1+81=82", "82-71=11" ]
Current State: 11:[21, 50, 1, 81], Operations: [] Exploring Operation: 21+50=71, Resulting Numbers: [1, 81, 71] Generated Node #2: [1, 81, 71] from Operation: 21+50=71 Current State: 11:[1, 81, 71], Operations: ['21+50=71'] Exploring Operation: 1+81=82, Resulting Numbers: [71, 82] Generated Node #3: [71, 82] from Operation: 1+81=82 Current State: 11:[71, 82], Operations: ['21+50=71', '1+81=82'] Exploring Operation: 82-71=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[21, 50, 1, 81], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [1, 81, 29] Generated Node #0,0: 11:[1, 81, 29] Operation: 50-21=29 Exploring Operation: 81-50=31, Resulting Numbers: [21, 1, 31] Generated Node #0,1: 11:[21, 1, 31] Operation: 81-50=31 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[21, 1, 31], Operations: ['81-50=31'] Exploring Operation: 31-21=10, Resulting Numbers: [1, 10] Generated Node #0,1,0: 11:[1, 10] Operation: 31-21=10 Exploring Operation: 21-1=20, Resulting Numbers: [31, 20] Generated Node #0,1,1: 11:[31, 20] Operation: 21-1=20 Moving to Node #0,1,0 Current State: 11:[1, 10], Operations: ['81-50=31', '31-21=10'] Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[21, 50, 1, 81], Operations: [] Exploring Operation: 81-50=31, Resulting Numbers: [21, 1, 31] Generated Node #0,1: 11:[21, 1, 31] Operation: 81-50=31 Moving to Node #0,1 Current State: 11:[21, 1, 31], Operations: ['81-50=31'] Exploring Operation: 31-21=10, Resulting Numbers: [1, 10] Generated Node #0,1,0: 11:[1, 10] Operation: 31-21=10 Moving to Node #0,1,0 Current State: 11:[1, 10], Operations: ['81-50=31', '31-21=10'] Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 35, 71, 72, 9 ]
98
[ "35+71=106", "72/9=8", "106-8=98" ]
Current State: 98:[35, 71, 72, 9], Operations: [] Exploring Operation: 35+71=106, Resulting Numbers: [72, 9, 106] Generated Node #2: [72, 9, 106] from Operation: 35+71=106 Current State: 98:[72, 9, 106], Operations: ['35+71=106'] Exploring Operation: 72/9=8, Resulting Numbers: [106, 8] Generated Node #3: [106, 8] from Operation: 72/9=8 Current State: 98:[106, 8], Operations: ['35+71=106', '72/9=8'] Exploring Operation: 106-8=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[35, 71, 72, 9], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [35, 9, 1] Generated Node #0,0: 98:[35, 9, 1] Operation: 72-71=1 Moving to Node #0,0 Current State: 98:[35, 9, 1], Operations: ['72-71=1'] Exploring Operation: 35+9=44, Resulting Numbers: [1, 44] Generated Node #0,0,0: 98:[1, 44] Operation: 35+9=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[1, 44], Operations: ['72-71=1', '35+9=44'] Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,98 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
[ 51, 38, 52, 41 ]
80
[ "51-38=13", "52+41=93", "93-13=80" ]
Current State: 80:[51, 38, 52, 41], Operations: [] Exploring Operation: 51-38=13, Resulting Numbers: [52, 41, 13] Generated Node #2: [52, 41, 13] from Operation: 51-38=13 Current State: 80:[52, 41, 13], Operations: ['51-38=13'] Exploring Operation: 52+41=93, Resulting Numbers: [13, 93] Generated Node #3: [13, 93] from Operation: 52+41=93 Current State: 80:[13, 93], Operations: ['51-38=13', '52+41=93'] Exploring Operation: 93-13=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[51, 38, 52, 41], Operations: [] Exploring Operation: 52-51=1, Resulting Numbers: [38, 41, 1] Generated Node #0,0: 80:[38, 41, 1] Operation: 52-51=1 Exploring Operation: 51-41=10, Resulting Numbers: [38, 52, 10] Generated Node #0,1: 80:[38, 52, 10] Operation: 51-41=10 Exploring Operation: 52-38=14, Resulting Numbers: [51, 41, 14] Generated Node #0,2: 80:[51, 41, 14] Operation: 52-38=14 Moving to Node #0,0 Current State: 80:[38, 41, 1], Operations: ['52-51=1'] Exploring Operation: 38+1=39, Resulting Numbers: [41, 39] Generated Node #0,0,0: 80:[41, 39] Operation: 38+1=39 Exploring Operation: 38+41=79, Resulting Numbers: [1, 79] Generated Node #0,0,1: 80:[1, 79] Operation: 38+41=79 Exploring Operation: 41-38=3, Resulting Numbers: [1, 3] Generated Node #0,0,2: 80:[1, 3] Operation: 41-38=3 Moving to Node #0,1 Current State: 80:[38, 52, 10], Operations: ['51-41=10'] Exploring Operation: 38+52=90, Resulting Numbers: [10, 90] Generated Node #0,1,0: 80:[10, 90] Operation: 38+52=90 Exploring Operation: 52-38=14, Resulting Numbers: [10, 14] Generated Node #0,1,1: 80:[10, 14] Operation: 52-38=14 Exploring Operation: 52-10=42, Resulting Numbers: [38, 42] Generated Node #0,1,2: 80:[38, 42] Operation: 52-10=42 Moving to Node #0,2 Current State: 80:[51, 41, 14], Operations: ['52-38=14'] Exploring Operation: 51-41=10, Resulting Numbers: [14, 10] Generated Node #0,2,0: 80:[14, 10] Operation: 51-41=10 Exploring Operation: 51+41=92, Resulting Numbers: [14, 92] Generated Node #0,2,1: 80:[14, 92] Operation: 51+41=92 Exploring Operation: 51-14=37, Resulting Numbers: [41, 37] Generated Node #0,2,2: 80:[41, 37] Operation: 51-14=37 Moving to Node #0,0,0 Current State: 80:[41, 39], Operations: ['52-51=1', '38+1=39'] Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,80 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,80 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[51, 38, 52, 41], Operations: [] Exploring Operation: 52-51=1, Resulting Numbers: [38, 41, 1] Generated Node #0,0: 80:[38, 41, 1] Operation: 52-51=1 Moving to Node #0,0 Current State: 80:[38, 41, 1], Operations: ['52-51=1'] Exploring Operation: 38+1=39, Resulting Numbers: [41, 39] Generated Node #0,0,0: 80:[41, 39] Operation: 38+1=39 Moving to Node #0,0,0 Current State: 80:[41, 39], Operations: ['52-51=1', '38+1=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
0.983507
hs_3
sum_heuristic
[ 22, 88, 52, 93 ]
25
[ "88-22=66", "93-52=41", "66-41=25" ]
Current State: 25:[22, 88, 52, 93], Operations: [] Exploring Operation: 88-22=66, Resulting Numbers: [52, 93, 66] Generated Node #2: [52, 93, 66] from Operation: 88-22=66 Current State: 25:[52, 93, 66], Operations: ['88-22=66'] Exploring Operation: 93-52=41, Resulting Numbers: [66, 41] Generated Node #3: [66, 41] from Operation: 93-52=41 Current State: 25:[66, 41], Operations: ['88-22=66', '93-52=41'] Exploring Operation: 66-41=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[22, 88, 52, 93], Operations: [] Exploring Operation: 93-52=41, Resulting Numbers: [22, 88, 41] Generated Node #0,0: 25:[22, 88, 41] Operation: 93-52=41 Exploring Operation: 93-88=5, Resulting Numbers: [22, 52, 5] Generated Node #0,1: 25:[22, 52, 5] Operation: 93-88=5 Exploring Operation: 88-52=36, Resulting Numbers: [22, 93, 36] Generated Node #0,2: 25:[22, 93, 36] Operation: 88-52=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[22, 52, 5], Operations: ['93-88=5'] Exploring Operation: 22+5=27, Resulting Numbers: [52, 27] Generated Node #0,1,0: 25:[52, 27] Operation: 22+5=27 Exploring Operation: 52-5=47, Resulting Numbers: [22, 47] Generated Node #0,1,1: 25:[22, 47] Operation: 52-5=47 Exploring Operation: 52-22=30, Resulting Numbers: [5, 30] Generated Node #0,1,2: 25:[5, 30] Operation: 52-22=30 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 25:[5, 30], Operations: ['93-88=5', '52-22=30'] Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[22, 88, 52, 93], Operations: [] Exploring Operation: 93-88=5, Resulting Numbers: [22, 52, 5] Generated Node #0,1: 25:[22, 52, 5] Operation: 93-88=5 Moving to Node #0,1 Current State: 25:[22, 52, 5], Operations: ['93-88=5'] Exploring Operation: 52-22=30, Resulting Numbers: [5, 30] Generated Node #0,1,2: 25:[5, 30] Operation: 52-22=30 Moving to Node #0,1,2 Current State: 25:[5, 30], Operations: ['93-88=5', '52-22=30'] Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 32, 53, 18, 16 ]
83
[ "32+53=85", "18-16=2", "85-2=83" ]
Current State: 83:[32, 53, 18, 16], Operations: [] Exploring Operation: 32+53=85, Resulting Numbers: [18, 16, 85] Generated Node #2: [18, 16, 85] from Operation: 32+53=85 Current State: 83:[18, 16, 85], Operations: ['32+53=85'] Exploring Operation: 18-16=2, Resulting Numbers: [85, 2] Generated Node #3: [85, 2] from Operation: 18-16=2 Current State: 83:[85, 2], Operations: ['32+53=85', '18-16=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[32, 53, 18, 16], Operations: [] Exploring Operation: 53+16=69, Resulting Numbers: [32, 18, 69] Generated Node #0,0: 83:[32, 18, 69] Operation: 53+16=69 Exploring Operation: 53+18=71, Resulting Numbers: [32, 16, 71] Generated Node #0,1: 83:[32, 16, 71] Operation: 53+18=71 Exploring Operation: 18+16=34, Resulting Numbers: [32, 53, 34] Generated Node #0,2: 83:[32, 53, 34] Operation: 18+16=34 Exploring Operation: 32+16=48, Resulting Numbers: [53, 18, 48] Generated Node #0,3: 83:[53, 18, 48] Operation: 32+16=48 Exploring Operation: 32+18=50, Resulting Numbers: [53, 16, 50] Generated Node #0,4: 83:[53, 16, 50] Operation: 32+18=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[32, 18, 69], Operations: ['53+16=69'] Exploring Operation: 18+69=87, Resulting Numbers: [32, 87] Generated Node #0,0,0: 83:[32, 87] Operation: 18+69=87 Exploring Operation: 32-18=14, Resulting Numbers: [69, 14] Generated Node #0,0,1: 83:[69, 14] Operation: 32-18=14 Exploring Operation: 69-18=51, Resulting Numbers: [32, 51] Generated Node #0,0,2: 83:[32, 51] Operation: 69-18=51 Exploring Operation: 32+69=101, Resulting Numbers: [18, 101] Generated Node #0,0,3: 83:[18, 101] Operation: 32+69=101 Exploring Operation: 32+18=50, Resulting Numbers: [69, 50] Generated Node #0,0,4: 83:[69, 50] Operation: 32+18=50 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 83:[69, 50], Operations: ['53+16=69', '32+18=50'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,83 unequal: No Solution Exploring Operation: 69*50=3450, Resulting Numbers: [3450] 3450,83 unequal: No Solution Exploring Operation: 69+50=119, Resulting Numbers: [119] 119,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[32, 87], Operations: ['53+16=69', '18+69=87'] Exploring Operation: 32+87=119, Resulting Numbers: [119] 119,83 unequal: No Solution Exploring Operation: 32*87=2784, Resulting Numbers: [2784] 2784,83 unequal: No Solution Exploring Operation: 87-32=55, Resulting Numbers: [55] 55,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[69, 14], Operations: ['53+16=69', '32-18=14'] Exploring Operation: 69*14=966, Resulting Numbers: [966] 966,83 unequal: No Solution Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[32, 53, 18, 16], Operations: [] Exploring Operation: 53+16=69, Resulting Numbers: [32, 18, 69] Generated Node #0,0: 83:[32, 18, 69] Operation: 53+16=69 Moving to Node #0,0 Current State: 83:[32, 18, 69], Operations: ['53+16=69'] Exploring Operation: 32-18=14, Resulting Numbers: [69, 14] Generated Node #0,0,1: 83:[69, 14] Operation: 32-18=14 Moving to Node #0,0,1 Current State: 83:[69, 14], Operations: ['53+16=69', '32-18=14'] Exploring Operation: 69+14=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 4, 20, 85, 28 ]
58
[ "28/4=7", "85-20=65", "65-7=58" ]
Current State: 58:[4, 20, 85, 28], Operations: [] Exploring Operation: 28/4=7, Resulting Numbers: [20, 85, 7] Generated Node #2: [20, 85, 7] from Operation: 28/4=7 Current State: 58:[20, 85, 7], Operations: ['28/4=7'] Exploring Operation: 85-20=65, Resulting Numbers: [7, 65] Generated Node #3: [7, 65] from Operation: 85-20=65 Current State: 58:[7, 65], Operations: ['28/4=7', '85-20=65'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[4, 20, 85, 28], Operations: [] Exploring Operation: 20/4=5, Resulting Numbers: [85, 28, 5] Generated Node #0,0: 58:[85, 28, 5] Operation: 20/4=5 Exploring Operation: 85-28=57, Resulting Numbers: [4, 20, 57] Generated Node #0,1: 58:[4, 20, 57] Operation: 85-28=57 Exploring Operation: 85-20=65, Resulting Numbers: [4, 28, 65] Generated Node #0,2: 58:[4, 28, 65] Operation: 85-20=65 Exploring Operation: 85-4=81, Resulting Numbers: [20, 28, 81] Generated Node #0,3: 58:[20, 28, 81] Operation: 85-4=81 Exploring Operation: 4+20=24, Resulting Numbers: [85, 28, 24] Generated Node #0,4: 58:[85, 28, 24] Operation: 4+20=24 Moving to Node #0,2 Current State: 58:[4, 28, 65], Operations: ['85-20=65'] Exploring Operation: 65-4=61, Resulting Numbers: [28, 61] Generated Node #0,2,0: 58:[28, 61] Operation: 65-4=61 Exploring Operation: 4+28=32, Resulting Numbers: [65, 32] Generated Node #0,2,1: 58:[65, 32] Operation: 4+28=32 Exploring Operation: 28/4=7, Resulting Numbers: [65, 7] Generated Node #0,2,2: 58:[65, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [65, 24] Generated Node #0,2,3: 58:[65, 24] Operation: 28-4=24 Exploring Operation: 65-28=37, Resulting Numbers: [4, 37] Generated Node #0,2,4: 58:[4, 37] Operation: 65-28=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[28, 61], Operations: ['85-20=65', '65-4=61'] Exploring Operation: 61-28=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 28+61=89, Resulting Numbers: [89] 89,58 unequal: No Solution Exploring Operation: 28*61=1708, Resulting Numbers: [1708] 1708,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 58:[65, 32], Operations: ['85-20=65', '4+28=32'] Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,58 unequal: No Solution Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 58:[4, 37], Operations: ['85-20=65', '65-28=37'] Exploring Operation: 4+37=41, Resulting Numbers: [41] 41,58 unequal: No Solution Exploring Operation: 4*37=148, Resulting Numbers: [148] 148,58 unequal: No Solution Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 58:[65, 7], Operations: ['85-20=65', '28/4=7'] Exploring Operation: 65*7=455, Resulting Numbers: [455] 455,58 unequal: No Solution Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,58 unequal: No Solution Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[4, 20, 85, 28], Operations: [] Exploring Operation: 85-20=65, Resulting Numbers: [4, 28, 65] Generated Node #0,2: 58:[4, 28, 65] Operation: 85-20=65 Moving to Node #0,2 Current State: 58:[4, 28, 65], Operations: ['85-20=65'] Exploring Operation: 28/4=7, Resulting Numbers: [65, 7] Generated Node #0,2,2: 58:[65, 7] Operation: 28/4=7 Moving to Node #0,2,2 Current State: 58:[65, 7], Operations: ['85-20=65', '28/4=7'] Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
sum_heuristic
[ 16, 2, 55, 62 ]
94
[ "16+62=78", "78/2=39", "55+39=94" ]
Current State: 94:[16, 2, 55, 62], Operations: [] Exploring Operation: 16+62=78, Resulting Numbers: [2, 55, 78] Generated Node #2: [2, 55, 78] from Operation: 16+62=78 Current State: 94:[2, 55, 78], Operations: ['16+62=78'] Exploring Operation: 78/2=39, Resulting Numbers: [55, 39] Generated Node #3: [55, 39] from Operation: 78/2=39 Current State: 94:[55, 39], Operations: ['16+62=78', '78/2=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[16, 2, 55, 62], Operations: [] Exploring Operation: 16+62=78, Resulting Numbers: [2, 55, 78] Generated Node #0,0: 94:[2, 55, 78] Operation: 16+62=78 Exploring Operation: 55-16=39, Resulting Numbers: [2, 62, 39] Generated Node #0,1: 94:[2, 62, 39] Operation: 55-16=39 Exploring Operation: 62-55=7, Resulting Numbers: [16, 2, 7] Generated Node #0,2: 94:[16, 2, 7] Operation: 62-55=7 Exploring Operation: 62-16=46, Resulting Numbers: [2, 55, 46] Generated Node #0,3: 94:[2, 55, 46] Operation: 62-16=46 Exploring Operation: 16/2=8, Resulting Numbers: [55, 62, 8] Generated Node #0,4: 94:[55, 62, 8] Operation: 16/2=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[2, 55, 46], Operations: ['62-16=46'] Exploring Operation: 2+46=48, Resulting Numbers: [55, 48] Generated Node #0,3,0: 94:[55, 48] Operation: 2+46=48 Exploring Operation: 55-46=9, Resulting Numbers: [2, 9] Generated Node #0,3,1: 94:[2, 9] Operation: 55-46=9 Exploring Operation: 55-2=53, Resulting Numbers: [46, 53] Generated Node #0,3,2: 94:[46, 53] Operation: 55-2=53 Exploring Operation: 2*46=92, Resulting Numbers: [55, 92] Generated Node #0,3,3: 94:[55, 92] Operation: 2*46=92 Exploring Operation: 55+46=101, Resulting Numbers: [2, 101] Generated Node #0,3,4: 94:[2, 101] Operation: 55+46=101 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[2, 9], Operations: ['62-16=46', '55-46=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,94 unequal: No Solution Exploring Operation: 2*9=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 #0,3,2 Current State: 94:[46, 53], Operations: ['62-16=46', '55-2=53'] Exploring Operation: 46+53=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 46*53=2438, Resulting Numbers: [2438] 2438,94 unequal: No Solution Exploring Operation: 53-46=7, Resulting Numbers: [7] 7,94 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 #0,3,4 Current State: 94:[2, 101], Operations: ['62-16=46', '55+46=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 2*101=202, Resulting Numbers: [202] 202,94 unequal: No Solution Exploring Operation: 2+101=103, Resulting Numbers: [103] 103,94 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:[55, 48], Operations: ['62-16=46', '2+46=48'] Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,94 unequal: No Solution Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,94 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:[55, 92], Operations: ['62-16=46', '2*46=92'] Exploring Operation: 92-55=37, Resulting Numbers: [37] 37,94 unequal: No Solution Exploring Operation: 55*92=5060, Resulting Numbers: [5060] 5060,94 unequal: No Solution Exploring Operation: 55+92=147, Resulting Numbers: [147] 147,94 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:[16, 2, 7], Operations: ['62-55=7'] Exploring Operation: 16/2=8, Resulting Numbers: [7, 8] Generated Node #0,2,0: 94:[7, 8] Operation: 16/2=8 Exploring Operation: 7-2=5, Resulting Numbers: [16, 5] Generated Node #0,2,1: 94:[16, 5] Operation: 7-2=5 Exploring Operation: 16-2=14, Resulting Numbers: [7, 14] Generated Node #0,2,2: 94:[7, 14] Operation: 16-2=14 Exploring Operation: 16-7=9, Resulting Numbers: [2, 9] Generated Node #0,2,3: 94:[2, 9] Operation: 16-7=9 Exploring Operation: 16*7=112, Resulting Numbers: [2, 112] Generated Node #0,2,4: 94:[2, 112] Operation: 16*7=112 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 94:[2, 9], Operations: ['62-55=7', '16-7=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,94 unequal: No Solution Exploring Operation: 2+9=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 #0,2,0 Current State: 94:[7, 8], Operations: ['62-55=7', '16/2=8'] Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,94 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,94 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:[16, 5], Operations: ['62-55=7', '7-2=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 16-5=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 #0,2,2 Current State: 94:[7, 14], Operations: ['62-55=7', '16-2=14'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,94 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,94 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:[2, 112], Operations: ['62-55=7', '16*7=112'] Exploring Operation: 112/2=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 2*112=224, Resulting Numbers: [224] 224,94 unequal: No Solution Exploring Operation: 2+112=114, Resulting Numbers: [114] 114,94 unequal: No Solution Exploring Operation: 112-2=110, Resulting Numbers: [110] 110,94 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:[2, 62, 39], Operations: ['55-16=39'] Exploring Operation: 2+39=41, Resulting Numbers: [62, 41] Generated Node #0,1,0: 94:[62, 41] Operation: 2+39=41 Exploring Operation: 62-2=60, Resulting Numbers: [39, 60] Generated Node #0,1,1: 94:[39, 60] Operation: 62-2=60 Exploring Operation: 62+39=101, Resulting Numbers: [2, 101] Generated Node #0,1,2: 94:[2, 101] Operation: 62+39=101 Exploring Operation: 62-39=23, Resulting Numbers: [2, 23] Generated Node #0,1,3: 94:[2, 23] Operation: 62-39=23 Exploring Operation: 62/2=31, Resulting Numbers: [39, 31] Generated Node #0,1,4: 94:[39, 31] Operation: 62/2=31 Moving to Node #0,1,2 Current State: 94:[2, 101], Operations: ['55-16=39', '62+39=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 2+101=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 2*101=202, Resulting Numbers: [202] 202,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[39, 60], Operations: ['55-16=39', '62-2=60'] Exploring Operation: 60-39=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 39+60=99, Resulting Numbers: [99] 99,94 unequal: No Solution Exploring Operation: 39*60=2340, Resulting Numbers: [2340] 2340,94 unequal: No Solution Moving to Node #0,1,0 Current State: 94:[62, 41], Operations: ['55-16=39', '2+39=41'] Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 62+41=103, Resulting Numbers: [103] 103,94 unequal: No Solution Exploring Operation: 62*41=2542, Resulting Numbers: [2542] 2542,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[2, 23], Operations: ['55-16=39', '62-39=23'] Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,94 unequal: No Solution Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,94 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[39, 31], Operations: ['55-16=39', '62/2=31'] Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,94 unequal: No Solution Exploring Operation: 39*31=1209, Resulting Numbers: [1209] 1209,94 unequal: No Solution Exploring Operation: 39+31=70, Resulting Numbers: [70] 70,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[2, 55, 78], Operations: ['16+62=78'] Exploring Operation: 78/2=39, Resulting Numbers: [55, 39] Generated Node #0,0,0: 94:[55, 39] Operation: 78/2=39 Exploring Operation: 55-2=53, Resulting Numbers: [78, 53] Generated Node #0,0,1: 94:[78, 53] Operation: 55-2=53 Exploring Operation: 78-55=23, Resulting Numbers: [2, 23] Generated Node #0,0,2: 94:[2, 23] Operation: 78-55=23 Exploring Operation: 2+55=57, Resulting Numbers: [78, 57] Generated Node #0,0,3: 94:[78, 57] Operation: 2+55=57 Exploring Operation: 2+78=80, Resulting Numbers: [55, 80] Generated Node #0,0,4: 94:[55, 80] Operation: 2+78=80 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[55, 39], Operations: ['16+62=78', '78/2=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[16, 2, 55, 62], Operations: [] Exploring Operation: 16+62=78, Resulting Numbers: [2, 55, 78] Generated Node #0,0: 94:[2, 55, 78] Operation: 16+62=78 Moving to Node #0,0 Current State: 94:[2, 55, 78], Operations: ['16+62=78'] Exploring Operation: 78/2=39, Resulting Numbers: [55, 39] Generated Node #0,0,0: 94:[55, 39] Operation: 78/2=39 Moving to Node #0,0,0 Current State: 94:[55, 39], Operations: ['16+62=78', '78/2=39'] Exploring Operation: 55+39=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.93316
hs_5
mult_heuristic
[ 57, 90, 48, 88 ]
11
[ "57+90=147", "48+88=136", "147-136=11" ]
Current State: 11:[57, 90, 48, 88], Operations: [] Exploring Operation: 57+90=147, Resulting Numbers: [48, 88, 147] Generated Node #2: [48, 88, 147] from Operation: 57+90=147 Current State: 11:[48, 88, 147], Operations: ['57+90=147'] Exploring Operation: 48+88=136, Resulting Numbers: [147, 136] Generated Node #3: [147, 136] from Operation: 48+88=136 Current State: 11:[147, 136], Operations: ['57+90=147', '48+88=136'] Exploring Operation: 147-136=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[57, 90, 48, 88], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [57, 48, 2] Generated Node #0,0: 11:[57, 48, 2] Operation: 90-88=2 Exploring Operation: 90-57=33, Resulting Numbers: [48, 88, 33] Generated Node #0,1: 11:[48, 88, 33] Operation: 90-57=33 Exploring Operation: 88-57=31, Resulting Numbers: [90, 48, 31] Generated Node #0,2: 11:[90, 48, 31] Operation: 88-57=31 Moving to Node #0,0 Current State: 11:[57, 48, 2], Operations: ['90-88=2'] Exploring Operation: 57-48=9, Resulting Numbers: [2, 9] Generated Node #0,0,0: 11:[2, 9] Operation: 57-48=9 Exploring Operation: 48/2=24, Resulting Numbers: [57, 24] Generated Node #0,0,1: 11:[57, 24] Operation: 48/2=24 Exploring Operation: 57-2=55, Resulting Numbers: [48, 55] Generated Node #0,0,2: 11:[48, 55] Operation: 57-2=55 Moving to Node #0,1 Current State: 11:[48, 88, 33], Operations: ['90-57=33'] Exploring Operation: 88-48=40, Resulting Numbers: [33, 40] Generated Node #0,1,0: 11:[33, 40] Operation: 88-48=40 Exploring Operation: 88-33=55, Resulting Numbers: [48, 55] Generated Node #0,1,1: 11:[48, 55] Operation: 88-33=55 Exploring Operation: 48-33=15, Resulting Numbers: [88, 15] Generated Node #0,1,2: 11:[88, 15] Operation: 48-33=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 11:[33, 40], Operations: ['90-57=33', '88-48=40'] Exploring Operation: 33+40=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 40-33=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 33*40=1320, Resulting Numbers: [1320] 1320,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 11:[48, 55], Operations: ['90-57=33', '88-33=55'] Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 48*55=2640, Resulting Numbers: [2640] 2640,11 unequal: No Solution Exploring Operation: 48+55=103, Resulting Numbers: [103] 103,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 11:[88, 15], Operations: ['90-57=33', '48-33=15'] Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 88*15=1320, Resulting Numbers: [1320] 1320,11 unequal: No Solution Exploring Operation: 88+15=103, Resulting Numbers: [103] 103,11 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: 11:[90, 48, 31], Operations: ['88-57=31'] Exploring Operation: 90-48=42, Resulting Numbers: [31, 42] Generated Node #0,2,0: 11:[31, 42] Operation: 90-48=42 Exploring Operation: 90-31=59, Resulting Numbers: [48, 59] Generated Node #0,2,1: 11:[48, 59] Operation: 90-31=59 Exploring Operation: 48-31=17, Resulting Numbers: [90, 17] Generated Node #0,2,2: 11:[90, 17] Operation: 48-31=17 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[31, 42], Operations: ['88-57=31', '90-48=42'] Exploring Operation: 31*42=1302, Resulting Numbers: [1302] 1302,11 unequal: No Solution Exploring Operation: 31+42=73, Resulting Numbers: [73] 73,11 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[57, 90, 48, 88], Operations: [] Exploring Operation: 88-57=31, Resulting Numbers: [90, 48, 31] Generated Node #0,2: 11:[90, 48, 31] Operation: 88-57=31 Moving to Node #0,2 Current State: 11:[90, 48, 31], Operations: ['88-57=31'] Exploring Operation: 90-48=42, Resulting Numbers: [31, 42] Generated Node #0,2,0: 11:[31, 42] Operation: 90-48=42 Moving to Node #0,2,0 Current State: 11:[31, 42], Operations: ['88-57=31', '90-48=42'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 72, 36, 12, 1 ]
68
[ "72-1=71", "36/12=3", "71-3=68" ]
Current State: 68:[72, 36, 12, 1], Operations: [] Exploring Operation: 72-1=71, Resulting Numbers: [36, 12, 71] Generated Node #2: [36, 12, 71] from Operation: 72-1=71 Current State: 68:[36, 12, 71], Operations: ['72-1=71'] Exploring Operation: 36/12=3, Resulting Numbers: [71, 3] Generated Node #3: [71, 3] from Operation: 36/12=3 Current State: 68:[71, 3], Operations: ['72-1=71', '36/12=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[72, 36, 12, 1], Operations: [] Exploring Operation: 72-1=71, Resulting Numbers: [36, 12, 71] Generated Node #0,0: 68:[36, 12, 71] Operation: 72-1=71 Exploring Operation: 36/12=3, Resulting Numbers: [72, 1, 3] Generated Node #0,1: 68:[72, 1, 3] Operation: 36/12=3 Exploring Operation: 72-36=36, Resulting Numbers: [12, 1, 36] Generated Node #0,2: 68:[12, 1, 36] Operation: 72-36=36 Exploring Operation: 72/36=2, Resulting Numbers: [12, 1, 2] Generated Node #0,3: 68:[12, 1, 2] Operation: 72/36=2 Exploring Operation: 72/12=6, Resulting Numbers: [36, 1, 6] Generated Node #0,4: 68:[36, 1, 6] Operation: 72/12=6 Moving to Node #0,4 Current State: 68:[36, 1, 6], Operations: ['72/12=6'] Exploring Operation: 36-1=35, Resulting Numbers: [6, 35] Generated Node #0,4,0: 68:[6, 35] Operation: 36-1=35 Exploring Operation: 36/6=6, Resulting Numbers: [1, 6] Generated Node #0,4,1: 68:[1, 6] Operation: 36/6=6 Exploring Operation: 6-1=5, Resulting Numbers: [36, 5] Generated Node #0,4,2: 68:[36, 5] Operation: 6-1=5 Exploring Operation: 36/1=36, Resulting Numbers: [6, 36] Generated Node #0,4,3: 68:[6, 36] Operation: 36/1=36 Exploring Operation: 36*1=36, Resulting Numbers: [6, 36] Generated Node #0,4,4: 68:[6, 36] Operation: 36*1=36 Moving to Node #0,3 Current State: 68:[12, 1, 2], Operations: ['72/36=2'] Exploring Operation: 12/2=6, Resulting Numbers: [1, 6] Generated Node #0,3,0: 68:[1, 6] Operation: 12/2=6 Exploring Operation: 12/1=12, Resulting Numbers: [2, 12] Generated Node #0,3,1: 68:[2, 12] Operation: 12/1=12 Exploring Operation: 12+1=13, Resulting Numbers: [2, 13] Generated Node #0,3,2: 68:[2, 13] Operation: 12+1=13 Exploring Operation: 12+2=14, Resulting Numbers: [1, 14] Generated Node #0,3,3: 68:[1, 14] Operation: 12+2=14 Exploring Operation: 12*1=12, Resulting Numbers: [2, 12] Generated Node #0,3,4: 68:[2, 12] Operation: 12*1=12 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 68:[1, 6], Operations: ['72/36=2', '12/2=6'] Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,68 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 68:[2, 13], Operations: ['72/36=2', '12+1=13'] Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 68:[1, 14], Operations: ['72/36=2', '12+2=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,68 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 68:[2, 12], Operations: ['72/36=2', '12/1=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,68 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 68:[2, 12], Operations: ['72/36=2', '12*1=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,68 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: 68:[72, 1, 3], Operations: ['36/12=3'] Exploring Operation: 72*1=72, Resulting Numbers: [3, 72] Generated Node #0,1,0: 68:[3, 72] Operation: 72*1=72 Exploring Operation: 1+3=4, Resulting Numbers: [72, 4] Generated Node #0,1,1: 68:[72, 4] Operation: 1+3=4 Exploring Operation: 72-3=69, Resulting Numbers: [1, 69] Generated Node #0,1,2: 68:[1, 69] Operation: 72-3=69 Exploring Operation: 3-1=2, Resulting Numbers: [72, 2] Generated Node #0,1,3: 68:[72, 2] Operation: 3-1=2 Exploring Operation: 72-1=71, Resulting Numbers: [3, 71] Generated Node #0,1,4: 68:[3, 71] Operation: 72-1=71 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 68:[1, 69], Operations: ['36/12=3', '72-3=69'] Exploring Operation: 1*69=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 1+69=70, Resulting Numbers: [70] 70,68 unequal: No Solution Exploring Operation: 69/1=69, Resulting Numbers: [69] 69,68 unequal: No Solution Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[72, 36, 12, 1], Operations: [] Exploring Operation: 36/12=3, Resulting Numbers: [72, 1, 3] Generated Node #0,1: 68:[72, 1, 3] Operation: 36/12=3 Moving to Node #0,1 Current State: 68:[72, 1, 3], Operations: ['36/12=3'] Exploring Operation: 72-3=69, Resulting Numbers: [1, 69] Generated Node #0,1,2: 68:[1, 69] Operation: 72-3=69 Moving to Node #0,1,2 Current State: 68:[1, 69], Operations: ['36/12=3', '72-3=69'] Exploring Operation: 69-1=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 93, 78, 77, 64 ]
87
[ "77-64=13", "78/13=6", "93-6=87" ]
Current State: 87:[93, 78, 77, 64], Operations: [] Exploring Operation: 77-64=13, Resulting Numbers: [93, 78, 13] Generated Node #2: [93, 78, 13] from Operation: 77-64=13 Current State: 87:[93, 78, 13], Operations: ['77-64=13'] Exploring Operation: 78/13=6, Resulting Numbers: [93, 6] Generated Node #3: [93, 6] from Operation: 78/13=6 Current State: 87:[93, 6], Operations: ['77-64=13', '78/13=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[93, 78, 77, 64], Operations: [] Exploring Operation: 93-64=29, Resulting Numbers: [78, 77, 29] Generated Node #0,0: 87:[78, 77, 29] Operation: 93-64=29 Moving to Node #0,0 Current State: 87:[78, 77, 29], Operations: ['93-64=29'] Exploring Operation: 78-77=1, Resulting Numbers: [29, 1] Generated Node #0,0,0: 87:[29, 1] Operation: 78-77=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[29, 1], Operations: ['93-64=29', '78-77=1'] Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,87 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
[ 38, 11, 25, 4 ]
47
[ "11+25=36", "36/4=9", "38+9=47" ]
Current State: 47:[38, 11, 25, 4], Operations: [] Exploring Operation: 11+25=36, Resulting Numbers: [38, 4, 36] Generated Node #2: [38, 4, 36] from Operation: 11+25=36 Current State: 47:[38, 4, 36], Operations: ['11+25=36'] Exploring Operation: 36/4=9, Resulting Numbers: [38, 9] Generated Node #3: [38, 9] from Operation: 36/4=9 Current State: 47:[38, 9], Operations: ['11+25=36', '36/4=9'] Exploring Operation: 38+9=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[38, 11, 25, 4], Operations: [] Exploring Operation: 11*4=44, Resulting Numbers: [38, 25, 44] Generated Node #0,0: 47:[38, 25, 44] Operation: 11*4=44 Exploring Operation: 38+4=42, Resulting Numbers: [11, 25, 42] Generated Node #0,1: 47:[11, 25, 42] Operation: 38+4=42 Exploring Operation: 11+4=15, Resulting Numbers: [38, 25, 15] Generated Node #0,2: 47:[38, 25, 15] Operation: 11+4=15 Exploring Operation: 11+25=36, Resulting Numbers: [38, 4, 36] Generated Node #0,3: 47:[38, 4, 36] Operation: 11+25=36 Moving to Node #0,0 Current State: 47:[38, 25, 44], Operations: ['11*4=44'] Exploring Operation: 38-25=13, Resulting Numbers: [44, 13] Generated Node #0,0,0: 47:[44, 13] Operation: 38-25=13 Exploring Operation: 44-25=19, Resulting Numbers: [38, 19] Generated Node #0,0,1: 47:[38, 19] Operation: 44-25=19 Exploring Operation: 25+44=69, Resulting Numbers: [38, 69] Generated Node #0,0,2: 47:[38, 69] Operation: 25+44=69 Exploring Operation: 38+25=63, Resulting Numbers: [44, 63] Generated Node #0,0,3: 47:[44, 63] Operation: 38+25=63 Moving to Node #0,2 Current State: 47:[38, 25, 15], Operations: ['11+4=15'] Exploring Operation: 38-15=23, Resulting Numbers: [25, 23] Generated Node #0,2,0: 47:[25, 23] Operation: 38-15=23 Exploring Operation: 25+15=40, Resulting Numbers: [38, 40] Generated Node #0,2,1: 47:[38, 40] Operation: 25+15=40 Exploring Operation: 25-15=10, Resulting Numbers: [38, 10] Generated Node #0,2,2: 47:[38, 10] Operation: 25-15=10 Exploring Operation: 38+15=53, Resulting Numbers: [25, 53] Generated Node #0,2,3: 47:[25, 53] Operation: 38+15=53 Moving to Node #0,1 Current State: 47:[11, 25, 42], Operations: ['38+4=42'] Exploring Operation: 11+42=53, Resulting Numbers: [25, 53] Generated Node #0,1,0: 47:[25, 53] Operation: 11+42=53 Exploring Operation: 42-11=31, Resulting Numbers: [25, 31] Generated Node #0,1,1: 47:[25, 31] Operation: 42-11=31 Exploring Operation: 25-11=14, Resulting Numbers: [42, 14] Generated Node #0,1,2: 47:[42, 14] Operation: 25-11=14 Exploring Operation: 11+25=36, Resulting Numbers: [42, 36] Generated Node #0,1,3: 47:[42, 36] Operation: 11+25=36 Moving to Node #0,3 Current State: 47:[38, 4, 36], Operations: ['11+25=36'] Exploring Operation: 4+36=40, Resulting Numbers: [38, 40] Generated Node #0,3,0: 47:[38, 40] Operation: 4+36=40 Exploring Operation: 38-4=34, Resulting Numbers: [36, 34] Generated Node #0,3,1: 47:[36, 34] Operation: 38-4=34 Exploring Operation: 36-4=32, Resulting Numbers: [38, 32] Generated Node #0,3,2: 47:[38, 32] Operation: 36-4=32 Exploring Operation: 38+4=42, Resulting Numbers: [36, 42] Generated Node #0,3,3: 47:[36, 42] Operation: 38+4=42 Moving to Node #0,2,1 Current State: 47:[38, 40], Operations: ['11+4=15', '25+15=40'] Exploring Operation: 38*40=1520, Resulting Numbers: [1520] 1520,47 unequal: No Solution Exploring Operation: 38+40=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[38, 40], Operations: ['11+25=36', '4+36=40'] Exploring Operation: 38*40=1520, Resulting Numbers: [1520] 1520,47 unequal: No Solution Exploring Operation: 38+40=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[36, 42], Operations: ['11+25=36', '38+4=42'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 36+42=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 36*42=1512, Resulting Numbers: [1512] 1512,47 unequal: No Solution Moving to Node #0,1,3 Current State: 47:[42, 36], Operations: ['38+4=42', '11+25=36'] Exploring Operation: 42-36=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 42+36=78, Resulting Numbers: [78] 78,47 unequal: No Solution Exploring Operation: 42*36=1512, Resulting Numbers: [1512] 1512,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[44, 63], Operations: ['11*4=44', '38+25=63'] Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,47 unequal: No Solution Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,47 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,47 unequal: No Solution Moving to Node #0,3,1 Current State: 47:[36, 34], Operations: ['11+25=36', '38-4=34'] Exploring Operation: 36*34=1224, Resulting Numbers: [1224] 1224,47 unequal: No Solution Exploring Operation: 36+34=70, Resulting Numbers: [70] 70,47 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,47 unequal: No Solution Moving to Node #0,3,2 Current State: 47:[38, 32], Operations: ['11+25=36', '36-4=32'] Exploring Operation: 38+32=70, Resulting Numbers: [70] 70,47 unequal: No Solution Exploring Operation: 38*32=1216, Resulting Numbers: [1216] 1216,47 unequal: No Solution Exploring Operation: 38-32=6, Resulting Numbers: [6] 6,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[25, 53], Operations: ['11+4=15', '38+15=53'] Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,47 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[25, 53], Operations: ['38+4=42', '11+42=53'] Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,47 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[38, 69], Operations: ['11*4=44', '25+44=69'] Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,47 unequal: No Solution Exploring Operation: 38+69=107, Resulting Numbers: [107] 107,47 unequal: No Solution Exploring Operation: 38*69=2622, Resulting Numbers: [2622] 2622,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[44, 13], Operations: ['11*4=44', '38-25=13'] Exploring Operation: 44*13=572, Resulting Numbers: [572] 572,47 unequal: No Solution Exploring Operation: 44+13=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,47 unequal: No Solution Moving to Node #0,0,1 Current State: 47:[38, 19], Operations: ['11*4=44', '44-25=19'] Exploring Operation: 38*19=722, Resulting Numbers: [722] 722,47 unequal: No Solution Exploring Operation: 38+19=57, Resulting Numbers: [57] 57,47 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[42, 14], Operations: ['38+4=42', '25-11=14'] Exploring Operation: 42*14=588, Resulting Numbers: [588] 588,47 unequal: No Solution Exploring Operation: 42/14=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 42+14=56, Resulting Numbers: [56] 56,47 unequal: No Solution Exploring Operation: 42-14=28, Resulting Numbers: [28] 28,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[25, 31], Operations: ['38+4=42', '42-11=31'] Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,47 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,47 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[25, 23], Operations: ['11+4=15', '38-15=23'] Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,47 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 25*23=575, Resulting Numbers: [575] 575,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[38, 10], Operations: ['11+4=15', '25-15=10'] Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 38*10=380, Resulting Numbers: [380] 380,47 unequal: No Solution Exploring Operation: 38+10=48, Resulting Numbers: [48] 48,47 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 33, 7, 93, 11 ]
61
[ "33-11=22", "7*22=154", "154-93=61" ]
Current State: 61:[33, 7, 93, 11], Operations: [] Exploring Operation: 33-11=22, Resulting Numbers: [7, 93, 22] Generated Node #2: [7, 93, 22] from Operation: 33-11=22 Current State: 61:[7, 93, 22], Operations: ['33-11=22'] Exploring Operation: 7*22=154, Resulting Numbers: [93, 154] Generated Node #3: [93, 154] from Operation: 7*22=154 Current State: 61:[93, 154], Operations: ['33-11=22', '7*22=154'] Exploring Operation: 154-93=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[33, 7, 93, 11], Operations: [] Exploring Operation: 7*11=77, Resulting Numbers: [33, 93, 77] Generated Node #0,0: 61:[33, 93, 77] Operation: 7*11=77 Exploring Operation: 33+7=40, Resulting Numbers: [93, 11, 40] Generated Node #0,1: 61:[93, 11, 40] Operation: 33+7=40 Moving to Node #0,0 Current State: 61:[33, 93, 77], Operations: ['7*11=77'] Exploring Operation: 77-33=44, Resulting Numbers: [93, 44] Generated Node #0,0,0: 61:[93, 44] Operation: 77-33=44 Exploring Operation: 93-33=60, Resulting Numbers: [77, 60] Generated Node #0,0,1: 61:[77, 60] Operation: 93-33=60 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[77, 60], Operations: ['7*11=77', '93-33=60'] Exploring Operation: 77+60=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 77-60=17, Resulting Numbers: [17] 17,61 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 #0,0,0 Current State: 61:[93, 44], Operations: ['7*11=77', '77-33=44'] Exploring Operation: 93+44=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 93-44=49, Resulting Numbers: [49] 49,61 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: 61:[93, 11, 40], Operations: ['33+7=40'] Exploring Operation: 93-11=82, Resulting Numbers: [40, 82] Generated Node #0,1,0: 61:[40, 82] Operation: 93-11=82 Exploring Operation: 11+40=51, Resulting Numbers: [93, 51] Generated Node #0,1,1: 61:[93, 51] Operation: 11+40=51 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[40, 82], Operations: ['33+7=40', '93-11=82'] Exploring Operation: 40+82=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[93, 51], Operations: ['33+7=40', '11+40=51'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,61 unequal: No Solution Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 2, 52, 24, 41 ]
59
[ "2*24=48", "52-41=11", "48+11=59" ]
Current State: 59:[2, 52, 24, 41], Operations: [] Exploring Operation: 2*24=48, Resulting Numbers: [52, 41, 48] Generated Node #2: [52, 41, 48] from Operation: 2*24=48 Current State: 59:[52, 41, 48], Operations: ['2*24=48'] Exploring Operation: 52-41=11, Resulting Numbers: [48, 11] Generated Node #3: [48, 11] from Operation: 52-41=11 Current State: 59:[48, 11], Operations: ['2*24=48', '52-41=11'] Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[2, 52, 24, 41], Operations: [] Exploring Operation: 2+52=54, Resulting Numbers: [24, 41, 54] Generated Node #0,0: 59:[24, 41, 54] Operation: 2+52=54 Exploring Operation: 2*24=48, Resulting Numbers: [52, 41, 48] Generated Node #0,1: 59:[52, 41, 48] Operation: 2*24=48 Moving to Node #0,1 Current State: 59:[52, 41, 48], Operations: ['2*24=48'] Exploring Operation: 52+41=93, Resulting Numbers: [48, 93] Generated Node #0,1,0: 59:[48, 93] Operation: 52+41=93 Exploring Operation: 41+48=89, Resulting Numbers: [52, 89] Generated Node #0,1,1: 59:[52, 89] Operation: 41+48=89 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[52, 89], Operations: ['2*24=48', '41+48=89'] Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,59 unequal: No Solution Exploring Operation: 52+89=141, Resulting Numbers: [141] 141,59 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:[48, 93], Operations: ['2*24=48', '52+41=93'] Exploring Operation: 93-48=45, Resulting Numbers: [45] 45,59 unequal: No Solution Exploring Operation: 48+93=141, Resulting Numbers: [141] 141,59 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: 59:[24, 41, 54], Operations: ['2+52=54'] Exploring Operation: 24+41=65, Resulting Numbers: [54, 65] Generated Node #0,0,0: 59:[54, 65] Operation: 24+41=65 Exploring Operation: 24+54=78, Resulting Numbers: [41, 78] Generated Node #0,0,1: 59:[41, 78] Operation: 24+54=78 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[54, 65], Operations: ['2+52=54', '24+41=65'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 54+65=119, Resulting Numbers: [119] 119,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[41, 78], Operations: ['2+52=54', '24+54=78'] Exploring Operation: 41+78=119, Resulting Numbers: [119] 119,59 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,59 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
[ 30, 96, 79, 64 ]
99
[ "30*64=1920", "1920/96=20", "79+20=99" ]
Current State: 99:[30, 96, 79, 64], Operations: [] Exploring Operation: 30*64=1920, Resulting Numbers: [96, 79, 1920] Generated Node #2: [96, 79, 1920] from Operation: 30*64=1920 Current State: 99:[96, 79, 1920], Operations: ['30*64=1920'] Exploring Operation: 1920/96=20, Resulting Numbers: [79, 20] Generated Node #3: [79, 20] from Operation: 1920/96=20 Current State: 99:[79, 20], Operations: ['30*64=1920', '1920/96=20'] Exploring Operation: 79+20=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[30, 96, 79, 64], Operations: [] Exploring Operation: 30+64=94, Resulting Numbers: [96, 79, 94] Generated Node #0,0: 99:[96, 79, 94] Operation: 30+64=94 Exploring Operation: 96-64=32, Resulting Numbers: [30, 79, 32] Generated Node #0,1: 99:[30, 79, 32] Operation: 96-64=32 Exploring Operation: 96-79=17, Resulting Numbers: [30, 64, 17] Generated Node #0,2: 99:[30, 64, 17] Operation: 96-79=17 Exploring Operation: 64-30=34, Resulting Numbers: [96, 79, 34] Generated Node #0,3: 99:[96, 79, 34] Operation: 64-30=34 Exploring Operation: 79-64=15, Resulting Numbers: [30, 96, 15] Generated Node #0,4: 99:[30, 96, 15] Operation: 79-64=15 Moving to Node #0,4 Current State: 99:[30, 96, 15], Operations: ['79-64=15'] Exploring Operation: 30+15=45, Resulting Numbers: [96, 45] Generated Node #0,4,0: 99:[96, 45] Operation: 30+15=45 Exploring Operation: 30-15=15, Resulting Numbers: [96, 15] Generated Node #0,4,1: 99:[96, 15] Operation: 30-15=15 Exploring Operation: 96+15=111, Resulting Numbers: [30, 111] Generated Node #0,4,2: 99:[30, 111] Operation: 96+15=111 Exploring Operation: 96-15=81, Resulting Numbers: [30, 81] Generated Node #0,4,3: 99:[30, 81] Operation: 96-15=81 Exploring Operation: 30/15=2, Resulting Numbers: [96, 2] Generated Node #0,4,4: 99:[96, 2] Operation: 30/15=2 Moving to Node #0,3 Current State: 99:[96, 79, 34], Operations: ['64-30=34'] Exploring Operation: 79-34=45, Resulting Numbers: [96, 45] Generated Node #0,3,0: 99:[96, 45] Operation: 79-34=45 Exploring Operation: 96-34=62, Resulting Numbers: [79, 62] Generated Node #0,3,1: 99:[79, 62] Operation: 96-34=62 Exploring Operation: 96+34=130, Resulting Numbers: [79, 130] Generated Node #0,3,2: 99:[79, 130] Operation: 96+34=130 Exploring Operation: 79+34=113, Resulting Numbers: [96, 113] Generated Node #0,3,3: 99:[96, 113] Operation: 79+34=113 Exploring Operation: 96-79=17, Resulting Numbers: [34, 17] Generated Node #0,3,4: 99:[34, 17] Operation: 96-79=17 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 99:[34, 17], Operations: ['64-30=34', '96-79=17'] Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,99 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 99:[96, 45], Operations: ['64-30=34', '79-34=45'] Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 99:[96, 113], Operations: ['64-30=34', '79+34=113'] Exploring Operation: 96+113=209, Resulting Numbers: [209] 209,99 unequal: No Solution Exploring Operation: 113-96=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 96*113=10848, Resulting Numbers: [10848] 10848,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 99:[79, 62], Operations: ['64-30=34', '96-34=62'] Exploring Operation: 79*62=4898, Resulting Numbers: [4898] 4898,99 unequal: No Solution Exploring Operation: 79+62=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 79-62=17, Resulting Numbers: [17] 17,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 99:[79, 130], Operations: ['64-30=34', '96+34=130'] Exploring Operation: 130-79=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 79+130=209, Resulting Numbers: [209] 209,99 unequal: No Solution Exploring Operation: 79*130=10270, Resulting Numbers: [10270] 10270,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 99:[30, 79, 32], Operations: ['96-64=32'] Exploring Operation: 79+32=111, Resulting Numbers: [30, 111] Generated Node #0,1,0: 99:[30, 111] Operation: 79+32=111 Exploring Operation: 32-30=2, Resulting Numbers: [79, 2] Generated Node #0,1,1: 99:[79, 2] Operation: 32-30=2 Exploring Operation: 79-32=47, Resulting Numbers: [30, 47] Generated Node #0,1,2: 99:[30, 47] Operation: 79-32=47 Exploring Operation: 79-30=49, Resulting Numbers: [32, 49] Generated Node #0,1,3: 99:[32, 49] Operation: 79-30=49 Exploring Operation: 30+79=109, Resulting Numbers: [32, 109] Generated Node #0,1,4: 99:[32, 109] Operation: 30+79=109 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 99:[32, 109], Operations: ['96-64=32', '30+79=109'] Exploring Operation: 109-32=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 32*109=3488, Resulting Numbers: [3488] 3488,99 unequal: No Solution Exploring Operation: 32+109=141, Resulting Numbers: [141] 141,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 99:[30, 111], Operations: ['96-64=32', '79+32=111'] Exploring Operation: 30+111=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 111-30=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 30*111=3330, Resulting Numbers: [3330] 3330,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 99:[30, 47], Operations: ['96-64=32', '79-32=47'] Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,99 unequal: No Solution Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 99:[32, 49], Operations: ['96-64=32', '79-30=49'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,99 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 99:[79, 2], Operations: ['96-64=32', '32-30=2'] Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 99:[96, 79, 94], Operations: ['30+64=94'] Exploring Operation: 96-79=17, Resulting Numbers: [94, 17] Generated Node #0,0,0: 99:[94, 17] Operation: 96-79=17 Exploring Operation: 96-94=2, Resulting Numbers: [79, 2] Generated Node #0,0,1: 99:[79, 2] Operation: 96-94=2 Exploring Operation: 94-79=15, Resulting Numbers: [96, 15] Generated Node #0,0,2: 99:[96, 15] Operation: 94-79=15 Exploring Operation: 79+94=173, Resulting Numbers: [96, 173] Generated Node #0,0,3: 99:[96, 173] Operation: 79+94=173 Exploring Operation: 96+79=175, Resulting Numbers: [94, 175] Generated Node #0,0,4: 99:[94, 175] Operation: 96+79=175 Moving to Node #0,2 Current State: 99:[30, 64, 17], Operations: ['96-79=17'] Exploring Operation: 30+64=94, Resulting Numbers: [17, 94] Generated Node #0,2,0: 99:[17, 94] Operation: 30+64=94 Exploring Operation: 64+17=81, Resulting Numbers: [30, 81] Generated Node #0,2,1: 99:[30, 81] Operation: 64+17=81 Exploring Operation: 30-17=13, Resulting Numbers: [64, 13] Generated Node #0,2,2: 99:[64, 13] Operation: 30-17=13 Exploring Operation: 64-30=34, Resulting Numbers: [17, 34] Generated Node #0,2,3: 99:[17, 34] Operation: 64-30=34 Exploring Operation: 64-17=47, Resulting Numbers: [30, 47] Generated Node #0,2,4: 99:[30, 47] Operation: 64-17=47 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 99:[17, 34], Operations: ['96-79=17', '64-30=34'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,99 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 17+34=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 17*34=578, Resulting Numbers: [578] 578,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 99:[17, 94], Operations: ['96-79=17', '30+64=94'] Exploring Operation: 17+94=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 17*94=1598, Resulting Numbers: [1598] 1598,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 99:[30, 47], Operations: ['96-79=17', '64-17=47'] Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,99 unequal: No Solution Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 99:[30, 81], Operations: ['96-79=17', '64+17=81'] Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 30*81=2430, Resulting Numbers: [2430] 2430,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[64, 13], Operations: ['96-79=17', '30-17=13'] Exploring Operation: 64+13=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 64-13=51, Resulting Numbers: [51] 51,99 unequal: No Solution Exploring Operation: 64*13=832, Resulting Numbers: [832] 832,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,4 Current State: 99:[96, 2], Operations: ['79-64=15', '30/15=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[96, 15], Operations: ['30+64=94', '94-79=15'] Exploring Operation: 96+15=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 96*15=1440, Resulting Numbers: [1440] 1440,99 unequal: No Solution Exploring Operation: 96-15=81, Resulting Numbers: [81] 81,99 unequal: No Solution Moving to Node #0,4,1 Current State: 99:[96, 15], Operations: ['79-64=15', '30-15=15'] Exploring Operation: 96-15=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 96+15=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 96*15=1440, Resulting Numbers: [1440] 1440,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[94, 17], Operations: ['30+64=94', '96-79=17'] Exploring Operation: 94-17=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 94+17=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 94*17=1598, Resulting Numbers: [1598] 1598,99 unequal: No Solution Moving to Node #0,4,0 Current State: 99:[96, 45], Operations: ['79-64=15', '30+15=45'] Exploring Operation: 96+45=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 96*45=4320, Resulting Numbers: [4320] 4320,99 unequal: No Solution Exploring Operation: 96-45=51, Resulting Numbers: [51] 51,99 unequal: No Solution Moving to Node #0,4,2 Current State: 99:[30, 111], Operations: ['79-64=15', '96+15=111'] Exploring Operation: 111-30=81, Resulting Numbers: [81] 81,99 unequal: No Solution Exploring Operation: 30+111=141, Resulting Numbers: [141] 141,99 unequal: No Solution Exploring Operation: 30*111=3330, Resulting Numbers: [3330] 3330,99 unequal: No Solution Moving to Node #0,4,3 Current State: 99:[30, 81], Operations: ['79-64=15', '96-15=81'] Exploring Operation: 30*81=2430, Resulting Numbers: [2430] 2430,99 unequal: No Solution Exploring Operation: 30+81=111, Resulting Numbers: [111] 111,99 unequal: No Solution Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[79, 2], Operations: ['30+64=94', '96-94=2'] Exploring Operation: 79*2=158, Resulting Numbers: [158] 158,99 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[96, 173], Operations: ['30+64=94', '79+94=173'] Exploring Operation: 96+173=269, Resulting Numbers: [269] 269,99 unequal: No Solution Exploring Operation: 173-96=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 96*173=16608, Resulting Numbers: [16608] 16608,99 unequal: No Solution Moving to Node #0,0,4 Current State: 99:[94, 175], Operations: ['30+64=94', '96+79=175'] Exploring Operation: 94*175=16450, Resulting Numbers: [16450] 16450,99 unequal: No Solution Exploring Operation: 94+175=269, Resulting Numbers: [269] 269,99 unequal: No Solution Exploring Operation: 175-94=81, Resulting Numbers: [81] 81,99 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 81, 98, 2 ]
22
[ "61+81=142", "142-98=44", "44/2=22" ]
Current State: 22:[61, 81, 98, 2], Operations: [] Exploring Operation: 61+81=142, Resulting Numbers: [98, 2, 142] Generated Node #2: [98, 2, 142] from Operation: 61+81=142 Current State: 22:[98, 2, 142], Operations: ['61+81=142'] Exploring Operation: 142-98=44, Resulting Numbers: [2, 44] Generated Node #3: [2, 44] from Operation: 142-98=44 Current State: 22:[2, 44], Operations: ['61+81=142', '142-98=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[61, 81, 98, 2], Operations: [] Exploring Operation: 98-61=37, Resulting Numbers: [81, 2, 37] Generated Node #0,0: 22:[81, 2, 37] Operation: 98-61=37 Exploring Operation: 81-61=20, Resulting Numbers: [98, 2, 20] Generated Node #0,1: 22:[98, 2, 20] Operation: 81-61=20 Exploring Operation: 98-81=17, Resulting Numbers: [61, 2, 17] Generated Node #0,2: 22:[61, 2, 17] Operation: 98-81=17 Exploring Operation: 98/2=49, Resulting Numbers: [61, 81, 49] Generated Node #0,3: 22:[61, 81, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[61, 2, 17], Operations: ['98-81=17'] Exploring Operation: 61-17=44, Resulting Numbers: [2, 44] Generated Node #0,2,0: 22:[2, 44] Operation: 61-17=44 Exploring Operation: 61-2=59, Resulting Numbers: [17, 59] Generated Node #0,2,1: 22:[17, 59] Operation: 61-2=59 Exploring Operation: 17-2=15, Resulting Numbers: [61, 15] Generated Node #0,2,2: 22:[61, 15] Operation: 17-2=15 Exploring Operation: 2+17=19, Resulting Numbers: [61, 19] Generated Node #0,2,3: 22:[61, 19] Operation: 2+17=19 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 22:[2, 44], Operations: ['98-81=17', '61-17=44'] Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,22 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[61, 81, 98, 2], Operations: [] Exploring Operation: 98-81=17, Resulting Numbers: [61, 2, 17] Generated Node #0,2: 22:[61, 2, 17] Operation: 98-81=17 Moving to Node #0,2 Current State: 22:[61, 2, 17], Operations: ['98-81=17'] Exploring Operation: 61-17=44, Resulting Numbers: [2, 44] Generated Node #0,2,0: 22:[2, 44] Operation: 61-17=44 Moving to Node #0,2,0 Current State: 22:[2, 44], Operations: ['98-81=17', '61-17=44'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 60, 37, 3, 35 ]
44
[ "60+37=97", "35+97=132", "132/3=44" ]
Current State: 44:[60, 37, 3, 35], Operations: [] Exploring Operation: 60+37=97, Resulting Numbers: [3, 35, 97] Generated Node #2: [3, 35, 97] from Operation: 60+37=97 Current State: 44:[3, 35, 97], Operations: ['60+37=97'] Exploring Operation: 35+97=132, Resulting Numbers: [3, 132] Generated Node #3: [3, 132] from Operation: 35+97=132 Current State: 44:[3, 132], Operations: ['60+37=97', '35+97=132'] Exploring Operation: 132/3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[60, 37, 3, 35], Operations: [] Exploring Operation: 60-35=25, Resulting Numbers: [37, 3, 25] Generated Node #0,0: 44:[37, 3, 25] Operation: 60-35=25 Exploring Operation: 37-35=2, Resulting Numbers: [60, 3, 2] Generated Node #0,1: 44:[60, 3, 2] Operation: 37-35=2 Exploring Operation: 60-37=23, Resulting Numbers: [3, 35, 23] Generated Node #0,2: 44:[3, 35, 23] Operation: 60-37=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[37, 3, 25], Operations: ['60-35=25'] Exploring Operation: 25-3=22, Resulting Numbers: [37, 22] Generated Node #0,0,0: 44:[37, 22] Operation: 25-3=22 Exploring Operation: 37+3=40, Resulting Numbers: [25, 40] Generated Node #0,0,1: 44:[25, 40] Operation: 37+3=40 Exploring Operation: 37-25=12, Resulting Numbers: [3, 12] Generated Node #0,0,2: 44:[3, 12] Operation: 37-25=12 Moving to Node #0,0,2 Current State: 44:[3, 12], Operations: ['60-35=25', '37-25=12'] Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[37, 22], Operations: ['60-35=25', '25-3=22'] Exploring Operation: 37-22=15, Resulting Numbers: [15] 15,44 unequal: No Solution Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,44 unequal: No Solution Exploring Operation: 37*22=814, Resulting Numbers: [814] 814,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[25, 40], Operations: ['60-35=25', '37+3=40'] Exploring Operation: 25*40=1000, Resulting Numbers: [1000] 1000,44 unequal: No Solution Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[3, 35, 23], Operations: ['60-37=23'] Exploring Operation: 3+35=38, Resulting Numbers: [23, 38] Generated Node #0,2,0: 44:[23, 38] Operation: 3+35=38 Exploring Operation: 35-23=12, Resulting Numbers: [3, 12] Generated Node #0,2,1: 44:[3, 12] Operation: 35-23=12 Exploring Operation: 35-3=32, Resulting Numbers: [23, 32] Generated Node #0,2,2: 44:[23, 32] Operation: 35-3=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[3, 12], Operations: ['60-37=23', '35-23=12'] Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,44 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,44 unequal: No Solution No 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: 44:[23, 38], Operations: ['60-37=23', '3+35=38'] Exploring Operation: 23*38=874, Resulting Numbers: [874] 874,44 unequal: No Solution Exploring Operation: 23+38=61, Resulting Numbers: [61] 61,44 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,44 unequal: No Solution No 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: 44:[23, 32], Operations: ['60-37=23', '35-3=32'] Exploring Operation: 23*32=736, Resulting Numbers: [736] 736,44 unequal: No Solution Exploring Operation: 32-23=9, Resulting Numbers: [9] 9,44 unequal: No Solution Exploring Operation: 23+32=55, Resulting Numbers: [55] 55,44 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: 44:[60, 3, 2], Operations: ['37-35=2'] Exploring Operation: 60/2=30, Resulting Numbers: [3, 30] Generated Node #0,1,0: 44:[3, 30] Operation: 60/2=30 Exploring Operation: 60/3=20, Resulting Numbers: [2, 20] Generated Node #0,1,1: 44:[2, 20] Operation: 60/3=20 Exploring Operation: 60-3=57, Resulting Numbers: [2, 57] Generated Node #0,1,2: 44:[2, 57] Operation: 60-3=57 Moving to Node #0,1,1 Current State: 44:[2, 20], Operations: ['37-35=2', '60/3=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,44 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[3, 30], Operations: ['37-35=2', '60/2=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,44 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,44 unequal: No Solution Moving to Node #0,1,2 Current State: 44:[2, 57], Operations: ['37-35=2', '60-3=57'] Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,44 unequal: No Solution Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,44 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,44 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
[ 26, 6, 62, 35 ]
77
[ "26-6=20", "62+35=97", "97-20=77" ]
Current State: 77:[26, 6, 62, 35], Operations: [] Exploring Operation: 26-6=20, Resulting Numbers: [62, 35, 20] Generated Node #2: [62, 35, 20] from Operation: 26-6=20 Current State: 77:[62, 35, 20], Operations: ['26-6=20'] Exploring Operation: 62+35=97, Resulting Numbers: [20, 97] Generated Node #3: [20, 97] from Operation: 62+35=97 Current State: 77:[20, 97], Operations: ['26-6=20', '62+35=97'] Exploring Operation: 97-20=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[26, 6, 62, 35], Operations: [] Exploring Operation: 62+35=97, Resulting Numbers: [26, 6, 97] Generated Node #0,0: 77:[26, 6, 97] Operation: 62+35=97 Exploring Operation: 62-35=27, Resulting Numbers: [26, 6, 27] Generated Node #0,1: 77:[26, 6, 27] Operation: 62-35=27 Exploring Operation: 26+62=88, Resulting Numbers: [6, 35, 88] Generated Node #0,2: 77:[6, 35, 88] Operation: 26+62=88 Exploring Operation: 35-26=9, Resulting Numbers: [6, 62, 9] Generated Node #0,3: 77:[6, 62, 9] Operation: 35-26=9 Exploring Operation: 26+35=61, Resulting Numbers: [6, 62, 61] Generated Node #0,4: 77:[6, 62, 61] Operation: 26+35=61 Moving to Node #0,3 Current State: 77:[6, 62, 9], Operations: ['35-26=9'] Exploring Operation: 62+9=71, Resulting Numbers: [6, 71] Generated Node #0,3,0: 77:[6, 71] Operation: 62+9=71 Exploring Operation: 9-6=3, Resulting Numbers: [62, 3] Generated Node #0,3,1: 77:[62, 3] Operation: 9-6=3 Exploring Operation: 6+9=15, Resulting Numbers: [62, 15] Generated Node #0,3,2: 77:[62, 15] Operation: 6+9=15 Exploring Operation: 6+62=68, Resulting Numbers: [9, 68] Generated Node #0,3,3: 77:[9, 68] Operation: 6+62=68 Exploring Operation: 62-6=56, Resulting Numbers: [9, 56] Generated Node #0,3,4: 77:[9, 56] Operation: 62-6=56 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 77:[6, 71], Operations: ['35-26=9', '62+9=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,77 unequal: No Solution Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[26, 6, 62, 35], Operations: [] Exploring Operation: 35-26=9, Resulting Numbers: [6, 62, 9] Generated Node #0,3: 77:[6, 62, 9] Operation: 35-26=9 Moving to Node #0,3 Current State: 77:[6, 62, 9], Operations: ['35-26=9'] Exploring Operation: 62+9=71, Resulting Numbers: [6, 71] Generated Node #0,3,0: 77:[6, 71] Operation: 62+9=71 Moving to Node #0,3,0 Current State: 77:[6, 71], Operations: ['35-26=9', '62+9=71'] Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 42, 67, 18, 96 ]
31
[ "42+67=109", "96-18=78", "109-78=31" ]
Current State: 31:[42, 67, 18, 96], Operations: [] Exploring Operation: 42+67=109, Resulting Numbers: [18, 96, 109] Generated Node #2: [18, 96, 109] from Operation: 42+67=109 Current State: 31:[18, 96, 109], Operations: ['42+67=109'] Exploring Operation: 96-18=78, Resulting Numbers: [109, 78] Generated Node #3: [109, 78] from Operation: 96-18=78 Current State: 31:[109, 78], Operations: ['42+67=109', '96-18=78'] Exploring Operation: 109-78=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[42, 67, 18, 96], Operations: [] Exploring Operation: 67-18=49, Resulting Numbers: [42, 96, 49] Generated Node #0,0: 31:[42, 96, 49] Operation: 67-18=49 Exploring Operation: 96-18=78, Resulting Numbers: [42, 67, 78] Generated Node #0,1: 31:[42, 67, 78] Operation: 96-18=78 Exploring Operation: 96-42=54, Resulting Numbers: [67, 18, 54] Generated Node #0,2: 31:[67, 18, 54] Operation: 96-42=54 Exploring Operation: 96-67=29, Resulting Numbers: [42, 18, 29] Generated Node #0,3: 31:[42, 18, 29] Operation: 96-67=29 Exploring Operation: 67-42=25, Resulting Numbers: [18, 96, 25] Generated Node #0,4: 31:[18, 96, 25] Operation: 67-42=25 Moving to Node #0,3 Current State: 31:[42, 18, 29], Operations: ['96-67=29'] Exploring Operation: 18+29=47, Resulting Numbers: [42, 47] Generated Node #0,3,0: 31:[42, 47] Operation: 18+29=47 Exploring Operation: 42+18=60, Resulting Numbers: [29, 60] Generated Node #0,3,1: 31:[29, 60] Operation: 42+18=60 Exploring Operation: 29-18=11, Resulting Numbers: [42, 11] Generated Node #0,3,2: 31:[42, 11] Operation: 29-18=11 Exploring Operation: 42-29=13, Resulting Numbers: [18, 13] Generated Node #0,3,3: 31:[18, 13] Operation: 42-29=13 Exploring Operation: 42-18=24, Resulting Numbers: [29, 24] Generated Node #0,3,4: 31:[29, 24] Operation: 42-18=24 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 31:[29, 24], Operations: ['96-67=29', '42-18=24'] Exploring Operation: 29*24=696, Resulting Numbers: [696] 696,31 unequal: No Solution Exploring Operation: 29+24=53, Resulting Numbers: [53] 53,31 unequal: No Solution Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[42, 47], Operations: ['96-67=29', '18+29=47'] Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,31 unequal: No Solution Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,31 unequal: No Solution Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[29, 60], Operations: ['96-67=29', '42+18=60'] Exploring Operation: 29*60=1740, Resulting Numbers: [1740] 1740,31 unequal: No Solution Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,31 unequal: No Solution Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[42, 67, 18, 96], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [42, 18, 29] Generated Node #0,3: 31:[42, 18, 29] Operation: 96-67=29 Moving to Node #0,3 Current State: 31:[42, 18, 29], Operations: ['96-67=29'] Exploring Operation: 42+18=60, Resulting Numbers: [29, 60] Generated Node #0,3,1: 31:[29, 60] Operation: 42+18=60 Moving to Node #0,3,1 Current State: 31:[29, 60], Operations: ['96-67=29', '42+18=60'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 76, 86, 46, 47 ]
41
[ "76*47=3572", "3572-46=3526", "3526/86=41" ]
Current State: 41:[76, 86, 46, 47], Operations: [] Exploring Operation: 76*47=3572, Resulting Numbers: [86, 46, 3572] Generated Node #2: [86, 46, 3572] from Operation: 76*47=3572 Current State: 41:[86, 46, 3572], Operations: ['76*47=3572'] Exploring Operation: 3572-46=3526, Resulting Numbers: [86, 3526] Generated Node #3: [86, 3526] from Operation: 3572-46=3526 Current State: 41:[86, 3526], Operations: ['76*47=3572', '3572-46=3526'] Exploring Operation: 3526/86=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[76, 86, 46, 47], Operations: [] Exploring Operation: 86-46=40, Resulting Numbers: [76, 47, 40] Generated Node #0,0: 41:[76, 47, 40] Operation: 86-46=40 Exploring Operation: 86-76=10, Resulting Numbers: [46, 47, 10] Generated Node #0,1: 41:[46, 47, 10] Operation: 86-76=10 Moving to Node #0,0 Current State: 41:[76, 47, 40], Operations: ['86-46=40'] Exploring Operation: 76-40=36, Resulting Numbers: [47, 36] Generated Node #0,0,0: 41:[47, 36] Operation: 76-40=36 Exploring Operation: 76-47=29, Resulting Numbers: [40, 29] Generated Node #0,0,1: 41:[40, 29] Operation: 76-47=29 Moving to Node #0,1 Current State: 41:[46, 47, 10], Operations: ['86-76=10'] Exploring Operation: 47-10=37, Resulting Numbers: [46, 37] Generated Node #0,1,0: 41:[46, 37] Operation: 47-10=37 Exploring Operation: 46-10=36, Resulting Numbers: [47, 36] Generated Node #0,1,1: 41:[47, 36] Operation: 46-10=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[46, 37], Operations: ['86-76=10', '47-10=37'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[47, 36], Operations: ['86-76=10', '46-10=36'] Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,41 unequal: No Solution Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,41 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: 41:[47, 36], Operations: ['86-46=40', '76-40=36'] Exploring Operation: 47-36=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 47+36=83, Resulting Numbers: [83] 83,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[40, 29], Operations: ['86-46=40', '76-47=29'] Exploring Operation: 40-29=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 40+29=69, Resulting Numbers: [69] 69,41 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 84, 2, 1, 59 ]
49
[ "84-59=25", "2*25=50", "50-1=49" ]
Current State: 49:[84, 2, 1, 59], Operations: [] Exploring Operation: 84-59=25, Resulting Numbers: [2, 1, 25] Generated Node #2: [2, 1, 25] from Operation: 84-59=25 Current State: 49:[2, 1, 25], Operations: ['84-59=25'] Exploring Operation: 2*25=50, Resulting Numbers: [1, 50] Generated Node #3: [1, 50] from Operation: 2*25=50 Current State: 49:[1, 50], Operations: ['84-59=25', '2*25=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[84, 2, 1, 59], Operations: [] Exploring Operation: 84-2=82, Resulting Numbers: [1, 59, 82] Generated Node #0,0: 49:[1, 59, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [1, 59, 42] Generated Node #0,1: 49:[1, 59, 42] Operation: 84/2=42 Exploring Operation: 84-59=25, Resulting Numbers: [2, 1, 25] Generated Node #0,2: 49:[2, 1, 25] Operation: 84-59=25 Moving to Node #0,1 Current State: 49:[1, 59, 42], Operations: ['84/2=42'] Exploring Operation: 59-42=17, Resulting Numbers: [1, 17] Generated Node #0,1,0: 49:[1, 17] Operation: 59-42=17 Exploring Operation: 59-1=58, Resulting Numbers: [42, 58] Generated Node #0,1,1: 49:[42, 58] Operation: 59-1=58 Exploring Operation: 1+42=43, Resulting Numbers: [59, 43] Generated Node #0,1,2: 49:[59, 43] Operation: 1+42=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[1, 17], Operations: ['84/2=42', '59-42=17'] Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,49 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,49 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 #0,1,1 Current State: 49:[42, 58], Operations: ['84/2=42', '59-1=58'] Exploring Operation: 42*58=2436, Resulting Numbers: [2436] 2436,49 unequal: No Solution Exploring Operation: 58-42=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 42+58=100, Resulting Numbers: [100] 100,49 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:[59, 43], Operations: ['84/2=42', '1+42=43'] Exploring Operation: 59+43=102, Resulting Numbers: [102] 102,49 unequal: No Solution Exploring Operation: 59-43=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 59*43=2537, Resulting Numbers: [2537] 2537,49 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: 49:[2, 1, 25], Operations: ['84-59=25'] Exploring Operation: 2+1=3, Resulting Numbers: [25, 3] Generated Node #0,2,0: 49:[25, 3] Operation: 2+1=3 Exploring Operation: 25-2=23, Resulting Numbers: [1, 23] Generated Node #0,2,1: 49:[1, 23] Operation: 25-2=23 Exploring Operation: 2*25=50, Resulting Numbers: [1, 50] Generated Node #0,2,2: 49:[1, 50] Operation: 2*25=50 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 49:[1, 50], Operations: ['84-59=25', '2*25=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[84, 2, 1, 59], Operations: [] Exploring Operation: 84-59=25, Resulting Numbers: [2, 1, 25] Generated Node #0,2: 49:[2, 1, 25] Operation: 84-59=25 Moving to Node #0,2 Current State: 49:[2, 1, 25], Operations: ['84-59=25'] Exploring Operation: 2*25=50, Resulting Numbers: [1, 50] Generated Node #0,2,2: 49:[1, 50] Operation: 2*25=50 Moving to Node #0,2,2 Current State: 49:[1, 50], Operations: ['84-59=25', '2*25=50'] Exploring Operation: 50-1=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 90, 88, 89, 15 ]
52
[ "90-88=2", "89+15=104", "104/2=52" ]
Current State: 52:[90, 88, 89, 15], Operations: [] Exploring Operation: 90-88=2, Resulting Numbers: [89, 15, 2] Generated Node #2: [89, 15, 2] from Operation: 90-88=2 Current State: 52:[89, 15, 2], Operations: ['90-88=2'] Exploring Operation: 89+15=104, Resulting Numbers: [2, 104] Generated Node #3: [2, 104] from Operation: 89+15=104 Current State: 52:[2, 104], Operations: ['90-88=2', '89+15=104'] Exploring Operation: 104/2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[90, 88, 89, 15], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [88, 89, 6] Generated Node #0,0: 52:[88, 89, 6] Operation: 90/15=6 Exploring Operation: 89-88=1, Resulting Numbers: [90, 15, 1] Generated Node #0,1: 52:[90, 15, 1] Operation: 89-88=1 Exploring Operation: 90-88=2, Resulting Numbers: [89, 15, 2] Generated Node #0,2: 52:[89, 15, 2] Operation: 90-88=2 Exploring Operation: 90-89=1, Resulting Numbers: [88, 15, 1] Generated Node #0,3: 52:[88, 15, 1] Operation: 90-89=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[89, 15, 2], Operations: ['90-88=2'] Exploring Operation: 89+2=91, Resulting Numbers: [15, 91] Generated Node #0,2,0: 52:[15, 91] Operation: 89+2=91 Exploring Operation: 15-2=13, Resulting Numbers: [89, 13] Generated Node #0,2,1: 52:[89, 13] Operation: 15-2=13 Exploring Operation: 89-15=74, Resulting Numbers: [2, 74] Generated Node #0,2,2: 52:[2, 74] Operation: 89-15=74 Exploring Operation: 89-2=87, Resulting Numbers: [15, 87] Generated Node #0,2,3: 52:[15, 87] Operation: 89-2=87 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[2, 74], Operations: ['90-88=2', '89-15=74'] Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,52 unequal: No Solution Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[89, 13], Operations: ['90-88=2', '15-2=13'] Exploring Operation: 89*13=1157, Resulting Numbers: [1157] 1157,52 unequal: No Solution Exploring Operation: 89-13=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 89+13=102, Resulting Numbers: [102] 102,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 52:[15, 87], Operations: ['90-88=2', '89-2=87'] Exploring Operation: 15*87=1305, Resulting Numbers: [1305] 1305,52 unequal: No Solution Exploring Operation: 15+87=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[15, 91], Operations: ['90-88=2', '89+2=91'] Exploring Operation: 15*91=1365, Resulting Numbers: [1365] 1365,52 unequal: No Solution Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 15+91=106, Resulting Numbers: [106] 106,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[88, 15, 1], Operations: ['90-89=1'] Exploring Operation: 88-15=73, Resulting Numbers: [1, 73] Generated Node #0,3,0: 52:[1, 73] Operation: 88-15=73 Exploring Operation: 88*1=88, Resulting Numbers: [15, 88] Generated Node #0,3,1: 52:[15, 88] Operation: 88*1=88 Exploring Operation: 88-1=87, Resulting Numbers: [15, 87] Generated Node #0,3,2: 52:[15, 87] Operation: 88-1=87 Exploring Operation: 15-1=14, Resulting Numbers: [88, 14] Generated Node #0,3,3: 52:[88, 14] Operation: 15-1=14 Moving to Node #0,3,0 Current State: 52:[1, 73], Operations: ['90-89=1', '88-15=73'] Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,52 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 1+73=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 1*73=73, Resulting Numbers: [73] 73,52 unequal: No Solution Moving to Node #0,3,3 Current State: 52:[88, 14], Operations: ['90-89=1', '15-1=14'] Exploring Operation: 88+14=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 88*14=1232, Resulting Numbers: [1232] 1232,52 unequal: No Solution Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,52 unequal: No Solution Moving to Node #0,3,2 Current State: 52:[15, 87], Operations: ['90-89=1', '88-1=87'] Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 15*87=1305, Resulting Numbers: [1305] 1305,52 unequal: No Solution Exploring Operation: 15+87=102, Resulting Numbers: [102] 102,52 unequal: No Solution Moving to Node #0,3,1 Current State: 52:[15, 88], Operations: ['90-89=1', '88*1=88'] Exploring Operation: 88-15=73, Resulting Numbers: [73] 73,52 unequal: No Solution Exploring Operation: 15*88=1320, Resulting Numbers: [1320] 1320,52 unequal: No Solution Exploring Operation: 15+88=103, Resulting Numbers: [103] 103,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[90, 15, 1], Operations: ['89-88=1'] Exploring Operation: 15-1=14, Resulting Numbers: [90, 14] Generated Node #0,1,0: 52:[90, 14] Operation: 15-1=14 Exploring Operation: 90-1=89, Resulting Numbers: [15, 89] Generated Node #0,1,1: 52:[15, 89] Operation: 90-1=89 Exploring Operation: 90-15=75, Resulting Numbers: [1, 75] Generated Node #0,1,2: 52:[1, 75] Operation: 90-15=75 Exploring Operation: 90/15=6, Resulting Numbers: [1, 6] Generated Node #0,1,3: 52:[1, 6] Operation: 90/15=6 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[1, 6], Operations: ['89-88=1', '90/15=6'] Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,52 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,52 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[1, 75], Operations: ['89-88=1', '90-15=75'] Exploring Operation: 75-1=74, Resulting Numbers: [74] 74,52 unequal: No Solution Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,52 unequal: No Solution Exploring Operation: 1+75=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 1*75=75, Resulting Numbers: [75] 75,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[90, 14], Operations: ['89-88=1', '15-1=14'] Exploring Operation: 90-14=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 90+14=104, Resulting Numbers: [104] 104,52 unequal: No Solution Exploring Operation: 90*14=1260, Resulting Numbers: [1260] 1260,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[15, 89], Operations: ['89-88=1', '90-1=89'] Exploring Operation: 15+89=104, Resulting Numbers: [104] 104,52 unequal: No Solution Exploring Operation: 15*89=1335, Resulting Numbers: [1335] 1335,52 unequal: No Solution Exploring Operation: 89-15=74, Resulting Numbers: [74] 74,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[88, 89, 6], Operations: ['90/15=6'] Exploring Operation: 89-6=83, Resulting Numbers: [88, 83] Generated Node #0,0,0: 52:[88, 83] Operation: 89-6=83 Exploring Operation: 88-6=82, Resulting Numbers: [89, 82] Generated Node #0,0,1: 52:[89, 82] Operation: 88-6=82 Exploring Operation: 88+6=94, Resulting Numbers: [89, 94] Generated Node #0,0,2: 52:[89, 94] Operation: 88+6=94 Exploring Operation: 89-88=1, Resulting Numbers: [6, 1] Generated Node #0,0,3: 52:[6, 1] Operation: 89-88=1 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 52:[6, 1], Operations: ['90/15=6', '89-88=1'] Exploring Operation: 6+1=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 6*1=6, Resulting Numbers: [6] 6,52 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 52:[88, 83], Operations: ['90/15=6', '89-6=83'] Exploring Operation: 88*83=7304, Resulting Numbers: [7304] 7304,52 unequal: No Solution Exploring Operation: 88+83=171, Resulting Numbers: [171] 171,52 unequal: No Solution Exploring Operation: 88-83=5, Resulting Numbers: [5] 5,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[89, 82], Operations: ['90/15=6', '88-6=82'] Exploring Operation: 89-82=7, Resulting Numbers: [7] 7,52 unequal: No Solution Exploring Operation: 89+82=171, Resulting Numbers: [171] 171,52 unequal: No Solution Exploring Operation: 89*82=7298, Resulting Numbers: [7298] 7298,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 52:[89, 94], Operations: ['90/15=6', '88+6=94'] Exploring Operation: 94-89=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 89+94=183, Resulting Numbers: [183] 183,52 unequal: No Solution Exploring Operation: 89*94=8366, Resulting Numbers: [8366] 8366,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 37, 84, 9, 69 ]
98
[ "84-69=15", "9*15=135", "135-37=98" ]
Current State: 98:[37, 84, 9, 69], Operations: [] Exploring Operation: 84-69=15, Resulting Numbers: [37, 9, 15] Generated Node #2: [37, 9, 15] from Operation: 84-69=15 Current State: 98:[37, 9, 15], Operations: ['84-69=15'] Exploring Operation: 9*15=135, Resulting Numbers: [37, 135] Generated Node #3: [37, 135] from Operation: 9*15=135 Current State: 98:[37, 135], Operations: ['84-69=15', '9*15=135'] Exploring Operation: 135-37=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[37, 84, 9, 69], Operations: [] Exploring Operation: 84-37=47, Resulting Numbers: [9, 69, 47] Generated Node #0,0: 98:[9, 69, 47] Operation: 84-37=47 Exploring Operation: 69-37=32, Resulting Numbers: [84, 9, 32] Generated Node #0,1: 98:[84, 9, 32] Operation: 69-37=32 Exploring Operation: 84-69=15, Resulting Numbers: [37, 9, 15] Generated Node #0,2: 98:[37, 9, 15] Operation: 84-69=15 Exploring Operation: 37+69=106, Resulting Numbers: [84, 9, 106] Generated Node #0,3: 98:[84, 9, 106] Operation: 37+69=106 Start Sub Search at level 1: Moving to Node #0,2 Current State: 98:[37, 9, 15], Operations: ['84-69=15'] Exploring Operation: 37+9=46, Resulting Numbers: [15, 46] Generated Node #0,2,0: 98:[15, 46] Operation: 37+9=46 Exploring Operation: 37-15=22, Resulting Numbers: [9, 22] Generated Node #0,2,1: 98:[9, 22] Operation: 37-15=22 Exploring Operation: 37+15=52, Resulting Numbers: [9, 52] Generated Node #0,2,2: 98:[9, 52] Operation: 37+15=52 Exploring Operation: 15-9=6, Resulting Numbers: [37, 6] Generated Node #0,2,3: 98:[37, 6] Operation: 15-9=6 Moving to Node #0,2,0 Current State: 98:[15, 46], Operations: ['84-69=15', '37+9=46'] Exploring Operation: 15+46=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,98 unequal: No Solution Exploring Operation: 15*46=690, Resulting Numbers: [690] 690,98 unequal: No Solution Moving to Node #0,2,2 Current State: 98:[9, 52], Operations: ['84-69=15', '37+15=52'] Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,98 unequal: No Solution Moving to Node #0,2,1 Current State: 98:[9, 22], Operations: ['84-69=15', '37-15=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,98 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,98 unequal: No Solution Moving to Node #0,2,3 Current State: 98:[37, 6], Operations: ['84-69=15', '15-9=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 37*6=222, Resulting Numbers: [222] 222,98 unequal: No Solution Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 98:[9, 69, 47], Operations: ['84-37=47'] Exploring Operation: 69-9=60, Resulting Numbers: [47, 60] Generated Node #0,0,0: 98:[47, 60] Operation: 69-9=60 Exploring Operation: 69+47=116, Resulting Numbers: [9, 116] Generated Node #0,0,1: 98:[9, 116] Operation: 69+47=116 Exploring Operation: 9+69=78, Resulting Numbers: [47, 78] Generated Node #0,0,2: 98:[47, 78] Operation: 9+69=78 Exploring Operation: 69-47=22, Resulting Numbers: [9, 22] Generated Node #0,0,3: 98:[9, 22] Operation: 69-47=22 Moving to Node #0,0,3 Current State: 98:[9, 22], Operations: ['84-37=47', '69-47=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,98 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,98 unequal: No Solution Moving to Node #0,0,0 Current State: 98:[47, 60], Operations: ['84-37=47', '69-9=60'] Exploring Operation: 47+60=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 47*60=2820, Resulting Numbers: [2820] 2820,98 unequal: No Solution Exploring Operation: 60-47=13, Resulting Numbers: [13] 13,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[9, 116], Operations: ['84-37=47', '69+47=116'] Exploring Operation: 116-9=107, Resulting Numbers: [107] 107,98 unequal: No Solution Exploring Operation: 9*116=1044, Resulting Numbers: [1044] 1044,98 unequal: No Solution Exploring Operation: 9+116=125, Resulting Numbers: [125] 125,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[47, 78], Operations: ['84-37=47', '9+69=78'] Exploring Operation: 47+78=125, Resulting Numbers: [125] 125,98 unequal: No Solution Exploring Operation: 78-47=31, Resulting Numbers: [31] 31,98 unequal: No Solution Exploring Operation: 47*78=3666, Resulting Numbers: [3666] 3666,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 98:[84, 9, 106], Operations: ['37+69=106'] Exploring Operation: 84+9=93, Resulting Numbers: [106, 93] Generated Node #0,3,0: 98:[106, 93] Operation: 84+9=93 Exploring Operation: 106-84=22, Resulting Numbers: [9, 22] Generated Node #0,3,1: 98:[9, 22] Operation: 106-84=22 Exploring Operation: 106-9=97, Resulting Numbers: [84, 97] Generated Node #0,3,2: 98:[84, 97] Operation: 106-9=97 Exploring Operation: 84-9=75, Resulting Numbers: [106, 75] Generated Node #0,3,3: 98:[106, 75] Operation: 84-9=75 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 98:[9, 22], Operations: ['37+69=106', '106-84=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,98 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,98 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 98:[106, 93], Operations: ['37+69=106', '84+9=93'] Exploring Operation: 106+93=199, Resulting Numbers: [199] 199,98 unequal: No Solution Exploring Operation: 106*93=9858, Resulting Numbers: [9858] 9858,98 unequal: No Solution Exploring Operation: 106-93=13, Resulting Numbers: [13] 13,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 98:[84, 97], Operations: ['37+69=106', '106-9=97'] Exploring Operation: 84+97=181, Resulting Numbers: [181] 181,98 unequal: No Solution Exploring Operation: 84*97=8148, Resulting Numbers: [8148] 8148,98 unequal: No Solution Exploring Operation: 97-84=13, Resulting Numbers: [13] 13,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 98:[106, 75], Operations: ['37+69=106', '84-9=75'] Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,98 unequal: No Solution Exploring Operation: 106+75=181, Resulting Numbers: [181] 181,98 unequal: No Solution Exploring Operation: 106*75=7950, Resulting Numbers: [7950] 7950,98 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[84, 9, 32], Operations: ['69-37=32'] Exploring Operation: 84-32=52, Resulting Numbers: [9, 52] Generated Node #0,1,0: 98:[9, 52] Operation: 84-32=52 Exploring Operation: 84+32=116, Resulting Numbers: [9, 116] Generated Node #0,1,1: 98:[9, 116] Operation: 84+32=116 Exploring Operation: 84+9=93, Resulting Numbers: [32, 93] Generated Node #0,1,2: 98:[32, 93] Operation: 84+9=93 Exploring Operation: 9+32=41, Resulting Numbers: [84, 41] Generated Node #0,1,3: 98:[84, 41] Operation: 9+32=41 Moving to Node #0,1,0 Current State: 98:[9, 52], Operations: ['69-37=32', '84-32=52'] Exploring Operation: 9*52=468, Resulting Numbers: [468] 468,98 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 9+52=61, Resulting Numbers: [61] 61,98 unequal: No Solution Moving to Node #0,1,1 Current State: 98:[9, 116], Operations: ['69-37=32', '84+32=116'] Exploring Operation: 9*116=1044, Resulting Numbers: [1044] 1044,98 unequal: No Solution Exploring Operation: 9+116=125, Resulting Numbers: [125] 125,98 unequal: No Solution Exploring Operation: 116-9=107, Resulting Numbers: [107] 107,98 unequal: No Solution Moving to Node #0,1,3 Current State: 98:[84, 41], Operations: ['69-37=32', '9+32=41'] Exploring Operation: 84-41=43, Resulting Numbers: [43] 43,98 unequal: No Solution Exploring Operation: 84*41=3444, Resulting Numbers: [3444] 3444,98 unequal: No Solution Exploring Operation: 84+41=125, Resulting Numbers: [125] 125,98 unequal: No Solution Moving to Node #0,1,2 Current State: 98:[32, 93], Operations: ['69-37=32', '84+9=93'] Exploring Operation: 93-32=61, Resulting Numbers: [61] 61,98 unequal: No Solution Exploring Operation: 32+93=125, Resulting Numbers: [125] 125,98 unequal: No Solution Exploring Operation: 32*93=2976, Resulting Numbers: [2976] 2976,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 22, 44, 81, 85 ]
33
[ "85-81=4", "44/4=11", "22+11=33" ]
Current State: 33:[22, 44, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [22, 44, 4] Generated Node #2: [22, 44, 4] from Operation: 85-81=4 Current State: 33:[22, 44, 4], Operations: ['85-81=4'] Exploring Operation: 44/4=11, Resulting Numbers: [22, 11] Generated Node #3: [22, 11] from Operation: 44/4=11 Current State: 33:[22, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[22, 44, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [22, 44, 4] Generated Node #0,0: 33:[22, 44, 4] Operation: 85-81=4 Exploring Operation: 85-44=41, Resulting Numbers: [22, 81, 41] Generated Node #0,1: 33:[22, 81, 41] Operation: 85-44=41 Exploring Operation: 81-44=37, Resulting Numbers: [22, 85, 37] Generated Node #0,2: 33:[22, 85, 37] Operation: 81-44=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[22, 44, 4], Operations: ['85-81=4'] Exploring Operation: 44/4=11, Resulting Numbers: [22, 11] Generated Node #0,0,0: 33:[22, 11] Operation: 44/4=11 Exploring Operation: 44/22=2, Resulting Numbers: [4, 2] Generated Node #0,0,1: 33:[4, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [4, 22] Generated Node #0,0,2: 33:[4, 22] Operation: 44-22=22 Moving to Node #0,0,1 Current State: 33:[4, 2], Operations: ['85-81=4', '44/22=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,33 unequal: No Solution Moving to Node #0,0,0 Current State: 33:[22, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,33 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[22, 44, 81, 85], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [22, 44, 4] Generated Node #0,0: 33:[22, 44, 4] Operation: 85-81=4 Moving to Node #0,0 Current State: 33:[22, 44, 4], Operations: ['85-81=4'] Exploring Operation: 44/4=11, Resulting Numbers: [22, 11] Generated Node #0,0,0: 33:[22, 11] Operation: 44/4=11 Moving to Node #0,0,0 Current State: 33:[22, 11], Operations: ['85-81=4', '44/4=11'] Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
mult_heuristic
[ 74, 16, 86, 61 ]
89
[ "74-16=58", "86+61=147", "147-58=89" ]
Current State: 89:[74, 16, 86, 61], Operations: [] Exploring Operation: 74-16=58, Resulting Numbers: [86, 61, 58] Generated Node #2: [86, 61, 58] from Operation: 74-16=58 Current State: 89:[86, 61, 58], Operations: ['74-16=58'] Exploring Operation: 86+61=147, Resulting Numbers: [58, 147] Generated Node #3: [58, 147] from Operation: 86+61=147 Current State: 89:[58, 147], Operations: ['74-16=58', '86+61=147'] Exploring Operation: 147-58=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[74, 16, 86, 61], Operations: [] Exploring Operation: 16+61=77, Resulting Numbers: [74, 86, 77] Generated Node #0,0: 89:[74, 86, 77] Operation: 16+61=77 Exploring Operation: 74+16=90, Resulting Numbers: [86, 61, 90] Generated Node #0,1: 89:[86, 61, 90] Operation: 74+16=90 Exploring Operation: 16+86=102, Resulting Numbers: [74, 61, 102] Generated Node #0,2: 89:[74, 61, 102] Operation: 16+86=102 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[74, 86, 77], Operations: ['16+61=77'] Exploring Operation: 74+77=151, Resulting Numbers: [86, 151] Generated Node #0,0,0: 89:[86, 151] Operation: 74+77=151 Exploring Operation: 86-74=12, Resulting Numbers: [77, 12] Generated Node #0,0,1: 89:[77, 12] Operation: 86-74=12 Exploring Operation: 74+86=160, Resulting Numbers: [77, 160] Generated Node #0,0,2: 89:[77, 160] Operation: 74+86=160 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[86, 151], Operations: ['16+61=77', '74+77=151'] Exploring Operation: 86+151=237, Resulting Numbers: [237] 237,89 unequal: No Solution Exploring Operation: 151-86=65, Resulting Numbers: [65] 65,89 unequal: No Solution Exploring Operation: 86*151=12986, Resulting Numbers: [12986] 12986,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[77, 160], Operations: ['16+61=77', '74+86=160'] Exploring Operation: 77+160=237, Resulting Numbers: [237] 237,89 unequal: No Solution Exploring Operation: 77*160=12320, Resulting Numbers: [12320] 12320,89 unequal: No Solution Exploring Operation: 160-77=83, Resulting Numbers: [83] 83,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[77, 12], Operations: ['16+61=77', '86-74=12'] Exploring Operation: 77+12=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[74, 16, 86, 61], Operations: [] Exploring Operation: 16+61=77, Resulting Numbers: [74, 86, 77] Generated Node #0,0: 89:[74, 86, 77] Operation: 16+61=77 Moving to Node #0,0 Current State: 89:[74, 86, 77], Operations: ['16+61=77'] Exploring Operation: 86-74=12, Resulting Numbers: [77, 12] Generated Node #0,0,1: 89:[77, 12] Operation: 86-74=12 Moving to Node #0,0,1 Current State: 89:[77, 12], Operations: ['16+61=77', '86-74=12'] Exploring Operation: 77+12=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 56, 5, 8, 12 ]
49
[ "56/8=7", "12-5=7", "7*7=49" ]
Current State: 49:[56, 5, 8, 12], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [5, 12, 7] Generated Node #2: [5, 12, 7] from Operation: 56/8=7 Current State: 49:[5, 12, 7], Operations: ['56/8=7'] Exploring Operation: 12-5=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 12-5=7 Current State: 49:[7, 7], Operations: ['56/8=7', '12-5=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[56, 5, 8, 12], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [5, 12, 7] Generated Node #0,0: 49:[5, 12, 7] Operation: 56/8=7 Moving to Node #0,0 Current State: 49:[5, 12, 7], Operations: ['56/8=7'] Exploring Operation: 12-5=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 49:[7, 7] Operation: 12-5=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 49:[7, 7], Operations: ['56/8=7', '12-5=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[56, 5, 8, 12], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [5, 12, 7] Generated Node #0,0: 49:[5, 12, 7] Operation: 56/8=7 Moving to Node #0,0 Current State: 49:[5, 12, 7], Operations: ['56/8=7'] Exploring Operation: 12-5=7, Resulting Numbers: [7, 7] Generated Node #0,0,0: 49:[7, 7] Operation: 12-5=7 Moving to Node #0,0,0 Current State: 49:[7, 7], Operations: ['56/8=7', '12-5=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 15, 33, 77, 34 ]
92
[ "15+77=92", "34-33=1", "92*1=92" ]
Current State: 92:[15, 33, 77, 34], Operations: [] Exploring Operation: 15+77=92, Resulting Numbers: [33, 34, 92] Generated Node #2: [33, 34, 92] from Operation: 15+77=92 Current State: 92:[33, 34, 92], Operations: ['15+77=92'] Exploring Operation: 34-33=1, Resulting Numbers: [92, 1] Generated Node #3: [92, 1] from Operation: 34-33=1 Current State: 92:[92, 1], Operations: ['15+77=92', '34-33=1'] Exploring Operation: 92*1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[15, 33, 77, 34], Operations: [] Exploring Operation: 77-33=44, Resulting Numbers: [15, 34, 44] Generated Node #0,0: 92:[15, 34, 44] Operation: 77-33=44 Exploring Operation: 15+77=92, Resulting Numbers: [33, 34, 92] Generated Node #0,1: 92:[33, 34, 92] Operation: 15+77=92 Exploring Operation: 77-34=43, Resulting Numbers: [15, 33, 43] Generated Node #0,2: 92:[15, 33, 43] Operation: 77-34=43 Exploring Operation: 34-33=1, Resulting Numbers: [15, 77, 1] Generated Node #0,3: 92:[15, 77, 1] Operation: 34-33=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[15, 34, 44], Operations: ['77-33=44'] Exploring Operation: 44-15=29, Resulting Numbers: [34, 29] Generated Node #0,0,0: 92:[34, 29] Operation: 44-15=29 Exploring Operation: 15+34=49, Resulting Numbers: [44, 49] Generated Node #0,0,1: 92:[44, 49] Operation: 15+34=49 Exploring Operation: 34-15=19, Resulting Numbers: [44, 19] Generated Node #0,0,2: 92:[44, 19] Operation: 34-15=19 Exploring Operation: 44-34=10, Resulting Numbers: [15, 10] Generated Node #0,0,3: 92:[15, 10] Operation: 44-34=10 Moving to Node #0,0,1 Current State: 92:[44, 49], Operations: ['77-33=44', '15+34=49'] Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 44+49=93, Resulting Numbers: [93] 93,92 unequal: No Solution Exploring Operation: 44*49=2156, Resulting Numbers: [2156] 2156,92 unequal: No Solution Moving to Node #0,0,2 Current State: 92:[44, 19], Operations: ['77-33=44', '34-15=19'] Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,92 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,92 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,92 unequal: No Solution Moving to Node #0,0,3 Current State: 92:[15, 10], Operations: ['77-33=44', '44-34=10'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 15*10=150, Resulting Numbers: [150] 150,92 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[34, 29], Operations: ['77-33=44', '44-15=29'] Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,92 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,92 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,92 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 Current State: 92:[33, 34, 92], Operations: ['15+77=92'] Exploring Operation: 33+34=67, Resulting Numbers: [92, 67] Generated Node #0,1,0: 92:[92, 67] Operation: 33+34=67 Exploring Operation: 92-33=59, Resulting Numbers: [34, 59] Generated Node #0,1,1: 92:[34, 59] Operation: 92-33=59 Exploring Operation: 92-34=58, Resulting Numbers: [33, 58] Generated Node #0,1,2: 92:[33, 58] Operation: 92-34=58 Exploring Operation: 34-33=1, Resulting Numbers: [92, 1] Generated Node #0,1,3: 92:[92, 1] Operation: 34-33=1 Moving to Node #0,1,3 Current State: 92:[92, 1], Operations: ['15+77=92', '34-33=1'] Exploring Operation: 92+1=93, Resulting Numbers: [93] 93,92 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[15, 33, 77, 34], Operations: [] Exploring Operation: 15+77=92, Resulting Numbers: [33, 34, 92] Generated Node #0,1: 92:[33, 34, 92] Operation: 15+77=92 Moving to Node #0,1 Current State: 92:[33, 34, 92], Operations: ['15+77=92'] Exploring Operation: 34-33=1, Resulting Numbers: [92, 1] Generated Node #0,1,3: 92:[92, 1] Operation: 34-33=1 Moving to Node #0,1,3 Current State: 92:[92, 1], Operations: ['15+77=92', '34-33=1'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 4, 18, 17, 80 ]
84
[ "4+80=84", "18-17=1", "84*1=84" ]
Current State: 84:[4, 18, 17, 80], Operations: [] Exploring Operation: 4+80=84, Resulting Numbers: [18, 17, 84] Generated Node #2: [18, 17, 84] from Operation: 4+80=84 Current State: 84:[18, 17, 84], Operations: ['4+80=84'] Exploring Operation: 18-17=1, Resulting Numbers: [84, 1] Generated Node #3: [84, 1] from Operation: 18-17=1 Current State: 84:[84, 1], Operations: ['4+80=84', '18-17=1'] Exploring Operation: 84*1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[4, 18, 17, 80], Operations: [] Exploring Operation: 18-17=1, Resulting Numbers: [4, 80, 1] Generated Node #0,0: 84:[4, 80, 1] Operation: 18-17=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[4, 80, 1], Operations: ['18-17=1'] Exploring Operation: 4+80=84, Resulting Numbers: [1, 84] Generated Node #0,0,0: 84:[1, 84] Operation: 4+80=84 Moving to Node #0,0,0 Current State: 84:[1, 84], Operations: ['18-17=1', '4+80=84'] Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[4, 18, 17, 80], Operations: [] Exploring Operation: 18-17=1, Resulting Numbers: [4, 80, 1] Generated Node #0,0: 84:[4, 80, 1] Operation: 18-17=1 Moving to Node #0,0 Current State: 84:[4, 80, 1], Operations: ['18-17=1'] Exploring Operation: 4+80=84, Resulting Numbers: [1, 84] Generated Node #0,0,0: 84:[1, 84] Operation: 4+80=84 Moving to Node #0,0,0 Current State: 84:[1, 84], Operations: ['18-17=1', '4+80=84'] Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 46, 17, 22, 66 ]
15
[ "46-17=29", "66-22=44", "44-29=15" ]
Current State: 15:[46, 17, 22, 66], Operations: [] Exploring Operation: 46-17=29, Resulting Numbers: [22, 66, 29] Generated Node #2: [22, 66, 29] from Operation: 46-17=29 Current State: 15:[22, 66, 29], Operations: ['46-17=29'] Exploring Operation: 66-22=44, Resulting Numbers: [29, 44] Generated Node #3: [29, 44] from Operation: 66-22=44 Current State: 15:[29, 44], Operations: ['46-17=29', '66-22=44'] Exploring Operation: 44-29=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[46, 17, 22, 66], Operations: [] Exploring Operation: 66-46=20, Resulting Numbers: [17, 22, 20] Generated Node #0,0: 15:[17, 22, 20] Operation: 66-46=20 Exploring Operation: 66/22=3, Resulting Numbers: [46, 17, 3] Generated Node #0,1: 15:[46, 17, 3] Operation: 66/22=3 Exploring Operation: 66-22=44, Resulting Numbers: [46, 17, 44] Generated Node #0,2: 15:[46, 17, 44] Operation: 66-22=44 Exploring Operation: 46-17=29, Resulting Numbers: [22, 66, 29] Generated Node #0,3: 15:[22, 66, 29] Operation: 46-17=29 Exploring Operation: 46-22=24, Resulting Numbers: [17, 66, 24] Generated Node #0,4: 15:[17, 66, 24] Operation: 46-22=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[17, 22, 20], Operations: ['66-46=20'] Exploring Operation: 20-17=3, Resulting Numbers: [22, 3] Generated Node #0,0,0: 15:[22, 3] Operation: 20-17=3 Exploring Operation: 17+22=39, Resulting Numbers: [20, 39] Generated Node #0,0,1: 15:[20, 39] Operation: 17+22=39 Exploring Operation: 17+20=37, Resulting Numbers: [22, 37] Generated Node #0,0,2: 15:[22, 37] Operation: 17+20=37 Exploring Operation: 22-20=2, Resulting Numbers: [17, 2] Generated Node #0,0,3: 15:[17, 2] Operation: 22-20=2 Exploring Operation: 22-17=5, Resulting Numbers: [20, 5] Generated Node #0,0,4: 15:[20, 5] Operation: 22-17=5 Moving to Node #0,0,3 Current State: 15:[17, 2], Operations: ['66-46=20', '22-20=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,15 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,15 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[46, 17, 22, 66], Operations: [] Exploring Operation: 66-46=20, Resulting Numbers: [17, 22, 20] Generated Node #0,0: 15:[17, 22, 20] Operation: 66-46=20 Moving to Node #0,0 Current State: 15:[17, 22, 20], Operations: ['66-46=20'] Exploring Operation: 22-20=2, Resulting Numbers: [17, 2] Generated Node #0,0,3: 15:[17, 2] Operation: 22-20=2 Moving to Node #0,0,3 Current State: 15:[17, 2], Operations: ['66-46=20', '22-20=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 18, 67, 96, 27 ]
36
[ "96-67=29", "29-27=2", "18*2=36" ]
Current State: 36:[18, 67, 96, 27], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [18, 27, 29] Generated Node #2: [18, 27, 29] from Operation: 96-67=29 Current State: 36:[18, 27, 29], Operations: ['96-67=29'] Exploring Operation: 29-27=2, Resulting Numbers: [18, 2] Generated Node #3: [18, 2] from Operation: 29-27=2 Current State: 36:[18, 2], Operations: ['96-67=29', '29-27=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[18, 67, 96, 27], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [18, 27, 29] Generated Node #0,0: 36:[18, 27, 29] Operation: 96-67=29 Exploring Operation: 67-27=40, Resulting Numbers: [18, 96, 40] Generated Node #0,1: 36:[18, 96, 40] Operation: 67-27=40 Exploring Operation: 96-27=69, Resulting Numbers: [18, 67, 69] Generated Node #0,2: 36:[18, 67, 69] Operation: 96-27=69 Moving to Node #0,0 Current State: 36:[18, 27, 29], Operations: ['96-67=29'] Exploring Operation: 29-18=11, Resulting Numbers: [27, 11] Generated Node #0,0,0: 36:[27, 11] Operation: 29-18=11 Exploring Operation: 29-27=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 36:[18, 2] Operation: 29-27=2 Exploring Operation: 27-18=9, Resulting Numbers: [29, 9] Generated Node #0,0,2: 36:[29, 9] Operation: 27-18=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 36:[18, 2], Operations: ['96-67=29', '29-27=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[18, 67, 96, 27], Operations: [] Exploring Operation: 96-67=29, Resulting Numbers: [18, 27, 29] Generated Node #0,0: 36:[18, 27, 29] Operation: 96-67=29 Moving to Node #0,0 Current State: 36:[18, 27, 29], Operations: ['96-67=29'] Exploring Operation: 29-27=2, Resulting Numbers: [18, 2] Generated Node #0,0,1: 36:[18, 2] Operation: 29-27=2 Moving to Node #0,0,1 Current State: 36:[18, 2], Operations: ['96-67=29', '29-27=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 87, 6, 6, 24 ]
24
[ "6-6=0", "87*0=0", "24+0=24" ]
Current State: 24:[87, 6, 6, 24], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [87, 24, 0] Generated Node #2: [87, 24, 0] from Operation: 6-6=0 Current State: 24:[87, 24, 0], Operations: ['6-6=0'] Exploring Operation: 87*0=0, Resulting Numbers: [24, 0] Generated Node #3: [24, 0] from Operation: 87*0=0 Current State: 24:[24, 0], Operations: ['6-6=0', '87*0=0'] Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[87, 6, 6, 24], Operations: [] Exploring Operation: 87-24=63, Resulting Numbers: [6, 6, 63] Generated Node #0,0: 24:[6, 6, 63] Operation: 87-24=63 Exploring Operation: 87-6=81, Resulting Numbers: [6, 24, 81] Generated Node #0,1: 24:[6, 24, 81] Operation: 87-6=81 Exploring Operation: 87-6=81, Resulting Numbers: [6, 24, 81] Generated Node #0,2: 24:[6, 24, 81] Operation: 87-6=81 Exploring Operation: 6+6=12, Resulting Numbers: [87, 24, 12] Generated Node #0,3: 24:[87, 24, 12] Operation: 6+6=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[6, 6, 63], Operations: ['87-24=63'] Exploring Operation: 63-6=57, Resulting Numbers: [6, 57] Generated Node #0,0,0: 24:[6, 57] Operation: 63-6=57 Exploring Operation: 63-6=57, Resulting Numbers: [6, 57] Generated Node #0,0,1: 24:[6, 57] Operation: 63-6=57 Exploring Operation: 6+6=12, Resulting Numbers: [63, 12] Generated Node #0,0,2: 24:[63, 12] Operation: 6+6=12 Exploring Operation: 6/6=1, Resulting Numbers: [63, 1] Generated Node #0,0,3: 24:[63, 1] Operation: 6/6=1 Moving to Node #0,0,0 Current State: 24:[6, 57], Operations: ['87-24=63', '63-6=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,24 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,24 unequal: No Solution Moving to Node #0,0,1 Current State: 24:[6, 57], Operations: ['87-24=63', '63-6=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,24 unequal: No Solution Moving to Node #0,0,2 Current State: 24:[63, 12], Operations: ['87-24=63', '6+6=12'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,24 unequal: No Solution Exploring Operation: 63*12=756, Resulting Numbers: [756] 756,24 unequal: No Solution Moving to Node #0,0,3 Current State: 24:[63, 1], Operations: ['87-24=63', '6/6=1'] Exploring Operation: 63-1=62, Resulting Numbers: [62] 62,24 unequal: No Solution Exploring Operation: 63+1=64, Resulting Numbers: [64] 64,24 unequal: No Solution Exploring Operation: 63*1=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 63/1=63, Resulting Numbers: [63] 63,24 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:[6, 24, 81], Operations: ['87-6=81'] Exploring Operation: 81-24=57, Resulting Numbers: [6, 57] Generated Node #0,1,0: 24:[6, 57] Operation: 81-24=57 Exploring Operation: 81-6=75, Resulting Numbers: [24, 75] Generated Node #0,1,1: 24:[24, 75] Operation: 81-6=75 Exploring Operation: 6+24=30, Resulting Numbers: [81, 30] Generated Node #0,1,2: 24:[81, 30] Operation: 6+24=30 Exploring Operation: 24/6=4, Resulting Numbers: [81, 4] Generated Node #0,1,3: 24:[81, 4] Operation: 24/6=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 24:[6, 57], Operations: ['87-6=81', '81-24=57'] Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,24 unequal: No Solution Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,24 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 #0,1,1 Current State: 24:[24, 75], Operations: ['87-6=81', '81-6=75'] Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,24 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,24 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 #0,1,3 Current State: 24:[81, 4], Operations: ['87-6=81', '24/6=4'] Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,24 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,24 unequal: No Solution Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,24 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 #0,1,2 Current State: 24:[81, 30], Operations: ['87-6=81', '6+24=30'] Exploring Operation: 81*30=2430, Resulting Numbers: [2430] 2430,24 unequal: No Solution Exploring Operation: 81+30=111, Resulting Numbers: [111] 111,24 unequal: No Solution Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,24 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 #0,2 Current State: 24:[6, 24, 81], Operations: ['87-6=81'] Exploring Operation: 81-6=75, Resulting Numbers: [24, 75] Generated Node #0,2,0: 24:[24, 75] Operation: 81-6=75 Exploring Operation: 81-24=57, Resulting Numbers: [6, 57] Generated Node #0,2,1: 24:[6, 57] Operation: 81-24=57 Exploring Operation: 6+24=30, Resulting Numbers: [81, 30] Generated Node #0,2,2: 24:[81, 30] Operation: 6+24=30 Exploring Operation: 24/6=4, Resulting Numbers: [81, 4] Generated Node #0,2,3: 24:[81, 4] Operation: 24/6=4 Moving to Node #0,2,1 Current State: 24:[6, 57], Operations: ['87-6=81', '81-24=57'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,24 unequal: No Solution Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[24, 75], Operations: ['87-6=81', '81-6=75'] Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,24 unequal: No Solution Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,24 unequal: No Solution Moving to Node #0,2,3 Current State: 24:[81, 4], Operations: ['87-6=81', '24/6=4'] Exploring Operation: 81+4=85, Resulting Numbers: [85] 85,24 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,24 unequal: No Solution Exploring Operation: 81*4=324, Resulting Numbers: [324] 324,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[81, 30], Operations: ['87-6=81', '6+24=30'] Exploring Operation: 81+30=111, Resulting Numbers: [111] 111,24 unequal: No Solution Exploring Operation: 81*30=2430, Resulting Numbers: [2430] 2430,24 unequal: No Solution Exploring Operation: 81-30=51, Resulting Numbers: [51] 51,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 24:[87, 24, 12], Operations: ['6+6=12'] Exploring Operation: 87-12=75, Resulting Numbers: [24, 75] Generated Node #0,3,0: 24:[24, 75] Operation: 87-12=75 Exploring Operation: 87-24=63, Resulting Numbers: [12, 63] Generated Node #0,3,1: 24:[12, 63] Operation: 87-24=63 Exploring Operation: 24-12=12, Resulting Numbers: [87, 12] Generated Node #0,3,2: 24:[87, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [87, 2] Generated Node #0,3,3: 24:[87, 2] Operation: 24/12=2 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 24:[12, 63], Operations: ['6+6=12', '87-24=63'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 12*63=756, Resulting Numbers: [756] 756,24 unequal: No Solution Exploring Operation: 12+63=75, Resulting Numbers: [75] 75,24 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 #0,3,0 Current State: 24:[24, 75], Operations: ['6+6=12', '87-12=75'] Exploring Operation: 75-24=51, Resulting Numbers: [51] 51,24 unequal: No Solution Exploring Operation: 24*75=1800, Resulting Numbers: [1800] 1800,24 unequal: No Solution Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,24 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 #0,3,2 Current State: 24:[87, 12], Operations: ['6+6=12', '24-12=12'] Exploring Operation: 87*12=1044, Resulting Numbers: [1044] 1044,24 unequal: No Solution Exploring Operation: 87-12=75, Resulting Numbers: [75] 75,24 unequal: No Solution Exploring Operation: 87+12=99, Resulting Numbers: [99] 99,24 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 #0,3,3 Current State: 24:[87, 2], Operations: ['6+6=12', '24/12=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,24 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,24 unequal: No Solution Exploring Operation: 87*2=174, Resulting Numbers: [174] 174,24 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 No solution found.
0
hs_4
sum_heuristic
[ 32, 18, 61, 4 ]
21
[ "32+61=93", "18*4=72", "93-72=21" ]
Current State: 21:[32, 18, 61, 4], Operations: [] Exploring Operation: 32+61=93, Resulting Numbers: [18, 4, 93] Generated Node #2: [18, 4, 93] from Operation: 32+61=93 Current State: 21:[18, 4, 93], Operations: ['32+61=93'] Exploring Operation: 18*4=72, Resulting Numbers: [93, 72] Generated Node #3: [93, 72] from Operation: 18*4=72 Current State: 21:[93, 72], Operations: ['32+61=93', '18*4=72'] Exploring Operation: 93-72=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[32, 18, 61, 4], Operations: [] Exploring Operation: 32-18=14, Resulting Numbers: [61, 4, 14] Generated Node #0,0: 21:[61, 4, 14] Operation: 32-18=14 Exploring Operation: 61-32=29, Resulting Numbers: [18, 4, 29] Generated Node #0,1: 21:[18, 4, 29] Operation: 61-32=29 Exploring Operation: 32-4=28, Resulting Numbers: [18, 61, 28] Generated Node #0,2: 21:[18, 61, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [18, 61, 8] Generated Node #0,3: 21:[18, 61, 8] Operation: 32/4=8 Exploring Operation: 61-18=43, Resulting Numbers: [32, 4, 43] Generated Node #0,4: 21:[32, 4, 43] Operation: 61-18=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[18, 4, 29], Operations: ['61-32=29'] Exploring Operation: 4+29=33, Resulting Numbers: [18, 33] Generated Node #0,1,0: 21:[18, 33] Operation: 4+29=33 Exploring Operation: 29-4=25, Resulting Numbers: [18, 25] Generated Node #0,1,1: 21:[18, 25] Operation: 29-4=25 Exploring Operation: 18-4=14, Resulting Numbers: [29, 14] Generated Node #0,1,2: 21:[29, 14] Operation: 18-4=14 Exploring Operation: 18+4=22, Resulting Numbers: [29, 22] Generated Node #0,1,3: 21:[29, 22] Operation: 18+4=22 Exploring Operation: 29-18=11, Resulting Numbers: [4, 11] Generated Node #0,1,4: 21:[4, 11] Operation: 29-18=11 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 21:[4, 11], Operations: ['61-32=29', '29-18=11'] Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,21 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,21 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 #0,1,1 Current State: 21:[18, 25], Operations: ['61-32=29', '29-4=25'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 18*25=450, Resulting Numbers: [450] 450,21 unequal: No Solution Exploring Operation: 18+25=43, Resulting Numbers: [43] 43,21 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 #0,1,3 Current State: 21:[29, 22], Operations: ['61-32=29', '18+4=22'] Exploring Operation: 29*22=638, Resulting Numbers: [638] 638,21 unequal: No Solution Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,21 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 #0,1,0 Current State: 21:[18, 33], Operations: ['61-32=29', '4+29=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,21 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 #0,1,2 Current State: 21:[29, 14], Operations: ['61-32=29', '18-4=14'] Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 29*14=406, Resulting Numbers: [406] 406,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 21:[32, 4, 43], Operations: ['61-18=43'] Exploring Operation: 32-4=28, Resulting Numbers: [43, 28] Generated Node #0,4,0: 21:[43, 28] Operation: 32-4=28 Exploring Operation: 32+4=36, Resulting Numbers: [43, 36] Generated Node #0,4,1: 21:[43, 36] Operation: 32+4=36 Exploring Operation: 32/4=8, Resulting Numbers: [43, 8] Generated Node #0,4,2: 21:[43, 8] Operation: 32/4=8 Exploring Operation: 43-4=39, Resulting Numbers: [32, 39] Generated Node #0,4,3: 21:[32, 39] Operation: 43-4=39 Exploring Operation: 43-32=11, Resulting Numbers: [4, 11] Generated Node #0,4,4: 21:[4, 11] Operation: 43-32=11 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 21:[4, 11], Operations: ['61-18=43', '43-32=11'] Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,21 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 #0,4,2 Current State: 21:[43, 8], Operations: ['61-18=43', '32/4=8'] Exploring Operation: 43*8=344, Resulting Numbers: [344] 344,21 unequal: No Solution Exploring Operation: 43+8=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,21 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 #0,4,0 Current State: 21:[43, 28], Operations: ['61-18=43', '32-4=28'] Exploring Operation: 43*28=1204, Resulting Numbers: [1204] 1204,21 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,21 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 #0,4,3 Current State: 21:[32, 39], Operations: ['61-18=43', '43-4=39'] Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,21 unequal: No Solution Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,21 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 #0,4,1 Current State: 21:[43, 36], Operations: ['61-18=43', '32+4=36'] Exploring Operation: 43*36=1548, Resulting Numbers: [1548] 1548,21 unequal: No Solution Exploring Operation: 43-36=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 43+36=79, Resulting Numbers: [79] 79,21 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 #0,3 Current State: 21:[18, 61, 8], Operations: ['32/4=8'] Exploring Operation: 18-8=10, Resulting Numbers: [61, 10] Generated Node #0,3,0: 21:[61, 10] Operation: 18-8=10 Exploring Operation: 61+8=69, Resulting Numbers: [18, 69] Generated Node #0,3,1: 21:[18, 69] Operation: 61+8=69 Exploring Operation: 61-18=43, Resulting Numbers: [8, 43] Generated Node #0,3,2: 21:[8, 43] Operation: 61-18=43 Exploring Operation: 18+8=26, Resulting Numbers: [61, 26] Generated Node #0,3,3: 21:[61, 26] Operation: 18+8=26 Exploring Operation: 61-8=53, Resulting Numbers: [18, 53] Generated Node #0,3,4: 21:[18, 53] Operation: 61-8=53 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 21:[8, 43], Operations: ['32/4=8', '61-18=43'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 8*43=344, Resulting Numbers: [344] 344,21 unequal: No Solution Exploring Operation: 8+43=51, Resulting Numbers: [51] 51,21 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 #0,3,4 Current State: 21:[18, 53], Operations: ['32/4=8', '61-8=53'] Exploring Operation: 18+53=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 18*53=954, Resulting Numbers: [954] 954,21 unequal: No Solution Exploring Operation: 53-18=35, Resulting Numbers: [35] 35,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 21:[61, 10], Operations: ['32/4=8', '18-8=10'] Exploring Operation: 61+10=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 61*10=610, Resulting Numbers: [610] 610,21 unequal: No Solution Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,21 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:[61, 26], Operations: ['32/4=8', '18+8=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,21 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,21 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, 69], Operations: ['32/4=8', '61+8=69'] Exploring Operation: 18*69=1242, Resulting Numbers: [1242] 1242,21 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 18+69=87, Resulting Numbers: [87] 87,21 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:[61, 4, 14], Operations: ['32-18=14'] Exploring Operation: 14-4=10, Resulting Numbers: [61, 10] Generated Node #0,0,0: 21:[61, 10] Operation: 14-4=10 Exploring Operation: 61+4=65, Resulting Numbers: [14, 65] Generated Node #0,0,1: 21:[14, 65] Operation: 61+4=65 Exploring Operation: 4+14=18, Resulting Numbers: [61, 18] Generated Node #0,0,2: 21:[61, 18] Operation: 4+14=18 Exploring Operation: 61-4=57, Resulting Numbers: [14, 57] Generated Node #0,0,3: 21:[14, 57] Operation: 61-4=57 Exploring Operation: 61-14=47, Resulting Numbers: [4, 47] Generated Node #0,0,4: 21:[4, 47] Operation: 61-14=47 Moving to Node #0,0,4 Current State: 21:[4, 47], Operations: ['32-18=14', '61-14=47'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,21 unequal: No Solution Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[61, 18], Operations: ['32-18=14', '4+14=18'] Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 61+18=79, Resulting Numbers: [79] 79,21 unequal: No Solution Exploring Operation: 61*18=1098, Resulting Numbers: [1098] 1098,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[61, 10], Operations: ['32-18=14', '14-4=10'] Exploring Operation: 61*10=610, Resulting Numbers: [610] 610,21 unequal: No Solution Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 61+10=71, Resulting Numbers: [71] 71,21 unequal: No Solution Moving to Node #0,0,3 Current State: 21:[14, 57], Operations: ['32-18=14', '61-4=57'] Exploring Operation: 14*57=798, Resulting Numbers: [798] 798,21 unequal: No Solution Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,21 unequal: No Solution Exploring Operation: 14+57=71, Resulting Numbers: [71] 71,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[14, 65], Operations: ['32-18=14', '61+4=65'] Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,21 unequal: No Solution Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,21 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:[18, 61, 28], Operations: ['32-4=28'] Exploring Operation: 18+61=79, Resulting Numbers: [28, 79] Generated Node #0,2,0: 21:[28, 79] Operation: 18+61=79 Exploring Operation: 61-28=33, Resulting Numbers: [18, 33] Generated Node #0,2,1: 21:[18, 33] Operation: 61-28=33 Exploring Operation: 61-18=43, Resulting Numbers: [28, 43] Generated Node #0,2,2: 21:[28, 43] Operation: 61-18=43 Exploring Operation: 18+28=46, Resulting Numbers: [61, 46] Generated Node #0,2,3: 21:[61, 46] Operation: 18+28=46 Exploring Operation: 28-18=10, Resulting Numbers: [61, 10] Generated Node #0,2,4: 21:[61, 10] Operation: 28-18=10 Moving to Node #0,2,1 Current State: 21:[18, 33], Operations: ['32-4=28', '61-28=33'] Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[28, 43], Operations: ['32-4=28', '61-18=43'] Exploring Operation: 28+43=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 28*43=1204, Resulting Numbers: [1204] 1204,21 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,21 unequal: No Solution Moving to Node #0,2,4 Current State: 21:[61, 10], Operations: ['32-4=28', '28-18=10'] Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 61*10=610, Resulting Numbers: [610] 610,21 unequal: No Solution Exploring Operation: 61+10=71, Resulting Numbers: [71] 71,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[28, 79], Operations: ['32-4=28', '18+61=79'] Exploring Operation: 28+79=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 79-28=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 28*79=2212, Resulting Numbers: [2212] 2212,21 unequal: No Solution Moving to Node #0,2,3 Current State: 21:[61, 46], Operations: ['32-4=28', '18+28=46'] Exploring Operation: 61+46=107, Resulting Numbers: [107] 107,21 unequal: No Solution Exploring Operation: 61*46=2806, Resulting Numbers: [2806] 2806,21 unequal: No Solution Exploring Operation: 61-46=15, Resulting Numbers: [15] 15,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 87, 29, 69, 8 ]
93
[ "87/29=3", "8*3=24", "69+24=93" ]
Current State: 93:[87, 29, 69, 8], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [69, 8, 3] Generated Node #2: [69, 8, 3] from Operation: 87/29=3 Current State: 93:[69, 8, 3], Operations: ['87/29=3'] Exploring Operation: 8*3=24, Resulting Numbers: [69, 24] Generated Node #3: [69, 24] from Operation: 8*3=24 Current State: 93:[69, 24], Operations: ['87/29=3', '8*3=24'] Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[87, 29, 69, 8], Operations: [] Exploring Operation: 29+69=98, Resulting Numbers: [87, 8, 98] Generated Node #0,0: 93:[87, 8, 98] Operation: 29+69=98 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[87, 8, 98], Operations: ['29+69=98'] Exploring Operation: 87+8=95, Resulting Numbers: [98, 95] Generated Node #0,0,0: 93:[98, 95] Operation: 87+8=95 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[98, 95], Operations: ['29+69=98', '87+8=95'] Exploring Operation: 98-95=3, Resulting Numbers: [3] 3,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 51, 64, 33, 61 ]
54
[ "51-33=18", "64-61=3", "18*3=54" ]
Current State: 54:[51, 64, 33, 61], Operations: [] Exploring Operation: 51-33=18, Resulting Numbers: [64, 61, 18] Generated Node #2: [64, 61, 18] from Operation: 51-33=18 Current State: 54:[64, 61, 18], Operations: ['51-33=18'] Exploring Operation: 64-61=3, Resulting Numbers: [18, 3] Generated Node #3: [18, 3] from Operation: 64-61=3 Current State: 54:[18, 3], Operations: ['51-33=18', '64-61=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[51, 64, 33, 61], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [51, 33, 3] Generated Node #0,0: 54:[51, 33, 3] Operation: 64-61=3 Exploring Operation: 64-51=13, Resulting Numbers: [33, 61, 13] Generated Node #0,1: 54:[33, 61, 13] Operation: 64-51=13 Exploring Operation: 61-33=28, Resulting Numbers: [51, 64, 28] Generated Node #0,2: 54:[51, 64, 28] Operation: 61-33=28 Exploring Operation: 64-33=31, Resulting Numbers: [51, 61, 31] Generated Node #0,3: 54:[51, 61, 31] Operation: 64-33=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[51, 33, 3], Operations: ['64-61=3'] Exploring Operation: 33-3=30, Resulting Numbers: [51, 30] Generated Node #0,0,0: 54:[51, 30] Operation: 33-3=30 Exploring Operation: 33/3=11, Resulting Numbers: [51, 11] Generated Node #0,0,1: 54:[51, 11] Operation: 33/3=11 Exploring Operation: 51+3=54, Resulting Numbers: [33, 54] Generated Node #0,0,2: 54:[33, 54] Operation: 51+3=54 Exploring Operation: 51-33=18, Resulting Numbers: [3, 18] Generated Node #0,0,3: 54:[3, 18] Operation: 51-33=18 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 54:[3, 18], Operations: ['64-61=3', '51-33=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[51, 64, 33, 61], Operations: [] Exploring Operation: 64-61=3, Resulting Numbers: [51, 33, 3] Generated Node #0,0: 54:[51, 33, 3] Operation: 64-61=3 Moving to Node #0,0 Current State: 54:[51, 33, 3], Operations: ['64-61=3'] Exploring Operation: 51-33=18, Resulting Numbers: [3, 18] Generated Node #0,0,3: 54:[3, 18] Operation: 51-33=18 Moving to Node #0,0,3 Current State: 54:[3, 18], Operations: ['64-61=3', '51-33=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 86, 13, 43, 3 ]
19
[ "86/43=2", "3*2=6", "13+6=19" ]
Current State: 19:[86, 13, 43, 3], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [13, 3, 2] Generated Node #2: [13, 3, 2] from Operation: 86/43=2 Current State: 19:[13, 3, 2], Operations: ['86/43=2'] Exploring Operation: 3*2=6, Resulting Numbers: [13, 6] Generated Node #3: [13, 6] from Operation: 3*2=6 Current State: 19:[13, 6], Operations: ['86/43=2', '3*2=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[86, 13, 43, 3], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [13, 3, 2] Generated Node #0,0: 19:[13, 3, 2] Operation: 86/43=2 Moving to Node #0,0 Current State: 19:[13, 3, 2], Operations: ['86/43=2'] Exploring Operation: 3*2=6, Resulting Numbers: [13, 6] Generated Node #0,0,0: 19:[13, 6] Operation: 3*2=6 Moving to Node #0,0,0 Current State: 19:[13, 6], Operations: ['86/43=2', '3*2=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[86, 13, 43, 3], Operations: [] Exploring Operation: 86/43=2, Resulting Numbers: [13, 3, 2] Generated Node #0,0: 19:[13, 3, 2] Operation: 86/43=2 Moving to Node #0,0 Current State: 19:[13, 3, 2], Operations: ['86/43=2'] Exploring Operation: 3*2=6, Resulting Numbers: [13, 6] Generated Node #0,0,0: 19:[13, 6] Operation: 3*2=6 Moving to Node #0,0,0 Current State: 19:[13, 6], Operations: ['86/43=2', '3*2=6'] Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 7, 75, 94, 92 ]
11
[ "75+94=169", "169-92=77", "77/7=11" ]
Current State: 11:[7, 75, 94, 92], Operations: [] Exploring Operation: 75+94=169, Resulting Numbers: [7, 92, 169] Generated Node #2: [7, 92, 169] from Operation: 75+94=169 Current State: 11:[7, 92, 169], Operations: ['75+94=169'] Exploring Operation: 169-92=77, Resulting Numbers: [7, 77] Generated Node #3: [7, 77] from Operation: 169-92=77 Current State: 11:[7, 77], Operations: ['75+94=169', '169-92=77'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[7, 75, 94, 92], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [7, 75, 2] Generated Node #0,0: 11:[7, 75, 2] Operation: 94-92=2 Exploring Operation: 94-75=19, Resulting Numbers: [7, 92, 19] Generated Node #0,1: 11:[7, 92, 19] Operation: 94-75=19 Exploring Operation: 75-7=68, Resulting Numbers: [94, 92, 68] Generated Node #0,2: 11:[94, 92, 68] Operation: 75-7=68 Exploring Operation: 92-75=17, Resulting Numbers: [7, 94, 17] Generated Node #0,3: 11:[7, 94, 17] Operation: 92-75=17 Moving to Node #0,0 Current State: 11:[7, 75, 2], Operations: ['94-92=2'] Exploring Operation: 75-2=73, Resulting Numbers: [7, 73] Generated Node #0,0,0: 11:[7, 73] Operation: 75-2=73 Exploring Operation: 7*2=14, Resulting Numbers: [75, 14] Generated Node #0,0,1: 11:[75, 14] Operation: 7*2=14 Exploring Operation: 7+2=9, Resulting Numbers: [75, 9] Generated Node #0,0,2: 11:[75, 9] Operation: 7+2=9 Exploring Operation: 75-7=68, Resulting Numbers: [2, 68] Generated Node #0,0,3: 11:[2, 68] Operation: 75-7=68 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[7, 73], Operations: ['94-92=2', '75-2=73'] Exploring Operation: 7+73=80, Resulting Numbers: [80] 80,11 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,11 unequal: No Solution Exploring Operation: 7*73=511, Resulting Numbers: [511] 511,11 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 #0,0,2 Current State: 11:[75, 9], Operations: ['94-92=2', '7+2=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,11 unequal: No Solution Exploring Operation: 75*9=675, Resulting Numbers: [675] 675,11 unequal: No Solution Exploring Operation: 75-9=66, Resulting Numbers: [66] 66,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 11:[2, 68], Operations: ['94-92=2', '75-7=68'] Exploring Operation: 2*68=136, Resulting Numbers: [136] 136,11 unequal: No Solution Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,11 unequal: No Solution Exploring Operation: 2+68=70, Resulting Numbers: [70] 70,11 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:[75, 14], Operations: ['94-92=2', '7*2=14'] Exploring Operation: 75*14=1050, Resulting Numbers: [1050] 1050,11 unequal: No Solution Exploring Operation: 75+14=89, Resulting Numbers: [89] 89,11 unequal: No Solution Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 11:[7, 94, 17], Operations: ['92-75=17'] Exploring Operation: 17-7=10, Resulting Numbers: [94, 10] Generated Node #0,3,0: 11:[94, 10] Operation: 17-7=10 Exploring Operation: 7+94=101, Resulting Numbers: [17, 101] Generated Node #0,3,1: 11:[17, 101] Operation: 7+94=101 Exploring Operation: 94-17=77, Resulting Numbers: [7, 77] Generated Node #0,3,2: 11:[7, 77] Operation: 94-17=77 Exploring Operation: 94-7=87, Resulting Numbers: [17, 87] Generated Node #0,3,3: 11:[17, 87] Operation: 94-7=87 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 11:[7, 77], Operations: ['92-75=17', '94-17=77'] Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,11 unequal: No Solution Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[7, 75, 94, 92], Operations: [] Exploring Operation: 92-75=17, Resulting Numbers: [7, 94, 17] Generated Node #0,3: 11:[7, 94, 17] Operation: 92-75=17 Moving to Node #0,3 Current State: 11:[7, 94, 17], Operations: ['92-75=17'] Exploring Operation: 94-17=77, Resulting Numbers: [7, 77] Generated Node #0,3,2: 11:[7, 77] Operation: 94-17=77 Moving to Node #0,3,2 Current State: 11:[7, 77], Operations: ['92-75=17', '94-17=77'] Exploring Operation: 77/7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 55, 76, 69, 38 ]
62
[ "55+69=124", "76/38=2", "124/2=62" ]
Current State: 62:[55, 76, 69, 38], Operations: [] Exploring Operation: 55+69=124, Resulting Numbers: [76, 38, 124] Generated Node #2: [76, 38, 124] from Operation: 55+69=124 Current State: 62:[76, 38, 124], Operations: ['55+69=124'] Exploring Operation: 76/38=2, Resulting Numbers: [124, 2] Generated Node #3: [124, 2] from Operation: 76/38=2 Current State: 62:[124, 2], Operations: ['55+69=124', '76/38=2'] Exploring Operation: 124/2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[55, 76, 69, 38], Operations: [] Exploring Operation: 76/38=2, Resulting Numbers: [55, 69, 2] Generated Node #0,0: 62:[55, 69, 2] Operation: 76/38=2 Exploring Operation: 76-69=7, Resulting Numbers: [55, 38, 7] Generated Node #0,1: 62:[55, 38, 7] Operation: 76-69=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[55, 69, 2], Operations: ['76/38=2'] Exploring Operation: 55+2=57, Resulting Numbers: [69, 57] Generated Node #0,0,0: 62:[69, 57] Operation: 55+2=57 Exploring Operation: 69-55=14, Resulting Numbers: [2, 14] Generated Node #0,0,1: 62:[2, 14] Operation: 69-55=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[69, 57], Operations: ['76/38=2', '55+2=57'] Exploring Operation: 69-57=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 69+57=126, Resulting Numbers: [126] 126,62 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:[2, 14], Operations: ['76/38=2', '69-55=14'] Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,62 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,62 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:[55, 38, 7], Operations: ['76-69=7'] Exploring Operation: 38-7=31, Resulting Numbers: [55, 31] Generated Node #0,1,0: 62:[55, 31] Operation: 38-7=31 Exploring Operation: 55+7=62, Resulting Numbers: [38, 62] Generated Node #0,1,1: 62:[38, 62] Operation: 55+7=62 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[55, 31], Operations: ['76-69=7', '38-7=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 62:[38, 62], Operations: ['76-69=7', '55+7=62'] Exploring Operation: 38+62=100, Resulting Numbers: [100] 100,62 unequal: No Solution Exploring Operation: 62-38=24, Resulting Numbers: [24] 24,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 62, 47, 38, 62 ]
47
[ "62-62=0", "38*0=0", "47+0=47" ]
Current State: 47:[62, 47, 38, 62], Operations: [] Exploring Operation: 62-62=0, Resulting Numbers: [47, 38, 0] Generated Node #2: [47, 38, 0] from Operation: 62-62=0 Current State: 47:[47, 38, 0], Operations: ['62-62=0'] Exploring Operation: 38*0=0, Resulting Numbers: [47, 0] Generated Node #3: [47, 0] from Operation: 38*0=0 Current State: 47:[47, 0], Operations: ['62-62=0', '38*0=0'] Exploring Operation: 47+0=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[62, 47, 38, 62], Operations: [] Exploring Operation: 62-38=24, Resulting Numbers: [47, 62, 24] Generated Node #0,0: 47:[47, 62, 24] Operation: 62-38=24 Moving to Node #0,0 Current State: 47:[47, 62, 24], Operations: ['62-38=24'] Exploring Operation: 62-24=38, Resulting Numbers: [47, 38] Generated Node #0,0,0: 47:[47, 38] Operation: 62-24=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[47, 38], Operations: ['62-38=24', '62-24=38'] Exploring Operation: 47+38=85, Resulting Numbers: [85] 85,47 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, 24, 88, 50 ]
96
[ "88/4=22", "24+50=74", "22+74=96" ]
Current State: 96:[4, 24, 88, 50], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [24, 50, 22] Generated Node #2: [24, 50, 22] from Operation: 88/4=22 Current State: 96:[24, 50, 22], Operations: ['88/4=22'] Exploring Operation: 24+50=74, Resulting Numbers: [22, 74] Generated Node #3: [22, 74] from Operation: 24+50=74 Current State: 96:[22, 74], Operations: ['88/4=22', '24+50=74'] Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[4, 24, 88, 50], Operations: [] Exploring Operation: 24/4=6, Resulting Numbers: [88, 50, 6] Generated Node #0,0: 96:[88, 50, 6] Operation: 24/4=6 Exploring Operation: 4+88=92, Resulting Numbers: [24, 50, 92] Generated Node #0,1: 96:[24, 50, 92] Operation: 4+88=92 Exploring Operation: 4*24=96, Resulting Numbers: [88, 50, 96] Generated Node #0,2: 96:[88, 50, 96] Operation: 4*24=96 Exploring Operation: 88/4=22, Resulting Numbers: [24, 50, 22] Generated Node #0,3: 96:[24, 50, 22] Operation: 88/4=22 Exploring Operation: 88-50=38, Resulting Numbers: [4, 24, 38] Generated Node #0,4: 96:[4, 24, 38] Operation: 88-50=38 Moving to Node #0,3 Current State: 96:[24, 50, 22], Operations: ['88/4=22'] Exploring Operation: 50-24=26, Resulting Numbers: [22, 26] Generated Node #0,3,0: 96:[22, 26] Operation: 50-24=26 Exploring Operation: 24+50=74, Resulting Numbers: [22, 74] Generated Node #0,3,1: 96:[22, 74] Operation: 24+50=74 Exploring Operation: 50-22=28, Resulting Numbers: [24, 28] Generated Node #0,3,2: 96:[24, 28] Operation: 50-22=28 Exploring Operation: 24-22=2, Resulting Numbers: [50, 2] Generated Node #0,3,3: 96:[50, 2] Operation: 24-22=2 Exploring Operation: 24+22=46, Resulting Numbers: [50, 46] Generated Node #0,3,4: 96:[50, 46] Operation: 24+22=46 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 96:[50, 2], Operations: ['88/4=22', '24-22=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,96 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,96 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 96:[22, 26], Operations: ['88/4=22', '50-24=26'] Exploring Operation: 22+26=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 22*26=572, Resulting Numbers: [572] 572,96 unequal: No Solution Exploring Operation: 26-22=4, Resulting Numbers: [4] 4,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 96:[24, 28], Operations: ['88/4=22', '50-22=28'] Exploring Operation: 24+28=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 24*28=672, Resulting Numbers: [672] 672,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 96:[50, 46], Operations: ['88/4=22', '24+22=46'] Exploring Operation: 50*46=2300, Resulting Numbers: [2300] 2300,96 unequal: No Solution Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[4, 24, 88, 50], Operations: [] Exploring Operation: 88/4=22, Resulting Numbers: [24, 50, 22] Generated Node #0,3: 96:[24, 50, 22] Operation: 88/4=22 Moving to Node #0,3 Current State: 96:[24, 50, 22], Operations: ['88/4=22'] Exploring Operation: 24+22=46, Resulting Numbers: [50, 46] Generated Node #0,3,4: 96:[50, 46] Operation: 24+22=46 Moving to Node #0,3,4 Current State: 96:[50, 46], Operations: ['88/4=22', '24+22=46'] Exploring Operation: 50+46=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 9, 58, 29, 13 ]
88
[ "9*13=117", "58-29=29", "117-29=88" ]
Current State: 88:[9, 58, 29, 13], Operations: [] Exploring Operation: 9*13=117, Resulting Numbers: [58, 29, 117] Generated Node #2: [58, 29, 117] from Operation: 9*13=117 Current State: 88:[58, 29, 117], Operations: ['9*13=117'] Exploring Operation: 58-29=29, Resulting Numbers: [117, 29] Generated Node #3: [117, 29] from Operation: 58-29=29 Current State: 88:[117, 29], Operations: ['9*13=117', '58-29=29'] Exploring Operation: 117-29=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[9, 58, 29, 13], Operations: [] Exploring Operation: 58+29=87, Resulting Numbers: [9, 13, 87] Generated Node #0,0: 88:[9, 13, 87] Operation: 58+29=87 Exploring Operation: 58/29=2, Resulting Numbers: [9, 13, 2] Generated Node #0,1: 88:[9, 13, 2] Operation: 58/29=2 Exploring Operation: 58-13=45, Resulting Numbers: [9, 29, 45] Generated Node #0,2: 88:[9, 29, 45] Operation: 58-13=45 Exploring Operation: 58-29=29, Resulting Numbers: [9, 13, 29] Generated Node #0,3: 88:[9, 13, 29] Operation: 58-29=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[9, 13, 2], Operations: ['58/29=2'] Exploring Operation: 13-9=4, Resulting Numbers: [2, 4] Generated Node #0,1,0: 88:[2, 4] Operation: 13-9=4 Exploring Operation: 9+13=22, Resulting Numbers: [2, 22] Generated Node #0,1,1: 88:[2, 22] Operation: 9+13=22 Exploring Operation: 9+2=11, Resulting Numbers: [13, 11] Generated Node #0,1,2: 88:[13, 11] Operation: 9+2=11 Exploring Operation: 13-2=11, Resulting Numbers: [9, 11] Generated Node #0,1,3: 88:[9, 11] Operation: 13-2=11 Moving to Node #0,1,0 Current State: 88:[2, 4], Operations: ['58/29=2', '13-9=4'] Exploring Operation: 2*4=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,88 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[2, 22], Operations: ['58/29=2', '9+13=22'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,88 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Moving to Node #0,1,3 Current State: 88:[9, 11], Operations: ['58/29=2', '13-2=11'] Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,88 unequal: No Solution Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[13, 11], Operations: ['58/29=2', '9+2=11'] Exploring Operation: 13+11=24, Resulting Numbers: [24] 24,88 unequal: No Solution Exploring Operation: 13*11=143, Resulting Numbers: [143] 143,88 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[9, 13, 87], Operations: ['58+29=87'] Exploring Operation: 9+13=22, Resulting Numbers: [87, 22] Generated Node #0,0,0: 88:[87, 22] Operation: 9+13=22 Exploring Operation: 13-9=4, Resulting Numbers: [87, 4] Generated Node #0,0,1: 88:[87, 4] Operation: 13-9=4 Exploring Operation: 9+87=96, Resulting Numbers: [13, 96] Generated Node #0,0,2: 88:[13, 96] Operation: 9+87=96 Exploring Operation: 87-9=78, Resulting Numbers: [13, 78] Generated Node #0,0,3: 88:[13, 78] Operation: 87-9=78 Moving to Node #0,0,0 Current State: 88:[87, 22], Operations: ['58+29=87', '9+13=22'] Exploring Operation: 87+22=109, Resulting Numbers: [109] 109,88 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 87*22=1914, Resulting Numbers: [1914] 1914,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[87, 4], Operations: ['58+29=87', '13-9=4'] Exploring Operation: 87*4=348, Resulting Numbers: [348] 348,88 unequal: No Solution Exploring Operation: 87+4=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[13, 96], Operations: ['58+29=87', '9+87=96'] Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,88 unequal: No Solution Exploring Operation: 13+96=109, Resulting Numbers: [109] 109,88 unequal: No Solution Exploring Operation: 13*96=1248, Resulting Numbers: [1248] 1248,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[13, 78], Operations: ['58+29=87', '87-9=78'] Exploring Operation: 78-13=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 78/13=6, Resulting Numbers: [6] 6,88 unequal: No Solution Exploring Operation: 13+78=91, Resulting Numbers: [91] 91,88 unequal: No Solution Exploring Operation: 13*78=1014, Resulting Numbers: [1014] 1014,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[9, 29, 45], Operations: ['58-13=45'] Exploring Operation: 9+29=38, Resulting Numbers: [45, 38] Generated Node #0,2,0: 88:[45, 38] Operation: 9+29=38 Exploring Operation: 29-9=20, Resulting Numbers: [45, 20] Generated Node #0,2,1: 88:[45, 20] Operation: 29-9=20 Exploring Operation: 45-29=16, Resulting Numbers: [9, 16] Generated Node #0,2,2: 88:[9, 16] Operation: 45-29=16 Exploring Operation: 45/9=5, Resulting Numbers: [29, 5] Generated Node #0,2,3: 88:[29, 5] Operation: 45/9=5 Moving to Node #0,2,1 Current State: 88:[45, 20], Operations: ['58-13=45', '29-9=20'] Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 45*20=900, Resulting Numbers: [900] 900,88 unequal: No Solution Exploring Operation: 45+20=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[9, 16], Operations: ['58-13=45', '45-29=16'] Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,88 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,88 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[45, 38], Operations: ['58-13=45', '9+29=38'] Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,88 unequal: No Solution Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,88 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[29, 5], Operations: ['58-13=45', '45/9=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,88 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,88 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 88:[9, 13, 29], Operations: ['58-29=29'] Exploring Operation: 29-13=16, Resulting Numbers: [9, 16] Generated Node #0,3,0: 88:[9, 16] Operation: 29-13=16 Exploring Operation: 9+13=22, Resulting Numbers: [29, 22] Generated Node #0,3,1: 88:[29, 22] Operation: 9+13=22 Exploring Operation: 29-9=20, Resulting Numbers: [13, 20] Generated Node #0,3,2: 88:[13, 20] Operation: 29-9=20 Exploring Operation: 13+29=42, Resulting Numbers: [9, 42] Generated Node #0,3,3: 88:[9, 42] Operation: 13+29=42 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 88:[9, 42], Operations: ['58-29=29', '13+29=42'] Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 88:[13, 20], Operations: ['58-29=29', '29-9=20'] Exploring Operation: 13*20=260, Resulting Numbers: [260] 260,88 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 13+20=33, Resulting Numbers: [33] 33,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 88:[9, 16], Operations: ['58-29=29', '29-13=16'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,88 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 88:[29, 22], Operations: ['58-29=29', '9+13=22'] Exploring Operation: 29+22=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 29*22=638, Resulting Numbers: [638] 638,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 28, 64, 73, 15 ]
11
[ "28+64=92", "73+92=165", "165/15=11" ]
Current State: 11:[28, 64, 73, 15], Operations: [] Exploring Operation: 28+64=92, Resulting Numbers: [73, 15, 92] Generated Node #2: [73, 15, 92] from Operation: 28+64=92 Current State: 11:[73, 15, 92], Operations: ['28+64=92'] Exploring Operation: 73+92=165, Resulting Numbers: [15, 165] Generated Node #3: [15, 165] from Operation: 73+92=165 Current State: 11:[15, 165], Operations: ['28+64=92', '73+92=165'] Exploring Operation: 165/15=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[28, 64, 73, 15], Operations: [] Exploring Operation: 73-64=9, Resulting Numbers: [28, 15, 9] Generated Node #0,0: 11:[28, 15, 9] Operation: 73-64=9 Exploring Operation: 64-15=49, Resulting Numbers: [28, 73, 49] Generated Node #0,1: 11:[28, 73, 49] Operation: 64-15=49 Exploring Operation: 73-28=45, Resulting Numbers: [64, 15, 45] Generated Node #0,2: 11:[64, 15, 45] Operation: 73-28=45 Exploring Operation: 64-28=36, Resulting Numbers: [73, 15, 36] Generated Node #0,3: 11:[73, 15, 36] Operation: 64-28=36 Exploring Operation: 28-15=13, Resulting Numbers: [64, 73, 13] Generated Node #0,4: 11:[64, 73, 13] Operation: 28-15=13 Moving to Node #0,0 Current State: 11:[28, 15, 9], Operations: ['73-64=9'] Exploring Operation: 28+9=37, Resulting Numbers: [15, 37] Generated Node #0,0,0: 11:[15, 37] Operation: 28+9=37 Exploring Operation: 15+9=24, Resulting Numbers: [28, 24] Generated Node #0,0,1: 11:[28, 24] Operation: 15+9=24 Exploring Operation: 28-15=13, Resulting Numbers: [9, 13] Generated Node #0,0,2: 11:[9, 13] Operation: 28-15=13 Exploring Operation: 28-9=19, Resulting Numbers: [15, 19] Generated Node #0,0,3: 11:[15, 19] Operation: 28-9=19 Exploring Operation: 15-9=6, Resulting Numbers: [28, 6] Generated Node #0,0,4: 11:[28, 6] Operation: 15-9=6 Moving to Node #0,3 Current State: 11:[73, 15, 36], Operations: ['64-28=36'] Exploring Operation: 73+36=109, Resulting Numbers: [15, 109] Generated Node #0,3,0: 11:[15, 109] Operation: 73+36=109 Exploring Operation: 73+15=88, Resulting Numbers: [36, 88] Generated Node #0,3,1: 11:[36, 88] Operation: 73+15=88 Exploring Operation: 36-15=21, Resulting Numbers: [73, 21] Generated Node #0,3,2: 11:[73, 21] Operation: 36-15=21 Exploring Operation: 73-36=37, Resulting Numbers: [15, 37] Generated Node #0,3,3: 11:[15, 37] Operation: 73-36=37 Exploring Operation: 73-15=58, Resulting Numbers: [36, 58] Generated Node #0,3,4: 11:[36, 58] Operation: 73-15=58 Moving to Node #0,2 Current State: 11:[64, 15, 45], Operations: ['73-28=45'] Exploring Operation: 64+15=79, Resulting Numbers: [45, 79] Generated Node #0,2,0: 11:[45, 79] Operation: 64+15=79 Exploring Operation: 64-45=19, Resulting Numbers: [15, 19] Generated Node #0,2,1: 11:[15, 19] Operation: 64-45=19 Exploring Operation: 45-15=30, Resulting Numbers: [64, 30] Generated Node #0,2,2: 11:[64, 30] Operation: 45-15=30 Exploring Operation: 64-15=49, Resulting Numbers: [45, 49] Generated Node #0,2,3: 11:[45, 49] Operation: 64-15=49 Exploring Operation: 45/15=3, Resulting Numbers: [64, 3] Generated Node #0,2,4: 11:[64, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 11:[15, 19], Operations: ['73-28=45', '64-45=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,11 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 11:[64, 3], Operations: ['73-28=45', '45/15=3'] Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,11 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,11 unequal: No Solution Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 11:[64, 30], Operations: ['73-28=45', '45-15=30'] Exploring Operation: 64+30=94, Resulting Numbers: [94] 94,11 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 64*30=1920, Resulting Numbers: [1920] 1920,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 11:[45, 49], Operations: ['73-28=45', '64-15=49'] Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,11 unequal: No Solution Exploring Operation: 45*49=2205, Resulting Numbers: [2205] 2205,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 11:[45, 79], Operations: ['73-28=45', '64+15=79'] Exploring Operation: 45+79=124, Resulting Numbers: [124] 124,11 unequal: No Solution Exploring Operation: 45*79=3555, Resulting Numbers: [3555] 3555,11 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,11 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: 11:[28, 73, 49], Operations: ['64-15=49'] Exploring Operation: 73-28=45, Resulting Numbers: [49, 45] Generated Node #0,1,0: 11:[49, 45] Operation: 73-28=45 Exploring Operation: 28+49=77, Resulting Numbers: [73, 77] Generated Node #0,1,1: 11:[73, 77] Operation: 28+49=77 Exploring Operation: 28+73=101, Resulting Numbers: [49, 101] Generated Node #0,1,2: 11:[49, 101] Operation: 28+73=101 Exploring Operation: 49-28=21, Resulting Numbers: [73, 21] Generated Node #0,1,3: 11:[73, 21] Operation: 49-28=21 Exploring Operation: 73-49=24, Resulting Numbers: [28, 24] Generated Node #0,1,4: 11:[28, 24] Operation: 73-49=24 Moving to Node #0,4 Current State: 11:[64, 73, 13], Operations: ['28-15=13'] Exploring Operation: 64+13=77, Resulting Numbers: [73, 77] Generated Node #0,4,0: 11:[73, 77] Operation: 64+13=77 Exploring Operation: 64-13=51, Resulting Numbers: [73, 51] Generated Node #0,4,1: 11:[73, 51] Operation: 64-13=51 Exploring Operation: 73-64=9, Resulting Numbers: [13, 9] Generated Node #0,4,2: 11:[13, 9] Operation: 73-64=9 Exploring Operation: 64+73=137, Resulting Numbers: [13, 137] Generated Node #0,4,3: 11:[13, 137] Operation: 64+73=137 Exploring Operation: 73-13=60, Resulting Numbers: [64, 60] Generated Node #0,4,4: 11:[64, 60] Operation: 73-13=60 Moving to Node #0,0,2 Current State: 11:[9, 13], Operations: ['73-64=9', '28-15=13'] Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,11 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,4,2 Current State: 11:[13, 9], Operations: ['28-15=13', '73-64=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,11 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,11 unequal: No Solution Moving to Node #0,0,3 Current State: 11:[15, 19], Operations: ['73-64=9', '28-9=19'] Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,11 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,11 unequal: No Solution Moving to Node #0,0,4 Current State: 11:[28, 6], Operations: ['73-64=9', '15-9=6'] Exploring Operation: 28-6=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 28+6=34, Resulting Numbers: [34] 34,11 unequal: No Solution Exploring Operation: 28*6=168, Resulting Numbers: [168] 168,11 unequal: No Solution Moving to Node #0,3,3 Current State: 11:[15, 37], Operations: ['64-28=36', '73-36=37'] Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,11 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[28, 24], Operations: ['73-64=9', '15+9=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,11 unequal: No Solution Moving to Node #0,1,4 Current State: 11:[28, 24], Operations: ['64-15=49', '73-49=24'] Exploring Operation: 28+24=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 28*24=672, Resulting Numbers: [672] 672,11 unequal: No Solution Exploring Operation: 28-24=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[15, 37], Operations: ['73-64=9', '28+9=37'] Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,11 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,11 unequal: No Solution Moving to Node #0,3,2 Current State: 11:[73, 21], Operations: ['64-28=36', '36-15=21'] Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,11 unequal: No Solution Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,11 unequal: No Solution Moving to Node #0,1,3 Current State: 11:[73, 21], Operations: ['64-15=49', '49-28=21'] Exploring Operation: 73*21=1533, Resulting Numbers: [1533] 1533,11 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 73+21=94, Resulting Numbers: [94] 94,11 unequal: No Solution Moving to Node #0,1,0 Current State: 11:[49, 45], Operations: ['64-15=49', '73-28=45'] Exploring Operation: 49*45=2205, Resulting Numbers: [2205] 2205,11 unequal: No Solution Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,11 unequal: No Solution Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,11 unequal: No Solution Moving to Node #0,3,4 Current State: 11:[36, 58], Operations: ['64-28=36', '73-15=58'] Exploring Operation: 58-36=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 36*58=2088, Resulting Numbers: [2088] 2088,11 unequal: No Solution Exploring Operation: 36+58=94, Resulting Numbers: [94] 94,11 unequal: No Solution Moving to Node #0,4,1 Current State: 11:[73, 51], Operations: ['28-15=13', '64-13=51'] Exploring Operation: 73-51=22, Resulting Numbers: [22] 22,11 unequal: No Solution Exploring Operation: 73+51=124, Resulting Numbers: [124] 124,11 unequal: No Solution Exploring Operation: 73*51=3723, Resulting Numbers: [3723] 3723,11 unequal: No Solution Moving to Node #0,4,4 Current State: 11:[64, 60], Operations: ['28-15=13', '73-13=60'] Exploring Operation: 64*60=3840, Resulting Numbers: [3840] 3840,11 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 64+60=124, Resulting Numbers: [124] 124,11 unequal: No Solution Moving to Node #0,3,1 Current State: 11:[36, 88], Operations: ['64-28=36', '73+15=88'] Exploring Operation: 36+88=124, Resulting Numbers: [124] 124,11 unequal: No Solution Exploring Operation: 88-36=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 36*88=3168, Resulting Numbers: [3168] 3168,11 unequal: No Solution Moving to Node #0,3,0 Current State: 11:[15, 109], Operations: ['64-28=36', '73+36=109'] Exploring Operation: 15+109=124, Resulting Numbers: [124] 124,11 unequal: No Solution Exploring Operation: 15*109=1635, Resulting Numbers: [1635] 1635,11 unequal: No Solution Exploring Operation: 109-15=94, Resulting Numbers: [94] 94,11 unequal: No Solution Moving to Node #0,4,0 Current State: 11:[73, 77], Operations: ['28-15=13', '64+13=77'] Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[73, 77], Operations: ['64-15=49', '28+49=77'] Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,11 unequal: No Solution Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,11 unequal: No Solution Moving to Node #0,4,3 Current State: 11:[13, 137], Operations: ['28-15=13', '64+73=137'] Exploring Operation: 137-13=124, Resulting Numbers: [124] 124,11 unequal: No Solution Exploring Operation: 13+137=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 13*137=1781, Resulting Numbers: [1781] 1781,11 unequal: No Solution Moving to Node #0,1,2 Current State: 11:[49, 101], Operations: ['64-15=49', '28+73=101'] Exploring Operation: 101-49=52, Resulting Numbers: [52] 52,11 unequal: No Solution Exploring Operation: 49+101=150, Resulting Numbers: [150] 150,11 unequal: No Solution Exploring Operation: 49*101=4949, Resulting Numbers: [4949] 4949,11 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 2, 38, 27, 85 ]
72
[ "2+38=40", "27+85=112", "112-40=72" ]
Current State: 72:[2, 38, 27, 85], Operations: [] Exploring Operation: 2+38=40, Resulting Numbers: [27, 85, 40] Generated Node #2: [27, 85, 40] from Operation: 2+38=40 Current State: 72:[27, 85, 40], Operations: ['2+38=40'] Exploring Operation: 27+85=112, Resulting Numbers: [40, 112] Generated Node #3: [40, 112] from Operation: 27+85=112 Current State: 72:[40, 112], Operations: ['2+38=40', '27+85=112'] Exploring Operation: 112-40=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[2, 38, 27, 85], Operations: [] Exploring Operation: 38-2=36, Resulting Numbers: [27, 85, 36] Generated Node #0,0: 72:[27, 85, 36] Operation: 38-2=36 Exploring Operation: 85-2=83, Resulting Numbers: [38, 27, 83] Generated Node #0,1: 72:[38, 27, 83] Operation: 85-2=83 Exploring Operation: 27-2=25, Resulting Numbers: [38, 85, 25] Generated Node #0,2: 72:[38, 85, 25] Operation: 27-2=25 Exploring Operation: 38-27=11, Resulting Numbers: [2, 85, 11] Generated Node #0,3: 72:[2, 85, 11] Operation: 38-27=11 Exploring Operation: 85-38=47, Resulting Numbers: [2, 27, 47] Generated Node #0,4: 72:[2, 27, 47] Operation: 85-38=47 Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[2, 85, 11], Operations: ['38-27=11'] Exploring Operation: 11-2=9, Resulting Numbers: [85, 9] Generated Node #0,3,0: 72:[85, 9] Operation: 11-2=9 Exploring Operation: 85-11=74, Resulting Numbers: [2, 74] Generated Node #0,3,1: 72:[2, 74] Operation: 85-11=74 Exploring Operation: 2+11=13, Resulting Numbers: [85, 13] Generated Node #0,3,2: 72:[85, 13] Operation: 2+11=13 Exploring Operation: 2*11=22, Resulting Numbers: [85, 22] Generated Node #0,3,3: 72:[85, 22] Operation: 2*11=22 Exploring Operation: 85-2=83, Resulting Numbers: [11, 83] Generated Node #0,3,4: 72:[11, 83] Operation: 85-2=83 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[2, 74], Operations: ['38-27=11', '85-11=74'] Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,72 unequal: No Solution Exploring Operation: 2*74=148, Resulting Numbers: [148] 148,72 unequal: No Solution Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[2, 38, 27, 85], Operations: [] Exploring Operation: 38-27=11, Resulting Numbers: [2, 85, 11] Generated Node #0,3: 72:[2, 85, 11] Operation: 38-27=11 Moving to Node #0,3 Current State: 72:[2, 85, 11], Operations: ['38-27=11'] Exploring Operation: 85-11=74, Resulting Numbers: [2, 74] Generated Node #0,3,1: 72:[2, 74] Operation: 85-11=74 Moving to Node #0,3,1 Current State: 72:[2, 74], Operations: ['38-27=11', '85-11=74'] Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 28, 36, 13, 40 ]
99
[ "40-36=4", "28*4=112", "112-13=99" ]
Current State: 99:[28, 36, 13, 40], Operations: [] Exploring Operation: 40-36=4, Resulting Numbers: [28, 13, 4] Generated Node #2: [28, 13, 4] from Operation: 40-36=4 Current State: 99:[28, 13, 4], Operations: ['40-36=4'] Exploring Operation: 28*4=112, Resulting Numbers: [13, 112] Generated Node #3: [13, 112] from Operation: 28*4=112 Current State: 99:[13, 112], Operations: ['40-36=4', '28*4=112'] Exploring Operation: 112-13=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[28, 36, 13, 40], Operations: [] Exploring Operation: 40-28=12, Resulting Numbers: [36, 13, 12] Generated Node #0,0: 99:[36, 13, 12] Operation: 40-28=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[36, 13, 12], Operations: ['40-28=12'] Exploring Operation: 36/12=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 99:[13, 3] Operation: 36/12=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[13, 3], Operations: ['40-28=12', '36/12=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 79, 84, 48, 6 ]
45
[ "79-48=31", "84/6=14", "31+14=45" ]
Current State: 45:[79, 84, 48, 6], Operations: [] Exploring Operation: 79-48=31, Resulting Numbers: [84, 6, 31] Generated Node #2: [84, 6, 31] from Operation: 79-48=31 Current State: 45:[84, 6, 31], Operations: ['79-48=31'] Exploring Operation: 84/6=14, Resulting Numbers: [31, 14] Generated Node #3: [31, 14] from Operation: 84/6=14 Current State: 45:[31, 14], Operations: ['79-48=31', '84/6=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[79, 84, 48, 6], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [48, 6, 5] Generated Node #0,0: 45:[48, 6, 5] Operation: 84-79=5 Moving to Node #0,0 Current State: 45:[48, 6, 5], Operations: ['84-79=5'] Exploring Operation: 48/6=8, Resulting Numbers: [5, 8] Generated Node #0,0,0: 45:[5, 8] Operation: 48/6=8 Moving to Node #0,0,0 Current State: 45:[5, 8], Operations: ['84-79=5', '48/6=8'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,45 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 64, 53, 56, 14 ]
53
[ "64-53=11", "56-14=42", "11+42=53" ]
Current State: 53:[64, 53, 56, 14], Operations: [] Exploring Operation: 64-53=11, Resulting Numbers: [56, 14, 11] Generated Node #2: [56, 14, 11] from Operation: 64-53=11 Current State: 53:[56, 14, 11], Operations: ['64-53=11'] Exploring Operation: 56-14=42, Resulting Numbers: [11, 42] Generated Node #3: [11, 42] from Operation: 56-14=42 Current State: 53:[11, 42], Operations: ['64-53=11', '56-14=42'] Exploring Operation: 11+42=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[64, 53, 56, 14], Operations: [] Exploring Operation: 56-14=42, Resulting Numbers: [64, 53, 42] Generated Node #0,0: 53:[64, 53, 42] Operation: 56-14=42 Exploring Operation: 64-14=50, Resulting Numbers: [53, 56, 50] Generated Node #0,1: 53:[53, 56, 50] Operation: 64-14=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[53, 56, 50], Operations: ['64-14=50'] Exploring Operation: 56-53=3, Resulting Numbers: [50, 3] Generated Node #0,1,0: 53:[50, 3] Operation: 56-53=3 Exploring Operation: 56-50=6, Resulting Numbers: [53, 6] Generated Node #0,1,1: 53:[53, 6] Operation: 56-50=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[53, 6], Operations: ['64-14=50', '56-50=6'] Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,53 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[50, 3], Operations: ['64-14=50', '56-53=3'] Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[64, 53, 56, 14], Operations: [] Exploring Operation: 64-14=50, Resulting Numbers: [53, 56, 50] Generated Node #0,1: 53:[53, 56, 50] Operation: 64-14=50 Moving to Node #0,1 Current State: 53:[53, 56, 50], Operations: ['64-14=50'] Exploring Operation: 56-53=3, Resulting Numbers: [50, 3] Generated Node #0,1,0: 53:[50, 3] Operation: 56-53=3 Moving to Node #0,1,0 Current State: 53:[50, 3], Operations: ['64-14=50', '56-53=3'] Exploring Operation: 50+3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 76, 21, 33, 12 ]
52
[ "76+21=97", "33+12=45", "97-45=52" ]
Current State: 52:[76, 21, 33, 12], Operations: [] Exploring Operation: 76+21=97, Resulting Numbers: [33, 12, 97] Generated Node #2: [33, 12, 97] from Operation: 76+21=97 Current State: 52:[33, 12, 97], Operations: ['76+21=97'] Exploring Operation: 33+12=45, Resulting Numbers: [97, 45] Generated Node #3: [97, 45] from Operation: 33+12=45 Current State: 52:[97, 45], Operations: ['76+21=97', '33+12=45'] Exploring Operation: 97-45=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[76, 21, 33, 12], Operations: [] Exploring Operation: 76-12=64, Resulting Numbers: [21, 33, 64] Generated Node #0,0: 52:[21, 33, 64] Operation: 76-12=64 Exploring Operation: 76-33=43, Resulting Numbers: [21, 12, 43] Generated Node #0,1: 52:[21, 12, 43] Operation: 76-33=43 Exploring Operation: 76-21=55, Resulting Numbers: [33, 12, 55] Generated Node #0,2: 52:[33, 12, 55] Operation: 76-21=55 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[33, 12, 55], Operations: ['76-21=55'] Exploring Operation: 33-12=21, Resulting Numbers: [55, 21] Generated Node #0,2,0: 52:[55, 21] Operation: 33-12=21 Exploring Operation: 55-33=22, Resulting Numbers: [12, 22] Generated Node #0,2,1: 52:[12, 22] Operation: 55-33=22 Exploring Operation: 33+12=45, Resulting Numbers: [55, 45] Generated Node #0,2,2: 52:[55, 45] Operation: 33+12=45 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 52:[12, 22], Operations: ['76-21=55', '55-33=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[55, 21], Operations: ['76-21=55', '33-12=21'] Exploring Operation: 55*21=1155, Resulting Numbers: [1155] 1155,52 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 55+21=76, Resulting Numbers: [76] 76,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 52:[55, 45], Operations: ['76-21=55', '33+12=45'] Exploring Operation: 55*45=2475, Resulting Numbers: [2475] 2475,52 unequal: No Solution Exploring Operation: 55+45=100, Resulting Numbers: [100] 100,52 unequal: No Solution Exploring Operation: 55-45=10, Resulting Numbers: [10] 10,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[21, 12, 43], Operations: ['76-33=43'] Exploring Operation: 43-12=31, Resulting Numbers: [21, 31] Generated Node #0,1,0: 52:[21, 31] Operation: 43-12=31 Exploring Operation: 12+43=55, Resulting Numbers: [21, 55] Generated Node #0,1,1: 52:[21, 55] Operation: 12+43=55 Exploring Operation: 43-21=22, Resulting Numbers: [12, 22] Generated Node #0,1,2: 52:[12, 22] Operation: 43-21=22 Moving to Node #0,1,2 Current State: 52:[12, 22], Operations: ['76-33=43', '43-21=22'] Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[21, 55], Operations: ['76-33=43', '12+43=55'] Exploring Operation: 21*55=1155, Resulting Numbers: [1155] 1155,52 unequal: No Solution Exploring Operation: 21+55=76, Resulting Numbers: [76] 76,52 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[21, 31], Operations: ['76-33=43', '43-12=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,52 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[76, 21, 33, 12], Operations: [] Exploring Operation: 76-33=43, Resulting Numbers: [21, 12, 43] Generated Node #0,1: 52:[21, 12, 43] Operation: 76-33=43 Moving to Node #0,1 Current State: 52:[21, 12, 43], Operations: ['76-33=43'] Exploring Operation: 43-12=31, Resulting Numbers: [21, 31] Generated Node #0,1,0: 52:[21, 31] Operation: 43-12=31 Moving to Node #0,1,0 Current State: 52:[21, 31], Operations: ['76-33=43', '43-12=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 22, 78, 62, 16 ]
22
[ "22+78=100", "62+16=78", "100-78=22" ]
Current State: 22:[22, 78, 62, 16], Operations: [] Exploring Operation: 22+78=100, Resulting Numbers: [62, 16, 100] Generated Node #2: [62, 16, 100] from Operation: 22+78=100 Current State: 22:[62, 16, 100], Operations: ['22+78=100'] Exploring Operation: 62+16=78, Resulting Numbers: [100, 78] Generated Node #3: [100, 78] from Operation: 62+16=78 Current State: 22:[100, 78], Operations: ['22+78=100', '62+16=78'] Exploring Operation: 100-78=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[22, 78, 62, 16], Operations: [] Exploring Operation: 78-22=56, Resulting Numbers: [62, 16, 56] Generated Node #0,0: 22:[62, 16, 56] Operation: 78-22=56 Exploring Operation: 78-62=16, Resulting Numbers: [22, 16, 16] Generated Node #0,1: 22:[22, 16, 16] Operation: 78-62=16 Moving to Node #0,1 Current State: 22:[22, 16, 16], Operations: ['78-62=16'] Exploring Operation: 16/16=1, Resulting Numbers: [22, 1] Generated Node #0,1,0: 22:[22, 1] Operation: 16/16=1 Exploring Operation: 16-16=0, Resulting Numbers: [22, 0] Generated Node #0,1,1: 22:[22, 0] Operation: 16-16=0 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[22, 1], Operations: ['78-62=16', '16/16=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[22, 78, 62, 16], Operations: [] Exploring Operation: 78-62=16, Resulting Numbers: [22, 16, 16] Generated Node #0,1: 22:[22, 16, 16] Operation: 78-62=16 Moving to Node #0,1 Current State: 22:[22, 16, 16], Operations: ['78-62=16'] Exploring Operation: 16/16=1, Resulting Numbers: [22, 1] Generated Node #0,1,0: 22:[22, 1] Operation: 16/16=1 Moving to Node #0,1,0 Current State: 22:[22, 1], Operations: ['78-62=16', '16/16=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 81, 43, 78, 79 ]
12
[ "81-78=3", "79-43=36", "36/3=12" ]
Current State: 12:[81, 43, 78, 79], Operations: [] Exploring Operation: 81-78=3, Resulting Numbers: [43, 79, 3] Generated Node #2: [43, 79, 3] from Operation: 81-78=3 Current State: 12:[43, 79, 3], Operations: ['81-78=3'] Exploring Operation: 79-43=36, Resulting Numbers: [3, 36] Generated Node #3: [3, 36] from Operation: 79-43=36 Current State: 12:[3, 36], Operations: ['81-78=3', '79-43=36'] Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[81, 43, 78, 79], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [43, 78, 2] Generated Node #0,0: 12:[43, 78, 2] Operation: 81-79=2 Moving to Node #0,0 Current State: 12:[43, 78, 2], Operations: ['81-79=2'] Exploring Operation: 78-43=35, Resulting Numbers: [2, 35] Generated Node #0,0,0: 12:[2, 35] Operation: 78-43=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[2, 35], Operations: ['81-79=2', '78-43=35'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,12 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
[ 87, 60, 18, 6 ]
95
[ "87+18=105", "60/6=10", "105-10=95" ]
Current State: 95:[87, 60, 18, 6], Operations: [] Exploring Operation: 87+18=105, Resulting Numbers: [60, 6, 105] Generated Node #2: [60, 6, 105] from Operation: 87+18=105 Current State: 95:[60, 6, 105], Operations: ['87+18=105'] Exploring Operation: 60/6=10, Resulting Numbers: [105, 10] Generated Node #3: [105, 10] from Operation: 60/6=10 Current State: 95:[105, 10], Operations: ['87+18=105', '60/6=10'] Exploring Operation: 105-10=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[87, 60, 18, 6], Operations: [] Exploring Operation: 87-60=27, Resulting Numbers: [18, 6, 27] Generated Node #0,0: 95:[18, 6, 27] Operation: 87-60=27 Exploring Operation: 60/6=10, Resulting Numbers: [87, 18, 10] Generated Node #0,1: 95:[87, 18, 10] Operation: 60/6=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 95:[18, 6, 27], Operations: ['87-60=27'] Exploring Operation: 27-6=21, Resulting Numbers: [18, 21] Generated Node #0,0,0: 95:[18, 21] Operation: 27-6=21 Exploring Operation: 27-18=9, Resulting Numbers: [6, 9] Generated Node #0,0,1: 95:[6, 9] Operation: 27-18=9 Moving to Node #0,0,0 Current State: 95:[18, 21], Operations: ['87-60=27', '27-6=21'] Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,95 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[6, 9], Operations: ['87-60=27', '27-18=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[87, 18, 10], Operations: ['60/6=10'] Exploring Operation: 87+10=97, Resulting Numbers: [18, 97] Generated Node #0,1,0: 95:[18, 97] Operation: 87+10=97 Exploring Operation: 18-10=8, Resulting Numbers: [87, 8] Generated Node #0,1,1: 95:[87, 8] Operation: 18-10=8 Moving to Node #0,1,0 Current State: 95:[18, 97], Operations: ['60/6=10', '87+10=97'] Exploring Operation: 97-18=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 18+97=115, Resulting Numbers: [115] 115,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[87, 8], Operations: ['60/6=10', '18-10=8'] Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,95 unequal: No Solution Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[87, 60, 18, 6], Operations: [] Exploring Operation: 60/6=10, Resulting Numbers: [87, 18, 10] Generated Node #0,1: 95:[87, 18, 10] Operation: 60/6=10 Moving to Node #0,1 Current State: 95:[87, 18, 10], Operations: ['60/6=10'] Exploring Operation: 18-10=8, Resulting Numbers: [87, 8] Generated Node #0,1,1: 95:[87, 8] Operation: 18-10=8 Moving to Node #0,1,1 Current State: 95:[87, 8], Operations: ['60/6=10', '18-10=8'] Exploring Operation: 87+8=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_2
sum_heuristic
[ 1, 10, 2, 42 ]
96
[ "1+2=3", "42-10=32", "3*32=96" ]
Current State: 96:[1, 10, 2, 42], Operations: [] Exploring Operation: 1+2=3, Resulting Numbers: [10, 42, 3] Generated Node #2: [10, 42, 3] from Operation: 1+2=3 Current State: 96:[10, 42, 3], Operations: ['1+2=3'] Exploring Operation: 42-10=32, Resulting Numbers: [3, 32] Generated Node #3: [3, 32] from Operation: 42-10=32 Current State: 96:[3, 32], Operations: ['1+2=3', '42-10=32'] Exploring Operation: 3*32=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[1, 10, 2, 42], Operations: [] Exploring Operation: 10+42=52, Resulting Numbers: [1, 2, 52] Generated Node #0,0: 96:[1, 2, 52] Operation: 10+42=52 Exploring Operation: 42/2=21, Resulting Numbers: [1, 10, 21] Generated Node #0,1: 96:[1, 10, 21] Operation: 42/2=21 Exploring Operation: 42-10=32, Resulting Numbers: [1, 2, 32] Generated Node #0,2: 96:[1, 2, 32] Operation: 42-10=32 Exploring Operation: 1+10=11, Resulting Numbers: [2, 42, 11] Generated Node #0,3: 96:[2, 42, 11] Operation: 1+10=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[1, 2, 32], Operations: ['42-10=32'] Exploring Operation: 1*32=32, Resulting Numbers: [2, 32] Generated Node #0,2,0: 96:[2, 32] Operation: 1*32=32 Exploring Operation: 1+2=3, Resulting Numbers: [32, 3] Generated Node #0,2,1: 96:[32, 3] Operation: 1+2=3 Exploring Operation: 1*2=2, Resulting Numbers: [32, 2] Generated Node #0,2,2: 96:[32, 2] Operation: 1*2=2 Exploring Operation: 2/1=2, Resulting Numbers: [32, 2] Generated Node #0,2,3: 96:[32, 2] Operation: 2/1=2 Moving to Node #0,2,0 Current State: 96:[2, 32], Operations: ['42-10=32', '1*32=32'] Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,96 unequal: No Solution Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[32, 2], Operations: ['42-10=32', '1*2=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,96 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[32, 3], Operations: ['42-10=32', '1+2=3'] Exploring Operation: 32+3=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,96 unequal: No Solution Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[1, 10, 2, 42], Operations: [] Exploring Operation: 42-10=32, Resulting Numbers: [1, 2, 32] Generated Node #0,2: 96:[1, 2, 32] Operation: 42-10=32 Moving to Node #0,2 Current State: 96:[1, 2, 32], Operations: ['42-10=32'] Exploring Operation: 1+2=3, Resulting Numbers: [32, 3] Generated Node #0,2,1: 96:[32, 3] Operation: 1+2=3 Moving to Node #0,2,1 Current State: 96:[32, 3], Operations: ['42-10=32', '1+2=3'] Exploring Operation: 32*3=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
sum_heuristic
[ 34, 5, 7, 76 ]
59
[ "34-7=27", "5*27=135", "135-76=59" ]
Current State: 59:[34, 5, 7, 76], Operations: [] Exploring Operation: 34-7=27, Resulting Numbers: [5, 76, 27] Generated Node #2: [5, 76, 27] from Operation: 34-7=27 Current State: 59:[5, 76, 27], Operations: ['34-7=27'] Exploring Operation: 5*27=135, Resulting Numbers: [76, 135] Generated Node #3: [76, 135] from Operation: 5*27=135 Current State: 59:[76, 135], Operations: ['34-7=27', '5*27=135'] Exploring Operation: 135-76=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[34, 5, 7, 76], Operations: [] Exploring Operation: 34+5=39, Resulting Numbers: [7, 76, 39] Generated Node #0,0: 59:[7, 76, 39] Operation: 34+5=39 Exploring Operation: 5*7=35, Resulting Numbers: [34, 76, 35] Generated Node #0,1: 59:[34, 76, 35] Operation: 5*7=35 Moving to Node #0,1 Current State: 59:[34, 76, 35], Operations: ['5*7=35'] Exploring Operation: 34+35=69, Resulting Numbers: [76, 69] Generated Node #0,1,0: 59:[76, 69] Operation: 34+35=69 Exploring Operation: 76-34=42, Resulting Numbers: [35, 42] Generated Node #0,1,1: 59:[35, 42] Operation: 76-34=42 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 59:[76, 69], Operations: ['5*7=35', '34+35=69'] Exploring Operation: 76-69=7, Resulting Numbers: [7] 7,59 unequal: No Solution Exploring Operation: 76+69=145, Resulting Numbers: [145] 145,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[35, 42], Operations: ['5*7=35', '76-34=42'] Exploring Operation: 35+42=77, Resulting Numbers: [77] 77,59 unequal: No Solution Exploring Operation: 42-35=7, Resulting Numbers: [7] 7,59 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: 59:[7, 76, 39], Operations: ['34+5=39'] Exploring Operation: 7+39=46, Resulting Numbers: [76, 46] Generated Node #0,0,0: 59:[76, 46] Operation: 7+39=46 Exploring Operation: 76-7=69, Resulting Numbers: [39, 69] Generated Node #0,0,1: 59:[39, 69] Operation: 76-7=69 Moving to Node #0,0,0 Current State: 59:[76, 46], Operations: ['34+5=39', '7+39=46'] Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,59 unequal: No Solution Exploring Operation: 76+46=122, Resulting Numbers: [122] 122,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[39, 69], Operations: ['34+5=39', '76-7=69'] Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,59 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,59 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 16, 45, 41, 21 ]
81
[ "16+45=61", "41-21=20", "61+20=81" ]
Current State: 81:[16, 45, 41, 21], Operations: [] Exploring Operation: 16+45=61, Resulting Numbers: [41, 21, 61] Generated Node #2: [41, 21, 61] from Operation: 16+45=61 Current State: 81:[41, 21, 61], Operations: ['16+45=61'] Exploring Operation: 41-21=20, Resulting Numbers: [61, 20] Generated Node #3: [61, 20] from Operation: 41-21=20 Current State: 81:[61, 20], Operations: ['16+45=61', '41-21=20'] Exploring Operation: 61+20=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[16, 45, 41, 21], Operations: [] Exploring Operation: 45+41=86, Resulting Numbers: [16, 21, 86] Generated Node #0,0: 81:[16, 21, 86] Operation: 45+41=86 Exploring Operation: 45-41=4, Resulting Numbers: [16, 21, 4] Generated Node #0,1: 81:[16, 21, 4] Operation: 45-41=4 Moving to Node #0,1 Current State: 81:[16, 21, 4], Operations: ['45-41=4'] Exploring Operation: 16/4=4, Resulting Numbers: [21, 4] Generated Node #0,1,0: 81:[21, 4] Operation: 16/4=4 Exploring Operation: 21-16=5, Resulting Numbers: [4, 5] Generated Node #0,1,1: 81:[4, 5] Operation: 21-16=5 Moving to Node #0,0 Current State: 81:[16, 21, 86], Operations: ['45+41=86'] Exploring Operation: 16+21=37, Resulting Numbers: [86, 37] Generated Node #0,0,0: 81:[86, 37] Operation: 16+21=37 Exploring Operation: 21-16=5, Resulting Numbers: [86, 5] Generated Node #0,0,1: 81:[86, 5] Operation: 21-16=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[86, 5], Operations: ['45+41=86', '21-16=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[16, 45, 41, 21], Operations: [] Exploring Operation: 45+41=86, Resulting Numbers: [16, 21, 86] Generated Node #0,0: 81:[16, 21, 86] Operation: 45+41=86 Moving to Node #0,0 Current State: 81:[16, 21, 86], Operations: ['45+41=86'] Exploring Operation: 21-16=5, Resulting Numbers: [86, 5] Generated Node #0,0,1: 81:[86, 5] Operation: 21-16=5 Moving to Node #0,0,1 Current State: 81:[86, 5], Operations: ['45+41=86', '21-16=5'] Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 80, 65, 2, 63 ]
81
[ "65-2=63", "63/63=1", "80+1=81" ]
Current State: 81:[80, 65, 2, 63], Operations: [] Exploring Operation: 65-2=63, Resulting Numbers: [80, 63, 63] Generated Node #2: [80, 63, 63] from Operation: 65-2=63 Current State: 81:[80, 63, 63], Operations: ['65-2=63'] Exploring Operation: 63/63=1, Resulting Numbers: [80, 1] Generated Node #3: [80, 1] from Operation: 63/63=1 Current State: 81:[80, 1], Operations: ['65-2=63', '63/63=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[80, 65, 2, 63], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [65, 2, 17] Generated Node #0,0: 81:[65, 2, 17] Operation: 80-63=17 Exploring Operation: 80-65=15, Resulting Numbers: [2, 63, 15] Generated Node #0,1: 81:[2, 63, 15] Operation: 80-65=15 Exploring Operation: 65+2=67, Resulting Numbers: [80, 63, 67] Generated Node #0,2: 81:[80, 63, 67] Operation: 65+2=67 Exploring Operation: 65-63=2, Resulting Numbers: [80, 2, 2] Generated Node #0,3: 81:[80, 2, 2] Operation: 65-63=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[80, 2, 2], Operations: ['65-63=2'] Exploring Operation: 2*2=4, Resulting Numbers: [80, 4] Generated Node #0,3,0: 81:[80, 4] Operation: 2*2=4 Exploring Operation: 80+2=82, Resulting Numbers: [2, 82] Generated Node #0,3,1: 81:[2, 82] Operation: 80+2=82 Exploring Operation: 80+2=82, Resulting Numbers: [2, 82] Generated Node #0,3,2: 81:[2, 82] Operation: 80+2=82 Exploring Operation: 2+2=4, Resulting Numbers: [80, 4] Generated Node #0,3,3: 81:[80, 4] Operation: 2+2=4 Moving to Node #0,3,0 Current State: 81:[80, 4], Operations: ['65-63=2', '2*2=4'] Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,81 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,81 unequal: No Solution Moving to Node #0,3,2 Current State: 81:[2, 82], Operations: ['65-63=2', '80+2=82'] Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,81 unequal: No Solution Moving to Node #0,3,1 Current State: 81:[2, 82], Operations: ['65-63=2', '80+2=82'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[80, 4], Operations: ['65-63=2', '2+2=4'] Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,81 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[65, 2, 17], Operations: ['80-63=17'] Exploring Operation: 65+17=82, Resulting Numbers: [2, 82] Generated Node #0,0,0: 81:[2, 82] Operation: 65+17=82 Exploring Operation: 17-2=15, Resulting Numbers: [65, 15] Generated Node #0,0,1: 81:[65, 15] Operation: 17-2=15 Exploring Operation: 65-17=48, Resulting Numbers: [2, 48] Generated Node #0,0,2: 81:[2, 48] Operation: 65-17=48 Exploring Operation: 65+2=67, Resulting Numbers: [17, 67] Generated Node #0,0,3: 81:[17, 67] Operation: 65+2=67 Moving to Node #0,0,0 Current State: 81:[2, 82], Operations: ['80-63=17', '65+17=82'] Exploring Operation: 2+82=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 2*82=164, Resulting Numbers: [164] 164,81 unequal: No Solution Exploring Operation: 82/2=41, Resulting Numbers: [41] 41,81 unequal: No Solution Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[2, 48], Operations: ['80-63=17', '65-17=48'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,81 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,81 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,81 unequal: No Solution Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[65, 15], Operations: ['80-63=17', '17-2=15'] Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 65*15=975, Resulting Numbers: [975] 975,81 unequal: No Solution Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[17, 67], Operations: ['80-63=17', '65+2=67'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 17+67=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 17*67=1139, Resulting Numbers: [1139] 1139,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[2, 63, 15], Operations: ['80-65=15'] Exploring Operation: 2+63=65, Resulting Numbers: [15, 65] Generated Node #0,1,0: 81:[15, 65] Operation: 2+63=65 Exploring Operation: 2*15=30, Resulting Numbers: [63, 30] Generated Node #0,1,1: 81:[63, 30] Operation: 2*15=30 Exploring Operation: 15-2=13, Resulting Numbers: [63, 13] Generated Node #0,1,2: 81:[63, 13] Operation: 15-2=13 Exploring Operation: 63+15=78, Resulting Numbers: [2, 78] Generated Node #0,1,3: 81:[2, 78] Operation: 63+15=78 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 81:[2, 78], Operations: ['80-65=15', '63+15=78'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 2*78=156, Resulting Numbers: [156] 156,81 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 2+78=80, Resulting Numbers: [80] 80,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[63, 30], Operations: ['80-65=15', '2*15=30'] Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,81 unequal: No Solution Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,81 unequal: No Solution Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[15, 65], Operations: ['80-65=15', '2+63=65'] Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 81:[63, 13], Operations: ['80-65=15', '15-2=13'] Exploring Operation: 63-13=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 63+13=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 63*13=819, Resulting Numbers: [819] 819,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[80, 63, 67], Operations: ['65+2=67'] Exploring Operation: 63+67=130, Resulting Numbers: [80, 130] Generated Node #0,2,0: 81:[80, 130] Operation: 63+67=130 Exploring Operation: 80-63=17, Resulting Numbers: [67, 17] Generated Node #0,2,1: 81:[67, 17] Operation: 80-63=17 Exploring Operation: 80-67=13, Resulting Numbers: [63, 13] Generated Node #0,2,2: 81:[63, 13] Operation: 80-67=13 Exploring Operation: 67-63=4, Resulting Numbers: [80, 4] Generated Node #0,2,3: 81:[80, 4] Operation: 67-63=4 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 81:[80, 4], Operations: ['65+2=67', '67-63=4'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 80*4=320, Resulting Numbers: [320] 320,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 81:[67, 17], Operations: ['65+2=67', '80-63=17'] Exploring Operation: 67-17=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 67+17=84, Resulting Numbers: [84] 84,81 unequal: No Solution Exploring Operation: 67*17=1139, Resulting Numbers: [1139] 1139,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 81:[63, 13], Operations: ['65+2=67', '80-67=13'] Exploring Operation: 63-13=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 63+13=76, Resulting Numbers: [76] 76,81 unequal: No Solution Exploring Operation: 63*13=819, Resulting Numbers: [819] 819,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 81:[80, 130], Operations: ['65+2=67', '63+67=130'] Exploring Operation: 130-80=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 80*130=10400, Resulting Numbers: [10400] 10400,81 unequal: No Solution Exploring Operation: 80+130=210, Resulting Numbers: [210] 210,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 58, 17, 50, 10 ]
80
[ "58+17=75", "50/10=5", "75+5=80" ]
Current State: 80:[58, 17, 50, 10], Operations: [] Exploring Operation: 58+17=75, Resulting Numbers: [50, 10, 75] Generated Node #2: [50, 10, 75] from Operation: 58+17=75 Current State: 80:[50, 10, 75], Operations: ['58+17=75'] Exploring Operation: 50/10=5, Resulting Numbers: [75, 5] Generated Node #3: [75, 5] from Operation: 50/10=5 Current State: 80:[75, 5], Operations: ['58+17=75', '50/10=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[58, 17, 50, 10], Operations: [] Exploring Operation: 58-17=41, Resulting Numbers: [50, 10, 41] Generated Node #0,0: 80:[50, 10, 41] Operation: 58-17=41 Exploring Operation: 58-10=48, Resulting Numbers: [17, 50, 48] Generated Node #0,1: 80:[17, 50, 48] Operation: 58-10=48 Exploring Operation: 58+17=75, Resulting Numbers: [50, 10, 75] Generated Node #0,2: 80:[50, 10, 75] Operation: 58+17=75 Exploring Operation: 58-50=8, Resulting Numbers: [17, 10, 8] Generated Node #0,3: 80:[17, 10, 8] Operation: 58-50=8 Moving to Node #0,3 Current State: 80:[17, 10, 8], Operations: ['58-50=8'] Exploring Operation: 10-8=2, Resulting Numbers: [17, 2] Generated Node #0,3,0: 80:[17, 2] Operation: 10-8=2 Exploring Operation: 17-10=7, Resulting Numbers: [8, 7] Generated Node #0,3,1: 80:[8, 7] Operation: 17-10=7 Exploring Operation: 10*8=80, Resulting Numbers: [17, 80] Generated Node #0,3,2: 80:[17, 80] Operation: 10*8=80 Exploring Operation: 17-8=9, Resulting Numbers: [10, 9] Generated Node #0,3,3: 80:[10, 9] Operation: 17-8=9 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 80:[17, 2], Operations: ['58-50=8', '10-8=2'] Exploring Operation: 17*2=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 80:[8, 7], Operations: ['58-50=8', '17-10=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 8*7=56, Resulting Numbers: [56] 56,80 unequal: No Solution Exploring Operation: 8-7=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 #0,3,2 Current State: 80:[17, 80], Operations: ['58-50=8', '10*8=80'] Exploring Operation: 17+80=97, Resulting Numbers: [97] 97,80 unequal: No Solution Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,80 unequal: No Solution Exploring Operation: 17*80=1360, Resulting Numbers: [1360] 1360,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 80:[10, 9], Operations: ['58-50=8', '17-8=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,80 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,80 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:[50, 10, 41], Operations: ['58-17=41'] Exploring Operation: 50/10=5, Resulting Numbers: [41, 5] Generated Node #0,0,0: 80:[41, 5] Operation: 50/10=5 Exploring Operation: 50+41=91, Resulting Numbers: [10, 91] Generated Node #0,0,1: 80:[10, 91] Operation: 50+41=91 Exploring Operation: 50-10=40, Resulting Numbers: [41, 40] Generated Node #0,0,2: 80:[41, 40] Operation: 50-10=40 Exploring Operation: 50-41=9, Resulting Numbers: [10, 9] Generated Node #0,0,3: 80:[10, 9] Operation: 50-41=9 Moving to Node #0,2 Current State: 80:[50, 10, 75], Operations: ['58+17=75'] Exploring Operation: 75-50=25, Resulting Numbers: [10, 25] Generated Node #0,2,0: 80:[10, 25] Operation: 75-50=25 Exploring Operation: 10+75=85, Resulting Numbers: [50, 85] Generated Node #0,2,1: 80:[50, 85] Operation: 10+75=85 Exploring Operation: 50/10=5, Resulting Numbers: [75, 5] Generated Node #0,2,2: 80:[75, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [75, 40] Generated Node #0,2,3: 80:[75, 40] Operation: 50-10=40 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[10, 25], Operations: ['58+17=75', '75-50=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,80 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,80 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:[75, 5], Operations: ['58+17=75', '50/10=5'] Exploring Operation: 75-5=70, Resulting Numbers: [70] 70,80 unequal: No Solution Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,80 unequal: No Solution Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[58, 17, 50, 10], Operations: [] Exploring Operation: 58+17=75, Resulting Numbers: [50, 10, 75] Generated Node #0,2: 80:[50, 10, 75] Operation: 58+17=75 Moving to Node #0,2 Current State: 80:[50, 10, 75], Operations: ['58+17=75'] Exploring Operation: 50/10=5, Resulting Numbers: [75, 5] Generated Node #0,2,2: 80:[75, 5] Operation: 50/10=5 Moving to Node #0,2,2 Current State: 80:[75, 5], Operations: ['58+17=75', '50/10=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
mult_heuristic
[ 64, 48, 58, 25 ]
79
[ "64+48=112", "58-25=33", "112-33=79" ]
Current State: 79:[64, 48, 58, 25], Operations: [] Exploring Operation: 64+48=112, Resulting Numbers: [58, 25, 112] Generated Node #2: [58, 25, 112] from Operation: 64+48=112 Current State: 79:[58, 25, 112], Operations: ['64+48=112'] Exploring Operation: 58-25=33, Resulting Numbers: [112, 33] Generated Node #3: [112, 33] from Operation: 58-25=33 Current State: 79:[112, 33], Operations: ['64+48=112', '58-25=33'] Exploring Operation: 112-33=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[64, 48, 58, 25], Operations: [] Exploring Operation: 48+25=73, Resulting Numbers: [64, 58, 73] Generated Node #0,0: 79:[64, 58, 73] Operation: 48+25=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[64, 58, 73], Operations: ['48+25=73'] Exploring Operation: 64+58=122, Resulting Numbers: [73, 122] Generated Node #0,0,0: 79:[73, 122] Operation: 64+58=122 Moving to Node #0,0,0 Current State: 79:[73, 122], Operations: ['48+25=73', '64+58=122'] Exploring Operation: 122-73=49, Resulting Numbers: [49] 49,79 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
[ 38, 16, 42, 88 ]
68
[ "38-16=22", "88-42=46", "22+46=68" ]
Current State: 68:[38, 16, 42, 88], Operations: [] Exploring Operation: 38-16=22, Resulting Numbers: [42, 88, 22] Generated Node #2: [42, 88, 22] from Operation: 38-16=22 Current State: 68:[42, 88, 22], Operations: ['38-16=22'] Exploring Operation: 88-42=46, Resulting Numbers: [22, 46] Generated Node #3: [22, 46] from Operation: 88-42=46 Current State: 68:[22, 46], Operations: ['38-16=22', '88-42=46'] Exploring Operation: 22+46=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[38, 16, 42, 88], Operations: [] Exploring Operation: 88-42=46, Resulting Numbers: [38, 16, 46] Generated Node #0,0: 68:[38, 16, 46] Operation: 88-42=46 Exploring Operation: 88-16=72, Resulting Numbers: [38, 42, 72] Generated Node #0,1: 68:[38, 42, 72] Operation: 88-16=72 Exploring Operation: 42-38=4, Resulting Numbers: [16, 88, 4] Generated Node #0,2: 68:[16, 88, 4] Operation: 42-38=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[38, 42, 72], Operations: ['88-16=72'] Exploring Operation: 72-42=30, Resulting Numbers: [38, 30] Generated Node #0,1,0: 68:[38, 30] Operation: 72-42=30 Exploring Operation: 42-38=4, Resulting Numbers: [72, 4] Generated Node #0,1,1: 68:[72, 4] Operation: 42-38=4 Exploring Operation: 72-38=34, Resulting Numbers: [42, 34] Generated Node #0,1,2: 68:[42, 34] Operation: 72-38=34 Moving to Node #0,1,1 Current State: 68:[72, 4], Operations: ['88-16=72', '42-38=4'] Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,68 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[38, 16, 42, 88], Operations: [] Exploring Operation: 88-16=72, Resulting Numbers: [38, 42, 72] Generated Node #0,1: 68:[38, 42, 72] Operation: 88-16=72 Moving to Node #0,1 Current State: 68:[38, 42, 72], Operations: ['88-16=72'] Exploring Operation: 42-38=4, Resulting Numbers: [72, 4] Generated Node #0,1,1: 68:[72, 4] Operation: 42-38=4 Moving to Node #0,1,1 Current State: 68:[72, 4], Operations: ['88-16=72', '42-38=4'] Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 5, 6, 26, 97 ]
43
[ "5+97=102", "102/6=17", "26+17=43" ]
Current State: 43:[5, 6, 26, 97], Operations: [] Exploring Operation: 5+97=102, Resulting Numbers: [6, 26, 102] Generated Node #2: [6, 26, 102] from Operation: 5+97=102 Current State: 43:[6, 26, 102], Operations: ['5+97=102'] Exploring Operation: 102/6=17, Resulting Numbers: [26, 17] Generated Node #3: [26, 17] from Operation: 102/6=17 Current State: 43:[26, 17], Operations: ['5+97=102', '102/6=17'] Exploring Operation: 26+17=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[5, 6, 26, 97], Operations: [] Exploring Operation: 5+26=31, Resulting Numbers: [6, 97, 31] Generated Node #0,0: 43:[6, 97, 31] Operation: 5+26=31 Exploring Operation: 5*6=30, Resulting Numbers: [26, 97, 30] Generated Node #0,1: 43:[26, 97, 30] Operation: 5*6=30 Exploring Operation: 6+26=32, Resulting Numbers: [5, 97, 32] Generated Node #0,2: 43:[5, 97, 32] Operation: 6+26=32 Exploring Operation: 97-5=92, Resulting Numbers: [6, 26, 92] Generated Node #0,3: 43:[6, 26, 92] Operation: 97-5=92 Exploring Operation: 5+6=11, Resulting Numbers: [26, 97, 11] Generated Node #0,4: 43:[26, 97, 11] Operation: 5+6=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[26, 97, 30], Operations: ['5*6=30'] Exploring Operation: 30-26=4, Resulting Numbers: [97, 4] Generated Node #0,1,0: 43:[97, 4] Operation: 30-26=4 Exploring Operation: 26+30=56, Resulting Numbers: [97, 56] Generated Node #0,1,1: 43:[97, 56] Operation: 26+30=56 Exploring Operation: 26+97=123, Resulting Numbers: [30, 123] Generated Node #0,1,2: 43:[30, 123] Operation: 26+97=123 Exploring Operation: 97-26=71, Resulting Numbers: [30, 71] Generated Node #0,1,3: 43:[30, 71] Operation: 97-26=71 Exploring Operation: 97-30=67, Resulting Numbers: [26, 67] Generated Node #0,1,4: 43:[26, 67] Operation: 97-30=67 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 43:[30, 71], Operations: ['5*6=30', '97-26=71'] Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 30+71=101, Resulting Numbers: [101] 101,43 unequal: No Solution Exploring Operation: 30*71=2130, Resulting Numbers: [2130] 2130,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 43:[26, 67], Operations: ['5*6=30', '97-30=67'] Exploring Operation: 67-26=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 26*67=1742, Resulting Numbers: [1742] 1742,43 unequal: No Solution Exploring Operation: 26+67=93, Resulting Numbers: [93] 93,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[97, 56], Operations: ['5*6=30', '26+30=56'] Exploring Operation: 97-56=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 97*56=5432, Resulting Numbers: [5432] 5432,43 unequal: No Solution Exploring Operation: 97+56=153, Resulting Numbers: [153] 153,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[97, 4], Operations: ['5*6=30', '30-26=4'] Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,43 unequal: No Solution Exploring Operation: 97*4=388, Resulting Numbers: [388] 388,43 unequal: No Solution Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[30, 123], Operations: ['5*6=30', '26+97=123'] Exploring Operation: 30*123=3690, Resulting Numbers: [3690] 3690,43 unequal: No Solution Exploring Operation: 123-30=93, Resulting Numbers: [93] 93,43 unequal: No Solution Exploring Operation: 30+123=153, Resulting Numbers: [153] 153,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[6, 97, 31], Operations: ['5+26=31'] Exploring Operation: 6+97=103, Resulting Numbers: [31, 103] Generated Node #0,0,0: 43:[31, 103] Operation: 6+97=103 Exploring Operation: 97-6=91, Resulting Numbers: [31, 91] Generated Node #0,0,1: 43:[31, 91] Operation: 97-6=91 Exploring Operation: 31-6=25, Resulting Numbers: [97, 25] Generated Node #0,0,2: 43:[97, 25] Operation: 31-6=25 Exploring Operation: 97-31=66, Resulting Numbers: [6, 66] Generated Node #0,0,3: 43:[6, 66] Operation: 97-31=66 Exploring Operation: 6+31=37, Resulting Numbers: [97, 37] Generated Node #0,0,4: 43:[97, 37] Operation: 6+31=37 Moving to Node #0,0,1 Current State: 43:[31, 91], Operations: ['5+26=31', '97-6=91'] Exploring Operation: 31*91=2821, Resulting Numbers: [2821] 2821,43 unequal: No Solution Exploring Operation: 31+91=122, Resulting Numbers: [122] 122,43 unequal: No Solution Exploring Operation: 91-31=60, Resulting Numbers: [60] 60,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[97, 37], Operations: ['5+26=31', '6+31=37'] Exploring Operation: 97+37=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 97-37=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 97*37=3589, Resulting Numbers: [3589] 3589,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[6, 66], Operations: ['5+26=31', '97-31=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 6*66=396, Resulting Numbers: [396] 396,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[31, 103], Operations: ['5+26=31', '6+97=103'] Exploring Operation: 103-31=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 31+103=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 31*103=3193, Resulting Numbers: [3193] 3193,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[97, 25], Operations: ['5+26=31', '31-6=25'] Exploring Operation: 97-25=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 97*25=2425, Resulting Numbers: [2425] 2425,43 unequal: No Solution Exploring Operation: 97+25=122, Resulting Numbers: [122] 122,43 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 Current State: 43:[5, 97, 32], Operations: ['6+26=32'] Exploring Operation: 32-5=27, Resulting Numbers: [97, 27] Generated Node #0,2,0: 43:[97, 27] Operation: 32-5=27 Exploring Operation: 5+32=37, Resulting Numbers: [97, 37] Generated Node #0,2,1: 43:[97, 37] Operation: 5+32=37 Exploring Operation: 97-5=92, Resulting Numbers: [32, 92] Generated Node #0,2,2: 43:[32, 92] Operation: 97-5=92 Exploring Operation: 5+97=102, Resulting Numbers: [32, 102] Generated Node #0,2,3: 43:[32, 102] Operation: 5+97=102 Exploring Operation: 97-32=65, Resulting Numbers: [5, 65] Generated Node #0,2,4: 43:[5, 65] Operation: 97-32=65 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[97, 37], Operations: ['6+26=32', '5+32=37'] Exploring Operation: 97-37=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 97*37=3589, Resulting Numbers: [3589] 3589,43 unequal: No Solution Exploring Operation: 97+37=134, Resulting Numbers: [134] 134,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 43:[32, 92], Operations: ['6+26=32', '97-5=92'] Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 32+92=124, Resulting Numbers: [124] 124,43 unequal: No Solution Exploring Operation: 32*92=2944, Resulting Numbers: [2944] 2944,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 43:[5, 65], Operations: ['6+26=32', '97-32=65'] Exploring Operation: 5*65=325, Resulting Numbers: [325] 325,43 unequal: No Solution Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 5+65=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 43:[97, 27], Operations: ['6+26=32', '32-5=27'] Exploring Operation: 97-27=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 97*27=2619, Resulting Numbers: [2619] 2619,43 unequal: No Solution Exploring Operation: 97+27=124, Resulting Numbers: [124] 124,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 43:[32, 102], Operations: ['6+26=32', '5+97=102'] Exploring Operation: 32*102=3264, Resulting Numbers: [3264] 3264,43 unequal: No Solution Exploring Operation: 102-32=70, Resulting Numbers: [70] 70,43 unequal: No Solution Exploring Operation: 32+102=134, Resulting Numbers: [134] 134,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 43:[6, 26, 92], Operations: ['97-5=92'] Exploring Operation: 6+92=98, Resulting Numbers: [26, 98] Generated Node #0,3,0: 43:[26, 98] Operation: 6+92=98 Exploring Operation: 92-26=66, Resulting Numbers: [6, 66] Generated Node #0,3,1: 43:[6, 66] Operation: 92-26=66 Exploring Operation: 92-6=86, Resulting Numbers: [26, 86] Generated Node #0,3,2: 43:[26, 86] Operation: 92-6=86 Exploring Operation: 26-6=20, Resulting Numbers: [92, 20] Generated Node #0,3,3: 43:[92, 20] Operation: 26-6=20 Exploring Operation: 6+26=32, Resulting Numbers: [92, 32] Generated Node #0,3,4: 43:[92, 32] Operation: 6+26=32 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[6, 66], Operations: ['97-5=92', '92-26=66'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 6*66=396, Resulting Numbers: [396] 396,43 unequal: No Solution Exploring Operation: 6+66=72, Resulting Numbers: [72] 72,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 43:[26, 86], Operations: ['97-5=92', '92-6=86'] Exploring Operation: 26+86=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 26*86=2236, Resulting Numbers: [2236] 2236,43 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 43:[92, 32], Operations: ['97-5=92', '6+26=32'] Exploring Operation: 92-32=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 92*32=2944, Resulting Numbers: [2944] 2944,43 unequal: No Solution Exploring Operation: 92+32=124, Resulting Numbers: [124] 124,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 43:[26, 98], Operations: ['97-5=92', '6+92=98'] Exploring Operation: 26+98=124, Resulting Numbers: [124] 124,43 unequal: No Solution Exploring Operation: 98-26=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 26*98=2548, Resulting Numbers: [2548] 2548,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 43:[92, 20], Operations: ['97-5=92', '26-6=20'] Exploring Operation: 92*20=1840, Resulting Numbers: [1840] 1840,43 unequal: No Solution Exploring Operation: 92+20=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 43:[26, 97, 11], Operations: ['5+6=11'] Exploring Operation: 97-11=86, Resulting Numbers: [26, 86] Generated Node #0,4,0: 43:[26, 86] Operation: 97-11=86 Exploring Operation: 26+11=37, Resulting Numbers: [97, 37] Generated Node #0,4,1: 43:[97, 37] Operation: 26+11=37 Exploring Operation: 97-26=71, Resulting Numbers: [11, 71] Generated Node #0,4,2: 43:[11, 71] Operation: 97-26=71 Exploring Operation: 26-11=15, Resulting Numbers: [97, 15] Generated Node #0,4,3: 43:[97, 15] Operation: 26-11=15 Exploring Operation: 97+11=108, Resulting Numbers: [26, 108] Generated Node #0,4,4: 43:[26, 108] Operation: 97+11=108 Moving to Node #0,4,0 Current State: 43:[26, 86], Operations: ['5+6=11', '97-11=86'] Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,43 unequal: No Solution Exploring Operation: 26*86=2236, Resulting Numbers: [2236] 2236,43 unequal: No Solution Exploring Operation: 26+86=112, Resulting Numbers: [112] 112,43 unequal: No Solution Moving to Node #0,4,2 Current State: 43:[11, 71], Operations: ['5+6=11', '97-26=71'] Exploring Operation: 11+71=82, Resulting Numbers: [82] 82,43 unequal: No Solution Exploring Operation: 11*71=781, Resulting Numbers: [781] 781,43 unequal: No Solution Exploring Operation: 71-11=60, Resulting Numbers: [60] 60,43 unequal: No Solution Moving to Node #0,4,1 Current State: 43:[97, 37], Operations: ['5+6=11', '26+11=37'] Exploring Operation: 97+37=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 97*37=3589, Resulting Numbers: [3589] 3589,43 unequal: No Solution Exploring Operation: 97-37=60, Resulting Numbers: [60] 60,43 unequal: No Solution Moving to Node #0,4,3 Current State: 43:[97, 15], Operations: ['5+6=11', '26-11=15'] Exploring Operation: 97+15=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 97*15=1455, Resulting Numbers: [1455] 1455,43 unequal: No Solution Exploring Operation: 97-15=82, Resulting Numbers: [82] 82,43 unequal: No Solution Moving to Node #0,4,4 Current State: 43:[26, 108], Operations: ['5+6=11', '97+11=108'] Exploring Operation: 26*108=2808, Resulting Numbers: [2808] 2808,43 unequal: No Solution Exploring Operation: 26+108=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 108-26=82, Resulting Numbers: [82] 82,43 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
[ 18, 34, 90, 12 ]
21
[ "90+12=102", "102/34=3", "18+3=21" ]
Current State: 21:[18, 34, 90, 12], Operations: [] Exploring Operation: 90+12=102, Resulting Numbers: [18, 34, 102] Generated Node #2: [18, 34, 102] from Operation: 90+12=102 Current State: 21:[18, 34, 102], Operations: ['90+12=102'] Exploring Operation: 102/34=3, Resulting Numbers: [18, 3] Generated Node #3: [18, 3] from Operation: 102/34=3 Current State: 21:[18, 3], Operations: ['90+12=102', '102/34=3'] Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[18, 34, 90, 12], Operations: [] Exploring Operation: 90-34=56, Resulting Numbers: [18, 12, 56] Generated Node #0,0: 21:[18, 12, 56] Operation: 90-34=56 Exploring Operation: 90/18=5, Resulting Numbers: [34, 12, 5] Generated Node #0,1: 21:[34, 12, 5] Operation: 90/18=5 Exploring Operation: 90-18=72, Resulting Numbers: [34, 12, 72] Generated Node #0,2: 21:[34, 12, 72] Operation: 90-18=72 Moving to Node #0,1 Current State: 21:[34, 12, 5], Operations: ['90/18=5'] Exploring Operation: 34-12=22, Resulting Numbers: [5, 22] Generated Node #0,1,0: 21:[5, 22] Operation: 34-12=22 Exploring Operation: 34-5=29, Resulting Numbers: [12, 29] Generated Node #0,1,1: 21:[12, 29] Operation: 34-5=29 Exploring Operation: 12-5=7, Resulting Numbers: [34, 7] Generated Node #0,1,2: 21:[34, 7] Operation: 12-5=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[5, 22], Operations: ['90/18=5', '34-12=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,21 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,21 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[12, 29], Operations: ['90/18=5', '34-5=29'] Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,21 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,21 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,21 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 #0,1,2 Current State: 21:[34, 7], Operations: ['90/18=5', '12-5=7'] Exploring Operation: 34*7=238, Resulting Numbers: [238] 238,21 unequal: No Solution Exploring Operation: 34+7=41, Resulting Numbers: [41] 41,21 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 21:[18, 12, 56], Operations: ['90-34=56'] Exploring Operation: 56-12=44, Resulting Numbers: [18, 44] Generated Node #0,0,0: 21:[18, 44] Operation: 56-12=44 Exploring Operation: 18-12=6, Resulting Numbers: [56, 6] Generated Node #0,0,1: 21:[56, 6] Operation: 18-12=6 Exploring Operation: 56-18=38, Resulting Numbers: [12, 38] Generated Node #0,0,2: 21:[12, 38] Operation: 56-18=38 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[12, 38], Operations: ['90-34=56', '56-18=38'] Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,21 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[18, 44], Operations: ['90-34=56', '56-12=44'] Exploring Operation: 18*44=792, Resulting Numbers: [792] 792,21 unequal: No Solution Exploring Operation: 18+44=62, Resulting Numbers: [62] 62,21 unequal: No Solution Exploring Operation: 44-18=26, Resulting Numbers: [26] 26,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[56, 6], Operations: ['90-34=56', '18-12=6'] Exploring Operation: 56+6=62, Resulting Numbers: [62] 62,21 unequal: No Solution Exploring Operation: 56-6=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 56*6=336, Resulting Numbers: [336] 336,21 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: 21:[34, 12, 72], Operations: ['90-18=72'] Exploring Operation: 72/12=6, Resulting Numbers: [34, 6] Generated Node #0,2,0: 21:[34, 6] Operation: 72/12=6 Exploring Operation: 34-12=22, Resulting Numbers: [72, 22] Generated Node #0,2,1: 21:[72, 22] Operation: 34-12=22 Exploring Operation: 72-34=38, Resulting Numbers: [12, 38] Generated Node #0,2,2: 21:[12, 38] Operation: 72-34=38 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[34, 6], Operations: ['90-18=72', '72/12=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,21 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,21 unequal: No Solution Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[12, 38], Operations: ['90-18=72', '72-34=38'] Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,21 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 #0,2,1 Current State: 21:[72, 22], Operations: ['90-18=72', '34-12=22'] Exploring Operation: 72+22=94, Resulting Numbers: [94] 94,21 unequal: No Solution Exploring Operation: 72-22=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 72*22=1584, Resulting Numbers: [1584] 1584,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 57, 34, 46, 74 ]
23
[ "74-57=17", "34/17=2", "46/2=23" ]
Current State: 23:[57, 34, 46, 74], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [34, 46, 17] Generated Node #2: [34, 46, 17] from Operation: 74-57=17 Current State: 23:[34, 46, 17], Operations: ['74-57=17'] Exploring Operation: 34/17=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 34/17=2 Current State: 23:[46, 2], Operations: ['74-57=17', '34/17=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[57, 34, 46, 74], Operations: [] Exploring Operation: 74-46=28, Resulting Numbers: [57, 34, 28] Generated Node #0,0: 23:[57, 34, 28] Operation: 74-46=28 Exploring Operation: 57-46=11, Resulting Numbers: [34, 74, 11] Generated Node #0,1: 23:[34, 74, 11] Operation: 57-46=11 Exploring Operation: 57-34=23, Resulting Numbers: [46, 74, 23] Generated Node #0,2: 23:[46, 74, 23] Operation: 57-34=23 Exploring Operation: 74-57=17, Resulting Numbers: [34, 46, 17] Generated Node #0,3: 23:[34, 46, 17] Operation: 74-57=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[34, 46, 17], Operations: ['74-57=17'] Exploring Operation: 34-17=17, Resulting Numbers: [46, 17] Generated Node #0,3,0: 23:[46, 17] Operation: 34-17=17 Exploring Operation: 46-34=12, Resulting Numbers: [17, 12] Generated Node #0,3,1: 23:[17, 12] Operation: 46-34=12 Exploring Operation: 46-17=29, Resulting Numbers: [34, 29] Generated Node #0,3,2: 23:[34, 29] Operation: 46-17=29 Exploring Operation: 34/17=2, Resulting Numbers: [46, 2] Generated Node #0,3,3: 23:[46, 2] Operation: 34/17=2 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 23:[17, 12], Operations: ['74-57=17', '46-34=12'] Exploring Operation: 17*12=204, Resulting Numbers: [204] 204,23 unequal: No Solution Exploring Operation: 17+12=29, Resulting Numbers: [29] 29,23 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 23:[34, 29], Operations: ['74-57=17', '46-17=29'] Exploring Operation: 34*29=986, Resulting Numbers: [986] 986,23 unequal: No Solution Exploring Operation: 34+29=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 23:[46, 17], Operations: ['74-57=17', '34-17=17'] Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,23 unequal: No Solution Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,23 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 23:[46, 2], Operations: ['74-57=17', '34/17=2'] Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[57, 34, 46, 74], Operations: [] Exploring Operation: 74-57=17, Resulting Numbers: [34, 46, 17] Generated Node #0,3: 23:[34, 46, 17] Operation: 74-57=17 Moving to Node #0,3 Current State: 23:[34, 46, 17], Operations: ['74-57=17'] Exploring Operation: 34/17=2, Resulting Numbers: [46, 2] Generated Node #0,3,3: 23:[46, 2] Operation: 34/17=2 Moving to Node #0,3,3 Current State: 23:[46, 2], Operations: ['74-57=17', '34/17=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 78, 62, 70, 42 ]
28
[ "78+62=140", "70+42=112", "140-112=28" ]
Current State: 28:[78, 62, 70, 42], Operations: [] Exploring Operation: 78+62=140, Resulting Numbers: [70, 42, 140] Generated Node #2: [70, 42, 140] from Operation: 78+62=140 Current State: 28:[70, 42, 140], Operations: ['78+62=140'] Exploring Operation: 70+42=112, Resulting Numbers: [140, 112] Generated Node #3: [140, 112] from Operation: 70+42=112 Current State: 28:[140, 112], Operations: ['78+62=140', '70+42=112'] Exploring Operation: 140-112=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[78, 62, 70, 42], Operations: [] Exploring Operation: 78-62=16, Resulting Numbers: [70, 42, 16] Generated Node #0,0: 28:[70, 42, 16] Operation: 78-62=16 Exploring Operation: 70-62=8, Resulting Numbers: [78, 42, 8] Generated Node #0,1: 28:[78, 42, 8] Operation: 70-62=8 Exploring Operation: 78-70=8, Resulting Numbers: [62, 42, 8] Generated Node #0,2: 28:[62, 42, 8] Operation: 78-70=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[62, 42, 8], Operations: ['78-70=8'] Exploring Operation: 62-8=54, Resulting Numbers: [42, 54] Generated Node #0,2,0: 28:[42, 54] Operation: 62-8=54 Exploring Operation: 62-42=20, Resulting Numbers: [8, 20] Generated Node #0,2,1: 28:[8, 20] Operation: 62-42=20 Exploring Operation: 42-8=34, Resulting Numbers: [62, 34] Generated Node #0,2,2: 28:[62, 34] Operation: 42-8=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[8, 20], Operations: ['78-70=8', '62-42=20'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,28 unequal: No Solution Exploring Operation: 8*20=160, Resulting Numbers: [160] 160,28 unequal: No Solution Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[78, 62, 70, 42], Operations: [] Exploring Operation: 78-70=8, Resulting Numbers: [62, 42, 8] Generated Node #0,2: 28:[62, 42, 8] Operation: 78-70=8 Moving to Node #0,2 Current State: 28:[62, 42, 8], Operations: ['78-70=8'] Exploring Operation: 62-42=20, Resulting Numbers: [8, 20] Generated Node #0,2,1: 28:[8, 20] Operation: 62-42=20 Moving to Node #0,2,1 Current State: 28:[8, 20], Operations: ['78-70=8', '62-42=20'] Exploring Operation: 8+20=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 23, 45, 49, 5 ]
43
[ "49-45=4", "5*4=20", "23+20=43" ]
Current State: 43:[23, 45, 49, 5], Operations: [] Exploring Operation: 49-45=4, Resulting Numbers: [23, 5, 4] Generated Node #2: [23, 5, 4] from Operation: 49-45=4 Current State: 43:[23, 5, 4], Operations: ['49-45=4'] Exploring Operation: 5*4=20, Resulting Numbers: [23, 20] Generated Node #3: [23, 20] from Operation: 5*4=20 Current State: 43:[23, 20], Operations: ['49-45=4', '5*4=20'] Exploring Operation: 23+20=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[23, 45, 49, 5], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [23, 49, 40] Generated Node #0,0: 43:[23, 49, 40] Operation: 45-5=40 Exploring Operation: 23+5=28, Resulting Numbers: [45, 49, 28] Generated Node #0,1: 43:[45, 49, 28] Operation: 23+5=28 Exploring Operation: 49-5=44, Resulting Numbers: [23, 45, 44] Generated Node #0,2: 43:[23, 45, 44] Operation: 49-5=44 Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[45, 49, 28], Operations: ['23+5=28'] Exploring Operation: 49-28=21, Resulting Numbers: [45, 21] Generated Node #0,1,0: 43:[45, 21] Operation: 49-28=21 Exploring Operation: 45+28=73, Resulting Numbers: [49, 73] Generated Node #0,1,1: 43:[49, 73] Operation: 45+28=73 Exploring Operation: 45-28=17, Resulting Numbers: [49, 17] Generated Node #0,1,2: 43:[49, 17] Operation: 45-28=17 Moving to Node #0,1,0 Current State: 43:[45, 21], Operations: ['23+5=28', '49-28=21'] Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[49, 17], Operations: ['23+5=28', '45-28=17'] Exploring Operation: 49*17=833, Resulting Numbers: [833] 833,43 unequal: No Solution Exploring Operation: 49+17=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 49-17=32, Resulting Numbers: [32] 32,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[49, 73], Operations: ['23+5=28', '45+28=73'] Exploring Operation: 49+73=122, Resulting Numbers: [122] 122,43 unequal: No Solution Exploring Operation: 73-49=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 49*73=3577, Resulting Numbers: [3577] 3577,43 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 Current State: 43:[23, 45, 44], Operations: ['49-5=44'] Exploring Operation: 44-23=21, Resulting Numbers: [45, 21] Generated Node #0,2,0: 43:[45, 21] Operation: 44-23=21 Exploring Operation: 23+45=68, Resulting Numbers: [44, 68] Generated Node #0,2,1: 43:[44, 68] Operation: 23+45=68 Exploring Operation: 45-23=22, Resulting Numbers: [44, 22] Generated Node #0,2,2: 43:[44, 22] Operation: 45-23=22 Moving to Node #0,2,2 Current State: 43:[44, 22], Operations: ['49-5=44', '45-23=22'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 44+22=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[45, 21], Operations: ['49-5=44', '44-23=21'] Exploring Operation: 45+21=66, Resulting Numbers: [66] 66,43 unequal: No Solution Exploring Operation: 45*21=945, Resulting Numbers: [945] 945,43 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[44, 68], Operations: ['49-5=44', '23+45=68'] Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,43 unequal: No Solution Exploring Operation: 44+68=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 44*68=2992, Resulting Numbers: [2992] 2992,43 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 Current State: 43:[23, 49, 40], Operations: ['45-5=40'] Exploring Operation: 23+49=72, Resulting Numbers: [40, 72] Generated Node #0,0,0: 43:[40, 72] Operation: 23+49=72 Exploring Operation: 23+40=63, Resulting Numbers: [49, 63] Generated Node #0,0,1: 43:[49, 63] Operation: 23+40=63 Exploring Operation: 49-23=26, Resulting Numbers: [40, 26] Generated Node #0,0,2: 43:[40, 26] Operation: 49-23=26 Moving to Node #0,0,2 Current State: 43:[40, 26], Operations: ['45-5=40', '49-23=26'] Exploring Operation: 40*26=1040, Resulting Numbers: [1040] 1040,43 unequal: No Solution Exploring Operation: 40-26=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 40+26=66, Resulting Numbers: [66] 66,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[49, 63], Operations: ['45-5=40', '23+40=63'] Exploring Operation: 63-49=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 49*63=3087, Resulting Numbers: [3087] 3087,43 unequal: No Solution Exploring Operation: 49+63=112, Resulting Numbers: [112] 112,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[40, 72], Operations: ['45-5=40', '23+49=72'] Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,43 unequal: No Solution Exploring Operation: 40*72=2880, Resulting Numbers: [2880] 2880,43 unequal: No Solution Exploring Operation: 40+72=112, Resulting Numbers: [112] 112,43 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
[ 98, 87, 39, 3 ]
46
[ "87-39=48", "3*48=144", "144-98=46" ]
Current State: 46:[98, 87, 39, 3], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [98, 3, 48] Generated Node #2: [98, 3, 48] from Operation: 87-39=48 Current State: 46:[98, 3, 48], Operations: ['87-39=48'] Exploring Operation: 3*48=144, Resulting Numbers: [98, 144] Generated Node #3: [98, 144] from Operation: 3*48=144 Current State: 46:[98, 144], Operations: ['87-39=48', '3*48=144'] Exploring Operation: 144-98=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[98, 87, 39, 3], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [98, 3, 48] Generated Node #0,0: 46:[98, 3, 48] Operation: 87-39=48 Exploring Operation: 98-39=59, Resulting Numbers: [87, 3, 59] Generated Node #0,1: 46:[87, 3, 59] Operation: 98-39=59 Exploring Operation: 87/3=29, Resulting Numbers: [98, 39, 29] Generated Node #0,2: 46:[98, 39, 29] Operation: 87/3=29 Exploring Operation: 98-87=11, Resulting Numbers: [39, 3, 11] Generated Node #0,3: 46:[39, 3, 11] Operation: 98-87=11 Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[39, 3, 11], Operations: ['98-87=11'] Exploring Operation: 39-11=28, Resulting Numbers: [3, 28] Generated Node #0,3,0: 46:[3, 28] Operation: 39-11=28 Exploring Operation: 39+11=50, Resulting Numbers: [3, 50] Generated Node #0,3,1: 46:[3, 50] Operation: 39+11=50 Exploring Operation: 39+3=42, Resulting Numbers: [11, 42] Generated Node #0,3,2: 46:[11, 42] Operation: 39+3=42 Exploring Operation: 11-3=8, Resulting Numbers: [39, 8] Generated Node #0,3,3: 46:[39, 8] Operation: 11-3=8 Moving to Node #0,3,1 Current State: 46:[3, 50], Operations: ['98-87=11', '39+11=50'] Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[3, 28], Operations: ['98-87=11', '39-11=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,46 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[39, 8], Operations: ['98-87=11', '11-3=8'] Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[11, 42], Operations: ['98-87=11', '39+3=42'] Exploring Operation: 11*42=462, Resulting Numbers: [462] 462,46 unequal: No Solution Exploring Operation: 42-11=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 11+42=53, Resulting Numbers: [53] 53,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[98, 3, 48], Operations: ['87-39=48'] Exploring Operation: 98+3=101, Resulting Numbers: [48, 101] Generated Node #0,0,0: 46:[48, 101] Operation: 98+3=101 Exploring Operation: 48-3=45, Resulting Numbers: [98, 45] Generated Node #0,0,1: 46:[98, 45] Operation: 48-3=45 Exploring Operation: 98-3=95, Resulting Numbers: [48, 95] Generated Node #0,0,2: 46:[48, 95] Operation: 98-3=95 Exploring Operation: 98-48=50, Resulting Numbers: [3, 50] Generated Node #0,0,3: 46:[3, 50] Operation: 98-48=50 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 46:[3, 50], Operations: ['87-39=48', '98-48=50'] Exploring Operation: 3*50=150, Resulting Numbers: [150] 150,46 unequal: No Solution Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,46 unequal: No Solution No 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: 46:[48, 95], Operations: ['87-39=48', '98-3=95'] Exploring Operation: 48+95=143, Resulting Numbers: [143] 143,46 unequal: No Solution Exploring Operation: 48*95=4560, Resulting Numbers: [4560] 4560,46 unequal: No Solution Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,46 unequal: No Solution No 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: 46:[98, 45], Operations: ['87-39=48', '48-3=45'] Exploring Operation: 98+45=143, Resulting Numbers: [143] 143,46 unequal: No Solution Exploring Operation: 98*45=4410, Resulting Numbers: [4410] 4410,46 unequal: No Solution Exploring Operation: 98-45=53, Resulting Numbers: [53] 53,46 unequal: No Solution No 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: 46:[48, 101], Operations: ['87-39=48', '98+3=101'] Exploring Operation: 101-48=53, Resulting Numbers: [53] 53,46 unequal: No Solution Exploring Operation: 48*101=4848, Resulting Numbers: [4848] 4848,46 unequal: No Solution Exploring Operation: 48+101=149, Resulting Numbers: [149] 149,46 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[87, 3, 59], Operations: ['98-39=59'] Exploring Operation: 59-3=56, Resulting Numbers: [87, 56] Generated Node #0,1,0: 46:[87, 56] Operation: 59-3=56 Exploring Operation: 87/3=29, Resulting Numbers: [59, 29] Generated Node #0,1,1: 46:[59, 29] Operation: 87/3=29 Exploring Operation: 87-59=28, Resulting Numbers: [3, 28] Generated Node #0,1,2: 46:[3, 28] Operation: 87-59=28 Exploring Operation: 87-3=84, Resulting Numbers: [59, 84] Generated Node #0,1,3: 46:[59, 84] Operation: 87-3=84 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 46:[3, 28], Operations: ['98-39=59', '87-59=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,46 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,46 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,46 unequal: No Solution No 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: 46:[59, 29], Operations: ['98-39=59', '87/3=29'] Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,46 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,46 unequal: No Solution No 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: 46:[87, 56], Operations: ['98-39=59', '59-3=56'] Exploring Operation: 87+56=143, Resulting Numbers: [143] 143,46 unequal: No Solution Exploring Operation: 87*56=4872, Resulting Numbers: [4872] 4872,46 unequal: No Solution Exploring Operation: 87-56=31, Resulting Numbers: [31] 31,46 unequal: No Solution No 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: 46:[59, 84], Operations: ['98-39=59', '87-3=84'] Exploring Operation: 59+84=143, Resulting Numbers: [143] 143,46 unequal: No Solution Exploring Operation: 59*84=4956, Resulting Numbers: [4956] 4956,46 unequal: No Solution Exploring Operation: 84-59=25, Resulting Numbers: [25] 25,46 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[98, 39, 29], Operations: ['87/3=29'] Exploring Operation: 98-39=59, Resulting Numbers: [29, 59] Generated Node #0,2,0: 46:[29, 59] Operation: 98-39=59 Exploring Operation: 39-29=10, Resulting Numbers: [98, 10] Generated Node #0,2,1: 46:[98, 10] Operation: 39-29=10 Exploring Operation: 98-29=69, Resulting Numbers: [39, 69] Generated Node #0,2,2: 46:[39, 69] Operation: 98-29=69 Exploring Operation: 39+29=68, Resulting Numbers: [98, 68] Generated Node #0,2,3: 46:[98, 68] Operation: 39+29=68 Moving to Node #0,2,0 Current State: 46:[29, 59], Operations: ['87/3=29', '98-39=59'] Exploring Operation: 29*59=1711, Resulting Numbers: [1711] 1711,46 unequal: No Solution Exploring Operation: 29+59=88, Resulting Numbers: [88] 88,46 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[39, 69], Operations: ['87/3=29', '98-29=69'] Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,46 unequal: No Solution Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[98, 10], Operations: ['87/3=29', '39-29=10'] Exploring Operation: 98*10=980, Resulting Numbers: [980] 980,46 unequal: No Solution Exploring Operation: 98+10=108, Resulting Numbers: [108] 108,46 unequal: No Solution Exploring Operation: 98-10=88, Resulting Numbers: [88] 88,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[98, 68], Operations: ['87/3=29', '39+29=68'] Exploring Operation: 98*68=6664, Resulting Numbers: [6664] 6664,46 unequal: No Solution Exploring Operation: 98+68=166, Resulting Numbers: [166] 166,46 unequal: No Solution Exploring Operation: 98-68=30, Resulting Numbers: [30] 30,46 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
[ 58, 15, 28, 23 ]
94
[ "58-15=43", "28+23=51", "43+51=94" ]
Current State: 94:[58, 15, 28, 23], Operations: [] Exploring Operation: 58-15=43, Resulting Numbers: [28, 23, 43] Generated Node #2: [28, 23, 43] from Operation: 58-15=43 Current State: 94:[28, 23, 43], Operations: ['58-15=43'] Exploring Operation: 28+23=51, Resulting Numbers: [43, 51] Generated Node #3: [43, 51] from Operation: 28+23=51 Current State: 94:[43, 51], Operations: ['58-15=43', '28+23=51'] Exploring Operation: 43+51=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[58, 15, 28, 23], Operations: [] Exploring Operation: 28-23=5, Resulting Numbers: [58, 15, 5] Generated Node #0,0: 94:[58, 15, 5] Operation: 28-23=5 Exploring Operation: 15+28=43, Resulting Numbers: [58, 23, 43] Generated Node #0,1: 94:[58, 23, 43] Operation: 15+28=43 Exploring Operation: 28+23=51, Resulting Numbers: [58, 15, 51] Generated Node #0,2: 94:[58, 15, 51] Operation: 28+23=51 Moving to Node #0,0 Current State: 94:[58, 15, 5], Operations: ['28-23=5'] Exploring Operation: 15/5=3, Resulting Numbers: [58, 3] Generated Node #0,0,0: 94:[58, 3] Operation: 15/5=3 Exploring Operation: 58-15=43, Resulting Numbers: [5, 43] Generated Node #0,0,1: 94:[5, 43] Operation: 58-15=43 Exploring Operation: 58-5=53, Resulting Numbers: [15, 53] Generated Node #0,0,2: 94:[15, 53] Operation: 58-5=53 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[5, 43], Operations: ['28-23=5', '58-15=43'] Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,94 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[58, 3], Operations: ['28-23=5', '15/5=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,94 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,94 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 94:[15, 53], Operations: ['28-23=5', '58-5=53'] Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,94 unequal: No Solution Exploring Operation: 15*53=795, Resulting Numbers: [795] 795,94 unequal: No Solution Exploring Operation: 53-15=38, Resulting Numbers: [38] 38,94 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: 94:[58, 15, 51], Operations: ['28+23=51'] Exploring Operation: 58-15=43, Resulting Numbers: [51, 43] Generated Node #0,2,0: 94:[51, 43] Operation: 58-15=43 Exploring Operation: 51-15=36, Resulting Numbers: [58, 36] Generated Node #0,2,1: 94:[58, 36] Operation: 51-15=36 Exploring Operation: 58-51=7, Resulting Numbers: [15, 7] Generated Node #0,2,2: 94:[15, 7] Operation: 58-51=7 Moving to Node #0,1 Current State: 94:[58, 23, 43], Operations: ['15+28=43'] Exploring Operation: 58+43=101, Resulting Numbers: [23, 101] Generated Node #0,1,0: 94:[23, 101] Operation: 58+43=101 Exploring Operation: 58-23=35, Resulting Numbers: [43, 35] Generated Node #0,1,1: 94:[43, 35] Operation: 58-23=35 Exploring Operation: 58+23=81, Resulting Numbers: [43, 81] Generated Node #0,1,2: 94:[43, 81] Operation: 58+23=81 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 94:[43, 35], Operations: ['15+28=43', '58-23=35'] Exploring Operation: 43*35=1505, Resulting Numbers: [1505] 1505,94 unequal: No Solution Exploring Operation: 43-35=8, Resulting Numbers: [8] 8,94 unequal: No Solution Exploring Operation: 43+35=78, Resulting Numbers: [78] 78,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 94:[43, 81], Operations: ['15+28=43', '58+23=81'] Exploring Operation: 43+81=124, Resulting Numbers: [124] 124,94 unequal: No Solution Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 43*81=3483, Resulting Numbers: [3483] 3483,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 94:[23, 101], Operations: ['15+28=43', '58+43=101'] Exploring Operation: 23*101=2323, Resulting Numbers: [2323] 2323,94 unequal: No Solution Exploring Operation: 23+101=124, Resulting Numbers: [124] 124,94 unequal: No Solution Exploring Operation: 101-23=78, Resulting Numbers: [78] 78,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 94:[51, 43], Operations: ['28+23=51', '58-15=43'] Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,94 unequal: No Solution Exploring Operation: 51*43=2193, Resulting Numbers: [2193] 2193,94 unequal: No Solution Exploring Operation: 51+43=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[58, 15, 28, 23], Operations: [] Exploring Operation: 28+23=51, Resulting Numbers: [58, 15, 51] Generated Node #0,2: 94:[58, 15, 51] Operation: 28+23=51 Moving to Node #0,2 Current State: 94:[58, 15, 51], Operations: ['28+23=51'] Exploring Operation: 58-15=43, Resulting Numbers: [51, 43] Generated Node #0,2,0: 94:[51, 43] Operation: 58-15=43 Moving to Node #0,2,0 Current State: 94:[51, 43], Operations: ['28+23=51', '58-15=43'] Exploring Operation: 51+43=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
0.967882
hs_3
sum_heuristic
[ 72, 1, 48, 37 ]
12
[ "72+1=73", "48+37=85", "85-73=12" ]
Current State: 12:[72, 1, 48, 37], Operations: [] Exploring Operation: 72+1=73, Resulting Numbers: [48, 37, 73] Generated Node #2: [48, 37, 73] from Operation: 72+1=73 Current State: 12:[48, 37, 73], Operations: ['72+1=73'] Exploring Operation: 48+37=85, Resulting Numbers: [73, 85] Generated Node #3: [73, 85] from Operation: 48+37=85 Current State: 12:[73, 85], Operations: ['72+1=73', '48+37=85'] Exploring Operation: 85-73=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[72, 1, 48, 37], Operations: [] Exploring Operation: 72-37=35, Resulting Numbers: [1, 48, 35] Generated Node #0,0: 12:[1, 48, 35] Operation: 72-37=35 Exploring Operation: 72-1=71, Resulting Numbers: [48, 37, 71] Generated Node #0,1: 12:[48, 37, 71] Operation: 72-1=71 Exploring Operation: 48-37=11, Resulting Numbers: [72, 1, 11] Generated Node #0,2: 12:[72, 1, 11] Operation: 48-37=11 Exploring Operation: 72-48=24, Resulting Numbers: [1, 37, 24] Generated Node #0,3: 12:[1, 37, 24] Operation: 72-48=24 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[1, 37, 24], Operations: ['72-48=24'] Exploring Operation: 37-24=13, Resulting Numbers: [1, 13] Generated Node #0,3,0: 12:[1, 13] Operation: 37-24=13 Exploring Operation: 1*37=37, Resulting Numbers: [24, 37] Generated Node #0,3,1: 12:[24, 37] Operation: 1*37=37 Exploring Operation: 24-1=23, Resulting Numbers: [37, 23] Generated Node #0,3,2: 12:[37, 23] Operation: 24-1=23 Exploring Operation: 37-1=36, Resulting Numbers: [24, 36] Generated Node #0,3,3: 12:[24, 36] Operation: 37-1=36 Moving to Node #0,3,0 Current State: 12:[1, 13], Operations: ['72-48=24', '37-24=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,12 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,12 unequal: No Solution Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[72, 1, 48, 37], Operations: [] Exploring Operation: 72-48=24, Resulting Numbers: [1, 37, 24] Generated Node #0,3: 12:[1, 37, 24] Operation: 72-48=24 Moving to Node #0,3 Current State: 12:[1, 37, 24], Operations: ['72-48=24'] Exploring Operation: 37-24=13, Resulting Numbers: [1, 13] Generated Node #0,3,0: 12:[1, 13] Operation: 37-24=13 Moving to Node #0,3,0 Current State: 12:[1, 13], Operations: ['72-48=24', '37-24=13'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 98, 39, 63, 91 ]
21
[ "98*39=3822", "3822/91=42", "63-42=21" ]
Current State: 21:[98, 39, 63, 91], Operations: [] Exploring Operation: 98*39=3822, Resulting Numbers: [63, 91, 3822] Generated Node #2: [63, 91, 3822] from Operation: 98*39=3822 Current State: 21:[63, 91, 3822], Operations: ['98*39=3822'] Exploring Operation: 3822/91=42, Resulting Numbers: [63, 42] Generated Node #3: [63, 42] from Operation: 3822/91=42 Current State: 21:[63, 42], Operations: ['98*39=3822', '3822/91=42'] Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[98, 39, 63, 91], Operations: [] Exploring Operation: 91-63=28, Resulting Numbers: [98, 39, 28] Generated Node #0,0: 21:[98, 39, 28] Operation: 91-63=28 Exploring Operation: 98-91=7, Resulting Numbers: [39, 63, 7] Generated Node #0,1: 21:[39, 63, 7] Operation: 98-91=7 Exploring Operation: 98-63=35, Resulting Numbers: [39, 91, 35] Generated Node #0,2: 21:[39, 91, 35] Operation: 98-63=35 Moving to Node #0,1 Current State: 21:[39, 63, 7], Operations: ['98-91=7'] Exploring Operation: 39-7=32, Resulting Numbers: [63, 32] Generated Node #0,1,0: 21:[63, 32] Operation: 39-7=32 Exploring Operation: 63/7=9, Resulting Numbers: [39, 9] Generated Node #0,1,1: 21:[39, 9] Operation: 63/7=9 Exploring Operation: 63-39=24, Resulting Numbers: [7, 24] Generated Node #0,1,2: 21:[7, 24] Operation: 63-39=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[7, 24], Operations: ['98-91=7', '63-39=24'] Exploring Operation: 7*24=168, Resulting Numbers: [168] 168,21 unequal: No Solution Exploring Operation: 7+24=31, Resulting Numbers: [31] 31,21 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[39, 9], Operations: ['98-91=7', '63/7=9'] Exploring Operation: 39+9=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 39*9=351, Resulting Numbers: [351] 351,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[63, 32], Operations: ['98-91=7', '39-7=32'] Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 63*32=2016, Resulting Numbers: [2016] 2016,21 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 21:[98, 39, 28], Operations: ['91-63=28'] Exploring Operation: 98-39=59, Resulting Numbers: [28, 59] Generated Node #0,0,0: 21:[28, 59] Operation: 98-39=59 Exploring Operation: 39-28=11, Resulting Numbers: [98, 11] Generated Node #0,0,1: 21:[98, 11] Operation: 39-28=11 Exploring Operation: 98-28=70, Resulting Numbers: [39, 70] Generated Node #0,0,2: 21:[39, 70] Operation: 98-28=70 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[28, 59], Operations: ['91-63=28', '98-39=59'] Exploring Operation: 28+59=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 28*59=1652, Resulting Numbers: [1652] 1652,21 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[39, 70], Operations: ['91-63=28', '98-28=70'] Exploring Operation: 39+70=109, Resulting Numbers: [109] 109,21 unequal: No Solution Exploring Operation: 39*70=2730, Resulting Numbers: [2730] 2730,21 unequal: No Solution Exploring Operation: 70-39=31, Resulting Numbers: [31] 31,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[98, 11], Operations: ['91-63=28', '39-28=11'] Exploring Operation: 98+11=109, Resulting Numbers: [109] 109,21 unequal: No Solution Exploring Operation: 98-11=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 98*11=1078, Resulting Numbers: [1078] 1078,21 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: 21:[39, 91, 35], Operations: ['98-63=35'] Exploring Operation: 91-39=52, Resulting Numbers: [35, 52] Generated Node #0,2,0: 21:[35, 52] Operation: 91-39=52 Exploring Operation: 39-35=4, Resulting Numbers: [91, 4] Generated Node #0,2,1: 21:[91, 4] Operation: 39-35=4 Exploring Operation: 91-35=56, Resulting Numbers: [39, 56] Generated Node #0,2,2: 21:[39, 56] Operation: 91-35=56 Moving to Node #0,2,0 Current State: 21:[35, 52], Operations: ['98-63=35', '91-39=52'] Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,21 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[39, 56], Operations: ['98-63=35', '91-35=56'] Exploring Operation: 39+56=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 39*56=2184, Resulting Numbers: [2184] 2184,21 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[91, 4], Operations: ['98-63=35', '39-35=4'] Exploring Operation: 91+4=95, Resulting Numbers: [95] 95,21 unequal: No Solution Exploring Operation: 91-4=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 91*4=364, Resulting Numbers: [364] 364,21 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 56, 48, 28, 6 ]
22
[ "56+48=104", "28+104=132", "132/6=22" ]
Current State: 22:[56, 48, 28, 6], Operations: [] Exploring Operation: 56+48=104, Resulting Numbers: [28, 6, 104] Generated Node #2: [28, 6, 104] from Operation: 56+48=104 Current State: 22:[28, 6, 104], Operations: ['56+48=104'] Exploring Operation: 28+104=132, Resulting Numbers: [6, 132] Generated Node #3: [6, 132] from Operation: 28+104=132 Current State: 22:[6, 132], Operations: ['56+48=104', '28+104=132'] Exploring Operation: 132/6=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[56, 48, 28, 6], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [48, 6, 2] Generated Node #0,0: 22:[48, 6, 2] Operation: 56/28=2 Exploring Operation: 56-48=8, Resulting Numbers: [28, 6, 8] Generated Node #0,1: 22:[28, 6, 8] Operation: 56-48=8 Moving to Node #0,1 Current State: 22:[28, 6, 8], Operations: ['56-48=8'] Exploring Operation: 28-6=22, Resulting Numbers: [8, 22] Generated Node #0,1,0: 22:[8, 22] Operation: 28-6=22 Exploring Operation: 28-8=20, Resulting Numbers: [6, 20] Generated Node #0,1,1: 22:[6, 20] Operation: 28-8=20 Moving to Node #0,0 Current State: 22:[48, 6, 2], Operations: ['56/28=2'] Exploring Operation: 48/6=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 22:[2, 8] Operation: 48/6=8 Exploring Operation: 48/2=24, Resulting Numbers: [6, 24] Generated Node #0,0,1: 22:[6, 24] Operation: 48/2=24 Moving to Node #0,1,0 Current State: 22:[8, 22], Operations: ['56-48=8', '28-6=22'] Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,22 unequal: No Solution Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,22 unequal: No Solution Moving to Node #0,0,0 Current State: 22:[2, 8], Operations: ['56/28=2', '48/6=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,22 unequal: No Solution Moving to Node #0,1,1 Current State: 22:[6, 20], Operations: ['56-48=8', '28-8=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[6, 24], Operations: ['56/28=2', '48/2=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,22 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 92, 70, 28, 10 ]
40
[ "92-70=22", "28-10=18", "22+18=40" ]
Current State: 40:[92, 70, 28, 10], Operations: [] Exploring Operation: 92-70=22, Resulting Numbers: [28, 10, 22] Generated Node #2: [28, 10, 22] from Operation: 92-70=22 Current State: 40:[28, 10, 22], Operations: ['92-70=22'] Exploring Operation: 28-10=18, Resulting Numbers: [22, 18] Generated Node #3: [22, 18] from Operation: 28-10=18 Current State: 40:[22, 18], Operations: ['92-70=22', '28-10=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[92, 70, 28, 10], Operations: [] Exploring Operation: 92-28=64, Resulting Numbers: [70, 10, 64] Generated Node #0,0: 40:[70, 10, 64] Operation: 92-28=64 Exploring Operation: 92-70=22, Resulting Numbers: [28, 10, 22] Generated Node #0,1: 40:[28, 10, 22] Operation: 92-70=22 Exploring Operation: 70-28=42, Resulting Numbers: [92, 10, 42] Generated Node #0,2: 40:[92, 10, 42] Operation: 70-28=42 Exploring Operation: 70/10=7, Resulting Numbers: [92, 28, 7] Generated Node #0,3: 40:[92, 28, 7] Operation: 70/10=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[28, 10, 22], Operations: ['92-70=22'] Exploring Operation: 28-10=18, Resulting Numbers: [22, 18] Generated Node #0,1,0: 40:[22, 18] Operation: 28-10=18 Exploring Operation: 28-22=6, Resulting Numbers: [10, 6] Generated Node #0,1,1: 40:[10, 6] Operation: 28-22=6 Exploring Operation: 28+22=50, Resulting Numbers: [10, 50] Generated Node #0,1,2: 40:[10, 50] Operation: 28+22=50 Exploring Operation: 28+10=38, Resulting Numbers: [22, 38] Generated Node #0,1,3: 40:[22, 38] Operation: 28+10=38 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[10, 6], Operations: ['92-70=22', '28-22=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,40 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,40 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,40 unequal: No Solution No 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: 40:[22, 18], Operations: ['92-70=22', '28-10=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[92, 70, 28, 10], Operations: [] Exploring Operation: 92-70=22, Resulting Numbers: [28, 10, 22] Generated Node #0,1: 40:[28, 10, 22] Operation: 92-70=22 Moving to Node #0,1 Current State: 40:[28, 10, 22], Operations: ['92-70=22'] Exploring Operation: 28-10=18, Resulting Numbers: [22, 18] Generated Node #0,1,0: 40:[22, 18] Operation: 28-10=18 Moving to Node #0,1,0 Current State: 40:[22, 18], Operations: ['92-70=22', '28-10=18'] Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 7, 70, 52, 81 ]
70
[ "70-7=63", "52+81=133", "133-63=70" ]
Current State: 70:[7, 70, 52, 81], Operations: [] Exploring Operation: 70-7=63, Resulting Numbers: [52, 81, 63] Generated Node #2: [52, 81, 63] from Operation: 70-7=63 Current State: 70:[52, 81, 63], Operations: ['70-7=63'] Exploring Operation: 52+81=133, Resulting Numbers: [63, 133] Generated Node #3: [63, 133] from Operation: 52+81=133 Current State: 70:[63, 133], Operations: ['70-7=63', '52+81=133'] Exploring Operation: 133-63=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[7, 70, 52, 81], Operations: [] Exploring Operation: 81-52=29, Resulting Numbers: [7, 70, 29] Generated Node #0,0: 70:[7, 70, 29] Operation: 81-52=29 Moving to Node #0,0 Current State: 70:[7, 70, 29], Operations: ['81-52=29'] Exploring Operation: 7+29=36, Resulting Numbers: [70, 36] Generated Node #0,0,0: 70:[70, 36] Operation: 7+29=36 Moving to Node #0,0,0 Current State: 70:[70, 36], Operations: ['81-52=29', '7+29=36'] Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,70 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 63, 27, 23, 89 ]
22
[ "63+27=90", "23+89=112", "112-90=22" ]
Current State: 22:[63, 27, 23, 89], Operations: [] Exploring Operation: 63+27=90, Resulting Numbers: [23, 89, 90] Generated Node #2: [23, 89, 90] from Operation: 63+27=90 Current State: 22:[23, 89, 90], Operations: ['63+27=90'] Exploring Operation: 23+89=112, Resulting Numbers: [90, 112] Generated Node #3: [90, 112] from Operation: 23+89=112 Current State: 22:[90, 112], Operations: ['63+27=90', '23+89=112'] Exploring Operation: 112-90=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[63, 27, 23, 89], Operations: [] Exploring Operation: 89-63=26, Resulting Numbers: [27, 23, 26] Generated Node #0,0: 22:[27, 23, 26] Operation: 89-63=26 Exploring Operation: 89-23=66, Resulting Numbers: [63, 27, 66] Generated Node #0,1: 22:[63, 27, 66] Operation: 89-23=66 Exploring Operation: 89-27=62, Resulting Numbers: [63, 23, 62] Generated Node #0,2: 22:[63, 23, 62] Operation: 89-27=62 Exploring Operation: 63-23=40, Resulting Numbers: [27, 89, 40] Generated Node #0,3: 22:[27, 89, 40] Operation: 63-23=40 Exploring Operation: 63-27=36, Resulting Numbers: [23, 89, 36] Generated Node #0,4: 22:[23, 89, 36] Operation: 63-27=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[27, 23, 26], Operations: ['89-63=26'] Exploring Operation: 27+23=50, Resulting Numbers: [26, 50] Generated Node #0,0,0: 22:[26, 50] Operation: 27+23=50 Exploring Operation: 27+26=53, Resulting Numbers: [23, 53] Generated Node #0,0,1: 22:[23, 53] Operation: 27+26=53 Exploring Operation: 27-26=1, Resulting Numbers: [23, 1] Generated Node #0,0,2: 22:[23, 1] Operation: 27-26=1 Exploring Operation: 26-23=3, Resulting Numbers: [27, 3] Generated Node #0,0,3: 22:[27, 3] Operation: 26-23=3 Exploring Operation: 27-23=4, Resulting Numbers: [26, 4] Generated Node #0,0,4: 22:[26, 4] Operation: 27-23=4 Moving to Node #0,0,2 Current State: 22:[23, 1], Operations: ['89-63=26', '27-26=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,22 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[63, 27, 23, 89], Operations: [] Exploring Operation: 89-63=26, Resulting Numbers: [27, 23, 26] Generated Node #0,0: 22:[27, 23, 26] Operation: 89-63=26 Moving to Node #0,0 Current State: 22:[27, 23, 26], Operations: ['89-63=26'] Exploring Operation: 27-26=1, Resulting Numbers: [23, 1] Generated Node #0,0,2: 22:[23, 1] Operation: 27-26=1 Moving to Node #0,0,2 Current State: 22:[23, 1], Operations: ['89-63=26', '27-26=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 38, 91, 38, 27 ]
42
[ "91-38=53", "38-27=11", "53-11=42" ]
Current State: 42:[38, 91, 38, 27], Operations: [] Exploring Operation: 91-38=53, Resulting Numbers: [27, 53] Generated Node #2: [27, 53] from Operation: 91-38=53 Current State: 42:[27, 53], Operations: ['91-38=53'] Exploring Operation: 38-27=11, Resulting Numbers: [53, 11] Generated Node #3: [53, 11] from Operation: 38-27=11 Current State: 42:[53, 11], Operations: ['91-38=53', '38-27=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[38, 91, 38, 27], Operations: [] Exploring Operation: 91-27=64, Resulting Numbers: [38, 38, 64] Generated Node #0,0: 42:[38, 38, 64] Operation: 91-27=64 Exploring Operation: 91-38=53, Resulting Numbers: [38, 27, 53] Generated Node #0,1: 42:[38, 27, 53] Operation: 91-38=53 Exploring Operation: 91-38=53, Resulting Numbers: [38, 27, 53] Generated Node #0,2: 42:[38, 27, 53] Operation: 91-38=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 42:[38, 27, 53], Operations: ['91-38=53'] Exploring Operation: 53-27=26, Resulting Numbers: [38, 26] Generated Node #0,1,0: 42:[38, 26] Operation: 53-27=26 Exploring Operation: 38-27=11, Resulting Numbers: [53, 11] Generated Node #0,1,1: 42:[53, 11] Operation: 38-27=11 Exploring Operation: 53-38=15, Resulting Numbers: [27, 15] Generated Node #0,1,2: 42:[27, 15] Operation: 53-38=15 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 42:[27, 15], Operations: ['91-38=53', '53-38=15'] Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,42 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,42 unequal: No Solution Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[38, 91, 38, 27], Operations: [] Exploring Operation: 91-38=53, Resulting Numbers: [38, 27, 53] Generated Node #0,1: 42:[38, 27, 53] Operation: 91-38=53 Moving to Node #0,1 Current State: 42:[38, 27, 53], Operations: ['91-38=53'] Exploring Operation: 53-38=15, Resulting Numbers: [27, 15] Generated Node #0,1,2: 42:[27, 15] Operation: 53-38=15 Moving to Node #0,1,2 Current State: 42:[27, 15], Operations: ['91-38=53', '53-38=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 5, 69, 46, 76 ]
34
[ "69-5=64", "76-46=30", "64-30=34" ]
Current State: 34:[5, 69, 46, 76], Operations: [] Exploring Operation: 69-5=64, Resulting Numbers: [46, 76, 64] Generated Node #2: [46, 76, 64] from Operation: 69-5=64 Current State: 34:[46, 76, 64], Operations: ['69-5=64'] Exploring Operation: 76-46=30, Resulting Numbers: [64, 30] Generated Node #3: [64, 30] from Operation: 76-46=30 Current State: 34:[64, 30], Operations: ['69-5=64', '76-46=30'] Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[5, 69, 46, 76], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [5, 46, 7] Generated Node #0,0: 34:[5, 46, 7] Operation: 76-69=7 Exploring Operation: 69-5=64, Resulting Numbers: [46, 76, 64] Generated Node #0,1: 34:[46, 76, 64] Operation: 69-5=64 Exploring Operation: 76-46=30, Resulting Numbers: [5, 69, 30] Generated Node #0,2: 34:[5, 69, 30] Operation: 76-46=30 Exploring Operation: 69-46=23, Resulting Numbers: [5, 76, 23] Generated Node #0,3: 34:[5, 76, 23] Operation: 69-46=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[5, 46, 7], Operations: ['76-69=7'] Exploring Operation: 5*7=35, Resulting Numbers: [46, 35] Generated Node #0,0,0: 34:[46, 35] Operation: 5*7=35 Exploring Operation: 46-5=41, Resulting Numbers: [7, 41] Generated Node #0,0,1: 34:[7, 41] Operation: 46-5=41 Exploring Operation: 7-5=2, Resulting Numbers: [46, 2] Generated Node #0,0,2: 34:[46, 2] Operation: 7-5=2 Exploring Operation: 46-7=39, Resulting Numbers: [5, 39] Generated Node #0,0,3: 34:[5, 39] Operation: 46-7=39 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 34:[5, 39], Operations: ['76-69=7', '46-7=39'] Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,34 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[5, 69, 46, 76], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [5, 46, 7] Generated Node #0,0: 34:[5, 46, 7] Operation: 76-69=7 Moving to Node #0,0 Current State: 34:[5, 46, 7], Operations: ['76-69=7'] Exploring Operation: 46-7=39, Resulting Numbers: [5, 39] Generated Node #0,0,3: 34:[5, 39] Operation: 46-7=39 Moving to Node #0,0,3 Current State: 34:[5, 39], Operations: ['76-69=7', '46-7=39'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic